ENGINEERING RESEARCH INSTITUTE UNIVERSITY OF MICHIGAN ANN ARBOR SUBJECT REPORT LOCAL RATES OF MASS TRANSFER IN A PACKED BED OF SPHERES, WITH ORIFICE ENTRY OF AIR C -) J. C. RIER S. W. HURCHILL F. N. DAWSON C. M. THATCHER Project M985 DEPARTMENT OF THE NAVY, BUREAU OF ORDNANCE CONTRACT NOrd 12109 September, 1954

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PREFACE It was the purpose of this investigation to make experimental measurements of local rates of mass transfer in a packed bed, and to determine the effects on these rates of position within the bed, gas flow rate, pellet diameter, and velocity perturbations at the entrance to the bed. In the absence of precedent work of this kind, considerable work of a preliminary nature was required before any data could —be taken, and the complete program involved the following stages: 1. Design and construction of equipment to supply to a cylindrical bed of random-packed spheres, a gas stream of controlled temperature, pressure, and composition. 2. Development of a technique for the experimental determination of the variation of mass-transfer rates with position in the bed, for any given conditions of flow rate, pellet diameter, and entrance geometry. 3. Experimental determination of the variation of mass-transfer rates with position as a function of the other variables. 4. Correlation and interpretation of the experimental results. More than 3000 experimental runs were needed to provide the data for meaningful, correlations, and the task would have been almost impossible without the assistance of the following people: J. S. Berray, E. D. Blum, L. D. Boddy, A. H. Bonnell, D. L. Engibous, P. G. Friedman, A. D. Gowans, D. J. Groff, H. D. Hall, R. C. Hannenberg, W. P. Hegarty, L. Kaufman, R. W. Kruggel, C. F. Lombard, D. A. Maron, A. E. Molini, A. S. Nicholas, D. A. Olson, E. T. Sherman, J. Mo VandenBoegaerde, C. E. Wise, and I. Zwiebel.

ABSTRACT Local rates of mass transfer in a packed bed were determined by measuring the loss in weight of individual spherical pellets of p-dibromobenzene, carefully positioned in an otherwise inert bed of spheres through which a stream of air was passed. The tests were made in a cylindrical bed 4 inches in diameter, measurements being made to within 1/32 inch from the wall, with packing diameters of 1/8, 1/4, and 1/2 inch, and covered a Reynolds number range of 150<DpG/p 7000. Measuurememts were also made with the air entering the bed though 1- and 2-inch orifices, to determine the effect of the resulting velocity perturbations on mass-transfer rates. The experimental equipment consisted of an air-supply system capable of supplying air at a temperature of approximately 80~F and at rates ranging from 10 to 120 standard cubic feet per minute, and a packed test section which could be quickly detached from the air-supply line to facilitate the loading and recovery of the active pellets. Measured weight losses were first corrected for minor fluctuations in air temperature and for the loss attributable to exposure to the atmosphere during the loading and recovery operations, and were then converted to mass-transfer rates by introducing the surface area of the pellets and the running time over which the weight loss was incurred. Within the scope of the investigation, it was found that local rates of mass transfer in a packed bed could be correlated by the general equation k'/G' x 106 = B ) (1) where k' is the transfer rate in pound-mols per square foot of surface per hour, G is the superficial mass velocity (prime denotes molal units), D p is the packing diameter, p the viscosity of air, and B and m generally depend on position within the bed and orifice diameter, but are independent of air flow rate and packing diameter. When no orifice was used, entrance effects were observed only in the first 1/2 inch of bed depth, where the transfer rates were slightly higher than elsewhere. The rates were found to be independent of radius at all depths, however. With an orifice across the entrance to the bed, the exponent in Equation (1) is independent of orifice diameter and position in the bed, and is equal to -0.35. B, on the other hand, varies with both of these parameters. Transfer rates as much as 300 percent higher than elsewhere were observed in the vicinity of the orifice, but the perturbations created by the orifice are completely dissipated at a bed depth of approximately 2 inches. The nature of the data does not permit direct comparison with the results of previous investigations of overall mass-transfer rates in packed beds. By making certain assumptions, however, a limited comparison is possible and indicates that the present correlation may be high by a factor of approximately two. Despite this lack of agreement, the relative effects of pellet diameter, air flow rate, position in the bed, and orifice diameter on local rates of mass transfer are believed to be correctly delineated.

TABLE OF CONTENTS Page LIST OF TABLES....... vi LIST OF FIGURES.... * *. * * vii LIST OF APPENDICES o....., * * ix INTRODUCTION o........ 1 REVIEWu OF PREVIOUS WVORK...... 4 GENERAL EXPERIMEq TAL METHOD....... 28 EXPERIMENTAL APPARATUS AND EQUIPMENT.... 32 Air Supply System 33 Test Section 40 P-dibromobenzene Pellets 43 EXPERIMENTAL PROCEDURE........ 45 Pre-weighing 46 Warm-up of Equipment 47 Loading the Bed 48 Run Procedure 50 Pellet Recovery 53 Post-weighing 53 DATA PROCESSING.......... 55 Dry-Run Correction 55 Temperature Correction 56 Conversion to Transfer Rate 61 Reynolds Number 61 CORRELATION OF DATA....... o. 63 Preliminary Correlation 63 Cross-Correlation, No Orifice 66 Cross-Correlation, Orifice Entry 67 EXPER IMEN TAL RESULTS........ 101 Conclusions 105 A' No Orifice at Bed Entrance 106 B. Orifice at Bed Entrance 107 RELIABILITY OF RESULTS..... o. 119 iv

TABLE OF CONTENTS (Continued) Page APPLICATION OF RESULTS..... 133 No Orifice at Bed Entrance 133 Orifice at Bed Entrance 134 Sample Problem 135 SUMMARY......... 140 APPENDICES.......... 142 BIBLIOGRAPHY.......... 212 NOMENCLATURE....... 217

LIST OF TABLES Table Page 1. Constants Used in Equation 34, for No Orifice. 0..... 101 2. Constants for Use in Equation 36, for 1-inch Orifice...... 104 3. Constants for Use in Equation 36, for 2-inch Orifice....... 104 4. kg of Naphthalene as a Function of Depth. 138 5. Summary of Original and Processed Data.. 144 6. Dimensions of 1/8-inch Inert Pellets.. 194 7. Dimensions of 1/4-inch Inert Pellets. 195 8. Dimensions of 1/2-inch Inert Pellets.. 196 9. Temperature Correction Factor Data... 202 10. Temperature Correction Factor Calculations. 203 vi

LIST OF FIGURES Figure Page 1. Schematic Diagram of Apparatus.... 34 2. Air Supply System..... 0 35 3. Close-ups of Test Section.. 0 v 0 36 4. Test Section in Operating Position. 0 37 5, Sample Data Sheet. v v.. v 0 54 6. Vapor Pressure of P-dibromobenzene.. 58 7. Effect of Temperature on Mass Transfer.. 59 8. Original Data Plots for No Orifice, 1/8-inch Pellets........71-72 9. Original Data Plots for No Orifice, 1/4-inch Pellets.......73-75 10. Original Data Plot for No Orifice, 1/2-inch Pellets........ 75 11. Effect of Depth on Mass Transfer Rate.. 76 12. Original Data Plots for 1-inch Orifice, 1/8-inch Pellets.......77-81 13. Original Data Plots for 1-inch Orifice, 1/4-inch Pellets........82-89 14. Original Data Plot for 1-inch Orifice, 1/2-inch Pellets........ 89 15. Original Data Plots for 2-inch Orifice, 1/8-inch Pellets......90-92 16. Original Data Plots for 2-inch Orifice, 1/4-inch Pellets.......93-98 17. Original Data Plot for 4-inch Orifice, 1-inch Depth (Consolidation)..... 99 18. Original Data Plot for 1-inch Orifice, 2-inch,Depth, 1-inch Radius (Consolidation). 100 19. Effect of Radius and Depth on Mass-Transfer Rate —Transverse Profiles for No Orifice.. 110 vii

Figure Page 20. Effect of Radius and Depth on Mass-Transfer Rate —Transverse Profiles for 1-inch Orifice........ 112 21. Effect of Radius and Depth on Mass-Transfer Rate —Longitudinal Profiles for 1-inch Orifice........ 114 22. Effect of Radius and Depth on Mass-Transfer Rate —Transverse Profiles for 2-inch Orifice...... 116 23. Effect of Radius and Depth on Mass-Transfer Rate —Longitudinal Profiles for 2-inch Orifice....... 118 24. Comparison of Equation 41 with Correlations of McCune and Wilhelm, Gamson et al., and Hobson and Thodos... 125 25. Comparison of Equation 43 with Correlation of Gaffney and Drew....... 126 26. Comparison of Equation 45 with Correlation of Gamson......... 127 27. Surface Condition of P-dibromobenzene Pellets......... 130 28. kg of Naphthalene as a Function of Depth. 138 29. Temperature Correction Factor Plot.. 204 viii

LIST OF APPENDICES Appendix Page A. Summary of Original and Processed Data. 144 No Orifice, 1/8-inch Pellets 144 No Orifice, 1/4-inch Pellets- 149 No Orifice, 1/2-inch Pellets 157 1-inch Orifice, 1/8-inch Pellets 158 1-inch Orifice, 1/4-inch Pellets 166 1-inch Orifice, 1/2-inch Pellets 177 2-inch Orifice, 1/8-inch Pellets 178 2-inch Orifice, 1/4-inch Pellets 183 B. Pellet Dimensions and Properties 193 Glass Bead Dimensions 194 P-dibromobenzene Pellet Dimensi ons 197 Bed Porosity 199 Co Temperature Correction Factor De termination....... 201 Temperature Correction Factor Data 202 Temperature Correction Factor Calculations 203 Temperature Correction Factor Plot 204 Do Data Processing... e e 205 Eo Miscellaneous Calculations.... 208 Diffusivity and Schmidt Number for P-di bromobenzene 209 Surface Temperature Calculation 210 ix

I i'TRCLU CTION During the past decade, considerable progress has been made in the development of quantitative correlations for the prediction of pressure drop and heat- and masstransfer rates in packed beds. The interest in this field is a natural outgrowth of the increased use of packed beds in engineering operations and processes of many types. Absorption, fixed-bed catalytic reaction, heating and cooling, leaching, and fluid mixing, for example, are fields in which packed beds are already being used to advantage, and new applications will naturally result as a broader understanding of the pertinent principles is attained. The transfer of mass and heat in packed beds is of major interest in most of these applications, and pertinent data have been accumulated and correlated by many research investigators. In general, the studies in this field have been concerned with overall properties, i.e., the bed has been considered as an integral unit of equipment and transfer rates have been studied.from the overall viewpoint. Many of the problems involved in the commercial application of packed beds have been overcome through the use of such overall rate data. There are, however, other problems which can never be resolved without supplementary information regarding l cal or point conditions within such beds. The overall approach cannot, for example, predict the location of hot-spots in a fixed-bed catalytic reactor.

Thus, there is a definite need for data on local heat- and masstransfer rates in packed beds, and the present work was undertaken with the objective of making direct measurement of such rates. This is by no means the first attempt to obtain information regarding l1cal conditions in packed beds. Other things being equal, the local transfer rate should be a function only of the local velocity, and for many years a flat velocity profile, i.e., a uniform mass flow rate across the bed, was generally assumed as being both reasonable and also affording mathematical relationships which could be easily handled. Recently, however, several investigators have attempted to determine experimentally actual velocity profiles in packed beds, and to use their results to predict transfer-rate profiles. Unfortunately, most of this work has been of a qualitative nature, and even at best it provides only an indirect insight into the phenomena of mass and heat transfer. The present work should, therefore, be a worthwhile contribution to available knowledge of the behavior of packed beds. In this work, local mass-transfer rates in packed beds were determined by measuring the loss in weight of individual spherical pellets of p-dibromobenzene, carefully positioned in an otherwise inert bed of spheres through which a stream of air was passed. The tests were made in a cylindrical bed 4 inches in diameter with spheres having diameters of 1/8, 1/4, and 1/2 inch, and covered a reasonable range of Reynolds number (DpG//). Measurements were made at enough positions

in the bed to permit the mapping of local mass-transfer rates at all points. Particular attention was given to entrance effects in these studies, and the results are therefore applicable even to very thin beds made up of only a few layers of pellets. In addition to determining mass-transfer rates in the first few layers of pellets in a bed whose surface was completely exposed to the entering air stream, measurements were also made with the air entering the bed through an orifice, to determine the effect of the resulting local velocity perturbations on masstransfer rates. Orifice diameters of 1 and 2 inches were used in this phase of the work. The experimental data and correlations are presented in this report, and the results are interpreted in terms of present-day mass-transfer theory. The equipment and experimental procedure are described in detail, as is the method of processing and correlating the data. Conclusions relative to the effect of position in the bed, pellet diameter, air flow rate, and velocity perturbations at the entrance to the bed on local mass-transfer rates in packed beds are drawn and discussed. Insofar as the analogy between heat and mass transfer is valid, these conclusions should be equally applicable to heat-transfer work.

REVIEW OF PREVIOUS WVORK Although no previous work directly parallel to tne present investigation has been reported in the literature, many studies have been made which are pertinent to some extent. These previous studies can be roughly divided into two categories: those concerned with overall rather than local mass-transfer rates for packed beds, and those concerned with point conditions but which did not include a quantitative investigation of mass-transfer rates as such. Before discussing any of the work done in the first of these categories, it is advisable to review briefly the development of the basic correlations for mass-transfer data, derived for the most part from studies of mass transfer from isolated surfaces or in open tubes. The fundamental rate equation for molecular diffusion was stated as early as 1855 by Fick (22), and may be expressed in the form _ (o Vx )'(1) A where D is the coefficient of diffusion. For molecular diffusion of one gas through another, the equation can be expressed in a modified form originally derived by Maxwell (45) and Stefan (64) and later by Colburn and Hougen (16):

_ =_ C]TP ( a PV) (2) A RTPg Although this equation is still used to describe molecular diffusion, it has become customary in modern work to make use of a dimensionless mass-transfer factor, j, to characterize total diffusion, which includes eddy or turbulent transfer as well as molecular processes. The development of this concept was an outgrowth of the analogy between heat transfer and fluid friction originally suggested by Reynolds (57.) and later improved by Prandtl (53) and Taylor (66). Colburn (15) extended the development of the analogy and proposed the use of a transfer factor, j, to parallel the use of the friction factor, f, in pressure-drop calculations. The transfer factor was related to the heat-transfer coefficient by the equation h'C' 2/3 ---- = G(3) CpG and for turbulent flow conditions it was proposed that j be equal to f/2, making it a function only of the Reynolds number, DG/r. Previously, Colburn had also extended the analogy between heat transfer and fluid friction to include mass transfer (14), and with the development of the j-factor for heat transfer, he then sought to obtain a similar factor for use in masstransfer work. The relationship finally proposed by Chilton and Colburn (10) was

jvpf ( DG 4) where again, for turbulent flow conditions, j was set equal to f/2, making the factor for mass transfer identically equal to that for heat transfer. Colburn selected the exponent 2/3 for the Prandtl number in Equation 3 as being an average value of exponents recommnended in the correlations of several earlier investigators (17, 31, 50, 62). This exponent was merely carried over to the Schniidt number in the development of the j-factor for mass transfer, without any supporting experimental evidence. Since then, however, the use of the 2/3 exponent has been confirmed by Linton and Sherwood (41) from tests covering a wide range of Schmidt number. Gaffney and Drew more recently correlated similar data with an exponent of 0.58 (25), while Bedingfield and Drew used an exponent of 0.56 to correlate their data for single cylinders (5). However, the exponent of 2/3 has been generally accepted by most investigators. It should be re-emphasized that all the original data supporting the use of the j-factor in the correlation of mnasstransfer data were obtained from experiments with single, isolated surfaces or in open tubes, and it remained to be shown that the proposed method of correlation could also be applied to mass transfer in packed beds. As a matter of fact, Colburn's original development of the j-factor was also based entirely on gas-phase data, but 1cCune and iilhelm (48) and

Hobson and Thodos (32) have recently shown the factor to be equally applicable to transfer in liquids. An alternate method of correlation specifically applicable to packed-bed data was proposed by Chilton and Colburn in 1935 (11), and has found some acceptance. It was their suggestion that the difficulty of separation in a packed distillation or absorption column be expressed as a number of "transfer units", equivalent to the number of theoretical plates used in plate-column calculations, Column efficiency is correspondingly expressed as the "height of a transfer unit"t, paralleling the "height equivalent to a theoretical plate" in plate columns. The height of a transfer unit is, of course, equal to the total column height divided by the number of transfer units, and was defined by the equation H.T.U. HM G lZ \ 2/3 H T.U. n k aMmpgf ja (5) From the indicated relationship between the height of a transfer unit and the j-factor, it can be seen that for any given system H.T.U. will also be a function of Reynolds number only. The study of transfer processes as specifically encountered in packed beds undoubtedly received its greatest impetus from the work of Gamson, Thodos, and Hougen in 1943 (27). In their experiments, spherical and cylindrical solid pellets of various materials, densities, and sizes were soaked in distilled water, drained and rolled in cheeseclcth

to remove loose surface water, placed on a tray to form a bed of from 1 to 2-1/2 inches in thickness, and weighed. Air was then blown through the bed while the inlet and outlet temperature and humidity were recorded, and the tray was reweighed at the end of the run. Since the running time covered only a fraction of the constant-rate drying period, the mass-transfer rate could be calculated from the total weight loss and the running time, and could be verified by the humidity and temperature data. Further, since the process was adiabatic and since the total resistance to mass and heat transfer was in the gas film alone, the gas-film transfer coefficients for both heat and mass transfer could be evaluated. When the j-factor for mass transfer, Jd, was plotted against the Reynolds number, DpG/,, on log-log paper, most of the data were correlated within ~4 per cent by a straight line, DG -0.41 id gm0.989 (6) for Reynolds numbers above 350. Below this value, the data deviated progressively from the correlation, and in view of the analogy between transfer phenomena and fluid friction, the deviation was attributed to the transition from turbulent to laminar flow. Experimental difficulties prevented the accumulation of data at Reynolds numbers below 100, but it was proposed that in the laminar flow region jd be correlated by the equation

thixpnntoteRdeynolds b-d 9 -16k jd - 16-8c (,u<)'c (7) the exponent on the Reynolds number being taken from the analcgy with fluid friction in the laminar region as proposed by Colbum (14). Data taken at Reynolds numbers below 350 bracketed a smooth curve connecting the line of Equation 6 with that of Equation 7, which it joined at DpG// - 40. A similar correlation was obtained for the j-factor for heat transfer, the corresponding equations being D G -0041 jh " 1.064 -) (8) for Reynolds numbers above 350, and jo R 18.1 K) (9) for Reynolds numbers below 40. It was noted that h and jd were not quite identical as had been hypothesized by Chilton and Colburn (10), but that they did bear a constant ratio to each other: ih/Jd' 1.076. However, there is some question as to whether the measured wet-bulb temperature is truly equal to the temperature at the pellet surface, as was assumed in arriving at this ratio, and its validity is therefore somewhat in doubt. It will be noted that the pellet diameter was used as the characteristic length in the Reynolds number in these correlations, and this practice permitted the use of the

same correlation for all pellet sizes. urtl'her, bj defining an equivalent diameter for the cylindrical peulits equal to the diameter of a sphere having the same surface area, thei data for cylindrical sbapes 7.Pere also brought into agreement with the correlation. Using the same technique as Gamson et al., Wilke and lougen (67) later obtained additional data at lower Reynolds numbers and recotmmended the equation -0.51 jd = 1.82\(j (10) for Reynolds numnbers below 350. The critical Reynolds number of 350 was retained from the earlier work to facilitate comparison of the correlations, but it was noted that a plot of jd versus DpG// on log-lcg paper actually yielded a single continuous curve over the range 50 < 5,000. Ergun, in an excellent resum6 and critique of most of the significant studies of mass-transfer rates in packed beds (20), notes that because the technique used by Gamson, -Wilke, et al., involved the removal of capillary mroisture, "'it is expected that the interfacial surface area between the gas stream and the liquid was different from the geometric surface area of the solids on which the calculation of the transfer coefficients were based." IHle also calls attention to the relatively shallow beds used in the experiments, and suggests that a rather undefinable void volule and possible entrance and exit effects may also detract from the validity

11 of the data. The latter criticism is to be discussed further in the light of the findings of the present work. Studies along the same general lines as those conducted by Gamson et al. were carried out at about the same time but independently by Hurt (36), who used a similar technique in investigating the humidification of air over water-wetted pellets of silica gel. Other experiments were concerned with the adsorption of water from moist air by particles of silica gel and by particles coated with phosphorous pentoxide, and with the evaporation of naphthalene pellets and flakes into air and hydrogen. In contrast to the findings of Gamson et al., Hurt was unable to correlate data from particles of different sizes with a single curve, although Ergun (20) noted later that a log-log plot of H.T.U./Dp versus DpG//A would bring the data for different sizes into a single straight line. At the same time, however, Ergun calls attention to significant discrepancies in the values used by Hurt for the Schmidt number and for the vapor pressure of naphthalene, and states that a different set of vapor pressure data, for example, would materially alter Hurt' s results. In an extension of the work by Gamson et al, and using the same method, Taecker and Iiougen studied masstransfer rates from Raschig rings, partition rings, and Berl saddles (65). With an effective particle diameter equal to NAI/T, where Ap is the surface area of a particle, the data were correlated by the equations

12-0.41 jd =1.251 () (11) for DpG/ > 620, and -0.51 jd'2.24 (.) (12) for DpG4// < 620. A significant separation between each of the three sets of data for rings, for saddles, and for cylinders and spheres suggests that the use of an effective particle diameter based on the surface area was not adequate to account for the variation in particle shape. Mass transfer in solid-liquid systems was studied by McCune and Wilhelm (48) by dissolving 2-naphthol pellets in a water stream. Spherical pellets of three different diameters were used in a 4-inch-diameter bed. The data were correlated by the equations /DG\ -0.327 jd 0.687 (13) for DpG/ > 120, and Jd 1.625 /( - (14) for DpG/, 120, and are in fair agreement with those of Gamson et al. Except for its use as the characteristic length in the Reynolds number, no effect of pellet diameter was observed in these studies.

Resnick and wJhite (56) were primarily interested in mass transfer in fluidized beds, but also reported some data from fixed beds. Air, hydrogen, and carbon dioxide were blown through beds of naphthalene granules, over a Reynolds number range of from 0.8 to 30, and the data were correlated 1.5 empirically by plotting jd/Dp versus DpG/ O Plotted in this manner, the data for all particle sizes were correlated by a single straight line, the eauation for which was not reported but which appears to be -0.279 jd/Dp.*5 a 0.19 (15) where Dp is in millimeters.'When jd was directly plotted versus DpG/, a separate line was obtained for each particle size, as was the case with Hurt's data (36). However, the two sets of data were inconsistent in other respects, which may be attributable to the deficiencies in Hurt's data already noted or, as Ergun points out (20), to the fact that Resnick and White really did not obtain enough fixed-bed data to yield a correlation having any statistical significance. Good agreement with the data of Gamson, Wilke, et al. (27, 6&T has been reported by Hobson and Thodos (32), who passed water through a bed of cellite pellets soaked with a saturated solution of water in either isobutyl alcohol or methyl ethyl ketone and measured the ef-fluent concentration. These new data and those of Gamson, Wilke, et al., were correlated by the equation

~14D G D G 2 log Jd = 0.7683 - 0*9175 log " + 0.0817 (log Dp), (16) in whi ch particle diameter appears only in the Reynolds number. Transfer rates were calculated by plotting the variable effluent concentration versus time and extrapolating back to zero time, when the pellets were presumably completely wetted. In view of the fact that the extrapolation of curved lines could lead to significant errors, this procedure was later questioned by Gaffney and Drew (25), who also wondered about the initial presence of excess solution on the surface of the pellets. These objections were eliminated in subsequent work by Hobson and Thodos (33), in which additional data pertaining to mass transfer across gas films at Reynolds numbers in the range 20-300 were obtained using a modified technique. The liquids studied were n-butanol, n-dodecane, n-octane, toluene, and water, while hydrogen, nitrogen, carbon dioxide, and air were used as gases. Both the new and old data, plus that of Gamson et al. (27) and of McCune and Wilhelm (48) were correlated by the equations DG -0.45 lw 1.s~~~3O~ ~(17) jd = 1.30 (0) and for DpG/ > 150, and Jd 10 (18) for DpG// < 50.

-15A thorough investigation of transfer rates between organic solvents and pellets of solid organic acids was conducted by Gaffney and Drew (25). To cover a wide range of Schmidt number, three solvent-acid combinations were used: acetone and succinic acid, benzene and salicylic acid, and n-butanol and succinic acid. The data were correlated by 0058 plotting (HI.T.U.)a/Sc versus DpG//E, and are in excellent agreement with those of IVicCune and Wilhelm (48). The data were fitted by a curved line for which no equation was given, and subsequent data reported by Ishino and Otake (38) for pellets of benzoic acid dissolving in water could also be correlated by this line. To facilitate comparison of the Gaffney-Drew data with those of others, Ergun (20) suggests that the former can be approximately represented by the equations /D G\ -0.254 jd 0.290( E (19) for DpG//e > 200, and G\ -0.613 Jid 1.97 (20) for DpG/,e < 200, where 0.58 k D58 =dt c, kgM=PE gf a(HTU) G eDG Gaffney and Drew note that their correlation is significantly poorer if the usual exponent of 2/3 is used on the Schmidt numb er.

- -16Shulman and DeGouff (63) blew air through beds of Raschig rings made of naphthalene and correlated their data with the equation id = 1.07 -0.41(21) for G- Ar// > 400. The data are in agreement with those of Taecker and Hougen (65), but by the same token are not comparable with data for cylindrical and spherical shapes. Water was passed through fixed and fluidized beds of benzoic acid pellets by Evans and Gerald (21), who found that the line 1 ~4 -*0.52 1.48 (22) fit their data for fixed beds, all taken at DpG/ < 70. In addition to the investigators who collected and correlated mass-transfer data for packed beds, there are several authors who have sought improved correlations by reworking the data of others. Much of this work has been aimed at developing correlations applicable to both packed beds and open tubes on the one hand and to both fixed and fluidized beds on the other. A brief review of such correlations, insofar as they apply to fixed beds, is pertinent to the present work and is given in the paragraphs which follow. A theoretical study of the relationship between mass transfer in open tubes and that in packed beds was made by Pratt (54), who recommended the introduction of the fractional

17 — void space, e, into the Reynolds number: DpG/ue. Use of this modified Reynolds number does not appear to result in any significant improvement in the agreement among the data of Gamson et al. (27), Wilke and Hougen (67), Taecker and Hougen (65), and Hobson and Thodos (32). It will be noted, however, that Gaffney and Drew chose to use the same modified Reynolds number in correlating their data (25). Kaufman and Thodos (39) reworked the data of Gamson et al. for cylinders (27) and that of Taecker and Hougen (65) for Raschig rings, partition rings, and Berl saddles, in an attempt to resolve these data to those for spheres. The resolution was accomplished by the empirical calculation of effective particle diameters for each of the various shapes and by introducing a "critical area factor", fAa into the j-factor. The area factors for each of the shapes were also determined empirically. Similar shape factors were also evolved by Gamson (26), who chose to introduce them into the denominator of the Reynolds number for theoretical reasons. The use of empirical effective particle diameters was avoided by using 6G/a,/, equal to DpG//, (1 - E ) for spheres, in place of the usual Reynolds number. In a further modification, he was able to correlate some fluidized bed data with that for fixed beds by including the term (1 - E )'2 in the j-factor, and his final correlations then became -0.41 0.2 14d 1.46 (1 e) (23) for 6G/a4/u > 100, and

-18Jd' 17 (a- ) (1 - )2 (24) for 6G/a,/A c 10, where p is the shape factor given empirically for various shapes, and was found to differ slightly from the corresponding factors recommended by Kaufman and Thodos (39). In his comprehensive analysis of mass-transfer phenomena in packed beds, Ergun (20) suggests that the concept of hydraulic radius requires that a modified Reynolds number equal to DpG//4 (1 - ) be used if the analogy between mass transfer and fluid friction is to be preserved, and this modification is in agreement with that proposed by Gamson (26). A new mass-transfer factor, J, is also proposed, and is equal to the old factor, j, tirnes 6 6 (Sc)1/3 On the basis of his earlier analysis of pressure drop data (19) and the presumed analogy between mass transfer and fluid friction, Ergun proposes the correlation J - 150 (Re') + 1.75, (25) where Re' - DpG//M (1 - e). The data of McCune and Wilhelm (48), Hobson and Thodos (32), and Gaffney and Drew (25), all for liquid streams, are shown to be fairly well correlated by this equation, but the attempt to apply it to gas-phase data was not successful. As has been noted previously, Ergun calls attention to deficiencies and uncertainties in these latter data, but also

19states that the ihilton- $olburn j-factor and hence the Jfactor used in Equation 25 are strictly applicable only to systems in which there is no mixing along the length of the tube, a questionable assumption in the case of gas flow. Indeed, Ergun's analysis of Hurt's data (36) indicates complete longitudinal mixing in his experiments, and it is presumed that similar conditions existed to an unknown degree in the other gaseous systems. Two recent investigators have found it convenient to use the modified Reynolds number as proposed by Gamson and Ergun, perhaps because their primary concern was with fluidized rather than fixed beds. In any event, the data of Hsu (34), obtained by passing carbon tetrachloride through a bed of activated charcoal, were found to be in satisfaction with Gamson's correlation, while Chu et al, (12), recommended the use of the equations d 1.77 (Re')44 (26) for 30 > Re' > 5000, and -0.o 78 Jd' 5.7 (Re') (27) for 1 > Re' > 30, vwhere Re' D DpG/ (1 - E), to correlate their data obtained by passing air through a bed of inert pellets coated with naphthalene. The correlation is shown to fit the data of Gamson et al. (27), Ifilke and Hougen (67), Hobson and Thodos (32), McCune and Wilhelm (48), and Gaffney

-20and Drew (25), with the inclusion of suitable area factors in the modified Reynolds number for the data on non-spherical particles. In an analysis of the problem of mass transfer in packed beds made from a somewhat different angle, Ranz (55) relates the transfer from spheres in a packed bed to the transfer from single spheres. Data for single spheres are plotted as kgDppgf/DG versus (DpG/ ) ( / p DG)2/3 and are displaced laterally from the packed bed data of Gamson et al. (27) by a constant factor of approximately 10, i.e., the transfer rate in a bed can be predicted from the correlation for single spheres by entering the plot at an abscissa approximately 10 times that calculated for the packed bed, On the basis of the relationship advanced by Ranz, it is perhaps pertinent to mention some of the studies made of mass transfer for single particles, since at least the slope of the line correlating the data from such studies should be in agreement with slopes obtained in correlating packed bed data. Such is apparently the case: for the correlation of data on evaporation from a cylinder transverse to a fluid stream, Powell (52) used a slope of -0.5, Maisel and Sherwood (44) a slope of -0.43, and Bedingfield and Drew (5) a slope of -0.4. As was noted at the outset of this review, all the foregoing studies have been concerned with overall masstransfer rates in packed beds, as opposed to point conditions within the bed. It was also pointed out that other

-21studies were concerned with point conditions, but that they did not include a quantitative investigation of mass transfer as such. Previous work done in this latter category will be reviewed in the paragraphs which follow. It will be noted that the major share of the studies of point conditions in packed beds were concerned with the velocity distribution. The pertinence of such investigations lies in the fact that mass-transfer rates have already been shown to be a function of velocity as embodied in the Reynolds number. Although superficial mass velocities, based on the cross-sectional area of the empty bed, are almost universally used in packed bed correlations, a fixed ratio between the superficial velocity and actual point velocities has been tacitly assumed in most work, Indeed, the use of a modified Reynolds number equal to DpG/ue in the correlation proposed by Gaffney and Drew (25) was occasioned by the belief that mass-transfer rates should more properly be functions of the interstitial velocity. The earliest work of interest from the standpoint of point conditions within a packed bed was that of Mayo, Hunter, and Nash (46), who were primarily interested in determnining the extent to which packing surfaces were wetted in a packed absorption column. The measurements were made by passing a red dye solution through a bed of paper rings, made of paper strips wrapped to give double thickness so that only one side of the strip was exposed. The fractional area of the rings which became colored was determined by

... 22 - the rather unique method of cutting apart the dyed and undyed sections of each strip and weighing the separate piles of scraps. In conjunction with their other findings, Mayo et al. reported noting a greater degree of wetting in the layers of rings near the entrance to the bed, and also more wetting near the tube wall than at the center of the bed. These indications of higher porosity at the wall were also present in photographs of packed beds made by Furnas (24' and Graton and Fraser (29), and suggested that higher velocities might also be encountered at the wall. That such is the actual case was confirmed by Saunders and Ford (58), who made measurements with a movable Pitot tube just beyond the outlet of a packed bed of spheres. Although their readings were found to be somewhat erratic owing to jets of air from the interstices, they reported a uniform mean velocity across the bed except in an annulus within about one sphere diameter from the wall, where it was about 50 per cent higher. A more detailed study of the velocity distribution in packed beds has been made by Smith and co-workers (49, 61), who also reported higher velocities near the wall. In their experiments, circular hot-wire anemometers of various diameters were centered over the outlet end of a packed bed, and the variation of velocity with radius was thereby determined. The velocity was found to be lower both at the center of the bed and at the wall, reaching a maximum value at a point about 7/10 of the distance from the center to the wall, where velocities up to 100 percent greater than those at the

23center were observed. In the later work (61), it was indicated that the maxima were actually located at a distance of approximately one pellet diameter from the pipe wall, regardless of pipe or pellet size. Other conclusions reached on the basis of these experiments were: (1) for 1/2-inch spheres in a 4-inch pipe, velocity profiles were unchanged for bed depths of from 3 to 23 inches, but the profiles gradually approach that observed in an empty pipe as bed thicknesses are successively decreased below 3 inches; (2) the ratio of point velocities to the average velocity is independent of total flow rate; (3) the divergence from a flat velocity profile increases as packing size increases and as pipe size decreases; and (4) the larger the pipe, the more uniform the velocity. Velocity profiles were also obtained in earlier work by Kinney (40), who made his measurements with a Pitot tube driven down into the charge in a blast furnace. In contrast to the findings of Smith et al., Kinney found the maximum velocity at the center in two of the four radial planes investigated, although wall velocities were slightly higher than those at the center in the two other planes. Because of the marked difference in bed size and packing, however, these results are hardly comparable to those of Smith. On the other hand, Kinney also made some preliminary tests in a bed 16 inches in diameter packed with 1- to 2-inch limestone particles, and found the velocity to increase with distance from the center of the bed, although no data were

-24 — taken near the wall. Also interesting in his conclusion that "the area available for flow of gas in a bed of broken solids is not the area as determined by voids but only a part thereof." Arthur et al. (4) also reported higher gas flow along the wall of a packed bed, on the basis of findings from five different types of experiments: (a) the exit stream from a packed bed was separated into central and annular portions and the two flow rates were measured; (b) hydrogen sulfide was passed through a bed of coppered charcoal, and the bed was then divided into central and annular portions and the degree of adsorption in each section was determined; (c) sulfur dioxide was passed through a bed of silica gel colored with alkaline phenolphthalein and the location of the initial color change in the layer of granules at the bed exit was observed; (d) sulfur dioxide was passed through a bed of coppered charcoal, and the location of the first color change on strips of litmus paper placed across the tube immediately beyond the bed was observed; and (e) the rate of temperature rise at various radial positions was noted in a charcoal bed through which either sulfur dioxide or hydrogen sulfide was blown, It was concluded that the velocity distribution is very sensitive to the detailed pressure conditions both above and below the bed, but that there is always an excess flow rate along the wall of the bed, the maximum rate being observed in the region slightly removed from the wall.

The colorimetric methods of Arthur et al. were used earlier by Saunders and?Wild (59) and by Hughes (35). Saunders and WVild passed a chlorine-air mixture through a glasswalled bed of marble chips impregnated with potassium iodide, and took photographs of the advancing front of sorption at intervalso Unfortunately, their work was concerned with flow distribution in blast furnaces, and in all cases the gas entered the bed through a slotted grate which protruded into the bed. Further, their observations of velocity distribution were confined to the region immediately adjacent to the grate, and no information regarding radial velocity profiles was obtained. The work of Hughes (35) is of particular interest inasmuch as it included a study of flow into a packed bed through a small orifice. The technique used was similar to that of Saunders and Wild, except that the marble chips were treated with lead acetate and a mixture of hydrogen sulfide and air then used for the gas. For a bed of 20-30 mesh particles, Hughes observed that the flow of gas at relatively low velocities from a small orifice produced a hemispherical wave front emanating at the orifice, and also noted that "the gas velocity may be varied considerably with little effect on the wave front produced." He was aware that preferential flow along the glass front of his bed might give misleading results, but reported that later work shcvred the wall effect to be surprisingly small.

-26When 3/16- to 1/4-inch chips were used in the bed, Hughes' results were significantly different. Under these conditions the wave front was Observed to spread horizontally to the full width of the bed at a distance of only 3/4 of an inch into the bed, and then advance through the bed as an almost horizontal line. Aerov and Umnik (1) passed a mixture of hydrogen sulfide and air through pellets treated with lead acetate until darkening was first noted in the exit layer of pellets, and then removed successive thin layers of the bed and observed the degree of blackening in each layer. The velocity of the gas near the wall was found to be 30 to 70 per cent higher than that at the center of the bed. Similar work had been done earlier by Chernyshev et al. (9) using iodine vapor and starch pellets, but no data pertaining to velocity distribution were reported. Further indication of higher velocities at the wall is reported by Schuler et al. (60), who found a radial variation in the effective thermal conductivity of a packed bed which was consistent with the velocity profiles obtained by Smith et al. (49, 61). On the other hand, Coberly and Marshall (13) concluded that velocities are uniform across a packed bed, on the basis of hot-wire anemometer readings taken at the bed exit. Since the anemometer was placed very close to the exit layer of pellets, the data were widely scattered due to the presence of interstitial jets of gas, but no

*27significant trend away from a flat profile was noted, either in shallow (1.25-inch) or deep beds. The analogy between heat and mass transfer suggests that information pertinent to the present work might also be found in reports of heat-transfer studies. Such studies have been almost entirely concerned with overall rates, although measurements have been made of temperature profiles in packed beds during heating and cooling (3,8,13,30,42,43). Despite the local nature of such measurements, they are still applicable only to the problem of overall heat transfer between the flowing fluid and the walls of the bed, and are of no use whatsoever in analyzing local transfer rates between the fluid and individual particles in the bed.

GENERAL EXPERIIENTAL METIHOD) It is significant that the effects of local turbulence in the interstitial spaces in packed beds are not to be deduced from most of the work done by previous investigators. Smith, et al. (49, 61), for example, recorded rapidly fluctuating readings in preliminary work when their hot-wire anemometers were placed close to the exit layer of pellets in the bed, but elected to make the bulk of their measurements with the anemometers located farther downstream, where such fluctuations were no longer present. In the same regard, the work of Arthur, et al. (4), and all the other colorimetric work may be conclusive as far as average velocities are concerned, but leaves the question of the fluctuations in velocity associated with turbulence unresolved. The significance of local turbulence to transfer phenomena in packed beds should be apparent, since it is actually the local velocity near the interface of each pellet in the bed, rather than any average velocity in the direction of main flow, which affects transfer rates. Indeed, if high velocities- at the tube wall go hand in hand with higher porosity, it would seem that the interstitial space along the wall would be less tortuous, and that local turbulences might be reduced accordingly. This could be the explanation for the discrepancies between the results obtained by Smith et al. (49, 61) and those of Coberly and Miarshall (13). Although the latter merely state that their anemometer readings were made "very close" to the exit layer of pellets, it may -28 -

— 29be that they actually recorded transient velocity effects as well as the main-stream velocity component. In any event, it is entirely conceivable that radial variations in the average velocity in the main-stream direction are of little significance in either heat- or mass-transfer phenomena. Actual measurement of true interstitial velocities in a packed bed was given some consideration at the outset of the present investigation, but was rejected in view of the many experimental difficulties involved. The use of a hot-wire anemometer would presumably be involved, and the wire itself would occupy a significant fraction of the interstitial space under study. Further, it seemed apparent that an individual pellet surrounded by interstitial space having a completely undefinable shape would have its surface exposed simultaneously to many different levels of velocity, all bearing an extremely uncertain relationship to the anemometer readings. Finally, it was realized that a knowledge of the flow characteristics within a packed bed would be useful primarily for its bearing on problems involving transfer phenomena, and that the measurement of actual local transfer rates would be a much more direct approach to the ultimate problem. Local rates of heat transfer in a packed bed could conceivably be measured, and this approach was also considered and rejected at the outset of the present work~ Such an approach would require the quantitative measurement of heat flux to a particle in a packed bed, an almost impossible

task for the particle sizes of interest, as well as the accurate determination of the temperature difference between the particle surface and the adjacent fluid stream. The latter problem is almost as formidable as the former, in view of evidence that such temperature differences are extremely small (3, 8). In contrast to the difficulties inherent in the measurement of either local heat-transfer rates or true local velocities, the determination of loccal rates of mass transfer could be accomplished by relatively simple and direct methods, and this approach to the problem was therefore selected. After a review of the literature and consideration of several methods by which meaningful data might be obtained, it was decided that the most suitable technique would be to pass a liquid or gas through an inert bed containing carefully positioned soluble or volatile solid pellets, and to determine mass-transfer rates by measuring the loss in weight of the active pellets. Since the effect of fluid properties was not a major concern, water and air were obvious choices and air was arbitrarily selected. The choice of a suitable volatile solid was based on the following criteria: (1) the volatility should not be so high as to result in inordinately large weight losses during the packing and recovery operations, when the pellets would be exposed to the atmosphere; (2) the volatility should not be so low as to require inconveniently long running times to obtain measurable weight losses; (3) the specific gravity

should be as high as possible, so that measurable weight losses would be accompanied by a minimal change in pellet volume and surface area; and (4) inter-granular cohesion should be good in order to permit the pressing of pellets of various sizes, preferably without the addition of a binder. Naphthalene, camphor, p-dichlorobenzene, and p-dibromobenzene were considered and subjected to preliminary tests, and p-dibromobenzene was finally selected as best meeting the requirements. In summary, then, the experimental method used in this investigation involved the careful positioning of preweighed individual pellets of p-dibromobenzene in an otherwise inert bed, blowing air through the bed, recovering and reweighing the active pellets, and calculating mass-transfer rates from the loss in weight as a function of position in the bed, air flow rate, pellet diameter, and geometry at the entrance to the bed, i.e., air entry through an orifice as compared with unimpeded entry over the entire cross-section. This technique proved to be completely satisfactory for the study of local transfer rates in a packed bed, and is to be commended to anyone interested in conducting similar studies.

EXPERIMENTAL APPARATUS AND EQUIPMENT The basic apparatus required to produce a measurable loss in weight of individual pellets of p-dibromobenzene in an otherwise inert bed through which a stream of air is passed is relatively simple. Broadly speaking, the only requirements are a controllable air supply system, a test section affording easy access, and the necessary instrumentation, As a result of preliminary tests, however, it became apparent that the problem of equipment design was by no means that simple, and an apparatus comprising the following units was eventually developed and found to be suitable: 1) A motor-driven blower with suitable controls. 2) A finned-tube heater-cooler to permit regulation of the temperature of the air entering the test section. 3) A calming section to insure against an abnormal velocity profile at the entrance to the test sectiono 4) A test section which was clamped in place during actual runs, but which could be swung aside to facilitate the introduction and recovery of the active p-dibromobenzene pellets. 5) A mercury manometer for measuring the pressure drop across the packed test section, 6) Chromel-alumel thermocouples and a potentiometer for the measurement of temperatures in the bed. 7) A rotameter for measuring air flow rates,

-33Auxiliary equipment such as orifice plates, glass beads, p-dibromobenzene pellets, radius and depth gauges, weighing bottles, and an analytical balance completed the requirements. The entire apparatus is shown schematically in Figure 1, and most of the components can also be seen in Figures 2-4. A detailed description of each of the components of the apparatus is presented in the sub-headed paragraphs which follow. Air Supply System Motor and blower. Atmospheric air was drawn directly into the inlet of a two-lobe rotary blower, which was driven by a General Electric 7.5-horsepower 230-volt shunt-wound DC motor, Model No. 5B294A14. Since the blower was obtained from Navy surplus and was apparently a special design, no exact specifications can be given, other than that it was built by the Sutorbilt Corporation and appeared to be similar to their blower No. 5-E, which has a displacement of 0.18 cubic feet of air per revolution and a rated capacity of 115 cubic feet per minute at a discharge head of 4.9 pounds per square inch. With a belt drive, major changes in the operating range of the blower could be effected by changing the diameter of either of the two sheaves. F'or closer control, the speed of the motor could be regulated by means of a rheostat in the field circuit as well as by introducing resistance

AIR -* FINNED TUBE HEATER - COOLER CALMING SECTION, 34' LONG INLET VARIABLE BLOWER MOTOR OPEN-END MOTO V MERCURY MANOMETER OUTDOOR [ DISCHARGE I THERMOCOUPLE ROTAMETER LEADS TEST SECTION Fig. I Schematic Diagram of Apparatus 34

3~ 5 ~~~~~.... 1 i?... i~:.2.Ar Supply System - Motor and Bl1ower,!it:sitot Board, and Heater-Cooler Inrlet and _'a ir Lines.

36 Fig. 5. Close-ups of Test Section. Above - Loading p-dibromobenzene pellets. Below- Assembling into air supply line.

37 d 04-) 4-' 0 0.' i'i~i~,%~- e _: - 0 Et o I b's i'tX *...r%g;: A t1 W. ) I,h:: $ ^~~~~~~~~~~~~~~o 4

into the armnature circuit. Thqne resistor board for the latter circuit, visible in Figure 2, consisted of six fixed and two variable slide-wire resistors which could be wired in various parallel and series combinations to provide a wide range of resistance without overload. Piping. Pipe having a nominal inside diameter of 4 inches was used throughout the air supply line, including the calming section and test section. Except for flanges, which were hard rubber, all piping and fittings were made of styrene co-polymer and were obtained from the lMichigan Carlon Pipe Company. Fittings were of the "slip-sleeve" type and all permanent joints were cemented with solvent supplied by the same company, Naturally black, the pipe and fittings were painted with white enamel to minimize the effect of solar radiation on the air temperature. Heater-cooler, During preliminary tests it was found that the blower heated up during its operation, and that the temperature of the outlet air gradually rose accordingly. In view of the sensitivity to temperature of the vapor pressure of p-dibromobenzene, steady-state operation was highly desirable and was achieved by installing a combination heater and cooler in the air supply line immediately over the blower outlet. The heater-cooler consisted of three parallel lengths of 1-inch (fin diameter) helically-finned copper tubing obtained through the courtesy of the -iolverine Tube Division of the Calumnet and Hecla Consolidated Copper Companyo The

tubes were bent into a tight spiral approximately 9 feet long which could be inserted into the 4-inch air line, and were connected to a manifold at each end. ~Nater was supplied to the upper manifold and passed down the tubes countercurrent to the direction of air flow. Because the heater-cooler was designed to maintain an outlet air temperature closely approaching that of the inlet water, regardless of fluctuations over a reasonable range in the air temperature at the blower outlet, air temperatures could be controlled by regulating the inlet water temperature. This was accomplished by bleeding low-pressure steam into the water line, the steam rate being controlled by a needle valve. The steam and water inlet lines and the drain line can be seen in Figure 2. Calming section. By locating the motor and blower on one floor of the laboratory and the test section on the floor below, it was possible to include in the air supply line a straight section of piping completely devoid of elbows or other fittings which might disturb the flow. This calming section, approximately 34 feet long, was connected directly to the top of the test section and thereby insured against abnormal velocity perturbations in the air entering the bed. Manometer. An open-end mercury manometer was connected to the air supply line just above the test section. Since runs made with an empty test section showed a negligible pressure drop between the manometer tap and the exhaust

-40end of the air line, manometer readings taken when the test section was packed with pellets were a direct indication of the pressure drop across the bed and the inlet orifice (when one was used). Rotameter. Because of the calming section upstream from the test section, the rotameter was located between the packed bed and the exhaust point. The meter itself was a size 12 Fischer and Porter Flowrator (Tube No. 12-LL25, Serial No. D8-1612), with a capacity of 0-200 standard cubic feet per minute of 0.877 specific gravity gas, at 14.7 psia and 60~F. The scale was graduated in increments of 2 SCFM. In the absence of test equipment suitable for calibrating the meter at high rates of flow, calibration was accomplished by passing through the meter an air stream enriched with oxygen metered through a calibrated smaller meter, and determining the concentration of oxygen in the enriched air mixture. Calibration by this method was found to be reprOducible within approximately ~ 1.5 per cent. Exhaust. To insure against the presence of p-dibromobenzene vapor in the air entering the blower, the air-vapor mixture leaving the test section and rotameter was discharged out-of-doors. Test Section The test section consisted of a 6-inch length of the same piping as was used in the air supply system, flanged at both ends for assembly into the line. The lower flange was

bolted to its mate on the downstream end of the air supply line, but C-clamps were used with the upper flange to facilitate assembly and disassembly between runs With the clamps removed, the test section could be swung out from under the air supply line, as shown in Figure 3, exposing the top of the bed and facilitating the introduction and recovery of the active pellets. This lateral movement of the test section was made possible by mounting the rotameter section of the line in wall brackets within which it could turn and using an uncemented slip-sleeve fitting above the rotameter. Thus the test section could be rotated about an axis through the meter. Inert pellets. Spherical glass beads of the type obtainable from any laboratory supply company were used as inert pellets for two of the diameters tested —1/8-inch or 3-mm, and 1/4-inch or 6-mm. For tests with a nominal pellet diameter of 1/2 inch, ordinary glass marbles were used The precise dimensions of all three sizes of inert spheres together with indications of size uniformity are presented in Appendix B. Pellet support screen. Since air flow was downward through the bed, and exit geometry was not significant, no special considerations were involved in designing a pellet support screen, and a heavy-duty screen mounted in a steel ring having the same diameter as the flanges was used. Orifices. Preliminary tests showed that the packed bed always settled slightly during runs because of vibration.

42When rigid orifice plates werc useC- the resulting separation, however slight, between the plate and the top layer of pellets was found to have a significant effIect on the flow distribution in the bed. To overcome this difficulty, orifice rings of 1/32-inch cellulcse acetate were cemented to annular rubber gaskets whose flexibility permitted the orifice to settle with the bed. As an added precaution, the bed was always loaded to a level about 1/16 of an inch above the surface of the upper flange, so that the orifice gasket was placed under slight tension when the bed was clamped to the line. Temperature measurement. Two chromel-alumel the rmocouple junctions were placed in the bed at the same depth and radius as the active pellets, except at locations close to the center of the bed where the junctions were placed imrrediately above and below the active pellets. No particular care was exercised in locating the couples at or away from pellet surfaces, since tests indicated a negligible difference between readings made at the pellet surface and those made in the interstitial space. 2his observation was in agreement with those of other investigators (3, 8)o From the test section, the thermocouple leads were run to a cold junction in a melting ice bath and to a rotary selector switch from which one couple at a time could be routed to a Leeds and Northrup Portable Precision Potentiometer (Model 8662, Serial No, 729427).

-. 43Position measurement. ~The depths at which active pellets were located were indicated by rings scribed at 1/2inch intervals on the inside wall of the test section. Radial positions were measured with a circular Lucite plate, closely fitting the test section, upon which concentric circles were scored in 1/4-inch radial increments, or with a 1/32-inch sheet of cellulose acetate, similarly scored, which was aligned by means of two small studs projecting from the upper flange surface and was used at shallow bed depths. The studs also served to center the orifice gaskets. Due to radial symmetry, angular measurements were not required. Since all active pellets used in a run were located at the same depth and radius, the identity of individual pellets was preserved by consistently loading and unloading in a clock-wise direction from a reference mark on the face of the upper flange. P-dibromobenzene Pellets Spherical pellets of p-dibromobenzene were pressed in a Stokes Model F Pelleting Machine (F. J. Stokes Company), using special 1/8-, 1/4-, and 1/2-inch spherical punches and dies obtained from the same company. Granulated p-dibromobenzene was obtained from the Eastman Kodak Company and was ground in a Stokes Oscillating Granulator, Model 2A, equipped with a No. 10 heavy wire screen, before feeding to the pelleting machine. As formed by the press, the pellets were essentially spherical except for a narrow "waist" around the middle,

-44where the punches came together. The pellets were then "cured" before use by storing for a week or ten days in a covered jar at atmospheric temperature. Normal temperature fluctuations caused alternate vaporization and condensation on a limited scale, with the result that the waist was practically non-existent by the tiLme the pellets were used. The actual dimensions and other physical characteristics of the active pellets are presented in Appendix B. The pellets were weighed in glass-stoppered weighing bottles 25 millimeters in diameter and 40 millimeters high (Kimble No. 15145), using a notched-beam chain-o-matic analytical balance (Win. Ainsworth & Sons, Inc., Type DLB; Serial No. 16644) equipped with a magnetic damper.

EXPERIMENTAL PRO CEDURE In the original planning of the research program, it was anticipated that the experimental operating procedure would consist of six basic steps: pre-weighing of the active p-dibromobenzene pellets, warming up the apparatus and establishing desired operating conditions, loading the active pellets into the bed, making the experimental run, recovering the pellets, and post-weighing. The active pellets to be used in any single run would be located at the same radius and depth, to avoid any possibility of the transfer from one pellet being affected by that from another, but full advantage would be taken of radial symmetry. Thus, more pellets would be used per run at positions near the wall than at positions near the center of the bed. In general, experimental runs were to be grouped into two-man'shifts"t of from 3 to 4 hours in duration, including weighing time, in order to minimize the time spent warming up and adjusting the apparatus. Preliminary work indicated that from 30 to 45 minutes would be required for pre-weighing, 20 to 30 minutes for warm-up, and another 30 to 45 minutes for post-weighing. Although this basic plan was found to be suitable, experience dictated several modifications in the detailed procedure, and the actual method of operation is described in the paragraphs which follow, under appropriate sub-headings. 45

46 Pre-we ighing Preliminary runs indicated that little advantage was to be derived from the separate weighing of each of the active pellets to be used in a multi-pellet run, and all pellets to be used in a given run were therefore placed in the same weighing bottle and weighed together. Individual weighings were, of course, necessary when positions close to the center of the bed were being investigated and only one pellet could be run at a time. The data for these runs (Appendix A) provide an indication of the degree to which individual weight losses were found to deviate from the average. Except for the determination of pellet density (Appendix B), no attempt was made to obtain the absolute weights of the pellets used. Although all weighings were made with an empty tare bottle on the opposite pan, the weights of the various weighing bottles were all different, and the balance reading was therefore somewhat different from the actual weight of the pellets. This difference obviously cancels out when the final weight is subtracted from the initial to obtain the weight loss. The analytical balance used for the weighings had a sensitivity of ~ 0.05 milligrams, and weighings made during any one weighing period were reproducible within that range. It was discovered, however, that reproducibility could not be carried over from one period to another. Attempts to identify the cause of this discrepancy were unsuccessful,

47 but its effects were circumvented by a technique which will be described in the section on run procedure. MWarm-up of Equipment Before the blower was turned on for the warm-up period, the motor control resistances were wired to provide the approximate air flow rate desired and the temperature of the water entering the heater-cooler was set at an approximate value by adjusting the needle valve on the steam line. The *two thermocouple junctions were placed in position at the bed location to be tested, and the bed was then packed with inert pellets, fitted with the desired orifice if one was to be used, and clamped in running position. Except for the absence of active pellets, the equipment was thus warmed up under actual test conditions. During the warm-up period, the water and/or steam valves were adjusted until the potentiometer readings indicated a temperature closely approximating 80~F. in the test section. The desired air flow rate was established at the same time by making minor adjustments in the motor control resistance. When steady-state conditions with respect to both flow rate and temperature had been attained, the blower was stopped, the bed unclamped and swung aside, and the loading of active pellets was immediately started. The warm-up procedure was also followed whenever any of the run conditions were changed in the middle of a shift.

48 Loading the Bed Inert pellets were scooped out of the bed until the proper test depth was reached, as indicated by the lines on the inside wall of the test section, and the bed was then carefully leveled at this depth. Active pellets were then quickly removed from the weighing bottle with a pair of tweezers and pushed into the exposed inert layer at approximate radial and angular positions. Radial distances to the center of each pellet were checked with the radius gauge and corrected as necessary by gently pushing the pellets into place with the point of the tweezers. The distances were rechecked after each adjustment, until all active pellets were correctly located within approximately 1/32 of an inch. Several inert pellets we.re then carefully placed around and on top of each active pellet, to minimrize movement when the rest of the inert pellets were replaced. There was, of course, no assurance that the active pellets did not shift slightly during this process, although positions were usually found to be unchanged if the pellets were carefully reexposed after running. When all inert pellets had been replaced, a 1/4-inch steel plate was placed over the bed and the bed was rapped sharply several times to settle the pellets. Since the inert pellets returned to the bed were the same ones previously removed, and since the rapping procedure established a final bed level which was reproducible within approximately 1/32 of an inch, bed porosity could be assumed to be essentially

49 constant from run to run. Experimental measurement showed the fractional void space to be 0.36, 0.37, and 0.42 for pellet diameters of 1/8-inch, 1/4-inch, and 1/2-inch, respectively (Appendix B). A procedure slightly different from that described above was followed when tests were to be made at bed depths of one or two pellet diameters. In this case, the active pellets were pushed into place without removing any inert pellets from the bed. For runs at the topmost layer, it would have been possible to avoid disturbing the inert bed completely by merely placing the active pellets in the holes left when pellets from the preceding run were removed. Because this practice would result in an exact reproduction of bed geometry which could not be achieved when inert pellets had to be removed and replaced, the bed was always deliberately scrambled between such runs by stirring with the point of the tweezers. The inert pellets were then leveled and settled as usual, and the active pellets emplaced by merely substituting them for inert pellets which were located at the desired positions. The time required for the entire loading operation was usually between one and two minutes, depending on the test depth and the number of active pellets to be loaded. This variable time meant that the weight lost by the active pellets due to exposure to the atmosphere during loading was also variable, but this problem was surmounted by the "dry run" technique to be described in the following section.

50 Run Procedure As soon as the test section was clamped in running position, the blower was turned on and came up to speed in about five seconds. The initial potentiometer readings were made as soon as steady-state temperature conditions were established in the bed, usually about 30 seconds after startup. Additional readings were made throughout the run at one-minute intervals, and the rotameter and manometer were read at mid-run. Running times were measured with a stop watch, and the stop button in the motor circuit was pushed at the end of the desired running time. The blower came to rest almost immediately, the second or two of extra operation compensating for the start-up time to some extent. The test section was then unclamped and the active pellets recovered as quickly as possible. It was necessary that running times be long enough to produce a weight loss which could be determined within a few per cent by normal laboratory weighing techniques, and fiveminute runs were found to be adequate in this regard. On the other hand, shorter runs obviously permitted the accumulation of more data in a shorter time. Preliminary tests made with running times varying from 1-1/2 to 5 minutes yielded consistent results and indicated that the start-up and shutdown times, as well as the time required to attain a steadystate temperature, were not critical factors. On the basis of these findings, actual running times were varied depending

51 on the test location, the air flow rate, and the number of active pellets in the bed. Because of the time required for a man to balance the potentiometer and to record the rotameter and manometer readings, running times of less than 1-1/2 minutes were not feasible. Five runs were normally made with each given set of test conditions, and a shift normally comprised four of these five-run series, each made at a different air flow rate with the other run conditions constant. Nominal flow rates of 12.5, 25, 50, and 100 CFM were used, and a typical shift therefore provided all the necessary data for a given combination of pellet diameter, orifice diameter, and position within the bed, over the attainable range of air flow rates. As noted, the active pellets lost some weight when they were exposed to the atmosphere during the loading and recovery operations, and a correction for this loss was necessary. One run in each five-run series, usually the middle run, was a "dry run" made without any air flowing through the bed but exactly duplicating the other runs in the series in every other respect, including running time. The loss in weight for this run could thus be attributed to the exposure during loading and recovery and to the slight amount of natural convection in the bed during the "run". Subtracting this loss from the measured weight losses for the other runs in the series yielded corrected weight losses which could be ascribed to the flow conditions alone. This operation is discussed further in the next section,

52 Although the weight losses obtained with the zerovelocity runs made during the same shift were generally in excellent agreement, considerable variations were observed from shift to shift, and the t'losses" were even found to be negative, i.e., the final weight was greater than the initial, on some occasions. This can be seen from an inspection of the original data (Appendix A). These discrepancies were finally attributed to the actual weighing of the pellets, as was noted in detailing the weighing procedure, but attempts to identify the exact source of the trouble were unsuccessful. Since weighings made at any one time were reproducible, however, the measured dry-run weight loss also constituted a correction for changes in balance readings between weighing periods, and corrected weight losses were generally found to be consistent, even when compared with re-runs made several days or even weeks later. In view of the obvious importance of the measured dryrun weight losses in obtaining the correct losses for the actual data runs, at least three dry runs were included in each group of weighings, and the losses for these runs were checked for consistency. Agreement within 0.10 or 0.20 milligrams was usually obtained among all three measurements. In preliminary work, the true dry-run weight loss was measured by adding a sixth weighing bottle to each set of five and leaving it untouched during the experimental runs. The change in weight of this spare bottle was therefore a measure of the actual weighing correction, and could be

53 subtracted from the indicated dry-run weight loss to obtain the true loss attributable to exposure and natural convection. The true losses determined in this manner were found to lie between 0.05 and 0.15 milligrams, and shift-to-shift consistency was very good. Pellet Recovery As soon as the blower stopped at the end of a run, the test section was unclamped and swung aside, and inert pellets were quickly scooped out of the bed until the active pellets were located. No attempt was made to avoid moving the active pellets during this operation, except in preliminary runs made to determine the extent to which the pellets shifted from their original positions during the loading of the bed. As fast as the active pellets were uncovered, they were picked up with the tweezers and returned to the weighing bottle. The entire recovery operation usually took less than 30 seconds. Pos t-weigghing All active pellets were post-weighed at the end of the same shift in which they were run, to avoid any possibility of loss in weight due to prolonged storage, and the actual weighing procedure was the same as that used in pre-weighing. A sample data sheet for the experiments is shown in Figure 5. In addition to the experimental data, pertinent processed data were also included on each sheet, and the completed form thus constitutes an integrated record of the results for each run.

56 Date 14 AVov 5:3 Page 2 iDp -,. Bed,iRheo.Set 5- o Rm~n iTie Z i, IT:est Depthi 3/R" I,, I n~.e. Depth 4 jest -ac.'' 9A.,) 4R R44eo. o p ] I,oz /.023 r.l ve s o~ o-,ve. 06 Z. > 212- /.cO2-Elo-4 | 10 t i iGTl 1 )0 G6 1 t5I- i CT Rn Ma,=g. rO am, ot I9 p&Wd 7. 4 TBunt Z4 -aWd 46Z8 LW! - -. t..L, 40/i _._ Re k),y`r_ Wf to, I o4? ~,~.... t s'~r/ GP T t; 8L10 14 "C G 146.9 Tost: 10.X4 tW4715~.~10/o 3 3S 8, To, Tot 3, 4 ^ ivl l;-g- 1t030 3,og Ave I. 2 Z jve E- 2| 12 - I Z!,05 0,E, oo 2 ICT /,o _ et-iGo' 09 If an nom ]Bot uo ad 6 514 i + anom,!|Bot Z S i-blvd G,s | ~R,dg., -_- R9.o-'Rdg, _"Hg, ~ 0't47 8 I -t, -— < so rt to 5,; 33 7 -A Vto "H, Zol 7? 1r ~~~tiQ I ID8 toft l, l,30 k"47.0,...V - t S..I.t_... _. i 1- r,oz 020 I OeAv - j 105 (4e 5 1.4 ve f'q2- oS,1~1W _ jC> E-_ _ 1 12- /.0o3 1 o 36 _ IC~ _' E-1 2 - ilr,-; r U | -X-~1 Ma!aQ o t - I _'Td j | 1< Manom,iBot z / d |x{~te3. I~,t Rd,o ~f Il o.T.e bt Rdg, Hg% I AO~ ~~t {.0 @5t',RPt -W.&S A I R'V~ Iolt, l$ I T'ar "I/ Lft o t 1_v% I.& ilel Tot, j-WVO r~s ~~ I1-1:.o7o l 1.o0 03;'ve i,o4 i |:l-I,o., I.0oq 19 4Ae l,o! rF; 2- 1.lo0 1,.o 6 0 ICT o.9?, | E2- 1.04 t,.o....!,o030 | un tll Manae C Bot Z {'Nd 41_iL Manom. iBot t7'Wd 7 7o lPe -it 4I1 1 -, i p i- t,9 1 I p, ~ ~...... -7 t Pdg............_7,.Lft 3,o ~ I _ IC r f, S Vf lR z. k" S 3.2" L || 1Lft 1S0 |fS IGI ol, 0l z. 3.( Z i;'s 4, i Po 4; a- v w'4.so j,d.99| IG' t,1o "Tot 3,319 i-W 1.,s k /6' 4 ~ 1 Ica1- 1 071 0 1or,'Ave l o |l J,o8 / /,Dse 1.s S4 E-t f.j2 - I.oL i, OdZ_kr_L __ _,CT O -. _ _971 2! _ __J ot| |f Boun2 M t t-8 id _Go | 0 r Mtas n Om 7o/,0 a i-7 Manom. Rot 7 1, Lawtz 3 %,04 r, J _,Z 5, o9+ jLC t o,,5 |rre,!,53 - t $98 a SG 8t.o Tot 33bj-m' lols/-rc 4.o G -b/fzt2- _ Gt - r b-mols/rt2-h r k' -mg/cm2 r; k' - lb-mols/m/Zh,r; all wrenight~s in milligrams. k'/G' is x l 0 Figo 5o Sample Data Sheeto

DATA PROCESSING Dr-Run Correction The first step in processing the raw data was to compare the measured weight losses for the dry runs (three or more) made during each shift and to reject any inconsistent values. In general, the agreement among all these losses was good, and only rarely was more than one found to be inconsistent. The measured losses in weight for the actual data runs in each five-run series, obtained by merely subtracting final from initial weights, were then corrected to true losses by subtracting the dry-run weight loss for the same series. As noted in the preceding section, this procedure eliminated the effect of pellet exposure during the loading and recovery operations and also corrected for any fixed error in either the pre- or post-weighings, and therefore yielded a true weight loss which was directly attributable to the actual flow of air through the bed during the experimental run. If the dry run in a particular series had been rejected, the dry-run correction for that series was obtained by averaging the other dry runs in the shift. The true weight loss for each data run, i.e., the loss in weight corrected for the dry run, is designated AWd on the original data sheets (Figure 5). 55

56 Te_erature Correction The driving force for the transfer of mass from a solid surface into a gas stream is usually taken to be the difference between the partial pressure of the transferring component in the main gas stream and that at the gas-solid interface, Assuming equilibrium at the interface and ideal gases, the partial pressure at the interface will be equal to the vapor pressure of the solid, making the driving force for the transfer, and hence the actual rate of transfer itself, a function of the vapor pressure. The latter, in turn, is a function of the temperature, and it is therefore essential that the temperature at the interface be known if the mass-transfer data are to be correctly interpreted. As has been noted, temperature measurement was accomplished in these studies by placing thermocouple junctions in the bed at positions equivalent to those occupied by the active pellets. Since junctions were actually located in the interstitial space between pellets rather than on a pellet surface, the true surface temperature was not determinedo However, preliminary tests indicated that the measured temperature was within a fraction of a degree of the temperature at the surface. This observation is in agreement with the findings of other investigators (3,8) and is further confirmed by the analytical study presented in Appendix E. Because it was not possible to make all runs at exactly the same temperature, the data had to be corrected to an arbitrary base temperature before they could be compared

57 and correlated. Experimental conditions made it desirable to take most of the data at temperatures around 800F., and this temperature was therefore selected as the base to which the data were corrected. Unfortunately, the agreement among the vapor pressure data reported in the literature is not particularly good, as can be seen from Figure 6, and experimental measurement of the vapor pressure was therefore considered. At the same time, it was recognized that the effect of temperature might not be confined to its influence on vapor pressure, and it was therefore decided to check the temperature effect directly under actual experimental conditions rather than to make a separate investigation of vapor pressure. Accordingly, a series of experimental runs were made at various temperatures covering the range of interest, with all other run conditions held constant. The weight losses for these runs, corrected for the dry-run weight loss, were plotted against the reciprocal of the absolute temperature on semi-log paper, and a straight line was drawn through the data in keeping with its presumed relation to vapor pressure. As a check on the slope of the line thus obtained, a second series of runs was made under completely different test conditions, and these data were found to fit a line of the same slope. The original data for both series of runs are tabulated in Appendix C, and are plotted along with the correlating lines in Figure 7. The slope of the lines is also shown in Figure 6, for comparison with the slopes of the various vapor pressure curves, and is seen to be in general agreement.

58 TEMPERATURE,0 F 95 90 85 80 75 70 0. I I I I I I I 0.09 0.08 0.07 It%_ _ __ 0.0, E ~,,z cr ~o 0.03 a> 0.02 0.01 1.80 1.82 1.84 1.86 1.88 RECIPROCAL TEMPERATURE, 103/~R Fig. 6. Vapor Pressure of p-dibromobenzene -, INTERNATIONAL CRITICAL TABLES (37) — m —---— CHEM ICAL ENGINEERS' HANDBOOK (51)1..I.- BEDINGFIELD AND DREW (5)2 in __. ZIBBERMAN (68) EXPERIMENTAL CT CORRELATION FOR COMPARISON OF SLOPE ONLY EXTRAPOLATED FROM 142~ F 2 EXTRAPOLATED FROM 114~ F

59 60 50 5 IN. PELLETS, 40 la 2-in. ORIFICE, 0o I I I I I~~~~~~ 1/2-in. RADIUS, ~~~~~~~~~~~30 1/8-in. DEPTH, SLOPE:-8250 20 20 I 0 E I0 E 9 7 cC 0 L 50 F-~_~~~~L 5-IN. PELLETS, 4 (_ 40 I-in. ORIFICE, 0 2-in. RADIUS, ~30 I I I \LQ I I I 1 ~5 /8 in. DEPTH, 20 S LO PE = - 8 250 02~0 2O 0o 0 0 0. I0 I 0 III 9 8 7 1.80 1.81 1.82 1.83 1.84 1.85 1.86 1.87 1.88 1.89 1.90 I03 OR Fig. 7. Effect of Temperature on Mass Transfer,

60 The lines in Figure 7 can be represented by the equation 8250 log (- AWd)m B - 82 (28) where B is a constant for any given combination of pellet diameter, orifice diameter, position in the bed, and air flow rate. At 800F., then, log [- Wd (8o0)] B 8250 (29) 540 and subtracting Equation 28 from Equation 29 yields l - AWd(800) 8250 8250 log: _:-"_ log C (30) - aWd (To) T 540 which defines the temperature correction factors, CT. A plot of this factor versus temperature is presented in Appendix C. The first step in correcting the measured weight losses for temperature was to average the potentiometer readings for each run. As indicated in the section on Experimental Apparatus and Equipment, two thermocouples were used with each run, and the readings from these two couples usually differed by less than 0.01 millivolts (0.450F.), equivalent to a change of approximately 3 per cent in the temperature correction factor, CTO Temperature changes during runs were equally small, and the average potentiometer reading was therefore considered an adequate basis for the temperature correction.

61 Both the average potentiometer reading and the corresponding temperature correction factor were entered on the data sheet, and the actual weight loss for the run ( AWd) was then multiplied by the temperature correction factor and the product ( Awt) recorded on the data sheet, as can be seen in Figure 5. Conversion to Transfer Rate The corrected weight loss, AWt, was divided by the number of pellets in the weighing group and by the surface area per pellet (Appendix B) to obtain the weight loss per square centimeter of surface area, and then by the running time in hours to obtain the actual rate of mass transfer in milligrams per square centimeter per hour. This figure appears on the data sheet as k"o Reynolds Number Rotameter readings were converted to standard cubic feet (600F. and one atmosphere) per minute by means of the rotameter calibration curve, and the volumetric flow rate thus obtained was multiplied by the density of air at 600F. and divided by the cross-sectional area of the bed to obtain the superficial mass flow rate, G, based on the empty bed. The Reynolds number, DpG/, was then calculated, using the diameter of the inert pellets as the characteristic length and a viscosity equal to 0.0436 pounds per foot per hour (at 800F.) as given by McAdams (47). The Reynolds number for each run was entered on the original data sheet.

62 For reasons to be explained in the section on correlation, the dimensionless ratio of the transfer rate to the mass flow rate, both in molal units, was also calculated, and appears on the data sheet as k'/G' (times 104). A summary of all original and processed data is presented in Appendix A. Sample processing calculations for Run No. 608, which is included on the sample data sheet in Figure 5, are summarized in Appendix D.

CORRELATION OF DATA Preliminary Correlation In the survey of the literature presented at the outset of this report, it was noted that almost all previous mass-transfer data were correlated in terms of the j-factor for mass transfer, defined as 2/3 id kgpgf (4) jd' G/Mm DG (4) Further, almost all previous investigators found jd to be a straight-line function of the Reynolds number, DpG/r, when plotted on log-log paper. Although these findings were based entirely on overall mass-transfer data, it appeared likely that local mass-transfer rates might be satisfactorily correlated in a similar manner, and this method of correlation was therefore given first consideration. It is apparent, however, that the j-factor as defined by Equation 4 includes terms which were not directly investigated in these studies, and a basic correlation including these terms would therefore be one step removed-from the actual experimental data. Insofar as these terms were constant throughout the present work, they could be eliminated without altering the form of the correlation. The Schmidt number obviously falls in this category, and the mean partial pressure of the inert gas in the film, pgf, is also constant for practical purposes since it can be effectively replaced 63

b, the total pressure in view of the very low vapor pressure of p-dibromobenzene. The group to be correlated is thus reduced to kgILm/G, which should be a straight-line function of the Reynolds number to the same extent that Jd is. In one further reduction, the mass-transfer coefficient, kg, was replaced by the mass-transfer rate, k', to which it is related by the equation kt * kg(p~ - PV)Lm. (31) This substitution would also leave the form of the correlation unaltered provided the mean driving force, (pO - Pv)lmm could be assumed to be constant. At first glance this seemed highly unlikely, but a more careful analysis in the light of actual experimental conditions provided considerable justification for the assumption. As applied in correlating overall mass-transfer data, the logarithmic mean driving force is defined as (Po - P2) - (Po - Pl) (PO - Pv)lm P~ P2, (32) In p -'P2 where P1 and P2 refer to the partial pressure of the diffusing component at the inlet and outlet of the bed, respectively. In the present studies, it is apparent that these subscripts correspondingly refer to the partial pressures immediately upstream and downstream from the individual active pellet being considered, each active pellet being completely surrounded by inert pellets. Under the experimental

conditions, no p-dibromobenzene vapor was present in the inlet air, making the upstream partial pressure always zero, and Equation 32 therefore reduces to -P2 -P2 (PO - Pv)lm = - (33) in in 1 - If considerable turbulent mixing occurred in the interstitial space surrounding each active pellet, the p-dibromobenzene vapor transferred from the solid surface would be continuously swept away from the surface and replaced with vaporfree air, making P2 quite small and the logarithm of 1 - p2/pO approximately equal to -p2/p~. From Equation 33, the logarithmic mean driving force is then seen to be equal to the vapor pressure. Since all weight losses were corrected to the same temperature, the driving force would accordingly be constant. Because each active pellet was completely isolated from all other active pellets, it appeared likely that considerable mixing and dilution would in fact be encountered. It was hoped that previous studies of fluid mixing in packed beds (6,7) might provide some indication of the degree of interstitial mixing to be expected, but the data reported pertain only to overall mixing phenomena. Subject only to the assumption that the ratio p2/p~ would be small under actual experimental conditions, then, it was anticipated that the data could be correlated by a straight line on a log-log plot of k'Mm/G versus the Reynolds number, DpG/4. It will be noted that the mass flow

66 rate, G, appears in both the ordinate and abscissa of such a plot, and that the data might be correlated equally well by plotting k' itself against the Reynolds number. The particle diameter, Dp, was found to be a parameter when the data were plotted in this manner, however, whereas the data for all particle diameters could be correlated by a single straight line when G was included in the ordinate. In summary, then, the first step in correlating the data was to plot k'/G' (G' - G/Mn) versus DpG/ for each combination of pellet diameter, orifice diameter, and position within the bed, and to draw least-square lines through the plotted data, the general equation of the lines being k'/G' x 106 = B. (34) Equation 34 correlated all the data with an average deviation of less than 8 per cent. However, the lines are not completely independent of each other and cross-correlation was also required. The two different procedures used for this purpose will be described separately in the sections which follow, Cross-Correlation, No Orifice In comparing the initial correlations for the data obtained with no orifice across the entrance to the bed, it was first noted that the correlating lines for a given depth were practically identical, i.e., that mass-transfer rates were independent of radius, and the data for each depth were therefore combined on a single plot, Plots for each of the depths investigated are presented in Figures 8-10. Slopes

67 and intercepts of the least-square lines (not shown in the figures) through the combined data were then plotted against depth as shown in Figure 11, and smooth curves drawn through the points. The lines shown in Figures 8-10 have been drawn using smoothed values of both slope and intercept, and therefore indicate the validity of the complete correlation. Pellet diameter was not found to be a parameter in plotting either slope or intercept versus depth. Further support for this conclusion is presented in Figure 17, in which data for all three pellet diameters taken at the same position in the bed are consolidated. It will be noted that the flat portions of both curves in Figure 11 lie below all the points which they presumably correlate, suggesting that the lines should be raised. Actually, the correlation presented is also influenced by data taken with the 1- and 2-inch orifices, since these data and those for no orifice should become identical at some bed depth sufficiently far from the entrance and should remain unchanged thereafter. Thus, the flat portions of the curves in Figure 11 have been pulled down slightly to bring the correlation into agreement with those for the 1- and 2-inch orifices. Cross-Correlation, Orifice Entry In cross-correlating the data taken when the air entered the bed through an orifice, it was not sufficient merely to draw smooth curves through the cross-plotted data in view of certain other requirements: (1) the transverse

68 and longitudinal profiles had to be in agreement at comparable points; (2) the correlations for both the 1- and 2-inch orifices and for no orifice had to become identical at some sufficient bed depth and remain unchanged thereafter; and (3) transverse profiles had to have zero slope at zero radius. The first requirement in particular was found to be exceedingly helpful in determining how the correlating lines should be drawn. With these considerations in mind, then, the slopes and intercepts of all the least-square lines on the original data plots were plotted against both radius at constant depth and depth at constant radius, for each of the two orifices. It was immediately observed that the variation of slope with radius and with depth was completely random, but that distinct trends were present in the intercept plots. The first observation suggested that all the data should be correlated with lines of the same slope, and horizontal lines were therefore drawn through the points on each slope crossplot and adjusted until all were in agreement. The average slope thus obtained was -0.35. The no-orifice data for bed depths greater than 1/2 inch were included in this step, as has been noted previouslyo New lines, having a common slope of -0.35, were then drawn throuagh each set of data on the original data plcts, and the intercepts of these lines determined and plotted against radius and against depth0 Smooth curves were drawn through the points in keeping with the qualitative requirements noted above, -nd the smoothed intercepts thus obtained

69 were then used to put the final correlating lines on the original data plots. The decision to determine first the smoothed slope and then the smoothed intercepts was somewhat arbitrary, since the determinations might equally well have been made in the reverse order. As a check against the suitability of the order actually used, the reverse-order determination was carried out for the I-inch orifice data, Smooth curves were drawn through the transverse and longitudinal profiles of intercepts taken from the original least-square lines through the data, and new "best" lines were then drawn through the original data using the smoothed intercept values. The variation in slope of these lines with radius and with depth was found to be as random as that of the original leastsquare lines, and again the use of an average slope seemed warranted. When the average was determined, it was found to agree closely with that previously established, -0.35, and the two methods of correlation therefore yield identical results. The final correlating lines and their agreement with the original data can be seen in Figures 12-16. Figures 12a-e are for the 1-inch orifice with 1/8-inch pellets; Figures 13a-g, for the -inch orifice with 1/4-inch pellets; Figure 14, for the 1-inch orifice with 1/2-inch pellets; Figure 15a-c, for the 2-inch orifice with 1/8-inch pellets; and Figures 16a-f, for the 2-inch orifice with 1/4-inch pellets

70 The smoothed transverse and longitudinal profiles fitted the data for all pellet diareters equally well, and it was therefore concluded that pellet diameter was not a parameter beyond its use as the characteristic length in the Reynolds number, as was the case with no orifice. This is also indicated in Figure 18, which shows the consolidated data for all three pellet diameters taken with the I-inch orifice at a depth of 2 inches and a radius of 1 inch. A comparison of Figures 17 and 18 also shows that at this position the data for the 1-inch orifice are in agreement with those for no orifice, the same line having been used to correlate both.

71 8 I 1?6. k',, 6_ I 7 1 16 IN. DEPTH 6-X x 10695(Re)0'5O 3 xo 2 1.5 x I. r.. - 10 ~ti'~~~~9 "~163~~ IN. DEPTH 8 * 16 6 -,,,,-X I106=70(Re)'0'43 4 o 100 200 300 400 500 600 800 1000 DpG k' Pellets Fig.8a.Original Data Plot, P vs Re, for. No Orifice, in.Pellets. (x = I in. radius, o =l1Lin. radius,. = 2 in. radius)

72 10 89 ~ t l l | |IN. DEPTH 8 2 k X leo6 =48(Re) 0-35 6 5 4 3 (10 10 20 (x~ 16 1 IN. DEPTH' X 106 = 48 (Re)-~035 G' 9 xl, 8 C. 7 Xx x 6 x 5 4 3 ___ x 100 200 300 400 500600 800 1000 DpG Fig. 8b. Original Data Plot- vs Re, for No Orifice, in. Pellets. (x= I in. radius, = 2 in radius

73 7 6F 5 IN. DEPTH PA 8 6 AL'S kg X le- 80(Re)- 0.4'~ 0 GI~~~~~~~~~G 4 x Ad 4~~~~~~~ 106 80.R 48 o A~~~~~~~~~X~ 4 x A 3a x 0 1.5 _ _ _ _ _. _ _._ _ _ _. _ _ _. 2~~~~~~~~~~~~~~ 8 IN DEPTH 7 a 6 1 0~ ~ ~ %xle 10= 50(Re)-0.36 5 A 6~ OI~ 4 3 OA 200 300 400 500 600 800 K000 2000 DpG /L Fig. 9a. Original Data Plot, vs Re, for No Orifice, -- in. Pellets. I.a (A =O in. radius, A — in radius, x = lin. radius, o = in. radius, = 2in radius) 2 2

74 9 8 7h 5 IN. DEPTH 7 ~~~~~~~8' A k' s 6~~o, oX 10 48(R)ro. 35 X:~~~Xx0 4&0G 0 0 A 3 A A 00,I I ~~~~~~~~~~~~~~I ii ~ I ~I 200 $00 400 500 600 800 I000 2000 DpG Fig. 9b. Original Data Plot, G'v Re, for No Orifice, in eles 0 2 __ 9 a ~~~~~~~~~~~~~I IN. DEPTH 6 X~~~~~~~~~~ 106=s 48 (Re)7035 4 3 2 200 300 400 500 600 800 1000 2000 DpG Fig. 9b. Original Data Plot vs Re) for No Orifice in. Pellets. (A: in.radius,x: lin ra4s In ais n ais

75 0 8 k 1 _ I I I I ) I I -' x 106 = 48(Re)-~'35 0O 6 o x 5 2 200 300 400 500 600 800 1000 2000 3000 DpG Fig. 9c. Original Data Plot, G) vs Re, for No Orifice,in. Pellets 2 in. Depth, 2 in. Radius. 7 5o 5Pt-~ x i0= 48(Re)X4 1.5 600 800 1000 2000 3000 4000 5000 7000 DpG Fig.10 Original Data Plot, k, vs Re, for No Orifice, 2in. Pellets I in. Depth, I in. Radius.

76 O O C~~~~~~~~~~~~~~Q I ~~ Il I I I I c C E O V C o I I I I II I o o (I) 4-E O C 0 0 LO ~~~~~~~0 W' 10 0 LO L o3 0) 0 >.C E c - I) 0.~~~~~~~~. CODO 0) o (1) LO LO.o 0 4 — 3 0 10 cr 0 LLJ 0 0O LO 0 LOI 1 i10 r 0; 0 ctsb 0 (L) o 0o " 10 LL o 0. 0~~~~~~~~~~ oo 0 0~~~~~ N ~......0 0 W LO 10 0 O0 0 O O O O O O O O O O O O O - E

77 ~~~40 1 T~~1611T- IN. DEPTH, -IN. RADIUS 30 Is~~~~~~~~~~~~~~6I GI X. l06= 150 (Re)-3 20 31~~~~~~0~~~ k'0 10 ~~~~~~~~~~~~~~0 20'IN. DEPTH, I IN. RADIUS 66 k' X 10 = 89 (Re)-Y0'$ ~~~~~~ t~~~~~~~~~~~o0 10 8 6 0 _ _ 15 20o - I IN. DEPTH, I IN. RADIUS 10 ~: xler22 0 -X I1= 43.5 (Rer-0' 3 8 G 6 5 4 3 __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 7 6 I's IN. DEPTH, 2 IN. RADIUS 4.. X ICP=22.5 (Rerf0.35 0 G o 2 1.4 100 200 300 400 500 600 800 1000 DpG Fig.12a.5Original Data Plots K, vs Re, for 1inch Orifice, 2 in. Pellets 4"""~.,~a. Oriia aaPos

78 50 40 40'~~ ~~~~~~~ _ 3 ~- IN. DEPTH, -IN. RADIUS 30 k2 20 I0... 20 ~~~~~~ I a ~ 0 10L 25 20 3 ~~~~20 3~~~ IIN. DEPTH, I IN. RADIUS x ioC =82.5(Re)-'. G 00 6 x C1D 156 15 3I6N. DEPTH, I IN. RADIUS 6 6 IN. DEPTH, 2 IN. RADIUS 8 X I06- 2 44.5(Re)- 0.35 5 ~~~~oo ~G 6 50 4 e 3 8 1IN DEPTH 2 IN. RADIUS._ X00 200 300 400 500 600 800 I 000 0~0 GDpG k'~~/ Fig. Ib. Original Data Plots, 5 vs Re, for linch Orifice(R inch Pellets, (ont'd) 4 a 3 2 i.5 _ _ _ _ _ _ _ 100 200 300 400 500 600 800 1000 DpG Fig. 12 b. Original Data Plots, kr Vs Re, for I inch Orifice;, inch Pellets, (cont'd)

79 50 40 I 40 IN. DEPTH, 2 IN. RADIUS 30 | | kGI X 0l6= 159(Re)-0' 35 20 I I0 25 20| l l l |1 56 IN. DEPTH, I IN. RADIUS 66 10 6= 76.5(Re)-03 I 0 0 oq 8 _5 1 5 L;~~ lo~~ l | |,51~ IN. DEPTH, II N. RADIUS I X 106= 45.3(Re)-~35 100 200 300 400 500 600 800 1000 DpG k'' Fig.12c.Original Data Plot, i in.Pellets (cont'd) g. vs Re, for I inch Orifice, in. Pellets (cont'd)

80 35 30 ~~~~~~~30 ~~~J IN. DEPTH IN. RADIUS 2'2 20 k' ~0 O,Q~ 0% X IC0 =121 (Re)-~'53 ~~~~~~~~~~~~~~~~~~~~Mf,o 10 7 A_______ _______________ 10 IN. DEPTH, 2 IN. RADIUS 7 2 0 0 k 0.35 kX 106= 37(Re)~~~~~~5 ~O Go 4 0, 3 (0 2 022 _____ 20 I IN. DEPTH, 1 IN.RADIUS G-X 106= 75(Re)'0.35 10 7 5 4 15 I IN. DEPTH, I IN. RADIUS IO 0 6X Id' = 54.5(R')-0.3 70G 0 ~ ~ ~ ~ ~~~0 5 0 00 4 3 i i _ _ _ _ i _ _ _ -......... i i 100 200 300 400 500 600 800 I000 DpG Fig. 12d. Original Data Plots, vs Re, for I in. Orifice, in. Pellets (cont'd)

81 15 I IN. DEPTH, I- IN. RADIUS x, X I6= 48(Re)-0.35 7 6 5 4 I IN. DEPTH, 2 IN. RADIUS X 106 = 45 (R.)'~3 5 15 2 IN. DEPTH, I IN. RADIUS I0 k' X IO = 48 (Re)-0.3 100 200 300 400 500 600 800 1000 DpG Fig.12e. Original Data Plots, - vs Re, for I in. Orifice, in. Pellets (concluded)

82 30 20 i-IN. DEPTH, O,IN. RADIUS )k( XI0Id- 115 (Re- 035 G 10 IO0 7 6 30 IN. DEPTH, -IN. RADIUS 208 4 k' X 106 = 122 (Re)-0'35 G a 0;0 L -00 7 6 40 30 { —I (IN,. DEPTH 1'. IN. RADIUS 30I~~~~~~~~~~~~~~~~ ~0 20~~~~~~~~~~~~~~k -~x 106 = ni (Ref.3 0 10 30e k ~~~~~~~~~~~IN. DEPTH, IN. RADIUS {8 I 8k' 6 4S 20 =... 106=,- 137(Re 35 )O~~~~~~~~~~~ 0 0 0 7 200 300 400 500 600 800 1000 2000 3000 DpG k'I Fig.13a. Original Data Plots, -~ vs Re, for linch Orifice, -inch Pellets.

83 20 J IN. DEPTH, I IN. RADIUS i _x IC 6= 86 (Re)-0. 5 10 IN. DE'TH IN RADIUS 7 0 I I I- I k' x Io6 = 44( (Re) 0'35 G 5 4 02 5 8 j IN. DEPTH, 2 IN. RADIUS 4 ~ ~ J~Y I I I /I - X106 = 26 (Re)-f035 3 0 0 0 2 1.4 40 30 8II I I IN. DEPTH, 0 IN. RADIUS o o 0 "~-X10 = (Re)-'35 20 10 200 300 400 500 600 800 1Q00 2000 3000 DpG Fig.13b. Original Data Plots, vs Re, I in. Orifice, in. Pellets. (cont'd)

84 35 8IN. DEPTH, - IN. RADIUS k' 20 k' X 106 k147 (Re)6-0.35 10~~~~~~~~~~~~~~~ C0 20 3 IN. DEPTH, 1 IN. RADIUS k' X 106 73.5 (Re)035 00 G'~~~~~~~ 10 8 O~~~~~~~~~~~~~~~~~~~~~~O 6 0 4 I0 8 IN DEPTH, I~ IN. RADIUS YIz3 8 8 k' 2 661 R ~L -~ X 106= 46 (Re)-0.35 0 0 4 o a 2 bIN. DEPTH, 2 IN. RADIUS X 106 33.5 (Re)-0.35 1.61~ ~ ~ ~ ~ ~ ~ ~ ~~~' DpG Fig.13c. Originol Data Plot, A vs Re, for I inch Orifice, in. Pellet (cont'd)

35 30 I~~~~~~~~~0 20 5- IN. DEPTH, O- IN. RADIUS -r x:0: 104 (Re)-~35 G' 25 2 & I ( II IN. DEPTH,2 IN. RA~DIUS kt x 106 104 (Re)70.3' 89 0'~~~~~~~~~G I 0 1 I I $ 8 6 (0 ~ ~ ~ ~ ~ ~ ~ ~ o 5 0 - 15' IN. DEPTH I IN. RADIUS ~~-10 k 106 64.5 (Re)'0 35 8 6 4 31 lO 8 8~~~~~~~~~~~~ N DEPTH, I-' IN. RADIUS 2~~~~~~~~~~~~~~~~ 6 G 0~~~~ 4 2200 300 400 500 600 800 1000 2000 3000 DpG k' (cont'd) Fig.13d. Original Data Plot, vs Re,for I inch Orifice i in. Pellet (cont'd) Fig.13dOriOi-a'4aPlt

86 5 5 IN. DEPTH) 2 IN. RADIUS 8.~I. ETH k' 603 ~~~~~~~~~~~~~~~~~6' - x 106 40 (Re)-~'$5 ~a.~ G' 4~~~~~~~~~ 20 I IN. DEPTH, 0 IN. RADIUS k- X 106 =90 (Re)-35 10 0 %o 4 (0 I IN. DEPTH,'~ IN. RADIUS I IN. DEPTH, IIN. RADIUS k' 05 10to kl ~~~~~~~~~X 106 = 575 (Re)-03' 200 300 400 500 600 800 1000 2000 3000 Dp G i0 F eOi D Pt -v e ri Oi in Pellet (cont'd) 8 gl3.OrPial ot Pot,G,vs e,fo I nc Orfie,0 6~~~~~~~~~~~~~~~~~~~~ 4 ~ DpG~~~~G,'M, k' I~~~~~~ Fi.4. Oiio oaPo,c'v e frIic rfc,-i elt(otd

87 10 I IN. DEPTH, I IN. RADIUS X 106 = 48(Re)-o.35 5 4 3 l0 I IN.'DEPTH, 2 IN. RAQIUS 57G'x 10 IO6= 45(Re)-0.35 4 3 0 2 ae'1~g I 0 2 IN. DEPTH, 0 IN RADIUS 7'ftftlw, i4~x k 10 51(Re)-0.35 DpG~~~ Fi0131~ ~o,o~n G', f X IC 5I= 4 3 2-' I0 2 IN. DEPTH, IN. RADIUS 5~~~.X 10 I6 = 48.5 (Re )'~35 $~~~~~~~~~~~~~ 2 200 300 400 500 600 800 I000 2000 3000 DpG Fig. 13 f.OrgnlDtPlt v.Iet,(ntd Oriina Daa Pot,G- vsRe, l n. Orifice, -~ in. Pellt,(atd

89 10 7 2 IN. DEPTH, I IN. RADIUS 5~ ~ 0~, ~k' x o06= 48 (Re)-0.35 4D0 G. 2 FIN. DEPTH, 2 IN. ReADIUS 4 3 oo 2.. 500 00 100 0 00 0 00 3000 5000 7000 Fig.14. Original Data Plot, G- vs Re, Iin. Orifice,-2 in. Pellets. 6 __ _ 2 IN. DEPTH, 2 IN. RADIUS. iG — X I0 = 48 (Re)-0'35 200 30 0 1000 6 2000 30002000 3000 Fig.13g. Original Data Plots, - s. Re in. Orifice, in. Pellets. concluded)

90 I0,7 t-;F I I I A 1 IN.DEPTH,2 IN. RADIUS k7 -'035 ~~~~5 t~~~~~~~~k' -1X 39(Re) 5 G_ 4 20 IN1NDEPTH I IN. RADIUS kI ico-k X -,f:73(Re)-~"35 10 F' 1 IN DEPTH I'IN. RADIUS I0, -~ X 0 50(Re)' 10.75 4 --- 15 1 IN.DEPTH IN RADIUS 3 I- RIU 15 o o1N. D E PTH 1 N RADIUS I100 200 300 400 500 600 800 1000 DpG FIG.15a. Original Data Plot,.vs Re, for 2 inch Orifice,X in PRelles

91 20...... 20 3 IN. DEPTH, I -IN. RADIUS 4~~~1 0ti r~16 k 10:70(R e)-035 5 4, 14 10l l 15- IN.DEPTH,I-IN. RADIUS 0 ~1;~-X Ik= 49(Re)0.5 7 G X 1& Fig 15b. Original Data Plot,G, vs Re,for 2 In. Orife, In. RADIUS 0 5 IN. DEPTH, IN. RADIUS -10~~~~~~k 106: 6. 35 5 00FGix I5O= 67.5(RP,'~P' 10 7~1 k' I Inch Pellet (corrt'dFg 5 Oiia a Po,G R,o n Oice

92 I0 | -0,, 5 IN. DEPTH,1IN. RADIUS 10r l | | 2 IN. DEPTH, I IN. RADI 1-E 2? mR 20 a201................. ~I N. DEPTH, I IN RADIUS 10 G200 300 400 500 600 800 1000 FigIN.EPTH. Re; 2 Inch Orifice Inch IDIUets (concluded) k X 106 =41.5(Re)- 0.35 I00 200 300 400 500 600 800 I000.7 rs 2

93 |0 ~~io r \ I \ I I I ~ ~-IN.DEPTH,O IN. RADIUS 7 o' kXIO6C 48(ROfO035 5 G 400 3 I0 r- IN.DEPTH, IN. RADIUS H~~ 7k _ x I6= 48(R)o)" 5 4 3. 2 ~~10,5~~~~~~ 11 7IX \IN.DEPTH- LIN.RADIUJS?~~~~~~~~~~~ k7 6 o-O --.-~io~~~~~~~G X lo= 49(Re) 5 5~~~~~~~~~~~~~ I~~~~ 0 0 4 3 2'5 -LIN.DEPTH, I IN.RADIU6 10 6 03 Ui X 10 =7115 (Re}''3 7 5 4 200 300 400 500 600 800 I000 aOOO 3000 DpG kl'4 F.. Inch Pellets. FieGa~Orginl DtaPlot$,-~vs Rea; 2 Inch Orifice,4

94 13 10 -IN.DEPTH,1- IN. RADIUS 7 ~~~-~ ~ Xk106= 49,5( Re)"~'35 5 0 4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 3 0 7 3IN.DEPTH, 0 IN. RADIUS ~0 E I X Io6: 38(Re)'035 5 4 3 2 18 -K- IN.DEPTH, IN.RADIUS 00 k' -s IN.DEPTH,-P IN RADIUS k' 6 x074.5(Ref 035 10 XI 7 5) 7 5 4 200 300 400 500600 800 1000 2000 3000 DpG /~ k' Fig.16b. Original Data Plots, vs Re; 2Inch Orifice,- Inch Pellets G' ~~~~4 (Cont'd)

95 15 IN. DEPTH, I IN. RADIUS 2008 -00 40 50 60 800 x 1 0 6 = 26(R,)'0'35 ~~~~~~~~10~~~0 D G 4 0k' 5,) ~~~6 Q* -jc~ X 106 = 400.5(R)-o.35 2_~~~~0...0 20 _ IN. DEPTH, 0 IN. RADIUS 610~~~~~~~~~ ~X 106 =72.5 (Re-035 200 300 400 500 600 800 1000 2000 3000 DpG Fig.16c.Original Data Plots, K. vs Re, for 2 inch Orifice, inch Pellets(cond)

96 20 IN. DEPTH, iN. RADIUS 8'2 03 k, 106I- 71.5(Re)035 10 G' 10~~~~ 7 0 5 4 15 5 - IN. DEPTH, I IN. RADIUS 5 1~~~~~~~~~0 (D 4 00~~~~~~~~~~ 3 x __ 10~ I 1 I I ~ X 106= 48(Re)'0'$5 ~~~~~~~~~~~~~5 ~~~~~~~~7 ~~~~IN. DEPTH, I IN. RADIUS 0.35 7 2 4 3 45~~~ G~~~'* 2 _ I, 2 _N R I 200 300 400 500 60C 800 K)00 2000 3000 DpG Fig.16d. Original Dota Plot, vs Re, 2 in. Orifice, in Pellets (cont'd)

97 15 I IN. DEPTH, I IN. RADIUS 2 kx iod- 59(Re)'O05 7 5 4 3 - 15 I IN. DEPTH, I IN. RADIUS 1 00 I300X 00 5= 55.5 (Re)-0'35 DpG G 5 4 ~~'o10 7 I IN. DEPTH I IN. RADIUS 5 - R 4 10 7 I IN. DEPTH, 2 IN. RADIUS'"'5,. ~ G- X I06:= 45(Re)-0'35 2 -6 A _ 200 300 400 500 600 800 1000 2000 3000 DpG Fig.16e. Original Dota Plots, vs Re, 2in. Orifice, - in. Pellets, (cont'd)

98 10 2 IN. DEPTH, 21N. RADIUS 7 k' 0 kI 10: 48(Re)'35 X 4 2 200 300 400 600 800 1000 2000 3000.Dp G Fig.16f. Original Data Plot, —1 vs Re; 2 Inch Orifice, in. Pellets (Concluded )

99 0 0 0, c,0 0 at ~ ~ ~~~~~o 0 e:5~ 0 10 0 ~~o O ~~~~o ~e~~~I.1.~~~~. o -C oo x~~~~~~~~~~~.8 0 CM~~ 0 Oeo 00 ~o EPo ~~ 0 z:~ ~~0 o o4 ~~~~~~~~cr Oc~~~~~~~~~0O~~~ ~ 4o 0 J1b 0 0 > a tI'~~~~~~~~~ 0 0 o.. o a. O C::-I:ID - 0 w o 0 u 0 0 LL 901 aix9 )>

100 I,~~7 ~~~~cSr~~~~~~~~~~~~~c o CS ~~~~~~~~~~~~~C~~C h._ 0 CL K 8or O. x~~~~~ 00~~~~~~~~~~~~~~0 C K~o 0 ciw K~~~ 0, 00~~~~~~~ 0 c 0~~~~~~ 0 oD -D to t r\ N In 901 x

All experimental data were satisfactorily correlated by straight lines on log-log plots of k'/G' versus the Reynolds number, DpG/, separate plcts being made for each combination of pellet diameter, orifice diameter, and position in the bed. These original data plots are included in the preceding section, and the correlating lines can be represented by an equation of the form k'/G' x 106 - B (B2) f (34) where B and m are constant for any given combination of the experimental conditions. vWith no orifice at the entrance to the bed, B and m were found to be independent of radial position and pellet diameter, but to vary with depth up to a depth of 1/2 inch, beyond which they were constant. The values used in correlating the data and to be used in applying the correlation are given in Table 1. Table 1 Constants Used in Equation 34, for No Orifice Depth, in, B -m 1/16 95 0.56 1/8 80 0.48 3/16 70 0.43 1/4 61 0.40 5/16 55 0.375 3/8 50 0.36 1/2 48 0.35 >1/2 48 0.35 101

102 As was explained in the section on correlation, smoothing was accomplished by cross-plotting the intercepts and slopes of the individual straight lines through the data, the intercepts being equivalent to the value of k'/G' x 106 at a Reynolds number of unity as is apparent from Equation 34. Since the original data were taken at various Reynolds numbers, it was not possible to show them on a plot of this type. Once the exponent m was found to be independent of radius, however, the original data could be shown on transverse profiles of the intercept, B, In essence, this was done by solving Equation 34 for B, giving EB T) /-) x 106 (35) and calculating the value of the right-hand group in this equation for each experiniental datum point. Plots of this group versus radial position, with depth as a parameter, are shown in Figure 19. Longitudinal profiles might have been prepared in a similar manner, but would be less meaningful since the exponent m is not independent of depth. The experimental results for the case of no orifice at the entrance to the bed, then, are described by Equation 34 with values of B and m as given in Table 1, and are shown graphically along with the original data in Figure 19. The conclusions to be drawn from these results will be listed and discussed at the end of this section, along with those obtained from the results of the orifice studies.

103 The experimental results obtained when the air stream entered the bed through an orifice were also correlated by the general Equation 34, but the exponent on the Reynolds number was. found to vary randomly with orifice diameter, pellet diameter, and position within the bed, and was therefore assigned an average constant value of -0.35. Equation 34 thus becomes kt/G' x 106 u B ), (36) where B depends only on orifice diameter and position within the bed. Values of B used in correlating the data and to be used in applying the correlation are given in Tables 2 and 3. Since all these data were correlated with lines having the same slope, the original data could be shown on the transverse and longitudinal cross-plots by means of the same technique used with the no-orifice data. Equation 36 was solved for B, giving B =( G) (t x 106 (37) and the right-hand group in this equation was evaluated for each datum point and plotted against radius with depth as a parameter and also against depth with radius as a parameter. The resulting plots are shown in Figures 20-23, Figures 20 and 21 being the transverse and longitudinal profiles for the 1-inch orifice and Figures 22 and 23 the corresponding profiles for the 2-inch orifice, WThere no experimental data

104 Table 2 Constants for Use in Equation 36 for 1-inch orificel Radius 0 1 1 1/2 3/4-1/2 1-3/4 2 Deptth 1/16 102 111 150 130 89 62 43.5 31 22.5 1/8 115 122 171 137 86 61 44 32.5 24.5 3/16 142 150 175 125 82.5 59.5 44.5 34.5 27 1/4 162 165 170 117 79.5 59 45 35*5 29 5/16 175 174 159 110 76.5 58 45.5 37 31.5 3/8 177 172 147 103 73.5 57 46 38.5 33.5 1/2 154 143 121 92 68,5 55*5 46.5 41 37 5/8 130 120 104 81.5 64*5 54 47 43 40 3/4 113 106 92 75 60*5 52*5 47.5 44.5 42 1 90 86.5 75 62 54.5 50.5 48 46.5 45 1-1/2 64.5 62 56 50*5 48*5 48 48 48 48 2 51 50 48*5 48 48 48 48 48 48 1 Radius and depth given in inches. Table 3 Constants for Use in Equation 36 for 2-inch orifice1 Radius 0 1/4 2 3/4 1 1-1/4 1-1/2 1-3/4 2 Depth 1/16 38 38.5 39 44 73 61.5 50 42*5 37 1/8 48 48 49 54.5 71.5 62 49.5 43 38 3/16 58 5 58 57 60.5 70 60 49 43 38.5 1/4 67.5 66.5 63.5 63 68,5 58 49 43 39.5 5/16 73 72 69 67 67o5 57.5 49 43,5 40 3/8 76 76 74.5 71.5 66 56.5 48.5 44 40.5 1/2 77.5 77 76.5 73 63.5 54.5 48*5 44.5 41.5 5/8 72.5 73 71.5 67 61*5 54 48 45 42.5 3/4 68 68 67 64 59 52.5 48 45.5 43.5 1 60 60 59 57.5 55*5 52 48 46.5 45 1-1/2 50.5 50.5 50*5 50 50 49 48 47.5 47 2 48 48 48 48 48 48 48 48 48 Radius and depth given in inches.

105 are shown, the profiles were obtained by interpolation and are included to show more clearly how the transverse profiles change with depth and the longitudinal profiles with radius. When either the longitudinal or transverse profiles are viewed by themselves, it may seem that other curves would fit the data more closely, and that poor judgment was exercised in drawing the curves actually usedo It must be remembered, however, that the two sets of profiles are interdependent and must give identical values at comparable points. and if a transverse profile seems low, for example, it is because the curve is pulled down by adjacent points on the corresponding longitudinal profile. Indeed, the required agreement between the two sets of profiles was a powerful factor in smoothing the data, and lends much to the acceptability of the final correlationo Conclusions Local rates of mass transfer in a packed bed of spheres have been measured and correlated with respect to position within the bed, pellet diameter, air flow rate, and velocity perturbations at the entrance to the bed. A cylindrical bed 4 inches in diameter was used, with measurements being taken to within 1/16'of an inch of the wallI, and the investigation covered pellet diameters of 1/8, 1/4, and 1/2 A nominal radial distance of two inches has been used in correlating data taken adjacent to the wall, although distances to the center of the pellets were really only 1-15/16 and 1-7/8 inches for the 1/8- and 1/4-inch pellets respectivelyo

106 inch and embraced a Reynolds number range of 150 < DpG/ < 7,000. The entrance conditions studied included completely unobstructed air entry and entry through 1- and 2-inch orifices o Subject to the above limitations in scope, the conclusions to be drawn from the results of this investigation are as follows: A. No Orific e at Bed Entrance (1) Local mass-transfer rates are proportional to a power function of the Reynolds number, and may be correlated by the general equation k'/G' x 106 = B ) (34) (2) Entrance effects are confined to the first 1/2 inch of bed depth, beyond which local mass-transfer rates are uniform, ioeo,, independent of both radial and longitudinal position, and are given by the equation -DOG35 k'/G' x 106 = 48 (/) (38) (3) Within the entrance length, the absolute values of B and m in Equation 34 are highest at the exposed surface layer of packing and decrease with depth until Equation 38 applies, the actual values for these constants being given in Table lo All experimental data fit the correlation with an average deviation of 707 per cent0

107 (4) Local rates of mass transfer within the entrance length are independent of radial position, i.e., the radial transfer-rate profiles are flat. (5) The entrance length is independent of pellet diameter. (6) Except for its use as the characteristic length in the Reynolds number, pellet diameter is not a parameter in correlating local mass-transfer rates in packed beds. B. Orifice at Bed Entrance. Since only two orifice diameters were used in these studies, no attempt has been made to obtain a quantitative correlation of the effeet of orifice diameter. Hovwever, the following additional conclusions are to be inferred: (7) Local mass-transfer rate data may be correlated by Equation 34 with a constant value of -0.35 assigned to the exponent m. (8) The values to be assigned to B in Equation 34 are functions of orifice diameter and position in the bed, and are given in Tables 2 and 3o The data fit the correlation with an average deviation of 10.7 per cent. (9) The shape of all transverse and longitudinal transfer-rate profiles is independent of air flow rate, i.e., changes in total flow affect all positions within the bed equally. (10O The local mass-transfer rate is significantly higher in the vicinity of the orifice than elsewhere and reaches a maximum at a point on the axis of the bed approximately 3/8 of an inch in from the inlet.

108 (11) At depths of less than 3/8 of an inch, wall-towall profiles of local transfer rates are characteristically M-shaped, with maxima corresponding to the edges of the orifice. (12) Perturbations in mass-transfer rate created by the orifice are completely dissipated at a bed depth of approximately 2 inches, beyond which the rates are the same as when no orifice is present and can be correlated by Equation 38 (131 The depth required to dissipate entrance perturbations is slightly less for the 2-inch orifice than for the 1-inch, as would be expected. (14) At bed depths between 3/8 of an inch and approximately 2 inches, the wall-to-wall transfer-rate profiles are dome-shaped, with a maximum at the center of the bed and minima at the walls. It is interesting to note that these profiles are quite similar to the velocity profiles produced by a free jet (23)o (15) Near the wall of the bed, local mass-transfer rates are lowest in the entrance layer of packing and increase with depth until they become constant as required by (12) above. (16) As in the no-orifice case, pellet diameter is not a parameter in correlating local rates, beyond its use as the characteristic length in the Reynolds number. This statement correctly implies that the transfer rate at any point in the bed depends on the absolute coordinates of the

109 point rather than on coordinates expressed in terms of the pellet diameters. (17) On the basis of preliminary tests, it can also be noted that if the orifice is separated from the top layer of packing by as little as 1/16 of an inch, the perturbations in mass-transfer rate created by the orifice are drastically reduced.

110 90 12 1IN. DEPTH 8 INDEPTH 100 _ o -. - 99 0 I I o LD T- T 70 x o 60,.0 _~50~T 40 3560 IN. IN. DEPTH IN. DEPTH 5 i0 19 Ee o..i O ice. 50 = L -, 01" 40 35 x I IN. DEPTH::L - IN. DPTH 50 Radius, Inches Fig. 19. Effect of Radius and Depth on Mass Transfer Rate - Transverse Profles wi-th No Orifice.

230 200 0 IN. DEPTH IN. DEPTH IN. DEPTH 16 8 =6 150T _ =,i 100 90 80 70 60 _ 1 50 T ~ ~ ~ ~~T 40 o 30 U, 60 150 o~~ 20 IN.H IR DT 8 EPTH IN. DEPTH zv (-~3 1 12 8 4 100 90 j80 70 60 50 40 30 0.5 1.0 1.5 20 0.5 1.0 1.5 2.0 0.5 1.0 1.5 2.0 Radius, Inches

112 230 200 - IN. DEPTH 1 IN. DEPTH IN.DEPTi II 150 - f 100 90 80 70 60 50 40 o 30 oC) 2 0~~~~~~~~~~~~~ 0~ 20 =8 150 I I IN. DEPTH I2 IN. DEPTH 2 IN. DEPTH lOOk 40 80 7 _ r 60 50 3 0 0.5 1.0 1.5 2.0 0.5 1.0 1.5 2.0 0.5 1.0 1.5 2.0 Radius, Inches Fig.20. Effect of Radius and Depth on Mass Transfer Rate - Transverse Profiles for I-Inch Orifice.

113 200 0 IN. RADIUS 150 00 90 80 70 60 50 40 - 40 Inf~~ I — I I I I I I~~~~~~~~ I IN. RAD IUS o~ I00-_ ~ 90 80 - T B(3 7o1 60 - - 50 _= 40 35..... 60 2 IN. RADIUS 50 T~ 40 = 30 0 1/4 1/2 3/4 1-1/4 1-1/2 2 Depth, Inches

114.m 200 IN. RADIUS 150 - FZ I00 90 80 80 70,n 60 0 6 50 40 3~~~~~~~~~~~~~~~~~~~~~~~~~~~~Ib~~~~~~~~~~~~~~~~~~~~~~~~~~ I- IN. RADIUS 1 00 90 80 70 60 - 5050 = ___ ___ __- - -,a, -' Uimm = =m 40 - ~~~~~~~~~~~~~1-t 35- " 0 1/4 1/2 3/4 I 1-1/4 1-1/2 1-3/4 2 Depth, Inches Fig.21. Effect of Radius and Depth on Mass Transfer RateLongitudinal Profiles for I-Inch Orifice.

115 100 - 90 j IN.PTH ~~80 -;~IN. DEPTH IN. DEPTH I NPTH 80 = 70 60 50 40 -- T O I ~I I'l I "I,7F T7L or~~~~~ 100'(,~90 11IN DEPTH IN. DEPTH - IN. DEPTH 80 2 4 701 60 50 40 30 2.5 0.5 1.0 1.5 2.0 0.5 1.0 1.5 2.0 0.5 1.0 1.5 2.0 Radius, Inches

116 100 ~'90 IN. DEPTH j AIN. DEPTH - IN DEPTH 80 4 I = 70 o -r 60 =1-r 50 w T T 0 90 3~~~~L (3 1 ~~~~~~~~~I IN. DPH 2~N ET IN, DEPTH 480 7O —-- C; 30 q~~ — 50 30 -- - - - - - 3ji 0 j I IN. DEPTH I- IN. DEPTH IN. DEPTH 30 70 60 50407 30 251 0.5 O 1.5 2.0 0.5 1.0 1.5 2.0 0.5 1.0 1.5 2.0 Radius, Inches Fig.22. Effect of Radius and Depth on Mass Transfer RateTransverse Profiles for 2-Inch Orifice.

117 100... 90 0 IN. RADIUS 80 70 60 - 50 - 40I 30 0 00 x 90 I!H. RADIUS cij 80 -t~I 70 60 - - 50 40 30_= 60 50 - 2 IN. RADIUS _~~=L 70-' - __ 50 - 40 30 2.5 2 1/4 1/2 I/4 1-1/4 1-1/2 1-3/4 2 60 1/4 1/2 3/4Depth, Inches

118 500 0l i 90.. J-~~~?80~~~~~ IN. RADIUS 80 2 70 60 50 - _ o x 40 In- - 30 ~J 30,rl -t Qi100 90 Depth I~~ IIN. RADIUS 80 70 60 50 401 30 0 1/4 1/2 3 /4 1 1-1/4 1-1 /2 1-3/4 2 Depth, nches Fig.23. Effect of Radius and Depth on Mass Transfer RateLongitudinal Profiles for 2-Inch Orifice.

RELIABILITY OF RESULTS The reliability of the results obtained in any experimental investigation can be measured by the application of three general criteria: (1) the extent to which the experimental apparatus and technique can be criticized on either theoretical or practical grounds; (2) the degree of reproducibility of the experimental data and the extent to which they are internally consistento and (3) the extent to which the results agree or conflict with the results of other investigations of a parallel nature. When interpretation of the data is required in order to arrive at the final results, this must also be considered. From the standpoint of the first of these criteria, the various precautions taken to insure the validity of the data have been detailed in the sections on experimental apparatus and procedure, and are believed to have been adequate. Internal consistency of the data was generally found to be good, while the reproducibility was excellento Ample evidence of the consistency of the data is present in the original data plots, Figures 8-18, and in the transverse and longitudinal profile plots, Figures 19-23. The degree of reproducibility of the data, on the other hand, was established at the outset of the investigation and was checked periodically throughout its course by making duplicate runs several days or even weeks apart. Exact reproduction was 119

120 impossible, of course, because of the random packing of the bed, but duplicate sets of data almost always agreed to the extent that either set fit the general correlation equally well. Check runs were also made whenever the data for any given series of runs were not consistent with the comparable data from other runs. These check runs usually showed the original data to be in error. However, in some cases the check runs confirmed the original data. For example, it can be seen from the bottom-center plot of Figure 14b that the data taken at a depth of 1/8 inch and a radius of 2 inches, with the I-inch orifice across the entrance to the bed, lie well above the correlating line and might therefore be questioned. These data were reproduced not once but twice by two separate series of check runs. Although this and similar results attest to the reproducibility of the data, they also suggest that tke data are valid and hence that the correlation is poor. Fortunately, appreciable disagreement between the actual data and the correlating line is the exception rather than the rule, as can be seen from a study of the other original data plots, and the general correlation is therefore supported by the bulk of the experimental data. However, the significance of reproducible data disagreeing with the general correlation cannot be disregarded. The use of a constant slope in correlating all 1- and 2-inch orifice data and the smooth profiles shown in Figures 19-23 perhaps constitute an overly

121 simplified correlation. With the majority of the data supporting the correlation, however, the anomalies can only be left as points for conjecture. As was noted in the survey of the literature presented at the beginning of this report, there are few quantitative data available which are comparable to the present findings, and any comparison with previous data must therefore be largely qualitative. The transfer-rate profiles obtained do not appear to be consistent with the velocity profiles of Smith, et al. (50,62), for example, but an explanation for this has already been advanced. The profiles are in agreement with the findings of Coberly and Marshall (13). As a minor point, it might also be noted that the present studies show the shape of all transverse and longitudinal transferrate profiles to be independent of total air flow rate, which is consistent with Smith's conclusion that velocity profiles are independent of the total flow rate. As far as a comparison with other mass-transfer rate correlations is concerned, it is pe rhaps significant that mass-transfer rates were found to be proportional to a power function of the Reynolds number, as has also been observed by others, Further, the observation that pellet diameter is a factor in the correlation only through its presence in the Reynolds number is consistent with the conclusions drawn by the majority of previous investigators. Perhaps the most informative analysis of the results of this investigation in the light of previous work is to be

122 made by comparing the correlation obtained at bed positions beyond the entrance length with previous correlations for the j-factor for mass transfer. If it is true that the entrance length in a packed bed is only 1/2 inch as has been indicated, the inclusion of entrance effects in the work done by others should be of little consequence provided their beds were sufficiently deep. Their overall correlations, therefore, might be expected to agree reasonably well with Equation 38, k'/G' x 106 - 48 (, (38) which correlates all the present data taken beyond the entrance length. The primary difficulty in effecting such a comparison lies in converting Equation 38 to its equivalent in terms of the j-factor for mass transfer. The first step in the conversion is to introduce the mass-transfer coefficient, kg, by use of the equation k' i kg(P~ - Pv)lm (31) and the difficulty in accurately defining the driving force, (pO - Pv)lm, has already been mentioned. It will be assumed that this term may be replaced by pO, the vapor pressure of p-dibromobenzene, in accordance with the previous discussiono In view of the disagreement among the data reported in the literature for the vapor pressure of p-dibromobenzene, a second difficulty now arises, naimely, what value to assign to pO0 The decision must necessarily be somewhat arbitrary,

123 and a value of 0.038 millimeters of mercury, obtained by interpolation from the data given in the International Critical Tables (see Figure 6), is probably as good as any. The relationship between the mass-transfer rate, k', and the j-factor for mass transfer can now be determined, recognizing that the partial pressure of the inert gas, Pgfw is for practical purposes equal to the total pressure, P: j p f 2 (4)2/3 k'P / t 2/3 G' p \DG 00038 DG )G t 2/3 0.02 D. ) x 106 (39) The molecular diffusivity of air and p-dibromobenzene at 80~F, DG, must be known in order to evaluate the Schmidt number, and in the absence of experimental data can be calculated by use of the Gilliland equation (28). The calculations are summarized in Appendix E, and yield a value of 0.245 square feet per hour. The Schmidt number is then found to be 2.41 (Appendix E), which is consistent with the value of 2.37 obtained by Bedingfield and Drew (5) at OOC. Substituting this value in Equation 39 gives d 0.036 () x 106 (40)

124 and combining Equation 38 with this equation produces the final relationship, DG -0.35 1.73 p (41) Written in this form, the present correlation can be directly compared with those of Gamson et al. (27), McCune and Wilhelm (48), and Hobson and Thodos (33), and the comparison is presented graphically in Figure 24. By suitably modifying the Reynolds number, comparison may also be made with the correlations of Gaffney and Drew (25) and Gamson (26). Using a fractional void volume, E, of 0.37 (Appendix B), Equation 41 becomes -0.35 Jd' 1.73 (e )-0' 35 () 1.73 (0.37)-0.35 (p ) -0.35 2.45(.) (42) Since Gaffney and Drew used an exponent of 0.58 on the Schmidt number in defining their j-factor, Equation 42 must be further corrected by introducing the factor (Sc)-0'087 G-0.35 jd,= 2.45 (2.41)-0'087 (j) DoG. 2.27(. (43) This equation is compared with the Gaffney-Drew correlation as approximated by Ergun (20) in Figure 25.0

125 co E 00 8 ~C 0 C-0~~~~~~~~~_ U o Cu 0 Q 0 C., C~~~~~. F') ~~30 10 - 0 0 Uo C,' o oC 0 - 0 O~CO 0 o 0 1,0 o~ Cn I". 0'E l 00-I E c o 0c5 c~ 0 o o C) to~~~~~ ~ d NLC o~~~~ 0 ~ 0_0 0 0 ~O N -~ N- LO~ ro-N=U

126 I~~~~I 0-~~ (V C\C Q:oC 0 Q ~' 0 E 0 41 ~~o ~i~~~~~~~~~~~~u ~1 ~ w C\ cj LI. -0~~~~L 0 ci ci 0 KO) 0 -d 0ci 0 (.9I ~. o~~~o~ d d d o d 0 0 0 ~~~~~~~~~~~~~c~ -~~~~~~~~~~~~~~~~~~~~~~~qj

127 Ln t3~~~c...... I I f /..... o N o uO (.0 s-~~~~~~~~~~~~~~~~~~U 8 0 2 ~~~~00 ~_ ~ o o o ~~~~ 0 b _ /~ o =~0 / -4-1 o" ~~o or 0~~ 0.4 L_ c~ o 0 o o oj o o c ~.'~..(~-i)P[

128 Converted to correspond to the Gamson correlation, Equation 41 becomes -0.35 Jd - 1.73 (1 - )-035DpG and M-0.35 jd(l - E)-02 = 1.73 (1 - e) 55 [DpG ] = 1.73 (063)55 -0.35 *(1, - e(44 = 2.155 D[ (44) For the spherical shapes used in these studies, DpG//u (l - ) is equal to the group 6G/a p used by Gamson, and Equation 44 thus becomes -)02 -2.155 ( -0.35 5 The comparison with Gamson's correlation is shown in Figure 26. Figures 24-26 show rather conclusively that the present correlation as represented by Equation 41, although of the same order of magnitude as the others, lies above all of them by a factor of approximately two. Even though some encouragement is to be drawn from the similarity in slope, the discrepancy is rather disturbing at first glance.

129 A careful review of the experimental technique failed to disclose any factors which might account for this discrepancy, and the original data are believed to be valid. This being the case, the difficulty must lie either in converting these data to transfer rates or in converting the rates, in turn, to actual coefficients. Both of these steps are somewhat vulnerable to the introduction of errors which could account for the vertical displacement of the j-factor correlation, and will therefore be discussed separately. In converting the raw weight-loss data to transfer rates expressed as mass per unit time per unit surface area, the significant factors are obviously the actual weight loss, the time interval over with the loss occurred, and the effective surface area of the pellet. The first two may be dismissed in view of the reproducibility of the data, but the surface area cannot be affirmed quite so readily. Areas were calculated from pellet diameters, which were in turn determined both by direct measurement and by calculation from the measured volumetric displacement, with the results from both methods being in good agreement (Appendix B)o Calculation of the area from the measured diameter, however, presumes a completely smooth surface, and this condition was not entirely realized. The p-dibromobenzene pellets appeared to have a smooth, shiny surface as they came from the pelleting press, but the alternate vaporization and condensation presumed to occur on a limited scale during storage eventually produced a much

130 Fig. 27. Surface Condition of the P-dibromobenzene Pellets. Left as pressed; Right after storage. rougher surface, crystalline in appearance, as can be seen in Figure 27. It was accordingly expected that fresh pellets would lose weight less rapidly under test conditions than would those which had been stored for some time, but no sig. nificant difference was noted in comparative tests. The calculated specific gravity of the pressed pellets was found to be slightly less than the specific gravity of pure p-dibromobenzene (Appendix B), which suggests the presence of at least some pore space in the pellets. This might well mean an effective surface area significantly larger than the calculated spherical area because of exposed surface pores, particularly if the pressed pellets should happen to be more porous near the surface than at the center.

131 In any event, the spherical areas calculated from pellet diameters are conservative at best, and the actual surface roughness might well account for the displacement of the processed data. As for the conversion of the transfer rates to actual coefficients, the use of a higher value for the vapor pressure of p-dibromobenzene would obviously lower the correlation somewhat, and might be justified in view of the disagreement among the reported data. Also pertinent is the basic difference between the experi.mental conditions which prevailed during this study and those which pertained to the work of others, namely, the isolation of each individual active pellet from other active pellets. The partial pressure of p-dibromobenzene in the gas stream immediately adjacent to each active pellet is probably quite low under these conditions, because the transfer process is localized and considerable dilution of the air-vapor mixture is to be expected. With transfer occurring throughout the bed, however, there will be no vapor-free air available for dilution, and the partial pressure will therefore be higher. No quantitative appraisal of the significance of this difference is possible in the absence of actual data, and it has presumably been taken into account in setting the driving force, (pO - Pv)lm, equal to the vapor pressure. Indeed, if partial pressures were appreciable in these studies, the final correlation should be raised further, since for the same

132 value of k' a lower value Of (pO - Pv)lm will yield a higher value of kg, as can be seen from Equation 31. Even so, it is possible that the present results might have been altered somewhat, and in the right direction, if each active test pellet had been surrounded by other active pellets. In sumnmary, it is firmly believed that the original data presented in this report may be accepted as valid within rather close limits of experimental error, and hence that the relative effects of packing diameter, air flow rate, position in the bed, and orifice diameter on local rates of mass transfer are correctly delineated. On the other hand, the absolute correlations obtained for both transfer rates and the j-factor are admittedly less definitive in view of their obvious displacement from the other correlations. Indeed, if these previous correlations are presumed to be correct, it might be entirely proper to compensate for the possible inaccuracies discussed in the foregoing paragraphs by introducing into the present correlation an empirical factor of 0.43, which would make it practically coincident with that of McCune and Wilhelm (48).

APPLICATION OF RESULTS It is fully anticipated that the application of the results of this investigation will be largely qualitative rather than quantitative, not only because of the disagreement with other correlations noted in the preceding section, but also because the conclusions reached are themselves largely qualitative. In terms of their application, these conclusions may be restated as follows, using the same general order of listing as was used at the end of the section on Experimental Results. No Orifice at Bed Entrance (1) Insofar as it affects transfer phenomena, the assumption of a uniform velccity distribution in packed beds has long been useful, but was supported by only very limited experimental evidence. The present findings provide such evidence and thereby permit a freer use of the assumption. (2) The fact that the entrance length was found to be surprisingly short provides a firmer basis for the general assumption that entrance effects are negligible in packed beds of reasonable depth. (3) The quantitative correlations found to apply within the entrance length may be used to predict overall rates of mass transfer in shallow beds, This application is given further consideration below.

134 (4) The findings relative to the effect of pellet diameter are not new, but do provide additional confirmnnation for the conclusions reached by others. Orifice at Bed Entrance The conclusions pertaining to the effect of velocity perturbations at the entrance to a packed bed are probably even less likely to be applied quantitatively than are the foregoing, since extrapolation to other conditions is much more difficult. However, certain of the findings are apt to be useful in a qualitative sense and may be listed as follows: (5) Conditions within a packed bed at any flow rate may be predicted from known conditions at a single flow rate, on the basis of the conclusion that changes in total flow affect all positions within the bed equally. (6) Local transfer rates will be maximized in any regions subjected to perturbations in velocity. This implies, for example, that a fixed-bed catalytic reactor will be more susceptible to local hot spots in the region immediately adjacent to the catalyst support. (7) Velocity perturbations such as those created by an orifice can result in local rates of transfer which are as much as 300 per cent higher than those obtainable when fully developed flow prevails. (8) The fact that even abnormal velocity perturbations are dissipated within a relatively few inches of bed depth adds to the significance of conclusion (2).above.

135 ( ) The observation that the velocity perturbations created by orifice entry into a packed bed (and hence by any similar stricture of the flow) are drastically reduced by a slight separation between the orifice plate and the bed may be of practical importance when it is desired to distribute the flow as evenly as possibleO For example, the air entering a blast furnace would be dispersed throughout the charge more quickly if a lateral free space could be maintained around the inlet openingo The complete analogy between heat and mass transfer in packed beds considered from the overall viewpoint has been questioned (2) because different transfer mechanisms may be involved. For example, heat may be transferred by intra-particle conduction, but there is no comparable mechanism in mass transfer. These objections are obviously not applicable to the present studies, which are concerned entirely with convective transfer between the gas stream and the surfaces of individual pelletso For this case, the analogy should hold, and the results summarized above should therefore be equally applicable in the field of heat transfer. Sample Problem It was noted in sub-paragraph (3) above that the quantitative correlations found in this investigation to be applicable within the entrance length in a packed bed may be used to predict overall rates of mass transfer in shallow beds~ As an example of this application, and also as a means

136 of clarifying the interpretation of the present results, the solution to a sample problem will be outlined. Problem: Calculate the concentration of naphthalene in the effluent stream when air at 20OC. and one atmosphere pressure is blown at a rate of 500u pounds per square foot per hour through a 1-inch layer of uniform spherical naphthalene pellets having a diameter of 0.20 inches. The layer may be assumed to have a fractional void volume of 0542. Solution: The following physical constants and derived quantities will be needed: For the bed, let S = 1 ft2; H = 0 0833 ft; 6 = 0 42; Dp = 0.01667 ft; a = (1 ) 6D2 2085 ft2/ft3 For air, G = 5000 lbs/ft2/hr; / = 0Ou428 lbs/ft-hr (471;. Re = DpG _ (0.01667)(50uQ) = 1950; and Re 0~0428 and 5000 GI' 29= 172o5 lb-mols/ft2-hrO For p-dibromobenzene at 800Fo, po = 00o38 mm Hg (37); Sc = 2.41;:. (Sc)2/3 = 18Oo For naphthalene at 200Co, p = 0~0527 mm Hg (37); Sc = 2o57 (28); o~o (Sc)2/3 = 1o887o Since the transfer rate is variable, the rate equation must be written in differential form: dNv' = kg(p~ - Pv) dA = kg(p~ - Pv aS dH.. dy = - (P P Pv) aSdH _g(P - Pv) adH(46) G'S G'S' (46)

137 But y = pv/P, and hence dy = dpv/Po Making this substitution in Equation 46 and separating variables yields dpv = (Pa)kgdH Integrating and substituting known numerical values, 0 0527 - P2 (760)(208o5).0~0833 - b27 17205 kgdH 0 o0833 920 kg dH (47) O The effluent partial pressure, P2, may now be determined by evaluating the right-hand side of Equation 47 graphicallyo First, kg for naphthalene can be related to ks for p-dibromobenzene as follows: _ 0 kg Mm P 2/3 Jnap = jpdb = G (Sc)/ "t G (Sc)2/3]p = [k GM (Sc 2/3 pdb Cancelling Mim, P? and G9 and subst:,tuting for (Sc)2/3s lo887 kgnap = 1o80 kgpdb lo0 ( pdb = 0038 k ~ kgnap = 25o1 k' (48) Substituting Equation 48 into Equation 38, ke/G' x 106 = B (HRem (38)

138 kgnap = (25.1)(G')(B)(Re)m x 10-6 = 4.33 (B) (1950)m x 10-3. (49) Taking values of B and M from Table 1, numerical values of kg may now be calculated and plotted as follows: Table 4 kgnap as a function of H H, in. B -m 1950-m kg x 10-3 1/16 95 0.55 64.0 6~42 1/8 80 0.48 37.9 9.14 3/16 70 0.43 26.0 11.66 1/4 61 0o40 20.7 12.77 5/16 55 0.375 17.1 13.92 3/8 50 0.36 15.3 14.27 1/2 48 0,35 14.2 14.63 15 0 0,!0 0 1/4 1/2 3/4 1 H, inches Fig. 28. kgnap vs H (for graphical integration).

139 Graphical integration of Figure 28 yields an area under the curve of 13.0806x10'3 for H in inches, or 1.090 x 10-3 for H in feet. This figure may then be substituted for the integral in Equation 47: - In 0.0527 - 2 (920)(1.090 x 10-3) 0.0527 = 1.0028 0.0527 - P2 0 367 " 0.0527' P2 = 0.0334 mm Hg (Neglecting entrance effects and using only Equation 38 yields an effluent partial pressure of 0.0356 mm Hg, which indicates that no appreciable error is introduced in neglecting entrance effects in even fairly shallow beds.)

SUMIvIARY Local rates of mass transfer in a packed bed were determined by measuring the loss in weight of individual spherical pellets of p-dibromobenzene, carefully positioned in an otherwise inert bed of spheres through which a stream of air was passed. The test bed was 4 inches in diameter, sphere diameters were 1/8, 1/4, and 1/2 inch, and measurements were made to within 1/32 of an inch from the tube wall. The investigation covered a Reynolds number range of 150DpG//U < 7,000o The following conclusions were reached: (1) Local rates of mass transfer may be correlated by the general equation k'/G x 106 B (34) where B and m generally depend on axial distance but are independent of radial position, air flow rate, and pellet diameter. (2) Entrance effects are confined to the first 1/2 inch of bed depth, beyond which transfer rates at all positions are given by 0.&35 k'/Gi x 106 w 48 (Lk) (38) (3) Wtithin the entrance length, B and m are highest at the inlet and decrease with depth, the actual values for these constants being given in Table 1. (4) Except for its use as the characteristic length in the Reynolds number, pellet diameter is not a parame te r. Measurements were also made with the air entering the bed through 1l and 2-inch orifices to determine the effect 140

of the resulting local velocity perturbations on transfer rates. Under these conditions, the following additional conclusions were drawn: (5) The exponent m in Equation 34 is independent of pellet diameter, orifice diameter, position in the bed, and air flow rate, and is equal to -0.35. (6) The values to be assigned to B in Equation 34 are functions of position in the bed and orifice diameter only, and are given in Tables 2 and 3. (7) Perturbations created by the orifice are completely dissipated at a bed depth of approximately 2 inches. (8) Transfer rates are as much as 300 per cent in the vicinity of the orifice than elsewhere, and are maximized at a point on the axis of the bed approximately 3/8 of an inch in from the surface. At lesser distances, the transverse transfer-rate profiles are characteristically M-shaped, with maxima corresponding to the edge of the orifice, while at greater distances the profiles are domeshaped, with a maximum at the center of the bed and minima at the walls. (9) As in the no-orifice case, pellet diameter is not a parameter, except for its use in the Reynolds numnb er (10) Perturbations created by an orifice are drastically reduced if the orifice is separated from the packing surface by as little as 1/16 of an inch. The relative effects of pellet diameter, air flow rate, position in the bed, and orifice diameter on local rates of mass transfer are believed to be correctly delineated by the proposed correlations, but the absolute correlations are less definitive in view of their displacement from the correlations based on previous investigations of overall transfer rates in packed beds,

APPENDICES

APPENDIX A EXP'ERIMENTAL DATA

APPENDIX A EXPERIMENTAL DATA Table 5 SUMMARY OF ORIGINAL AND PROCESSED DATA FOR LOCAL MASS TRANSFER RATES A. 4-inch orifice, 1/8-inch pellets Air, Rate x 104 Run lb-mol Temp AE, -AW, -AW0 DpG lb-mols/hr-ft2 % No. hrft2 ~F min mg mg - CT Exper. Eqn 34 Dev. 1/16-in, depth, 1-in. radius; 6 pellets per run 2579 40.7 79.6 2.5 2.10 0.60 291 1.027 1.50 1.71 14.0 80 40.7 79 *8 n 2.25 n 291 1*012 1 62 1.71 5.6 82 41.5 79.0 220 " 297 1*070 1.66 1.72 3.6 83 41 *5 79.0 n 2.25 n 297 1.064 1.71 1*72 0.6 84 161.7 79*0 1.5 2.30 0,,25 1156 1*070 3.55 3.17 10N7 85 162.7 79.3 " 2.35 " 1163 1.045 3.55 3.19 10.1 87 162.7 79o3 200 " 1163 1.049 2.98 3.19 7.0 88 163.7 7997 n 2.05 n 1170 1.018 2.97 3*19 7'4 2716 87.9 79.7 2.0 2.10 0.15 628 1;018 2 42 2*42 0.0 17 87.9 80.2 "' 2.20 " 628 0.985 2 46 2*42 1 6 19 87.9 80.2 " 2*20 628 0.985 2;46 2.42 1.6 20 88.9 81.1 M 2.45 n 636 0.929 2.60 2.42 6.9 42 22.8 82.0 3*0 2,30 0.45 163 0.875 1*31 1,32 0.8 43 22.0 82.5 tf 2.05 " 157 0.851 1. 10 1,30 18,2 45 23.5 79.5 2.00 168 1,033 1.30 1.33 203 46 22.8 78.5 f 2.05 n 163 1.106 1.43 1.32 7.7 Ave* 6.1 1/16-in. depth, 1-1/2-in. radius* 6 pellets per run 2615 37.5 80.8 2.5 2.30 0*75 268 0,950 1.43 1.65 15.4 16 37.5 82.0 ft 2.75 " 268 0*878 1.71 1.65 3.5 18 37.5 81,5 " 2.80 n 268 0.904 1.80 1*65 8.3 19 37.5 81, 7 f 2.60 " 268 0.895 1 61 1.65 2.5 21 163.07 80.3 1.5 2.35 0,50 1170 0,979 2.93 3.19 8.9 24 162.7 80.0 " 2.50 " 1163 1.003 3.26 3019 2.1 25 162o7 79*7 n 2*55 n 1163 1.018 3.39 3.19 5.9 26 23 5 82*4 3*0 2.35't 168 0*855 1*28 1.33 3.9 27 23*5 82.7 " 2.55 n 168 0.838 1.39 1.33 4.3 29 23.5 80.8 2.30 t 168 0.947 1.38 1.33 3.6 30 23.5 79.8 3.33 2.35 " 168 1.012 1.36 1.33 2.2 144

145 Table;SA (Continued) Air, Rate x 104 Run lb-mol Temp A0, -1W, - AW lb-molsAr-ft2 % No. hr-ftz ~F min mg mg /,U CT Exper. Eqn 34 Dev. 1A6-in. depth, 1-l/2-ino radius; 6 pellets per run 2631 83.0 79.3 2.5 2.90 0.50 593 1.049 2*45 2.35 4.1 32 8300 79.4 " 2.85 " 593 1.039 2.37 2.35 0,8 34 8300 79.4 n 2.50 n 593 1.042 2.02 2.35 16.3 35 83.0 7906 " 2.85 a 593 1.027 2.34 2.35 0.4 Ave. 5.5 1/16-in. depth, 2-in radius; 6 pellets per run 2604 165.6 80.8 1.5 2.80 0.65 1184 0.950 3.31 3.21 3.0 05 167*6 80*7 n 2.60 1198 0.953 3.01 3.23 7.3 07 163.7 80.9 n 2.95' 1170 0.945 3,52 3019 9.4 08 165.6 81.0 " 2.65 1184 0.937 3.03 3.21 509 09 3901 79.5 2e5 2.50 0,80 280 1.036 1.74 1.67 4*0 12 38.3 79*5 3,0 2*70 " 274 1.036 1.59 1.66 4.4 13 3803 79*5 2.5 2*50 " 274 1.009 1.67 1.66 006 2727 88.9 78*4 2.0 3.10 1.30 636 1*113 2*43 2.43 0.0 28 89.9 7902 n 2.95 a 643 1,055 2.11 2*44 15.6 30 88.9 79 ol t 3030' 636 1.061 2.58 2.43 5.8 31 88,09 79.0 t 3.10' 636 1.064 2*33 2.43 4.3 32 21.2 78.5 3.0 2.40 1.05 152 1*102 1.21 1*27 500 33 1907 78.5 tt 2.50 141 1,102 1.30 1,23 5,4 35 20,5 77,9 " 2.30 t 147 1.150 1.17 1.25 6.8 36 21 o2 76.7' 2.60 M 152 1.243 1.56 1.27 13.6 Ave. 6.4 36-in. depth, 1-in. radius; 6 pellets per run 2375 2500 80.4 3.0 2,75 0.40 179 0.976 1.86 1088 1ol 76 24.3 80.4 t 2,80 t 174 0.976 1.90 1.85 2.6 78 2500 80.5'f 2.40' 179 0.971 1.57 1.88 19.7 79 2500 80.8 " 2.40 " 179 0.950 1.57 1.88 19,7 80 3909 79.1 " 3.25 0.50 285 1.036 2.31 2.46 6.5 81 39 o9 79,2 " 3.35 a 285 1.052 2 o43 2.46 o2 83 39,1 7804 n 3.30 280 1.110 2.51 2,43 302 84 391l 7805 " 3,30 n 280 1.099 2050 2.43 2.8 85 9009 79,5 " 5*40' 660 1.036 4.12 3.93 406 86 90,9. 793 4e95 n 650 1.042 3.76 3.93 4.5 88 90,9 78e8 tt 5005' 650 1.080 3,98 3,93 1.3 89 9009 7809' s5o10 l 650 1.077 4,01 3.93 2,0 2451 16906 79,6 1.5 4.10 0.65 1213 1.024 5.72 5.60 2,1 52 N169,6 79.4 " 4.25 a 1213 1.039 6.06 5.60 7,6 54 169.6 81f.7't 4.35 " 1213 0,893 5.35 5.60 4.7 55 169.6 80e5 " 4,30 " 1213 0.965 5.70 5.60 5.1 Ave, 505

146 Table 5A (Continued) Air, Rate x 104 Run lb-mol Temp L\, -LW, -0o DG lb-mols/hr-ft2 % No. hrft ~F min mg mg CT Exper. Eqn 34 Dev.,* h- _ mg, -T 3/16-in. depth, 2-in. radius; 6 pellets per run 2487 9009 79.6 2.0 3.40 0.25 650 1.027 3.94 3e93 0.3 88 89.9 80.1 t' 3.35 " 643 0.991 3*73 3.90 4.6 90 9009 78.8' 3.25 650 1.080 3.94 3.93 0.3 91 90,9 79.0o 3,50' 650 1.064 4.21 3.93 607 93 162o7 79.6 " 4.85 -0.20 1163 1.024 6.28 5e47 9.7 94 165*6 80.6 " 4.40 1184 0.959 5,36 5,53 3.2 96 164,7 79.8 " 4.55 n 1178 1.015 5*86 5050 6,1 97 166*6 7907' 3.80 1191 1o021 4.96 5.55 11.9 99 3909 79.5 2.5 3*60 1.20 285 1*033 2.41 2.46 2.1 2500 39,9 79Q7' 3.65'f 285 1.018 2.42 2.46 1.7 02 39*9 80*7' 4.20 " 285 0.953 2.78 2.46 11.5 03 39,9 80,5 n 3.80'8 285 0*971 2.45 2.46 0*4 2737 21*2 80*5 3.0 2.60 0.45 152 0.971 1.69 1.71 1.2 38 21,2 80,2 " 2.35't 152 0.988 1.52 1.71 12.5 40 22.0 80.1 t 2.95 tt 157 0.991 1.99 1.75 12.1 41 21 2 80.2 ft 2.65 ft 152 0.985 1.76 1.71 2.8 Ave. 5.4 1/2-in. depth, 1-in, radius; 6 pellets per run 2330 84.0 81.6 3.0 5.85 0.45 600 0.901 3.95 4*30 8.9 31 84.0 80.8 t 5*40 tt 600 0*950 3.81 4.30 12.9 33 83.0 80,5 f 5.05 t 593 0.965 3.60 4.26 18,3 34 83.0 80.4 t 5*20 It 593 0.976 3.76 4.26 13.3 40 41. 5 78.6 " 3.45 0.35 297 1.096 2.76 2.71 108 41 41,5 81.5 n 3*90 f 297 00909 2.62 2*71 3.4 43 41.5 80*1 n 3,60 n 297 0*994 2e62 2.71 3.4 44 41.5 79e8 " 3.60' 297 1.015 2*67 2.71 1.5 2440 168o6 81.3 1*5 3,80 0,15 1205 0.918 5.43 6.76 24.5 41 168o6 81. 3 " 3.70' 1205 0*920 5.30 6.76 27.5 43 166o6 80*3 n 3,90 93 1191 0.979 5.95 6*70 12.6 44 166.6 80.0 " 3o45 n 1191 1,003 5.36 6.70 25.0 2540 220o 83,1 300 2090 0*55 157 00818 1*56 1080 15.4 41 22.o0 79.4 " 2.60 t' 157 1.039 lo73 1.80 4.0 43 22.0 78,1 " 2.35 " 157 10134 1.65 1,80 90.1 44 2200 78~0 f 2,40 " 157 1.141 1.71 17 80 5,3 Ave. 11.7..24n. depth, 2-ino radius 6 pellets 2273 163,7 78,0 3~0 8.15 0.45 1170 10141 7o12 6,63 6,9 74 165e6 79,1 an 8,05 " 1184 1.061 6(53 6067 2.1 76' 164,7 79,7'f 8,05 " 1178 1.021 6.29 6.65 5.7 77 166,6 79,9 " 8.30 " 1191 1 006 6.40 6,70 4.7

147 Table A (Continued) Air, Rate x 104 Run lb-mol Temp OQ, C-tAW, -aW0o D G No. hrft2 ~F min mg mg CT Exper. Eqn 38 Dev.!/2-ino depth, 2-ino radius- 6_pellets per run 2284 40o7 80,8' 3.0 4~05 0.50 291 0.950 2.73 2~68 1.8 85 43ol 79.8 n 3,75 " 308 1.012 2o67 2.78 4.1 87 4301l 78o7 It 3.60 H 308 1.086 2,73 2,78 1.8 88 42.3 78f2 tt 3.50 f 302 1.123 2073 2.75 007 2425 8400 79,7 t 5,25 0.40 601 1.018 4.00 4e30 7,5 26 8300 7909 " 5.60 tt 593 1o006 4,24 4e26 0.5 27 83,0 8001, t 5050 n 593 0,994 4.11 4.26 3.6 29 83,0 79.4 tt 5030 t 593 1.039 4,13 4.26 301 2535 22.0 7804 " 2.65 0,55 157 1.113 lo90 1,80 5,3 36 22*0 78.4 n 2.40 ti 157 1,109 1o66 1080 8,4 38 22,0 78,7 f 2,40 n4 157 1,086 1o63 1 80 10,4 39 220oO 79o3 tt 2.65 n 157 1,045 1077 1.80 1,7 Ave. 4.3 1-in, depth, 1-in, radius, 4* and 6 pellets p run 2227 22o0 78,5 3o0 1.70 0,25 157 1,099 1o93 1.80 6.7 28 22.8 78o3 " 1,35't 163 1.120 1,50 1.84 22.7 30 22,8 78o8 " 1.80 t 163 1.080 2,03 1,84 9.4 31 220O 7905 11.40 n 157 1,033 1.45 1.80 24.1 43 86,9 79,4 " 3.50 0.35 621 1,042 3099 4,39 100 44 85.0 79,00 4,10 " 608 1,064 4.85 4.33 1007 46 87.9 78,8 n 3055 a 628 1,080 4,20 4.42 5.2 47 8609 78.2 n 3075 " 621 1,124 4,64 4.39 5.4 2415 3909 79,5 " 3,30 0.15 285 1.033 2,63 2.65 008 16 3909 79.3 n 3,10 n 285 1. 04 5 2.50 2.65 6.0 18 39.9 79.2 " 3.25 n 285 1,052 2,64 2,65 0.4 19 39,9 79,0 " 2,90 " 285 1,067 2.37 2,65 11.8 2557 169,6 78,0 1.5 3,90 0 45 1213 10141 6.39 6078 6.1 58 167o6 79.3 " 3.65 n 1198 1.045 5.41 6.74 24,6 60 167.6 78,5 tt 3,70 1198 1.099 5.79 6074 16,4 61 16706 78,5 n 3.65' 1198 10099 5.70 6o74 18,2 Ave, 11.2 1in, depth. 2-ino radius5 6 pellets per run 2188 39,9 79,0 2,0 3,00 0.65 285 1,069 3005 2,65 1301 89 39.01 79,3 " 2,90 t 280 1o049 2o87 2o61 9ol 91 39,1 79.3 tt 2.70 280 1.049 2.61 2,61 0.0 92 39.1 79,2 "t 2.80 n 280 1,052 2.75 2.61 5*1 99 179,4 80,5 t 6.70 0,20 1283 0,968 7,65 7,03 8.1 2200 179,4 81.3 it 6,95 n 1283 0.917 7,52 7003 6.5 02 179,4 80.5 tt 6,65 " 1283 0,965 7,56 7.03 7,0 *Runs 2227~47

148 Table 5& (Continued) Air, Rate x 104 Run lb-mol Temp A0, -TW, -WVo D lb-mols/hr-ft2 % No. hr.Z OF min mg mg, C-T Exper. Eqn 38 Dev. 1-in, depth, 2-in, radius; 6 pellets per run 2203 183.4 81*0 2.0 6.15 0.20 1311 0.942 6.81 7*13 4.7 10 89.9 79.0 3.0 5.40 0.00 643 1.067 4.66 4.49 3.6 11 88.9 -79.2 5.45 " 636 1.052 4.64 4.45 4.1 12 88.9 79.2 5 5.30 n 636 1.052 4.52 4.45 1.5 14 88.9 78*2' 5.40 " 636 1.127 4.93 4.45 9.7 16 22.0 76*7 n 2.00 0.30 157 1.243 1.71 1.80 5.3 17 22.8 77.7 " 2.20 n 163 1.165 1.79 1.84 2.8 19 22.0 77*6 n 2.25 " 157 1.204 1.90 1.80 5.3 20 22.8 77.7 " 2.45 t 163 1.161 2.03 1.84 9.4 Ave. 6.0

149 Table 5 B. 4-inch orifice, 1/4-inch pellets Air, Rate x 104 Run lb-moll Temp AG, -aW, -o D G lb-mols/hr-ft2 % No -f F m inmg mg T Exper. Eqn 34 Dev 1/8-in, depth, O-in, radius; 1 pellet per run 743 185.3 80.2 2.0 1.55 0.15 2472 0*988 3.28 3.48 6.1 44 183.4 80.2 " 1045 n 2447 0.988 3.05 3.47 13.8 46 181.4 80.2 " 1.55 t 2420 00985 3'28 3'45 5 2 47 179.'4 80.0 t 1*65 " 2393 1,003 3.57 3,43 3.9 53 39.9 8000 5*0 1.95 t 532 1.000 172 1.57 8.7 54 39.9 80.2 t 1,095 " 532 0,985 1.69 1.57 7.1 56 39. 9 80.1 tt 1.85 " 532 0.991 1.60 1057 1.9 57 3909 80.1 "n 1.75 tt 532 00994 1,51 1057 4.0 2125 85.9 79.8 3.0 1.35 0*05 1146 1.012 2o10 2o34 11o4 26 88.9 80.2 f 1.40 2 1186 0.988 2411 2.38 12;8 28 88 6'9 80.0 1.*35 1186 0.997 20 06 2 38 15.5 29 88449 80.0 t 1.35 n 1186 1.000 2.06 2 38 15.5 3132 21.2 80,0 5*.0 140 0,25 283 0.997 1;09 1'13 3.7 34 22.0 81.6 H 1.70' 293 0`898 1.24 1.15 7.3 35 22.8 81*5 n 1.45 " 304 0.907 1.04 1.17 12.5 Ave. 8.6 1/8-in. depth, 1/2-in. radius; 2 pellets per run 2069 40;7 79.4 2.0 1.55 0*25 543 1.039 1.61 1.58 1.9 70 40.7 79.5 " 1.45 tt 543 1;033 1. 48 1.58 6.8 72 40.*7 794 n 1.50 t 543 1.039 1.55 1.58 1*9 73 40.7 79,4 t 1.45 " 543 1*042 1.49 1.58 6,0 80 81.0 80.0 " 2.00 0.10 1081 1,003 2,27 2.27 0.0 -81 83.0 80.1 n 2,15 J 1107 0.994 2 43 2*30 5 3 83 83 0 79.9 2" "2,15 n 1107 1,006 2,51 2,30 8 4 84 83*0 80.0 " 2;05 f 1107 1;000 2632 2030 0.9 85 2 00 1 81.0' 2090 2669 0937 3.12 3,62 16;0 86 200.1 80.3 " 3;45 n 2669 0.982 3,92 3.62 7`7 88 198. 1 80,1 n 3;35 2" 2643 0.991 3,84 3.61 6,0 89 197*1 80.2 3 3;45 " 2629 0,985 3;93 3061 8.1 3136 22;8 82`5 2*5 1.55 0.30 304 0,853 1.02 1.17 14.7 37 24.3 80.4 w 1.60 " 324 0,976 1;21 1;21 0.0 38 240.3 78,9 " 1.50 " 324 1,074 1;23 1;21 1o6 39 24*3 77.6 It 1,40 It 324 1l171 1l23 1o21 1,6 Ave. 5*4 1/8-in, depth, 1-in, radius; 4 pellets per run 517 21 2 84;8 5.0 5.10 0.40 283 0*735 0,82 1,13 3708 18 207 80.9 5,25 n 273 0.942 1;09 11 1811 1 20 20,5 80,0 " 4105.1 273 1 003 0,87 1 11 27,6

150 Table 5B (Continued) Air, Rate x 104 Run lb-mol Temp AQ, -tW, -AW0 Ib-mols/hr-ft2 % No hrO7 F min mg mg C.T 34 DevE 1/8-in. depth, 1-in. radiuS r 4pellets per run 540 127.3 80.3 5.0 13.05 0.80 1698 0.979 2.86 2,86 0.0 41 12"7.3 80.7 " 10.85'f 1698 0o953 2 28 2.86 25.4 43 130.2 79.2' 11.40 " 1737 1,052 2,66 2,90 9,0 1847 8809 79.8 2o0 4,30 0o35 1186 1.012 2.38 2.38 0.0 48 88,9 79.0 4.e25 n 1186 1.067 2.48 2.38 4.0 50 88.9 79.3 n 4.35 1186 1.045 2,49 2*38 4,4 51 87,9 79,5 "f 3.80 " 1173 1,030 2,11 2,36 1108 3152 39.9 79.5 1o5 2"00 f 532 1.033 1o35 1.57 16.3 53 39e9 79,4 " 210 2O 0 532 1,042 1.45 1.57 8*3 55 40,7 790 5 2. 10 n 543 1.036 1o44 1958 9.7 56 39,9 79,4 2o10 n 532 1o039 1,45 1.57 8,3 Ave. 11,7 1/8-in, depth9, 1-1/2-in, radius; 4 and 6 pellets per run 648 39.9 79.3 2.0 47 2.0 220 532 1*049 1.56 1*57 0*6 49 3909 80.3 2 4.80 n 532 0,982 1o52 1*57 3.3 51 39.9 80.5 5.15 a; 532 00968 1. 70 1o57 7o6 52 39.9 80.5 " 4.70, 532 0Q968 1.44 1,57 9.0 54 22,0 80.8 " 3,90' 293 0.947 0.96 1o15 1908 56 22,0 80,9 " 4ao00 293 0*944 1 01 1 5 13.9 57 22,0 80.5 4*00 " 293 0*965 1*04 1*15 10*6 3162 193.2 79,3 1,5 6,45 0,45 2577 1049 333 3 a 55 6.6 63 192*2 79*4 n 6,25 n 2564 1,039 3ol9 3.56 11 6 65 191.2 79.4 n 6.50 n 2551 1,039 3,33 3054 603 66 192o2 79.6 6 30' 2564 10O24 3*17 3*56 12*3 68 8509 81 ol " 5*00 0.40 1146 0,932 2.27 2.34 3*1 69 86.9 81,1 5OO n 1159 0*932 2.27 2E35 3,5 71 85,9 81,0 n 5,00 1146 0,937 2 28 2.34 2 o6 72 85.0 81,0 N 5.15 n 1134 0,937 2,36 2,33 1.3 Ave e 7,5 1/8 —n. deth, 2-in radius; 6 pellets per run 496 39.1 81,2 500 1045 0.30 522 0,926 1.49 1,55 4.0 98 39,9 80,4 " 9,95 " 532 0.973 1 49 1 57 594 514 22,0 77o6 " 13,95 7,55 293 1,168 1019 1.15 3.4 16 22.0 78.0 " 13.9S f 293 1.141 1,12 1,15 2,7 3173 85*9 80*5 1,5 4,70 o040 1146 0.965 2,20 2,34 604 74 85,9 80,9 "t 4,55 " 1146 0,945 2007 2,34 13*0 76 85*9 80,9 4,95 " 1146 0,942 2,27 2,34 3ol 77 85*0 80,8 " 5e25 " 1134 0.947 2,43 2*33 4,1 78 194.2 81.4't 7,45 " 2591 0.915 3.41 3,57 4,7 79 193.2 8194 " 6,95 " 2577 0.915 3.17 3,55 12.0 81 195.2 81.3 n 7,60 " 2604 0.920 3.50 3057 2,0 82 193,2 81,2' 6,90 n 2577 00,923 3,18 3,55 11,6 Ave 6,0 Runs 31628.72

151 Tab' 5B (Continued) Air, Rate x 104 2 Run lb-mol Temp AG, -&W, -We DG lb-mols/hr-ft2 No* hrf F rain mg mgCDeve NO, hh F ft mg mg CT Exper. Eqn 34 Dev. 3/8-in, depth, O-in, radius; Ipellet per run 793 71o2 79.6 5~0 3,70 0.20 950 1.027 3.42 3.02 11.7 94 69.2 796 n 3~45 t 923 1.024 3,17 2.96 606 96 68 o2 79. O " 3 50 " 910 1oO67 3.35 2~93 12.5 97 68.2 79.3 " 3.25 " 910 1o049 3005 2e93 3.9 98 149.9 81.0 " 5,50 Oe15 2000 0.934 4.76 4.86 2.1 99 150,9 80,9 " 5500 t' 2013 0.942 4.35 4687 12 O 801 151,09 79e2 tf 4,65 n 2026 10052 4,5-1 4.91 809 02 150 09 79.05 tt 4435 t 2013 10036 4.14 4.87 17.6 09 40.7 81.1.1 4045 1.95 543 00932 2,22 2 11 5.0 10 40,7 78.6 " 4.25 " 543 1.093 2e39 2,11 11.7 13 ~4O7 77,9 it 4,10 n 543 1.150 2.35 2.11 10.2 14 3909 79.1 n 4.15 n 532 1,061 2.22 2*08 6.3 60 22.0 79*0 " 1.65 0*30 293 1,067 1.37 1042 3,6 61 22.0 79.2 " 1 65 W 293 1o055 1o35 1,42 5,2 63 22*8 79.1 1*70 " 304 1*061 1.42 1.46 2.8 64 22,0 79,2 n 1.65 n 293 1,055 1,46 1*42 2.7 Ave* 7.7 3/8-in. depth, 1-in. radius; 2 pellets per run 693 39,9 80.1 2,0 2.20 0.20 532 0.994 2.37 2.08 12.2 94 39.9 80.0C 1l95 " 532 1.000 2.08 2,08 0,0 96 39,9 79,8 " 1680 n 532 1,015 1093 2.08 7.8 97 39o9 79,8 " 1.75 n 532 10015 1.87 2,08 11,2 98 82.0 80,2 " 4.50 1.70 1094 0.988 3.30 3030 0.0 99 83, o 80,0 0 4e35 " 1107 0.997 3*14 3.33 6.1 701 83,o0 80,3 " 4.45 n 1107 0.979 3.20 3.33 4.1 02 83,0 8003 t 5.10 1107 0.982 3,86 3.33 13,7 03 209,9 80.5 n 5.95 1.55 2800 0.971 5009 6002 1 83 04 208,9 8005 " 6,35 n 2787 0.965 5.51 6.02 9.3 06 206,0 80,08 " 6 60 a 2748 0,947 5,69 5,95 4.6 07 205,0 81,O n 6,00' 2735 0.937 4.97 5.95 19.7 2107 2500 82.8 1" 1 35 0.10 334 0.835 1,24 1.54 24,2 08 266 80.9 n 1.o50 tt 355 0.942 1.57 1o61 2,5 10 26,6 79.7 1 o15i 355 1.018 lo27 1 61 26,8 11 26,6 79.6 " 1,25' 355 10024 lo41 1,61 14,2 Ave 0 10.9 3/8=in. depthD.l..in, radius; 2 and 4* pellets per run 930 3909 79.8 2,0 070 -0,95 532 10015 1,99 2,08 4.5 31 39.9 _ 80.1' 0A55 " 532 0,994 1.77 2,08 17,5 33 3909 7909 "i 095 n 532 1.006 2.27 2.08 8,4 34 39.9 80.1 0,90 532 0,994 2.19 2,08 5,0 Runs 2102=06

152 Table 5B (Continued) Air0 Rate x 104 Run lb-mol Temp AG, -ADW, -A lb-molshr-ft2 Noo h F mi:n mg mg T CT Exper o Eqn 3 4 Dev 3/8-ino depth, 1-in, radius, 2 and 4 pellets per run 935 19801 75.8 2.0 3.70 0*15 2643 1.319 5*57 5e80 401 36 197*1 76,7 "t 4425 " 2629 1,240 6,05 5.79 4.3 38 197.1 78,1 " 4.30 n 2629 1.130 5.59 5.79 3.6 39 196.1 78,6 " 4.70 tt 2616 1.093 5.92 5e77 2.5 40 71,2 78.6 " 3*00 " 950 1.093 3.72 3*02 18.8 41 70,2 78.2 " 3*10 " 950 1.083 3.80 3,02 20 o.5 43 70*2 78e2' 2. 50 " 936 1.127 3.16 2,99 5,4 44 67,2 78.6 n 2.50 896 10093 3006 2o91 4,9 2102 27o3 78,9 " 2,65 0o10 364 1,074 1,63 1.63 0.0 03 260,6 79,5 2o70 " 355 1,030 1,60 1.61 0,6 05 27o3 80*0 " 2 075 n 364 1.000 1.58 1*63 3,2 06 26e6 80e2 " 2.80 355 0,988 1,59 1,61 103 Ave, 6.5 3/8in. depth, 1-1/2-ine radius; 3 ellets per run 9'75 24.3 78.0 2,0 2.40 0.50 324 1.137 1,72 1,52 11,6 76 24.3 79.2 n 22o2Q n 324 1,052 1.42 1.52 700 78 24,3 79,7 " 2,o10 324 10018 1,29 1,52 17,8 79 24.3 80,0 " 2020 " 324 0.997 1.34 1,52 130.4 80 39,1 79,4 270 " 522 1,042 1 82 2,05 12,6 81 39,1 79,3 g 3.15 g 522 1,049 2.21 2.05 7,2 83 39,1 79.1 o 3a.00 * 522 1,061 2,10 2005 2,4 84 3901 78,9 9 2095 522 1,074 2,09 2e05 1,9 85 205,0 80.2 9,20 2.20 2735 0,988 5,49 5,95 8.4 86 205,0 80,7 " 9,25 " 2735 0,956 5,35 5*95 1102 88 204,0 381,1 10o75 " 2721 0.932 6,33 5o92 6,5 89 203.0 81,4 " 12,30 M 2708 0,915 7,34 5,91 19.5 90 80o0 79,3 630 " 1067 1 049 3 41 3,22 5.6 91 79,0 78,9 " 6,50' 1054 1.074 3,67 3e22 12,3 93 79*0 78.5 " 5,55 1054 1.099 2,92 3.22 10,3 94 71o2 78.7 " 5,55 " 950 1 090 2.90 3.02 4.1 Avee 9.5 3/8.in, depth. 2.in. radius; 4 pellets per run 1030 25.8 78.7 2,0 2.50 0.25 344 1.086 1,45 1.58 9,.0 31 25.8 78.7 n 2.70 " 344 1.086 1l58 lo58 0,0 33 25e8 78,5 " 2e25 " 344 1.106 1.32 1.58 19,7 34 25,8 78.3 " 2.55 " 344 1.113 1.52 lo58 3.9 40 39.9 80.0 " 5e55 1,60 532 1.003 2.36 2,08 11.9 41 39.9 80.5 " 5.45 " 532 0.968 2.22 2.08 6.3 43 39,9 79.5 " 6.00 " 532 1.030 2,70 2.08 23.0 44 39,9 79e9 n 5,5 50' 532 1.006 2.33 2 08 10.7 * Runs 2102-06o

153 Table SB. (Continued) Air, Rate x 104 2 Run lb-mol Temp $ 0,.-=W,.-W G lb-mols/hr-t % No. hr@ptz ~F min mg mg, C Exper. Eqn 36 3/8,in? depth, 2-in. radius; 4 pellets per run 2091 81.0 79.8 2e0 4e55 0.25 1081 1 oO012 2 59 3.27 26.3 92 82.0 78.1 4,a55 1094 1,130 2.89 3.30 14,2 94 810o 7704 t 5e05 " 1081 1,190 3,40 3,27 308 95 81,0.79.3 5,75 " 1081 1.049 3044 3027 409 96 195.2 79,5 9,55 0,35 2604 1,033 5e66 5,76 1,8 97 194.2 79,8 955 n 2591 1 015 5*56 5,73 3e,1 99 193e2 79.6 n 9.45 " 2577 1*027 5.57 5*72 2*7 2100 193,2 80,4 " 9.25 2577 0,976 5e17 5e72 10.7 Ave o 95 5/8in.o depth, 1/2-in, radius 2 pellets per run 1409 40,7 80*6 2*0 2e20 0,20 543 0,962 2.29 2.18 4.8 10 4<0.7 80* 2 " 2.50 n 543 0.985 2,70 2*18 1903 12 40*7 79.3 1,95 543 1,046 2,18 2,18 0,0 13 40.7 79.5 " 2.35 " 543 1,033 2.64 2.18 17.4 14 22,0 79.1 " 1.30 0.15 293 1.061 1.45 1.45 0.0 15 23o5 78 9 le 1.25 n 313 1 074 1*41 1,51 7.1 17 24.3 78,5 n) 1,40 " 324 1.106 1 64 1 o54 6,ol 18 24,3 78.4 1" 1,30 n 324 10113 1,52 1,54 1,3 20 79*0 79.9 " 3.45 0,35 1054 1.006 3072 3032 10.8 21 74.1 80.1 " 320 tt 988 0,994 3037 3,18 5*6 23 73.1 79.6 t 3.00 " 975 1.024 3.23 3.16 2,2 24 80,0 79.8 " 3,45 " 1067 1.012 3.74 3.34 10.7 25 200.1 81,1 5,05 0.25 2669 0.932 5e32 6,06 13,9 26 199.1 79.9 n 5.50' 2656 1.009 6,30 6,05 4,0 28 197.1 79*9 " S585 " 2629 10009 6*73 6.01 10.7 29 197,1 79o8 n 4,65 W 2629 10oO12 5,30 6.01 13.4 Ave. 8,0 5/8-ino depth 1-in. radius_ 2* and 4 pellets per run 1327 8100 79,7 2,0 3,25 0*70 1080 1e021 3e10 3037 807 28 75.1 79*6 " 3*50 n 1002 1,024 3042 3.o21 6ol 30 81.0 79.4 " 4e00 " 1080 1.039 4e09 3037 17,6 31 84.0 7905 " 3.65 1121 1,036 3.64 3.45 5e2 32 21.2 8001 " 1.70 " 283 0o994 1,17 lo41 20.5 33 21.2 81.0 " 1.60 n 283 0o940 1.01 1o41 39,6 35 22.0 80*1 n 1.95 n 293 0.994 1.48 1,45 2,0 36 22,0 80.0 n 1,70 293 0,997 1619 1.45 21,8 2004 193,2 80,3 " 10o00 -0o05 2577 0.982 5.88 5093 0,9 07 193o2 80,4 " 9,85 " 2577 0.976 5,75 5.93 3,1 08 193e2 80.4 " 9.50 " 2577 0.976 5,55 5093 608 Runs 1327-36

154 Table 5B (Continued) Air, Rate x 104 Run lb-mol Temp.;.l), AW -thWd D lb-mols/hr-f2 % No r a F min mg- CT -gDeve Nlo. 1rft2 BF min mg mg CT Exper Eqn 36 5/8-in, depth, 1-in. radius 2* and 4 pellets per run 2142 48.0 81e1 2o0 11.50 7,20 640 0.932 2~39 2.40 0,4 43 40.7 80,3 ll11.20 " 543 0o982 2,34 2o18 6,8 45 39.9 79.8 " 11.15' 532 1o012 2o38 2013 10.5 46 39,1 79.3 " 10.8-I80 522 l1045 2.24 2o10 6o3 Ave, 10o4 5/8-ino depth, 1-1/2-ino radius; 3 ellets per run 1171 41,5 82e6 2 0 4025 1.10 554 00845 2.11 2o18 303 72 41.5 81,5' 3*55 " 554 00906 1,76 2o18 23,9 74 41,5 79.7 4.05 554 1o018 2038 2.o18 8.4 75 41.5 79o7 n 3010 n 554 10018 lo62 2,18 34,6 76 2011 T9 oO " 7o25 1. 20 2683 1 oO67 5,13 6,09 18 o7 77 205,0 79,9 " 7,70 7 2735 1.006 5,19 61e7 18o9 79 205.0 79,3 " 8o75 2735 1 o049 6o29 6.17 1o9 80 205.0 79*7 R 8095 n 2735 1o018 6,26 6o17 1,4 82 24e3 80,8 " 2e10 0o35 324 00950 1l32 lo54 16o7 83 24.o3 8103 2,35 " 324 0,920 1a46 1 54 5,5 85 25oO 79,5 t 2.40 " 334 1,030 168 1.57 6o5 86 25,8 79,6 235 " 344 10024 lo63 lo60 lo9 87 84.0 79,6 " 4995 Os30 1121 1,024 3078 3.45 8.7 88 8300 79,3 "f 4.25' 1107 10049 3o29 3043 4,o3 90 81,0 78,6 " 4,10' 1081 1,l093 3o30 3,37 2ol 91 74,1 78,6 n 3055 988 10096 2,83 3.18 12.4 Ave. 10.6 5/8-in, depth, 2-in, radius; 4 pellets per run 1060 205o0 79e5 2e0 11.85 l135 2735 10036 6,48 6.17 4,8 61 2030O 78,5 " 10090 " 2708 10099 6o25 6.13 109 63 201,l1 78e0 " 10e70 n 2683 1o144 6e37 6009 4 4 64 201.1 78,5 12 20 " 2683 1o106 7.15 6.09 14,8 70 42,3 78,1 3o70 0,55 564 10130 2o12 2o21 4,2 71 42.3 78o3 " 3075 " 564 1,120 2o13 2.21 308 72 41.5 78.2 n 4025 " 554 1,127 2.48 2o18 12.1 74 41,5 77,6 " 3,80 n 554 1o171 2,27 2,18 4,0 75 22,0 8001 n 4,55 2.40 293 0,994 lo27 1o45 14o2 76 22 0 79,8 " 4,55 " 29 3 1 015 1 030 1,45 1105 78 23.5 79,5 " 4,45 " 314 1,030 lo26 lo51 1908 2147 8609 77,3 12050 7o30 1159 10193 3069 3053 4e3 48 88,9 77o6 " 13,30 f 1186 - 1.171 4,19 3 58 14,6 50 87,9 78,2 " 13000 1173 1.123 3082 3.56 6.8 51 87,9 78.7' 13,20 " 1173 1.090 3,83 3o56 7.0 Ave o 8 5 Runs 1327-36

155 Table 5B (Continued) Air,, Rate x 104 Run lb-mol Temp, w, -, Wo DG lb-mols/hr-ft2 % No. hr-ft2 ~F min mg mg C, T Exper. Eqn 38Dev 1-in, depth, 1-in,o radius; 3 pellets per run 1654 86*9 79.6 2.0 4*85 0.35 1159 1,024 3,66 3.53 3,6 55 86.9 79.3 n 4*55 1n 159 1.049 3.50 3.53 0.9 57 86.9 79,0 n 4,60 1159 1.070 3.61 3053 2.2 58 86.9 79*3 n 4,70 " 1159 1.049 3,62 3.53 2.5 59 200.1 79e7 765 Os50 2669 10018 5.78 6,06 4.8 60 199.1 80ol " 7*35'f 2656 0.994 5*41 6*05 11.8 62 198,1 8001 " 7*45 2643 0,991 5,47 6,04 10.4 63 198.1 80,6' 7*45 " 2643 0.962 5,31 6.04 13.7 65 27.3 79al1 2*30 0,25 364 1.061 1,73 1,66 4,0 66 27o3 78.8' 2,35 364 1,083 1.80 1.66 7.8 68 27,3 78.0 " 1.95 n 364 1.141 1.54 1.66 7.8 69 27e3 78.6 w 2*05' 364 1.095 1.56 1.66 6*4 70 3909 79,7 33,15 t 532 1,018 2.34 2.13 9.0 71 39.9 79o8' 3010 tt 532 1.015 2.29 2.13 7.0 73 39 9 78.8 " 2.35' 532 1 o080 180 2,13 18 3 74 39,9 79,2 " 2.75 t 532 1,055 2*10 2e13 1,4 Ave. 7.0 l-in. deth2-in. readius 4 pe! lets per run 1536 27,3 78,3 2,0 3.30 0.55 364 1.120 1o83 1o66 9.3 37 27*3 78.9 n 2.80 " 364 1*074 1.44 1,66 15.3 39 27.f3 79,1 " 3*10' 364 1.061 1*61 1.66 301 40 28 9 78, 8 n 3 20 " 386 1,080 1. 70 1.73 1 8 41 198.1 79,2 " 10.90 0,35 2643 1,055 6,63 6,04 8.9 42 1971l 79.1 " 9,30 " 2629 1.058 5*64 6.01 6,6 44 195*2 78,4 n 9.00' 2604 1*113 5.73 5,97 4.2 45 195,2 78 5 " 9.45 " 2604 1,099 5,96 5,97 0,2 46 95,8 79.2 " 8*00 0,60 1278 1.052 4,63 3,76 18.8 47 94e8 79,5 n 6*75 " 1265 1,036 3,79 3,74 1.3 49 94,8 78.0 " 6.35' 1265 10137 3,89 3574 3,9 50 92.8 79.0 " 6.80 " 1238 1.070 3.95 3.68 608 51 41.5 79.3 " 3,85 0.40 554 1.049 2.16 2o18 0,9 52 41,5 78.6 " 3.90 " 554 1.093 2,28 2.18 4.4 54 41,5 79.3' 3,90 n 554 1,045 2,18 2,18 0,0 55 4105 79, 5 " 3e95 n 554 1,030 2.18 2o18 0.0 Ayve 5.3. 2-in, depth, 2-ino radius; 4 pellets per run 1715 43ol 77,6 2,0 4.35 0.7575 575 1,171 2.51 2.24 10,8 16 43.l 79,1 " 4.85 " 575 1,061 2,59 2,24 13,5 18 44r7i 78.8 r' 4.65 " 596 1.080 2,51 2.29 8.8 19 43.1 79,1 " 4.80 n 575 1,061 2,56 2.24 12.5

156 Table 5B (Continued) Air, Rate x 104 Run lb-mol Temp A., -AW, -W,o D lb-molsAr-ft2 % No. hrft2 F mrain mg mg T C T Exper. Eqn 38 Dev. 2-in. depth, 2-in, radius; 4 pellets per run 1720 24.3 78.9 2.0 3.50 0.75 324 1.077 1.76 1054 12.5 21 26,6 78.90 3.25' 354 1.141 1,70 1.64 3.5 23 27.3 77 6 s 3*25' 364 1.171 1.74 1.66 4,6 24 27.3 77.6 3.05 " 364 1.168 1*60 1.66 3.8 26 86.9 80.7 7.35 0.50 1159 0.956 3.90 3.53 9.5 27 86.9 80.4 " 6.60 f 1159 0.976 3.54 3.53 0.3 29 86*9 79*5 ff 6.35 1159 1.036 3.61 3.53 2.2 30 87.9 79e2 " 5.80 " 1173 1.055 3*27 3*56 8.9 31 203.0 80*6 1 11.50 0*45 2708 0.959 6.31 6.13 2.9 32 203*0 80*5' 11.00 2708 0.971 6.10 6,13 0,5 34 201.1 79.3 " 10.45 " 2683 1.049 6.25 6.09 2.6 35 201*1 79,1 n 10*15 6 2683 1.061 6*13 6*09 0.7 Ave. 6.1

157 Table.5 C. 4-inch orifice, 1/2-inch pellets Air, Rate x 104 Run lb-mol Temp 6e, -dW, -AWo DpG lb-mo lsAr-ft2 % No. F rin mg mg CDev, hr.ft2 OF in mg mg vu -T Exper. Eqn 38 1-in. depth, 1-1/2-in. radius; 1 pellet er run 3183 35.9 79.0 5.0 8.75 0.45 1122 1.064 1.43 1.48 3.5 84 3509 79.0 f 8*75 1122 1.064 1.43 1.48 3.5 86 35.9 79*2 " 8.30 t 1122 1.055 1.35 1.48 9.6 87 35.9 79.2 f 8.30 t 1122 1.055 1.35 1.48 9.6 88 67.2 79.4 3.0 7.50 0.25 2101 1.039 2.04 2 22 8.1 89 67.2 79.4 it 7.80 " 2101 1.039 2.12 2,22 4.7 91 67.2 79.6 ti 8.05 2101 1.027 2.17 2 22 2.3 92 67.2 7906 t 7.45' 2101 1.027 2.00 2.22 11.0 94 124.3 80.0 2.0 7.00 0.00 3886 0.997 2.84 3.31 16.5 95 12 4.3 80.0 It 6.95 " 3886 0*997 2.81 3.31 17.8 97 12403 80.0 0 6*55 " 3886 1.000 2.66 3.31 24.4 98 124.3 80.0 " 7.95 " 3886 1.000 3.23 3.31 2.5 3261 226*6 80 *4 1.5 9.25 0.20. 7084 0.974 4.77 4.89 2.5 62 226.6 80.4 " 8.40 " 7084 0.974 4.33 4.89 12.9 64 228.6 81.7 " 10*05 " 7146 0.895 4.78 4.91 2.7 65 228.6 81.7' 8.80 " 7146 0.895 4*17 4.91 17.7 Ave. 9.3

158 Table 5. D. lAinch orifice, 1/8-inch pellets Air, Rate x 104 Run lb-mol Temp ae, -LW, -AWd lbnols/rf t2 % Noe ~ f F min mg mg T Exper 37 Dev 1/16-in depth, 1/2-in radius 4 pellets per run 2772 73,1 7915 2.0 6.55 0.20 523 1.033 11.96 12.26 2.5 73 67,2 7905 t 6.35 480 1.036 11.61 11*62 0.1 75 73.1 79.5 t 6e15 n 523 1.033 11,21 12.26 9,4 76 75,1 79.0 " 5,55 " 537 1.067 10,41 12.48 19.9 77 123.3 78,5 1,5 6.50 O030 882 1.102 16.60 17*23 3*8 78 122.3 77,0O nt 5,80 " 874 1,221 16,34 17015 5,0 80 120.4 80,3 i" 5,95 f9 861 0.982 13.49 16.95 2506 81 122.3 80.4 " 6,90 " 874 0,976 15,66 17.15 9,5 82 37,5 80.4 2.5 5,90 0,55 268 0.974 7,60 7,95 4.6 83 40,7 80e7 tt 595 n 291 0.953 7051 8,38 11e6 85 39*1 81,1 o 6,55' 280 0,929 8*12 8.16 0.5 86 38,3 80.8'f 6.35 n 274 0*947 8.01 8.06 0.6 87 22.0 81.3 3e0 5.40 157 0.920 5.42 5,62 3*7 88 22 00 80.9 ff 5.00 f 157 0.945 5.11 5.62 10O0 90 22 0e 77.8 5*05 t 157 1,154 6*31 5*62 1009 91 22o0 78.8 " 4,95 n 157 1,083 5.80 5.62 3,1 Aveo 7.6 1/16-in, depth, -in. radius; 6 pellets per run 372 22*0 77*8 5,0 7,95 1.30 157 1,158 3.74 3,34 10.7 74 22,0 78,7 " 8800 n 157 1,086 3.54 3,34 5 6 75 38.3 79,6 " 13,15 " 274 1,024 5,90 4,78 19,0 77 39 1 80.9' 11,90 " 280 0*942 4.86 4*84 0.4 78 81l0 80*9 " 192 5 2,05 579 0.945 7.90 7.78 1,5 80 69.2 82,5 " 18,85' 495 0,853 6,97 7,02 0,7 82 78,1l 81*6 t 18*05 " 558 0.901 7.38 7,60 3.0 84, 79,0 81,e3 tt 18,75 n 565 0,918 7.83 7.65 2,3 85 136.1 79,2 " 21*30 1.35 973 1,055 10*23 10.90 605 87 1371l 79,3 u 22.00 " 980 1,045 10.50 10.95 4,3 88 3909 79,6' 10o25 0.50 285 1,024 4.e85 4,91 1.2 90 39.1 79, l n 10,00 n 280 1.058 4e89 4,84 1.O 91 22,0 79o9 n' 7.05 157 1.0009 3.21 3,34 4.0 93 22,8 79,8 7,65 " 163 1,012 3,52 3,41 3,1 Aveo 4,5 1/16-in, depth, 1-1/2-ino radius, 4* and 6 pellets per un 2792 22,0 81,0 4-0 2,40 0.55 157 0.935 1.58 1,63 3,2 93 22.8 81,4 " 3.20 " 163 0.915 2. 21 1. 67 24.4 95 22,8 81,5 " 2,75 1" 163 O0904 1,81 1.67 7.7 96 22,8 80o9 " 3030 1 163 0.942 2~36 lo67 29,2 Runs 2792-96

159 Table 5D (Continued) Air, Rate x 104 Run lb-mol Temp al, -AMW, -AWo lb-mols/hr-ft2 % No, hr-fte OF min mg mg A CT Exper. Eq 37 Dev. 1/16-in. depth, 1-1/2-in. radius; 4* and 6 pellets per run 2797 66o2 79e9 2.0 3o15 0.30 473 1,006 3.49 3.34 4.3 98 74.1 77e9 "t 3o35 " 530 1.150 4,27 3.59 15.9 2800 74.1 8009' 4.10 " 530 0.945 4.36 3.59 1707 01 7401 80.5 t 3.80't 530 0.965 4.11 3.59 12,7 02 35.1 8103 " 2.60 0,55 251 0,918 2,29 2.21 3.5 03 35,1 80ol 2,5 3.15 " 251 0.991 2,51 2.21 12.0 05 34.3 795* 3,15't 245 1.033 2.62 2.17 17.2 06 3305 78,5 3' 3o10 t 240 1.106 2.74 2.14 21.9 07 118o4 79.9 1,5 3.95 0.30 847 1,006 5*95 4.86 18.3 08 121.4 79.4 " 3.80 " 868 1.042 5,92 4.94 16.6 10 123.3 8005 " 3065 " 882 0.971 5.27 4099 503 11 124.3 80,1 tt 3.30 " 889 0.994 4.83 5.02 309 Ave. 13.6 1/16-i.n. depth, 2-in. radius; 8 pellets per run 251 3109 91.0 5e0 6.80 1.70 228 0.494 0.92 1o07 16o3 52 30,4 91.1 " 7.35' 217 0.492 1.01 1,04 3.0 70 55.5 86e0 " 9.25 2,80 397 0.679 1060 1.54 308 71 54.6 86*2't 9.40 " 390 0.671 1.62 1,52 6,2 329 23.5 81.0 5.00 2.40 168 0.935 0.89 0o88 1.1 41 22.0 79.4 " 3,30 0e90 157 10039 0091 0.84 7.7 43 2208 82.9 " 3.75 n 163 0.830 0.86 0.86 0,0 50 13002 8009 8 00 0.85 931 0,945 2.46 2.68 8,9 52 120,4 80,9 " 7*15 " 861 0.945 2.17 2',54 17,1 53 127.3 81.8 " 8,60 0055 910 0*890 2*61 2.64 1.1 55 126,3 8009 " 7.70 " 903 0.945 2.46 2,62 605 63 54*6 81.6 " 6,00 1,10 390 00901 1.61 1,52 5,6 65 53,8 81.6 " 5065 f 385 0.901 1o50 1051 0o7 69 33e5 79.5 375 0095 240 1.036 1.06 1.11 4.7 71 30,4 799,3 " 3.75 M 217 1,049 1. 07 1.04 208 Ave. 5.7 3/16-in, depth, 1/2-in. radius; 4 pellets per run 2752 20.5 80.3 3.0 4.60 0.40 147 0.982 5001 6.o25 24.8 53 20.5 79,5 tt 5.45 147 1033 6.34 6025 1.4 55 22,0 78,9 tt 5,20 t- 157 1.074 6,27 6,56 4o6 56 21o2 78*6 tt 4,90 a 152 1.093 5.98 6.40 7.0 57 37.5 79.0 2,5 6,10' 268 1.067 8,87 9.27 4.5 58 38 o3 79.0 " 5.95 " 274 1.070 8.66 9.40 8e5 60 39,1 79,01' 5.,65 - 280 1.061 8,12 9.52 17.2 61 38.3 78.7 " 5,90 n 274 1.086 8.71 9,40 7,9 * Runs 2792-96

160 Table;5D (Continued) Air, Rate x 104 Run lb-mol Temp 6e, -W., -AW lb-mols/hr-ft2 % No. hr.ft'2 F min mg mg Cu C Exper Eq 56Dev 3/16-in. depth, 1/2.in. radius; 4 pellets per run 2762 124.3 78.5 1.5 7*00 0o20 889 1 102 18o21 20o20 10o9 63 123,3 8009 n 7.40 i 882 0,942 16.48 20,09 2109 65 122e3 81.3 " 8.45' 874 0,920 18.45 20 01 8.5 66 125.3 81 9 t 7.55 896 0.885 15.80 20o30 28, 5 67 66.2 79.8 2,0 6.10 0.30 473 1,015 10o74 13.43 25o0 68 75*1 79.3 " 6.35 537 1 o049 158 14o55 25o6 70 62,6 80,0 5 5.e85 4 48 1.000 10.12 12o93 27.8 71 64*4 78. 3 n 5.90 t 460 1 120 11.43 13,18 1503 Ave, 15.0 3/16-ino depth, 1-in. radius; 6 pellets per run 419 68.2 80*2 5*0 12.90 -Ool5 488 0.985 6.25 6.44 3,0 21 65o3 81*0 " 12.50 " 467 0*935 5.75 6o26 809 23 70*2 8006 " 14.10: 502 0.959 6.69 6o57 1.8 2395 21.2 79.9 3,0 3.75 0040 152 1.006 2o73 3001 10.3 96 21*2 79.7 " 3.85 152 1.021 2,85 3.01 5,6 98 21.2 79*5 " 4.00' 152 10033 30 01 3o01 0,0 99 21,2 79,9' 3.60 n 152 1.009 2062 3001 14.9 2400 3909 80.00 n 6,50 0.65 285 1.0003 4.76 4055 4o4 01 39. l 8001 " 5,85 n 280 0*994 4o19 4.48 609 03 39 o1 80*2 " 5.75' 280 0.988 4008 4048 908 04 39.9 8003 f 6,30 285 0,982 4.50 4o 55 1ol 56 122 3 8008 1 5 6.30 0,30 874 0.950 9,24 9, 43 2 1 57 126,3 78,3 " 6.00't 903 1.117 10o32 9,62 6,8 59 122.3 79.5 " 6.15 n 874 1,036 9.82 9o43 400 60 131*2 80*8't 6.20 938 0.947 9.06 9.87 809 Ave. 5o9 3/1i6-in depth, 1-1/2-in, radius; 6 pellets per run 2658 12203 79.4 105 4915 1oOO 874 1.039 5,30 5.09 4o0 59 126.3 80,7 " 4,20 4 903 00953 4094 5019 50l 61 126o3 80.8 " 4a35' 903 Oo947 5.14 5019 100 62 1250,3 81 0 " 4.40' 896 0,935 5'o15 5016 0,2 64 39.9 79.2 3,0 3.75 0.60 285 10055 2069 2,46 8,6 65 39.9 80,2 t 3,80 " 285 0,988 2,54 2046 301 67 3909 81.0 0 3.65 285 0,937 2.32 2046 6,0 68 39.9 8001 3 3,65' 285 0 994 2 o46 2,46 00O 74 75,1 78 o2 2 0O 3045 " 537 1 127 3o90 3070 501 75 74.l 77.8 " 3.20 t 530 1.154 3.65 3.67 005 77 73,1 79.1 t 3,40 R 523 1,061 3.61 3.64 0,8 78 751 79.4 " 3.15 " 537 1,042 3023 3070 14,6 2879 21.2 78.5 3,0 1.90 0.05 152 1.106 1,66 1,o63 1,8 80 21,2 78,8 t' 1.95 152 12 083 lo67 1,63 2,4 82 21,2 7804 n 1165 n 152 11019 1l44 lo63 13.2 83 21,2 78.9 " 1,65 n 152 1, 077 1,39 1,63 17.3 Ave, 5o2

161 Table 5D (Continued) Air, Rate x 104 Run lb-mol Temp ae, -1WO, -OWo DpG lb-molslr-f~t2 % No. hrft2 ~F min mg mg m / CT Expero Eqn 36 Dev. 3/16-in. depth, 2-ine radius; 6 pellets per run 2636 7301 79.1 2,5 2.40 0.20 523 1.058 2.27 2.21 2o6 37 67e2 79*1 tU 2.00 t 480 1.061 1.86 2,09 12.4 39 67.2 78.9 lt 2410 t 480 1o074 1,98 2o09 5,6 40 7501 79.0*'i 2.10 tt 537 1.067 1.97 2,25 14o2 42 22.0 80.0 3.0 1.60 0.40 157 1.003 0.97 1l01 4.1 43 22.0 80.5 If 1.55 tt 157 00965 0.90 1.01 12.2 45 22.8 77.5 It 1,65 t 163 1.182 1.20 1.03 14,2 46 22.8 79.8 tt 1065 t 163 1.012 1.02 1.03 1.0 47 39.1 80,7 2.5 2.20 0.60 280 0.953 1.48 1,47 0,7 48 39,1 81.3 " 2,25 280 0,920 1.48 1,47 0o7 50 39*1 8102 " 2.30 280 0.926 1.53 1.47 3.9 51 39.9 81.1' 20o25 " 285 0.932 1.50 1.49 0.7 53 121.4 80.0 1,5 2.00 0.65 868 1.000 2.19 3.07 40.2 54 120.4 79.4 "f 2.30 t 861 1 039 2.77 3.05 10,1 56 124.3 79.2 t 2.25 n 889 1.055 2.74 3.12 13.9 57 125.3 78.7' 2.85 1.00 896 1.086 3.26 3,13 4,0 Ave. 808 5/16-in, depth, 1/2-in. radius; 4 pellets per run 2524 22.8 81.3 4.0 6.60 0.50 163 0.920 5,11 6.09 19.2 25 22.8 80.8 n 6.30 n 163 0,947 5*00 6,09 21,o8 27 24.3 80.4 " 5e55 tt 174 0*974 4.48 6,35 41.7 28 24,3 80.0 n 5.55 n 174 lo000 4,60 6,35 3800 2679 77.1 79e2 1.5 4,95 0,20 551 1.055 12,18 13,45 10.4 80 81.0 80.0 n 4.45 tt 579 1.000 10,03 13,89 38.5 82 79,0 79.1 " 4.60 tt 565 1.058 11.33 13.67 20,7 83 66.2 79,4 n 4.75 n 473 1 039 11.50 12e19 6~0 84 110,5 7898 5.80 0.10 790 1,080 14097 17e01 13,6 85 123.3 79.6 " 6.65 n 882 1.024 16,31 18.25 11.9 87 12303 79.7 " 6.30 n 882 1.018 15,34 18c,25 19.0 88 126,3 79.3 " 6.05 " 903 1.049 15.17 18.54 22.2 95 38*3 79.5 2*0 4.20 0.15 274 1.030 7,60 8,54 1294 96 39.1 79.6 4,00 i 280 1.024 7,18 8,65 2005 98 39.9 78.8 1* 4e00 n 285 1,080 7.58 8,77 1507 99 39,1 79e5 n 4.10 280 1,030 7,42 8,65 16.6 Ave 20 5 5/16-in. depth, 1-in. radius; 6 pellets per run 394 22,0 83.5 5.0 6.35 1.15 157 0, a 799 202 2e87 42e,1 96 22.03 84.5' 6.80 1.45 157 0g749 2,31 2,87 24,2 98 21.2 80.7 " 5.75 152 0.953 1,99 2,80 40.7

162 Table 5D (Continued) Air, Rate x 104 2 Run lb-tool Temp Ae, - aW0 DG lb-mols/hrft % No. hrftZ ~F min mg mg / C T Exper, Eqn 36 Dev. 5/16-in. depth, 1-in. radius; -6 pellets per run 399 38,-3 79*2 5*0 7.85 1*45 274 1.055 3,28 4*11 25.3 401 38.3 80.6 " 8015 n 274 0.959 3.13 4.11 31S3 03 39*1 80.4' 8.30 1*20 280 0.976 3*37 4.16 23.4 04 67*2 858.6 " 15.65 1.90 480 0;697 4.66 5.92 27.0 06 69.2 80.6 n 14.55 2.00 495 0*959 5.85 6.04 3.2 08 75.1 79.1 " 13.30 " 537 1.058 5.81 6.36 9.5 09 129.2 81. C: " 17.65 0.70 924 0.935 7.71 9.05 17.4 11 130.2 8105 n 17.60 t 931 0.909 7.03 9,10 29.5 13 126*3 80*8 t 16*80 n 903 0.950 7.44 8*92 19,9 Ave. 24.5 5/16-in, depth, 1-1/2-in, radiusi 6 pellets per run 2462 22,0 77,9 3.0 2.75 0.95 157 1.150 1*68 1*70 1.2 63 23-5 78.1 " 2.40 n 168 1*130 1,33 1*77 33.1 65 23.5 78.8' *2.75 " 168 1.083 1.58 1.77 12.0 66 24.3 79.0 0 2.90 174 1.070 1*69 1.81 7.1 67 116.4 80*8 1.5 3*85 n 832 0.950 4.47 5,01 12.1 68 11 9.64 80.1 ff 3.80 n 854 0*991 4*57 5*09 11..4 70 122.3 80.4 n 3*55 874 0'976 4.12 5*18 25.7 71 120.4 80.2 tt 3.80 n 861 0.988 4.57 5*14 12.5 72 39.1 79.2 2.5 2*30 0*15 280 1.052 2.20 2.46 11.8 73 39.1 79*0 n 2.35 " 280 1.067 2*29 2o46 704 75 39.1 78.5 n 2040 t 280 1.102 2.41 2.46 2.1 76 3901 78.4'l 1.95 n 280 1.113 1.94 2.46 26.8 Ave. 13.6 5/16-in. depth, 2-in. radius; 6 pellets per run 2504 36,7 79.8 3.0 3,20 1*10 262 1.012 1 73 1.64 5,2 05 36,7 79*4 " 3.15 262 1.039 1,73 1.64 5,2 07 36.7 80.0 n 3.00 " 262 0.997 1,53 1.64 7e2 08 39.1 80.7 " 303.20 280 0.953 1.62 1,70 409 09 21*2 81*0 " 2.55 n 152 0.937 1.13 1,14 0.8 10 21.2 816 "6 2*45 152 0,901 0.99 1.14 15.2 12 22.0 81.1 " 2.60 " 157 0.929 1,13 1.17 3*5 13 22,00 83.1 " 2.55 f 157 0.818 0.96 1,17 21.9 14 125.3 79,1 2.0 2.50 0.50 896 1,061 2i58 3.63 40,7 15 126.3 78.,0 tt 2.55 t 903 1.137 2.83 3*65 29.0 17 126.3 79,3 It 3.10' 903 1.045 3.31 3065 10.3 18 125.3 78.5 ff 3*10 896 1'106 3.50 3.63 3*7 19 83.0 80.0 2.5 3.40' 593 0.997 2*81 2078 1.1 20 87.9 79. 5 " 3.40 n 628 1.030 2.91 2.88 1,0 22 86.9 80.8 " 3.55 n 621 0.950 2.82 2,86 1,4 23 87.9 80.3 - 3.35 628 0.982 2.72 2e88 2.2 Avee 9.6

163 Table 5D (Continued) Air, Rate x 104 Run lb-nmol Temp Le, -aWV, -'Wo D lb-mols/hr-ft2 % Noir. ~ F min mg mg r CT Exper. Eqn 36 Dev. 1/2-in, depth, 1/2-in. radius; 4 pellets per run 2812 31.1 78.7 2*5 4.00 0.25 222 1.086 5.94 5.68 4.4 13 35.9 80.1't 4*05 n 257 0.994 5,51 6.23 13.1 15 36.7 80*4 t 4.30 t 262 0*974 5*75 6,33 10.1 16 3501 8006 tt 4.30 t' 251 0*962 5*69 6*14 7q9 17 19.0 80.9 3,0 2.80 0.20 136 0.944 2.98 4o12 38.3 318 19.0. 80.a 2 " 3.00 et 136 0e985 3.35 4o12 23.0 20 19 00 80.*0 t 2.80 n 136 l000 3 o16 4,12 30.4 21 1900 79*7 It 2*85 h 136 1.018 3*28 4.12 25.6 23 61.7 7901 2o0 4.65 0.00 441 1.061 8*99 8*86 1.4 24 63,5 79,9 t 4.70 t 454 1.006 8.62 9.03 4.8 26 65o3 80,1 " 4.60 467 0.994 8.33 9,19 10.3 27 75,1 80,2 t 5.55 " 537 0,988 9o99 10.06 0,7 28 120.4 80.0 1.5 5.30 -0.20 861 1*000 13.37 13-68 2.3 29 125.3 79.9 " 4~60 t 896 1.006 11,74 14.04 19.6 31 124.3 80.0 -tf 4.70 n 889 1.000 11*91 13*97 17.3 32 122.3 80.0 " 4.90 n 874 1.003 12.45 13.83 11.1 Ave. 13.8 1/2-in. depth, 2-ino radius; 6 pellets per run 2289 39,9 79,2 3.0 3*30 0*30 285 1.052 2*56 2,04 20,3 90 38.3 78.7 n 2.15 " 274 1.090 1.64 1.99 21.3 92 38.3 780 t" 2.80 n 274 lo144 2032 1,99 14.2 93 37.5 78.5 n 2.30 f 268 1*099 1.78 1,96 10.1 2431'18,2 78*9 1,.70 0,40 130 1,077 1.13 1.23 8,8 32 18,2 79,1'" 1*80 " 130 1.061 1.21 1.23 1.7 34 190,0 78.9 1n 170 " 136 1.077 1.13 1.26 11.5 35 19,0 79.0 n' 1.80 " 136 1l067 1.21 1.26 4.1 2870 65.3 80.0 2.0 2.75 " 46 7 1003 2 2.81 2 71 71*2 80.4 e 2.70 509 0,974 2,72 2,97 909 73 67,2 80*5 " 2.60 t 480 0.965 2*58 2,86 10.9 74 75,1 80.9 n 2 80 t 537 0.942 2,75 3,08 12.0 75 116.4 80,9 la5 2.*65 832 0*944 3*45 4.09 18e6 76 121.4 80.5' 2.60 868 0.965 3.44 4.21 22.4 78 122.3 8003 t' 2e65 t 874 0.982 3,58 4,23 18.2 Ave. 12e4 1-in. depth 1/2-in. radius; 4 pellets per run 2834 63.5 79.5 2,0 3,75 lo10 454 1,036 5.01 5,60 11o8 35 63,5 79c,9 n 3,85 r' 454 le006 5005 5e60 1009 37 64,4 80,0 n 3,90' 460 1,003 5.12 5e65 10.4 38 64,4 80.2 - 4.35 t' 460 0.985 5.83 5.65 3 1 39 21.2 80.5 30 300 " 152 0e971 2,24 2,74 22.3 40 21,2 80,5 " 3.00 152 0.965 2023 2,74 22,9 42 21,2 80,2' 3e00 n 152 0,985 2o27 2.74 20,7 43 21,2Z 81.0 "n 2.95 152 0,937 2,10 2, 74 30o5

164 Table 5D (Continued) Air, Rate x 104 Run lb-mol Temp ae, -LW, -vWo D lb-mols/hr-ft2 % Noe hr2 ~F min mg mg C/ T - Dev. hr_-f_ t Exper. Eqn 36 1-in. depth, 1/2-in. radius; 4 pellets per run 2844 36.7 79.3 2.5 3.40 1.10 262 1,049 3*52 3.92 11o4 45 36.7 79,0 tS 3,60 t 262 1.070 3.9l 3o92 0e3 47 37o5 79.2 t 3.30 tt 268 1.055 3o38 3o97 17o5 48 36.7 79.2 t 3.50 " 262 1,055 3,69 3.92 6.2 49 121*4 79*0 1*5 2*95 0*20 868 1.064 7.12 8.53 19.8 50 108.6 79.4 tt 2.60 t 776 1.042 6.22 7.93 27a5 62 114.5 79,0 tt 2.85 t 819 1.070 6,90 8e20 18.8 63 117,4 79.0 tt 3.15 " 839 1.064 7.63 8,35 9.4 Ave. 15.2 1-in, depths 1-in. radius; 4 and 6* pellets per run 2253 19*0 82.1 3.0 1l45 -0o10 130 0.870 1.64 1,89 15,2 54 19.0 77.7 ft 1*30 t 130 1,165 1,98 1.89 4,5 56 2005 77e4 n 1.25 t 147 1 190 1,96 1.95 005 57 21a2 77.8' 1.30 tt 152 1*154 le97 1o99 1,0 58 36*7 80,3 " 2.40 " 262 0*982 2e99 2o85 4,7 59 37e5 81e0 n 2,10 n 268 0.934 2*49 2,89 20,1 61 36*7 79e5 f 2.20 n 262 1.030 2,88 2,85 loO 62 38,03 8002 tt 2,25 t 274 0.988 2 82 2,93 3,9 63 117.4 80e8 t 4*45 " 839 0,950 5,25 6,06 15.4 64 118.4 80,7 t 5,15 847 0,953 6.08 6.09 0.2 66 120*4 79.7 " 4.30 t 861 1,018 5e45 6.16 1300 67 122*3 80,0 0' 4.90' 874 1*000 6.08 6.23 2,5 2420 61,7 79*5 4,e75 0O20 441 1O030 3.80 3*99 5*0 21 63*5 79.7 M 4.90 454 1e018 3,87 4,07 5,2 23 63e5 79,5 l 4,90 454 1 030 3,92 4,07 3,8 24 63, 5 79.e9 5.00 0 454 1 009 3o92 4,07 3o8 Ave. 6e2 1-in. depth, 1-1/2-in. radius; 6 pellets per run 2884 21.2 78,09 3e0 1.90 0,05 152 1,077 1o61 1,75 8,7 85 21,2 79o5 n 2.05 " 152 1,030 1.67 1,o75 4,8 87 21.2 79e5 3,5 2.05 5 152 1,036 1.44 o175 21,5 88 21,2 79e6 3.0 1,80 " 152 1,027 1*46 1,75 19,o9 89 91194 80.3 1,5 2,85 8" 54 0,982 4e46 5,40 21,1 90 114.5 8000 ti 2,85 *t 819 lo000 4e54 5e25 15.6 92 122o3 81 5 tt 2.90 t 874 0.907 4.18 5.49 31 o3 93 122e3 81.1 n 3.05 n 874 0.932 4e54 5,49 20,9 94 68,2 82,0 2,0 3*45 0.50 488 0.878 3.15 3.75 19.0 95 67.2 81.1 "t 3,30 it 480 0,932 3e17 3.72 1704 97 71,2 81,*3' 3.65 509 0,920 3.52 3,86 9,7 98 69.2 80.7 t 3,75 t 495 0.953 3,77 3079 0o5 Runs 2420-24

165 Table 5D (Continued) Air, Rate x 104 Run lb-mol Temp ae, -\W, -_Wo D G lb-mols/hr-ft2 % No. hrft2 F min mg mg C T Exper. Eqn 36 1-in, depth, 1-1/2-ino radius; 6 ellets per r un 2899 39,9 80.7 2.5 3.65 0*65 285 0.956 2.79 2.65 5,0 2900 39.1 79,8 n 3.40 tt 280 1.012 2070 2o61 3.3 02 3909 80,2 tt 3.20 tt 285 0.988 2o45 2.65 8.2 03 3909 800'it 3.15 285 0,997 2.42 2,65 9.5 Ave. 13.5 1-in, depth, 2-in. radius; 4 and 6* pellets per run 2904 39*9 80*3 205 3*20 0*55 285 00982 2.53 2.48 2.0 05 39,9 800 3*05 t 285 0.997 2*42 2,48 2~ 5 07 39, o9 79.7 " 2. 85 " 285 1 021 2 29 2 48 803 08 39.1 79*7 " 2.70 t 280 lo018 2o13 2o45 1500 09 115.5 79.8 2,0 2,40-0415 826 10012 4.70 4.95 5.3 11 121*4 79*5 " 2.10 868 10036 4.25 5e12 20e5 12 118,4 79*6 " 2.30 1 847 1,024 4058 5o03 9.8 14 120*4 79*6 n 2,30 N 861 1,027 4.59 5,09 1009 Aveo 7,6 2-ino depth, 1-in. radius; 4 pellets per run 3502 65.3 81,9 2.0 2*35 0.15 467 0,883 3*54 3*64 2,8 03 63.5 8062 t 2.10 454 0e988 3,52 3 58 lo7 05 67,2 79.,9 n 2,35' 480 10006 4.03 3.72 8,2 06 66.22 79,5 It 1*90 tt 473 1,033 3.30 3.68 11o5 07 21.2 80.2 3.0 1. 30 0,05 152 0*985 1l50 1l75 16.7 08 21.2 80,3 " 1*45 " 152 0,982 1.67 1,75 408 10 21*2 80,3 tt 1.20 tl 152 0*979 1,37 lo75 27o7 11 21,2 80,2 tt 1,30 tt 152 0,985 1.50 1a75 16o7 13 37o5 8005 2.5 1*95 0o15 268 0.971 2.55 2.54 0.4 14 36.7 80.1' 1.85 t 262 0,994 2.47 2,51 1,6 16 36.7 80.1 "t 2.00 t 262 0,994 2o68 2o51 603 17 36.7 80.1 "f 1.75 t 262 0.994 2o32 2o 51 8o2 20 lll,S 80,2 1.5 2.15 I 797 00988 4.81 5.16 703 22 109o6 80*3 t' 2.15 " 784 0,982 4.76 5,10 7.1 23 106 6 80*5 n 2.20 " 762 0.971 4.84 5.02 3.7 Ave, 8o3 Runs 2904-08

166 Table 5 E., lminch orifice, 1/4-inch pellets Air, Rate x 104 Run lb-mol Temp a, -.W.- o DpG lb-mols/hr-ft2 % Noo hr-ft2 ~F min mg mg Exper Eqn 36 Dev 1/8-in depth, 0- Oin. radius; 1 pellet per run 709 157.8 79.5 2~0 5.15 0.05 2105 1.033 12.55 12o46 0o7 11 153 e8 79 0 "0 508 5 2052 1 067 14.74 12 26 16 o8 12 154.8 79*7 n 5.50 2065 1 018 1.3 22 12e31 6.9 13 75.1 79*7 " 3.20 " 1002 1.018 7.65 7.69 0.5 14 74.1 79.8 " 2.80 n 988 1.015 6,65 7*62 14.6 16 73*1 79,5' 3.00 n 975 1o030 7.24 7,56 4.4 17 71*2 79*4 " 3*30 a 950 1.039 8.05 7*43 7.7 2970 39.9 80.9 " 2.35 -0.10 532 0.942 5.50 5,10 7.3 71 39.9 8loO " 2.35 " 532 0,937 5.48 5.10 6.9 73 39e9 80,9 n 1.85 " 532 0e942 4.38 5e10 1604 74 3909 81*0' 1.95 n 532 0.935 4.57 5.10 11.6 75 22*8 81.1 2.0 0.95 -0*35 304 0,929 2.88 3.54 2209 76 22*8 80,6 2.25 1.25' 304 0.959 3.24 3.54 9,3 78 23*5 78.8' 1.30 " 314 1.080 4,24 3.61 12,5 79 23*5 79.0 t' 0.95 " 314 1.067 3e31 3,61 901 Ave.o 908 1/8-in, depth, 1/4-in. radiusg 1 pellet per run 1880 39.1 8004 200 2.60 0.25 522 0.974 5e45 5,34 200 81 39.9 80.6 " 2.50 " 532 0,962 5015 5*41 500 83 3909 80.5 2.40 532 0.965 4,93 5.41 9o7 84 39.1 80*6 n 2.75 " 522 0,962 5.74 5e34 7.0 85'22.0 80.0 t 1.40 0.05 293 1.003 3.22 3.68 14.3 86 2200 79.8 n 1.80 t 293 1.012 4.22 3.68 12o8 88 22,00 79-.5 n 1035 t 293 1.033 3.19 3.,68 1504 89 22*0 79*5 it 1.15 tt 293 10033 2,72 3068 3106 90 82.0 80.0 " 3*70 " 1094 10000 8069 8.64 0,6 91 83,0 80.3 " 4.15 R 1107 00982 9060 8.71 9,3 93 83e0 80.1 " 3.80 n 1107 0.994 8.88 8.71 1 09 94 85.9 79.9 " 3.30' 1146 10006 7079 8.90 14.2 95 157.8 8103' 4.45 -0,5 2105 0,917 12.01 13022 10ol 96 151.9 79.5 " 5.80' 2026 1.030 14036 12o90 10o2 98 150.9 78.9 n 5.10 " 2013 1.074 13.17 12,85 2.4 99 154.8 78.9 n 4.85 " 2065 1.074 12.53 13.06 4,2 Ave e 9.4 /8,-in depthi /l2-ino. radius; 2 pellets per run 850 38.3 76.7 2.0 5.10 0.35 511 1.,240 7,01 7.38 503 51 38.Z3 77.5 i 5.35 " 511 1.182 7.04 7.38 4,8 53 38.3 78.2 " 6.45 " 511 1.127 8.18 7.38 908 54 3803 78.05 ~ f 5.45 " 511 1.106 6.72 7038 9.8

167 Table 5E Continued) Air, Rate x l04 Run lb-mol Temp e, _L-r, -l,Wc DpG lb-mols/hr-ft2 % No f2'F min mg mg_ _ Exp Eqn 36 Dev. 1/8-in. depth,. 1/2-in. radius; 2 pellets per run 2948 149.9 75*3 2,0 13.65 0*20 2000 1*363 21.83 17093 17.9 49 145.9 78*4 n 14.95 n 1946 1.113 19.56 17.63 9.9 51 146*9 77*0 1 164615 " 1960 1*218 23.14 17*69 23.6 52 147w9 77*0'" 16.15 197-3 1.218 23014 17.77 23,2 53 69*2 79.7 10.20 0.25 923 1.018 12*06 10.85 10.0 54 672W 79*9' 10655 896 1.006 12*.4 10o64 13.8 56 67o2 79,8 n 10*25' 896 1,012 12.05 10.64 11.7 57 6'742 77 # 92495' 896 1.018 11.76 10.64 9*6 2991 27.3 79,2 1 5 3.65 0*35 364 1*052 5.51 5.92 7.4 92 2288 79.3 n 2490 " 304 1*049 4.26 5,27 23.7 94 22*0 79*9 " 2.95 0 293 1*006 4.17 5,15 23.5 95 22.0 79*3 n 2.90 " 293 1*049 4,26 5.15 20.9 Ave. 14.1 1/8-in. depth 3/4-in, radius; 2 pellets er run 1864 84*0 78*9 2,0 9,95 0.25 1121 1.074 12*41 9.85 20.6 65 85.9 79.9 n 9.65 n 1146 1.006 11.27 10.00 12.7 67 84*0 79*6' 8*95' 1121 1*024 10.61 9.85 7.2 68 83.0 79*4 n 9,20 1" 107 1,042 11.11 9.79 11.9 69 22*0 79*7 n 3.55 0.10 293 1*021 4.19 4.13 1.4 70 22.0 79*8 " 3.45 " 293 1.01 5 4*05 4*13 2.0 72 22*0 79*7 " 3.25 n 293 1.018 3.82 4*13 8.1 73 21.2 80*5 " 2.90 n 283 0.971 3.24 4a03 24.4 75 39*9 80.0 5,05 0.25 532 1.000 5.72 6.07 6.1 76 39*9 80*2' 5.70 " 532 0.988 6.41 6 07 5.3 78 39.01 80.0 " 5.55 522 1.003 6*34 5099 5.5 79 39 *9 799'9 4.60 " 532 1 006 5.22 6.07 16*3 20 1 51.9 78.7 1,5 10.80 0.40 2026 1.086 17.93 14.48 19.2 21 153*8 80*8 " 10.75 " 2052 0.947 15.56 14.60 6.2 23 149.9 80,9 N 11.40 n 2000 0*.42 16.45 14.36 12.7 24 142 *O 80.3 " 10.10' 1894 0.979 1 509 13 *87 8.1 Ave. 10.5 1/8-in. depth, 1-in. radius; 4 pellets per run 458 22.0 78,9 5*0 10*75 0*90 293 1*077 2*53 2.59 2,4 59 22*0 79. 2 10.05 293 1.055 2.30 2*59 12,6 61 2102 82,0 " 9,90 " 283 1.110 2.38 2*53 6.3 62 39*1 79*5 " 16.75 1.05 522 1.030 3.85 3.76 2.3 63 39.o9 80. 6 16.85 " 532 0.962 3.62 3.81 5.2 85 3901 79.6 " 16.05 522 1.027 3.67 3.76 2.5 78 126.3 80.9 " 40.75 040 1685 0.942 9.05 8.06 10e9 79 126.3 81.5 n 38.85 n 1685 0.906 8.30 8.06 2.9 81 12 53 79.1 " 40.00' 1672 1.061 10.01 8.02 19 9 86 73.1 79.1 n 24.95 0.05 975 1.061 6.29 5.65 10.2 87 73.1 79.7 n 24415 975 1.021 5.86 5.65 3.6 89 72.2 79*0 " 26.50 " 963 1.067 6072 5,60 16.7 Ave. 8.0

168 Table 5 E (Continued) Air, Rate x 104 Run lb-mol Temp e,,.-W, -rwo DG lb-mols/hr-ft2 % No. hr-ft2'F min mg mg C Eer. Eqn36 Deve 1/8indepth, 1/2inradus; 4 pllets er r 628 75*1 79.9 2.0 7.95 0.40 1002 1.006 4.53 2.94 35.1 29 76.1 79.5, 6.75 1015 1.036 3e92 2.97 49e7 31 85.0 78.8 n 7~05 " 1134 1.080 4,28 3019 25~5 32 85*0 78*9 " 5.45 " 1134 1.077 3e24 3.19 1.5 33 160*7 79.8 n 10.70 " 2144 1.015 6.22 4.83 22.3 34 165.6 79.8 " 12.10 n 2209 1.012 7.05 4.e92 30.2 36 163*7 79.5 n 12.20' 2184 1.036 7.28 4.88 33.0 37 157.8 79,9 n 11.70' 2105 1,006 6*77 4,77 29,5 39 22.)0 80.9 3.45 1.10 293 0.942 1.32 1.33 0.8 41 22*0 80.4 n 3.40 " 293 0.976 1033 1033 0,0 42 22.0 80.1 " 3.40' 293 00991 1o36 lo33 2,2 43 39.9 78ol " 4.60 " 532 1.134 2*36 1.95 17.4 44. 39.9 79.3 It 4.70 tt 532 1.049 2.25 1.95 13 o3 46 39*9 80.0 " 4*75 532 1.000 2.17 1.95 10,1 47 39.9 79*6 4.45 n 532 1.024 2,04 1,95 4.4 Ave. 18o3 /8-in. depth, 2-in, radius; 6 peets pr run 434 71.2 80*3 5.0 18.50 1.90 950 0.979 2.58 2.05 20.5 36 68.2 81.1 t 16.45 " 910 0*932 2.15 1,63 24.2 37 126.3. 78.8 " 19.20 1*10 1685 1o080 3o10 2.44 21.3 39 126.3 80.8 " 21.35 n 1685 0,950 3.06 2,44 20.3 40 22.8 83.4 12.95 4.45 304 0.799 1.08 0.80 25.9 42 23.5 86.l N 14.35 a 314 0*675 1.06 0.82 22.6 43 39.9 84.5 13.70 4.20 532 0.745 1*12 1 15 2,7 45 40.7 82,1 " 13.75 " 543 0.870 1.32 1.17 11.4 46 129.2 81*3' 19.05 -3.00 1724 0.920 3e22 2.47 23.3 48 126.3 80*5' 14.85' 1685 0.968 2.74 2.44 10.9 49 73.1 79.7 n 15*25 0.35 975 1.021 2.42 1.71 29.3 51 790o 79.5 " 13.70 " 1054 1.033 2.19 1.80 17.8 52 23.5 77.7 9.05 3.30 314 1.161 1*06 0*82 22.6 54 23.5 80.2' 10.85 314 0.985 1.18 1017 30.5 55 40.7 80,2' 12.90 1.55 543 0.988 1.78 1.17 34,3 57 39.9 80*4 t 10*95 532 0,976 1.46 1.15 21,o2 Ave. 21o2 3/8-in. depth, 0-in. radius; 1 pellet per run 778 37*5 80*4 5.0 9.05 0.60 500 0*973 7*83 7.54 3.7 79 38*3 81.2 t 8.50 tt 511 0.923 6.95 7*64 9.9 81 37.5 79.5 " 8.50' 500 1.033 7.77 7.54 3.0 82 38.3 79.8 " 7.40 511 1,015 6.57 7,64 16',3

169 Table 5 E (Continued) Air, Rate x 104 Run lb-mol Temp Ae, -SW, -LWro DpG lb-mols/hr-ft2 No. h _ft2 F min mg mg er Eqn 36 Dev. 3/8-in. depth, O-in, radius; 1 pelletper run 783 76.1 80.2 5.0 12.00 0.60 1015 0.988 10.73 11.94 11.3 84 86.9 80.9 14.25 " 1159 0*944 12*28 13.02 6.0 86 82.0 80.9 13.50' 1094 0*944 11.61 12.53 7.9 87 86.9 80.3 3 17.10 t 1159 0.982 15.44 13*02 15.7 3023 22.0 79.7 1.5 1.35 0.00 293 1.021 4.38 5*33 21.7 24 23*5 79.6 t" 1.55 t 314 1.024 5.05 5.56 10.1 26 23*5 79*6 " 1*30 -0.15 314 1.024 4.70 5e56 18,3 27 23.5 79.7 "t 1.30 " 314 1.018 4*70 5*56 18.3 34 145.9 79.9' 7.30 0.25 1946 1.006 22.52 18.25 19.0 35 147.9 80.5 f 6.65 1973 0*965 19.63 18.40 6.3 37 161.7 79.8 " 6.60 n 2157 1.012 20.42 19o50 4.5 38 153*8 81.0 t 6.45 2052 0.935 18.42 18.87 2.4 Aveo 10.9 3/8-in. depth, 1/2-in. radius; 2 pellets per run 678 43.1 80.5 2.0 7*10 0*30 575 0*971 7*86 6*85 12.8 79 42*3 80*8 It- 7*50 " 564 0.947 8*12 6.77 16.6 81 42.3 80.6't 7.05 n 564 0.959 7*71 6,77 12.2 82 43.1 81.0 " 7.70 " 575 0.940 8.29 6.85 17.4 83 21.2 807 4.05 283 0.953 4.25 4*32 1.6 84 21.2 80.7 " 4.05 283 0.953 4.25 4.32 1.6 86 21.2 810 " 3.95 f 283 0.940 4.09 4a32 5,6 87 21.2 81.0 t 4*05 t 283 0.940 4.20 4.32 2.9 3006 153.8 79*3 1*5 11*85 0*60 2052 1a049 18*74 15*67 1 6.4 07 153*8 80.0 " 12.05' 2052 1.000 18*18 15e67 1308 09 157.8 78.8't 10*60 t 2105 L.080:17.15 15.93 7.1 10 161.7 78*9 " 10.90 n 2157 1.077 17.61 16.19 8.1 12 75.1 79*4 t 5.80 0.10 1002 1*042 9*43 9.83 4*2 13 73.1 79.0 t} 7.10 ". 975 1.067 11e86 9.66 18 5 15 80.0 7904 " 6*25 1t - 1067 1.042 10.18 10*24 0*6 16 73.1 79*2 6*.90 2 975 1.055 11*39 9.66 1583 Ave. 3/8-in depth, 1-in. radi 4 llL 3067 77.1 80.2 1.5 9.70 0.30 1029 0.988 7.38 5,00 32.2 68 82.0 79.4 t 8.50 tt 094 1 0 1,042 678 5.20 233 70 73.1 79.1 t 8.55 tt 975 1.061 6.95 4e83 30,5 71 76.1 78.7 tt 9.25 " 1015 1,086 7 72 4,96 3508 72 24.3 80.0 t 3050 I 324 1.003 2.55 2*36 7.5 73 25.0 80.7 " 3.90 " 334 0.953 2.72 2.41 11.4 75 25.0 81.1 " 3.55 n 334 0.932 2041 2,41 0.0 76 24.3 81.5 " 4.25 90 324 0909 20.85 2.36 1 7-2

170 Table 5 E (Continued) Air, Rate x l04 Run lb-mol Temp ne, -QW, -AW0 DG lb-nmols/i-ft2 % Noe hr ft2 ~F min mg mg CT.. xper.Eqn 3 Pt;2 + T~~~~/ ExPer. Eqn 36 3/8-in, depth, 1-in, radius; 4 pellets per run 3078 39.9 80.0 1.5 6.20 0.45 532 1.000 4 57 3.26 28 7 79 39.9 80.2 t 6.15 T 532 0.988 4.47 3.26 27 ol, 81 41.5 79.3 " 5.15 " 554 1.049 3.91 3034 14.6 82 41.5 79.3 w 5.50 " 554 l1049 4.21 3.34 20.7 83 156.a8 79 2 n 11.60 " 2092 1.055 9.34 7.93 15.1 84 146.9 79.0 t 15.30 n 1960 1.067 12.58 7060 3906 86 153.a8 79.9' 13.95' 2052 10006 10.78 7083 27.04 87 156.8 79.0 n 12.95'f 2092 1.067 10.59 7,93 25.1 Ave. 22.3 e~ Y 3/8-in. depth, 1-1/2-in. radius; 4 pellets per run 608 146.9 78.5 2.0 9.10 1.6'5 1960 1.106 4.93 4,76 3,4 09 15508 78.7 t 10.20 r' 2078 1.090 5e56 4095 10.'6 11 1 54.8 80.2 n 9.50 I 2065 0.988 4.63 4.92 6.3 12 153.a8 80.a5 t 9.95 t 2052 0.971 4081 4.90 1.9 13 80.0 80.3 8.70 1.85 1067 0.982 4.01 3,21 20,0 14 7401 80.0 f 8.40 988 1o000 3090 3.05 2108 16 81.0 79.5 t 7.25 " 1081 1,030 3.31 3.23 2.4 17 82.0 80.0' 8.05 1094 1.000 3o69 3.26 1107 18 41,5 79.8 4.40 0.80 554 1.012 2.17 2.09 3.7 19 41.a5 80.1 " 5.00 n 554 0.994 2.48 2009 15.7 21 4007 80.5 n 4.50 It 543 0.971 2.14 2007 3.3 22 41.5 80.7' 4.80 554 0.956 2.27 2,09 7.9 23 22.0 80.5 n 3.10 293 0.971 1.33 1039 405 24 22.8 80.6 " 3.05 " 304 0.959 1029 1.42 10l.1 26 22.8 80.8 23.35 M 304 00947 1o44 1.42 1 04 27 22.8 81.0 3025 " 304 0,937 1.37 1.42 3.6 Ave. 8 1 _3/8-in. depth, 2-in. radius; 4 pellets per run 588 22.0 79. 2.0 2.25 0.80 293 1.018 0088 1 01 1408 89 22.0 79.6 n 2.3 5 n 293 1.024 0095 1 01 6.3 91 22.0 80.2' 2.40 t 293 0.985 0.94 1,01 7.4 92 22,0 80.5 n 2.70 t 293 0.965 1o09 1.01 7~3 93 39.9 80.4 t 3.55 0.85 532 0,976 1,57 1.49 51 94 39.1 80.4 I 3.85 " 522 0.976 1,74 1.47 15.5 96 39.1 80,3 n 3.60 f 522 0.982 1.61 1,47 807 97 39.1 80.3 " 3.60 n 522 0.982 1.61 1.47 8.7 98 81,O 79.7 5,0 12.85 2.30 1081 1.018 2.56 2.35 8.2 99 74s1 79.6 " 11.85 988 1,027 2.34 2,22 5o1 601 82.0 79.,5 " 12.05 1094 10030 2.39 2,37 0,8 02 85.0 79.2 " 12,o10 1134 1,052 2.46 2.43 1.2 03 160.7 79.5 2.0 8.00O 1.75 2144 1.030 3.84 3.67 4.4 04 160.7 79.3 " 7.75 n 2144 10049 3.75 3,67 201 06 157o8 79.2 " 7.55 n 2105 1.055 3.64 3.63 0,3 07 159.7 7904 e 7,65 " 2131 10039 3.65 3,66 0o3 Ave o 6.0

171 Table 5 E (Continued) Air, Rate x 104 Run lb-mol Temp Ab, -btif, -eo0 DpG lb-mols/hr-ft % No, O.F min mg mg. 3 Dev. h1r-ft ~F mn mg m CT* Exper. Eqn 36 5/8-in. depth, 0-in. radius 1 pelleter run 3089 157.8 77.9 2.0 5.05 0.15 2105 1.147 13.39 14,09 5,2 90 150.9 78.7 nt 5.45 t 2103 1.090 13.77 13.69 0.6 92 159.7 79.2 "' 5.85 2131 1,055 14.32 14,20 0.8 93 157.8 79*6 n 5*35 n 2105 1.024 12,67 14.09 11,2 94 39.9 80.5 " 2.55 532 0.965 5.53 5.76 4.2 95 39*9 81.2 tf 2.40 * 532 0,923 4o95 5*76 16.4 97 39.9 80.3'i 2.50't 532 0.979 5,48 5.76 5,1 98 39*9 79*4 tt 2.80 t 532 1.042 6,57 5.76 12.3 99 61.7 80.0 t 3.25 0.30 823 1o003 7o05 7,65 8,5 3100 66.2 80e1 t 3*80 t 883 0.994 8.27 8,01 31l 02 60.8 8000 t 3*70 t 811 1,003 8.12 7,58 6.7 03 61.7 78e7 t 3.35 I 823 1.086 7.88 7.65 2,9 04 22.8 81.1 " 1.60 0.20 304 0.932 3.10 4.01 29.4 05 22.8 81*5 " 2.00 t 304 0.909 3.91 4001 2.6 08 22,8 80*0 t 1.95 304 1.000 4*17 4.01 3,8 Ave. 7.5 5/8-in. depth, 1/2-in. radius; 2 pellets per run 1949 85.0 79.4 2.0 8.00 0.05 1134 1.042 9.86 7.54 23.5 50 86,9 80.2 n 8.95 " 1159 0.988 10.47 7,65 26e9 52 88.9 80.1 " 7*45 " 1186 0.994 8.77 7.76 1105 53 87*9 80.5 n 7.85 n 1173 0.971 9,02 7e71 14.5 54 25.0 80.0 t 2.45 -0.15 334 0.977 3.19 3*40 6.6 55 25.8 80.2 " 2.85 I 344 0.988 3.53 3e48 lo4 57 25.8 80.3 " 3.05 " 344 0.988 3.76 3.48 7.4 58 25.0 80*3 N 2.75 I 334 0*982 3*39 3,40 0.3 60 39.9 80.5 " 4.60 0.20 532 0,971 5.09 4.61 9,4 61 38*3 80.5 " 4.60 " 511 0.965 5.06 4,49 11,3 63 38.3 80.1 " 4*10 " 511 0.994 4.62 4.49 2,8 64 39.1 80,0 0 4*35 522 1,000 4*94 4.55 7,9 65 153.8 78*8 " 10.30 0.15 2052 1,080 13.05 11,08 1501 66 153.8 79.4 " 11,60 n 2052 1.042 14.21 11.08 22,0 68 153.8 79.2 n 9.20 " 2052 1,055 11,37 11,08 2.6 69 153.8 79,1 n 9.80 t 2052 1,061 12.20 11,08 9,2 Ave. 10o8 5/8-in. depth, 1-in. radius; 2 pellets per run 1387 86,9 76.3 2.0 3.90 0.60 1159 1,272 4.99 4,75 4,8 88 83.0 78.7 " 4e15 1 1107 1.086 4.60 4r61 0,2 90 83.0 79.7 n 5.05 " 1107 1.018 5.40 4.61 14.6 91 86.9 80.0 t 5.50 1159 0.997 5e82 4.75 18,3 92 22.0 80.1 n 2.20 " 293 0.991 1.89 1.94 2,6 93 22.8 80,3' 2.60 1o00 304 0.979 1.87 1,99 604 96 23.5 80.4 " 2.70 " 314 0.976 1,98 2003 2.5

172 Table 5E (Continued) Air, Rate x 104 Run lb-mol Temp /L, -tIW, b-m rlb-mols/hr-ft2 % No hr 2 F min mg mg C Eqn 36Dev /t CT Exper. Eqn 36 5/8-in. depth, 1-in. radius; 2 pellets per run 1398 39.1 80.4 2.0 3.45 0*45 522 0.973 3.48 2.82 19.0 99 38.3 80.0 t" 2.70 t 511 0.997 2.67 2e79 4.5 1401 39.1 80.0't 2.75 t 522 1.000 2.74 2082 2.9 02 38. 3 80*0 " 2.80 U 511 1.000 2.80 2.79 0.4 03 146.9 79.2 " 7.70 " 1960 1*052 9 09 6.67 26,6 04 149 9 80.2 i 6.65't 2000 0.988 7.29 6.76 7,3 06 157.8 80*3 t" 8.20't 2105 0.982 9.06 6.99 33 9 07 155,8 80.1 tt 6.35 " 2078 0.994 6.98 6,94 0.6 Ave 9a6 5/8-in. depth, 1-1/2-in. radiuse t 4 pellets er run 3045 364.7 78.9 1.5 2.65 0.65 490 1.074 1.71 1.97 15.2 46 38.3 78*6 " 2.95' 511 1.096 2.00 2.03 1.5 48 38 *3 80.3 t 3*40' 511 0,982 2.14 2.03 4.2 49 37.5 80.1 n 3.40 " 500 0*994 2.17 2.00 7.8 50 24.3 80.1 " 2*65 0.95 324 0.991 1,33 1,51 13.5 51 24.3 79.8 t 2.80 324 1,012 1*48 1.51 2,0 53 24.3 7996 t 2*80 " 324 1,027 1.51 l151 0.0 54 25.0 79.5 n 2.80 334 1*036 1.52 1.54 1.3 56 70.2 78.9' 4.30 0.65 936 1,074 3.11 3.01 3.2 57 83.0 78*1 " 4*35 n 1107 1.130 3.32 3,36 1,2 59 83.0 79*4'" 4*65 It 1107 1.042 3.31 3.36 1,5 60 83.0 79.3 It 4.75 t 1107 1.049 3.41 3.36 1,5 61 148.9 78*2 5.55 0.50 1986 1.127 4*52 4.90 10.6 62 151.9 79.7 Ut 6.40 t 2026 1.021 4.78 4,97 4*0 64 149.9 79.5 tt 5.75 " 2000 1.036 4.32 4,93 14,1 65 149*9 79.6 " 6.80 It 2000 1.024 5*12 4,93 3.7 Ave. 503 5/8-in, depth, 2-in, radius; 4 pellets per run 1101 159.7 79.7 2.0 9e20 0.60 2131 1.018 5*21 4.37 1601 02 161.7 80.0 " 7.45 Is 2157 1,000 4*08 4a41 801 04 151. 9 80.3 " 7.45 F 2026 0.979 4a00 4o23 5 8 05 149*9 7997 U 6.30' 2000 1,018 3,45 4.19 21 o.4 06 20.5 80.0 n 2.35 0.65 273 1.003 1,02 1.15 12.7 07 21.2 80.6 U 2.80't 283 0,962 1,23 il18 4.1 09 21.2 80.9 n 2.70 I 283 0o945 1l15 lol8 2.6 10 19.7 81.2 It 3.10 It 263 00926 1.35 1.12 17.0 12 85.0 80.2 n 7.80 1.40 1134 0.988 3.76 2.90 22.9 13 850 80.1 n 7.50 n 1134 0,994 3.61 2.90 19.7 15 83.0 79.5 " 6.40 1107 l1030 3*07 2,86 6.8 16 88.9 79.8 n 6.70 t 1186 1.015 3e20 2,99 606

173 Table 5 E (Continued) Air, Rate x 04 Run lb-mol Temp le, -W1, -WOt D_p lb-mols/hir-ft2 % No, h_ft2 ~F min mg mg r CT EDper.1Eqn36 e 5/8-in. depth, 2-in. radius; 4 ellets per run 1122 39.9 73.5 2.0 3.45 1.40 532 1.529 1.86 1.77 4.8 23 39.1 75*4 t 3.80 t 522 1.351 1.93 1,75 9.3 25 39,9 76*7 " 3,90 n 532 1.244 lo85 lo77 4,3 26 39.9 78.5 n 4035 n 532 1.103 lo94 1077 8,8 Ave. 10,7 1-in, depth, 0-in. radius; 1 pellet per run 1825 76*1 80*4 3.0 4.30 0*15 1015 0,973 6.42 6o07 5,5 26 76.1 8009 tt 3 95 " 1015 0.945 5,70 6,07 6,5 28 8300 80.5 it 3.45 t 1107 0,971 5,08 6.43 26,6 29 83.0 81,2 tt 3e30 " 1107 0.926 4.64 6,43 38,6 30 146.9 82.7't 6.35' 1960 0.840 8,27 9.31 12,6 31 150.9 80*0 t 6.30 " 2013 1.000 9.77 9.48 3.0 33 150.9 79*1 n 6o05 f 2013 1,061 9,94 9,48 4.6 34 151.9 80.4 " 6.50 " 2026 0,973 9081 9,51 3,1 36 39.9 80.5 5.0 5*30 0,60 532 0.971 4,34 3.99 801 37 38.3 80,8 " 4,90 1 511 0.947 3,88 3.89 0,3 39 3901 80*7 It 5.20 522 0.956 4.19 3.94 6,0 40 39.1 81.4 " 4*45 i 522 0.912 3,34 3,94 18,0 41 22.0 80*9 270 0.25 293 0,945 2e21 2,71 22,6 42 22*0 8001 it 2,85 t 293 0,991 2.46 2.71 10,2 44 22*8 79*6 I 3.25 n 304 1,024 2*93 2.77 5.5 45 22.8 79.3 "t 2.40 t 304 1.049 2.15 2,77 28.8 Ave. 12.5 -!in.' depth, 1/2 -if6 radis; 2ypellets per run 1781 145,9 78,9 2*0 7,05 0.60 1946 1.074 8,25 7,73 6.3 82 149.9 79*4 n 6.50 n 2000 n1039 7*30 7086 7,7 84 147*9 79e8 " 6,90 1973 1,012 7,60 7.80 2o6 85 15308 80.1 n 7.90' 2052 00991 8.61 7,99 7o2 86 85.0 83,7 t 5.95 0030 1134 0,785 5,29 5.44 2,8 87 86e9 82.1 "t 5000 n 1159 0.873 4e88 5,52 13,1 89 8500 80.0 t4.45 tt 1134 0,997 4.93 5*44 10e3 90 87,9 7.9.9 Ut 5.35. 1173 10009 6.07 5,56 8,4 92 39.9 79.6 t 2.55 -0,20 532 1,027 3o36 3.32 lo2 93 40.7 79.7 lt 2.75 n 543 10018 3,57 3037 5,6 95 41.5 79.3 tt 2e80 t 554 1l049 3075 3041 901 96 3909 79*4 tt 2.60 t' 532 1,042 3,48 3.32 4,6 97 23.5 79.5 ft 1.40 314 1,030 1,97 2,36 19,8 98 24.3 79,4 t 1,75 n 324 1,039 2.42 2.41 0,4 1800 24.3 79.5 " 1.45 324 1,036 2,04 2.41 18ol 01 24.3 79.4 t 1055't 324 1,042 2.17 2,41 11 ol Ave. 8.0

174 Table 5 E (Continued) Air, Rate x 104 Run lb-mol Temp A9, -a 6, -AWo DpG lbmols/hr-ft2 % No ~F min mg mg T De hr-ft.2 Exper, Eqn 36 1-in. depth, 1-in, radius; 3 pellets per run 1632 3909 79o6 2.0 3.10 0o35 532 10024 2.24 2,42 8.0 33 39.9 79,6 n 3.10 532 10o27 2o24 2,42 8o0 35 39.1 79.o8 f 4o05 522 o,015 2.99 2o38 20,4 36 39,1 79o5 n 3*75 " 522 1,030 2,78 2,38 14.4 37 145.0 78.8 " 8,35 0,55 1934 1,080 6.69 5,59 16,4 38 149,9 78.9 n 7o25 2000 lo077 5.73 5o71 0o3 40 143.0 79,2 n 6.90 " 1908 1,052 5,30 5o54 4.5 41 145,9 79,2 " 8.45' 1946 1,055 6.61 5,62 15,0 43 23o5 80.0 n 2.35 0.40 314 l,000 1,55 1.71 10.3 44 24,3 80.2 2.65 M 324 0.988 1.76 1,75 0,6 46 2403 80.1 8 2o75 t 324 0,994 1,86 1075 5o9 47 24.3 80,2 " 2,80 324 0.988 1.88 1o75 6,9 48 86,9 80,0 " 5,55 0,60 1159 0.997 3,92 4,01 2.3 49 85.0 79.9 " 5,90 t 1134 1,006 4,23 3,95 6.6 51 85,0 79,8 6.55 1134 1.012 4,78 3,95 17,4 52 84,0 79,9 6 S,00 tt 1121 1.009 4o33 3,92 9,5 Aveo 9o2 i'-in, depth, 1-1/2-ino radiu.s; 4 pe lets per run 1676 39.9 79*1 2o0 3.75 0.40 532 1.061 2,11 2e13 10O 77 40.7 7904' 3.50' 543 1o042 1,92 2,16 12.5 79 40,7 790 "n 3.10 " 543 1.034 1l72 2o16 25,6 82 86o9 75.8 4,65 0,25 1159 1.315 3e45 3,53 2,3 83 7381 78*1 n 4.65 H 975 1,130 2.96 3.16 6.8 85 86.9 77*8 n 5,25 n 1159 1,154 3o44 3,53 2.6 86 8809 78.7 " 5.05 n 1186 1*086 3,10 3,58 15.5 87 145,9 7901 n 7*60 1946 1,061 4064 4095 6,7 88 150.9 80,3 6 7095 " 2013 0,982 4,50 505 12 o2 90 153.8 78.1 t 7o40 n 2052 1,134 4.83 5o12 6,0 91 149,9 78,6't 7.45 2000 10093 4.69 5e03 7o2 2178 21,2 78.3 " 2.20 0,20 283 1.116 1,o33 1 o41 6,0 79 22,8 79,2; 2,20 t2 304 1,055 1o26 1,48 17,5 81 22,8 79,5 t 2~20 3n 04 1 030 123 1,48 2003 82 22. 8 79e6 " 2o30 " 304 1,0027 1.29 1o48 14,7 Ave o 10o4 1-in, depth, 2-in, radius; 4 pellets per run 1580 8500 80,0 2.0 5,85 0,35 1134 1,003 3,29 3,26 0,9 81 86.9 79,7 "t 5.70 tI 1159 1o021 3,25 3o31 1,8 83 86,9 79,9 It 5.90 it 1159 1,009 3.33 3,31 0,6 84 8500'79,8 n 5.20' 1134 1,012 2,92 3.26 11o6 85 22,8 79,7 It 2030 n 304 100138 1 19 l,39 16,8 86 22,8 7908 " 2.45 t 304 1o,012 1 27 1l39 9~4 88 23,5 79.7 " 2.45 It 314 10021 l129 1,41 9.3 89 2403 79.9 n 2.40 324 1,006 1. 23 1,45 1709

175 Table' SE (Continued) Air Rate x. 104 Run lb-mol Temp AO,..tWD Wo W G lb-mols/hrft2 % No. hr=ft OF min mg mg C E.pe., qn 36 e 11)59l 39 9 80a5 2o0 4.15 Oo60 532 0,965 2.04 2.00 2.0 92 39,9 8065 " 3.90 532 0o965 1.89 2,00 5.8 94 39e9 80*5 " 3,90 532 0,968 1l90 2,00 5,3 95 391o 80,1 n 4.10 522 0,991 2.07 1.97 4.8 96 151,9 79o7 8 8,10 0e50 2026 1o021 4o62 4o76 300 97 144o0 79o3 n 7.70 " 1921 1o045 4~48 4o60 207 99 150,9 79,5' 7035 " 2013 1,033 4,22 4,74 12.3 Z1600 147,9 79.6 " 7,10 1 1973 1o027 4e04 4o68 15o8 Ave o 7o5 2_hin, depth, O-in, radius; 1 pellet per run 2015 2200 78.7 5o0 lo35 0.25 293;6 1o086 1013 1o54 3603 16 22oO 79o4 " 1o65 " 293 1,042 1 o39 l154 1008 18 22,0o 79o4' 20o0'2 293 10039 1 o73 1.54 11 o0 19 22oO 79 9 " 1o80' 293 1 006 1o49 1 o54 3.4 20 3803 80,1 f 2,75' 511 0o994 2 o28 2o20 305 21 38o3 80,8 " 2,70' 511 0,950 2.12 2e20 3,8 23 38,3 79.0 " 2 60 " 511 1,067 2,29 2.20 3$9 24 36.7 79,0 " 2,40 M 490 10067 2,09 2o14 2,4 26 85.0 77,5 3o0 1.90 0.05 1134 1o178 3,46 3.70 609 27 8809 79,6 " 2.o10 1186 1.027 3,35 3o85 14,9 29 85,9 78,9 2,35 f 1146 10377 3094 3o72 5,6 30 85,9 79,6 " 2.30 " 1146 1.027 3o67 3,72 1,4 31 152.8 81,0 " 3.55 6 2038 0940 5e22 5,41 3,6 32 156*8 80,2 " 3.55 " 2092 0e988 5,49 5.50 0o2 34 153,8 80,2 " 3.60 R 2052 0,988 5o57 5o44 2 3 35 147o9 813 3.60'" 1973 0,918 5018 5o30 203 Ave. 7,0 2-in, depth, 1/2-in, radius; 2 pellets per run 2037 143.0 79,3 2,0 4,65 0,40 1908 1o049 5,31 4,93 7o2 38 142,0 80,0 M 4.50 " 111894 lo000 4.88 4.91 6.2 40 1 48.9 79,5 " 4,80 1986 1,0C30 5,&O 5o06 603 41 153. 8 80,2 n 5 500 2052 0o985 5o40 5.17 403 42 88,9 79,5 335 0o60 1186 1,oO36 3~39 3062 6,8 43 86,9 80,0 3,65 " 1159 10003 3o64 3o57 1.9 55 8609 79,6 3,45 " 1159 Io027 3o49 3,57 2,3 56 88o9 80,0' 3,70 " 11186 1.000 3,69 3062 109 58 22o8 79,6 3,0 2o05 0020 304 1,024 lo50 1,49 0,7 59 24,3 80.1 " 2,10 " 324 0,994 1.50 1o59 60o 61 24o3 79o4 2,00 o' 324 1 042 149 o1.59 6.7 62 24,3 7905 " 1o95 " 324 10030 1o43 lo59 11o2 63 40,7 79e6 * 2o90 0030 543 1o024 2oll 2o18 3,3 64 39,9 80,5'" 3,10 532 0.971 2o16 2.15 0,5 66 39,9 80,2 " 3.10 n 532 00988 2,20 2,15 2.2 67 4:0,7 81,2 " 3.30 " 543 0,926 2o21 2o18 1.4 Ave. 4,3

176 Table 5E (Continued) Air, Ratte x lO4 Run lb-tnol Temp a4, -LAW, -.Wff D G lb-mols/hr-ft2 % No. hr ft2 ~F min mg mg T Exper. Eqn36 De 2-in, depth, 1-in. radius; 4 pellets per run 3525 142.0 80.9 1.5 6.30 0.70 1.894 0.942 4.19 4.86 16.0 26 140*1 81.1 6t 6.70 " 1869 0.929 4e42 4,81 8.8 28 213;8 1l 81*1 n 4.60 i 1842 0.932 5.11 4.77 6.7 29 130o2 81.4 " 7.50 t' 1736 00915 4o94 4.59 7ol 31 42o3 81o3 2,5 5.75 tt 564 0,918 2.21 2,21 0,0 32 43.1 80,6 "t 6,25 t 575 00959 2o53 2o24 12o3 34 44.7 81.5 n 6.40 t 596 0,904 2.45 2.29 6,5 35 43 *9 81 *5 it 6*05 tt 586 0.909 2.32 2.26 2o6 36 22,0 86.7 3,0 5.40 0,65 293 0.648 1o22 1o45 18,9 37 25.0 86.8 0 6.50 1 334 0,646 1.50 1057 407 39 25.8 86.6 n 6.35 " 344 0,652 1.48 1060 801 40 24*3 86*4 " 5.90 3 324 0.651 1.36 lo54 13o2 41 8100 82. 4 2.0 8.o00 1081 0.858 3.76 3.37 10.4 42 8709 80.7 " 7*90 1173 0*953 4.11 3e56 13e4 44 71e2 82,1't 75 950 950 0.870 3o55 3010 12 o7 45 81,0 8192 tt 7.00 " 1081 0O923 3.49 3.37 3 o4 Ave.o 9ol 24in. depth, 2-in, radius; 4 pellets per run 1759 39 9 79.5 2.0 3.95 0*40 532 1,030 2.18 2,13 2o3 60 40.7 79,7 " 3.85 " 543 1.021 2.10 2o16 2o9 62 39.9 79e5 " 3*65 532 1,033 2,00 2o13 605 63 39.9 80*2' 4.00 n 532 0.988 2.12 213 00,5 64 22.0 80,0 " 2.60 0.45 293 1 e003 1.29 lo45 12o4 65 22.0 795 275 293 1.030 le41 1,45 2.8 67 22.0 78.9 t' 2.75 n 293 1.074 1.52 1045 4.6 68 22*0 78*4 n 2.50 n 293 1e109 1.31 1,45 10,7 70 9009 78,2 n 6040 1213 1,127 4e00 3,64 9,0 71 83*0 77*9 5.90 1107 1.150 3,72 3.43 708 73 85,0 79e0 " 6*80 " 1134 1,067 4,04 3.48 13,9 74 87 9 78 o8 " 6*35 n 1173 1.080 3*78 3.56 5*8 75 142.0 80,6 t 9*75 0,50 1894 0,959 5,28 4,86 8.0 76 155.8 80.0 " 9.10 I 2078 0.993 5,10 5.16 1,2 78 147*9 79,2 n 8,80 II 1973 1.052 5o20 4o82 7o3 79 153,8 79,7 " 8080 n 2052 1.021 5.04 5,12 1,6 Ave. 601ol

177 Table 5 F. 1-inch orifice, 1/2-inch pellets Air, Rate x 104 Run lb-mol Temp A@, -tW, -Wo0 DG lb-mo 1 s/hr-ft2 % No. hrft2 ~F min mg mg, CT Der.......hr........t.... Exper. Eqn 36 2-inch depth, 1-in, radius; 1 pellet per run 3480 31*1 80*4 2.5 4.15 0o05 972 0.974 1*30 1*34 3.1 81 31.1 80.4 " 4*10 n 972 0*974 1.28 1.34 4.7 83 30.4 80.1 "r 4.15 950 0.991 1.32 1.32 0.0 84 30*4 80C.1 t 4*15 " 950 0.991 1.32 1.32 0.0 85 117.4 80.0 1*5 6.05 3670 1.003 3*26 3.19 2.1 86 117*4 80*0 t 5.80 f 3670 1.003 3.13 3.19 1.9 88 115.5 79.f3 " 6.00 " 3610 1.049 3.38 3.15 6.8 89 115*5 79.3 tt 5.55 n 3610 1*049 3.13 3.15 0.6 91 171.5 79.7 n 7*50 0*25 5361 1.021 4.01 4.08 1.7 92 171.5 79*7' 7*55 t 5361 1*021 4.03 4,08 1.2 94 161.7 80.5 R 7*45 " 5055 0.968 3*77 3*92 4.0 95 161*7 80*5 tw 7.25 n 5055 0.968 3.67 3.92 6.8 96 56*4 79*8 2*5 6*35 0.30 1763 1.015 2.00 1.98 1.0 97 56 4 79*8 n 6*30 " 1763 1*015 1.98 1098 0.0 99 56*4 79*9 n 6*75 " 1763 1.006 2.11 1.98 6.2 3500 56.4 79*9' 6*50 "1763 1*006 2*03 1098 2.5 Ave. 2.7

178 Table 5 G, 2-inch orifice:, 1/8-inch pellets Air, Rate x 104 Run lb-tmol Temp L9, -LWr, -AWo D lb-mols/hr-ft2 % No. hrft2 F min mg mg c Exer Eqn 36 1/16,in. depth, 1/2-in. rad,ius; 4 pellets per run 3340 155.8 80.3 105 2.05 0,30 1114 0.979 4.15 5.21 25.5 41 155.8 80.4 t} 2.25 " 1114 0,976 4,62 5,21 1-o3 43 154.8 80.3 2.0 2,80 t 1107 0.982 4,48 5.12 8.0 44 154.8 80.2 270 " 1107 0.988 4.32 5.12 18.5 46 86,9 80,3 " 1.90 0.10 621 0,979 3.21 3.57 11o2 47 8509 8000 o 1,70' 614 0.997 2.92 3,54 21,2 49 86.9 80,0 1" 1.95 621 lo000 3037 3057 5.9 50 85.9 79,9 2.00 614 1.006 3.48 3.54 1 7 3469 43.1 8106 2.5 2o55 0,55 308 0.898 2.63 2.26 1400 70 4309 80.4 " 2,35 " 314 0,974 2,55 2.25 11,8 72 43.9 79.3 n 2.15 " 314 1.045 2.44 2.25 7,8 73 43.9 78.9 n 2,25 " 314 1.074 2.67 2,25 15,7 74 24.3 8001 3.0 2.00 " 174 0.991 1.75 1.56 10.9 75 24*3 80.4 1n 1.85 174 0.976 1,54 1.56 103 77 24.3 79.8 " 1.90 " 174 1,012 1,67 1.56 6.6 78 24.3 79*9 n 1.85 n 174 1.009 1.59 1.56 1.9 Ave. 10.2 1/16-in. depth, 1-in. radius; 4 pellets per ru3266 86.9 8000 2,0 3.60 0.15 621 0,997 6.27 6,68 6.5 67 87,9 80,4 n 3.80 " 628' 0.976 6.49 6.73 307 69 86.9 80.0 0 4,40 621 0,997 7.73 6.68 13.6 70 88,9 80.0 " 3.30 " 636 1.003 5.76 6 77 1705 71 20.5 79.5 3.0 200 " 147 10030 2.32 2.61 12,5 72 20.5 79.5 " 2,05 f 147 10033 2.38 2.61 9.7 74 20.5 78o0 " 2.10 " 147 1*137 2,70 2.61 3,3 75 2059 79.2 " 1.90 147 1.055 2*25 2*61 16o0 77 39*9 80.1 2*5 3.10 0*40 285 0,994 3.91 4.03 3.1 78 39.9 80.9 " 3*45' 285 0*942 4.19 4.03 3.8 80 39.9 81*1 n 3.30 t 285 0.929 3.92 4,03 2,8 81 39.9 81.1 " 3.60 " 285 0,932 4*35 4,03 7.4 82 156*8 79.6 1.5 4.45 0.35 1121 1,027 10,23 9.80 4.2 83 157.8 79.9 380 " 1128 1.006 8.44 9.85 16.7 85 159.7 80*2' 3.90 1" 142 0*988 8,53 9.92 16.3 86 158.8 79,4 f 3,95 " 1135 1,042 9012 9,88 8.3 Ave, 9.1

179 Table 5G (Continued) Air, Rate x 10' Run lb-mol Temp ~3, -1W, -WXo D lb-mols/hr-ft2 % No. r t2 F min mg mg CT r Devp 1/16-in. depth, 1/2-ino rad'is- 4 and 6* pellets per rtm 3392 149.9 80.0 1.5 2.55 0.00 1072 0.997 6.17 6.52 5.7 93 153. 30.3' 2.65 1100 0.979 6.30 6.63 5.2 95 153*8 80.0 tt 2.225 tt 1l00 1.000 5.47 6.63 21.2 96 151.9 79.8 f' 2.10 " 1086 1.015 5.18 6*58 27.0 98 43.9 79.8 2.5 1.95 0.15 314 1.015 2.67 2.93 9.7 99 43.1 79.7' 1.85 n 308 1.018 2.52 2.90 15.1 3401 42.3 79.9 9 1o95 302 1.009 2.65 2.87 8.3 02 42 3 79.5 t" 1.90 " 302 1.036 2.64 2.87 8.7 03 25.0 79.9 3.0 2.10' 179 1.006 2.31 2.03 12.1 04 25.0 79.2 It 1.90 " 179 1.055 2.25 2o03 9.8 06 25.0 78.1 tt.15 -0.30 179 1.134 1.99 2.03 2.0 07 24.3 78.2 t 1.10 tt 174 1.123 1.91 2.00 4.7 09 88,9 80.9 2.0 4.45 0*20 636 0.945 4.89 4.64 5.1 10 90*9 79I.). t 4*20 It 6350 1.067 5.19 4.71 9.2 12.9.9 78.5. 4.35 643 1.099 5.54 4.68 15.5 13 90.9 786 390 650 1,096 4.93 4.71 4.5 Ave. 10.2 /16-in, depth, 1/2-in. radiu s; 4 pellets per r u 33$51 86.9 80.1 2.0 2~90 0.20 621 ).991 4.89 5*21 6.5 52 8 6.9C 80.31 6 3O00 0 621 )*,994 5.07 5.21 2.8 34 86. 9 80.2 " 2.95 i 621 ).988 4.96 5*21 5.0 55 26.9 80.4 n 3.5 E' 621 ).976 5.25 5.21 7.6 56 1Z3.3 * 80.6 1.5 3.30' 11t30 ).962 7.24 7.56 4*4 57 154.*8 80.8 it 2.90 tt 1107 ).950 6.25 7.59 21.4 59 153*8 30.6 n 3.25 1100 ).962 7.12 7.56 6,2 60 153.8 810.36 2.90 n 1100 ).962 6.32 7.56 19.6 61 39.9 80*7 2.5 2.90 0.40 285 ).953 3.47 3.15 9.2 62 39.09 80f.6 3*C10, " 285 ).959 3.78 3.15 16.7 64 39.9 80.9 " 3.30 28 ),.9l42 3.98 3.15 20.9 65 39.Z9 30.8 t~ 3.90 t 285 ).947 4.83 3o15 34.7 66 21.2 80*2 3.0 2.40 0.65 152 ).988 2.1 210 2.08 1.0 67 22.0 80. " 2.60 157.003 2.38 2.14 10,1 69 22*0 79*9 " 22.50 157.*006 2.26 2.14 5.3 70 228 80o*2, 3,05 T 16f3 j.988 2.88 2*18 24.3 Ave. 12.2 1h6-in,. d 1-in, radius; 4pellets per run 3288 39.1 79.7 2~b 2.65 0.40 280 1.021 3.35 3,81 13.7 9'9 39. 3 SQ0.3 " 3.05 " 230 0,9o2 3.79 3.81 0.5 91. +3 e.9 79.9 "9 3.30 285 1 009 R 4.27 3 86 9 6 92 S39. 80.3 "a 3.45' 285 0.982 4.38 3.86 11.9 *Runs 3409-13

180 Table 5 G (Continu.ed) Air, Rate x 104 Run lbnol Temnp aS, -VaW, -W DG lb-mols/hrft2 % No. hr' Oft2 ~F min mg mg Erqn 36ev 3/!6-in. depth.' 1,.in. radius, 4 ellets per run 3293 22.0 81o5 3.0 2.40 0.40 157 0,906 2*20 2.62 19.1 94 21L2 82*0 " 2.45 t 152 0*875 2,18 2,56 1704 96 22. O 79.3 " 2 *1 5 tt 157 1 045 2 22 2.62 1800 97 22.0 78,0'" 2.10 1 57 1.1ol71 242 262 8.3 98 87.9 78*1 2*0 3.60 " 628 1.134 6.62 6o45 2o6 99 87*9 77*8 " 3*75 5 628 1,157 7.07 6.45 8.8 3301 88.9 7700 n 3050 636 10218 6.89 6.50 5,7 02 88,9 77.6 " 3.45 t 636 1o168 6*49 6,50 0.2 03 153.8 78.6 1o5 5.05 0025 1100 1.093 12.76 9,28 27.3 04 154.8 78.3 t 4.60 " 1107 10120 11.84 9,35 21.2 06 155.8 78.8 " 4.30 n 1114 10080 10.62 9035 12.0 07 154.8 78.0 4.,20 " 1107 1.144 1099 9,33 15,1 Ave. 1200 3/16-in, depth, 1-1/2-ino radius; 6 pell,.e ts per run 3414 90.9 8001 2.0 3.35 0.10 650 0.991 3.91 4*61 17,9 15 9009 8009 " 3.45' 650 0o945 3085 4o61 19.7 17 90*9 80.4' 3.50 " 650 0.976 4*04 4.61 14.1 18 90.9 80.5 f 3.30 " 650 0.971 3.78 4.61 22,0 20 25*0 79e2 3.0 2.10 n 179 1.055 1 713. 200 1700 21 2500 7809 n 2*05 n 179 1,074 1,69 2.00 1803 23 25.8 79.1 " 2.20'2 184 1,061 1e81 2004 12.7 24 25.8 79*0 " 2.15 f 184 1,064 1,77 2.04 1503 58 39 9 80.0 2o5 2 80 0035 285 0.997 2.37 2.70 13 o9 59 39.9 80.6 n 2.65 f 285 0,962 2 15 2.70 25,6 61 39.9 80,0 " 3.20' 285 1,003 2.78 2.70 209 62 39o9 79. *5 3.30' 285 1.036 2,98 2.70 994 63 152.8 79.8 1.5 3.35 0.50 1093 10015 4,68 6047 38,2 64 153.8 7904 " 3.40' 1100 10039 4o88 6o50 3302 66 15308 80o3 n 3.50 " 100 0,982 4,78 6.50 3700 67 15508 81.6 n 4.60' 1114 00901 5.25 6.55 24.08 Ave. 20,1 5/16-in, depth, 1/2-in. radius- 4 pellets per run 3371 22,0 79.3 3.0 2e25 0.40 157 10042 2,35 2.59 10.2 72 22.0 79.0 n 2.10 n 157 1.067 2,20 2059 17*7 74 22.8 81,2 " 2.50 " 163 00926 2036 2064 1109 75 22,0 81,2' 2.35 157 00923 2.19 20S9 18.3 76 87.9 80.0 2.0 3.85 0.10 628 1.000 6.84 6,36 700 77 88,9 8000 W 3.15 " 636 1.000 5.56 6040 151o 79 90.9 80.5' 3.10 n 650 00968 5,29 6,50 22.9 80 90,9 80.2 " 3.535 " 650 0,985 5.83 6.50 10.8

181 Table 5 G (Continued) Air, Rate x 104 Run ib-mol Temp Ae, -MW, -aTi D G lb-molssAr4t2 % No. 2 hF min mg mg'CT Dev. NJo. h O ~F min rnlg mig,u T Exper. Sqn 36 5/16-in, depth, 1/2-in. radius; 4 pellets per run 3381 39.9 80.9 2.5 2.70 0*15 285 0.942 3.50 3.81 8,9 82 39.9 8101 t 2,90 t 285 0.932 3.73 3,81 2ol 84 39.9 81.6 it 3*45 " 285 0.898 4.32 3.81 11o8 85 39.9 80,4 It 3.15 tt 285 0.974 4.26 3.81 10,6 87 153.8 80.0 1*5 3*80 t 1100 0.997 8.85 9o15 3.4 88 153.8 80*0 3.20 t 1100 1.000 7.41 9.15 10,0 90 15308 8005 "t 3.85 " 1100 0.971 8,73 9.15 4.8 91 151.9 80*4 tt 3 75 t 1086 0.974 8.53 9.07 6,3 Ave. 10o7 5/16-in. depth, 1,in. radius; 4 pelletseru LZ_n.d2,1-i eius;~ye1ijets per run 3308 156.8 78. 9 1.5 4*25 0.25 1121 1.074 10.45 9.06 13.3 09 157.8 79.6 t" 4.50 if 1128 1.024 10057 9.10 13o9 11 155*8 79*2 it 3.80 t' 1114 1.052 9.07 9.02 0.6 14 88*9 77*5 2.0 3.25 t 636 1.182 6.47 6.26 3.2 15 88.9 79.8 it 3.80't 636 1.012 6.55 6*26 404 17 88.9 79.8 I 3.75 tt 636 1.015 6o47 6.26 3.2 18 86.9 79*3 " 3.90 t 621 1.049 6.98 6017 1106 19 25.0 79.5 3.0 2.65 0.25 179 1.036 3.03 2.75 9,2 20 25.8 79.4 ti 2.75 " 184 1.042 3,16 2.81 11ol 22 26o6 79.5 N 3.00 190 1.033 3,45 2o86 17ol 23 26,6 79.6 " 3.15 190 1.024 3061 2*86 20.8 25 43.1 80*3 2.5 2.75 0*20 308 0.979 3.65 3.92 7o4 26 43.1 79.7 t" 2.85 a 308 1.018 3,94 3.92 0,5 28 43.1 79.9 " 3*15 t 308 1.009 4,35 3o92 9o9 29 43.1 79*5' 3.05'i 308 10036 4,30 3.92 8o8 Aveo 9oO 5/16-in, depth, 1-1/2-in, radius; 6 pellets per run 3431 24.3 78.1 3.0 1.95 0.10 174 1.130 1.69 1o96 16.0 32 2403 79.8 " 1.90 n 174 1o012 1.47 lo96 33.3 33 24.3 80.8' 2.10 " 174 0,950 1,54 lo96 2703 35 24.3 80o5 "t 2.10 1t 174 0.965 1.56 1o96 25.6 43 86.9 78.7 2.0 2.90 0.20 621 1.086 3.56 4.48 25,8 44 86.*9 79.0 It 2.90 t 621 1.033 3,39 4.48 32o2 46 86.9 78.7 t" 3*10' 621 lo086 3.83 4o48 1700 47 8609 78.8 tf 3.00 t' 621 1.083 3,68 4.48 21.7 48 391ol 79.1 2.5 2.60 0.15 280 1o058 2.52 2,66 5.6 49 39.1 79.1 " 2.55't 280 1.061 2.48 2.66 7 o3 51 38.3 79.4'7 2.50 " 274 1.042 2.38 2.63 1005 52 38.3 79.2 " 2.70 " 274 1,055 2.62 2,63 0.4

182 Table 5G (Continued) Air, Rate x 104 Run Ib-mol Temp A@, -AW, -AWO DpG lb-mols/hr-t2 % No. h_ 2 F min mg mg mg T Eper. Eqn 36 hrLft er.....Eqn 3_ 5/16-in. depth, 1-1/2-in, radius; 6 pellets per run 3453 154.8 80.2 1*5 3*45 0*20 1107 0.988 5,20 6.53 21.7 54 155.8 80.4 tt 3,10 1114 0.973 4.54 6.55 44,3 56 154*8 80.0 " 3. 05 1107 1.003 4.64 6.53 40.7 57 156*8 79e9 it 3010 n 1121 1,006 4.73 6.58 39.1 Ave. 23.0 1/2-in. depth, -in. radius; 6 pellets per run 2350 41.5 81.6 3.0 5.15 0.20 297 0.898 3.24 3.59 10.8 51 40.7 81.9 n 5.35 tt 291 0*886 3,34 3.54 6.0 53 42.3 80e4 " 5.35' 302 0.976 3.68 3.64 11o 54 41.5 80.8 " 5.70' 297 0,950 3.85 3059 6.8 55 21*2 80.5 3,.00 0.35 152 0,965 2,07 2.32 12,1 56 21.2 79.9 n 3*20 n 152 1.009 2.33 2.32 0,4 58 21.2 80.3 n 2.95 i 152 0.982 2.07 2.32 12.1 59 21.2 79*9 " 0 3.05 1 152 1.006 2*20 2.32 5,5 60 86.9 80.5 " 7*20 0.70 621 0.965 5008 5081 14o4 61 8809 80*0 e' 7.65' 636 1.000 5,63 5089 4.6 63 87*9 79.4 " 7.85 62 8 1 039 6.02 5085 2.8 64 88.9 78,7 n 7*10' 636 1.086 5o75 5,89 2.4 2445 154o8 79.4 1.5 4.85 0.15 1107 1.039 7.91 8.46 7,0 46 155,8 80*5 t 4.90 t 1114 0.971 7.47 8,48 13.5 48 153.8 80.3 M 4.65 1100 0.982 7.16 8.41 17,5 49 154o8 80,5't 4.95 " 1107 0.965 7.50 8.46 12.8 Ave. 801 1/2-in. depth, 2-in. radius; 6 pellets per run 2310 161.7 80.6 3.0 5.70 0.45 1188 0,962 4*09 5,63 37.7 11 161 *7 80 03 " 5.30 t 1188 0.982 3.86 5.63 45.9 13 159.7 79.9 n 5~25 1142 1l009 3.92 5,64 43o9 14 157*8 79*7 n 5.45 n 1128 1.018 4.12 5.60 35,9 15 2102 81.0 n 2.35 t 152 0.934 1.55 1.52 1 09 16 21.2 81*1 " 2.25 " 152 0,932 1,47 1.52 3.4 18 21.2 80.4 n 1090' 152 0.974 1.26 1.52 20.6 19 21.2 80*4 " 1.95 152 0.974 1.30 1.52 16.9 20 41*5 79*3 " 3.15 0.60 297 1.045 2o16 2.35 8.8 21 40.7 80.2 " 3.15 " 291 00985 2.03 2,32 14,3 23 42.3 80.5 3. 15 " 302 0,968 2o00 2,38 19.0 24 41 5S 80.4 " 3.30 n 297 0,976 2.14 2.35 9,8 25 86.9 79.7 n 4.30 6 621 1,021 3.06 3.80 24,2 26 86,9 78,9 n 4015' 621 1,074 3.09 3,80 23.0 28 86.9 80.4 " 4.30 " 621 0,976 2,93 3.80 30.0 29 87,9 80,3 " 3.90 t 628 0,979 2.62 3,82 45,8 Ave. 23,8

183 Table S H. 2-inch orifice, 1/4-inch pellets Air, Rate x 10 Run lb-mol Temp ae, -AW, -AWo G lb-nols/hr-ft2 % No. hr_ft2 OF min mg mg CT Exper. Eqn 36 Dev 1/8-in, depth, O-in. radius; 1 pellet per run 1322 79.0 79.7 500 3.80 0.50 1054 10018 3,20 3.32 3.8 23 71.2 79.8 " 3*95 u 950 1.012 3033 3,10 609 25 70e2 7904 n 4e15' 936 10039 3.61 3,07 1500 26 7002 79.7 M 3.75 936 1.018 3.15 3.07 2.5 50 18903 79.2 " 6.00 0.05 2525 1.055 5.98 5.85 2.2 51 18703 78.7 " 5*05' 2499 1.090 5*19 5*82 12.1 53 185,3 77*7 *t 7.15 2472 1,065 7.20 5.78 801 54 186.3 79.0 " 6.70 " 2485 1.070 6o78 5080 14.5 55 43.1 80.0 n 2*30 " 575 0.997 2.13 2,24 5.2 56 41.5 80.2 " 1095' 554 0.985 1.78 2.18 22.5 58 41. 5 80.0 " 2.60 n 554 1.003 2,44 2.18 10,7 59 40*7 80.2 n 2*50 n 543 0*982 2.30 2.16 6.1 60 23.5 80.0 " 1.45 t 314 0.997 1.33 1.51 13,5 61 23.5 80.0 t' 1.50 314 1.003 1.38 1.51 904 63 25.0 79.7 " 1.60 " 334 10018 1.51 1.57 4.0 64 2500 79.8 tf 1.50 334 1.012 1,40 1o57 12.1 Ave o 9.3 /8-in. depth, 1/4-in. radius 1 pellet per run 1901 85.0 79.5 2.0 2.05 0.40 1134 1.033 4.05 3,48 14.1 02 85.9 79.2 " 1.50 " 1146 1 055 2076 3.50 26.8 04 86.9 79.4 " 1.85 1159 1.042 3.60 3.53 109 05 87*9- 79.5 7 1.75 1173 10033 3o43 3.56 3,8 06 189*3 80.9 n 2.70 0.15 2525 0.942 5.72 5.85 2.3 07 18903 8103 " 2.70 " 2525 0.917 5.57 5085 500 09 188.3 81.0'f 2.70 t 2512 0.940 5.72 5,83 1,9 10 18903 81.5 n 2*80 n 2525 0*904 5.72 5.85 2.3 12 25*8 79.1 " 0.75 0.10 344 1.036 1.60 1.60 0,0 13 25.0 79.7 " 0.70 "" 334 1.049 l 50 1.55 3.3 15 25.0 7902'0.80 n 334 1.055 1,76 1.55 11,9 16 25e0 79.1 " 0.75 " 334 1.061 1.64 1.55 505 17 42.3 79.4\ " 1*20 0.15 564 1,039 2.60 2,21 1500 18 41*5 79.0 11.10 " 554 1*067 2.51 2o18 130 1 20 4AAl5 79,3 " 1.00 " 554 1.045 2,12 2o18 2o8 21 4105 79,6'n 1.10 554 1,024 2.31 2.18 5,6 Ave. 7.2

184 Table 5H (Continued) Air, Rate x 104 Run lb-mol Temp Le, -A, -awo0 DG lb-molshr-ft2 % No. 2 OF min mg mg CT De. hr -ft Exper. Eqn 36 1/8-in, depth, 1/2,in. radius; 2 pel!ets per run 1219 40.7 78.6 2.0 1.95 0.10 543 1.096 2.42 2.20 9.1 20 40.7 77*0 " 1.65 " 543 1.218 2*25 2.20 2.2 22 41.5 71*1 n 1.45 " 554 1.815 2.92 2023 23.6 23 41.*5 72.0 " 1.30' 554 1.697 2.43 2.23 8.2 25 22.0 80*5 n 1.50 " 293 0.965 1.61 1.48 8.1 27 22.0 80.0 " 1.05' 293 1.003 1.13 1.48 31.0 28 22.8 80.2 n 0.95 304 0.988 1.00 1.51 51.0 29 79.0 79.8 " 2.55 " 1054 1,012 2.95 3039 14.9 30 79.0 79.2' 2o.50 n 1054 1,039 2.97 3039 14.1 32 790O 7807 " 2.45 n 1054 1.090 3.05 3.39 11.1 33 79.0 78.6 " 2.25 1054 1.093 2.80 3039 21.1 34 189*3 79.8 n 3.80 0.20 2525 1.015 4.35 5.98 37.5 35 189.3 80.1 " 3.70't 2525 0.981 4*09 5.98 46,2 37 187.3 80.4 " 4*45' 2499 0.974 4.93 5.94 20.5 38 187.3 80.8 " 4.40 " 2499 0.950 4.63 5.94 28.3 Ave. 21.8 1/8,in. depth, 1-in, radius; 2 pellets per run 1239 185.3 78.9 2.0 -580 0.05 2472 10077 7.37 8.60 16.7 40 185.3 79.1 n' 6.25 t 2472 1.061 7.84 8.60 9.7 42 186.3 77 8 ft 5.95 9 2485 1.154 8.11 8.63 6.4 43 187.3 79*6 " 6.30 " 2499 1.024 7.62 8.66 13.6 45 81. 0 79.7 " 4.15 0*00 1081 1*018 5.03 5.02 0.2 46 83.0 79.5 n 3.40 n 1107 1.036 4.19 5.11 22,0 48 81.0 79.0 " 3.*65 " 1081 1*064 4.62 5.02 8.7 49 79.0 79.0 tt 3.40 " 1054 1.067 4.32 4.94 14.4 50 38.3 80.3 ft 2.85 " 511 00982 3.33 3.09 7.2 51 38.3 80.5 n 2.30 " 511 0.971 2.66 3.09 16.2 52 39.1 80.2 n 2.50 " 522 0.988 2.94 3.13 6.5 54 39.1 79.5 " 2.55 n 522 1.030 3.13 3.13 0.0 55 23.5 82.6 " 2.60 0.15 314 0.843 2.47 2.25 8.9 56 24.3 80.5 " 2.15 " 324 0*971 2.31 2.30 004 58 2403 79*3 " 1.85 " 324 10045 2.12 2.30 8.5 59 24.3 82.8 n 1080 t 324 1.120 2.19 2.30 5.0 Ave, 9 o0 1/8-in. depth, 1-1/2-in. radius; 3 and 4* pellets per run 1273 72.2 78.7 2.0 5.30 0.45 963 1.086 4.18 3 23 22.7.74 71.2 79.0 n 5.50 i 950 1.070 4.29 3.20 25.4 76 7202 78.05 5.00 n 963 1.099 3097 3023 1806 77 71.2 78.6 4a.40 " 950 1 093 3.47 3.20 7.8 Runs 1286-95

185 Table 5 H (Continued) Air, Rate x 04 2 Run lb-mol Temp A8, -AW, -AWo G lb-mols/hr4ft % No. PF min mg mg CT Dev. hr-ft Exper. Eqn 36 1/8-inl degth i i-ii. radius 3 and 4* l...ets Lr run 1279 41.5 80.2 2.0 3.75 0.70 554 0.985 2.38 2.25 5.5 80 41.5 80.6' 4.10 " 554 0.959 2.59 2.25 130.1 82 41.5 79.7 3' 3.20 554 10018 2002 2.25 11.4 83 41.5 80.2 " 3.70 554 0.988 2.35 2.25 4.3 86 22.0 77.0 n 2.70 0.75 293 1.222 1.41 1.49 5.7 87 22.0 76.9 " 2.80 n 293 1.228 1.50 1,49 0.7 89 22,0 78.0 " 2.95 293 1.141 1.49 1.49 0.0 90 22.0 77.2 " 3.35 " 293 1.204 1.o86 1.49 19.9 91 192, 2 80.2 " 11.05 " 2564 0.985 6.04 6.10 1 0O 92 192. 2 79. 5 n 11.25 2564 1,036 6.48 6,10 5.9 94 190*2 79.3 n 12.70 2537 1.049 7047 6,06 18,9 95 188.3 7904 " 12,05 " 2512 1.042 7.01 6.02 14.1 Ave. 10.9 1/8-in, depth, 2-in, radius; 4 pellets per run 1297 22.8 79.2 2.0 2.15 0.30 304 1.052 1.16 1.17 0.9 98 23*5 79.0 " 2*10 " 314 1.067 1.14 1.19 4.4 1300 2403 78.5 n 2.45 " 324 1.106 1.42 1.22 1401 01 24.3 790 "n 2.15't 324 1.070 1.18 1.22 3 4 02 41.5 79.9 f 3*25 0.45 554 1.006 1.68 1073 3.0 03 41*5 80.1' 4.20 " 554 00991 2.22 1.73 22.1 05 41.5 80.3 " 3.43 " 554 00979 2,04 1.73 15.2 06 41*5 80.5 n 3.20 " 554 0.968 1058 1.73 9.5 07 77.1 80*5 n 4.60 n 1029 0.97. 2.40 2.58 7.5 08 84.0 80.9 " 5.10 " 1121 0.942 2.61 2,73 4.6 10 84.0 78.8' 5.70 1121 1.083 3.39 2~73 19.5 11 84*0 78 *9 " 4.70 " 1121 1.077 2.73 2.73 0.0 12 183.4 799 9.15 0.65 2447 1.006 5.09 4.54 10.8 13 183*4 80.0 " 9.10 "t 2447 1.000 5.03 4.54 12.1 15 181.4 79.6 n' 8.70 " 2420 10024 4.91 4.51 8.1 16 181*4 80.3 " 8.70 2420 0*982 4.71 4.51 4.2 Ave. 807 3/8in, depth, 0-in. radius; 1 pellet per run 865 21,2.79*4 5*0 2.75 0030 283 1.039 2.43 2.23 802 66 22.8 79.5' 2050 " 304 1*033 2.16 2.34 803 68 2102 79*3 " 2.65 283 1o049 2*35 2 23 5.1 69 22. 8 79. 4 2 A.60 3t 304 1,039 2. 28 2.34 2.6 80 39.9 79.6 3.80 0.45 532 1.027 3,28 3.37 2ao7 81 31 390 522 1021 391 797 390 52 102 35 332 009 83 39 09 79.7 " 4.00 " 532 1 o021 3o45 3o37 2,3 84 39.9 80.1 4.60 " 532 0.991 3092 3037 1400 Runs 1286-95

186 Table 5 H (Continue ) Air, Ra4e x _ e TRim lb-tmol Temp a4, -a, -LW D0G Gb-ml 1 D-G-tT b No 0 2F ai 2n mg mg T p Dero nr f /c Exper o Eqn 36 3/8-in. depth, -in. radius; 1 pellet pr r-IT 885 82.0 81.5 5.0 6,70 0.40 1094 0,909 5.46 5.38!o5 86 86.9 81.3 n 6 10 " 1159 0.920 4,99 5a 59. o0 8 8 85.9 77.1 t 5.20 t" 1146 1*211 5.54 5,55 0,2 89 88.9 81.0 7.10 tt 1186 0.940 6.00 5067 505 90 196.1 84*2 " 11.10 0.30 2616 0,761 7.83 9.49 21.2 91 3195.2 85.5 " 12.20 " 2604 0*699 7,93 9,45 19o2 93 193.2 83.7 " 11.75 t 2577 0*785 8.57 9039 9,6 94 195.2 86e1 " 12*70 U 2604 0.673 7,96 9o45 18.7 Ave 8o 3 3/8-in. doepth 1/2-in radius. 2 pellets per run 1875 75.1 78.2 2.0 3.70 0.10 1002 1.127 4.84 4,98 209 76 84.0 78.4 -" 4.00 " 1121 1.113 5o17 5036 3~7 78 83.0 79.0 tt 3.90 tt 1107 1.070 4*85 5.32 9 o,7 79 85.0 78*9 " 4.35 " 1134 1.077 5,45 5,40 0,9 95 40.7 79.9 3.40 0.10 543 1.006 3095 3035 15,2 96 39.9 80*0 " 3.45 " 532 0.997 3.98 3.30 7?o1 98 40.7 79.7 t 3*10 543 1,018 3.63 3,35 e,7 99 39*9 80.3 n 3.05 t 532 0.982 3.45 3.30 4,3 1927 185.3 80,3' 8.85 0.50 2472 0.979 9073 8096 709 28 185.3 80.3 it 8.85 t 2472 0.982 9,77 8096 803 30 185.3 80.0 "t 9.05 " 2472 1,000 10.18 8.96 12.0 31 186,3 80.7 it 8.70 " 2485 00953 9 30 8.99 303 38 24,3 78.9 290 o10 324 1,074 2,30 2,39 3~9 39 2463 78o7 t 2.95 2 324 1.086 2 39 2,39 0,0 41 24,3 78.3 2.095 324 1 120 2.47 2,39 3,2 42 24,3 78.1 4 2.95 324 1.141 2,51 2039 40, ~5/8-in. depth ]-in. radius- 2 0:lZets r 8-i lets r_ru 905 24.3 78.3 2.0 2.10 0,50 324 1 320 2, 13 2,3- a 06 24,l3 78*9 2 *25 324 1,074 2.24 2,408 24,3 78E6 It 2,40 324 1.093 2,48 2o12 145, 09 24o3 79.1 II 2o60 " 324. *061 2 066 2,2 20,3 10 38.3 8001 i 1.75 -0,95 511 0,994 31 9 2 o85 10,7 11 37*5 78,9 11 1.45 f 500 1.077 30o7 2o81 8,5 13 37,o5 78.2 o 10 500 1,123 2,74 2,81 2o6 14 37,5 79.4 " 1.20 1 500 10042 2,67 2,81,2 15 80,0 80.0 " 3.70 P 067 1,000 5.54 4,O0 %o0 16 81.o0 799 1? 2.95 " 08 l18 1 ^ 4.9 3 18 81.0 79.7 2.90 1081 1,018 4.67 4,3 19 81,0 79.7 U 2.90' 1081 1,021 4.68 4~64 008

187 Table 5H ( Continued) Air, Rate x 104 Run lb-stol Temp AO, WS, Ao DG lb-mols/ir-ft % Noo * F ain mg mg C De.. hr-ft2 n mg T Exper. Eqn 36 Deve 3/8-in, depth,.!-in,- radius, 2 pellets per run 920 196.1 79.7 2.0 6.90 -1.40 2616 1o018 10.06 8.24 183ol 21 1971*2 79.8 I 9*95 t 2629 1.012 13.68 8026 3906 23 197 ol 80.0 " 8o70 I 2629 1.003 12.06 8. 26 31.5 24 195.2 8003 n' 6*05 t 2604 0.982 8.72 8.21 5.8 Ave. 11 o3 3/8-in, depth, 1-1-in. radius; 2* and 3 pellets per run 955 23.5 75.6 2*0 2.75 1070 314 1.335 1.67 1.52 9.0 56 21o2 77.0 "t 2.85 n 283 1.218 1.67 1.43 14.4 58 21.2 76.5 " 3.15 2.20 283 1.262 1.43 1.43 00O 5i9 21.2 7609 " 3.05 M 283 10225 1.24 1.43 1503 60 3909 80.3 n 3.90 0.85 532 0.982 2038 2.15 9.7 61 3909 80.3 n 3.55 *" 532 00982 2,10 2, 15 2.4 63 39*9 80.1 t 4.30 532 0*994 2.72 2,15 210o 64 4007 80.0 " 4.90 n 543 00997 2.41 2018 9.5 65 79.0 79.3 n 6.85 1.85 1054 1.049 4,17 3.35 19.7 66 7900 78.8 n 5.20 n 1054 1,080 2090 3,35 1505 68 79,0 7803 5.55.t 1054 1.120 3.'29 3.35 1 8 69 19701 79. 5 " 10.70 n 2629 1.030 7.24 6,07 16.2 70 82.O 79.1 4.75 0.50 1094 1.058 3.57 3,43 309 71 197.1 80*5 t 10.00 t 2629 00971 7*32 6007 17 1 73 199.1 80.2 " 8020 n 2656 0.985 6.02 6 12 107 74 197*1 80.5 " 7075 n 2629 0*971 5059 6,07 8o6 Ave. 10,4 3/8-in, depth, 2-in. radius; 4 pellets per run 1015 70.2 80.6 2.0 5065 0090 936 0.962 2672 2.59 4e8 16 70.2 80.8 " 5.35 t 936 0.947 2,51 2.59 302 18 71e2 80*3 " 5.50 9 950 0,982 2,69 2.62 2o6 20 195.2 83*5 " 10.50 0040 2604 00795 4.78 5.04 5.4 21 194.2 83.1 " 9090 n 2591 00818 4a63 5.02 8,4 23 19302 82*5 n 11o10 n 2577 0.853 5.44 5,01 7.9 24 189,3 83.2 n 1000 " 2525 0.811 4064 4094 6.5 45 40,7 79. " 3.40 0,90 543 1.058 1.58 1e82 1 502 46 39 09 79.8 n 4*05 " 532 1 012 1 090 1 o80 5,3 48 40,7 790O n 4.40 o4 543 1 067 2.22 1,82 18,0 49 40.7 79.5 " 4.10 " 543 1o036 1098 1o82 8ol 50 22 8 75.5 r2.90 " 304 1 347 1 60 1 o2 5 21o9 51 2208 75.3 n 2.45 n 304 1.355 1 025 125 0o0 53 22.8 75.9 n 2.50 " 304 1.307 1,24 1.25 0.8 54 23.5 76.0 tt 2.40 " 314 10303 1o16 lo27 905 Ave o. 7 08 * Runs 9 55-59

188 Table 5 H (Continued) Air, Rate x 104 Run lbqnol Temp ae, - -W lb-mols/hrt2 % No h OF min mg mgCT Exper Eqn 6 Dev _5/8-in. d_ep_h,_ oin. radius; 1 pellet per run 1502 43 1 8005 2.0 1.20 0,0 575 0.971 2o79 3.38 211ol 03 43.1 80.6 l" 1. 50 " 575 00959 3.43 3. 38 1,5 05 42.3 8006 l" 1.35 t 564 00959 3.07 3034 8.8 06 42*3 80.6' 1,55' 564 Oe959 3,55 3934 59 30 25.8 76,0 5.0 1*95 0.10 344 1.299 2.29 2,42 507 31 25.8 78.4 " 2.20 " 344 1,109 2.22 2 42 9.0 33 25 8 77*9 2.40 n 344 1.147 2.52 2.42 400 34 26.6 78 ol 2.40 " 354 1 o34 2,49 2,47 0.8 2009 185,3 80,4 10O35 -0.05 2472 00976 9.67 8.72 9,8 10 186.3 8008'f 9975 n 2485 00950 8.87 8075 1,4 12 18503 79.2 n 9015 2472 1,055 9.25 8.72 5,7 13 18603 79.3 " 9.00 " 2485 1,045 9.01 8 75 2.9 2168 79.0 80,3 ff 5.30 1n 054 0,982 5e00 5,01 0,2 69 8100 80,6 " 00 0 1081 0,959 5.53 5009 8,0 71 84,0 80.5 50,25' 1121 0.968 4089 5.21 6,5 72 84,0 8009 " 5.60 1121 0,942 5,07 5.21 2,8 Ave. 5o9 5/8-in, depth, 1/2-in. radius; 2 ellets per run 1971 41e5 79,3 2.0 3.10 0.30 554 1,049 3.50 3,25 7.1 74 41.5 8000 2" 295 " 554 1.000 3.16 3,25 208 75 4007 80.1 n 3.20 n 543 0.994 3,43 3,21 6.4 76 2403 7902 " 1.75 0.20 324 1.055 1,95 2.30 1709 79 24.3 78.8 " 2.05 " 324 1.080 2 o38 2 o3G 3,4 80 24.3 79,1 " 2.05 n 324 1,058 2.33 2,30 103 82 85.9 78.7 " 4080 0.30 1146 1e086 5082 5,22 1003 83 85.0 78.5 n 4.40 1134 1,103 5038 5.19 3.5 85 85.0 78.4' 4.45' 1134 1.113 5.50 5.19 5,6 86 85.0 78*8' 4,45 " 1134 1.080 5034 5.19 208 87 18503 79,7 " 7.65 0,25 2472 1. o018 8,97 8060 4.1 88 185.3 8002 n 7*70 " 2472 0.988 8.77 8 60 1,9 90 183.4 8002 n 7.85 " 2447 0.988 8.94 8,54 4.5 91 182. 4 79. 6 n 6.95 n 2433 1,024 8,17 8.52 403 Ave o 5.4 5/8-in. depth, 1-in, radius; 2* and 4 pellets perrun 1370 3909 80,4 2.0 3,45 0.50 532 0,974 3042 2,77 19.0 71 3909 8100 30,45 n 532 0,937 3,29 2,77 1508 73 39. 9 8000 " 2.90 tt 532 lo000 2.86 2o77 3ol 74 39.9 80,V5 n 3.00 " 532 0,965 2,87 2.77 305 1998 185,3 78,1 " 13.40 0.55 2472 1.134 8.68 7,40 1407 99 185.a3 80.5 " 15.60 n 2472 0.965 8,65 7040 14o5 2001 185.3 80.4 n 14.60 n 2472 0o976 8,16 7.40 9,3 02 185.3 80.,5 n l ~13.45 n 2472 0o971 7046 7 40 008 * Runs 1370-74

189 Table 5H (Continued) Air, Rate x 104 Run lb-tmol Temp ae, -tW, -AW0 pG lb-mols/hr-ft2 % hr..t2 F min mg mg CT, Exper. Eqn 36 Dev. 5/8tin. depth. 1-in. radius; 2' and 4 pellets per run 2158 22.0 80.3 2.0 345 0*80 293 0.979 1.54 1.85 20.1 59 22.0 80.5 " 3.85 " 293 0.965 1075 1.85 5.7 61 22.0 80.7 " 3.85 " 293 0*956 1.74 1.85 6.3 62 22.0 80.7 n 3.35 293 0.956 1.45 1.85 27.6 63 75*1 79*9' 8.20 " 1002 1.006 4*43 4.11 7.2 64 84*0 80.0 " 7.50 " 1121 1.003 4o00 4.42 10.5 66 83.0 79.7 " 7.45 n 1107 1.018 4.03 4.39 8.9 67 83.0 79.7 " 7.40 " 1107 1.018 4.00 4.39 9.8 Ave e. 11.1 5/8-in, depth, 1-1/-in, radius; 3 pellets per run 1149 82.0 80*2 2.0 4.80 0.50 1094 0*985 3.37 3.40 0.9 50 76.1 80.4 " 4.50 t} 1015 0.974 3.10 3.24 4.5 52 76.1 79.6 n 4.20 1015 1.027 3.02 3.24 7.3 53 75*1 80.3 " 5*00 1002 0.982 3.51 3.21 8.5 55 197.1 79*2 t 6.75 0.20 2629 1.055 5.49 6.01 9.5 56 197.1 79.5 n 6.90 " 2629 1.036 5.51 6*01 9.1 58 19941 79.2 * 6.50 " 2656 1.052 5.26 6.05 15.0 59 201*1 79.5 t" 6*70 " 2683 1.033 5*32 6.09 14.5 60 24.3 78.2 " 2.45 0.80 324 1.123 1.47 1.54 4.8 61 25*8 78.4 tt 2.30 " 344 1.113 1.33 1.60 20.3 63 23.5 78.5 n 2.15 " 314 1.103 1.18 1.51 28.0 64 24*3 78.6 n 2.30 324 1.096 1.30 1.54 18.5 65 40.7 79.0 " 3.70 1.00 543 1.064 2.28 2.16 5.3 66 38.3 78.5 " 3.80 " 511 1.099 2.45 2.07 15.5 68 41.5 77.6 n 3.15 " 554 1.171 2.00 2.18 9.0 69 41*5 77*8 " 3.30 n 554 1.157 2.11 2.18 3.3 Ave. 10.9 5/8-in. depth, 2-in, radius; 4 p.ellets per run 4086 38.3 78*5 2.0 3.70 1.00 511 1.106 1.78 1.83 2.8 87 38+.3 78*6 " 3.35 n 511 1.096 1.54 1083 18.8 89 38.3 78 *4' 3.95 " 511 1.110 1.95 1.83 6.2 90 37.5 78.6' 3.60 " 500 1.093 1.69 1.81 7.1 91 81.0 80.4 " 6.60 1081 0.976 3.26 2.99 8.3 92 74*1 80*6' 5.60 " 988 0.962 2.64 2.82 6.8 94 75.1 80.3 " 5.55 n 1002 0.982 2.66 2,84 6.8 95 74.1 80*6 n 6.30 " 988 0*962 3.04 2.82 7.2 96 199. 1 78.8 " 9.00 0.95 26 S 1.083 5.19 5*34 2.9 97 196*1 77*9 n 8.55 " 2616 1.150 5.20 5*30 1.9 99 197.1 79.1 " 10.20 " 2629 1.058 5.83 5.32 8.7 1100 196.1 78.9' 8.55' 2616 1.077 4.88 5.30 10,7 2153 21.2 79.6 2.70 0.60 283 1.024 1.28 1.25 2.3 54 22.0 79.2 " 2.60 n 293 1.052 1.25 1.28 2.4 56 22.0 79.2 " 2.45' 293 1.052 1.16 1.28 10.3 Ave. 6.9 Runs 1370-74

190 Table 5H (Continued) Air, Rate x 104 Run lb-mol Temp Ag, -W, -aWVo D lb-mols/Arsft2 % No*. 2'F min mg mg E CT E EDev. CT Exper. Eqn 36 1_in. depth, /-in. r adiu ellets per run 1803 27.3 79.3 2.0 1.75 0.20 364 1.049 1.94 2.04 5.2 04 2735 79.7 n 1.75 n 364 1.018 1.88 2.04 8.5 06 27.3 80.1 1 L.60 f 364 0.994 1.66 2,04 22,9 07 27.3 80*1 " 1.95 " 364 0,994 2.07 2,04,o4 08 193.2 8008 n 7.00 2577 0.950 7.69 7.29 5.2 09 1912 80.6 5,*90 2551 0.959 6.51 7o24 11,2 11 189.3 80,2 " 6.50 tt 2525 0.988 7.41 7*20 2.8 12 191.2 79.6 " 6.00't 2551 1,024 7*07 7,24 2.4 14 43.1 79.4 2.40 0.15 575 1.042 2,79 2o75 lo4 15 43*1 79,O' 2.35 " 575 1.070 2.80 2.75 108 17 43,1 78.5 " 2.30 575 1.099 2.81 2.75 2ol 18 43.1 78*6.t -2.65' 575 1*093 3.25 2.75 15.4 19 87*9 78.1 " 3.35 0.00 1173 1.130 4.51 4,37 3,1 20 88.9 78.0 n' 3*60 t 1186 1.144 4,91 4,40 10o4 22 88.9 79.9 n 3.55 n 1186 1.009 4.26 4.40 303 23 90.9 8001't 3*65 t 1213 0.994 4.32 4*47 3.5 Ave. 6 3 1-in. depth, 1-in, radius; 3 pellets per run 1602 27.3 79, 0 2.0 2.70 0.25 364 1.067 2 07 1.92 7 o2 03 27,3 79.0 " 2.55 " 364 1.070 1.95 1e92 1.5 05 28.1 79.0 " 2.40 " 375 1.064 1.82 1.96 7.7 06 28.1 79.1 n 2.65't 375 1.061 2.02 1.96 300 07 181.4 79.6 " 8.05 n 2420 1.024 6*34 6,58 308 08 181.4 79.5 " 8.20 " 2420 1*033 6.52 6.58 0.9 11 181,4 78.8 " 7.50 n 2420 1.080 6.22 6,58 5,8 21 86.9 80.2 n 5*55 0*45 1159 0.988 4.00 4,08 2.0 22 86.9 80.5 n 5.40' 1159 0.971 3.82 4*08 5,2 24 87.9 79.7 " 5.55 n 1173 1,018 4.12 4.11 0,2 25 86.9 79.0, 5.60 " 1159 1.067 4*37 4o08 6.6 26 39.9 79.7 3.60 0.80 532 1.018 2,26 2o46 903 27 39.9 80.1 n 3.90 " 532 0,991 2,.44 2.46 0.8 29 39.9 80,0 " 3*95 532 oo000 2, 50 2,46 1o6 30 39,9 79*8 " 3,60 n 532 1.012 2.25 2,46 9o3 Ave o 4o3 -n.o depth 1-1/2-in. radius; 4 pellets per run 1693 187.3 80.3 2,0 9.75 0.45 2499 0.982 5.44 5.82 7.0 94 187,3 82.0 Xt 10.25 r 2499 0.878 5.12 5.82 13,6 96 187.3 79.8 n 9,80 " 2499 1.012 5.63 5.82 3,4 97 187,3 79.9 " 8.80 2499 1,006 5o00 5082 16,4

.91 Tabl e 5 H (Continued) Air, Rate x 104 Run l1b-mol Temp De, -aW, DG lb-mols/hr.t2 % No. OF min mg mg CT. Dev. hr-ft." Exper. Eqn 36 1-in. depth, 1-1/2in. radius 4 pellets per rin 1698 86.9 79.2 2.0 5.55 0.30 1159 1.055 3.30 3,53 7,0 99 85.9 7901 5 5.50 1 4 1146 1.061 3.29 3 50 6,4 1701 84.0 78.9 " 60 t 1121 1.074 3,39 3.45 1.8 02 84*0 78.7 " 5.35 1121 1.086 3.26 3.45 5.8 04 24.3 79.2 t 3.05 0075 324 1.055 1.45 1.54 602 05 25*8 79*1 3..15't 344 1.058 1.51 1.60 6.0 07 25.8 78.8 " 29.0 i 344 1.080 lo38 1.60 15.9 08 26*6 79.2 " 2,60 0.50 354 1*052 1.32 1.64 24,2 09 41. 5 79o8 " 4.15 tS 554 1.015 2.20 2o18 009 10 41.5 79.9 0 4.05 " 554 1.006 2.13 2.18 2.3 12 41*5 79.4 " 4.30 t 554 10042 2,36 2.18 7.6 13 41.5 79.5 tf 4,10 t 554 1E030 2.21 2.18 1.9 Ave. 709 1-in, depth, 2-in. radius 4 pellets per run 1558 39.1 81.0 2.0 4*00 0.85 522 0.935 o76 le97 11 o9 59 38.3 81.0 " 3.85 n 511 0.935 1.67 1,94 16*2 61 38.3 80.8 "' 4*15 511 00950 1.87 1 94 3. 7 62 39.1 80.9 M 4.30 t 522 0*942 1,94 1o97 1.5 63 23*5 80.7 " 2*85 0*70 314 0*953 1.22 lo41 15.6 64 24.3 80*8 n 2.85 324 0.950 1.21 1.45 19.8 66 23.5 80.7 " 2.85 H 314 00956 1.23 la41 14e6 67 24.3 80.8 " 2.90 n 324 0.947 1,24 1.45 16.9 69 83.0 803 6.00 0*65 1107 0,979 3*12 3o21 2.8 70 83.0 80.3' 5*75 " 1107 0*982 2.98 3.21 7.7 72 83.0 80.0 5.75 1 1107 0.997 3.03 3021 509 73 83.0 80*0 " 5o.70 1107 0.997 3,00 3.21 7.0 74 187.3 80.2 " 8.80 0.40 2499 00985 4.92 5.45 10.8 75 185.3 80.1 " 9.10' 2472 00994 5.15 5.41 500 77 185.3 80.6 t 8.85 2472 0.962 4.84 5.4l 11.8 78 185.3 80.4' 9.65 2472 0.976 5.38 5.41 006 Ave e 905 2-in, depth, 2-in, radius; 4 pellets pe run 1737 190.2 75.0 2*0 7.90 0.35 2537 1.384 6.22 5,88 5,5 38 190*2 76.3 " 8.50 " 2537 1.273 6,18 5088 409 40 89. 3 78 7 2 f7 8.80 252 5 l1123 5 65 5086 3.7 4l 189.3 79.5.s 9.25 " 2525 1.030 5.46 5086 7,3 A42 85.9 77,9 f 5.45 0.50 1146 1L147 3.38 3.50 5043 86,9 76,9 $4095 1159 1!225 3.25 3.53 8.6 45 85.0 77.6 t 5.1s0 11a34 1. 71 5.21 348 804 46 84.0 79.0 t 5.25' 1121 1.064 3001 3.45 146E

192 Table 5 1 (Continued) Air, Rate x 104 Run lb-mol Temp Ae, -AW, -W0 DG lb-mols/hr-ft2 % No 2 O~F min mg mg CT Dev, hr-ftT g Exper. Eqn 36 1748 22.8 77.3 2.0 2*15 0*25 304 1.193 1035 1.48 13 3 49 22.8 77.6 n 2.25 $ 304 1.168 1.39 1o48 605 51 22 8 77.6 " 1.85 " 304 1.168 1.11ll 1.48 33 3 52 22.8 78*1 2.30 304 1.130 1o38 1o48 7.2 53 58.2 80.6 5.30 0.50 776 0*959 2.74 2.72 0.7 54 40.7 80.3 " 4.00 543,:0.982 2.05 2.16 4.4 56 40.7 79.5 ff 4.15' 543 1.033 2.25 2.16 4.0 57 40.7 79*8 f 4.*15 " 543 1l012 2020 2.16 1.8 Ave. 8.0

APPENDIX B PELLET DIMENSIONS AND PROP0ERTIES -. K. I -.

APPEJiDIX B Pellet Dimensions and Bed Porosity I. Glass Bead Dimensions (Sample beads measured three times, orthogonally, to the nearest O.001-inch. ) Table 6. 1/8-inch pellets Miin. Mid. Max. Ave. Min. Mid. Max. Ave..128 *138 *142 *136 *130 *136.138.135 *117.124.125 *122.123.129.133 *128.133 *138.138 *136 *128.139.139.135.126.134 *134 *131.123 *130.131.128 *129.138.138.135.123.131 *132.129,123.129.131.128.126.139.140 *135 *123.128.130.127.128 *135.136 *133 *128.134 *134.132.129.131 *135.132.130 *135.136.134 *128,131.134.131 *113.124.126.121 *127 *133.133.131.128 *137.138 *134 *125 *133 *134 *131 *131.136 *137 *135.120 *124.129.124.122.132 *133.129 *121.129 *132.127 *127.136.136 *133.120.*130.131 *127 *126 *133 *134 *131.131.132 *137.133.122.131.131.128.110.122 *123 *118 124 *137.137.133.124.132.133.130.109.121.121.117.128.131.138.132.122 *135 *136 *131 *126.134.137.132.127.129.129.128 *117 *124.126.122 *122.129 *131.127.122.135.135.131.126 *129.130.128.120 *129.133.127 *119.124.126.123 *119.124.127 *123.118.128 *130.125.122 *135.138 *132 *125 *134 *136 *132.122 *.126 *128.125 *136.136 *143.138 *128.132 *135.132.128.135.138.134.116 *124 o124 *121 *121.130.133.128.118 *127 *129 *125 *125 *131.133.130.118.125 *126.123 *130 *135.135.133.129.139.139.136 Averages.125.132.133.130.123.131.133.129 Overall Averages:.124.131.133.1295 194

195 Table 7. 1/4-inch pellets Min. Mlid. Max. Ave. Min. Mid. Max. Ave..241.241.250.244.234.244.248.242.234.237.240.237.233.239.243.238 239.240.241.240.237.237.246.240.243.243.245.244.238.239.251.243.236 236.238.237.242.248.250.247.232.235.241.236.238.242.243.241.229.234.236.233.224.236.237.232.234.242.243.240.232.240.253.242.238.239.244.240.239.241.244.241.232.243.255.243.229.244.247.240.241.244.253.246.233.239.244.239.239.240.240.240.240.244.244.243.239.245.255.246.234.234.238.235.242.245.246.244.242.243.244.243.237.241.244.241.222.239.243.235.232.234.243.236.240.243.247.243.237.239.249.242.239.243.247.243.241.243.245.243.228.235.239.234.230.236.251.239.240.247.252.246,239.244.246.243.235.237,240.237.240.245.249.245.244.244.250,246 240.241.242.241.227 ~.234.241.234.239.240.240.240.235.241.244.240.243.245.249.246.237.238.240.238.238.239.239.239.238.240,240.239.237.238.243.239.240.241.247.243.240.243.243.242.231.239.240.237.238.241.245.241.238.240.244.240.230.240.243.238.238.243.247.243.238.243.243.241.235.238.239.237.237.241.245.241.235.240.244.240 Overall Averages:.236.240.245.2405

196 Table 8. 1/2-inch pelts Min. Mid. Max. Ave. Min. Mid. Max. Ave. *564.565.568.566 *569 *569.571.570 *556.557.557.557.538.539 *540.539.553.554.554.554.556.558.559.558 ~554.555.555.555.554.555.559.556.554.557.5576.546.548.54F.547 *591.593.596.593.565.566.567.566.566.567 *568 *567 *563.564.566.564.556.559.560.558 *600.601.604.602.563.564 *564 *564 *563.563 *565 *564.554.556.557 *556 *579.579.580.579.568.572.573 *571.580.581.582.581 *588.589.592.590.601 *602.602.602.552.552.553.552.552 *553.553.553.564.566 *566.565 *531.531.531.531.559.559.560.559.561.561.562.561 *547.550.553 *550.571.572.573.572 *541.544.544 *543.609 *609 *609.609 * 55 0.5.550.550 *560 *561 *554.558 *558 *559.559.559.580.580.582 *581 *563.565.567.565 *573.573.575 *574.579 *582 *583 *581.586.588.589.588.587 *589.592 *589.564.564 *565.564.552 *552 *553.552 *559.560.560 *560.561.561 *564.562 *547 *548 *548.548 *546.550.553.550 *562 *562 *564.563 *568 *570.571 *570 *557 *559 *560.559.557.560 *561.559 *584.586.588 *586.555.555 *555.555 *557.558 *558.558 *554 *554.556 *555 *572 *574.575.574 *556.556 *556.556.592 *593.595.593 Averages.561.562.563.562.568 *569.569.568 Overall Averages:.564 *565.566.5652

197 II. p-Dibromobenzene Pellet Dimensions 1/8-inch pellets 200 pellets displace 4.02 cc of water; Volume per pellet = 0.0201 cc; Dp - 0.3375 cm. - 0.1328 in. (Weight of 200 pellets = 8.7234 gmin; Specific gravity = 2.17 vs 2.26 for pure compound) As a check, ten sample pellets were measured three times, orthogonally, to the nearest 0.001-inch: Min. Mid. Max. Ave..127.131.132.130.127.132.132.130.125.130 *132.129 *125.130.131.129 *121.131.133.128 *127.131 *132.130 *124.131.131.129.127.132 *132.130 *124.131.133.129.126.132.132 *130 Average diameter = 0.129 in. - 0.3275 cm. Pellet surface area based on water displacement data, Ap = 0.358 cm2. j_/4-inch pellets 20 pellets displace 2.12 cc of water; Volume per pellet = 0.106 cc; Dp - 0.588 cm. = 0.2315 in. (Weight of 20 pellets = 4.6489 gins; Specific gravity ~ 2.19 vs 2.26 for pure compound)

198 Check measurements: Min. M,lid. Miax. Ave..227.230 *234.230.231.233.233.232.228.230.233 *230.230 *231 *233.231.228.228.232 *229.231.234.237.234.227.230.233.230.228 *231.234.231.230 *230.232.231 *225.228.230.228 Average diameter - 0.231 in. 5 0.587 cm. Pellet surface area based on water displacement data, Ap 1.086 cm2. 1/2-inch pellets 20 pellets displace 30.5 cc of water; Volume per pellet = 1.525 cc; Dp - 1.428 cm, 0.562 in. (Weight of 20 pellets = 58.8997 gms; Specific gravity = 1.93 vs 2.26 for pure compound) Check measurements: Min. Mid. Max. Ave..556.559.563.559.559.563 *565.562.561.565 *565.564.562 *563.567.564.555.556.556.556.561.563 *566.563.561 *563 *563.562.561 *562.564 *562.555.558.564.559 *556.558.563.559 Average diameter - 0.561 in. - 1.425 cm. Pellet surface area based on water displacement data, Ap - 6.406 cm2.

199 III. Bed Porosity 1/8-inch pellets D 0.1295 in.; Vp 0.001137 in.3 s 6.58 x 10'7 ft.3 P $ 400 pellets weigh 17.6327 gins - 0.0389 lbs. Pellet density a 0.0389. 147.8 lbs/ft (400) (6.58 x 10-7) UWeight of pellets in bed a 4.00 lbs. Total pellet volume - 4.0 - 0.02705 ft3 147.8 Bed volume - (1T)(2)2(6.125) a 76.95 in.3 a 0.04455 ft.3 Porosity = 0.04455 - 0.02705 x 100 0.04455 = 39.3 percent Alternate measurement by filling void space with water: Void volume = 455.5 cc o 27.80 in.3 * 0.0161 ft.3 Porosity =.040455 x 100 = 36.15 per cent. 1/4-inch pellets Dp -0.2405 in.; Vp - 0.00728 in.3 - 4.215 x 10"6 ft.3 200 pellets weigh 60.7331 gins = 0.1339 lbs. Pellet density - 0.1339.. 158.8 lbs/ft3 ( 200) (4, 25 x 10-6) Weight of pellets in bed a 4.46 lbs. Total pellet volume 446 0.0281 ft.3. Porosity 0.04455 -0.0281 x 100 * 36*9 per cent

200 Alternate measurement by filling void space with water: Void volumrne u 467 cc - 28.54 in.3 - 0.01652 ft.3 Porosity 001044525 x 100 m 37.1 per cent. l/2-inch pellets Dp 0.5652 in.; Vp 0.0945 in.3 5.47 x 10-5 ft.3 20 pellets weigh 80.8235 ginms 0.1782 lbs. Pellet density a 0.1782 - 162.9 lbs/ft3 (20)(547 x 105) WVVeight of pellets in bed = 4.164 lbs. Total pellet volume 4.164 9 0*02556 ft.3 162.9 Porosity n 0.04455 - 0.02556x 100 0.04455 = 42.6 per cent. Alternate measurement by filling void space with water: Void volume = 526 cc = 32.10 in. 0.01858.3 0Porosity 01858 Porosity - 0.04455 x 100 - 41.7 per cent.

APPENDIX C TEMPERATURE CORRECTION FACTOR DETERMINATION.~~~ __

APPENDIX C Table 9 Temperature Correction Factor Data Air Run lb-mol Temp. A e -aW, -aWo 103 Rate No r-ft ~ F min g mg mg/cm -hr 1-in. orifice, 5/8-in. depth, 2-in. radius; 3 and 4_ellets (1/4-n _per ru n 1117 36.7 68.68 2.0 3.55 1.70 1.8915 12.7 1118 39.9 69.59 2.0 3.40 1.70 1.8883 11.7 1120 39.9 70*73 2.0 3.50 1.70 1.8842 12.4 1121 39.9 71.68 2.0 3.35 1*70 1.8808 11.3 1122 39.9 73*55 2*0 3.45 1.40 1.8742 14.1 1123 39.1 75.41 2.0 3.80 1.40 1.8677 16.5 1125 39.9 76.68 2.0 3.90 1.40 1.8633 17.2 1126 39.9 78.50 2.0 4.35 1*40 1.8570 20.2 1193 39.9 84.91 2.0 4.35 2*00 1*8352 21.5 1194 40.7 84.36 2.0 5.25 2.00 1.8370 29.7 1196 39.1 82.64 2.0 4.40 2.00 1.8428 22.0 1197 39.9 81.91 2.0 4.75 2.00 1*8453 25.2 1198 39.9 81.05 2.0 5*10 2*60 1.8482 22.9 1201 40*7 78*09 2.0 5.05 2.60 1.8584 22.4 1203 39.9 76*00 2*0 3.75 2.00 1*8657 16.0 1204 40*7 75*05 2.0 3.70 2.00 1.8690 15.6 1206 40.7 73.41 2.0 3*60 2.00 1.8747 14.6 1207 40.7 70.36 2*0 2*95 2.00 1.8855 8.7 2-in. orifice, 1/8-in. depth, 1/2-in. radius; 2 pellets. ( 1/4-"in, per run 1208 41.5 91.41 2.0 2.55 0.05 1.8135 34.3 1209 41.5 88.23 2.0 2.90 0.05 1.8241 39.1 1211 41.5 84.23 2*0 2.30 0.05 1.8375 30.9 1212 41.5 82.00 2.0 1*85 0.05 1.8450 24.7 1213 42.3 79.86 2*0 1*65 0.05 1.8523 22.0 1215 41.5 76.05 2*0 1*50 0.05 1*8655 19.9 1217 41.5 67*86 2*0 1*25 0.05 1.8944 16.5 1219 40.7 78.59 2.0 1.95 0.10 1..8567 20.6 1220 40.7 77*00 2.0 1.65 0.10 1.8622 16.5 1222 41.5 71.05 2.0 1*45 0.10 1.8831 13.7 1223 41*5 72.00 2.0 1.30 0.10 1.8797 11.7 Runs 1117-26 202

203 Table 10 Temperature Correction Factor Calculations 8250 Bo-o 8 50 15.28+ log ( 80 - 250 15.+ LWt 540 1.C, t, t, 8250 mv OF OR T log CT CT 0.80 68.36 528.36 15*614 0.3366 2.171 O.82 69.27 529.27 15.588 0 3097 2.040 0.84 70.18 53013 15. 561 02830 1.919 0.86 71.09 531.09 15.534 0.2563 1.804 0.388 72.00 532.00 15.508 0.2297 1.697 0,90 72.91 532*91 15*481 0.2032 1.597 0.92 73.82 533.82 15.455 0.1768 1.502 0,94 74.73 534.73 15.428 0.1505 1.414 0.96 75.64 535.64 15.402 0*1243 1.331 0.98 76.55 536.55 15.376 0.0982 1.254 1.00 77.45 537.45 15.350 0.0725 1.182 1.02 78*36 536.36 15.324 0.0465 L.113 1.04 79.27 539.27 15.298 0.0206 1.049 1.06 80.18 540.18 15.273 -0.0051 0.988 1.08 81,09 541.09 15.247 -0*0308 0.932 1.10 82.00 542.00 15.221 -0*0564 0.878 1.12 82*91 542.91 15.196 -0.0819 00.28 1.14 83.82 543.82 15.171 -0.1073 0.761 1*16 84.73 544.73 15.145 -0.1327 0*737 1.18 85.64 545.64 15.120 -0.1580 0.695 1.20 86.55 546.55 15.095 -0.1831 0.656 1.22 87.45 547.45 15.070 -0.2079 0.620 1.24 88.36 548.36 15.045 -0.2329 0.585 1.26 89.27 549.27 15.020 -0.2579 0*552 1.28 90.13 550.18 14.995 -0.2827 0*522 1.30 91*09 551.09 14.970 -0.3075 0.493

204 N \D OD 0 CM ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~a cu ~ ~ ~ ~ ~~~~~~~~~~~~~~c U)~~~~~~~~~~~~~~~~~~~~~~~~~~~~X 0 co 0-. CM(0 ~~~ 0 CM U N 0 00 4)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. CL 0:3~~ N E~~L.. C) f~~~ I I I I I I I I I I I c~~~~~~~~~~~~~~~~(u I.i. -- a:)'0 c::~~~~~~ a co 0. 0 ~ E -- a. o E,.0.e Q.. (0 0 O L~~~~~~~~~~~~~~~~~~O CD C, CD- N~~~~~~~~~~~~~~~C 0,,I (X) ('u 09 ~~ ~. ~~. 0, CD (0 ~~4- Nr~~N..... 0 0 0 0 co I I I I ~~~I_ 1 I I I Ir

APPENDIX D DATA PROCESSING

APPENDIX D Data Processing The procedure used to process the raw data is outlined below, using data from Run No. 608 (see Figure 5, page 56). Ao The final weight is subtracted from the initial to obtain the uncorrected weight loss: -QW = Wi - Wf = 1071.40 - 1062.30 = 9.10 mg. B. The dry runs for the shift (Runs 610 and 615). are compared and seen to be consistent. A dry-run weight loss of 1.65 mg (Run 610) is therefore used for the run series 608-12. C. The raw weight loss is corrected for the dryrun loss: -AWd = -AW - (-AWo) = 9.10 - 1.65 = 7.45 mgo Do The average thermocouple reading is found to be 1.022 millivolts, and the temperature correction factor, CT, is obtained from Figure 29 (page 204) —1o.106. Applying the temperature correction, -AWt = (CT)(-AWd) = (1.106) (7o45) 8.24 mg. E. The pellet diameter used in this run was 1/4 inch, and four pellets were run for a period of two minutes (see top of data sheet, Figure 5). Taking the surfacec area, of 1/4-inch active pellets as 10086 cm2 (Appendix B), the transfer rate is then calculated: = -dWt~. 8.24 568 mg/cm2-hr, =(n)(@Y8fX~4 (4)(2/60) 086) = 68 mg/cm-hr. 206

207 Fo kt" is converted to lb-mols/ft2-hr: mg gm lb 1 cm2 in 2 lb-mol cm -hp-r mg (gm ( ( ft f rt fthr 1 1 1 k' = 56.8 ( — (453.6 (-) (2~54)2(12)2 = 4.93 x 10-4 lb-mols/ft2-hr. Go The rotameter reading of 80o5 corresponds to an air flow rate of 81.0 SCFM (60~Fo and 1 atmosphere) This is converted to the superficial mass velocity: p= 0.0765 lbs/ft3; S =1rr2 =(2/1l)2 = O473-ft2.: G -(SCFM)(60) () (81) (60)(0,0765) b4260 S 000873thr. GI' = 4260/29 = 146.9 lb-mols/ft2-hr. H. The Reynolds number is calculated, using Dp = 0.2405 in. (Appendix B) and = 0.0436 lbs/ft-hr (47): Re = DpG//t - (0o2405) (4260) =e Dp(12)(0.0436) = 1960 Io kt is divided by Gt to obtain a dimensionlessgroup which is plotted against the Reynolds number on loglog paper to yield the final correlation: kt 4~93 x 10-4 G- 1469 = 3,35 x 10-6 Gt ~146.9

APPENDIX E MISCELLANEOUS CALCULATI ONS

APPENDIX E Miscellaneous Calculations I. Diffusivity and Schmidt number for p-dibromobenzeneo The diffusivity is calculated by use of the Gilliland equation (28): DG = 0.0166 [lP /a 1b P(Va'V/3 bVB/3) Molecular weights: P-C6H4Br2 = 235o9; 1/M = 0.00424 Air = 28.85';' 1/M = 0.03465 0.03889 0 oO03889 = 0 1973 Molecular volumes: Air = 29.9; p-C6H4Br2 = (6) (14,8) + (4)(3o7) + (2) (27) - 15 = 142o6; ~29.9 + -+42.6 = 3o10 + 5.225 = 80325; (8.325)2 = 69.32 Temperature: 800F. = 300.00K.; (300)3/2 = 5200. DG (0.0166) (5200) (0.1973) = 02455 ft2/hr (l) (69.32) Schmidt number: /uair = 0 0436 lbs/ft-hr (47); Pair at 80oF = (28985) () = 0.0735 lbs/ft3; eair3(20 0043.'. Sc = 00436 24 (0.07359(0.2455) = 241 209

210 II. Surface Temperature Calculation. Since the heat needed to vaporize the solid p-dibromobenzene is transferred to the pellet from the air stream, an enthalpy balance may be written: kg(ps - o)A = h(Ta - Ts) where po is the vapor pressure of p-dibromobenzene at Ts. Rearranging this equation, (50) Ta - Ts k, h/kg can be evaluated by applying the analogy between heat and mass transfer. Assuming the identity of the two j-factors, (kRgmP)() = jd - ih =( =h S()2/ \2/3-= CpMmP(Sc)2/3(Pr)2/3 (51) = (0b24)(2) ( 760) (8o)(io227) = 11,680 BTU-mm Hg (0.24) (29) (76'0) (1.80) (I.227) =11,680 -mol_~the values for Cp and Pr being taken from McAdams (47). In the absence of actual data, the latent heat of sublimation of p-dibromobenzene can be approximated through the use of the Clapeyron Equation: d(ln P) dT - R~Z (52)

211 Using International Critical Table data for the vapor pressure, p0 = 0.0158 mm Hg at 21.0~C. and 0~0794 mm Hg at 32.8~Co Since the vapor pressure curve is essentially straight between these two points, 0.0794 d(ln P) -= (0.0158) 1.615 =O76 dT (11 8) (o8) (11.8) (1o8):. = (0.076)(1.987) (540)2 = 44,000 BTU/lb-mol. PS0 _ h 11,680 mm Hg = 0.2655 mm H Ta - T5 kgA 44,000 Using a vapor pressure at 800F. of 0.038 mm Hg (37), 0.038 Ta Ts 0.2655 = 0'1430F. The actual surface temperature is only negligibly different from the air temperature.

BIBLI OGRAPHYI

BIBL I OGRAPHY 1. Aerov, M. E., and Umnik, N N.,, Journal of Applied Chemistry (USSR), 23, 1071 (1950). 2. Argo, W. B., and Smith, J. M., Chemical Engineering Progress, 49, 443 (1953). 3. Arthur, J. R., and Linnett, J. W., Journal of the Chemical Society (London), 1947, 416. 4. Arthur, J. R., Linnett, J. W., Raynor, E. J., and Sington, E. P. C., Transactions of the Faraday Society, 46, 270 (1950). 5, Bedingfield, C. H., and Drew T. B., Industrial and Engineering Chemistry, 42, 1164 f1950). 6. Bernard, R. A., and Wilhelm, R. H., Chemical Engineering Progress, 46, 233 (1950). 7. Brotz, W., Chemie-Ingenieur-Technik, 23, 408 (1951). 8. Bunnell, D. G., Irvin, H, B., Olson, R. W., and Smith, J3.. Industrial and Engineering Chemistry, 41, 1977 (1949. 9. Chernyshev, A. B., Farberov, I. L., and Pomeranchuk, A. A., Doklady Akademii Nauk, S.S.S.R., 56, 727 (1947). 10, Chilton, T. H., and Colburn, A. P., Industrial and Engineering Chemistry, 26, 1183 (1934). ll. Chilton, T. H, and Colburn, A. P., Industrial and Engineering Chemistry, 27, 255 (1935). 12* Chu, J. C., Kalil, J., and Wetteroth, Wo A., Chemical Engineering Progress, 49, 141 (1953). 13. Coberly, C. A., and Marshall, W, R., Chemical Engineering Progress, 47, 141 (1951). 14. Colburn, A. P., Industrial and Engineering Chemistry, 22, 967 (1930). 15. Colburn, A. P., Transactions of the American Institute of Chemical Engineers, 29, 174 (1933). 16. Colburn, A. P., and Hougen, 0. A., Industrial and Engineering Chemistry, 22, 522 (1930). 213

214 BIBLIOGRAPHY (Continued) 17. Cox, E. R., Transactions of the American Society of Mechanical Engineers, 50, 13 (1923). 18. Dreisbach, R. R., PV-T Relationships of Organic Compounds, Handbook Publishers,,- Inc- Sandusky,Ohio (1952). 19. Ergun, S., Chemical Engineering Progress, 48, 89 (1952). 20, Ergun, S., Chemical Engineering Progress, 48, 227 (1952). 21. Evans, G. C., and Gerald, G. F., Chemical Engineering Progress, 49, 135 (1953). 22* Fick, A., Annalen der Physik, 94, 59 (1855). 23. Forstall, W.., and Shapiro, A, H., Journal of Applied Mechanics, 17, 399 (1950). 24* Furnas, C. C., U. S. Bureau of Mines, Bulletin No. 307 (1929 ) 25. Gaffney, B. J., and Drew, T. B., Industrial and Engineering Chemistry, 42, 1120 (1950), 26. Gamson, B. W., Chemical Engineering Progress, 47, 19 (1951). 27. Gamson, B. W., Thodos, G., and Hougen, 0. A,, Transactions of the American Institute of Chemical Engineers, 39, 1 (.1943). 28. Gilliland, E. R., Industrial and Engineering Chemistry, 26, 681 (1934). 29. Graton, L. C. and Fraser, H. J., Journal of Geology, 43, 785 (19351. 30. Hall, R. E., and Smith, J. M., Chemical Engineering Progress, 45, 459 (1949). 31. Hinton, A. G., quoted by H, M. Spiers, "World Power Conference, London, 1928,.Technical Data on Fuelt"' p. 101, World Power Conference (1928). 32. Hobson, M., and Thodos, G., Chemical Engineering Progress, 45, 517 (1949 ). 33. Hobson, NM, and Thodos, G,, Chemical Engineering Progress, 47, 370 (1951). 34. Hsu, C., Dissertation Abstracts, 13, 207 (1953).

215 BIBLIOGRAPHY (Continued) 35, Hughes, lI., L., Journal of the Iron and Steel Institute (London), 156, 371 (1947). 36. Hurt D, M,, Industrial and Engineering Chemistry, 35, 522 (1943). 37. International Critical Tables, Volume III, McGraw-Hill Book Company, New York (1928). 38, Ishino, T,, and Otake, T. Technology Reports of the Osaka University, 2, 123 h1952). 39. Kaufman, D. J., and Thodos, G., Industrial and Engineering Chemistry, 43, 2582 (1951). 40. Kinney, S. P. Uo S. Bureau of Mines, Technical Paper No. 442 (1929T. 41. Linton, W. H,, and Sherwood, T. K., Chemical Engineering Progress, 46, 258 (1950). 42. Maeda, S., Technology Reports of the Tohoku University, 16, No. 2, 1 (1952)* 43, Maeda, S., and Kawazoe, K., Chemical Engineering (Japan), 17, 276 (1953). 44. Maisel, D. S., and Sherwood, T. K., Chemical Engineering Progress, 46, 131 (1950). 45. Maxwell, J. C., The Philosophical Magazine, 35, 199 (1868). 46. Mayo, F., Hunter, T. 0,, and Nash, A, W., Journal of the Society of Chemical Industry (London), 54, 376 (1935). 47, McAdams, W, H., Heat Transmission, McGraw-Hill Book Company, New YorlkT942),. 48. McCune, L. K., and Wilhelm, R. H. Industrial and Engineering Chemistry, 41, 1124 (1949L. 49, Morales, M,, Spinn, C. W., and Smith, J. M., Industrial and Engineering Chemistry, 43, 225 (1951). 50, Morris, F. H,, and Whitman, WO G., Industrial and Engineering Chemistry, 20, 234 (1928) 51, Perry, J. H,, Chemical iEngineers' Handbook, McGraw-Hill Book Company, New York 1950)

216 BIBLIOGRA PHY ( Continued) 52. Powell, R. W., Transactions of the Institution of Chemical Engineers (London), 18, 36 (1940). 53, Prandtl, L., Zeitschrift far Physik, 11, 1072 (1910). 54. Pratt, H. R. C., Transactions of the Institution of Chemical Engineers (London), 28, 177 (1950). 55. Ranz, W, E., Chemical Engineering Progress, 48, 247 (1952), 56, Resnick, W,, and Vlhite, R. R,, Chemical Engineering Progress, 45, 377 (1949),o 57. Reynolds, 0,, Papers on Mechanical and Physical Subjects, Volume I, Cambridge nUniv versity Press (1900)., 58 Saunders, 0. A,, and Ford, H., Journal of the Iron and Steel Institute (London), 141, 291P (1940). 59. Saunders, H. L., and Wild, R., Journal of the Iron and Steel Institute (London), 154, 73P (1946). 60. Schuler, R. W., Stallings, V. P., and Smith, J. MN, Chemical Engineering Progress Symposium Series, 48 No. 4A Reaction Kinetics and Transfer Processes, 19 (1952. 61. Schwartz, C. E,, and Smith, J, M, Industrial and Engineering Chemistry, 45, 1209 (1953. 62, Sherwood, T, K,, and Petrie J, M,, Industrial and Engineering Chemistry, 24, 736 h1932). 63, Shulman, H. L,, and DeGouff, J. J., Industrial and Engineering Chemistry, 44, 1915 (1952)o 64, Stefan, J., Sitzungberichte der Akademie der Wissenschaften in -uein, 68, 403 (1873), 65o Taecker, R. G., and Hougen, 0o A,, Chemical Engineering Progress, 45, 188 (1949). 66, Taylor, G. I,, British Advisory Committee for Aeronautics, Reports and AMemoranda, No, 272 (1916)o 67, Wilke, C, R,, and Hougen, 0. A,, Transactions of the American Institute of Chemical Engineers, 41, 445 (1945)o 68. Zil'berman-Granovskaya, A, A. and Shugam, Eo Ao, Zhurnal Fizicheskoi Khimii, 14, 1004 (1940).

N OMENCLATURE

NOMENCLATURE A area, ft2 a square feet of transfer area per cubic foot of bed volume, ft-1 B variable in the correlating equations, dimensionless Cp heat capacity at constant pressure, BTU/lb-~F CT temperature correction factor, dimensionless D diameter, ft DG molecular diffusivity, ft2/hr f friction factor, dimensionless G superficial mass velocity, based on empty cross-section, lbs/ft2-hr H bed depth, ft h heat-transfer coefficient, BTU/ft2-hr-~F HTU height of a transfer unit, ft j Colburn factor for heat and mass transfer = f/2, dimensionless Jd Colburn factor fo mass transfer = (kgMmP/G)(Sc) 2, dimensionless Jh Colburn factor for heat transfer = (St)(Pr)2/3, dimensionless k thermal conductivity, BTU/ft2-hr- (F/ft) k, mass-transfer rate, lb-mols/ft2-hr k" mass-transfer rate, mg/cm2-hr kg mass-transfer coefficient, lb-mols/ft2-hr-mm Hg m variable exponent in the correlating equations, dimensionle ss M molecular weight, dimensionless 218

219 N mass-transfer rate, lbs/hr n number of active pellets per run; also number of transfer units in Equation 5 P pressure, mm Hg p partial pressure, mm Hg Pr Prandtl number, Cpu/k, dimensionless R Gas Law Constant, consistent dimensions r radius, ft Re Reynolds number, DpG/u, dimensionless S cross-sectional area of bed, ft2 Sc Schmidt number, /,/DG, dimensionless St Stanton number, h/CpG, dimensionless T absolute temperature, ~R v volume, ft3 W weight, lbM x distance in the direction of transfer, ft finite difference (state 2 minus state 1) fractional void volume or porosity, dimens i onle s s 93 time, minutes latent heat of sublimation, BTU/lb-mol,~ viscosity, lbs/ft-hr ge density, lbs/ft3 (P Gamson shape factor, dimensionless Superscripts P molal units vapor pre ssure

220 Subscripts a air d corrected for "dry run" f final; also film conditions g non-transferring component i initial lm logarithmic me an m mean o zero velocity p pellet s surface t corrected for temperature v transferring component Abbreviations CFM cubic feet per minute lbM pound mass ln natural logarithm, base e log common logarithm, base 10 SCFN standard cubic feet per minute (at 600F and 1 atmosphere) < less than > greater than equal to or greater than approximately equal to

UNIVERSITY OF MICHIGAN 3I1iIll 9011iiiiN11 1115111111111111111 3 9015 02526 2000