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IS 0 i O n'1iC.GES @. P sycho metri C rllt T- iuii-Air-Su er eate d Steamt nego n 7 2. a Ty'pical Dryin-g Curve Total Moisture Sasis b. Typical Drying Curve -Free'oist'ure B'asis 10 3 Drying Rate inT Period I! Th-e -Con stant B-ate Period l3asi s: Conlstant Power Exendi ture 28 4 Dryilng Time in Period I, The Con-stant Rate Period i Bsi s Constant'ower Expenditure 29 53 Mean Dryings Rate in Period ii. The First Falling Rlat- P3eriod- Basis: Constant Power Exp'end ~iture 31 6 Drying Time in Period II, The First Fai1incg fRate Period - asis: Constanit Povier Sxpenditure 32 7 Mean Dr'vin Rate in Period 11, Tl e Second'alling Rate Period - Basis: Constant Power Laxpediture 34 8. Dy 1 ing Time in Period I I T he Second Fa l ing Rate Peri.od -d Basis Constant Pow=er Expea,. itare 35 9. Total Drying Tile - asis' Constant Power Ex.,endit tur e 38 1.0. Eff, ect of Temrerature on iHeat Requirement 43!1 Effect of re ssure on Hea t Requi relent 44.1. 2. Ef.fect of Stock Th''icrkness and Film Coeffic ent on Thle Fac tor /" 49 13, Effect of Power- Conasumption U o Dr yi:ng atc in Constant Rat e Perio - sa.sisi Power aon.sum-i tion of 0.06 Units at (dF/Ad) I = 0. 500 51 14. Rela tivce dToi/dL FPo Dryin as - Basis' Conostant owr Ex.e' iditue T / d - L 0 at Pg 30( T 400 5,7 To 3..

, NIVERSITV OF NIWH11^. AN The relative importance of the various factors involved in the commercial drying of a -porous eid are discussed and related to the cost of the operatio an the quality of the products - A basic mechanism and quantitative theory of ir or super - heated steam yi dryi b irect surface ontact is presented the ssentiai similarity between the two fluids being stressed' Four -periodst of drying re discussed and fundaental quations are developed to describe the flow of heat liquid and vapor phase water, and the equilibrium involved in ea erio. The pre sent utility of tLhese equations is liitd because of te lac of experimental data needed both for the evaluation of coefficients and for the det ermination of the nature of ce relationshi'now, kanown only in functional form~ Experimental data made available Ii the &Suman and Fraser reports are analyzed in the ligit (f the theori de veoped0 These ata-are also used to develop' simplifiet r reI laios which, althouh not ccurately descriptive of the drying opera on are believed sufficiently sound for a preliminary stldy. The simplified equa — tios1 assume tnree periods of drying; a constant rate period, followed by two periods n which the rate decreases linearly with the free moisture content of the stock. A quantitative compari son of the relative merits of humid a.ir and steam aC-s drying media is made. The comparison cover-s air various humidities and steam at variou s pressures, both over a tem1 erature r- ange o.f 3 t5 3 t 0OF he asis chosen bei ontant pow e-'r xenditure. across the stock an Sto c (of i-3/4 inch thich snsss 20 pcf density) being dried from both sides0 The analysis shows the effect of the partial pressure of water vapor (related to the humidity in the case of humid air and equal to the pressure in the case of superheated steam) and drying

1 xIi~ARTI'EN[ F T C >T;INERi\,'i R F1-: AR1'l i i 1 \U 3 ^'^t N ti_. \ E I-t. ~ [. \. {F N...I A i. N.... The restrictions of conistair-t power exenditure an'Id stock thickiness are th'.en partially remov-'I by a further analysis shlowii-ng the effect of these variables I)on t e Cdrying rates0 ThIe more comlplex relationships between power nd tniiciness and the diying times are mentionaed but not elaborated. The influence of partial pressure of water vapor'and dry- ing temp erature upon the follolwing qualiity-dete'irmini g factors is discussed: a Equilibrium moisture content b Drying rate ) Temperature and moisture gradients in the stock d Temperature gradients in the drying gas A final analysis of the composite influe nce of pressure anld temperature upon the cost and quality factors indicates superh-eated steam to e preerabe to ir as a dyin medium, provided good quality is obtaina!ble at temperatures above 40F and in drying times of eight lhours or less, Experimental Cata is desir.ble to substantiate the theory uponl wlich this conclusion is based, ald to determine the effect of operating conditions on th e quality of th'e product.

| fIfi. } 1 I \' } I (. I. I I F (; A \ } H1UMID AIR fiAD SUPLEil^SATED STEi AS DRYIiU MC1Di~ fiOn A11GiD POI)OUb SOLIDS PHOG RESS hEPAIOhI 1MO. 2 I. 1lNTRODUCTION The study reported here has been made for the purposes of developing basic thieory and preparing a preliminary evaluation of the merits of superheated steam as an agent for direct-contact drying of a rigid porous insoluble solid. The agents normally considered for this type of dryingL are moist air or moist flue gases (whose properties approximate those of air). Such a-ents are employed at or near atmospheric pressure. 1n the case oI superheated s-teamu,.ioow-ever, it is reasonable to consider aiso operation at pressure above atmospJheric. The analysis covers, tierefo-e,' a detailed discussion of the basic thieory of drying andl the relative merits of air at various humidities alnd steam at various Lpres ures both over the temperature range of commercial interest. An evaluation of the "merits" of a dryiing agent must be preceded by a decision as to what constitutes merit in sucih a case. In drying, as in most industrial, operations, merit is obvious'y

I f }[1'.PARTM' Ol\1 tl' (_' I\ N:R iNG RF,:'l.\ }:H IS:'i I IX UN\'FRSITY\ OF Mtl("lIA\N 2 associated wit!h low cost of operationr aind high quality of product. The cost referred to is the total drying cost per mu-it of product, which1 in general may be considered to consist of: cc - Interest on capital investmentt, per runit:product cd Insurance, depreciatiol, obsolescence, taxes, etc, ail assumed proportional to the capital invest:entt per tuit product co - Fixed overhead, as lmanageiilent, etc., assumed inldependent of the capital i'lvestmeint per unelit product ci - Direct labor cost, per unlit product Ch - Cost of heat, per unit product C - Cost of electrical energy, per wuit product Costs cc and Cd, the interest and the irsuranlce, depreciation, etc., are proportional to the cost of installation aind inversely proportional to the production capacity. iNow, the production capacity of a given dryer unit is inversely proportional to th-e time required to dry the stock; thus Cc + Cd = kcCcO (I) whlere kc = proportionality factor Cc = total capital iilvestrme t in dryer - dryi, g time hours The variation of the total capital investment (Cc) witlh drying agent and conditions is hardly predictiabie at this t ime. As a first approximiation, ilowever, it may be conisidered that, for inlstallations of tlhe same production capacity and t'ie same degree of refirnement, this cost will be related directly to the operating

I nPARTML\ I F.A(IN[NELRIN(. R FS':. R(' i I I~e < _____r~. i __ f 3____ _, VNT\ I'RSI'1' N 01' Mr f ( HWA \~ N - temrerature and approximately to tV-le a;artiai oressue of thle water vapor* in the drying agent. Thus, C = kc (a + bTg) (d + ePg) (2) where a, D, d and e are'unknown1 constaonts Tg - temperature og( t11e d0ryi.ilg gases gases Labor cost (e) may- be taken, fori inlstaiia tions of the same production capacity and equivalent refinlelient, l as a p)proxximately indep!endent of thle drying time; i.e., cI =' constant Thus tlhe total ulit cost may be represented by C = kiCCc + c1 + co + ch + p ( C = kc (a + bTg)(d + ePg) 0 + cl + co h c + cp (4) an d the cost determining elements which are i influenced by the dryagent and its conditions are Tg, Pg,, ch and cp. Low unit cot is therefore favored by: 3. Sh e ort drying time 4. Loiw heat consumption *The rartial pressure of water vapor, as will be shown'later- deter nines the humidity of th'e air in the case of air crying at atLiospher ic pressure, a-i the total ressu lre in the -case of si erlizeated steam dryi ng. Tihus it serves as a measure oI' conimosition in -tie first instancle and as a measure of operating pnressure in the second. _..,,,,...~., -- ~ —4 L ~ i-.^^^.~~.....,t................... ~ ~ ~.,~~~,.~i o^~

1' I I PARTMN'1 F K GN; i r;.l: \R i {i': __' IVNi\'ERSI':l'Y 01-' M'IH}(.,AN 1.4 5. Lowv electrical energy consumption The influence of the drying agent and its partial pressure, temperature conditions upon product quality is not so readi; - ly visualized. It may bie e.xpected that the important factors in-, fluencing quality will be moisture content of tihe stoc', drying rate, temperature and moisture gradieznts through the stocn, and uniformity of temperature of drying i'as. The real influence and importance of suchi factors must be determined experimentailyo Fr the time being, however, it may be assum-ed that good quality is favored by: 1. iihI moisture content of stock 2. Low drying rate ~3 Low stocx tempera-ture gradients 4 Lovw stocn moisture gradients 5. Low temperatuar gradient of drying' agen't paral le, to its direction of flow These factors favoring low cost of o.peratio-n'and ligi quality of product are therefore of importance in evaluating 1tl-e relative merits of dryi.ng agets and drying condition s, n uade standing of the influence of t}he properti es a.nd the pJartiai pressure, temperatuIre conditions of the dr-ying agent uon, thes "factors of merit" is thle next esseltial step. Tl.s may best be done thirough a study of t.he relationship betw'een humtid air a-nd supe'rheated steam and the> mechanism and basic thleory of th-e drying. oper — a tion?': lt, is oil eved that r"" o....is much,:o? u.a' s.'L"i.iai;:;: i

D T:ARTE'NTr l)' OF INGIllEERINR ES.VRC F| _ UNIV\ERSITYV OF MICI'(IGAN III THE RE&ATiO^3KP N^SS^1_E;Ei HUMID AI Adj.i SUP'i\hAiED, STEAi It is desirable at the outset to clarify: the relationsJip between humid air at atImospheric pr-essure anld su,';,er',heateld stecam Iumlid air con'sSists, in'PlIase ules l -la-uae of G tws-.ocompollenlt systeaizl aand wiater The variance of such a system present at co-nstant atmosipheric pressure in a single phas-e is V = C + 1 - P = 2, whllere Vp - variance of system at con:stalt pressure, C numberl of components, lnd1 P n nutmberl oif phases Or 0 in thle presentce of licuid watrtr wiLere P. 2w Vp - This Llmea that fixing two variablAes, e.g., temprlerature and.C phase collpositionrl com)pl.tely def'ines tile sing le-pohs E system. Similarly, fixing one variable, e.g., temperature deter mines tile two-phase system. Of the- various ways irn whichl plhase coimposit10iol may be represe-rted (i.e., mol i ractionl absolute humidity, etc.) it is expedient here to reprlesen r i t by the partial pressiure of water vaporJ..'lt th;is is a true measure of phase composition. is evident ifro; thie relationr ships (22): moi iraction = ~ (5) and absolute h1umidity - - ) 2 s/i (6) i4,~7 - % k28.9/ / wheLe Pg is th:le partial. pressure of water va, or si. s Thus accord wit-h hth-e plas- irule, teh,'e tlrtwo)-phse water- -air systetm a-~'t - mospheric pr'essure may be represe:lted by a singlle line on a plot of1 partial pressure of iater. vapor ( g) vs. tenlperature (T ). This )~~~~~

line is tlie vapor pressure curve for water, designated later as Pg fE (Tg). Si-milarly, the single phase system may be represented by a family of lines on this same liot, one line for eaclh constant p value of. 7P~ x 100; i.e., one line for each, value of per(g) sat cent relative humidity. On the other hand, superiheated steam is a single-component system, and withlout restriction of constant pressure, exilibits a variance of V = C + 2 - P 2, where V variance of system. n the presence of liquid wacter, or when saturated, P 2 and the variance becomes V =. Thus, t~he phase rule predicts similar descrip tions of superheated steam and atmospheric pressure humid air. Tihe saturated steam system may be represented by a single line on a plot of Pg vs. Tg, and the superheated system by a family of linIes, one for each value of xO ~ 100, on thie same figure. Pg sat. Figure 1 is therefore a two-dimensional repsresentation of humid air at atmospheiric pressure (Pg -< 14.7 psi.abs.) and superheated steam (Pg > 14.7 psi.abs.). The essential continuity between humid air alnd superh1 -eated steam is clearly brought out. it is to be noted that for Pg < 14.7 psi.abs., Pg is th!e partiai a sure of water vapor in tihe air-water system -nder a total pressure of 14.7 psi.abs., and is therefore a measure of composition (mol fraction, humidity, etc.). For Pg 14.7 psi.abs., Pg, although still tle partial pressure of water vapor, is also the total pressure. Thi'e significance of tihe adia'batic saturation iines shown on Figure 1 will be discussed later.

7 200 - --- -- - -— o - - 100: 1:: -',/. -', J'',, -; >_, J313 g _ _ Zii I40 — I 50 1<i —, - -:f -- ~2 - 30 Q 30 I —:- "- I I - ---'^ 5^~-_ 2-L. - Q2 8 ^ * —0;- i2403 ~^ 0 ~ \::- - c_<.7 A I \ --- P: - 97 _- 1SP EA -' i. __7' L50 100 150 200 250 300 350 400 450 500 550 600 DRY BULB TEMPERATURE, T9. F_ 50 100 150 200 250 0 35 4.6*PL ~ D B T so ~- e'i Z ~_,5T';I.4 airP

___E___ _ _____LNI\VKRSITY OF MICHIGAN _ 8 III. BASIC MECHANIAi MiD TIHSORY Thie type of drying under consideration is that of a rigid, porous, insoluble solid by direct exposure to a gaseous imediiun w!hlich is unsaturated with. respect to water vapor. il-l heat for vapjorization, heating of stock, etc. is supplied directly fromi the eas wiich is assumed to flow parallel to the surface of the stoci in turbulent motion and at constarlt velocity, temperature, and partial pressure f water vapor. The literature related to this general problem is fairly extensive, although none too revealing. Most of the publis.hed work falls into the following categories: 1. Experimental drying rate data for specific materials; mostly in the form of instantaneous rate of drying per unit of exposed surface as a graphical function of tie instantaneous moisture content and tle conditions of drying (3)(9) (14) 2. Empirical equations based directly upoln experimental data expressing, for specific materials, drying rates in terms of the more imJortant variables (3) (14) (18) (19). 3. Studies of the mechanism of dryiing (3) (6)(5) (10)(19). 4. General articles dealing with methods of operation, practical considerations, etc. (2) (21) (5) Information from tlle first and third categories has proved ost helpful in developing t tlle following pictures of the mecl hanis of drying for the particular oroblem at'and. It is now well estacblished (3) (6) (22) that under constant drying conditions (i.e., constarnt temperature, water vapor pressure, and flow velocity) several distinct periods of dryilng are observed as th-,e moisture content of a solid is reduced from a high initial to a lwt.i f:.aL value,'r-se -pri:ods ar:e beset distirnbuis hed?l"',:ough: a -

I [')DIEitARTMENI- OF (..INf', I RIN(T RESlA.R R\I t ___________ ___________________I___________________ 9 study of a t-ypical dryin- curve. Figure 2a is such a curve, representing thle instantanieous rate of drying per unlit of exposed surface as a function of tzhe instantLeous moisture content. In tis figure: W O initial wvater conitent, pounds of water per pound of' dry. st ock | = - water conitent at beginninga of Period 1, lb/lb WV2 water con!tent at beginning of Period I, lb/lb W3 -= water conitent at begiining of Period III, lb/lb \H4 = final water content, lb/ib W =; water content corr eso olcdin, to zero dryini ratre. Ro, etc. instantaneous drying rates, ibs/ft2-r a corres pondinll water contents It is to be noted tlhat the drying operation divide's itsel naturally into four periods as follows: Period 1~: An initial stage whleein thle dryirng rate may increase (or decrease) rapidly from R0 (or R0 ) to RL R2. This period is usually short and,,may be Lunobserved. Period I: An early stage during whicht thle drying rate remains substantially constant. Period II: A stage immediately following Period I during which the drying rate decreases, more or less unii ormly, with continued decrease iin wiater content. Period 1II: A stage immediately following Period II, but not always clearly distingluishled from it, during wlichl the drying rate decreases, also ap.proximatly linzearly with the moisture content but in general at a different rate than in Period IIe

10 R I, 0~ 4 FIGURE 2Wa.. 3S 0|1 11 11 11 l0Wtt llttig T Y P I CAL D RYING CURVE 3 tL: lliliillll * <TOTAL MOISTURE BASIS i — R4 g- R 3 W E W4 WF W2 WI Wo TOTAL MOISTURE CONTENT, W, LBS. PER LB. r WRI,R2 cn i I T I. R a- IL IIFIGURE R R b.. Rs TYPICAL DRYIING CURVE I IL I #######~-~####~FREE MOISTURE BASIS aR1 I I a I a I L A I I W. sOVII*R o F4 Ft F, Fo

}!EPARTMENT OF EN CGI IN E( R S NGEK ARC( Pa' T___ __ ____UNI\VERSqITY OF ITICA HI(A N I On1 prolonged drying, Period III is terminated at W5, where the drying rate becomes equal to zero. W5 is.3lor as the equilibrium moisture contenit of hie material (22), designated as E, and represents the minimum moisture content attainab.le under the co:iditions of drying. This equilibrium moisture content is determined by the nature of the stock being dried, the ttempe-n rat-ure of the drying gases, and thi.e partial pressure of water vapor in the drying gases; i.e., E - f (stoc, T, Pg) (7) ThIe nature of this relationship, even for a given stock is coi,-)mlex and must be determined experimenttally, but it is i-:noVnrl generally that E decreases rapidly with increasing Tg and inlcreases with increasing Pg (22). The difficulties associated with th-e eval uation of E may be circumvented to some extent through the definition of F - W E where F is the so-called free water conteLnt of the stock in lbs/lb. This means, of course, that for a given total moisture content W, the free moisture content F will depend upon the factors controlling E. Usually, however, E is small compared with W, so that the variation of free moisture content with Pg a adt constant total moisture content is reasonably small. It shou-d be noted that at given conditions of pressure (Pg) and temperature (Tg) anid with a given stock, E = constant and dF - da-ryi.ng rate, lbs/ft2hr Figure 2b shows the drying rate curve of Figure 2a reported in term' __ ~~" "" "~~~"" """~~I~~ _,__,__. _ —-'. —~ —-I —-- -- --

EPA\ RTI''MENT F ENGINEERItNG RESI ARC C TVI l\RSl OF'(F MXIUfIGA N 12 of F, the free water content. Further discussion of drying rates will b based upon free water contents. The mechanismi of drying and the descriptive mathIematical relations are different in each of the different periods. In the following discussion of these factors, it is convenrielt, tlerefore, to consider each period separately. Period 1I - initial Period: This is essentially a period of uisteady state operation during which conditions are adjusting themselves to the steady start represented by Period I. Assuming that the stock is initially cold, i.e., below the adiabatic saturation temperature of the gas, the mecl-hanism is believed to be as follows (22). Heat is transferred to the cool wet surface of the stock from the hot gases. This heat supplies preheat and latent heat of evaporation to vaporizing water and also serves to increase the surface (and the average) temperature of the stock. Simultaneously evaporation is taking place at a rate controlled by the instantaneous difference in vapor pressure of water at the surface and in the drying gases. As this situation continues the surface temperature increase causes a corresponding increase in the rate of evaporation and a decrease in tlhe rate of heat supply. After a short time the decreased heat, supply just balances the increased heat requirement for evaporation and conditions become steady. Thlis is the end of the initial period. ~See Period I.

I EPARTMENT OF ENGINEERING RESE: \.ARCH Pae UNI VERSITY OF MICHIGAN ___ With the stock initially hot, i.e., above the adiabatic saturation temperature of the gas, the mechanism is similar but the latent heat requirement exceeds the heat supply from the gas, causing a decrease in the surface (and the average stock) temperatures, ultimately to the same steady state. Under special conditions where the initial temperature of the stock is at the adiabatic saturation point, no initial period is observed. The important physical phenomena of this period are: 1. Heat transfer from the drying gas to the stock surface. 2. Heat transfer from the stock surface to its interior. 3. Transfer of water vapor from the stock surface into the drying gas. 4. Thermal and pressure equilibrium established at the~ drying interface. The mathematical relationships describing, these phenomena and the balance of heat energy are presented and discussed in the Appelndix. Period I - Constant Rate Period: This period, which starts at the free moisture content F1 and ends at F2, is characterized by a uniform rate of drying and constancy of surface and interior temperatures. It is the steady state reached at the end of Period 1~. The period continues so long as water is supplied to the surface as rapidly as evaporation can take place (22). Up until this point, no reference has been made to the mechanism of water transfer from the stock interior. During Period I~ this mechanism is of little importance, since it has no significant effect upon

{ lI-1)FPARt't'NIEN'' OF ENG[NEER!NG RESI:ARCH j _____1________NiVERLs' OF MICHIGAN ______________ the drying rate or other factors. In Period I, however, the mechan ism of water transfer from the stock interior is important, since it determines the duration of the period (3)(6) It is now believed established tlhat in t-he drying of porous, insoluble solids, the mechanism of liquid water transfer from the interior to the surface is by capillary action (3)(6) (22). T'he origin of the capillary forces is discussed by Comings and Sherwood (6) and again by Ceaglske aild Hougen (3). It is assumed that surface menisci of small radii exert sufficient capillary pull to draw water through intricate interior passages endi-ng in gas-water iiterl faces of larger radii. To quote directly from Comings and Sherwood (6): "The water drawn to the surface is necessarily replaced by air which enters the solid through the larger passages connected with the larger openings at the surface. because of the complicated interconnecting passages beneath the surface, it is possible for the necessary air to enter;tirough a relatively few surface openings and thus for tIhe moisture concentration near tihe surface to remain relatively high.. The water will continue to rise to the surface thlroughl any system of interconnecting passages until all of the various menisci at thle lower ends of th-le water column have the same radius of curvature as the small menisci at the.surface from which evaporation is taking place. When this stage is reached a small amount of evaporation from the surface rmienisci may result in a retreat of these surface menisci into passages of smaller cross section, andc the increased capillary tension is sufficient to draw additional water -to t-he surface. It is possible, -in fact, for the increased te-nsion caused by this retreat of the: surface rmenisci to draw some of t-he menisci atC the lower ends of the water column tihrough the naIrrow constrictions into larger cavities and tlhus reduce the tension necessary to cause- movement toward the surface. The menisci in thle passages at t he surface caln then rise to the former position aiid' the i)rocess can continue. "As the drying process proceeds, a time will be reached when the men-isci, at the lower ends of the water column in any system of interconinecting passages, are, in general' about the same size as t.le small.iest cross section of

1-4 I:- PARTMElSTN'T' (NIOF EIN( RING RF:S.\AR(H' l UNIVERSITYx OF MICHIAAN 15 the surface openings, and water will not longer be drawn to the surface through these passages." Continued evaporation then resuits in the depletion of the surface moisture, a decrease in drying rate, aid the ena of Period I. The important physical phenomena of Period I are: 1. Heat transfer from the drying gas to the stock surface. 2. Transfer of liquid water from the stocz interior to its surface. 3. Transfer of water vapor from tie stoc'i surface into the drying gas. 4. Thermal and pressure equilibritu established at thle drying interface. The mathematical equations describing these processes, and tlhe balances of heat energy and water, are presented and discussed in the Appendix. It is also pointed out in the Appendix that F2, the first critical moisture content, depends upon tlhe nature of the stock, the drying rate in Period I, and the stock thick-iess. This may be expressed functionally by the relationship: F2 = f2 (stock, A XO) (22) Ad' x)(22) It is important to note that this critical moisture content is not a "property" of the stock being dried, but that it is dependent als upon the drying rate and thle stock thiiicknress. Tl.he constant surface temperature obtainled during this period is shown (Appendix) to be equivalent to the wet bulb temperature in the case of humid air and to tihe saturation temperature in tlhe

DPARTMENT I' OF ENGINEERL CNG RESi.ARCH I_______.ES__rTY_ (O)F MI,,rCHIGAN 16 case of superiheated steaml. Since inr the case of rumid air the wet bulb temperature is approximately equal to the adiabatic saturation temperature (22), it is convenient to refer to thie constant surface temperature as the adiabatic saturation temperature without distinction between huaid air and superhieated steam. Period II The First Falling Rate Period: This period starts at the free moisture content F2 aind ends at F3. It is characterized by a decreasing rate of evaporatior |which results from the spot-wise recession of the evaporation surface into the first layers of the stock, with the consequent exposure of small radii of curvature (6). The momenltarily undimiinisied heat supply causes an increase in the temperature at the recdedd zone of evaporation. This temperature approaches a clhangiing equilibrium value determined primarily by the radii of curvature of the menisci slightly below the surface. As drying proceeds, the fractional area accounted for by the receded water menisci increases to unity and the fraction of "wetted surface" decreases to zero. At this time all evaporation becomes subsurface and Period II ends. The important physical phenomena of this period are: 1. Heat transfer from the drying gases to the stock surface. 2. Heat transfer from the stock surface to its interior. 3. Transfer of liquid water from the stock interior to its surface. 4. Transfer of water vapor from the stock surface into the drying gas. 5. Thermal and pressure equilibrium established at the drying interface at the sto;ck surface.

DEPARTMENT OF ENGINEERING RESEARCH i __UNIVEIRSITy OF MICHIGAIN _ 17 6. Thermal and pressure equilibrium established at tie drying interface at the receded menisci. The mathematicai expressions describing these phenomena and the ieat and water balances are given and discussed in the Appendix. It is of interest to note here that the second critical moisture content, like the first, is not a "property" of the stock but is dependent also upon drying rate and stock thickness; i.e., F3 = f3 (stock, - X) (35) Period II - The Second Falling RBate: Period: The second falling rate period starts at F3 hen capillary flow to the surface has ceased (3) (6)0 and continues, uider prolonged time, to F 0 when tihe stock is at its equilibrium moisture content E. Tis period is characterized throughout by subsurface evaporation from a continuously recedinig planeo aiid by the necessity for the heat for evaporation to penetrate increasingthicikness of partially-dried stock. The surface of tie stock approaches, but does not reach, the temperature of tile drying gases, Tg. The temperature at the receding plane of evaporation approache a changing equilibrium value determined primarily by the radii of the exposed menisci. The important physical phenomena of this period may be summarized as follows: 1. Heat transfer from the drying gas through the surface "film" and thle partially-dried stock to the receded zone of evaporationi. 2, Transfer of water vapor from the receded plane of evaporation through the partially-dried stock and the surface "film" into the drying gas.

)PE'ARTNI EN OF N (-; INERI N RlS E''H I''-' UN__\'f.__ISI_'_TI () Illi-TVI(;S AN 18 3. Thermal and pressure equilibriuiE at the receded drying interface. The mathemtiatical relations describing these phienomena and the heat balance are presented and discussed in the Appendix. Over-all Process: The over-all drying process may include all periods or only parts of one or more, depending upon thle initial and final moisture contents. A complete understanding of the pro)ces; is b2st obtained in terms of the equations in the Appendix (or their counterparts) for the periods involved. Tihese equations are useful ill clarifying the mecllanism of the operation and in bringing to the fore those factors of importance in any, experimental study which is undertaken. Moreover, they suggest the proper way in whiichl the experimental variables should be correlated. As an imm-ediate practical latter, however, tle direct use of these particulary equations is difficult. T'iis is because many of tlhem are at present known only in functional form and because of the limited knowile.dge of important properties and coefficients.

DI:PARTMENT OF E:NGI;NEER.LNG'C RES;.\R'Hi PI: NV_____IT_____ OF MfCHI(.,X __ _ 19 IV. APPRi)OXIMiATSi PHACTICA l. RE'iATOI S TTle basic theory previously discussed is mlatiheLatically complex anld impossible of direct quantitative application in the light of the present limited knowled"ge of thei natare of certain relations and tle lack of experimental d ata. Data made availb le in the Shuman (20) and Praser (7) reports have been studied carefully with a view toward the simplification aind modification of the basic theory into a tool of immediate practical utility. It has been possible to develop a set of "practical" relations which, alth9oulLh r l n and a roximate at best, should serve to permit an intelligent comparison of air and superheated steam as drying media. The equations for the various periods of drying follow. General: E = f(stock, Pg, Tg): insufficient data are available to permit any reasonable estimate of the effect of Pg and Tg upon E, although for tlhe tests reported, E is close to and may be assume equal to zero. F = W - E - W for tthe tests re oted. where E = equilibrium moisture content, lb/lb F = free moisture content, lb/lb Pg = partial pressure of water vapor in the drying gases psi.abs. Tg - temperature of the drying gasesg F

DEPARTMENT OF ENGINEERING(; RESARC XR( ~ T____UNIVRSITY1 OF MICHIG(AN ______ 20 W total moisture content, lb/lb! Period I~: Tliis period is unobserved a id ay be neglected, Period I: F1 = 2.20 lb/lb F2 0.95 + 2Xo + 0.50RI ib/ib (42) R1i -- l (j g - s ) tb/ft2lhr (43) where F1 initial moisture content, ib/lb F2 = first critical moisture content, lb/lb X = thiClOle ss of stock drying from one side, ft oiie-hlalf thicikness of stoc drying from both sides, ft R1 = R2 = F) ( rate of drying in the constant I rate per iodc, lbs/ft2hr Ts = adiabatic sa-turation temperature of dry-in gases, OF (See Figure 1) I = latent heat of water, BTU/lb, aLt T h film coefficient of heat transfer for combined conduction and conivection, BTU/ft2hrOF Period II: The relationship between drying rate, dF, and free ilois ture content, F, may be assumed linear within this period.

DEPARTMENT OF EN(-,iNEERIGRESEAC PaRS..... UNIVERSITV OF MICHIGAN 21 F2 = 0.95 + 2Xo + 0.50R2 lb/lb (42) F3 F2 0.59 F2 lb/lb 1.70 R2, T (Tg - Ts) lb/ft2hr (43) R3 (Tg ^ sr) lb/ft2hr (45) -s XT Tr= L (P+ AP) ~F (46) s,r f g r where F3 = second critical moisture content, lb/lb R3 - (Ad= = rate of drying at P3, ib/ft2hr APr vapor pressure depression due to curvature of exposed menisci, psi.abs. -f denotes equilibrium relationship Ts" = temperature of surface at F3, F Period III: dFThe relationship between drying rate, d, and' free iioisture content, F, may be assumed linear withini this period d6n to values of F of the order of 0.10. F3.59 F2 lb/lb F4 = 0.10 lb/lb ___________ 4 ______________________________________________

DTPARTIMlEN'X OF F(;N:;INERING, RESEA R ~~~~_____~~~~j___ _______VUNI'VERSnIT' OF MICH[IGAN 2 22A B3 hC (T - tt) lb/f t211r (45) H - -~.x,(Tg - T) ib/ lb/ftt2r (47) where F = final moisture content, arbitrarily assumed - O.i.10 b/ b assumed cose to F4 0.1 lbst T average termal conducivit of t stoc it X fE g fequilibri mo t isture c onten t arbitrariy assumed o.io lb/lb /'dF F = rate of dryying,- at F- =wh.ic- i s assumed close to F4 = 0.!0,~ bs/ft2hr KE = average thermal conductivity oi' the stockr~, at its equilb1 riumi ioisture conLtent, BTU/rt h1rOF These equations embody a large number of assuimptions and must therefore be used with extreme caution. They represent satisfactorily the bulk of tieof present,xperimental data, but may be in error when applied to other conditions. They are not iapplicable to stock densities other than 20 pcf, althoughl similar equatiolls may be expected to hold for oth-er densities. It is believed that these "practical" relations are sufficiently sound for use in a study of the relative merits of different drying media and conditions of operation,.

TFi.PARTI'ENT O (F EN(.;tNE:NoS.AR P HKf.ItT UtNIV~ERSITY OF MICHITAN. 1 23 V. EFFECT OF TSi2M iLATUl P.ESJL" i4I i'U.IJ OF. DRYI LG ii fiEDIUJi O COST |DEr in. l T IAl, ING FACTO S As was discussed earlier, the relative merits of humid air and superheated steami as drying media depend upon thlose factors which influence tihe ultimate cost and quality of the.iroduct. Since the factors influencing cost are subject to a more quantitative treatment, they will be analyzed first. It will be recalled thlat the cost-determiIingll elements which are iinfluenced by the drying agent and its conditions are: Temperature (T,), Partial Pressure of Water Vapor (Pg), Drying Time (0), Cost of ieat (cl), and Cost of Electrical Elergy (c). The first two factors, Temperature anld Pressure, not only have their ownv direct influence on cost, but also exert an indirect effect through the remaining items of Time, Heat, anrd Electrica.' Energy. It therefore seems advisable to selecTemperature and Pressure as the independent variables aind to determine the effect of tles'e factors on Time, Heat and ilectrical Energy. Now in a study of this sort, it is inecessary to select some1 common basis for comparison; i.e., if drying times are to be compared at two different temperatures, it is necessary that the values of the other important variables be nimown, and preferably, that they be thie same for each case, in order that the effect of temp)erature alone upon drying time is determined. For this analysis the following conditio'ns are chiosen to defilne thle constant basis of the comparison:

I).EPARTMIENT OF ENG[NEERINXG RESI,.-I,(RI |: - jI____L_ UNIVERSITV OF MICHIGAN 24,1 Stock density: 20 lbs/ft3 2. Stock to be dried from both sides 3. Stock thickness: 1-3/4 in 4. Constant temperature of drying gases throughout all periods of the drying process 5. Constant partial pressure o~" water vapor in the drying gases throughout all periods of the drying process 6. Constant expenditure of power for circulation of the drying gases. This power expenditure is assumed constant, not only throughout all periods of drying, but in aii conditions wuder consideration.* 7. Drying gases flowing in turbulent motion On this basis, then, the influence of the temperature of the drying gases and the partial pressure of water vapor will be determined for the drying time, tie total heat consumlption, and the total electrical energy consumptioln. An analysis of the influence of change in stoc. tilici-iess and power expenditure is then presented, in order, partially, to remove the restrictions imposed by the arbitrarily-selected basis for comparison. *The power expenditure over the drying surface is arbitrarily taizen as that required to realize a film coefficient of theat transfer, for steam at 30 psi.abs. and 400~F, of hc = 3.15 BTU/ft2hroF. With steam at these conditions, this coefficient corresponds with a lineal velocity of approximately 550 fpm and a rate of drying in the constant rate period of 0.500 lbs/ft2hr. The actual value of the power requirement, per unit of drying surface, is dependent upon spatial arrangement, surface roughness, and other factors not considered in this report; its order of magnitude, however, is 0.06 watts per square foot.

I -I) D ^EPARTINIFNT OF ENG(INEER1N( RES,-\Rf(1 LNINVERSIT\ OF MICHTlAN _ 25 The Drying Time: The influence of temperatulre,.T., alnd pressure, Pg, Uponl the dryinlg time is of course complicated by the severaL periods of drying. A detailed analysis of this problem hlas been carried out, based upon the equations of the previous sectioil. Tliis analysis involves, as a preliminary step, the expression of the film coefficient for heat transfer, hc, in terms of the power expenditure per unit of drying surface and the properties of thle drying medium. The metiod of Parsons and Gaffney (17) was used in order to arrive at thle equation: h B0t Es286 (49) where B constant depending upon widti a dn spacinrg oi the stock c0.4 k 0.6o0.571 0t -,L thie Parsols and Gaifney (17) /0-457 ft functionli dependent upoi fluid properties C specific heat of drying gas, BTU/lb0F kg. tlhermal conductivity of drying gas, BTU/ft lr~F P = density of drying gas, ibs/ft3 = - viscosity of drying gas, lbs/ft hr E = power expenditure per utit drying surface, ft lbs/ hr ft2 With Esthen chiosen as a constalnt (and equal to tlie value necess&ary to realize an hc of 3.15 BTU/ft21ir~F with steam at 30.0 psi.abs. anld 400F), the influence of temperature, Tg, anid prssure, Pg, upo::. t': e dryi.lg r-.ae, and- dr: iC.lng{ time may'be de-3termi,-tned wi.+-tlh tih. a. i

DEPARTMEN'T OF 1ENGTfNEERIXG_ RESEARCH C^ H ___ UNIV^ERSITY OF' ICHIA 26 of the practical equations of the previous section. Period I - Constant Rate: The results of the calculations for this period are summarized in Figures 3 and 4. Figure 3 shows the net influence of temperature, T, and partial pressure of water vapor, Pg, upon the drying rate in this period. The following points are to be noted: 1. There is a continuous graduation in effect ranging from humid air (Pg = 1.5, 3.0 and 6.0) to superheated steam (Pg = 14.7, 30, 60 and 125). 2. At temperatures below about 3750F, the use of humid air results in hiigher rates, whereas above about 400F' the use of superheated steam gives higher rates. 3. The effect of temperature upon drying rate is more marked at the higher P values and is particularly marked inL tihe superheated steam region when Pg is greater than 30 psi. abs. 4. In the case of superheated steam there is a reversal in the effect of pressure at temperatures in the general neighborhood of 3500F. At the lower temperatures, increase in pressure results in a decrease in drying rate; whereas, at tthe higher temperature levels, increase in pressure results in an increase in drying rate. Figure 4 shows the effect oi temperature, Tg, and pressure Pg, upon the drying time in Period I. This reflects the influence of Tg and Pg upon bothi the drying rate (as in Figure 3) and tile first critical moisture content. T'he curves indicate several interesting features: 1. At 300~F humid air results in decidedly shorter dryiLng times than superheated steam; at 400F superheated steam is slightly superior; at 500F superheated steam is markedly superior. 2. At each temperature, t!he drying time increases sharply as the pressure is increased to a point approaching the adiabatic saturation value. Actually these times

I F.PA'1\ 1' i ENGINEEIlNG RESIR.\R.V El I' I'P i;Ni\IK1RSl'[LY ()01 F' I CHIGAN 27 become infinite at P- 67 )si.abs. for Tgo 3000F, P 2247 psi abs. fio T' 400F, and P 681 psi. sos. for T, 5000F, 3. A point of inf.l ecction (a maxiim- um) exists at each temperature at a P.. value of 14.7 psi ab) This reflects a slight tdiscontinu'lity iii thie chiiaiige of physicatL properties tlhrough hrumid air to su:erheated st eam. A secotin poinlt of iinfiectioin (a miminum) exists at each tem;;perature at pressures beyo-nd 147 jsi abis This point indicates, at each temp ra ti re ssure correspondiiig, withi t' i slhortst dr yin time in tile superhea sted am regio. Thsoe press ures may be considered the optimum values at t:e crs,)onding temp eratare s. T he- dtotted linei r eflects t.e t;renid of these o timrnui pressures toward higlier valu-s at higher temperatures. I MfY.XyE..................................s0~.... kWXbo~t L5;e~>/.................... ~,~f:^ffC

DRYING RATE, dF/AdG, LBS. PER HR. SQ. FT. _~ ~ ~o o o o o o o o o o o o o) N " ~_~~L.'__-"_L:::::!t 1 tt < -fr yt:' rt 0 Ijf 0OD 0 0 Da < o |~~~~~~~f TsL 7X wo Co ~~~~~~~~~~~~~~~~~~~~T t.................."t i ~" (7,~~~~~~M~...~~~~~~~~~~~~~~~~7:i.'7....,... ~.:; ~.....~y ]'[~ ~ ~ ~ ~ ~ ~~I t;.....;.........::i:~......... I~0:ill~~~~~~~~~~~~~~~~~~~~~~~~~~T't;.......i:........'.;.::!1 -' 0.i~t~ ~l..... z rn~-'tl::~ ltIltI:i o 0:: t ~,, f i l i: f l Itih I ft[;t f l' 4::l~: t t:::it:If~~~~~~~~filet []:':ttH:'111ilt it["~ ~ ~ ~ ~~~i o.,tt,,t,H,,!t~~~~~~~~~~~~~~~~~~t~~l,,Hltt,lI,,,,, ~ ~ ~ ~ ~ ~ ~ ~ ~ ~....... o~~~~~~~~~~~~~7...

14 13 t FIGURE 4 4l~itiiiiiil r ~ii1~ DRYING TIME IN PERIOD I, THE'CONSTANT RATeE PERIOD BASIS: CONSTANT POWER EXPENDITURE f 7p ------- i1i i I10 TI II.. -~ ~ ~ ~~~~ 111jiI 10 1 I i i;: 1 i i i iii~UGUST 194 II 2 3 4 6 8 10 _ 2 3 6 PARTIAL PRESSUREOF WATRVPOI PIII I IPSI ABS.I j i1/ i iI ii ij; i;:I: i; 6 // ( cr.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~i i;illiiiiiiIIi I' 5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~j I i j i i /Ijir ij/! D:~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. w il! iI::I Ii I U

DEPA~RTMEN\"T' OF EXNGlNEERiNG RtE1Si^tAR~'iARf _______________________ DIAR[NIEI (_ DG1NELRI NC RlPA.R -- P__ U. NIxVERSIT\' OF' NVfHIGAN_ 3~ Period II- First FalingRa t' le calculations for this period may De summarized by Figures 5 and 6, sihowing the effect of temperature, Tg, a;id pressure, Pg, upon tlle dryilng rates and times, respectively. Since the drying rate in Period II decreases constantly throughout the period, the logarithmic mean rate* for the period is lotted in Figure 5. The general trend o' this m.ean rate with change in Tg and Pg is seen to be similar to that of Period I, althought the rates are of course much smaller. The extreme importance f temperature and the reversal in the effect of pressure are again evident. Figure 6 indicates the influence of temperature, Tg, and ressure, Pg, upon drying time; the effect upon both drying rate (as in Figure 5) and first and second critical moisture contents being considered. Features similar to those of Figure 4 are exhibited: the superiority of humid air at low temperatures, the rapid increase in drying time as the pressure is increaLsed to the equilibrium alue, and the two points of inflection. As in Figure 4 the dotted line indicates the trend of the optimumL pressure toward higher values at higher temperatures. It may be shown that this is the proper mean when the rate is linear with F. **This value is less than the adiabatic saturationl value by the amount of the depression due to thie curvature of.the menisci.

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I DEPARTMENT OF rENGINEERING RESEARCH Pn. ~ UNIVERSITY)c OF MICHIGAN _ 33 Period III - Second Falling Rate: Figures 7 and 8 summarize the calculations of drying rate and time in Period III. Figure 7, which shows tlhe effect of temperature, Tg, aind |pressure, Pg, upon t'he logarithlmic mean drying rate, shows features similar to those of the two previous periods, although again at lower rates. The effect of partial pressure of water vapor, Pg., in the h-umid air range is seen to be of some importance at teimperatures below 400F, but of little above. Figure 8 indicates the net effect of Tg and Pg upon the time required for tlhe removal of all the water from the second critical moisture content, F3, down to F 0.10 lbs/lb. The tremendous influence of temperature,?articularly between 30u and 4u00 F, is immediately apparent. A shift in optimum Pg similar to that of the previous periods is evident, although) less pronounaced. It should be noted at this point that since W F+ E F + f (Pg, Tg) the reductionl of te water content to F - 0.10 does not mean to an absolute water content of 0.10 Ibs/lb, but to ti.is Tus the prevailing equilibrium moisture.

LL~~~~~~~~~~~~~~3 C,) U. w PC) ui ~~~~IG UREf 7 _o MEAN DRYING RATE IN PERIOD T 8 THE SECOND FALLING RATE PERIOD Q) ~~BASIS: CONSTANT POWER EXPENDITURE.6 cx~~~~~~~~~~~~~~~~~~~~c z z 4 w H 0.3 cr.2.1 0. C) ~ ~ ~ R BUL TEMERAURE Tg, *

.14. i ~~~13.,,,,: I:~~~ ~35 _10 _' *.:'^,,: ~:........... [! ~.:..', _:.-. — I~ ---: ~ —t'..i.....i-..... ______ 0 I ~I111. iDRYING TIME IN PERIOD, I8 e | _ —- - THE SECOND FALLING RATE PERIOD _^~... | -. ~......| | -,; BASIS: CONSTANT POWER EXPENDITURE 2 7 _ ___ __. ___^t X vT~t -1- U ^ -JL- - -^ -1"-;... - - ~:....:-.........................:............ I ~ ~ ~ ~t-~: ~ -~ - ~ - ~ 4 X-;~ ~:: -:- ~: ~: i- \ / ~ - - / 5' ~\~ ~~~.................1~i::'i!:!':.::::i:: i i!..........1... -... PART..A...::::.: L....; FIGURE 8 *,...~......................BASIS: CONSTANT POWE~ EXPENDITURE IL1 _..... I \. /: T =00 ~. -..- - ~..-.............. -.. \.. ~' ~~ -~~~l~~~~~~~ ~~~~ ~~-~~ - ~~~~ GEO. W. GOVIER 1__ __.,L__~-_~__ _________ __!~: i.!. AUGUST, 1947 2 3 4 6 810 20 3040 6080100 200 300400 PARTIAL PRESSURE OF WATER VAPOR, Pg, PSI. ABS.

I ); PART'IME'T F01' EX(GINEERINXG RESEARCH. I______NIVE'RS1TV OF MICHIIGAN. 36 Total Drying Time: The influence of temperature, Tg, ald partial ores sure of water vapor, P, upon the total time required for drying is of course the factor of most interest. Figure 9 lsn ows ts relatioship in full detail. Below the critical partial pressure values at which the dryingl tiies increase asymptotically to infinity, temperature is the important variable and particularly so in the region 3uO-400~F. At temperatures o 350~F and }less, l humid air offers shlor-ter dryinLl tini;es t:haii does supeIrheated steam. Above 400~F superheated steau is to be favored, especially in the optimum partial pressure range. This is con-sidered to be that range of P in whicl ti:e drying time is within five per cent of the minimum., T1lhez situcationt is summiarized in Table I. The-, Total lHeat Conswm;l;tion: The cost of heat consumed in the drying operation is of cours directly proportional to quatia ty of heat used, ad dependelnt also upon the temperature level at which the heat is required. The quantity of heat required for the evaporation of one pound of water" has been determined under the full range of conditions of temperature (Tg) and pres:ure (P). In the case of humid air drying (Pg < 14.7 psi.abs. ) the important factors determiniing the heat requirement are: I, T'he weig t of equipment per poundt of dry stock, and its specific heat *This is s the} amiouit of heat required for t-ihe drying of one poulcd of' bone dry stock divided by 2.10, the pounlds of water removed per pound of stock.

TALLE I SUMMARY - EF~LC0 OF TilJLLAThuLL &Ig) UPO2 PAki P 21 iiUK 0F VAL VA O\ (Pg) CO <iUL lBIiIG WI>lI MKI 1L TO Is DOT AL DYI~Tj TIlME Temperature Optimum Pressure Drying Time Optimum Drying iiedium and (Tg) (- F (P9g)op t. psi.abs. (9) - irs. Partial Pressure Range 1 300 Below 2 20.0 H umid air up to P 33 325 i About 2 153.4 Humid air up to Pg =.8 350 I About 2 141 Humid air up to P = 4.7 About/ 2t i5.4~Humid air up to Pg = 5.3 375 35 10.5 Steam rom Pg 23 to P 30 400 48 8.,4 Steam from P 28 to Pg 86 4 50 100 5.3 Steam from Pg = 46 to Pg 90 (?) 500 150 (?) 3.9 Steam from P. 82 to Pg 250 (?) I ^ ^~~~~~~~~~~~~~

28 11,~~~~~~ Ml "II ljjl ~ ~ ~ ~ 111 1: Il 28~~~~~~.........:I i*' i~ i ii'!. ii...i'i /'!..... ft/i If~ 1,~ ~ ~ ~i;~ i'i;~ i i... i~ i, ii i i' I 1!~i... 26 4 i::I I i:ii!i:i i 2 2 1:i 1i:', i2 I! ~ T 20 -,,, m,~~~~~~~~~~~~~~~~~~~~~~j Ob I H/1 Ii I 16 IM 11j I i 1 2~1 i u~~~~~~~~~~~~~~~~~~~~i ~ ~ ~ ~ ~ ~ ~ ~ i X i II!$, I 0~ I il! i i!ii, 2- I0.- 0 0.~ ~,! ~.... I IIT r1 ri i i jI -— i!L IL FIGURE 9II4 TOTAL DRYING TIME' Ii.. W... T7 Ii1 i, Ii l I I I Ft [ 11 I fl 111 ~ll~ IUGUST1 I 47I 0~~~~ I 2 $ 4 6 8:'' I0 20 300 0 000 20 ~9 PART I A PRSUEOFWTRVAOP I i i Ii I ii i P S. ABS

DEPARTMENT OF ENGINEERING RESEARCiH Pag. UNI\.ERSIT ()OF ICHIGAN 39_ 2. The specific heat of the dry stock 3. The temperature of the drying gases (Tg) 4. Thle average rate of fresh air supply, m, (lbs dry air)/ (lb stock) (hr) 5. The supply air temperature and relative humidity (taken arbitrarily as 700F and 65%,) 6. The drying time, 9 7. The exposed heat-dissipating surface of the equipment in ft2/lb of dry stock Item 4 of this list may be shomn to be related to the partial pressure of water vapor (Pg) ad the drying time () throuh the equation: 0Zo8O 0.715 2^10 + 2H Q 80 1 0.715 _ 029 (b -80 o0.715 2. zo + + H' + (5 where P H = 1 g. (1 6) = humidity of drying gas, 14.7 Pg 28.97/ lb/lb (6) ~^ - ^g lb/lb (6) ~, = density of humid air, lbs/ft3 = ddrying time, hlrs It is possible to estimate Items 1 and 7, and then to coLi bine the several items of heat consumption to give the total heat requirement per pound of dry stock as: 2.10 (ZQ) = 30 + (.058 +.260m) (Tg - 70) 0 (51) + 2.32 (Tg - 350) + 2.10 XT BTU/lb stock g

i.i TP.I'l\ITMET O i:f E:;NGiINEELING RESEARCH Pae U 1,N lII\'ET,RSrIT' OF MNItCHIGGAN 4o and 11 he -at requirement per -pound of water evaporated as: zQ = 14.3 + ('. 276 +.124m) (T; - 70) 9 (52) + 1.105 (Tg - 350) + As BTU/lb water Figure 10 is a plot silowing the influence of temperature (Tg) and pressure (Pg) upon the heat consumption. The importance of Pg, being a factor in detrmiining m, is particularly to be roted. In the case of superheated steam drying (Pg> 14.7 psi. abs.) the important factors influencing heat requirement are: 1, The weight of equipment per pound of dry stock and its specific heat 2. T'he specific heat of the' dry stock 3. Tlhe temperature of the drying gases, Tg 0 T Tie drying time, Q 5. T'he exposed heat-dissipating surface of the equipment in ft2/lb of dry stock 6e The operating pressure, P g These factors may be combined to give: 2.10, Q 2.10H 708 + Tg (.0589 +.22) - 4.063 Q HpgTg - 337 + T (.02769 +.1J5) - 1.9350 (54) + -- — (H -T 38) BTU/lb water v PgTg evaporated

DFIP\ARTIMJiNT OF ENGINE;ERING; RESEARCHI - _NI.NLVEIRRSIT-V OF MICHIGANrj 41 where H p T = enthalpy of steam at Pg, Tg BTU/lb v = specific volume of steam at Pg, Tg, ft3/lb The effect of Pg and Tg upon the heat requirement for this case is also shoiwn in Figure 10, where it will be noted that the influence of Pg is small. The situation covering the full ranige of ihumid air and supereated steam is also sEhovm- in Figure II, which is a plot of:Q vs. Pg with separate lines for the various temperatures. This figure brings out several important poinrts: 1. Low partial pressure values (i.e., low humidities) lead to excessive heat requirements.* 2. At low P. values, temperature (Tg) is an important factor in determinini; the heat requirement. 3. At high Pg values (say P - 6.0 psi.abs.), T is an unimportant factor in determining tile heat reqgirement. 4. At high Pg values the heat requirement becomes almost independent of Pg until a certain limiting PJ is reached, after which there is a rapid increase inl heat requirementt Table II summlarizes the effect of temperature (Tg) upon the optimum range of pressure (Pg) corresponding with the minimum heat requirement. The optimum pressure range is considered to be that in which h the heat requirement is within five per cent of the minimum. *So far as can be determined in tlhe. ShLunan report, the Owens-Illinois Glass Company now considers a wet bulb temperature of about 145~F as "normal" and one of I800F as "higi h umidity" when dryingi at 3300F (Dec.1946 Mionthly fReport). These wet bulb temperatures correszpond respectively- with partial pressures of water vapor of 2 2 psi.abs. and 7.1 psi.abs. (Figure 1). From Figure 11 it is seen that at 3300F and thiese partial pressures, the heat requirement is respectively 162u anld 1110 BTU/ib of water evaporated. These figures rejpresent 154 -per cent and 106 per cent of tlhe minimum heat requirement of 1050 BTU/ib at 3300F. I ^^~~^~^^... __^^______-~_-_________ __~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

TABLE II SU tMMiRY -S EFF CT OF T LMPEi:iRATUR (Tg) U'POi Pi JiTIiL P US:.L 1 OF iTER VAOR (Pg) HiGE CO iR.SSPON DITNG G Wi1TIi iI lWi- E.. sL,1i T i —------ i: kMinimum iHeat Optimum Drying Medium and Temperature Optimum Pres.u-e e Requirema ent Optimum Pressure Range 1 ~ ~F (Pg)opt. P i g (p r e) i psi.abs. Q. (Pg -i BTU/Ib water ) - 300 t23 1070 HIumid air from Pg 5 to 14.7 300 2 1070umi air fom 1 Steam from Pg 14.7 to 90 Humid air from Pg i to 14,7 3[0 29. I67 I ~~400 1~35 j~:~10)~5 t^ Steam from Pg 14.7 to 140 aa~~~~~~~~~~~I I Humid air from Pg = 1 to 14.7 4oo 35 o55 i ~i Steam from P- 14.7 to 140 Humid air from Pg 1 12 to 14 7 450 90 1035 Steam from P 14.7 to 250 (?)! 500 150 (?) 1015 Steam from P- 14.7 to 370 (?) L____________________________________________________________________________________________________________ii~~~~~~ ~ ~ ~',

23000 2800 FIGURE 10 EFFECT OF TEMPERATURE o 0 ON HEAT REQUIREMENT: 2600 Q. 2400 22002000 -1800 250 300 350 400 450 500 550 600 250 300: 50 400 4.50 00 550 600 DRY BULB TE.PERATURE, Tg,'~F

~_~ -~- -_-_- -"~^ ~ ^~ ~ ~~ ~ —. 7. ~:.. ^......l -....^~-. - - -... -- - -~ -~-~ C O "I ",I - 1< __~n 600 &3~~ ^_______ _______ ______ _______ ________ ________________ \__ __ _________ _ ______{__~ — 0 C..iiiiI A q 0 40, 1 _ _. ~;~::~~'. \.. I _ I\~i..____ _ _ ___ ___ ___.0 a ^^~~-~^ ~~^~^- CQ~j^^:~ -^ ^^ ~^~~~ a^~~ ~31-1 - 8dn1 ~-::~~:;::::;~i ii::~;:: i-i:.::: i:. ^ ^ i.:nJ L — t:':__~i:.^ 4 ~ ~.:~ ~.{.. - ~ ^ - ^i.~ra - i \ \.. ~.:- - \ i i:i: -: i- ^l~lll:IIcIflLllL t: j ___________ _^~!_.l~~ ~IJ'-~~~ g( ~^- ii^ ^'~'^^~ -''. ~ ^t-0 _____________._.____-, ___ _ _ _ _ _~ _~ _ _~I- ~ ~ ~~" ^^~^l^^. i ~T^i^_~~ ~- -- _ _ _ 0 __ -~f — ~ ~._: i ~ -~ - _____ ^ ^ii i iii:l:i- ll~i ji.-t' ~r:~ i-i~ r I -i ~rL._ ~~~ ll^^^__V__ ^B _-_____"- -"1-_-__-______ _ _ 0o __' - -_~ i _^^:ij-_ 4'i^ ^ ^- - i. - -^ T^ -~~-.- -: — _^i ^ ~ ^ ~^ ~ Lii _i _-,-i-A — ~ ~ ~ ~ ~ L - - - - - - 01~_ _____-_l _I.:~i_~3~_i C ii:: iI i iI Ii i II i1 iI i-i1__1_~-ti:' _ ___i +~ _ t::I — ~ ^ - ~'~ - - - - - ~ - ~-l ~ i —- i-~ ~l~ i - I ~.'-. 0~~~~~~~~~~~~~ _ 0 c s i - i.iii -i-l:^ _ L __ 0___ 10 00 In0 ~~~~~~c a3iLV^IOdVA3 -3iLVM ~9T 3d *fl'0'IN31N3 in03 IV3H

iDEPARTMENT OF E GINEERING RESEARCH Pr __________________ UNI\VERSITY- OF NIICHtIAN' _ 5 The possibility of nheat recovery must not be overlooked ir the case of superheated steam, whlere a high proportion of the total heat requiremelent is available for recovery in the form of latent heat in steam vented from the dryer. The efficient recovery of this heat is contingent upon a large multi-wuit installation permitting scheduling and load levelling, and upon additional capital outlay for a recovery system. The attractiveness of this is not to be denied, but t i is believed wise in tlhis preliminary ailaiysis to assume mernely t'hnat the possible savings of, "multiple-effect" or other steami re-use operationl will cancel the higher unit cost of heat at tihe pressure where re-use could be effected. Thie Total E lectrical Energy Consumption_ Electrical power is required for the purpose of circulatinlg the drying gases over tie stock, through any system of baffles which may be desirable, and over heating coils for suo)plying the h.Leat requirement. It is convenient to consider the power for these three purposes separately, although in practice all may be supplied together. Taking one pound of stock as a basis, the power over the stock is 1.46 Es, where Es is the unit power discussed earlier and taken as constant throughout the comparison. The actual numerical value of Es is dependent upon the spacing and arranzgemient of the stock and its effective surface roughness -- factors which are not analyzed in this study. *Since one pound of 1-3/4 inch thick, 20 pcf stociL exposes a surface of 1.4.6 square feet.

.1 D )PARTMAENiT OF [NGINEERIN G RESE )TAR CH P __________._ ___UNIVERSITY OF MICHIGAN 46 The power expenditure through the baffle system, etc., is also largely dependent upon the specific arrangement and is incapable of actual evaluation at this time. It may, however, be represented as: Eb kb (1i46 E) (55) where kb is a proportionality factor. Similarly the power expenditure over tie heating coils is dependent upon their spatial arrangement and, in addition, upon the ratio of heating coil surface to drying surface and the ratio of heating coil temperature differential to drying temperature differential. Regardless of these complications, however, the ipower expenditure over the heaters may be represented by: E = kh (1.46 Es) (56) where kl is a proportionality factor. The total power consumption is therefore: ZE = 1.46E(1 + kb + kh) (57) iHow~ever, Eshas been chosen as one of tie constant factors- in the comparison, which means that IE, the total power consumption, is also constalt, althoughl unnown in actual magnitude. Consequently, the total electrical energy cons'umption may be represented by: KWH 1.46EG (1 + b + kh) 1 (58) where KWH - kilowatt hours of electrical energy 6 = drying time, hrs and is directly proportional to the drying time, @.

D E PARTMENT F O(F L\GI NERING RI'lE AR( 1 4 _ _____U_______NI\'IRSI_ _V_ OF MIC(1I__ AN 47 The effect of temperature (Tg) and pressure (Pg) uponl the.total electrical energy requiremnent is therefore precisely the same as their effect upon the drying time (0). Figure 9 may be used as a direct indication of the relative electrical energy requireliient at various temperatures and pressures. nfluenlceof hane in Stock_ Thickiess and Power Consui!tion: Alt'hough it has been stated thlat a constanit stoc thiCkI ness of 2Xo 1-3/4 in -and a constant power ex;penditure are parts of tlhe chosen basis for the evaluation, it is nonetieless of interest to determilne the ir.f.luence of changes inl these quaniitiies on the drying rates. This situation has been given careful study, with results wh-ich are summarized')eow. Period I Con stant Rate: In this period the dryiZn rate is given by: dF hc dF (Tg s') ibs/ft2hr (43) (Tg T s I Substituting the expressionl or the film coefficienti he, in terms of the energy consump)tion, F is i() dFGG = Bot E0286 (59) Ts from which it may be seen tl:at the drying rate, AF is indep)endent of stock thickness, 2Xo, but directly dependent upon E0286.

i l:L.f)1P.\R OFI (\ I lf Ni. klXG.:N RESA. 4J l ___.~ _UNI _I VS Ji' -_~_ilLTV_ 4 Perio_ _II Frst Fallin, Rate: Here th:e 1ogaritlic i mean drying rate may be shownl- equal to: BdF l l\ Aat 1 E0.286 (Tg s_ ) lm o3 ).Ad~/lm r id d T s an-d aain, thle logaritlmic mean drying rate ('F ) s idep e ent of stock,thic:sless, 2X0o but depenlde:t directly uon E Period III. Seondl Fall in:' Rai- Intl thiis period the situation is more compiicated. an d t.e log'arit:ic..ei drying r.e. nmay be shlowni equal to: ~ F.65X o' Ad. 165Xh KE t f T (62) D esign ating tr e first part o f t l'e rillt-lland e.pressithn as f' t'h eq buatio a beomr es:: -'-~ —-i' = ~t Eos286s Pg- Ts" r'dtionsi is lotted in FiuV 12. 1 tis e;ic v is similar int form to te equatio ns of the previous eriods T e. exressio " heve depends upon thle film coe-frfiier'otl: B~+ E86a uo td, -to c th ick'ness' 2X. For convenience cvalues of' h.. alate d or vari us value s oa':to ani Xi; and te re-lationshi p is p lotted in Figure 12. I tis peiod t:,e ini'fiuence of Xo and Esiay b1) determined as foliows: Period lI.:AdG/! m 1 2. Evluate t:'- i"fluence of tihe: c.:.:ant on ~(from Figure 12:..,

4'9 1.0 If J- fill~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~f1 I FV J FIGURE 12.9 t EFFECT OF STOCK THICKNESS AND FILM COEFFICIENT ON Kill~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ THE FACTOR l -ir lr-14 +( _r, -4, tj 11~~~~~~~~~~~~i-.? {tt _ _f.1 - t I t +1 j1; I1;1 I. t. - i ft f f I ~:~: ~ i iC It r, t, 4 t~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ _~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~T F: - ~!ll ~i::5' i2:., +(~t _i", IC:;4-:: LI (+ t ~i; it l~~~~~~~~t.(t ~I+ i 1 i- it UGUST 194 II IIS 0~~~~~I t rI~~ii rt tr~~~ X O 4+ -I FJF ti-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -- -T-~ 1 T%...;3 1 ii,, t~~~~~~~~~~~~~~~~ 1: 77.6 ~.i 1~~~~4A.... STOO K t rTHI.O $ FO DRYN FRO B OT SIDES, IN.: 1 1 pill 4i t If - till: 4 T;: 1 1-: t ii _14- 4- r 4............. -4 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ STOCK THIOKNESS FOR DRYING FROM ONE SIDE, IN. I t i I 1 1 1 i T-T T t.5 t.r ttt - fit f I I;-. I 1-1 L *+ rr Lr; Jil l....... 7.... -.4 _Tt ~ 1: tt, I. I I I~i t.... -: I T.,.. - _ +t It -~ c~ i t -e~~-CCCCCI~~J~: Lr............~~,-~t I J I 1 7- - 4 1.... ++++ 4-t -- t~~~~~~~~~~~~~~~~+~~ ~I IIL 1, t' i L ~ ~ ~ ~ t? t~-I L Lillie I I I i ~i 44# +fi ti _ = —- + e —: I4 ---------- c —t'- ~ — [Jill[ IL 1_J +_ f II I I l ill I I:I IIIL I ~ ~ t CH- ~ i; t LI 1.,,-~C- i.,e."t -:-t+'Ci- -t-Hi ll Col l in s, 7t

I D FPAR TME X OF (; NGINEiE{,'ING RELSI\R(CH P\ __:__I\'}_____ O\ F 0MITCHIGA;\N 50'3. Multiply t-ie factors of (1) and (2) to obtain the net influence of te hange on ( in Period I11. im Figure 13 has been prepared to facilitate determinling the influence of E upon tihe drying rates in Periods I anld II. It is seen, thlerefore, that the influence of a Cliange in stock thicknless, 2Xo, or unit power expenditure, E, upon the drying rate may readily be determined. This, of course, is drying rate in terms of ibs/ft2hr which, except in Period IiI, is inldependent of stock thiclness. Obviously h',owever, the drying times in the vari|ous periods are not independent of thlicmkess, because the quantity of water to be evaporated is directly dependent upon the thickness. Clhanges in the two critical moisture contents with drying rate and thiickness of stock render an exact analysis of the net effect of 2Xo and Es upon drying ti.es difficult, ald in any case result in unwieldy expressions. As a rough approximation, the drying times in the vairious erios will bil ln versely proportional to the new drying rate anid directly proportional to tine new thiclness.

!O.00 i 8.00 6.00 4.00 I 3. 00 t _- I W _ 2.00 a: 14.00 a_.80.60 40 H.308 3.20...........08 "'J CONSTANT RATE PERIOD.01.21.0.04.0608..20.. 4 0 0 20 0 0 BASIS POWER C'ONSUM P T ION OF 0.06.04 ELJ t 4:1 111UNIT S AT (dF/Ade)T. I 500N AUCUST, 1947R.06 REL ATIVE POWER CONSUMPI TION PER UNIT SURFA E

i!'P-ARTI EN't; O F L\;i XEERING RE51 A: (-i H':lP UNI\E._ _RSI'I?\' ('):M4ICJ-tGA' 5 2 ON iQUALIiTYDEITIl FiAi 1 NC'SOS A|t the8 present time it is impossible, unloiortunatei-, to give oth-ler than the most preliminary qualitative treatment to the influence of temperature, Tg, and partial pressure, Pg, upon the quality of finished product. Earlier mention was made oi thie lact thlat tle a solute moisture conte nt W, the rate of drying the Adoi dw d T moisture and temperatur'e gradients ancd d and tlie temp)Ioerature dX dL importance in determining quality. Each of these will be discuss ed separately. Absoluite Moisture Content (W) It is believed that if data on strenigtlh and rigidity ver sus moisture content of tl.e finished material were available, they would show that tie ability of to wist the stoc o wtstand tage and thiermal stresses enlco-mutered during drying is greater when the stock is above some "criticalt" moisture contelnt. On this assumption it may be argued that the quality of th'e finished stock will depend upon tlhe approach of the local moisture concentration to tills "critical" valule. If the local concentration at any point should fall below the critical, there is ilcreased danger of the shrinkage and thermal stresses causing actual failure of the material with the resultant ttshrirdage cracks.'" Now, the numerical TThlis conteltion is not supported by actual data, but represents the ooint of view o0 Mr. J, XK SeldeI arld otilher workers in the field.'~~~ZE~C1=~~~U5~~1~~9___~_ U~II~~~CRiiP

I IKPARTMEINT OF L.FINFiKRI\GRESIR P value of the critical moisture content is unimlown. Also, thle minimum local moisture content,( (hich' is E, the equilibrium moisture content for the particular Tg, Pg conditions) is unL-nownI except by the functional equation: E (stock Tg. P, All thlat mlay 1)b said, therefore, is tlhat Jrobabb low temperature, an, hlnd higih pressurei,, values, which1 favor high values of E, will favor good quality. iRate of Driying (L = C ) It is usually assumed that rate oi dryiig, per se, may liave an influence upon quality. One cannot be sure whether tlis s the case, or wlhether it is merely that factors favoring high rates of drying,, such as thl:ose discussed below, also favor poor qiuality. In any case, iowever, it is safer to assumie that ligh drying rates may have deleterious ef'fects upon quality and that good quality is favored by those factors which f-avor low values of drying rate, AdF' or hligh values of drying time, 9. =_;t I ~ ~-~ dW d~ Moisture and Temperature Gradienlts (-), d M-oisture and temperature gradielts through the stock are responlsible for the stresses which arise during tiie latter staes of drying,. Naturally, the larger th ese gradients, thle greater tihe stresses and thle more serious thie possible damage to tthe stocki may )be. The previous ailalysis of t'Ge mechanism of dryi'ilL indicates i'4 and dT remain small until the second falling rate period. dX dX

D iIPAR1'MET O { (.NG INr~" G R [.I' ESA R. 1 I tA I,iVE S t I1 V F MN. t I C, (;.-.\,'54 Moreover, during tlis iperiod ctl will depend almost directly upon dT ~dXL1 X the'.-c d:y ing rate- and dT almost directly uponl -te dryin~g rate land, G "2 L " iLnversely upon! E, t the telrmal conlductivity of tile stock.'Tus, low grz adienits are dep)endent upon low drying rates and a higllh KE The the.ermal conductivity Ki is lknov to be depen dent upon both tempera-ture and,-cui libriulm ioisture conltenit; i.e., KE = f S" (stock, Tg, E) - f o (stock, Tg Pg) It may th'erefore be concluded that low gradients and good quality wili be favored by low rat-es of dryiilng low temp-eratures ald high-l p res s.;ures. Tem)perlature Gradient of the Drying Gaises (Gir): The temperature gradient in tle drying1S gases in the dire tioni of their flovw is an important factor ill determlining unLifor it of drying conditions and, therefore, the un-iformity of quality in the finisiled product. lThe permissible variation in T_ without givg ii-,, rise to appreciable non-unif ormity mUust be determined by' actualj test.. aonleteless, iit maay be seen from ~,lgures 4, 6, 8 and 9 th;Cat Iin the neighborhood of Tg -+400F and P? 30 psi.abs. variation in Tge of5~F (e}i,.~Tg I in Tg of 5~F (ATg - 5) will cause a variation in drying timLe of: Period I (Figure 4) 0.063 hrs 2.,5 Period II (Figure 6) 0.033 hrs 183 Period 1II (Figure 8) 0.086 hrs l.9KJ IQv Oe r-l (Fiu re i 9) O 0.182 hrs 2',

I )F'PART.ME1T OF ( 1'XGINEERfN(G RES;. \R(t'H -_ UNiX\'STI' (V)1'ES OF NM CHI(AN _______ 55 This means that stock ex p.osed to th.e higher Tg will be dried to the desired joint approximately 0.18 hours before that,x;-osed to th.e lower' T'. It is tlherefore inevitable that a portion of tihe charge will be overdried, wile anotrer portion will be underdried. Storae, aft.er d-rying will tend to alleviate this effect, but still it must be coilsidered uindesirable. In practice, tile solutio to e ro is to locate trollhe b eatelrrs at such intervals along the path of thle sases that the maximum inTg will not cause serious difficulty. if the distlace between heaters, measured alongI t:e pat-n of th'e gases, is ta:.en as AL t ih en: dTg dL = (Tg)max (d ) (63) and the significance of the gradient ~ and its reciprocal dL dL dTg becomes apparent. An analysis of tl:e effect of temperature, Tg; pressure, dT P; an th e properties of the drying medium upon hlas been carried out. It may be shown tlat th he maxilmum value of tile gradient is that obtained in Period I. \ adL ma ( h 4 E g (64) rn C)7i Shin 4 E.07(Ts wlere' Es ulit power expenditure, ft ibs/ft2hr N = a numerical constant

I \1EPARTMENT OF LN1NEERING RES[. RCI, P - __ _T._ NIV'ERSrS OF MCHIGAN 6__ h = the "tiliclness" of the flowing gas stream, ft |ZV " a combil;tion of fluid properties k 0 6 vO.144 C = O0 ~ O38- 5 and dependent upon Tg and P C0o,60. 0.385 g g Thle relative (d~, for COliStait values of gas stream. dL..max "thickness h, an.d power ev peiditure, Es may tilerei ore be expiessed in| t;erms of V7t alnd (Tg Ts ). Tle inllluence oi fg anic Pg upon this relative (drL) is siiovni il Figure 14, where thle radient at k demax T 40F anld Pg 30 psi.abs. is taklen arbitrarily as unity. g g The figure shows that low gradients are f'avcred by low temperatures ilnd high pressures, superheated steam giving lower values than humid air at the same temperatures'. Since low gradients mean greater uniformity with the same heater spaci ng, or, the slame uniformity at greater heater spacing, it is obvious that low temperatures and high pressures favor uWiorminty of roduct quality.

3 | - < < —t ~~~~~~~~~~~FIGURE 14X 3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ i |= t;\ i;; 0| 0 1 i |l ] FRELATIVE dT /L FOR DRYING GAS | BASIS: CONSTANT POWER EXPENDITURE i 2dTo/L = 4 60 0 = 4 400'RAPSR OWE VO TS00 ~~~~~~~~~~~~~~~~~~GE. "0, 0 0 3 06 8 0 0 0 PATIL RESUEOFWAERVAPORT0 P,,AS

D PARTIL\ (OF KN;.IE ERING RESfAI.\ It I \_________T,'KRS (O)F.tICH:JOAICNA_'__ I _zT 0_.. N1C 58 VII. COINC USION: il. COMPOSITE EFFECT OF iMLriOZ PrL: ANiD NATURE OF DRYING LEDIUM ON UNIT COT'SlD " UILiTY It has been stated that the reiative merits of differei-lt conditions of operation and of humid air versus steam depend upon tileir influence on uniit cost and quality. TIhese influences have novII been determined separately, and it remains to explore th-e comnbinied ef fect and to summarize the conclusions. Thle task is imade difficuitL. y thLe fact t.h-at thle relative importance of the various cost-dete;rI i:ingr and quality-determining factors may, at this tLi-e, only e assum t ed Amongl the cost-determining factors, T,,,Pg e c1 and Cp it will be assumed that the direct importance of temperatu re Tg I and pressure, Pg 5 is slight compared with' ch anld C ALso sincel the cost of electrical energy, cp, has been shiowln to be directly d-.; endent upon tlie drying time, 9, thIese thlree factors are reflected in two: drying time, U, aind cost of heat, ch; or, dryinr time and heat requirement. Now, the relative importance of Tdyiiig timLe, retflecting as it does the costs cc, cd acn cp, is considered to be reater te- a- tal hat of tlle heat reuirement, which? reflects only t.!e si'ngle cost ch. Thus, in attempting to determine from Tables I ad d II the range of conditions favoring minzimum cost, it is believed desirable to wveigh' tle conditions of Table I slightly more tliani those of Table II. Moreover, an examination of Table I indicates that withinl the optimum pressLure range, tlhe influence of temperataueJ *See Pa'ges 2 and 3.

i I, \ \.. i. [ (1...; 0 ( t E RESE N ( - FL R I I___ ^_1.UNIVELRSITY' OF MIHI(AN ____ 59 upon thie heat requir.ement is slighlt. This means that withini tihe optimum pressure range for both _!dri time anld heat re irement the variable part of the total unit cost will be about proportionial to the optimum dryitng time, min. Tg. The influence of temperature upon te composite optimum pressure range (ie., the range cov-ring the optimum pressures for both drying time and heat requirement) is summarized in Table 1III. This table represents, in effect, a sumaary of those findings of. this rep!ort whiclh are related to cost-determiining f'actors. The total unit cost oif drying may be considered as equal to acolnstantI pius a figure which is proportional to the dryinLg time, minl.ll reported in Table III. To complete the picture, consideration will nJow be given to the results whiich have been obtained for the effect of those factors controlling,product quality. IHere, even more difficulty is encountered in establishingi theJ relative importance of the factors dT E, d dW dT 3 and -n Fortunately however, xc pt for te dryE~ Adrtunad dT' except for the dryt ing rate, dF low values of all these factors, and consequentiy AdO good quality, are favored by high pressure and low temperature val — u es Low values of the drying rate require high values oi the dry-j ing time. Thus, good quality is favored generally by low templeratures, high pressures a.nd long drying times. A comparison of these lat-ter requiremlents with Table III indicates the need for a compromise between low total unlit cost and good quality. Operation should, of course, be carried out at the I..l;imuIm t'pa,;e t o''s lostent withi sati.factor'y quality a' n at n I~Drv r...........R~l~~MIJ~Y ~'~ _. llity~- aIIct at an

I DEPARTMENT OF ENGINEERIN- (G RESEARCH P a _.UNIVERS-ITYL" OF MICHIGAN _60 _ operating pressure within the range of optilum prsuress corresponding (in Table 111) with this temperature. Regarding, now the relative merits of humid air and superheated steam from the over-all viewpoint, it is evident that: 1. Below about 375~F hlulid air is superior to steam. 2. Above about 375~F steam is superior to humid air. The conclusion concerning the relative merits of the two media is thus seen to be dependent upon whether or not good quality is att:inable at temperatures in excess of 375~F. If this is the case, as is lii;ely, then superheated steam becomes an attractive medium for drying and offers promise of considerable economy. At this point it is well to recall that this is a preliminary study based udpon a minimum of exp erimental data. ThIus, alt!hough the indications favor superheated steam over air as a drying medium, an experimental study is required to determine the effects on quality and to substanltiate or refute the theory which has been developed.

TABLE III SUMMAiRiY - EFECCT O0F 1 Tpl iAU UPOQi COM2PO SiT i-" iWi Lu O T OPTiiMU Pi'ESl-;SUTE AND UPON TOTAL UNIT COST' It Composite Rlange of {min. @Tg - hrs. Temperature Optimum Mediun and Pressure Approximateiy Proportional (T) F (Pg) - psi.abs. to Total Unit Cost — 300 Humid air: P near 3-4 20.0 350 Humid air: P near 4-6 14 g 400 Steam: P 30-85 8.4 450 Steam: P 45-190 (?) 5.3 500 Steam: P 80-250 (?) 3.9 g *Exclusive of overhead, Co, acid labor, ci. 0^

I)L:PAtR'TAMEN' (;;J.i IN:EKT R`F,XSv\' Ul- t I UNlA IV\RSt` I5iO ANIO HUiITGAN \ 62 ii OastEif toiAtial oURE I as a subscript, refers to initial condition 2 as a. subscript, refers to condition at the first critical moisture content 3 as a suiscript, refers to condition at the second critical moisture conternt 4 as a subscript, refers to final condition 5 as a subscript, refers to condition corresponding with lthe equilibrium moisture conitent A total exposed area of 1 lb of stock, ft2 a a constant B - proportionality factor b = a constant C = number of components c = specific heat of drying gas, BTU/lb~F Cc = total capital investment in dryer cc c interest on capital investment, per unit product cd i insurance, depreciation, obsolescence, taxes, etc., all assumed proportional to the capital investment, per unit product ch = cost of heat, per unit product cI = direct labor cost, per unit product Co = fixed overhead, as management, etc., assumed independent of the capital invest;ment, per wlit product Cp = cost of electrical energy, per unit product d = a constant E = equilibrium moisture contenlt of stock, lbs water/lb dry stocl Be = a colnstant

DI'PAR IE N T O F.\ GiN EERI\G RESE AR-\ 63 _____________________________lm..UNIVE RSITJ C.OF ICIAN__3 Eb = powrer expenditure through thle baffle system per lb of stock, ft lbs/hr lb Eh = power expenditure over the heater per lb of stock, ft lbs/ hr lb Es = power expenditure per unit drying': surface, ft ibs/hr ft2 F W E free moisture content of stock, ilbs water/lb dry stock f = functional relationsilip fE = equilibrium functional relationship I = equilibrium reiationshiu fE H = humnidity of drying gas, lb/lb n = the "thickness" of the flowing gas stream, ft hc = film coefficient of heat transfer for combined conduction and convectiol, BT'U/ft2hr~F PgTg enthalpy of steam at pressure Pg, temperature T;; BTU/it KWVH = electrical energy requirement per ib of dry stock, kilowatt hrs KE = thermal conductivity of stock at mean temperature and at equilibrium moisture content, BTU/ft hr~F kb - proportionality factor kc = proportionality factor kc = a constant kc a constant = lckc. k g = thermal conductivity of drying gas, BTU/ft hr~F kh proportionality factor L = distance measured along the path of' tthe gases,.ft

TDEPARTMENT OF [NXGINEERING RESEARCH Pa I\__________SITY OF MICHIGAN __________________ 1m as a subscript, denotes logarithmic mean value In denotes natural logarith-i of m average rate of fresh air supply, lbs dry air/lb stock hr N = a numerical constant P nuimber of phases Pg partial pressure of water vapor in drying gLas, psi.absC (Pg)sat.= saturation vapor pressure of water at temperatur'e Tg R dF drying rate, lbs water/ft2hr AdG AdQ T. = dry bulb temperature of drying gas Ts = surface temperature of stock durinlg Period I, OF adiabatic saturation temperature of drying gases, OF T r' = surface temperature of stock at moisture coltent F3 OF T X = temperature of stoc. at receded plane of evaporation X ft below surface, ~F V = variance of system v = specific volume of steam, ft3/lb VP = variance of system at constant pressure W = water content of stock, lbs water/lb dry stock X, - one-half thicl-kess of stock drying both sides, ft t!hickness of stock drying from one side, ft L distance between heaters, measured along the, path of tl'le gases, ft AP vapor pressure depression due to curvature ot exposed menisci, psieabs. 1.9 ^ Cdrying time, iirs

IDEPARTMENT OF ENGINEERING RESEARCH PI t, 6 TTNIV'l[ERS'ITY' OF' MICH[IGAN 65 AX - latent heat of vaporizatiol of wvater at tLemplra ture T.?4 = viscosity of drying gas, ibs/ft hr ~^< = edensity of dryinL gas, ibs/ft3 q- =Q tot al heat requirenent of drying operationl, BTU/lb water evaporated c0.4 k 0,60.571:. ~. ~.7. = Parsons and Gaffney "0t function, t 0-,457 dependent upon fluid properties ^ *.- o652Xh,0, a combination of tne factors. /.65Xoh + KE Xo, lc anad KE enco i atered in (65Xoh +KE) l the equation for /3!m foA KE Period III. tX? = a combination of fluid properties =0 0 and dependent upon Tg and P o.6 0.3 85 g K = less than.> = greater than

DE-'ARTMENT OF EC;NGINEERING RESEARCH-I P 66/ _ UNIVEIRS[ITYS OF MI CHIGANN I36. B31 B13L10 GRAIP HY 1. Austin, J. B., tFactors Influencing the Thermal Conductivity of Non0-Metallic Materials," A.S.T.M. Symposium, March 8, 1939 2. Beach, D. D., Chem. Eng. News, 20, 740 (1942) 3. Ceaglske, N. i i. and Hlougen, 0. A C., I2, 7, 8U5 (1937) 4. Ceagiske, N. H. and Kiesling, F. C., Trans. Amer. Inst. Chem, Engrs., 36, 211 (1940) 5. Clegg, R. R., Papermaker, 108, TS5, 25, 41 (1944) 6, Comings, E. W. and Sherwood, T. K., Ind, Eng. Chem,, 26, 10, 1096 (1934) 7. Fraser, L. D., "Preliminary Report on Air Drying of Microporite," March 29, 1943, supplied by J. K. Selden, August, 1947 8. Hlougen, 0. A., Cheml. IMet. Eng., 47, 1, 15 (1940) 9. Hougen, O. A., Chem. set. Eng., 47, 3, 160 (1940) 10. Hougen, O. A., kcCauley, I. J., Marshall, W. B., Trans. Amer. Inst. Chem. Bngrs., 36, 183 (1940) 11. Jalobs, Max and Hawkins, G. H., tElements of Heat Transfer and Insulation," John Wiley and Sons (1942) 12. Ledoux, E., Chem. Met. Eng., 53, 9, 109 (1946) 13. McAdams,. iH,, "Heat Transmission," McGraw-Hill (1942) I 14. Moore, J W. and Vilbrandt, F. C., Trans. iAer. Inst. Ch.em. Engrs., 36, 579 (1944) 15. Muskat, M. "Tthe Flowfi of Homogeneous Fluids Through Porous Media," McGraw-Hill (1937) 16. Otimer, D. F., Chem. Met. Eng., 47, 5, 296 (1940) 17. Parsons, P. Wi. and Gaffney, b. J., Trans. Amer. Inlst. Chem. Bingrs., 40, 655 (1944) 18. Sherwood, T. K., Trans. Aner. Inst. Chiem. Engrs., 32, 150 {*2 rE e / \ X~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

DEPFART'MENT OF ENGINEERING RESEARCH PL Ie 6 i_____________ _ UNIVERSITY OF MICHIGAN__ _ 19. Shepherd, C. B., Hadlock, C., Brewer, B. C., Ind. Eng. Chem. 30, 388 (1938) 20. Shuman, E.C., Exerpts from Mionthly Reports of, supplied by J. K. Selden, August, 1947 21. Victor, V. P., Chem. Met. Eng.,. 52, 105 (1945) 22. Walker, W. H., Lewis, W. K., McAdams, W. H., Gilliland, E. R., "Principles of Chemical iEngineering," McGraw-Hill (1937)

DEPARTMENT OF ENXGINEERING RESEAR:CH Page U\NIVERSITY OF MICHIGAN A2_ P END _ IX MATHEMATICAL RELATIN0,S DESCRIPTIVE OF THE DRYXING MiECH;ANISM The following mat-hematical relations are descriptive of the important physical phenomena and heat and water balances during the various periods of drying. These relations supplelment the word description of the mechanism of drying as given in Section III, "Basic Mechanism and Theory." PERIOD IO INITIAL PERIOD Heat Transfer to Stock Sur.face (Reference 22): dQ - (hc + hr) (Tg Ts0) - ohc (Tg TO) (8) where dQL= heat supply from gas, BTU/ft2hr AdO h = coefficient of heat transfer by combined conduction and convection, BTU/ft2hr~F hr effective coefficient of heat transfer by radiation, BTU/ft2hrOF T = surface temperature of stock at an instant during Period IO, ~F Tg = temperature of drying gases, OF hc( -, dimellsionless factor ha'n

DEPARTMENT OF EXGINEERING RESEARCHI page I....UNIVERSITY OF MICHIGAN il. Heat Transfer _to Stock In terior (Ref erences 13 and 11): S1. /v cAv 2T = 12Ti 3 - KAv aXi- 2 av (2 where |v. = average density of stock, Ibs/ft3 IAv CAv = average specific heat of stock, BTU/lb~F KA = average thermal conductivity of stock, BTU ft/ft2 hrOF Ti interior temperature at time 9 and at Xi feet from the surface Av CAv Av -= AK average thermal diffusivity of stock, - AV hr/ft and the boundary counditions are: = 0; Ti = To for all values of X 91; Ti T- Ts; Xi = 0 T1; T S; X XO Water Transfer from Stock Surface (Reference 22): AFd = k (Po - Pg) (10) where k = coefficient of mass transfer, lbs/ft2hr (psi.) Pso = vapor pressure of water at temperature Tsv, psi.abs P = vapor pressure of water in drying gases,' sijabse g. I

I DEPARTMENT OF ENGINEERING RESEARCH Page j 1;_UNI\'V ERSITY OF MICHIGAN iii o Heat Balance (References 13. 11 and 22): =_ I dW./ _ dAV(. A dT T = sT o d + (Xo 4Av CAv) A (loa) AdO s"T dG 0 AVA dQ where Xp sO - latent heat of water at TS~ X0 thickness of stock for stock drying from one face, ft = one-half thicImess of stock for stock dryinlg from two faces, ft dTAv rate of increase of average stock temperature at dG any instant, OF/hr Equilibrium at the Drying Interface (Reference 22): Ps = fE (TSO) (i1) where fE denotes the equilibrium relatioilship between vapor pressure and temperature for water. The simultaneous solution of the above equations is possible in principle, but extremely difficult in practice. It is apparent, however, tiat dF T s and d s a function of X, dapparent, however, tht A' AdQ' dX are all determined at any given time 0. When dTAv dT dT v dX1 at 9 = and F Fi; conditions become temporarily stabilized and Period I begins with the surface temperature of the stock at its equilibrium value of T ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

I -EPARTMIENT OF.ENGINEERING RESEA\R(' C- Page UNI\VEIRSITY OF MJICHIIGAN iv PERLIOD I feat Transfer to Stocl Surface (Reference 22): - Xh (Tg - Ts,) (12) Heat Transfer to Stock Interior (References II and 13): c2i 32Ti (3 a v ~Xi2 Heat Balance References L 13 aid 22): d _'dF + 0 (14) Adg Ts AdG Wat.er Transfer from Stock Surface ( rencfe 22)_: dF (rAd?) = k (Ps p (g15) Equilibrium (R.eference 22)t Ps' = fE (Ts') (16) W ater Transfer from Stock Interior (References, 6 10 and 15): ) gd 1. ) _ dX (,7i)1 (17) A ax. J= -surface capillary puil, lbs/ft2

DEPARTMENT OF ENGINEINEERING RE)SEARCHI- _UNIV.ERSIT'Y OF MICHIGAIN _ Ve i - interior opposing capillary puii, ibs/ft2 * at ri K = permeability of porous solid, ft2 p/ = viscosity of water, lbs/ft hr e -= density of water, lbs/ft3 (J = surface tension of water, Ibs/ft rs = minimum effective radius of surface menisci, ft ri =corresponding effective radius of interior menisci ft at a constant g = gravitational constant, ft/iir2 /'dF) CrK/O dt^ ^ i d HQ^ _a tg IKP ca (i di (19) Max. Water Balanice: (lAd) =- (l(AdO) (20) A study of these equations shows that within Period I the rate of drying is controlled entirely by Equations (12), (14), (15). \ and (16). Their combination leads to: c (T -T) k (' ) P (21) /ATs T5) which:i, in the case of air drying, is the equation of the "wet bulb"t temperature (22). Tst is the wet bulb temperature whIich for the — ~-I --— "YPIPI C- ---- L~ —U~BI- 1~1~~-~ — i Y~- -~-~OI-~SIP~P I~TI~~. —~Ulsi~~Y~I IIRUIII^~

DEPARTMENrT OF ENGINEERING RESEARCH Page UNIVERSITY OF MICHIGAN vi _ air-water system is approximately equal to thie adiabatic saturation temperature (22). In the case Of drying with superheated steam, it may be shown that Ps = fE (TS ) is very close to Pt. This arises from the fact that the P - Pg factor necessary for the transfer of' dF (Equation 15) is of such a magnitude that the difference between AdQ the temperature in equilibrium with P -and the temperature in equilibrium with Pg is insignificantly small. Thus, in the case of stea Ts becomes, to an excellent approximation, 1 (P) or, the sat" fE 9) uration temperature corresponding to Pg* The relationships of Equa tion (16), i.e., the wet bulb or adiabatic saturation lines, are given in Figure 1 for various values of Ts. Data for these lines were obtained from References (16) and (22). The importance of Equations (19) and (20) lies in the fact that they indicate the circumstances which cause Period 1 to be terminated. As drying proceeds ri decreases, gradually approaching rs. When the difference between ri and rs is such that the maximumi capillary pull is just sufficient to maintain (dF) the period ends'* S at F = F2. The first critical moisture content F2 is thus seen to be dependent primarily upon' - Xo and nature of the Adg' /` t stock as it influences a, rs, ri, and Ke Since is dependent u-on temperature, F2 may be expressed functionally as: F2 " f2 (stock, dF, XO, Ts') or, neglecting the probably small influence of TS, d2 = f2 (Stoc, F2l =2 (stock AN' Xo'

j DEPfARTM\IEN OF ) E\'GiNEELLING RESIARC II't'sN\__________ INV IIT' F lC:IT(HIAN V__Vii H e at Tra s e r to Stock'urfa ce (l ei r el ce2 - Call -h) r (Thg T ti) T 1 C f) (2)Ts where ~w = Ifraction of surface remaining wet at alny irstanit;: 1 0 when F F2; iw 0 Wi^len F -, Ts" = temperature of "wetted" fraction of st)oc, surface during Period II, OF T = ^ temperature of "dried" fraction of stock surface during Period. II, OF Ileat Transfier to Stock I teior (References 11 and I3)_ ai axi2 (24) where the boundary conditions are: G = 2; Ti - Ts 2 for all values of X 0 G3; Xi 0; Ti T Heat Balance (References 1 13, and 221: dF i dTAv (25) dQ = T n —-- + Xd fv C v dM (25) Ad9 Ts" Ad9Av d Water Transfer from Stocl; Surface (Refe rence 21: dF = k f+ (Psn P) k ( I)(Y ) (26) J?, I,.','sr e^ w here Pt - vapor pressure of water at temperature Ts)

IPEPwIrTAENTr OF ENGINEERINGC RESII: \RCH Page _i__ UXVE.RSITYV OF MICHIGAN I viii and P t reduced vapor prelsure of water at temperature Ts ad radius of: curvature r Water Transfer from Stocuk Interior (feeferenice 6, 10 an 5),(dF at' K/~ f d (27) tAd ii P w X r dX i Water Balance: \AdG Ad s d (2)r whie re r effective radius of receded menisci, ft Xr, distance from surface to rceded me:nisci, ft Fr local moisture conternt of wet fraction of thicl-& ness Xr, lb/lb Elgulib fbriu1: (Reference 22): PSg = fE (Ts") (29) Psr fE (Ts"r) (30) As before, t'hese equations will serve, in principle, for thle complete definition of the period. In practice, however, their exact simultaneous solution, even with all factors knovnr, would prove extremely tedious, and certain simplifying assumptions are therefore justified. Equation (25) may be written: Ad = B \T AdO) (31)

DfEPARTMEJNT OF ENGINEERP ING R-SFEAR(H'I,1 (_ N1V S' 1 OF' i5NF ix. where B is a correction factor. Combining Equations (23) and (31): ^dF ^ ^ Kc [C T ( (d) )~ (TB Ts) (1 - W)(Tg Tsr (3.2 andT Now-, if it be assumed as before that Ps Pg P- sr g ad that both quantities are'numerically small, Ts (Pr) (34) s,r - g,r Equations (27), (28), (32), (33), and (34) now give an approximate accounting of the process. It is seen thiat the termination of the period, i.e., f = O, is determined by the recession of the last of the surface menisci to subsurface positions and the cessation of capillary flow. This corresponds to the "pendular" state of Ceaglske and Hougen (3). The moisture content at this second critical point, F1, may be expected, therefore, to depend upon dF a, K, o-, X and the nature of the stock as it influences the radii of the receded menisci. Thus, a Cfun-ction.al equation similar to (22) may be written: - F3 f3 (stocik,,g ) (35) Heat Transfer to va atin Surface ( eferenc 1 Adoi 1 (- T('T) (36) ~i;8 - ai6~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ "~ ~ -

I DIPARTMEN.X-T OF ENGINEERING RKESEAR RC 1 (This equation neglects, the effect of heat stored in the dried layer where X distance from the surface to the zone1 of evaporation, ft K thermal conductivity of the stock under conditions near its equilibrilu moisture content, BTU ft/ft hr F Tx = temperature at distance X from surface during Period III, OF Heat Balance (References II and 131; dQ IJ~-~` + - CA 0(dTAv (3) AdG Txt + v Cv VO -B fi(dt - O(38) x hWater Transfer from Evaporating Surface (References 15 and 22): dF V 1 (Px n Pg) (39) Ad9.yVX-"' —~ "' 6, r + - K to k where viscosity of water vapor, lbs/ft hr density of water vapor, ibs/ft hr vapor pressure of water at Txt and from radius r encountered at distance x, psi.abs.

DEIAR..R'TENT OF ENGINEERILG REF'SEAR(.'H P _.JUNI.'__RSITY OF CIICI AN | Xio EQuilibrium (Reference 22): x,r fE ( x (4) where r effective radius of menisci at distance X from surface, ft Again, if the assumption of P xr P be made, Equation. xr P g (40) becomes: Tx f- g x) (41) The drying phenomena in Period III are therefore described, approxi4 mately, by the Equations (36), (38) and (41)

UNIVERSITY OF MICHIGAN 3 9015 03127 2548