THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING MATHEMATICAL SIMULATION OF A FIXED BED TUBULAR REACTOR DURING PERIODS OF TRANSIENT OPERATION Donald R. Mason John 0. Cowles August, 1962 IP-577

TABLE OF CONTENTS Page LIST OF FIGURESoo........................................ iii INTRODUCTION.................................................. 1 THEORY..........0............................................. 2 EXPERIMENTAL.. o o o o o o o o o o o o o o.. o......... o o o o o o o o o..... 5 CORRELATION OF RESULTSo.o....o............ o e..o.o o.o o o... 8 DISCUSSIONo...... o....oo..o...................... o..o 12 REFERENCESoo..o.......oo oo..o..o o....o........... o............o 16

LIST OF FIGURES Figure Page 1 Schematic Flow Diagram Catalytic Decomposition of Nitrous Oxide....................................... 6 2 Cross Sectional View of Reactor and Arochlor Heater o.....oO................................. 7 3 Measurement and Control Systems.................... 9 4 Run 33C...o.....o..O.OOOOeooooo5.OOOOO. 14 Of f O a11

Introduction The present work considers a mathematical model for the fixed bed tubular reactor (hereafter referred to as FBTR) and the physical data required to test the validity of the solutions of the equations which represent this model. In order to compare this model with the experimental measurements, the heat transfer characteristics of the catalytic bed must be known. Unfortunately the correlations of the effective thermal conductivity of packed beds given in the literature are not in close agreement with one another. It was necessary then to select heat transfer parameters for insertion into the finite difference solution of the transient equations for a FBTR which would make the solution match with experimental data. Since a thorough study of a catalytic reaction was not within the scope of this work, the catalytic decomposition of nitrous oxide on manganese sesquioxide was used in the experimental check of the mathematical models~ Reliable rate data are available in the literature for this reaction(l) The reactor was operated under unstable conditions so as to observe the formation of a hot spot within the catalyst bed. Using the selected heat transfer parameters, the feasibility of predicting the transient behavior of the catalytic bed when chemical, reaction is occurring was investigated. -1

Theory The equations for the FBTR are presented below without the derivations which may be found in several texts(2) treating the problem of heat and mass transfer in packed beds. For the single irreversible reaction to be considered in the work only one mass transfer equation is needed to describe the system. There are three pertinent equations: one for heat transfer within the solid phase, another for heat transfer through the gas phase, and a third for mass transfer in the gas phase0 Cylindrical coordinates are used and angular symmetry is assumed. The equation for heat transfer through the solid is I 62TC I[lbTC 2TC1 T ka 52z2 + ke r r r + Rp (1-) h A (TC-T) = (1-~) p Cp 6TC where ka (ke) = axial (radial) thermal conductivity of the catalyst bed TC = catalyst temperature T = gas temperature dPN20 blPN20 ko exp (-E/RgT) d1 + bN21 + b PN2 + b3/2P021/2 R = reaction rate AH = - 19,400 cal/gm mol = heat of reaction p = 107 lb/ft3 = apparent density of catalyst pellets C v= 0o174 Btu/lb ~F = heat capacity of catalyst

The first term on the left represents axial heat flow, and the second term describes the radial heat transfer. The third term defines the heat released by an exothermic chemical reaction at the surface of the catalyst, where the reaction rate R is expressed as lb mols reacted/lb catalyst hour, and the heat of reaction AH is expressed as cal/gm mol o The fourth term represents the heat transferred from the catalyst to the gas~ The sum of these terms is equated to the rate of heat accumulation in the catalyst per unit reactor volume. The equation for heat transfer through the gas is GCp z + ka + ke r + h A (TC-T) = pC p bz a bz2 e br 2j (Ta P - where G = superficial mass flow rate of gas, lb/hr ft2 ka(ke) = axial (radial) thermal conductivity of the gas p = density of the gas Cp heat capacity of the gas E 0o40 = void fraction of bed A = 462 ft2/ft3 = heat transfer area between solid and gas The terms are similar to those defined in the heat transfer equation for the solid, except that the first term on the left now represents the heat carried by the flowing gas, having a superficial mass velocity of G lb/hr ft2 4

-4The equation for mass transfer through the gas is most conveniently written in terms of the conversion, X o This equation then is Da 6X 5X De [1 X 62X RpT (i.) e X +X R-' (, U,. X U bz2 z r r UO U where Da(De) = axial (radial) eddy diffusivity of gas U(UO) = gas velocity (at reactor inlet) Co Uo - CU X 0 0 = reactant conversion Co UO C(CO) = gas concentration (at reactor inlet) De/U = dp/Pem Pem = 11 = radial mass transfer Peclet number Da/U = dp/Pem Pem - 2 = axial mass transfer Peclet number 1 d = partical diameter P 8 Since turbulent diffusion normally controls the mass transfer rate, the equation is written with a coefficient of De/U, which is assumed to be invariant with radius and temperature~ The terms in the mass transfer equation are then analogous to the terms in the heat transfer equations, The mathematical model for a FBTR defined by these equations has been solved numerically in a closed form on an IBM 709 digital computer. The axial heat transfer has been investigated by Carberry and Bretton(3), but it has no significant influence on the computed results obtained in this work as long as large temperature peaks were avoided.

An extensive literature survey indicated that there was considerable diagreement concerning the appropriate values for the thermal conductivities and interphase heat transfer coefficients which must be used in these equations. Since the predictions from the computer solution are sensitive to small changes in these conductivities, it was decided to select empirically the values which could be used to match the predicted behavior of the FBTR with the experimentally observed behavior and compare these results with the literature. Experimental A FBTR was constructed and operated, and experimental data were obtained for the purposes of making the comparison with the behavior of the reactor as predicted on the basis of the mathematical modelo The equipment shown in Figure 1 was designed so that air or nitrous oxide could be fed through a gas heating system and into the reactor. The catalytic decomposition of N20 over Mn203 was chosen for the investigation since data are available. Except for the need to activate the catalyst there apperared to be few anomalies associated with this reaction which would impede the extrapolation of the data over a moderate temperature range. The reactor shown in Figure 2 was made from SAE 410 stainless steel, 2.375" ID and 36" long. This steel is substantially free of Ni, since NiO is a catalyst for the decomposition of the nitrous oxide. A jacket was constructed around the reactor tube and can be maintained at constant temperature with circulating chlorinated byphenylA

AIR FILTER IR BOOSTER VENT TO TE ATATALYTIC DECOMPOSITION OF CONTROLUS OXIDE FILTER Atl CFI SCHEMATIC FLOW DIAGRAM CATALYTIC DECOMPOSITION OF NITROUS OXIDE FIGURE I

THERMOCOUPLES E EXPANSION SCHED.40, 2" TUBE SCHED. 160,3'" PRODUCT EXHAUST FAN TANK 410 STAINLESS STEEL PIPE, STEEL orHA UST FARNHLOR NT LEVEL INDICATOR AROCHLOR THERMOMETER CATALYST THERMOCOUL SPLA N N TC LEADS c/ A( ET GLASS WOOL WATER OVER ASBESTOS REACTOR INSULATION o 101t AROCHLOR HEATER HEATER END VIEW- REACTOR THERMOCOUPLE SPACING ~~~~~ALUL~NDUM ~(INCHES FROM FRONT OF CATALYST BED) 11~ VOLT Y220 VOLT THERMOMETER _ HEATER HEATER CROSS SECTIONAL VIEW OF REACTOR AND WCOOATENR;...~} — 1 AROCHLOR HEATER THERMOCOUPLE CONTROL OR BY DRAIN FIGURE 2 PASS FIGURE 2 FEED -(, HOT I ED THER MOCOUPLES AROCHLOR PUMP

-8The reactor centerline temperature was measured using the circuit shown in Figure 3 by 1.4 chromel-alumel thermocouples placed along the centerline of the catalyst bed. The thermocouple leads were connected to the gold plated contacts of a rotating switch, which sent the thermocouple outputs sequentially to the vertical scale of an oscilloscope0 The oscilloscope traces were photographed and the data transcribed by enlarging the photographs and converting the millivolt readings to temperatures with a nomographic scale. The catalyst was prepared from MnCO oxidized to Mn203 and formed into pellets 1/8" diao x 1/81" long. The reactor was packed to a length of two feet with catalyst pellets. A total of 14 runs were made under various conditions of gas flow rate, reactor wall temperature, and reactor inlet temperature o Correlation of Results The various mechanisms which contribute to the radial heat transfer were identified and information from the literature was used insofar as possible to evaluate the various components0 In the fluid phase, the various radial heat transfer mechanisms are~ 1. Molecular conduction in the fluid0 2. Turbulent diffusion in the fluid0 53 Radiation between neighboring voids0 4o Gross radial flow of fluid0 54 Large scale fluid convection0

PRODUCT OSCILLOSCOPE 0.j lSWEEP TR[GGER..j fPULSE (12 VOLTS) N n,, ivS el,, 0 l 0 I.'- >, 3: ROC OU THE RMO COUPLE LEADS BASYSTEMS m ~ CH ARGE R ROTATING SWITCH SWITCH POWER 12 V. BATTERY THERMOCOUPLE 3-15 PSi MEASUREMENT 3-15 PS I oAND CONTROL AIR BOOSTER_ SYSTEMS 30 PS I RECORDER - FI GURE 3 30 PSI CONTROLLER CONTROL VALVE

-10 - In the solid, the various heat transfer mechanisms are: 6. Radiation between pellets. 7. Conduction through points of contact of the pellets. 8. Solid-fluid-solid series conduction through points of contact of the pellets. 9. Solid-fluid-solid series heat transfer by convection between adjacent pellets, Under the conditions of operation in this work, mechanisms 3, 5, 7 and 9 are believed to be insignificant. Therefore, for the solid phase ke = kr + kp + kseries where the radiation component of heat transfer is given by kr = 0.00173 5 4 ds( 2-6 )( 100avg)3 d = 1/8" = particle diameter c = void fraction 6 = 0o90 = emissivity of the pellets Tavg = (Twall + Tbed)/2 K K and is attribute to Damkoehler, as reported by Smith(2). Conduction through points of contact has been considered by Wilhelm et al ) and this correlation is

-11loglo kp = - 176 + 0o0129 ks/e ks = 0~50 Btu/hr ft ~F = thermal conductivity of the pellets The last term, kseries, had to be estimated from the empirical fit of the data, using a first approximation following Churchill and Gorring(5)~ For the fluid phase ke Ek + ktd where kc = the molecular thermal conductivity of the fluid ktd = G Cp dp/Peh The Peclet number for heat transfer, Peh' was determined from the empirical fit of the experimental data. The interphase heat transfer coefficient, h, was obtained from the Colburn equation h = ho Cp(4/dp) ~4 G0~6/(Npr)2/3 where the coefficient ho was determined from the empirical fit of of the experimental data.

-12The empirical fit of the data was best when kseries = 0,16 Btu/hr ft ~F Peh = 11 ho = o015 Btu/hr ft2 oF The operating conditions for the 14 experimental runs are shown in the table along with the absolute average error between the predicted temperatures and the measured temperatures. One representative run, No. 23, is shown in more detail in Figure 4o Discussion The absolute average error over all runs was 707~C temperature difference between a predicted temperature and a data point. In view of the manner in which the data were taken, the present state of knowledge about heat transfer in packed beds, and the inherent limitations of the mathematical model, the empirical fit of the data with these parameters is adequate. The empirical parameters obtained from this work can be used for extrapolation to other systems only with extreme caution. The static bed thermal conductivity probably could be extrapolated most satisfactorily by using the model described by Churchill and Gorring(5) or Yagi and Kunii(6) The value for the Peclet number for heat transfer, Peh, which was found is not unreasonable and a correlation by Singer and

TABLE OF EXPERIMENTAL CONDITIONS RUN FEED WALL FLOW GAS ABSOLUTE NUMBER TEMPERATURE TEMPERATURE RATE AVERAGE CENTIGRADE CENTIGRADE LB/HR. FT. SQ. ERROR INITIAL FINAL INITIAL TRANSIENT 23 349. 258. 278. 210. 198. Air 5.6 24 492. 363. 320. 218. 218. Air 9. 1 26 274. 170. 104. 240. 214. Air 9.0 27 160. 240. 104. 214. 214. Air 7. 2 28A 382. 273. 280. 256. 258. Air 8. 2 28B 261. 375. 291. 251. 232. Air 5.9 30A -441. 280. 304. 220. 224. Air 7. 1 30B 274. 37 3. 313. 224. 220. Air 7. 1 31 314. 198'. 186. 194. 220. Air 10. 1 32A 271. 168. 183. 225. 096. Air 8. 3 32B 168. 234. 196. 110. 225. Air 5. 5 33A 284. 312. 095. 137. 137. Air 12.0 330 254. 126. 094. 073. 202. Air 5. 1 40 393. 320. 305. 178. 370. Air 12. 8 42A 292. 385. 313. 270. 270. N 0 42B 388. 345. 310. 400. 123. N 20 43A 427. 439. 292. 168. 370. N 0 43B 423. 344. 352. 370. 053. N 20 44A 444. 500. 316. 213. 213. N 0 - 45 453. 300. 316. 213. 213. N 20 2

RUN 33C INITIAL FLOW RATE 73 #/hr. ft2 TRANSIENT FLOW RATE 202 / hr. ft2 WALL TEMPERATURE = 94'F ABSOLUTE AVERAGE DEVIATION =5. II F 250 x x~~~~~~~~ 200 x~~ x XXX~~~~~~~~ 150 1 00 _ _ _ _ _ O.4.8 0.4.8 0 4.8 0.4.8 0.4.8 0.4.8 0 TIME =0 TIME =Imin. TIME= 2 min. TIME=3min. TIME=4min. TIME =5mm. FIGURE 4

-15 - Wilhelm(7) relating Peh to dp/Dt and particle Reynolds number can be used. The proportionality constant in the interphase heat transfer coefficient correlation should not be used in systems dissimilar to the one of this work, for which it was derived. However, Bowers and Reintjes(8) have presented a correlation for hc as a function of dp and temperature which predicts a value sufficiently close to that which was needed in this work to give support for using this correlation for making predictions for other systems. These empirically derived constants were then used in this mathematical model to predict the behavior of the FBTR under conditions of run 44 wherein N20 was being decomposed0 The predictions followed the form of the experimental data, but not the position0 On close examination, it was apparent that the reactor bed temperature was falling due to a slight drop in feed temperature in the first 0~2 feet, while the hot spot was developing at a point about 0O4 feet from the entrance0 This combination is explainable only if the catalyst at the entrance of the bed is inactive0

REFERENCES 1. Parravano, G., and Rheaume, L., J. Phys. Chemo, 63, (1958), 264. 2. Smith, JO M,, Chemical Engineering Kinetics, McGraw-Hill Book Co., New York (1956). 3. Carberry, J. J,, and Bretton, R, H., AoIChE,.J., 4, (1958), 367. 4. Wilhelm, R. H., Johnson, W. C,, Wynkoop, R., and Collier, D. W,, Chemo Engo Prog., 44, (1948), 105. 5. Gorring, R, Lo, and Churchill, S. W., Chem. Eng. Prog., 57, (1961), 53. 60 Yagi. SO. and Kunii. D.. A.I.ChE.J., 32, (1957), 373. H.f, Chemo Eng. Prog., 46, (1950), 343. Ho., Chem. Eng. Progo, Symposium Series -16 -