analysis. We therefore conclude it makes sense-dollars cents-to purify before immobilizing.
i
J b
SA = 3.2 I
A
i
and
Acknowledgments We are indebted to Novo Enzyme Corporation for giving us an early experimental batch of cells to use. The properties we report here are not those of their current product. We also thank the Beckman Instrument Company for the generous loan of a Glucose Analyzer. Finally, the authors gratefully acknowledge the support of the Applied Research Directorate of the National Science Foundation (Grant GI-34919). Paper 6620 from the Purdue University Agricultural Experiment Station. L i t e r a t u r e Cited
CARRIER
COST, DOLLARS x LITER-'
Figure 2.
P r o d u c t i o n cost, exclusive o f feed cost, as a f u n c t i o n of carrier cost for i m m o b i l i z e d catalyst prepared f r o m soluble isomerase h a v i n g the indicated specific activities (SA),expressed as EU X mg-' o f p r o t e i n , corresponding t o t h e t h r e e isomerase preparations.
111). Labor costs associated with purification, if they had been included, increase with the degree of purity, but this is counteracted by the decreasing labor costs associated with emptying and refilling the reactor. The economic advantage indicated by our analysis is conservative. We did not attempt to optimize reagent quantities nor did we consider reclamation of the reagents. Consideration of factors such as these would further enhance the economic advantages indicated. Immediate improvement would, for example, be obtained by using solid material instead of a saturated solution of ammonium sulfate for preparing the Salt-Acetone Fraction. The volumes of protein-ammonium sulfate solution would be halved resulting in a proportional reduction in the quantities of ammonium sulfate and acetone required. Hence, purification reagent cost would be approximately halved, a decrease which would manifest itself as a significant decrease in production cost and again, an improvement in the economic advantage indicated by our
Chem. Mark. Rep., (Dec 22, 1975). Colton, C. R., Whitesides, G. M., "Prospects for Practical ATP Regeneration." paper delivered at American Chemical Society symposium, Purdue University, 1974. Danno, G.. Agr. Bioi. Chem., 34, 1795, 1805 (1970). Havewala. N. E., Pitcher, W. H.,Jr., in "Enzyme Engineering, Vol. 2," p 315, E. K. Pye and L. B. Wingard, Jr., Ed., Plenum Press, New York, N.Y., 1974. Lee, Y . Y., Fratzke, A. R., Wun, K., Tsao, G. T., Biofechnol. Bioeng., 18, 289 (1976). Lloyd, N. E., Khaieeludin, K., Lamm, W.R. Cereal Chem., 49, 544 (1972). Pitcher, W. H., Jr., Weetall, H. H.. Enzyme Techno/. Dig., 3, 127 (1975). Satterfield, C. N., "Mass Transfer in Heterogeneous Catalysis," p 142, M.I.T. Press, Cambridge, Mass.. 1970. Schnyder. B. J., Enzyme Technoi. Dig., 1, 165 (1973). Schnyder, B.J., Logan, R. M., "Commercial Application of immobilized Glucose Isomerase," Preprint for 77th National Meeting of AiChE, May 1974. Sirotti, D. A., Emery, A,. Lim, H. C., "Glucose Isomerase Immobilized on Cellulose," paper presented at 1st Chemical Congress of North American Continent, Dec 4, 1975. Sproull, R. D., Lim, H. C., Schneider, D. R., Biotechnol. Bioeng., 18, 633 (1976). Swanson, S. J., Emery, A,, Lim, H. C., J. Solid-Phase Biochern., 1, 116 (1976). Tatasaki. Y., Yoshiju, K., Kaobayashi, A,. Agr. Biol. Chern., 33, 1527 (1969). Wall Streef Journal, p 10, Dec 26, 1974. Weetali. H. H., Havewala. N. B., "Enzyme Engineering," p 255, L. E. Wingard, Ed., lnterscience Publishers, New York, N.Y., 1973. Weetall, H. H., Detar, C. C., Biofechnoi. Bioeng., 15, 1537 (1974). Weetall, H. H., Vann, W. P., Biotechnol. Bioeng.. 18, 105 (1976). Yamanaka, K., Agr. Biol. Chern., 27, 271 (1963). Yamanaka, K., Biochim. Biophys. Acta, 151, 670 (1968).
Receiivd /or reuieu, June 1, 1976 Accepted F e b r u a r y 10,1977
Simulation of High-Temperature Water-Gas Shift Reactors C. P. P. Singh and D. N. Saraf' Department of Chemical Engineering, lndian Institute of Technology, Kanpur-2080 16, india
A rate equation for water-gas shift reaction over a high-temperature shift catalyst (Fe203-Cr203)has been developed. This rate equation accounts for the effects of temperature, pressure, age of the catalyst, and H2S content of the reacting gases on the catalyst behavior. The effect of diffusion of reactants and products inside the catalyst pores has also been considered. Subsequently, this rate equation has been used in a mathematical model developed for design and simulation calculation of high-temperature water-gas shift reactors. Agreement between experimental data and the calculated results is generally very good.
This paper describes the development of a rate equation for the water-gas shift reaction and a mathematical model based on it for design and simulation calculations of water-gas shift reactors using a chromia-promoted iron oxide catalyst (72% Fe203-8% ( 3 2 0 3 ) . The reaction describing the process is
CO
+ H20
C02
+ H2
(1)
Some workers propose a first-order (Atwood et al., 1950; Laupichler, 1938; Mars, 1961) or a second-order (Moe, 1962; Padovani and Lotteri, 1937) rate equation to explain the conversion due to this reaction, but many others (AtrosInd. Eng. Chem., Process Des. Dev., Vol. 16,No. 3, 1977
313
chenko, 1959, 1962; Barkley et al., 1952; Bohlbro, 1964; Bortolini, 1958; Goodridge and Quazi, 1967; Hulburt and Srinivasan, 1961; Kirrillov, 1959; Kodama et al., 1952, 1955; Kulkova and Temkin, 1949; Popov, 1957;Puri et al., 1973)propose different rate equations. Each of the latter rate equations is of complex order and different from those proposed by others. It has experimentally been observed that catalysts of different manufacturers give different rate equations even under identical conditions (Goodridge and Quazi, 1967).The specific surface area of the catalyst is reduced considerably during use due to sintering (Hoogschagen and Zwietering, 1953) and the surface composition of the catalyst changes depending on the composition of the reacting gases which are a mixture of oxidizing and reducing gases. All these may help in qualitatively expiaining the difference in rate equations obtained by different workers, but it is unable to help us in getting a general rate equation which is not available in the literature. So in this work our approach is to start with a rate equation which explains the conversion under some constraints. Each of these constraints is subsequently eliminated, one a t a time, by introducing suitable correction terms. These are mostly empirical correlations obtained from experimental results of different workers on the same catalyst.
Development of the Rate Equation The rate equation most frequently referred to in the literature is first order or pseudo first order in carbon monoxide concentration or partial pressure (Atwood et al., 1950; Laupichler, 1938,M u s , 1961) and all attempts to correlate the rate data by power function models give reaction rates which are almost consistently first order with respect to partial pressures of carbon monoxide (Atroschenko et al., 1962; Bohlbro, 1964; Goodridge and Quazi, 1967). So a first order rate equation of the form given by eq 2 has been selected. r = k ’ ( P c 0 - P”c0)
(2)
where, r = rate of reaction, h’ = rate constant, Pco = partial pressure of CO, and P*CO= partial pressure of CO in equilibrium conditions. It is noted that this rate equation has been used under low pressures (of the order of 1 atrn), high steam to carbon monoxide ratio and below a temperature of 500 “C. In commercial reactors the latter two conditions are met but the operating pressure is generally high (15 to 30 atrn). SOwe use the above rate equation a t a constantppressure of 1atm, and account for the variation in pressure separately. At 1atm pressure, eq 2 can be written as
r
=
k ( x c 0 - x*co)
(3)
where, h = rate constant, xco = mole fraction of CO, X * C O = mole fraction of CO in equilibrium conditions = (XH* X x C o 2 ) / ( x H 2 0 X K,,), and K,, = equilibrium constant = exp[(9998.22/T - 10.213 2.7465 X 10-3T - 0.453 x 10-6T2 - 0.201 x In T ) / R ] T; i n K. The rate constant, k , is generally expressed in the form of the Arrhenius equation as
+
k
= a,-E/RgT
Ind. Eng. Chem.. Process Des. Dev., Vol. 16, No. 3, 1977
E’ = 13.88 kcal/g-mol For commercial shift reactor operating conditions, heat transfer and the external mass transfer resistances may be considered insignificant, but the intra-pellet mass transfer resistance is very high (Moe, 1962). In such a case, the true energy of activation, E , can be taken as twice the apparent energy of activation, E’ (Smith). Therefore
E
=
2E‘ = 27.76 kcallg-mol
(6)
In the above evaluation any temperature difference between the catalyst pellets and the bulk gas or between different points in a catalyst pellet has been taken to be insignificant. The close agreement in values of E thus obtained and those reported by different workers (Ruthven, 1969)who used small [
