Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 3, 1979
364
Van ‘t Riet, K., Boom, J. M., Smith, J. M., Trans. Inst. Chem. Eng., 54, 124 (1976). Votruba, J., Sobotka, M., Eiotechnol. Bioeng., 18, 1815 (1976). Votruba, J., Sobotka, M., Prokop, A,, Eiotechnol. Bioeng., 19, 435 (1977). Westerterp. K. R., Van Dierendonck, L. L., De Kraa, J. A,, Chem. Eng. Sci., 18. 157 119631. -~~ Wise, W. S., J . den. Microbial., 5, 167 (1951). Yoshida, F., Miura, Y., Ind. Eng. Chem. Process Des. Dev., 2, 263 (1963). Zlokarnik, M., Chem. Ing. Tech., 42, 1310 (1970).
~.
~
Zlokarnik, M., Chem. Ing. Tech., 47, 281 (1975). Zwietering, Th. N., Ingenieur, 75, 63 (1963).
Received for review June 26, 1978 Accepted December 20, 1978
\
Part of this article was presented as a paper a t the Engineering Foundation “Mixing” Conference, August 1977, Rindge, N. H.
ARTICLES
Simulation of Ammonia Synthesis Reactors Chandra P. P. Singh and Deokl N. Saraf” Department of Chemical Engineering, Indian Institute of Technology, Kanpur-2080 16, India
A workable method to calculate diffusion effects within pores of a catalyst pellet, for a complex reaction, has been developed. Suitable rate equations have been selected to describe the rate of ammonia synthesis reaction over catalysts of different make. This, in conjunction with the method developed to calculate the effectiveness factor, has been used to obtain a mathematical model for ammonia synthesis reactors. Reactors having ‘adiabatic catalyst beds with interstage cooling as well as autothermal reactors have been considered. Plant data and simulation results are, generally, in very good agreement.
Introduction Synthesis of ammonia from hydrogen and nitrogen is one of the simplest kinetic reactions. The synthesis is straightforward, there is no side reaction, and the product is stable. The physical and thermodynamic properties of the reactants and products are well known (Gillespie and Beattie, 1930). However, the mechanism of this reaction over the synthesis catalyst (iron catalyst) is not well understood. This has led to numerous rate equations, all of which are of complex order. Because of the complexity of these rate equations it is difficult to account for the diffusional resistances to the transport of reactants and product in catalyst pores. This, in addition to limited reliability of rate equation, makes it difficult to have a mathematical description of the processes taking place inside an ammonia synthesis reactor. Major changes have taken place in the design of ammonia synthesis reactors since the first commercial production started in 1925 (Johansen, 1970). Most of these changes have been based on historical plant data rather than an insight into the physical and chemical processes taking place in the reactors. However, the use of computers in design, optimization, and control made it necessary to have a mathematical description of the process. Simulation models for ammonia synthesis converters of different types have been developed for design, optimization (Murase et al., 1970; Singh, 1975), and control (Shah, 1967; Shah and Weisenfelder, 1969) purposes. T o describe the reactor operating conditions as accurately as possible, the simulation model should take into consideration all the physical and chemical processes taking place in the reactor. In order to avoid the complexity resulting from such a consideration, earlier workers have attempted only approximate simulations. 0019-7882/79/1118-0364$01.00/0
A mathematical model considering all physical and chemical processes in the reactor has been described in this paper. A method to solve transport equations to evaluate the effectiveness factor, up to the desired accuracy, is developed and used in the model calculations. Rate Expressions The literature contains innumerable rate expressions. Those reported until the early thirties have been summarized by Frankenburg (1933) and Emmett (1932,1940). In 1940 Temkin and Pyzhev developed a rate equation which offered a satisfactory kinetic approach to the synthesis and decomposition of ammonia over doubly promoted iron catalysts. Since then this rate equation as such or in modified forms has been most extensively used, although some doubts about the generality of the equation have been raised (Adams and Comings, 1953; Emmett and Kummer, 1943; Hays et al., 1964). The modified form of the Temkin equation (Dyson and Simon, 1968) used in this work, is as follows
where r N H 3 = reaction rate, kg-mol of NH,/(h m3 of catalyst), K 2 = velocity constant of the reverse reaction, kg-mol/(h m3),fN2, fH1, fNHB = fugacities of nitrogen, hydrogen, and ammonia, respectively, k , = equilibrium constant of the reaction: 1.5H2+ 0.5Nz * NH,, and a = constant. According to some workers a = 0.5 for all iron catalysts (Morozov et al., 1965; Temkin and Pyzhev, 1940; Temkin e t al., 1963) whereas others obtained values ranging from 0.4 to 0.8 (Anderson, 1960; Bokhoven et al., 1955; Bokhoven and Van Raayen, 1954; Brill, 1951; Buzzi 0 1979 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 3, 1979 365
Ferraris and Donati, 1970; Cappelli and Collina, 1972; Dyson and Simon, 1968; Emmett and Kummer, 1943; Guacci et al., 1977; Huber, 1962; Livshits and Sidorov, 1952; Love and Emmett, 1941; Mills and Bennett, 1959; Nielson, 1968; Ozaki et al., 1960; Sidorov and Livshits, 1947; Sholten, 1959). Having found different values of a, many authors suggest that it depends upon catalyst characteristics. It appears reasonable, considering that catalysts of different make differ in their promoter contents and physical characteristics. However, difference of the same order in the value of a has been reported for the same catalyst operating under two different conditions (before and after the thermoresistancy test). Even for two arbitrary sets of runs over the same catalyst, values of a show similar differences (Guacci et al. 1977). Generally to evaluate a , K 2 is expressed as a function of temperature in Arrhenius equation form, i.e.
K z = KZOe-E2/R,T
(2)
where Kzois a constant, E2 is the energy of activation, R, is the gas constant, and T i s the absolute temperature. The experimental results are then fitted with K20,E2, and a as parameters. Such a method of evaluation could lead to variations in values of a with a corresponding change in values of E 2 and Kzo. It has been suggested that there is a linear relationship between the value of log K 2 and a. This shows that to differentiate the effect of catalyst characteristics or promoter content from those associated with measurement errors or method of calculation is difficult. Based on this, it has been suggested that a constant value of a , independent of catalyst make, could be used (Guacci et al., 1977). However, for a fixed value of a, other parameters Kzoand E2 are not available for the two catalysts over which the present model has been tested. The values used for the Montecatini Edison catalyst are a = 0.55, E 2 = 39057 kcal/(kmol), log KZ0= 14.7102, and the corresponding rate equation is
For the Halder Topsoe catalyst, a = 0.692, E 2 = 42893, and log K2, = 15.2059; the rate equation is
occur if the concentration and temperature throughout the pellet were the same as those a t the outer surface, i.e. [molar flux of i across surf.] X II= [pellet vol] [pellet surf. area ] (5) [rate of formation of i a t surf. comp., T,P] Several authors (Bokhoven and van Raayen, 1954; Kubota and Shindo, 1956; Kubota et al., 1959; Nielsen, 1968; Dyson and Simon, 1968) have calculated this factor for ammonia synthesis reaction. In all these calculations but those due to Dyson and Simon (1968) either pseudo-first-order kinetics was used or the bulk flow terms in the equations for transport within the catalyst pellet were ommitted. Dyson and Simon (1968) have formulated the problem by considering all the aspects, but unable to solve it within practicable computation time limits, they also suggest the use of an empirical correlation to obtain effectiveness factor. The development of transport equations, to follow, are similar to those done by Dyson and Simon (1968). Catalyst particles are assumed to be spherical (Nielsen, 1968) and isothermal (Prater, 1958). Knudsen diffusion is neglected (Bokhoven and van Raayen, 1954) and diffusion coefficients of each component are assumed to be independent of position within a particle. The reaction considered for the development of the diffusion equation is '/2N2 + 3/2H2 NH3 A mole balance for component i gives I d ~ N H --(r2Ni) r2 d r = '1-E
dr
x . = x .kg
Effectiveness Factor The above expressions represent the intrinsic rate of reaction, i.e., the rate of reaction for small particles in which there is no resistance to transfer of mass or heat to the active surface. The large size industrial catalyst particles (6-12 mm for axial flow converters) are, however, subject to diffusion restriction in their pore structure. This effect can be taken care of by effectiveness factor, 7,which is defined as the rate at which the reaction occurs in a pellet divided by the rate a t which the reaction would
~
(7)
where r is the radial coordinate of spherical particle, Ni is the molar flux of the ith component in the r direction, r" is the rate of formation of ammonia given by eq 1, E is t i e void fraction of the packed bed, and ai represents the stoichiometric coefficient of the ith component in the reaction scheme given by eq 6. Following the ordinary convention, cyi is taken t o be positive if the component is a product, negative if the component is a reactant, and zero if the component is an inert substance. Nitrogen, hydrogen, ammonia, methane, and argon have been designated as components 1, 2, 3, 4, and 5 respectively. Boundary conditions for eq 7 are Ni=O atr=O
-dx=i o
All the above values of a, E2, and log Kzo have been obtained from the published work of Guacci et al. (1977).
(6)
atr=O a t r = R'
where R' is radius of spherical particle, x i is the mole fraction of component i a t any point of the catalyst particle, and xig is that a t the surface. It is taken to be same as that in a gas. The molar fluxes of any two components i and j a t steady state are related as follows a1, NJ .= (y.N. (9) 1 1 This implies that molar flux of any inert component is equal to zero. The molar flux, Ni of any active component i can be expressed in terms of its concentration gradient and the molar fluxes of other active components as
366
Ind. Eng. Chem. Process Des. Dev., Vol. 18,No. 3, 1979
where C is the total concentration of reacting gas mixture in kmol/m3 and D,, is the effective diffusion coefficient of component i. Substitution of eq 9 into eq 10 and utilization of the relationship 3 zff, =
i=l
-1
(11)
gives
1+“i
Substituting for Niand N j from eq 12 in eq 9 we have
Integrating this equation subject to boundary conditions 8 we get
As a consequence of this relationship, the solution of only one mole balance (eq 7 ) need be considered. Substituting for N ifrom eq 12 into eq 7 yields
Normalizing eq 15 by defining Z = r/R‘gives d2Xi
1
’
2 dxi
-[
CDie
+ xi)-1~ -Nt
H
Figure 1. Illustrating the instability of the numerical solution of the equations for diffusion and reaction.
calculated value of dx3/dZ from the true one, i.e., direction of shooting of dx3/dZ value as integration proceeds, depends on whether the assumed value of dx3/dZ (at 2 = 1) is smaller or greater than the true value. As shown in Figure 1, if the assumed value of dx3/dZ is smaller (A) integration would lead to shooting of its value in one direction as the center is approached whereas it would have the opposite direction if the assumed value (B) is greater than the true one. Therefore, by observing the direction of shooting, it is possible to obtain a range (AB) within which the true value lies. This range could be reduced to desired accuracy (A’B’) by repeated integration. After achieving the desired accuracy (range of dx3/dZ value reduced to A’B’) no further integration is called for although the boundary condition at the center has not been satisfied. In this work range A’B’ representing less than 0.5% of the true value of dx3/dZ has been used. The mean of the two extreme values (A’ and B’) is taken to represent the true value of dx3/dZ. The surface flux may now be substituted along with other terms in eq 5 to get the effectiveness factor
~
(16)
and the boundary conditions in terms of Z are dx i - = 0 a t Z = 0; x i = xig at Z = 1 (17) dZ This is a two-point boundary value problem and may be solved by either choosing the unknown condition at the center (Le., x i at Z = 0) and integrating eq 16 toward the surface (2 = 1)or choosing the unknown condition at the surface (dxi/dZ at Z = 1)and integrating inward. To solve the problem, in both cases, the value of the chosen quantity is varied and integration repeated until the boundary condition a t the other point is satisfied. It is convenient to write eq 16 for the product component (NH,), thereby ensuring that the denominator in the second term of eq 16 cannot go to zero. If the integration is carried out from center toward the surface, it is necessary to rewrite eq 16 because of the third term. This type of problem has been treated by Weisz and Hicks (1962). We use the inward integration procedure. It is reported (Dyson and Simon, 1968) that to satisfy the boundary conditions at the center with tolerable accuracy it is necessary to determine the flux a t the surface (i.e,, dx,/dZ, which represents ammonia concentration gradient at any point Z in the catalyst pellet) to within 1 part in lo5. However, it may not be necessary to satisfy the boundary condition a t the center, if it is recognized that the direction of rapid deviation of the
From eq 18, v is directly proportional to dx3/dZ. Therefore the percent error in the evaluation of 7 is the same as that for dx3/dZ. With the range A’B’ less than 0.5% of the absolute value of dx3/dZ, the maximum percent error in the evaluation of dx3/dZ and hence 7 will be 0.25 in the present calculations. The total concentration c is obtained from
i:fi (19)
where f i is the fugacity of component i. The radius, R’, for spheres equivalent to industrial size particles may be calculated from
+
where d and are equivalent diameter and shape factor, respectively. The effective diffusion coefficient is calculated from the relation given by Wheeler (1955)
,
Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 3, 1979
367
d T - A H V N H ~ (p~,”r ~) (25) dV Cp G where G = mass flow rate, AH = heat of reaction in kcal/kg-mol, V = catalyst volume in m3, and [” is the extent of reaction defined by g] = gJ0 + cy]mJt” (26) where g,, gJo= mass fraction of component j at any point and at the inlet, and m, = molecular weight of component j.
Nonadiabatic Catalyst Bed. Assumptions the same as those in the case of the adiabatic bed are made. Mass balance equation 24 holds for this case also. The heat balance is described by the equations dT, U.A.(T - T,) -- (27) dV G CPg
xit
Reactor with three adlabatlc beds
gases
Autothermal reactor
Figure 2. Schematic diagrams of a three-bed reactor and an autothermic reactor for synthesis of ammonia.
where 0 is the intraparticle porosity and D, is the bulk diffusion coefficient of component i. This coefficient a t 0 “C and 1 atm is calculated from the relation
where Dit is the diffusion coefficient of component j in component i. The diffusion coefficients calculated from eq 22 are then corrected for the temperature and pressure a t the surface of the catalyst pellet by / T I L 5
1
where P is in atmospheres. Description of the Mathematical Model Since the reaction is exothermic all reactor designs have arrangements for removing the heat generated in the catalyst bed by the progress of the reaction. The reactor also serves as its own heat exchanger to heat the incoming synthesis gas. Apart from flow pattern (axial or radial) the designs differ on heat removal strategy. In autothermic designs, heat is removed throughout the bed volume whereas other designs have adiabatic beds with cooling in between them either by external exchangers or by quench gas mixing. Figure 2 shows schematic diagrams of a reactor having three adiabatic beds with external cooling of the reaction mixture and an autothermal reactor. Both adiabatic as well as nonadiabatic beds, in an axial flow reactor, have been considered in the present study. Adiabatic Catalyst Bed. The temperature and composition throughout a general cross section of the bed is assumed uniform. Axial diffusion of mass and heat is neglected. Pressure drop is very small compared to the total pressure; therefore a uniform pressure equal to the average pressure in the reactor has been assumed. On the basis of these assumptions the material and heat balance equations which describe the evolution of the composition and temperature of the system along an adiabatic catalytic layer can be written as d_t ” dV
VNH~(F’, P, r ) G
(24)
d T- - -_ AH _ _V_N H ~ U.A.(T - Tg) - -AH??rNH3 d V - Cp G G-Cp cP G dT, CP, (28) d V Cp where T , is the temperature of the feed gas in the imbedded cooling tube, U is the heat transfer coefficient, A is the exchange area per unit volume of catalyst, and Cp, is the specific heat of the feed gas. On the basis of the cooling tube inside diameter value of U used in this work is 400 Kcal/(h m2 “C). The equilibrium constant K , is obtained from the Gillispie and Beattie equation (1930). The fugacity coefficients are calculated by means of the Cooper expression (1967) for nitrogen and hydrogen and by the Newton expression (1935) for ammonia. The composition and temperature of the reacting system a t the inlet of any layer being known, the material balance equation (24) is solved to obtain the extent of reaction which in turn gives the mole fraction of individual components (eq 26). For an adiabatic bed the solution of energy balance equation (25) gives the outlet temperature whereas for a nonadiabatic bed (cooling tubes imbedded in catalyst bed) eq 27 and 28 are to be solved simultaneously for the same purpose. The Runge-Kutta method of fourth order (Carnahan et al., 1969) has been used for the simultaneous solution of mass and energy balance equations. The size of the integration step has been varied according to the volume of catalyst used. Calculation Program. On the basis of the mathematical model described above, a calculation program in Fortran IV has been prepared for the IBM 7044 computer. The calculation time for checking the performance of a triple-bed reactor with interstage cooling is 3 min and 3 s when the step size for each bed is 1/100th of the bed volume. This program has been used only for checking the performance of existing ammonia synthesis reactors, but it can conveniently be used for design purposes as well. Results and Discussion The calculation results for six different cases having adiabatic as well as nonadiabatic beds (autothermal reactors) working under different conditions of pressure and composition of the reacting system are presented along with the plant data in Tables I to V and Figures 3 to 5. For the purpose of discussion we consider the reactors having adiabatic beds and those with nonadiabatic beds separately. The adiabatic reactors have Montecatini catalyst whereas in autothermal reactors (nonadiabatic beds) Haldor Topsoe catalyst is in use. Reactors with Adiabatic Catalyst Beds. Each reactor under consideration has three adiabatic catalyst beds. ~-
368 Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 3, 1979 Table I. Comparison between Experimental Data and Calculated Results. Case I. Triple Adiabatic Bed Reactor. (Total Feed Flow, Nm3/1i, 242 1 6 0 ; Pressure, atm, 226)
I 4.75 inlet
bed vol. of catalyst, m 3 compn of gas, %
22.19 67.03 2.76 5.46 2.56 385
N2 H, 3"
CH, Ar temp, "C
I1
I11
7.2 inlet
outlet calcd
exptl
20.03 60.58 10.74 5.89 2.76 504
20.1 61.0 10.5 5.7 2.7 507
20.03 60.58 10.74 5.89 2.76 433
cakd
exptl
18.58 56.25 16.11 6.17 2.89 505
18.2 57.1 15.9 6.1 2.7 502
Table 11. Comparison between Experimental Data and Calculated Results. (Total Feed Flow, Nm3/h, 1 8 0 0 0 0 ; Pressure, atm, 1 7 7 )
I 5.05 inlet
bed vol. of catalyst, m 3 compn of gas, % N2 H,
19.6 65.1 3.2 7.4 4.7 39 5
3"
CH, Ar temp, "C
exptl
17.71 59.83 9.60 7.86 5.00 490
17.2 60.3 9.7 7.8 5.0 496
calcd
exptl
16.63 56.79 13.30 8.12 5.16 49 2
15.7 57.2 13.8 8.2 5.1 502
temp, "C
20.6 65.3 3.2 7.3 3.8 39 0
18.23 59.33 10.60 7.72 4.12 504
18.4 59.0 10.7 7.8 4.1 512
calcd
exptl
15.70 54.20 16.45 8.35 5.30 445
15.5 54.5 16.4 8.3 5.3 440
Case 3. Triple Adiabatic Bed Reactor.
I11
7.35 inlet exptl
17.8 53.9 19.1 6.3 2.9 455
outlet
16.63 56.79 13.30 8.12 5.16 404
I1
calcd
17.55 53.16 19.93 6.37 2.99 463
8.10 inlet
outlet
17.71 59.83 9.60 7.86 5.00 442
outlet
exptl
I11
7.12 inlet
calcd
I 5.25 inlet *
18.58 56.25 16.11 6.17 2.89 415
I1 outlet
outlet calcd
Case 2. Triple Adiabatic Bed Reactor.
Table 111. Comparison between Experimental Data and Calculated Results. (Total Feed Flow, NM3/h; 19 5 0 0 ; Pressure, atm, 207) bed vol. of catalyst, m 3 compn of gas, %
7.8 inlet
outlet
8.30 inlet
outlet
18.23 59.33 10.60 7.72 4.12 $43
calcd
exptl
17.00 55.62 14.90 8.08 4.40 500
16.1 57.4 14.2 7.9 4.4 502
2nd bed
1st bod
t
2
17.00 55.62 14.90 8.08 4.40 400
calcd
exptl
16.12 52.90 18.28 8.28 4.42 446
16.1 53.0 18.3 8.1 4.5 439 ise
20 18
outlet
/
3rd bed
-
1614-
0
G
2 12 -
z
0
9 10-
1
350
,
I
I
,
I
1
I
1
Figure 3. Temperature profile in a triple-bed ammonia synthesis reactor.
The results for these are presented in Tables I to 111. Figures 3 and 4 show the temperature and ammonia percent profile along the beds for case I (Table I). For case I, maximum difference in measured and calculated ammonia concentration exists at the exit from bed I11 (Table I, Figure 4). The measured value is 4.2% less than the calculated one. This error is well within experimental error limits. A t the same point the difference in temperature is also maximum with a measured value
I
I
Volume
I
I o f bed ( m )
I
-
I
I
Figure 4. Ammonia concentration profile in a triple-bed synthesis reactor.
8 " C less than the calculated one. Deviations in concentration as well as temperature at this point are of the same sign. However, in general there is no such correspondence between the difference in calculated and measured values of composition and temperature. On the contrary, for bed I, the calculated conversion is more than
Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 3, 1979
369
Table IV. Comparison between Experimental Data and Calculated Values (Autothermic Reactors) case total feed flow, Nm3/h pressure, a t m vol. of catalyst, m 3 total heat transfer surface, m 2 heat transf. coeff., kcal/(m2 "C) compn of gas, % N2
4 47200 279 4.07 50.0 400 out let
inlet 21.9 65.0 5.2 4.3 3.6 421
H* 3"
CH4 Ar temp, "C
200 1
I
I
calcd
exptl
17.65 52.11 21.16 4.93 4.15 438
17.7 52.8 20.5 4.9 4.1 4 38
inlet
5 26350 268 2.3 25.2 400 outlet calcd
21.2 65.8 3.0 6.7 3.3 437
16.73 52.73 18.99 1.74 3.81 456
6 24259 35 7 2.3 25.2 400 inlet
exptl 17.1 52.3 19.1 1.8 3.7 460
18.82 59.45 3.00 13.21 4.52 417
o u t let
calcd
exptl
13.74 44.15 20.55 15.62 5.34 447
14.2 45.1 20.0 15.9 5.3 443
of case 4 (Table IV). This difference of 3.2% is well within the allowable error limits. For the same case, the measured
370
Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 3, 1979
The results very clearly show that in general the calculated values are in very good agreement with the plant data. It is to be noted that the deviations, in addition to being small, are randomly distributed with respect to actual plant observations both for temperature and composition. This confirms the reliability of the rate equations used as well as the validity of assumptions made, under all plant conditions. This also shows that the effect of diffusion of reactants and products inside the catalyst pores has been correctly accounted for. Conclusions A suitable pseudohomogeneous rate expression for ammonia synthesis reaction has been selected. A method of calculating the effectiveness factor for industrial catalysts by partially solving the transport equations has been developed. Subsequently, these have been used in a mathematical model developed for design and simulation calculations of axial flow ammonia synthesis reactors. Reactors having adiabatic as well as those with nonadiabatic beds have been considered. Although the models obtained are capable of satisfactorily representing the reactor, under varying conditions of operation, each model is limited in its use due to the dependence of rate equation on catalyst make. More extensive work is required using different catalysts to enable the development of a truly general rate equation which can fit the data from any plant irrespective of the catalyst in use. Nomenclature a = constant A = heat exchange area, m2 c_ = total concentration of reacting gas mixture, kg-mol/m3 Cp = specific heat of reacting gas mixture, kcal/kg K Cp, = specific heat of feed gas, kcal/kg K D, = diffusion coefficient of component i D,O = diffusion coefficient of component i at 0 "C and 1 atm D,, = effective diffusion coefficient of component i E2 = activation energy for ammonia decomposition, kcal/ kg-mol f , = fugacity of component i f N 2 , f H 2 , fNH3 = fugacity of nitrogen, hydrogen, and ammonia, respectively g, = mass fraction of component j g = mass fraction of component j at inlet cf = mass flow rate, kg/h AH = heat of reaction, kcal/kg-mol Kzo = frequency factor in Arrhenius equation for K 2 K 2 = velocity constant of reverse reaction K, = equilibrium constant of the reaction: 0.5N2 + 1.5H2 3"
m = molecular weight of component J = molar flux of component i P = pressure, atm r = radial coordinate of spherical catalyst particle r N H B = rate of ammonia formation, kg-mol of NH3/h m3 of catalyst
1\1:
R, = universal gas constant R' = radius of spherical particle T = temperature, K T = temperature of gas in cooling tubes, K d =heat transfer coefficient, kcal/h m2 V = catalyst volume, m3 xi = mole fraction of component i x i g = mole fraction of component i in gas (bulk phase) Greek Symbols ai = stoichiometric coefficient of component i 7 = effectiveness factor E" = extent of reaction c = void fraction of packed bed A = equivalent diameter rc/ = shape factor 8 = intraparticle porosity Literature Cited Adams, R. M., Commings, E. W., Chem. Eng. Prog., 49(7), 359 (1953). Anderson, R. B., Ind. Eng. Chem., 52, 89 (1960). Bokhoven, C., VanHeerden, C., Westrik, R., Zietering, P., "Catalysis", Vol. 111, Reinhold, New York. N.Y., 1955. Bokhoven, C., van Raayen, W., J . Phys. Chem., 58, 471 (1954). Brill, R., J. Chem. Phys., 19, 1047 (1951). Buzzi Ferraris, G., Donati, G., Ing. Chim. Ita/., 6, 1 (1970). Cappelli, A., Collina, A., I . Chem. E . Symp. Ser. No. 35, 5, 10 (1972). Carnahan, B., Luther, H. A,, Wilkes, J. O., "Applied Numerical Methods", Wiley, New York, N.Y., 1969. Cooper, H. W.. Hydrocarbon Process. Pet. Refiner, 46(2), 159 (1967). Dyson, D. C., Simon, J. M., Ind. Eng. Chem. Fundam., 7 , 605 (1968). Emmett, P. H., in Curtis "Fixed Nitrogen", Chapter VIII, New York, Chemical Catalogue Co., 1932. Emmett, P. H., 12th Report of Committee on Catatysis, National Research Council, Chapter XIII, Wiley, New York, N.Y., 1940. Emmett, P. H., Kummer, J. T., Ind. Eng. Chem., 35, 677 (1943). Frankenburg, W., 2.Electrochem.,39,45-50,97-103, 269-81,818-20 (1933). Gillespie, L. J., Beattie, J. A., Phys. Rev., 36, 734 (1930). Gwcci, U., Traina, F., Buzzi Ferraris, G., Barisone, R., Ind. Eng. Chem. Process Des. Dev., 16, 166 (1977). Hays, G. E., Poska, F. L., Stafford, J. D., Chem. Eng. Prog., 60, 61 (1964). Huber, A.. Chem. Ing. Techn., 3, 147 (1962). Johansen, K., Chem. Eng. World, 5(6), 107 (1970). Kubota, H., Shindo, M.. Chem. Eng. (Japan), 20, 11 (1956). Kubota, H.. Shindo, M., Akehata, T., Lin, A,, Chem. Eng. (Japan), 23, 284 (1959). Love, K. S., Emmett, P. H., J . Am. Chem. SOC.,63, 3297 (1941). Livshits, V. D., Sidorov, I.P., Zh. Fiz. Khim., 26, 538 (1952). Mills, A. K., Bennett, C. O., AIChE. J., 5 , 539 (1959). Kinet. Katal.,6, 82 (1965). Morozov, N. M., Luk'yanova, L. I., Temkin, M. I., Murase, A., Roberts, H. L.. Converse, A. O., Ind. Eng. Chem. Process Des. Dev., 9, 503 (1970). Newton, R. H., Ind. Eng. Chem., 2 7 , 302 (1935). Nielsen, A., "An Investigationon Promoted Iron Catalysts for the Synthesis of Ammonia", 3rd ed, Jul Gjellerups Forlang, Copenhagen, 1968. Ozaki, A., Taylor, H. S., Boudart, M., Proc. R . SOC.London, Ser. A , 256, 47 ( 1960). Prater, C. D.,Chem. Eng. Sci., 8, 284 (1958). Shah, M. J., Ind. Eng. Chem., 59, 72 (1967). Shah, M. J., Weisenfelder, A. J., Automatica, 5, 319 (1969). Sholten, J. J. F., Thesis, Delft, the Netherlands, 1959. Sidorov, I.P., Livshits, V. D., Zh. Fiz. Khim., 21, 1177 (1947). Singh, V. B., M. Tech. Thesis, I.I.T. Kanpur, India, 1975. Temkin, M. I., Morozov, N. M., Shapatina, E. N., Kinet. Katal. 4, 260, 565 (1963). Temkin, M. I., Pyzhev, V., Acta. Physicochem., 12, 327 (1940). Weisz, P. B.. Hicks, J. S., Chem. Eng. Sci., 17, 265 (1962). Wheeler, A., "Catalysis", P. H. Emmett, Ed., Chapter 2, Reinhold, New York, N.Y., 1955.
Received for review February 27, 1978 Accepted November 13, 1978
