Ind. Eng. Chem. Process Des. Dev. 1982, 21 465-470
465
setts Institute of Technology, Cambridge, MA, personal communication, 1978.
Chemicals from Biomass by Thermal Processing”; In-house Literature Review, Energy Laboratory, Massachusetts Institute of Technology, Cambridge, MA, 1978. Suuberg, E. M.; Peters, W. A.; Howard, J. B. Ind. Eng. Chem. Process Des. Dev. 1970. 17, 37. Suubera, E. M.: Peters, W. A.; Howard, J. B. Adv. Chem. Sef. 1979a, No. 183; 239. Suuberg, E. M.; Peters, W. A,; Howard, J. B. “Seventeenth Symposium (International) on Combustion”; The Combustion Institute: Pktsburgh, PA, 1979b: r 117. - . - Yurek, G. J. Department of Materials Science and Engineering, Massachu-
Received for review June 9, 1981 Revised manuscript received February 11, 1982 Accepted March 4 , 1982 Portions of this work were presented at the Specialists’Workshop On Fast Of sponsored by the Energy Research Institute,and held at Copper Mountain, CO, Oct 19-22,
__.
1980.
Product Distribution from Iron Catalysts in Fischer-Tropsch Slurry Reactors Charles N. Satterfleld,’ George A. Huff, Jr., and John P. Longwell Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02 139
The product distribution by carbon number on iron catalysts is well characterized by the chain growth probability factor a from the Flory equation. A review of previous slurry reactor studies with an iron catalyst shows values of a calculated from literature data on light products to vary from 0.55to 0.94. They are very sensitive to alkali content of the catalyst, reaction temperature to a lesser extent, and are relatively unaffected by pressure and gas
composition.
Most of the oxygenated species are of fairly low molecular weight. The overall reaction may be generalized as
As Americans shift to smaller and more efficient automobiles to economize fuel consumption, the use of diesel engines is expected to increase sharply as they inherently have a better thermodynamic efficiency than spark-ignited gasoline engines because of the higher compression at which they operate. This change will greatly increase the amount of mid-distillate fuels required relative to gasoline, a trend that will be accentuated by continued growth in aviation jet fuel and diesel fuel for trucks. In the future it will become necessary to produce an increasing fraction of transportation fuels from coal. Fuels produced by direct coal liquefaction are not well suited for diesel or jet fuel because their high aromatic content results in smoky and unsatisfactory combustion, but they can serve as an excellent source of high octane gasoline components. On the other hand, indirect liquefaction by the Fischer-Tropsch synthesis is well adapted to the production of paraffinic fuels in the mid-distillate boiling range. The two principal types of reactors which have been studied for the Fischer-Tropsch process are fixed- and fluidized-bed reactors. Both are currently employed on an industrial scale in South Africa by SASOL. However, another type of system gaining popularity is the bubblecolumn slurry reactor (Figure 1)wherein a finely divided catalyst is suspended in an inert liquid that removes the exothermic heat of reaction. In this paper, we outline the potential merits of carrying out the synthesis in a slurry reactor and describe the product distributions reported on iron catalysts in terms of a probability growth model that has been termed the Schulz-Flory distribution. Information of this type is crucial to catalyst development programs and process optimization. Slurry Reactors The Fischer-Tropsch synthesis over an iron catalyst produces chiefly straight chain hydrocarbons such as normal paraffins and a-olefins together with a smaller quantity of oxygenated species such as normal alcohols. 0196-4305/82/1121-0465$01.25/0
CO
+ 2H2
-
(-CH,-)
+ H 2 0 + 36 kcal
(1)
Water is formed as a primary product but in the presence of iron most of the water is converted to carbon dioxide by the simultaneous occurrence of the water-gas shift reaction, which proceeds essentially to equilibrium HzO + CO s COP + Hz + 9 kcal (2) Typical reaction conditions for an iron catalyst are 0.8-2.2 MPa (100-300 psig) and 230-280 “C, at which the equilibrium is well to the right. Carbon deposition by the Boudouard reaction can also occur simultaneously 2CO C + C02 + 41 kcal (3)
-
Slurry reactors for this highly exothermic synthesis offer several potential advantages over the more conventional fixed- and fluidized-bed reactors (Poutsma, 1980; Kolbel and Ralek, 1980; Bussemeier et al., 1976). (1)They provide a uniform temperature throughout the reactor as the liquid provides excellent heat transfer. This is particularly important since carbon deposition is aggravated by higher temperatures, such as “hot spots” that plague operation in fixed-bed reactors. (2) High mechanical strength of the catalyst is not required, whereas high crush strength is essential in fixedbed reactors, and attrition resistance is vital in fluidizedbed reactors. (3) Operation is not affected by formation of nonvolatile waxy hydrocarbons. Catalyst agglomeration and resultant operating problems in fluidized or entrained-bed reactors is attributed to the production of waxy carbonaceous material which coats the catalyst and causes the particles to stick together. In fixed-bed reactors, accumulation of waxy hydrocarbons in the catalyst pores can lead to diffusional resistances, lower conversion, and altered selectivity. 0
1982 American Chemical Society
466
Ind. Eng. Chem. Process Des. Dev., Vol. 21, No. 3, 1982 Reocl~or L ass2
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' I
."
(50 5 6 u b b I a s ( 0 . 7 - 3 . 0 mrr h o m o t a r ;
7
However, we have experimentally shown that the Flory or most probable molecular weight distribution for polymerization processes accurately describes cabon number distributions over the entire range of products of an iron catalyst, including C1 and Cz products, provided that oxygenated products (which are commonly neglected) are included with the hydrocarbons (Satterfield and Huff, 1982b). A simplified derivation of the Flory distribution, extended here to Fischer-Tropsch chemistry, is given below. Consider a catalyst surface on which No active carbon species Cl* are initially adsorbed. These species can either terminate and appear as a C1 product such as methane or methanol or grow by one more carbon unit C* to form C2*. Since higher carbon number species have a similar choice, the reaction scheme can be written as C"
I -1
c," Figure 1.
reactor.
(4) Slurry reactors have the reported ability to process
synthesis gas of low hydrogen to carbon monoxide ratio, characteristic of synthesis gas produced by coal gasification, without prior upgrading of the hydrogen content as is necessary in other reactor types. We suggest elsewhere (Satterfield and Huff, 1982a) that this may to a considerable extent stem from the excellent mixing of the liquid in the reactor, combined with the use of a catalyst such as iron that is highly active for the water-gas shift reaction. High hydrogen to carbon monoxide feeds are crucial to operation in fixed- and fluidized-bed reactors to avoid formation of carbon by the Boudouard reaction. (5) High conversion may be achieved in a single pass. (6) Carbon formation can be tolerated to some degree. We have shown (Satterfield et al., 1981) that large reported increases of viscosity in a bubble column reactor, attributed to carbon formation, were probably caused instead by accumulation of waxes. Catalyst suspension can be caused either by mechanical agitation or by the vigorous stirring action produced by the gas in a bubble-column reactor. The latter is probably the preferred configuration for a large reador and has been successfully operated in a semiindustrial scale demonstration plant in Germany (Kolbel et al., 1955). Mechanism The chemical mechanism of the Fischer-Tropsch synthesis is still being debated (Vannice, 1976). One group of models postulates that chain growth occurs by surface condensation reactions of an intermediate, such as a CH,O-metal species. Another group of models postulates chain growth by direct insertion, as of carbon monoxide, into the carbon-metal bond. Regardless of the detailed mechanism, the Fischer-Tropsch synthesis is thought to involve a sequential addition of single carbon units, as proposed by Herington (1946). This concept was later extended by Anderson and co-workers (1951) to include methyl-branching effects in order to account for the formation of isomers. More recently, Fischer-Tropsch products have been shown to obey Schulz's general polymerization distribution at carbon numbers greater than about three (Henrici-Oliv6 and Oliv6,1976). As is also assumed in many other studies, it was postulated in that paper that C1 and C2 hydrocarbons do not fit the distribution on iron catalysts due to secondary reactions and reinsertion into growing chains.
cn+1
C*
cf,;
Cn t 2
-* C*
Cnte
CX
etc
(4)
where n is the number of carbon atoms in the chain. The probability that any of the Cn* species will add another carbon and grow to C*,+, is a, where branching effects are considered to be secondary. As assumed by Flory (1953), the probability of chain growth a is taken to be constant over the entire carbon number distribution, and it is defined (Odian, 1970) as a = rp/(rp + rt) (5) where rp and rt are the rates of propagation and termination, respectively. The number of C1 molecules formed is therefore Nl = No(1 - a ) (6) Similarly, the number of C2 species produced is N , = (No - N,)(1 - a ) = Noa(1 - a) and generalizing
(7)
N , = Noc~"-'(l- CY) (8) On a mole fraction m, basis, this equation is equivalent to that developed by Flory (1953) for a linear polymerization process with a stepwise monomer addition. m, = N n / N o = (1- a)an-l (9) One test of this expression is that the sum of the mole fractions of each of the different chain lengths produced over the catalyst ( n = 1 to a) must equal unity. m
n=l
m
mn=
n=l
m
(1 - a)an-l = (1- a )
= (1- a)(1
an-l
n=l
(10)
+ a + a2 + ...)
= (1 - a)/(1 - a ) = 1
since the binomial series converges to 1
+ a + ay2 + a3 + ... = (1 - a)-1
(11)
The logarithmic form of eq 9 is a convenient way to represent experimental data because a plot of In (m,) should be linear with carbon number n. The probability of chain growth a may be obtained either from the slope [as In ( a ) ]or the ordinate intercept [as In (1- a ) at n = 11, and comparison of the two values is a useful test for internal consistency of data. In (m,) = n In ( a ) + In
(e)
Ind. Eng. Chem. Process Des. Dev., Vol. 21, No. 3, 1982 467
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c3
1 I
,
@@@@I
3
I
5
7
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CARBON
13
I!
15 l l
19 21
13
NLiMBER n
Figure 2. Application of Flory distribution to Fischer-Tropsch data of Satterfield and Huff (1982b). Fused-iron catalyst in a slurry reactor at 269 "C and 790 P a .
1
3
5
7
9
11 13 15 17 19 CARBON N U M B E R , n
21
23
25
A representative set of our data (Satterfield and Huff,
Figure 3. Product distributions in Fischer-Tropsch synthesis as predicted by the Flory equation.
198213) obtained with a fused-iron catalyst in a slurry reactor is illustrated in Figure 2. The mole fraction in the figure is the s u m of all organic products produced by the synthesis at each carbon number, i.e., alkanes, alkenes, alcohols, etc. Agreement between the line, calculated using a = 0.70, and the experimental points is good. The hydrogen to carbon monoxide feed ratio was 0.67 and the conversion at a space velocity of 209 v/v/h (gas at STP, liquid volume before addition of catalyst) was 48% for hydrogen and 59% for carbon monoxide. The data are for the products volatilized from the reactor. Those of high carbon numbers (n k 17) deviate below the theoretical line because of their increasing lower volatility which causes significant accumulation in the slurry reactor liquid. The weight fraction w, is often of greater interest than the mole fraction and a suitable expression may be derived as follows. It is assumed that the molecular weight of each additional carbon unit is the same. The total weight of desorbed molecules wt is given by m (1 - CY) wt = C n N , = N O aC na" (13)
genates changed greatly within each carbon number. Thus a becomes a particularly useful value for characterization of an iron catalyst at a set of reaction conditions, but it would be expected that a might vary with catalyst composition. In our study a varied from 0.67 to 0.71 over a temperature range of 269 to 234 OC, respectively. It is known that alkali, in particular potassium, increases the formation of higher molecular weight products (Dry and Oosthuizen, 1968). Theoretical product distributions of the FischerTropsch reaction for various values of a,the chain growth probability, are depicted in Figure 3, as calculated by eq 16. Although the average molecular Weight of the organic product increases with a,the spectrum of products also becomes broader. Since the synthesis follows the Flory distribution, the maximum weight fraction of hydrocarbon product of carbon number, w,,, is fixed (Madon, 1979) and can be determined from the following expression where n 2 2.
n-1
,=l
Wn,max
and therefore
nNn nan w, = - =- m *t C na" n=l
Since the series converges to m
a (1- CY)Z
Cnan= ,=l
(15)
the weight fraction is given by w, = nan-'(l - a)2
(16)
As has been noted by polymer chemists, eq 16, developed by Flory (1953), is equivalent to that derived earlier by Schulz (1935) at a > 0.5 and is given by w, = (ln2 a)nan (17) Control of Product Distribution For the synthesis of fuels, the boiling point range of products is of primary importance, and this is closely represented by the carbon number distribution. Recent experimental evidence (Satterfield and Huff, 198213) indicates that the carbon number distribution on an iron catalyst is uninfluenced by wide variations in contact time or gas composition in a slurry reactor, although the relative amount of alkanes, alkenes, and oxy-
-- 4n(n ( n + l),+'
Our data, illustrated in Figure 2, are again displayed in Figure 3. The slight deviation at low carbon numbers results from neglecting the added weight of oxygenated end groups in deriving the weight relationship (eq 16). Alcohols and aldehydes constituted 37 and 26 wt % of the C2 and C3 species, respectively, in this study so the error introduced by assuming that each carbon unit is proportional to chain length is significant. Deviations are smaller at higher carbon numbers because an oxygenated end group has less effect with increased molecular weight, and in addition there are fewer oxygenates present. The oxygenates made up almost 70 mol % of the Cz + C3 fraction. The C1 product fits the correlation well because less than 3 wt % was methanol, the remainder being methane. The weight fractions of various product cuts are plotted against chain growth probability in Figure 4. As before, these curves demonstrate that if it is desired to maximize the production of any particular hydrocarbon fraction, the quantities of other product fractions are effectively fixed. For example, the diesel fuel fraction is maximized at CY = 0.87 and 40 wt % of the organic product is produced in this range. Figure 4 differs from that published by Dry (1976) in that he assumes that the C2 species are twice as likely to react as any other species. Figure 4 can also be used to estimate a for a set of experimental data if the weight fraction of a particular
488
Ind. Eng. Chem. Process Des. Dev., Vol. 21, No. 3, 1982
08
i i
9
06
b-
V
2
IL
04
c I
9
02
3 0
0
02 04 06 08 10 PROBABILITY OF C H A I N GROWTH,&
Figure 4. Hydrocarbon cut selectivity in the Fischer-Tropsch synthesis.
product or group of produds is known. The degree of error will depend on the amount of oxygenated hydrocarbolls formed, as the added weight of oxygenated end groups has been neglected here. Evaluation of Literature Unfortunately, caibon distribution plots like that in Figtlre 2 cannot be made for many Fischer-Ttopsch slurry reactor studies that have appeared in the literature since detailed product information was not reported. This is undoubtedly because rapid and inexpensive analytical techniques such as gab chromatography wete not generally available when many of these were made. However, whenever sufficiently detailed information was provided we have estimated a value of a from the quantity of either the C1 or C1 + C2 fraction reported and then applying eq 16. This assumes that the Schulz or Flbry distribution is followed and that the effect of oxygenated end groups can be neglected. Although some tincertainties remain, it provides a quantitative way of comparing results of experimental studies previously reported in the literature. As can be seen in Table I, values of a for iron catalysts have varied from 0.55 to 0.94. The values of a estimated from the data of Schlesinger et al. (1954) are notably lower than the others. The catalyst, a fused iron, was pretreated with ammonia in order to form an iron nitride, a techhque known to produce a larger fraction of lighter compounds and more oxygenates. There was no trend in values of a with space velocity at 250 dC whereas a decreased from 0.66 to 0.55 as the temperature was increased from 220 to 250 "C. For the same nitrided catalyst (designated D-3001) in a vapor-phase reactor, we calculate from the data of Anderson et al. (1952) a value of (Y of 0.60 at 238 "C and 2.2 MPa (based on C1 w t %) which is in fairly good agreement with a value of 0.63 from the data of Schlesinger et al. (1954) at 240 "C and 2.2 MPa. In the studies of Hall et al. (1952) at 265 "C, increasing pressure from 2.2 to 4.2 MPa increased a slightly from 0.67 to 0.71, assuming no effect of space velocity, and a decreased with increased temperatures. The relatively higher a values from the data of Kolbel et al. 11955) suggest that the iron catalyst may have been modified to produce heavier material such as by altering alkali content. Perhaps coincidentally, an a of 0.84-0.85 corresponds to a maximum in the output of diesel fuel. Kolbel and Ralek (1982), emphasizi the flexibility of the liquid phase synthesis, report pro uct compositions that could be achieved by altering temperature and the type and dosing of iron catalysts, particularly alkali content. Reaction pressure, contact time, and synthesis gas composition were reported to have little effect. We have calculated values of a based on the C3and C4fraction for operations described as oriented toward low, intermediate,
7
and high molecular weight products, and these are also given in the table. We chose C1 and C2 compounds as the basis for calculating a since this is the information most readily available. Higher carbon numbers are often lumped together as C5+. Satterfield and Huff (1982b) have showh that this lighter material fits a Flory distribution prodded that oxygenates are included with hydrocarbons, particularly at C2 However, since the C1 function is mostly methane, little error is introduced by using CHI directly for the C1 product. The validity of using light gas composition is also illustrated by the results of Kolbel and Ralek (1982). An a of 0.64,0.88, and 0.94 is calculated for low, intermediate, and high molecular weight conditions, respectively, for the C3 C4 fraction. This is in good agreement with the corresponding a values of 0.69, 0.85, and 0.92 based on distillatibn cuts between 320 O C (C18) and 450 "C (C30). However, caution must be used in estimating an a value from higher carbon numbers as some data suggest that a hgher, second value of a is required to fit this fraction under some reaction conditions, as seen in the results of the 1943 German Schwarzheide experiments (Shultz et al., 1959). Some deviations from the Flory distribution may be intrinsic, as might be shown by a catalyst having more than one kind of site, by a catalyst or reacting environment that produces a different kind of termination process, by reentry of product into growing chains, occurrence of secondary reactions, etc. These factors may be much more important on other types of catalysts. However, many of the reported deviations, especially on an iron catalyst, appear rather to be experimental artifacts. In some cases the entire product distribution was not determined or certain groups of products were not considered. Some investigators report only liquid hydrocarbons and ignore gaseous proddcts, others vice versa. Some report only hydrocarbons and ignore oxygenated products. Perhaps even more important, however, is inadequate recognition of a variety of experimental artifacts that can give misleading results. As examples: (a) temperature gradients in a fixed-bed reactor can cause deviations; (b) insufficient time may have been allowed for steady state to be reached; (c) product is frequently recovered in more than one trap or sample and these may be improperly combined; (d) certain fractions may be preferentially lost by volatilization in handling. hydrocarbons in the range of about Cs-Cloare sometimes insufficiently accounted for, perhaps because of loss from a liquid trap by volatility and/or by an incorrectly low evaluation of their content in a gas sample; (e) high molecular weight material may be insufficiently accounted for because of condensation in pores of a catalyst or on portions of the apparatus downstream of the reactor. Leaving these factors aside, a wide range of values of a seems to be achievable on iron catalysts of various compositions not only in slurry reactors but other reactor configurationsas well. For example, for the S&ol fmed-bed reactors, Caldwell (1980) calculates from data of Wender values of a of 0.87 for the C1-C4 fraction and 0.90 for the C5-C, fraction. For fluidized bed pilot plant data reported by Weitkamp et al., Caldwell calculates a = 0.65 for the C3-C9 fraction and 0.71 for the Cg-C14 fraction.
+
Conclusions (1)Slurry reactors for the highly exothermic FischerTropsch synthesis offer several potential advantages: isothermal operation, flexibility of feed gas composition, reduced catalyst structural requirements, performance not fouled by waxy products, high conversion achievable in a single pass, and greater tolerance to carbon formation.
Ind. Eng. Chem. Process Des. Dev., Vol. 21, No. 3, 1982
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(2) Reaction of Synthesis gas over an iron catalyst follows a general polymerization process in which the product spectrum can be described broadly by the parameter a , which is the probability of chain growth relative to chain termination. (3) The probability of chain growth relative to termination on iron is very sensitive to catalyst alkali content, to reaction temperature to a lesser extent, but is relatively unaffected by pressure and gas composition. (4) Since a broad spectrum of organic material (primarily normal paraffins and a-olefins with some normal alcohols and other oxygenates) is obtained with classical FischerTropsch chemistry, the synthesis is well suited to producing certain transportation fuels. In particular, diesel and jet fuel can be made from the paraffinic product without extensive secondary processing. Literature Cited Anderson, R. B.; Friedel. R. A.; Storch, H. H. J. Chem. Phys. 1951, 79, 313. Anderson, R. B.; Seligman, B.; Shuk, J. F.; Kelly, R.; Elliott, M. A. Ind. Eng. Chem. 1952. 44, 391. Bussemeler, B.; Frohning, C. D.; Cornils, B. Hydrocarbon Process. 1978, 55(11). 105. Caldwell. L. CSIR Report CENG330, Pretoria, South Africa, June 1980. Dry, M. E. Ind. Eng. Chem. Prod. Res. Dev. 1978, 15, 282. Dry, M. E.; Oosthuizen, G. J. J. Catal. 1988, 7 1 , 18. Farley, R.; Ray, D. J. J. Inst. Pet. 1984, 50, 27.
Flory, P. J. "Principles of Polymer Chemistry"; Cornell University Press, Ithaca, NY, 1953; pp 317-323. Hall, c. c.; Gail, D.; Smith, S. L. J. Inst. Pet. 1952, 38, 845. HenrickOliv0, G.; Oliv6, S. Angew. Chem. Int. Ed. Engl. 1978. 75, 136. Herington, E. F. G. Chem. Ind. 1948, 65, 346. Kolbel, H.; Ackermann, P.; Engelhardt, F. "Proceedings, Fourth World Petroleum Congress". Rome, Section IV, 227, 1955. KGlbel, H.; Ralek, M. Catal.Rev. Sci. Eng. 1980, 27, 225. KGlbel, H.; Ralek, M. I n "Chemical Feedstocks from Coal"; J. Falbe, Ed., Wiley: New York, 1982; pp 370-392. Madon, R. J. J. Catal. 1979, 57, 183. see. e.g., Odlan. G. "Principles of Polymerizatlon": McGraw-Hill: New York. 1970; pp 260-263. Poutsma, M. L. Oak Ridge National Laboratory Report ORNL-5635 (1980). Satterfleld, C. N.; Huff, G. A., Jr. Can. J. Chem. Eng. 1982a, in press. SatterReM, C. N.; Huff, G. A., Jr. J. Catal. 1982b, 73, 187. Satterfleld, C. N.; Huff, G. A., Jr.; Stenger, H. G. Ind. Eng. Chem. Process Des. Dev. 1981, 2 0 , 666. Schlesinger, M. D.; Benson, H. E.;Murphy, E. M.; Storch, H. H. Ind. Eng. Chem. 1954. 46. 1322. Schlesinger;M. b.;-Crowil, J. H.; Leva, M.; Storch, H. H. Ind. Eng. Chem. 1951. 43. 1474. Shultz, J. F.;'Hofer, L. J. E.; Cohn, E. M.; Stein, K. C.; Anderson, R. B. Bull. U . S . Bur. Mines 1959, No. 578, Part 2. Schulz, G. V. Z . Phys. Chem. 1935, 830,379. Vannice, M. A. Catal. Rev. Sci. Eng. 1978, 74, 153.
Received for review June 11, 1981 Accepted February 5 , 1982 This study was supported in part by the National Science Foundation under Grant No. CPE-7914173.
Steady-State Simulation of an Ammonia Converter-Heat Exchanger System Mlchael J. Khayan and Filippo F. Pirontl' Universidad S i m h Bolivar, Apartado 80659, Caracas 1080A, Venezuela
A mathematical model has been developed for the steady-state simulation of a commerical system formed by an ammonia converter and a heat exchanger. The model based on a set of partial differential equations, solved numerically by a Crank-Nicolson technique, allows us to obtain two-dimensional temperature and concentration profiles through the reactor beds. Good agreement was observed, with deviations less than 2%, between the computer calculated values and plant data. The radial gradient of temperature and composition were found to be of little significance for the reactor studied. An overall activity of 67% was obtained for the catalyst converter as a result of the simulation of the actual operating conditions.
Introduction Ammonia synthesis is probably one of the first commercial processes subject to numerous research studies. With the computer, it has been shown that mathematical models can be developed and applied to simulate the conversion process. See Kjaer (1958), Hay et al. (1963), Brian et al. (1965), Shah (1967), Dyson and Simon (1968), Shah and Weisenfelder (1969), Murase et al. (1970),Kubec et al. (1974), Gaines (1977), Lutschutenkow et al. (19781, Singh and Saraf (1979). The vast majority of these studies have shown that mathematical modelling is a safe and convenient way to analyze ammonia converters over a wide range of operating conditions. The synthesis reactor is considered as the most important equipment for the production of ammonia, since any small variation in the degree of conversion will affect the overall economical balance of the process. The objective of this study was to implement a computational scheme to solve a particular case of a set of partial differential equations, corresponding to a commercial system 0196-4305/82/1121-0470$01.25/0
formed by a fixed bed reactor coupled to a heat exchanger. Through this study we intend first to develop a more accurate mathematical model by taking into consideration radial variations of temperature, concentration, and linear gas velocity intra-reactor combined with intra-particle transport, and secondly, the steady-state simulation of the mathematical model developed for design and actual operating conditions and its comparison with plant data. The Ammonia Converter-Heat Exchanger System Figure 1shows a diagram of the commercial system that includes a vertical reactor and a heat exchanger. The reactor is a 600 ton per day ammonia converter from Mitsubishi Heavy Industries L.T.D., located in Moron, Venezuela, and operated by Pequiven S.A. This unit is composed of three nonadiabatic fixed beds, with intercooling or quenching zones. A standard heat exchanger is in series with the reactor; flow is countercurrent with one tube and shell pass. Usually, the gas for synthesis coming from the compressors is distributed in three streams. One is conveyed to the cooling shell of the reador, 0 1982 American Chemical
Society
