sa0
Ind. Eng. Chem. Process Des. Dev. 1980, 19,580-586
must be taken regarding the temperatures used in its preparation and regeneration.
AC01-79ET10554. They also wish to thank the personnel of Southern Company Services, Inc., for supplying various materials for the reported experiment. The authors wish to acknowledge the technical assistance of D. Stewart, Donald Colgrove, and David Watson of the Auburn University Coal Conversion Laboratory. Literature Cited
Conclusions Fez03 accelerates the coal-dissolution reaction, and it is selective for hydrodesulfurization over hydrogenation reactions. One important feature is that hematite reacts with all the hydrogen sulfide released from the coal, thus preventing any reverse reaction of hydrogen sulfide with the organic constituents of coal process solvent. Only a stoichiometric amount of hematite is required to remove the sulfur from the coal, suggesting that sulfur removal in the presence of hematite is basically a chemical reaction. The presence of an excess of hematite up to several times the stoichiometric amount has an insignificant influence on either hydrogen consumption or sulfur removal. Hydrogen consumption and sulfur removal are strongly dependent on reaction temperature and time. Higher reaction temperature and longer times yield greater amounts of hydrogen consumption and sulfur removal. The formation of gases (CHI, C02,and C&5) is also directly related to reaction temperature as well as reaction time. The desulfurization reaction is found to be kinetically controlled within the range of conditions tested. Also, the effectiveness of Fez03 as a desulfurization agent is surface area dependent. The careful control of scavenger/catalyst preparation/regeneration temperature is necessary if active sulfur scavenger/catalysts are to be obtained.
Garg, D., Ph.D. Dissertation, Auburn University, Auburn, Ala., 1979. Garg, D., Tarrer, A. R., Guin, J. A., Lee, J. M., Curtis, C., Fuel Process. Techno/.,2, 189-208 (1979). Given, P. H., Spackman, W., Davis, A., Walker, P. L., Lovell, H. L., Report No. 3, National Sclence Foundation, Sept 1975. Granoff, B., Traeger, R. K., Paper Presented at the 85th National Meeting of AIChE, Phlladelphia, Pa., 1978. Guin, J. A., Tarrer, A. R., Lee, J. M., VanBrackle, H. F., Curtis, C., Ind. Eng. Chem. Process Des. D e v . , 18, 631 (1979). Guin, J. A., Tarrer, A. R., Lee, J. M., Lo, L., Curtls, C. W., Ind. Eng. Chem. Process Des. D e v . , 18, 371 (1979). Henley, J. P., M.S. Thesis, Auburn University, Auburn, Ala., 1975. Jackson, W. R., Larkins, F. P., Marshall, M., Rush, D., White, N., Fuel, 58, 281 (Apr 1979). Kawa, W., Friedman, S., Wu, W. R. F., Frank, L. V., Yavorsky, P. M., paper presented at the 167th National Meeting of the American Chemical Society, Los Angeles, Calif., Mar 31-Apr 5, 1974. Mukherjee, D. K., Chowdhury, P. B., Fuel, 55, 4 (Jan 1976). Owen, H., Venuto, P. B., Yan, T. Y., Mobil Oil Corporation, New York, U S . Patent 4 077 866 (Mar 7, 1978). Petersen, E. E., "Chemical Reaction Analysis", Prentice-Hall, Inc., Englewood Cliffs, N.J., pp 135-137, 1965. Roberts, G. W., "Catalysis in Organic Synthesis", P. N. Rylander and H. Greenfield, Academic Press, New York, 1976. Seitzer, W. H., Final Report Prepared for EPRI by Suntech, Inc. under Contract EPRI AF-612 (RP-779-7), Feb 1978. Turkdogan, E. T., Vinters, J. B., Metall. Trans., 2, 3175 (1971). Wright, C. H., Severson, D. E., Am. Chem. Soc. Div. FuelChem. Repr., 18(2), 68 (1972). Monthly Report Prepared by the Pittsburgh and Midway Coal Mining Co. Menian, Kansas for US. Department of Energy Under Contract No. EX-76441-496, Feb 1978.
Acknowledgment The authors are grateful to the US. Department of Energy for support of this work under Contract No. DE-
Received for review September 14, 1979 Accepted June 9, 1980
Vapor-Liquid Equilibrium Relationship for Ammonia in Presence of Other Gases K. V. Reddy and A. Husaln" Regional Research Laboratory, Hyderabad 500009, India
Multicomponent vapor-liquid equilibria for the five-com onent system NH,-N,-H,-CH,-Ar are successfully correlated in the range 273-323 K and 49 X IO5 to 490 X 10 Pa. Six alternate methods were tried for evaluating vapor phase fugacity coefficients. This leads to a successful application of the Redlich-Kwong equation of state, with one of its parameters being temperature dependent for NH3, along with the mixing rules using parametric data of the pure individual components. An algorithm for computing the equilibria is given.
P
and less than the critical temperature of NH3. Hence, only NH3 will condense at these conditions and the liquid N H , in equilibrium with the gaseous phase, will contain some amount of each of the above components dissolved in it. The solubilities of each of the gases N2,H2,Ar, and C H I in the liquid NH3 are reported by Nielsen (1956). Alesandrini et al. (1972) derived a set of equations for the V-L-E from binary data of the components; they plotted graphs from which vapor and liquid compositions in equilibrium can be calculated for the five-component system at temperatures from 253 to 378 K and at pressures 50.66 X lo5, 202.64 X lo5, and 405.28 X lo5 Pa, when the vapor phase molar ratio Hz:N2:Ar:CH4is 3:1:0.18:0.44.
Introduction Ammonia is industrially synthesized in a variety of systems incorporating converters of various designs, which operate either at low pressures, 152 X lo5to 304 X lo5Pa (150-300 atm), or a t higher pressures up to 608 X lo5 Pa (600 atm). In such systems, besides ammonia, other components are present, viz., unconverted Hz and Nz and small amounts of CHI and Ar. In the modeling and simulation of such an industrial synthesis loop, the vapor-liquid equilibrium relationships were needed in a range 293-333 K and 20.26 X lo5 to 608 X lo5 Pa (20-600 atm). Temperatures in this range are more than the critical temperatures of Nz, H2,Ar, and CHI 0196-4305/80/1119-0580$01 .OO/O
0
1980 American Chemical Society
Ind. Eng. Chern. Process Des. Dev., Vol. 19, No. 4, 1980
581
Table I. Coefficients of Eq 9
--
A
B
C
D
E
193.19389 -203.39420 483.54588 413.88343
2.4116593 2.4117042 -6.4121276 - 5.3949156
-0.84695638 X lo-* -0.84697111 X lo-* 0.34018649 X 10-I 0.29121251 X 10-I
0.10233027 X lo-' 0.10233186 X lo-' -0.80038523 x lo-' -0.69651858 X
0 0 0.71411916 X low7 0.63228243 X
d
55"' GrnS
USrnS
Guerreri and Prausnitz (1973) reported equilibrium relationships for the five-component system valid in the range of 243-333 K and 81 X lo5 to 304 X lo5Pa (80-300 atm). Highly reliable V-L-:E data for NH3 in presence of other gases were available to the authors from vendors of the plant (Ammonia Casale) under study in the range 273-323 K and 49 X lo5to 490 :< lo5 Pa, with a vapor phase molar ratio of H2:N2:Ar:CH4equal to 3:1:0.19:0.46;these will be referred to as the vendor-supplied data. The aim of this study is to correlate the vendor-supplied data with the reported equilibrium relationships, or, if necessary, to modify these based on1 the thermodynamic principles. Fundamental Equations At equilibrium, fugacity of each component in both the liquid and vapor phases should be equal giving (1) Both the vapor and liquid phases will be nonideal at the conditions under consideration. In the liquid phase, NH3 is the solvent (subcritical) and the other components are solute (supercritical). 'With the vapor pressure of NH3 the reference pressure, fugacity of NH, in this phase is given by fiL
= fiV
and the fugacity of ealch solute by
Pressure Correction For the pressure correction term in eq 2 and 3, experimental data on partial molar liquid volumes, ul and Dim, are required, which are rare for the binary systems and almost nonexistent for the multicomponent systems. Hence, an empirical correlation by Wada (1949) is used, as done by Alesandrini et al. (1972), for calculating the partial molar volumes; for use in this correlation, the saturated liquid NH, molar volumes at different temperatures as given in the International Critical Tables (1926) are fitted by the following equation VI' = 78.986133 - 0.43363766T 0.00087587742P (8)
+
For further use in the Wada correlation, in order to calculate partial molar volume, uim,a t the infinite dilution in NH3, uimsvalues are required a t pressure P18and the system temperature T; these are reported by Alesandrini et al. (1972) in the range 253-378 K, which are correlated as follows Dims = A + B T C P D P E P (i = 2, ..., 5) (9)
+
+
+
The coefficients of eq 9 are given in Table I. Henry's Constant The Henry's constants for various components, PI'^,^, for use in eq 3 are correlated by Alesandrini et al. (1972) in the range 253-378 K in the similar way as eq 7. Fugacity Coefficient The fugacity coefficient, &, in eq 4 is rigorously related to the volumetric properties of a vapor mixture by the equation
The vapor phase fugacity of each component is fiv = $;yip (i = 1, 2,...,5 ) (4) Activity Coefficientti At the high pressures under consideration, the method given by Prausnitz andl Chueh (1968) will be appropriate to compute the liquid phase activity coefficient, yi's, in eq 2 and 3. This method iis based on representing the excess free energy by summing up interaction of the molecules. By neglecting the dilation effect, the solvent (NHJ activity coefficient reduces to
However, due to nonavailability of sufficient volumetric data for the vapor mixture, di has to be calculated either by applying the theorem of corresponding states or with the help of an equation of state. Alesandrini et al. (1972) applied a modified form of the Redlich-Kwong (RK) equation to the system under consideration up to 405.28 X lo5 Pa; the same can be explored for higher pressures. The original RK equation is p = -RT U u - b P 5 u ( u + b) For a pure component, the parameters a and b are given by
and for the solute Component to In yi* =
The self-interaction constants of solute i in NH,, aii,l, as obtained from the binary solubility data are fitted by Alesandrini et al. (1972) by the following type of equation in the range 253-378 I.( B C In aii,l= A - + (7)
+T
T 2
For the polar component, NH,, Alesandrini et al. (1972) treated the parameter al defined by eq 12 as temperature dependent; for the other components, they used the dimensionless constants Qai = 0.4278 (i = 2, ..., 5) and Q b , = 0.0867 (i = 1, 2, ..., 5) as originally available in the AK equation. In the present study, however, both 9, and 9 b l for NH3 in eq 12 and 13, respectively, are consihered as
582
Ind. Eng. Chem. Process Des. Dev., Vol. 19, No. 4, 1980
temperature dependent in place of al. Further modifications of the RK equation for the mixtures fall under two groups-(i) estimation of am and b, for the mixture from ai and bi values of the individual components or (ii) estimation of pseudocritical properties of the mixture from component critical properties, which are then used to estimate a, and b,. Under the first group, Alesandrini et al. (1972) proposed to calculate
when occupying alone the total volume a t the given temperature, which should not be confused with its partial pressure. Now substituting eq 21 into eq 10 and integrating one obtains
n n
in which for those i-j pairs where neither i nor j is ammonia
ai; = q u i a ;
Furthermore, for use in eq 2, fugacity of the saturated liquid NH,, fPl'pwe,l,is given as follows by combining eq 10 and 11
(15)
In the present work, in addition, Lorentz combination (Dodge, 1944) is used to compute
fP,lpwe,l = Pls exp[ In
(E)
L(
RT1.5 b In
The b, is computed as originally proposed by Redlich and Kwong (1949), i.e. n
bm =
biyi i=l
Under the second group, Joffe's (1947, 1948) pair of equations are applied to define the pseudocritical temperature and pressure of the mixture; then eq 10 to 13 along with the constant values of Qa and Qb (already given) are used to derive the following relation for the fugacity coefficient In di = -In (u, - b,) + 4 n ( l / T c , m aTc,m/ayi - 1/Pc,dPc,m/aYi) -
and
(20) In another alternative, Dalton's law of additive pressures is assumed to hold. If the P V T behavior of each individual gas is represented by an equation of state of the pressure explicit form, such as the RK equation, the total pressure is given by
Here Pi stands for the pressure of component i exerted
b) + U b- b +
(u + b
-
L/] u+b (23)
Procedure For calculating the fugacity coefficient, di, of each component in the vapor phase, the following alternate methods are applied: (i) equation for di used by Alesandrini et al. (1972), incorporating the mixing rules described by eq 14 and 17 and eq 15 for aij;(ii) same as (i) but using eq 16 for a , .(Lorentz combination); (iii) eq 18 based on Joffe's pseuaocritical approach; (iv) eq 22 based on the additive pressure method; (v) considering temperature dependence of Q,, and Qb for the polar component NH, in eq 1 2 and 13; (vi) consihering temperature dependence of a,, alone, while Qbl is fixed a t a constant value equal to 0.0867 as originally available in the RK equation. The estimation algorithm is shown in Figure 1. For alternatives (v) and (vi), the following objective function is minimized in order to generate correct Q,, and Qbl or Q,, alone a t different selected temperatures 7
where
L,
- In (u -
C(y1,mPi- yl,cpi)2 i
(24)
where ylpi is the equilibrium ammonia concentration in the vapor phase at pressure Pi at a chosen temperature, and subscripts m and c pertain to the vendor supplied and computed data, respectively. In alternative (v), the Nelder and Mead (1964) procedure has been applied for updating the Q,, and Qbl values from iteration to iteration, while in the last alternative, a one-dimensional Fibonacci search (Husain and Gangiah, 1976) has been used. Results and Discussion The results for the first four alternatives are presented in Table I1 from which it will be clear that the first two methods, viz. that of Alesandrini et al. (1972) and that incorporating the Lorentz combination, give satisfactory agreement only at the lower pressures (up to 98.06 X lo5 Pa); among the two, the latter performs better, while a t the higher pressures, the pseudocritical and additive pressure methods indicate somewhat better performance. However, all of them fail to provide a close agreement as desired for the vendor-supplied data over the whole range of temperatures and pressures. The same is obvious from the high values of the root mean square deviations (RMSD) of y 1 values, given at the bottom of Table 11, which are calculated as follows
Ind. Eng. Chem. Process Des. Dev., Vol. 19, No. 4, 1980 583 Table 11. Equilibrium Ammonia Concentration in the Vapor Phase mole percent ammonia in the vapor phase
temp, K
pressure, Pa 49.03
X
98.06 X
lo5
lo5
294.18 x
490.30
273 283 293 303 313 323 333 27 3 283 293 303 313 323 333 273 283 293 303 313 3 23 333 273 283 293 303 313 323 333
X
lo5
lo5
vendorsupplied
Alesandrini method
Lorentz combination
10.20 14.90 20.00 26.20
10.01 14.33 20.07 27.46 36.68 47.80 60.63 5.48 7.82 10.94 15.00 20.16 26.58 34.34 2.37 3.33 4.60 6.25 8.35 10.98 14.22 1.66 2.31 3.16 4.25 5.63 7.34 9.36 1.698
10.14 14.50 20.02 27.68 36.92 48.00 60.81 5.64 8.03 11.20 15.32 20.55 27.03 34.85 2.56 3.58 4.92 6.67 8.89 11.67
-
-
5.5 8.2 11.6 15.8 20.5 26.0
-
2.9 4.0 5.6 7.6 10.2 13.2 17.2 2.30 3.05 4.30 6.20 8.20 10.60 14.00
RMSD Table 111. Estimation of n
Jof f e 's additive pseudocritical pressure method, eq 18 method, eq 22 9.78 13.72 18.83 25.33 33.40 43.21 54.87 5.63 7.81 10.63 14.19 18.61 23.99 30.45 2.89 3.89 5.17 6.75 8.68 10.99 13.73 2.28 3.03 3.97 5.12 6.51 8.14 10.04 1.595
-
1.84 2.55 3.48 4.67 6.17 8.03
-
0.994
9.80 14.14 19.94 27.42 36.78
-
5.29 7.66 10.87 15.08
-
2.42 3.53 5.07 7.19 10.11
-
2.03 3.01 4.43 6.59
-
1.211
and ~2 mole % NH, in the vapor phase
temp, K 273
0.345905
0.115777
283
0.350430
0.132681
293
0.3 59400
0.0992199
303
0.361988
0.108879
313
0.37 3 54 2
0.0850778
323
0.37 1647
0.111467
For alternative (v), the results are given in Table 111, indicating a highly satisfactory performance of this procedure. While O,, values show a regular pattern with the change in temperature, the same is not true with fib1. Hence, it can be safelly assumed that Ob1 is more or less
pressure, Pa ( x l o s )
vendor supplied
49.03 98106 294.18 490.30 49.03 98.06 294.18 490.30 49.03 98.06 294.18 490.30 49.03 98.06 294.18 490.30 49.03 98.06 294.18 490.30 49.03 98.06 294.18 490.30
10.20 5.50 2.90 2.30 14.90 8.20 4.00 3.05 20.00 11.60 5.60 4.30 26.20 15.80 7.60 6.20
20.50 10.20 8.20
26.00 13.20 10.60 RMSD
computed 10.17 5.88 2.97 2.25 14.35 8.21 4.03 2.99 19.89 11.37 5.59 4.21 26.99 15.45 7.64 5.84 35.84 20.59 10.31 8.01 46.32 26.60 13.12 10.05 0.3111
temperature independent and can be fixed at the value of 0.0867 as originally available in the RK equation. Table IV gives the results for alternative (vi), showing a highly satisfactory agreement for the vendor supplied data over the whole range of temperatures and pressures,
584
Ind. Eng. Chem. Process Des. Dev., Vol. 19, No. 4, 1980
Table IV. Estimation of aa1(a&,, = 0.0867)
temp, K
a,,
273
0.251429
283
0.268571
293
0.294286
303
0.331143
313
0.345714
323
0.362857
Road 1 Ond Noncmdmllbkc
Ratio
pressure, Pa ( x los)
49.03 98.06 294.18 490.30 49.03 98.06 294.18 490.30 49.03 98.06 294.18 490.30 49.03 98.06 294.18 490.30 49.03 98.06 294.18 490.30 49.03 98.06 294.18 490.30
mole % NH, in the vapor phase vendor simulated, supplied computed eq 26
9.97 5.70 2.86 2.23 14.15 8.06 4.00 3.10 19.68 11.21 5.57 4.33 26.94 15.45 7.82 6.16 35.64 20.4 2 10.22 8.00 46.29 26.64 13.36 10.46 0.3135
10.20 5.50 2.90 2.30 14.90 8.20 4.00 3.05 20.00 11.60 5.60 4.30 26.20 15.80 7.60 6.20
-
20.50 10.20 8.20
-
26.00 13.20 10.60 RMSD
9.97 5.70 2.86 2.22 14.18 8.09 4.04 3.15 19.71 11.24 5.60 4.37 26.79 15.30 7.63 5.96 35.64 20.41 10.22 8.00 46.39 26.75 13.51 10.62 0.3181
which is obvious from the low enough values of RMSD obtained as given in Tables I11 and IV. The values of Q,, so generated at different temperatures are then empirically fitted by the following polynominal Q,, = -0.39788936
+ 0.0023754678T
(26)
Raod
P,xI's and y,
The simulated results using eq 26 are also given in Table IV.
Recommended Met hod In the light of the results as discussed above, a new algorithm as shown in Figure 2 is recommended for computing V-L-E for NH3 in the presence of Hz, Nz, CH,, and Ar. In this algorithm, the pressure correction term for the fugacity of solvent NH3 in the liquid phase is given by
I
1
where the saturated-liquid compressibility of NH3, p:, is calculated using the Chueh-Prausnitz (1969) equation as follows UCJ pls = (1 - 0.89 ull/z) exp(6.9547
- 76.2853T~,1-IRTCJ 191.306T~,1~ - 2O3.5472TR,i3+ 82.7631T~,1~) (28)
The pressure correction term for the fugacity of each solute component in the liquid phase is given by
J;g
1;
Pa.ms
dP =
RT i-[l
+ 7Pims(P Pls)]-1/7dP -
(29)
in which partial compressibility of the solute component
Figure 1. Estimation algorithm
i at infinite dilution, pims,is given by Alesandrini et al.
Ind. Eng. Chem. Process Des. Dev., Vol. 19, No. 4, 1980
585
Table V. Measured and Computed Dew Point Temperatures of the Vapor Leaving the Ejector in the Ammonia Plant dew point temp, K vapor composition, mol % data pressure, plant measset Pa(x105) NH, N, H2 Ar CH, urements computeda computedb 460.9 336.7 368.5 370.2
1 2 3 4
8.98 7.92 8.13 8.85
Alesandrini method,,
18.86 19.32 18.66 20.23
62.70 64.67 64.67 62.13
2.74 2.73 2.13 2.85
6.72 5.36 5.21 5.94
317.4 310.1 313.8 312.9
329.3 315.3 321.6 321.8
316.7 307.6 312.1 312.4
Recommended method. any component i including NH3, based on the RK equation and the mixing rules described by eq 14, 15, and 17, is reproduced from the work of Prausnitz (1969)
I
/+/'7'
+zzq qradimt
method
Figure 2. Dew point calculation using recommended method. (1972) based on the psieudocritical relationships of GunnPrausnitz (1958); this reduces to
HJdF G axi
FHJdG +--+-FJdH GZ axi G axi
FHdJ G axi
1
(30)
T,nj
In eq 30
F = CX~U,,~
(31)
i
G = RCxiTC,i
(32)
i
H =l
- 0.89(C~iwi)'/~
(33)
i
J = exp[6.9547
How powerful is the algorithm of Figure 2 is now demonstrated by calculating the dew-point temperatures of the vapor leaving the ejector, which is part of the ammonia synthesis loop of the plant under study. For this unit, measured composition of the vapor along with its temperature and pressure were available for various plant data sets. The measured dew-point temperatures are compared in Table V with those computed using the Alesandrini method and the recommended method of this paper. The poor and excellent performances of the two methods, respectively, are quite obvious. Conclusion This paper presents a new algorithm for calculating V-L-E for the five components system NH3-N2-H2CH4-Ar, which is valid in the range 273-323 K and 49 X lo5 to 490 X lo5 Pa, and a t a vapor phase molar ratio of H2:N2:Ar:CH, equal to 3:1:0.19:0.46. It is expected that the algorithm will hold good for small variations in the vapor phase molar ratios of the noncondensables from the typical ratios as prevalent in an ammonia synthesis loop. The algorithm has been programmed and run to demonstrate its superiority and accuracy compared to any other known method such as that of Alesandrini et al. (1972). The computer code for implementing the algorithm is available on request. Nomenclature A = coefficient in eq 7 or 9 a = defined by eq 12, ( ~ m ~ / g - m oatm l ) ~K112 ai,a, = value of a for component i or j aij = defined by eq 15 or 16 a, = value of a for the vapor mixture, eq 14 B = coefficient in eq 7 or 9 b = defined by eq 13, cm3/g-mol b, = value of b for the vapor mixture, eq 17 C = coefficient in eq 7 or 9 D = coefficient in eq 9 E = coefficient in eq 9 F = defined by eq 31 ft = fugacity of component i in the liquid phase, atm f,",= fugacity of component i in the vapor phase, atm pure,l = fugacity of pure saturated liquid NH3, atm G = defined by eq 32 H = defined by eq 33 H p ~ i ,=l Henry's constant of component i in NH, at saturation pressure of NH3,.atm I = objective function defined by eq 24
+
- 76.2853(T/C~~T~,~) i
191.306(T/C~iT,,i)~ - 203.5472(T/C~iT~,i)~ + 1
i
82.7631(T/CX~T,,~)~] (34) 1
T h e relation for calculating the fugacity coefficient of
586
Ind. Eng. Chem. Process Des. Dev. 1900, 19, 586-592
i = component designation index: 1,NH3; 2, N,; 3, H,; 4, Ar; 5, CH,
Greek Letters self-interaction constant of molecule i or j in the environment of molecule 1 Pls = saturated liquid compressibility of NH3 pima= partial compressibility of solute i at infinite dilution y1 = activity coefficient of solvent NH3 y*i = activity coefficient of solute i ~ 1 - t 4 = prescribed constants $ ~ i = fugacity coefficient of component i R, = parameter in eq 12 R,, = value of Q, for NH3 fib = parameter in eq 13 a b , = value of for NH3 w = acentric factor ~ u i i , ~ ;u i j = ,~
J = defined by eq 34 j = component designation index (same as i)
n = total number of points, eq 25 ni,nj = number of moles of component i or j P = pressure, atm P, = critical pressure, atm P,,,,Pcj = critical pressure of component i or j , atm P,,, = critical pressure of vapor mixture, atm Pi' = saturation pressure of NH3, atm Pi = pressure of component i when occupying the total volume at the given temperature R = gas constant, (atm cm3)/(g-mol K) T = temperature, K T , = critical temperature, K T,,i,T,, = critical temperature of component i or j , K Tc,, = critical temperature of mixture, K T R ,=~ reduced temperature of NH3 u = molar volume, cm3/g-mol uc,+, = critical molar volume of component i or j , cm3/g-mol u1 = molar volume of saturated liquid NH3, cm3/g-mol u, = molar volume of the mixture, cm3/g-mol D l = partial molar volume of NH3, cm3/g-mol Dim = partial molar volume of component i for infinite dilution in NH3, cm3/g-mol D y = partial molar volume of component i for infinite dilution in NH3 at saturation temperature of NH3, cm3/g-mol x i , x j = mole fraction of component i or j in the liquid phase y, yj = mole fraction of component i or j in the vapor phase yyll,c;ypbl,, = calculated and measured equilibrium concentration of NH3 in the vapor phase, respectively, at pressure , P i at a chosen temperature, eq 24, mole % ~ ' 1 y'l,, , ~ ; = calculated and measured concentration of NH3 in the vapor phase, respectively, at different pressures and temperatures, eq 25, mole % 2 = compressibility factor
Literature Cited Alesandrini, C. G., Lynn, S., Prausnitz, J. M., Ind. Eng. Chem. Process Des. Dev.. 11. 253 (1972). Ammonk Casale S.A., Italy, Fig.No.TD 48. Chueh, P. L., Prausnitz, J. M., AIChE J., 15, 471 (1969). Dodge, 8. F., "Chemlcal Engineering Thermodynamics", p 197, McGraw-Hill Book Co., Inc., New York, 1944. Guerreri, G., Prausnitz, J. M., Process Technol. Int., 18(4/5), 209 (1973). Gunn, R. D., Prausnitz, J. M., AIChE J., 4, 494 (1958). Husaln, A., Gangiah, K., "Optimization Techniques for Chemical Engineers", pp 27-31, Macmillan Co. of India Ltd., Delhi, 1976. "International Critlcal Tables of Numerical Data, Physics, Chemistv and Technology", McGraw-Hill Book Co. Inc., New York, 1926. Joffe, J. Ind. Eng. Chem., 39, 837 (1947). Joffe, J., rnd. Eng. Chem., 40, 1738 (1948). Nelder, J. A., Mead, R., Comput. J., 7, 308 (1964). Nielsen, A., "An Investigation on Promoted Iron Catalysts for the Synthesis of Ammonia", pp 28-29, Jut. Gjellerup Forlag, Copenhagen, 1956. Prausnitz, J. M., Chueh, P. L., "Computer Calculations for High Pressure Vapor-Liquid Equilibria", pp 82-90, PrenticeHall, Englewood Cliffs, N.J., 1966. Prausnitz, J. M., "Molecular Thermodynamlcs of Fluid-Phase Equilibria", p 156, Prentice-Hall, Englewood Cliffs, N.J., 1969. Redlich, O., Kwong, J. N. S., Chem. Rev., 44, 233 (1949). Wada, Y., J . Phys. SOC. 4, 280 (1949).
Received f o r review September 25, 1979 Accepted June 18, 1980
Global Model of Countercurrent Coal Gasifiers Phlllp G. Kosky' and Joachlm K. Floess General Electric Research and Development Center, Schenectsdy, New York 1230 1
This is a model of a fixed-bed coal gasifier in which CO, C02, HO , and H, are assumed to be in thermodynamic shift equilibrium over a zone in which the primary gasification reactions occur. Exiting temperatures from this zone are in excess of 550 O C and the shift reaction is readily catalyzed by gas-borne impurities. Fresh coal is pyrolyzed in this gas stream and its gaseous products are added quantitatively to the shift gases. The final raw product gases thus calculated are close to experimentaldata from several sources for oxygen- and air-blown gasifiers. The model, which is simple conceptually and mathematically, correctly predicts the effect of heat leak in establishing the composition of the raw coal gas from a fixed bed gasifier. This important variable has not had the visibility that its significance demands.
Introduction It is possible to model coal gasifiers by assuming detailed knowledge of local chemistry and kinetics (Arri and Amundson, 1878; Amundson and Arri, 1978; Yoon et al., 1976,1978; Biba et al., 1978). The gross picture of a fixed bed (i.e., slowly descending) gasifier and reactant gases is as Figure 1. The reactor is presumed to have the approdimate zones shown. The coal which enters the reactor is rapidly heated by the upflowing gases. The coal is devolatilized in the process-which is to say that the chemical bonds of the original coal macerals are broken producing 0196-4305/80/1119-0586$01.00/0
gases as H2, CO, COz, CH4, H2S, NH,, and water, trace gases, some oils, and tars (Figure 2). A residue of coal char remains. This material is mostly carbon ("fixed carbon"). At the temperatures achieved in a fixed bed gasifier the devolatilization is near completion but the possibility remains that some small mass of hydrogen is retained in the char (Juntgen and van Heek, 1968). On a molar basis the hydrogen may not be quite negligible compared to the fixed carbon. The devolatilization process is ill understood and is is unwise to be dogmatic about the distribution of devolatilized gases from this zone. Their concentration 0 1980 American Chemical Society
