Equilibrium Data for Wet-Air Oxidation. Water Content ant 1 Thermodynamic Properties of Saturated Combustion Gases Robert A. Heidemann’’ and John M. Prausnitr Department of Chemical Engineering, University of California,Berkeley, Berkeley, California 94720
Thermodynamic calculations, based on correlated data, give the equilibrium water content, density, enthalpy, and entropy of saturated combustion gases from 20 to 320 OC and pressures to 200 atm. Attention is given to mixtures of 0, 13, 15, 17, and 20% carbon dioxide in nitrogen on a dry basis. The results are presented in tables which, at a fixed temperature and C02/N2 ratio, list the gas properties at pressures in intervals of 10 atm. The calculations are based on a modified Redlich-Kwong equation of state for the vapor phase and Henry’s law with the Poynting correction for the liquid phase. Good agreement is obtained with the limited available experimental data.
Introduction Combustion gases saturated with water vapor result from several processes which have increasing industrial importance. One such process is the wet oxidation of sewage sludge or other wastes as described by Zimmermann (1958). A second is in the enhanced recovery of heavy oil reservoirs through in situ combustion. These gases, often a t high temperature and pressure, have potential value because of their high energy content. For example, Stinson et al. (1976) have described a process for power recovery from exhaust gases resulting from in situ combustion in an oil reservoir. Design of gas-expansion turbines, or other devices for energy recovery, requires thermodynamic properties of the gases, including the water content. Recently, Luks et al. (1976) have computed the equilibrium moisture content of nitrogen-oxygen mixtures, including air. They use the volume-explicit virial equation for the vapor phase, truncated after terms in P2. For solutes in the liquid phase they use a version of Henry’s law. However, combustion gases are likely to contain carbon dioxide, which would have an effect on the equilibrium moisture content. Carbon dioxide was not included as a component in the work of Luks et al. (1976). Evelein et al. (1976) have correlated the phase behavior of the system carbon dioxide-water, using the Soave modification of the Redlich-Kwong equation for both phases. The approach they employed could be used in determining the moisture content of combustion gases. However, the Soave modification of the Redlich-Kwong equation is designed to match vapor pressure data and it is not clear that it can give accurate predictions of volumetric and other thermodynamic properties. In this work we have used a modified Redlich-Kwong equation of state, developed by de Santis et al. (1974) to fit P-V-T data for water-containing vapor mixtures. For the liquid phase we use the Krichevsky-Kasarnovski equation, which is Henry’s law with the Poynting correction. We consider a ternary, two-phase mixture containing nitrogen, carbon dioxide, and water; the liquid phase contains primarily water. Our purpose is to calculate the equilibrium composition and the enthalpy and entropy of the gaseous phase as a function of three independent variables: temperature, pressure, and the ratio of nitrogen to carbon dioxide.
Author to whom correspondence should be addressed at Department of Chemical Engineering, The University of Calgary, 2920-24 Avenue N.W., Calgary, Alberta, Canada T2N 1N4.
We do not consider combustion gases containing unexpended oxygen; wet oxidation processes are usually operated with complete oxygen consumption. The oxygen/nitrogen ratio would have an effect on the equilibrium water content of the gases, as discussed by Luks et al. (1976).
Phase-Equilibrium Calculations The equations governing equilibrium between the two phases are
(3)
where T is temperature, P is total pressure, f is fugacity, superscripts V and L designate, respectively, the vapor phase and the liquid phase, and subscript i designates the components (i = 1, 2, 3 corresponds to H20, Nz,CO2, respectively). The Vapor Phase. The vapor-phase fugacity is related to the vapor-phase mole fraction y by
+iYiP
fi” =
(4)
where +i is the fugacity coefficient. The equation of state for the vapor phase is (de Santis et al., 1974)
+
P = RT/(v - b ) - a/[T1/2v(v b ) ]
(5)
where a is a function of temperature, with mixing rules for a and b
and
b = C xibi
(7)
1
With this equation of state, the fugacity coefficient is given bY In & = in [u/(v- b ) ]
+ bi/(v - b )
1
- 2 [ E yjaij/RT3/2b In [ ( u + b ) / u ] + (abi/RT3/2b2) I
X
{ln [ ( v
+ b ) / v ] - b / ( u + b ) )- In (PVIRT)
Ind. Eng. Chem., Process Des. Dev., Vol. 16, No. 3, 1977
(8) 375
Table I. TemDerature-IndeDendent Parameters
1, H z 0 2, Nz 3, co2
0.0146 0.02678 0.0297
Table 11. Parameter
a11 for
Table 111. Parameter
35.0 15.462 46.0
HzO, (L/mol)2atm (K)l12
T , "C
a
daldT
20 30 40 50 60 70 80 90
500.0 461.5 427.3 397.0 368.0 342.0 320.0 300.0 282.5 267.5 254.0 242.5 232.0 224.0 216.3 211.0 205.0 200.1 194.7 189.7 184.5 180.1 174.9 170.7 165.9 162.1 157.7 153.3 150.3 146.6 143.5 140
-4.11 -3.63 -3.215 -2.965 -2.75 -2.40 -2.10 -1.875 -1.625 -1.425 -1.250 -1.100 -0.925 -0.785 -0.650 -0.565 -0.550 -0.540 -0.525
100 110
120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330
-0.50 -0.48 -0.47 -0.45 -0.43 -0.41 -0.39 -0.37 -0.35 -0.34 -0.33 -0.32
+ a,, (I)(T)
376
-0.0357 -0.0714 -0.0714 -0.0714 -0.0714 -0.0714 -0.0714 -0.0714 -0.0714 -0.0714 -0.0714 -0.0714 -0.0714 -0.0714 -0.0714 -0.0714 -0.0714 -0.0611 -0.0611 -0.0611 -0.0611 -0.0611 -0.0611 -0.0611 -0.0611 -0.0611 -0.0611 -0.0611 -0.0611 -0.0611
5953 2746 X 103 + 464.6 X 106 +T T2 T3
+ 21
a13 = a31 = [ ~ 1 1 ( 0 ) ~ 3 3 ( 0 ) ] ~-R2T5I2K /~
(12)
(13)
The Liquid Phase. For COz and Nz, the liquid-phase fugacities are given by the Krichevsky-Kasarnovski equation (Prausnitz, 1969)
(9) where His is Henry's constant, x is the liquid-phase mole fraction, and E$ is the partial molar volume of solute i in water. The vapor pressure of water is designated by Pws. Henry's constant is a function only of temperature in eq 14. For nitrogen in water, a correlation given by Himmelblau (1960) has been used; i.e. -log ("11.239 X lo5) = 1.142 - 2.486(1/T*) 2.486 (1/T*)2 - 0.9761(1/T*)3 0.2001(l/T*)4 (15)
+
+
where
(10)
T,, Ind. Eng. Chem., Process Des. Dev., Vol. 16, No. 3, 1977
-0.0 -0.0
where K is in reciprocal atmospheres and T is in kelvins. de Santis et al. (1974) show that
For a,, where i # j , the nature of intermolecular interactions between different species is taken into account. Hydrogen bonding and polar forces are presumed not to play a significant role in the interactions between N2 and other species. Therefore, for a12 = a21 and a23 = a32r and
71.0 71.0 70.8 70.1 69.4 68.7 68.0 67.4 66.7 66.0 65.3 64.5 63.8 63.1 62.3 61.6 60.9 60.2 59.5 58.9 58.3 57.6 57.0 56.4 55.8 55.2 54.6 54.0 53.4 52.8 52.2 51.6
In K = -11.07
111.
= (all@) a22)1/2
20 30 40 50 60 70 80 90 100
daldT
(11) Water and C o n , on the other hand, apparently react in the gas phase to form a compound. Equilibrium in the reaction is governed by an equilibrium constant
The temperature-dependent part, uLr(l),is attributed to intermolecular attractions from hydrogen bonding and polar forces; for Nz, a22(1)is zero. Coefficients b, and ulr(o)are tabulated in Table I. We have interpolated from the tables of de Santis et al. (1974) a l l and 1 2 3at ~ 10 "C intervals. These coefficients and their temperature derivatives are reported in Tables I1 and
a12
U
120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330
-0.51
COz, (L/mol)2 atm (K)112
T , "C
110
The molar volume u must be found from eq 5 a t a fixed temperature, pressure, and vapor composition. The constants a,, and b, in eq 6-8 are given for HzO, N2, and COz by de Santis et al. (1974). The a coefficient for pure components is split into two parts a,, = arr(0)
8 3 3 for
= 357 K
(17)
Table IV.= Properties of Saturated Nitrogen (Temperature = 160 "C) P , atm
Mol of HzO/ mol, dry gas
0.162E + 01 0.4663 + 00 0.2753 + 00 0.197E 00 50 0.154E 00 60 0.127E 00 70 0.109E + 00 0.954E - 01 80 0.8523 - 01 90 100 0.771E - 01 110 0.705E - 01 120 0.652E - 01 0.607E - 01 130 0.5683 - 01 140 150 0.5353 - 01 160 0.506E - 01 0.481E - 01 170 0.4593 - 01 180 0.4393 - 01 190 0.421E - 01 200 a Detailed tables (covering the R. A. Heidemann. 10 20 30 40
Entropy, btu/(lb. mol O R )
Density, lb,/ft3
+ +
+
Enthalpy, btuAb. mol Wet basis Dry basis
+
+
0.532E 04 0.3966 00 -0.115E + 01 0.203E + 04 0.2943 04 0.887E 00 -0.2643 + 01 0.200E + 04 0.2543 04 0.138E 01 -0.351E + 01 0.199E + 04 0.2373 04 -0.411E + 01 0.186E + 01 0.198E + 04 0.197E 04 0.2276 04 0.235E 01 -0.4593 01 0.2833 01 -0.4983 + 01 0.196E + 04 0.220E + 04 -0.531E 01 0.216E + 04 0.330E + 01 0.195E + 04 -0.560E 01 0.212E + 04 0.194E + 04 0.378E + 01 0.4253 + 01 -0.5863 + 01 0.193E + 04 0.209E 04 0.4723 01 -0.609E + 01 0.192E 04 0.207E 04 0.518E + 01 -0.630E + 01 0.192E + 04 0.205E + 04 0.191E 04 0.203E 04 0.5643 + 01 -0.650E 01 0.190E + 04 0.202E 04 0.609E + 01 -0.668E + 01 0.6543 + 01 -0.6853 + 01 0.190E + 04 0.201E + 04 -0.700E + 01 0.699E + 01 0.189E + 04 0.200E + 04 0.7433 01 -0.715E 01 0.199E + 04 0.189E + 04 0.7873 01 -0.729E + 01 0.189E + 04 0.198E 04 0.830E + 01 -0.743E + 01 0.188E + 04 0.197E + 04 0.8733 + 01 -0.756E + 01 0.188E + 04 0.196E + 04 0.915E + 01 -0.7683 + 01 0.188E + 04 0.195E + 04 conditions of temperature, pressure, and COz/N* ratio mentioned in the text) are available from
+ + + +
+
+ + + +
+
+ +
+
+
+ +
+
+ + +
+ +
+
+
Table V.a Properties of Saturated Gas, 13% C02 and 87% N2 (Temperature = 160 "C) Mol of HzO/ mol dry gas
P , atm
Density lb,/ft3
+ + + + + +
a
Entropy, btu/(lb mol OR)
+ + + + + + + + + + + + + + + + +
10 0.162E 01 20 0.4693 01 30 0.2783 00 40 0.199E + 00 50 0.157E 00 60 0.130E 00 70 O.lllE 00 80 0.978E - 01 90 0.8763 - 01 100 0.7953 - 01 110 0.730E - 01 120 0.6773 - 01 130 0.6323 - 01 140 0.5943 - 01 150 0.561E - 01 160 0.5326 - 01 170 0.507E - 01 180 0.4853 - 01 190 0.4663 - 01 200 0.4483 - 01 See footnote to Table IV.
0.411E 00 0.940E 00 0.147E + 01 0.199E 01 0.252E 01 0.304E 01 0.356E + 01 0.408E 01 0.459E 01 0.510E 01 0.561E 01 0.611E 01 0.661E 01 0.711E 01 0.760E 01 0.808E 01 0.857E 01 0.904E 01 0.951E 01 0.9983 + 01
-0.109E -0.2553 -0.3393 -0.400E -0.4473 -0.486E -0.519E -0.5483 -0.574E -0.597E -0.619E -0.638E -0.6563 -0.673E -0.689E -0.704E -0.719E -0.7323 -0.7453 -0.758E
and HS is in atmospheres. We prepared our own correlation for CO:,, based on diverse experimental data (Takenouchi and Kennedy, 1964; Todheide and Franck, 1963; and data quoted by Edwards et al., 1975). The expression employed is
+
Hs(atm)/6500 = -12.51379 51.28834(T/647) - 62.04960( T/647)2 23.27505(T/647)3
+
(18) A correlation by Lyckman et al. (1965) was used for the partial molar volumes, in the form
!&
R Tci
= 0.095
+ 2.35(TPci/cllTci)
(19)
The cohesive energy for water, c11, was evaluated a t each temperature from thermodynamic properties tabulated by Bain (1964), according to ~ 1= 1
+
(ho- ha - P w s ~ wRT)/VwE s
(20)
+ 01 + 01 + 01 + 01 + 01 + 01 + 01 + 01 + 01 + 01 + 01 + 01 + 01 + 01 + 01 + 01 + 01 + 01 + 01 + 01
Enthalpy, btuhb mol Wet basis Dry basis
+ +
0.206E 04 0.206E 04 0.205E + 04 0.203E + 04 0.202E + 04 0.201E + 04 0.199E + 04 0.198E + 04 0.197E + 04 0.196E + 04 0.195E + 04 0.194E 04 0.193E + 04 0.192E + 04 0.191E 04 0.190E + 04 0.189E 04 0.189E + 04 0.188E + 04 0.187E + 04
+ + +
+
0.540E 04 0.302E + 04 0.261E 04 0.2443 + 04 0.234E 04 0.227E + 04 0.222E + 04 0.218E 04 0.214E 04 0.212E + 04 0.209E 04 0.207E + 04 0.205E + 04 0.203E + 04 0.202E + 04 0.200E 04 0.199E + 04 0.198E + 04 0.197E + 04 0.196E + 04
+ + + + + +
where ho is the molar enthalpy a t the given temperature but a t zero pressure, and vws is the molar volume of the saturated liquid. The fugacity of water in the liquid phase is given by where fpure 1 designates the fugacity of pure liquid water a t system temperature and pressure; it is found from data in the NEL steam tables (Bain, 1964). Calculation Procedure A t fixed temperature, pressure and ratio of COz/N:,, the equilibrium moisture content in the vapor phase was determined by performing a flash calculation. Sufficient w a t a was included with the CO:,and N2 in the mixture being flashed to assure that the vapor phase was saturated. The equilibrium conditions are given by eq 1-3. The procedure employed is a Ind. Eng. Cham., Process Des. Dev., Vol. 16, No. 3. 1977 377
Table VI.0 Properties of Saturated Gas, 20% C02 and 80% N2 (Temperature = 160 "C) P , atm
Mol of H2O/ mol dry gas
Density, lb,/ft3
0.163E + 01 0.470E + 00 0.279E + 00 0.200E 00 0.158E + 00 0.131E + 00 0.112E + 00 0.990E + 01 0.8883 + 01 0.808E + 01 0.743E + 01 0.690E 01 0.6453 01 0.607E + 01 0.575E + 01 0.5473 Of 0.5223 + 01 0.500E + 01 0.480E + 01 0.463E 01 See footnote to Table IV. 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200
Entropy, btu/(lb mol "R)
0.419E + 00 0.969E 00 0.152E 01 0.207E 01 0.261E + 01 0.316E + 01 0.371E + 01 0.4253 + 01 0.479E + 01 0.5323 + 01 0.5853 01 0.638E 01 0.691E + 01 0.7433 01 0.7953 + 01 0.8463 01 0.8973 + 01 0.9473 + 01 0.9963 01 0.105E + 02
-0.106E -0.249E -0.3333 -0.3943 -0.441E -0.480E -0.513E -0.5423 -0.5683 -0.591E -0.613E -0.632E -0.651E -0.6683 -0.684E -0.6993 -0.714E -0.727E -0.740E -0.7533
+ + +
+
+ + + +
+ + +
+
+
+ 01 + 01 + 01 + 01 + 01 + 01 + 01 + 01 + 01 + 01 + 01 + 01 + 01 + 01 + 01 + 01 + 01 + 01 + 01 + 01
Enthalpy, btuhb-mol Wet basis Dry basis 0.208E + 04 0.208E 04 0.207E 04 0.206E + 04 0.205E + 04 0.203E + 04 0.202E 04 0.200E 04 0.199E + 04 0.197E + 04 0.196E + 04 0.195E + 04 0.193E 04 0.192E + 04 0.191E + 04 0.19OE 04 0.189E + 04 0.188E 04 0.187E + 04 0.186E + 04
Table VII. Water Content of Saturated Nitrogen
Temp, "C
Saddington and Krase (1934)
Calcd, this work
100
50
100 100 100
80
0.001837 0.00629 0.01137 0.0549 0.1404 0.379 0.00132 0.0322 0.0929 0.208
0.00156 0.00577 0.0122 0.0582 0.170 0.482 0.000970 0.0322 0.0883 0.201
100 100 200
200 200
200
100
150 190 230 50 150 190 225
and
(T)
In u + b
(23)
where POand To designate the reference pressure and temperature, 1atm and 273.15 K, respectively. In eq 22 and 23, C,O is the heat capacity of the mixture in the ideal gas state; it is given by 378
Ind. Eng. Chem., Process Des. Dev., Vol. 16, No. 3, 1977
+ +
+
+
+ + + + + +
Tables I1 and TI1 give the derivatives dallldT and da3sldT a t 10 "C intervals. Differentiation of eq 13 leads to
Enthalpy a n d Entropy For our enthalpy calculations we choose h = 0 for the pure fluid in the ideal gas state a t 0 "C. For our entropy calculations we choose s = 0 for a mixture at the same composition in the ideal-gas state at 0 "C and 1 atm. The enthalpy and entropy follow from the equation of state (eq 5) and heat capacity data. That is h = L>pOdT+--- RTb a/T1/2 U-b u+b
+--bI ddT (")J T
+ +
+ + + +
For the pure-component, ideal-gas heat capacities, Cpio,we have used results given by Kelley (1960). The quantity d ( a / T T ) / d T is given by
two-phase version of the flash-calculation procedure described by Heidemann (1974).
+ R In (?)
+
+
0.545E 04 0.306E + 04 0.265E + 04 0.2473 04 0.2373 04 0.230E 04 0.2243 04 0.220E + 04 0.216E + 04 0.213E + 04 0.210E 04 0.208E + 04 0.206E + 04 0.204E 04 0.202E 04 0.200E 04 0.199E 04 0.197E 04 0.196E 04 0.194E + 04
(24)
~
Mol of HnO/mol of N2 Pressure, atm
+
where In K is given in eq 12. Water Content of Combustion Gases Results of the calculations described above are presented in tables which, a t fixed temperature and C02/N2 ratio, list water content per mole of dry gas, gas density, enthalpy, and entropy at pressures increasing at intervals of 10 atm to 200 atm. The dry gas compositions considered are 0,13,15,17, and 20% C02 in N2, respectively. Temperatures range from 20 to 320 "C in intervals of 10 "C. Complete sets of the tables are available from R. A. Heidemann. Typical results are presented in Tables IV-VI. Figures 1 and 2 show the equilibrium water content per mole of dry gas a t various temperatures, over the pressure range of interest. Figure 1shows isotherms for representative temperatures 160 "C and lower, and Figure 2 shows isotherms at higher temperatures. The equilibrium water content a t fixed temperature and pressure is affected by the CO2/N2 ratio. While the effect is difficult to show in Figures 1 and 2, particularly at higher temperatures, it is significant over the whole range of temperatures and pressures considered. In Figure 3 we have plotted the ratio of the water content of gases containing 13% and 20% C02 (dry basis) to the water content of saturated nitrogen. This ratio is, in general, greater
00002
----
-
----_-----
100% N,
20 O b CO,, 80
Ob
N,
i
i
0 0001L
20
40
80 DO 120 I40 PRESSURE, ATMOSPHERES
60
160
180
200
Figure 1. Water content of nitrogen and combustion gases a t moderate temperatures.
-20 D/r
--- 13 %
C02,
1
80 % N 2
C02 , 8 7 % N 2
i I
I
01 20
40
60
80
I
I
100
120
140
160
I80
200
PRESSURE. bTMOSPHERES
0
100
200 TEMPERATURE
300
*C
Figure 2. LVater content of nitrogen a t high temperatures.
Figure 3. Effect of C O d N ? ratio on saturated water content.
than unity, and is largest at low temperatures and high pressures. Figure 4 shows a comparison between our calculated results and the data for water in nitrogen of Rigby and Prausnitz (1968).The data extend to 100 "C and 100 atm. The calculated results are in close agreement with the data; the errors do not exceed 2.5%,only slightly larger than the expected accuracy of the data. Some data for the solubility of water in nitrogen at higher temperatures and pressures are available from the measurements of Saddington and Krase (1934). Comparison with these data is presented in Table VII. The agreement is variable; our calculated results at 50 "C are lower but at 100 atm and 230 "C our calculated water content is about 25%larger
than the experimental value. There is no obvious way to assess the uncertainty in the experimental data but fortunately agreement with the other data of Saddington and Krase, particularly with the three high-temperature measurements at 200 atm, is much better and is comparable to the agreement with the data of Rigby and Prausnitz (1968). Both Webster (1953) and Rigby and Prausnitz (1968) have presented reasons for supposing that there are errors in the data of Saddington and Krase (1934). In particular, Webster argues that the reported water content at 50 "C and high pressures is too large. No comparison can be made for mixtures of nitrogen and carbon dioxide because no published experimental data on equilibrium water content are available. Ind. Eng. Chem., ProcessDes. Dev., Vol. 16,No. 3, 1977
379
0.018
t l
-looo6
\
-
- --
-
Ne SATURATED WITH
-
n20 (CALCULATED)
V
---DRY
0
0
20 % C 0 2 , 80 % N2 SATURATED WITH H20 ICALWLATED)
-
N21HILSENRATH ET AL 1960)
-
z
W c?
E 0016z a
-
W
zs
z F 0014V
E
-
W -I
z 0.012
-
0
t
ENTROPY OF SATURATED WATER VAPOR
\
m
100 TEMPERATURE
SATURATIONPOINT
300
C
F i g u r e 6. Entropy of saturated combustion gases.
aoi I PRESSURE, ATMOSPHERES
F i g u r e 4. Water content of nitrogen; comparison with data of Rigby and Prausnitz.
D R Y N2 (HILSENRATH E T AL 19601
ENTHALPY OF
, 3
c
m
-
c
I
I
1
1
I
1
1
100
l
1
I
200 TEMPERATURE
I
l
l 1 300
O C
F i g u r e 5. Enthalpy of saturated combustion gases.
Thermodynamic Properties Calculated enthalpies and entropies are presented in Figures 5 and 6. In both figures, isobars a t 50,100,150, and 200 atm are plotted against temperature. The results presented are primarly for a gas containing 20% COa on a dry basis. The isobar for nitrogen at 100 atm is also shown to demonstrate the effect of varying the ratio of carbon dioxide to nitrogen. At low temperatures, when the water content is small, the properties of the saturated gas differ little from the properties of the dry gas. The enthalpy and entropy of nitrogen a t 100 atm are tabulated in Hilsenrath et al. (1960). These values have been converted to the reference state used here and are 380
Ind. Eng. Chem., Process Des. Dev., Vol. 16, No. 3, 1977
also shown in Figures 5 and 6. The values given by Hilsenrath et al. (1960) agree almost exactly with our calculated enthalpy and entropy for saturated nitrogen when the water content is low. Deviations become important only at high temperatures when the gas contains appreciable quantities of water. Each isobar terminates at the boiling temperature of water for the given pressure. As this temperature is approached, the ratio of water to dry gas increases and the properties of the gas approach the properties of steam, regardless of the ratio of carbon dioxide to nitrogen. In Figures 5 and 6 we have included the enthalpy and entropy, respectively, of saturated steam. These values were taken from Bain (1964) and converted to our reference state. The enthalpy isobars of Figure 5 extrapolate smoothly to the curve for saturated steam. The entropy isobars for 50 and 100 atm terminate at points which almost lie on the entropy curve for saturated steam, indicating small error. The accuracy of the computed thermodynamic properties is determined by the accuracy of the modified Redlich-Kwong equation of state used for the vapor phase. As shown in Figures 5 and 6, the equation is very good for nitrogen. When applied to pure water vapor, de Santis et al. (1974) report that the equation is least accurate in the vicinity of the critical point. In our calculated results, any inaccuracies would increase, a t a given pressure, as the boiling temperature of water is approached. The errors could be expected to be somewhat higher at advanced pressures. However, the results presented in Figures 5 and 6 indicate that, for engineering work, errors are small. In the absence of adequate data, it is difficult to be definite in assessing the accuracy of our calculated results. We believe, however, that our results for water content and thermodynamic properties of saturated nitrogen, carbon dioxide mixtures are more accurate than any others now available. Combustion gases containing oxygen or other nonpolar supercritical species can be dealt with using the procedures described here. Henry's constants are the only additional data required. Coefficients a and b in the Redlich-Kwong equation would be evaluated, as for nitrogen, from critical data. At temperatures higher than the critical temperature of water there would be no liquid water phase; for this reason the saturated water content calculations could not be extended to temperatures higher than 374 "C. However, the enthalpy
and entropy of wet gases (even if not saturated) could be calculated at higher temperatures than those considered here, using eq 22 and 23.
Literature Cited Bain, R. W., “NEL Steam Tables 1964,” Her Majesty’s Stationery Office, Edinburgh, 1964. de Santis, R., Breedveld, G. J. F., Prausnitz,J. M., lnd. Eng. Chem., Process Des. Dev., 13, 374 (1974). Edwards, T. J., Newman, J., Prausnitz, J. M.,A.6Ch.E. J., 21, 248 (1975). Eveiein, K. A., Moore, R. G., Heidemann, R. A., Ind. Eng. Chem., Process Des. Dev., 15, 423 (1976). Heidernann, R. A.. A.l.Ch.€. J., 20, 847 (1974). Hilsenrath, J., Beckett, C. W., Benedict, W. S.,Fano, L.. Hoge, H. J., Masi, J. F., Nuttall. R. L., Touloukian, Y. S.,Wooiiey, H. W., “Tables of Thermodynamic and Transport Properties,” Pergamon Press, New York, N.Y., 1960. Himmelblau, D. M., J. Chem. Eng. Data, 5, 10 (1960). Kelley, K. K.. US.Bur. Mlnes Bull. 584 (1960). Luks, K. D., Fitzgibbon, P. D., Banchero, J. T., lnd. Eng. Chem., Process Des. Dev., 15,326 (1976). Lyckman. E. W., Eckert, C. A., Prausnitz, J. M., Chem. Eng. Sci., 20, 685
(1965). Prausnltz, J. M., “Molecular Thermodynamics of Fluid-Phase Equilibria,” Prentice-Hail, Inc., Engiewood Cliffs. N.J., 1969. Rigby, M., Prausnitz, J. M., J. Phys. Chem., 72, 330 (1968). Saddington, A. W., Krase, N. W., J. Am. Chem. Soc., 56, 353 (1934). StinSon, D. L., Carpenter, H. C., Cegieiski, J. M., J. Pet. Techno/., 645 (June, 1976). Takenouchi, S., Kennedy, G. C., Am. J. Sci., 262, 1055 (1964). TCjdheide, K., Franck, E. U., Z. Phys. Chem. (Frankfurt am Main), 37, 387 (1963). Webster. T. J., Discuss. Faraday SOC., 15, 243 (1953). Zimmerman, F. J., Chem. Eng., 65, 117 (Aug 25, 1958). Received for review October 11,1976 Accepted January 18,1977
T h e authors are grateful for financial support given by Zimpro Inc. o f Rothschild, Wisconsin, Associated Pulp and Paper, Ltd. of Devonport, Tasmania, the National Research Council o f Canada, and the National Science Foundation.
Optimal Temperatures for Ammonia Synthesis Converters Larry D. Gaines Systems Research Division, Applied Automation, lnc., Bartlesville, Oklahoma 74004
A steady-state model for a quench-type ammonia converter is developed and used to study the effect of converter temperature profile over a large range of operating conditions. A substantial improvement in converter efficiency is possible by maintaining optimal converter temperatures. The converter efficiency is shown to be primarily a function of fourth bed temperature. The optimal value of this temperature is a function of operating conditions and may be determined from the ammonia effluent concentration and equilibrium concentration. Based upon these results, a simple method of converter temperature control is proposed.
Introduction Ammonia synthesis, one of the oldest commercial highpressure processes, consists of reacting a hydrogen-nitrogen mixture over a catalyst a t elevated temperatures and pressures. Pressures employed in the reactor range from 120 to 600 atm. The reaction is exothermic and the high temperature in the reactor is sustained by the heat of reaction through the use of a feed-effluent interchanger. This process has been the subject of numerous studies and with the advent of computers, mathematical models have proven to be an accurate and convenient way to study ammonia synthesis converters over their entire operating region. Computers have been widely accepted in the area of ammonia plant control because of their abilities to increase operating efficiency and reduce process upsets. As computer control is extended to all parts of the process, a basic understanding of process characteristics is needed. Several studies (VanHeerdon, 1953; Hay et al., 1963; Brian, 1965; Shah, 1967; Baddour, 1965) have considered the effects of various pertinent variables upon ammonia production and converter stability. Annable (1952) fitted data from industrial reactors using the Temkin-Pyzhev rate expression and calculated ideal temperature and composition profiles. Baddour et al. (1965) modeled a TVA converter and compared model results with plant data. They found that the converter was close to instability a t temperatures favoring maximum ammonia production. They also found that these temperatures were a function of process conditions. Both Shah (1967) and Kjaer (1963) present model devel-
opments for quench-type converters. Shah (1967) proposed that his theoretical model be used for off-line optimization to determine quench flows and converter temperatures. Kubec et al. (1974) developed a model for a radial flow quench-type converter. They suggest the use of a model which would be optimized using dynamic programming. Model parameters would be adjusted using current process data. The objectives of this study are to develop a model of a synthesis converter, determine the effects of process variables upon converter operation, and use the resulting data to examine practical and easily implemented methods of converter temperature control. The ammonia plant chosen for this study is a low-pressure (150 atm) 600 T P D Kellogg plant which uses two quench-type converters in parallel. This model is used to determine the “best” converter temperature profile over a wide range of operating conditions. Process variables that affect converter efficiency are pressure, catalyst activity, space velocity, inerts, Hz/Nz ratio, feed temperature, and ammonia concentration in the converter feed; these variables and their impact on converter efficiency are amply investigated via model simulation. Ammonia Synthesis Converter The converter feed gas is split into five fractions. The bulk of the gas enters the top of the converter and flows downward around the outside of the catalyst section to the exchanger at the bottom of the pressure shell as shown in Figure 1. The gas is heated in the exchanger and passes through the riser tube to the first quench zone where it is mixed with cold feed gas Ind. Eng. Chem., Process Des. Dev., Vol. 16, No. 3, 1977
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