I d . Eng. Chem. Process Des. Dev. 1982, 21, 695-698 Ishida, M.; Oaki, H. “Chemlcal Process Design Based on the Structured Process Enerav-Exerav-Flow Diagram”: 91st Natlonai Meeting of AIChE, Detroit, 1981:-Nishida. N.; Kobayashi N.; Ichikawa A. Chem. Eng. Sci. 1971, 2 6 , 1841. Nishio, M.; Itoh, J.; Shiroko, K.; Umeda, T. Id.Eng. Chem. Process D e s . Dev. 1980, 79, 306. Oaki, H.; Ishida, M.; Ikawa, T. J . Jpn. Pet. Inst. 1981, 2 4 , 36. Oaki, H.; Ishida, M. J . Chem. Eng. Jpn. 1982, 75, 51. Rlekert. L. Chem. Eng. Sci. 1973, 2 9 , 1613.
695
Traupei, W. “Thermlsche Turbomachinen”;Springer: Berlln, 1946. Umeda, T.; Itoh, J.; Shiroko, K. Chem. Eng. - Prog. - 1978, 74(7),70.
Received for review August 13, 1981 Accepted May 12, 1982 Presented at the Gordon Research Conference on Thermodynamic Analysis, July 1981.
Enthalpy and Dew-Point Calculations for Aqueous Gas Mixtures Produced in Coal Gasification and Similar Processes Bernd Rittmann, Helmut Knapp, and J. M. Prauenltz’ Institute for Thermodynamics and Plant Design, Technical University of Berlln, Berlin (West) 12, Germany
A molecular-thermodynamic method is presented for calculating enthalpies and dew points for compressed, water-containing synthetic gases obtained from gasification of coal or other heavy fossikfuel sources. Ideal-gas contributions are calculated using Harmens’ method; gas-phase nonideality is taken into account using de Santis and Breedveld’s modification of the Redlich-Kwong equation of state. All necessary parameters are given for water and for 12 components common in synthetic gases. The computational method, applicable from 300 to 1000 K and to 300 atm, Is Illustrated by some typical calculated results.
Synthetic gases are produced by coal gasification or similar processes using high-boiling fossil fuels. These gases, leaving the reactor, are often at elevated pressures and temperatures and frequently contain appreciable concentrations of water vapor. For engineering design (energy balances), it is necessary to estimate enthalpies of synthetic gases as a function of composition, temperature, and pressure. Also, for design of process steps downstream of the reactor, it is useful to calculate the aqueous dew point, i.e., the conditions where water condenses. This work presents a molecular-thermodynamic method for calculating enthalpies and dew points for gas mixtures containing water in addition to the usual components found in synthetic gases. We consider the temperature range 300-1000 K and pressures to (about) 300 atm. The calculational method is performed with a corresponding computer program; copies of the program are available upon request. Thermodynamic Framework for Enthalpies Consider a gaseous mixture at absolute temperature T and totd pressure P containing components 1,2,3,...whose mole fractions are y , y2,y3,.... Per mole of mixture, enthalpy h is given by h = Cyihio Ah (1) i
+
where hio is the enthalpy of pure gas i at T; hio = 0 when T = 0. The isothermal effect of pressure is given by Ah
the essential equations as well as constants for water vapor and for 12 other gases commonly found in synthetic gases. To use eq 2, we require an equation of state for gases, including water vapor. We use a modification of the Redlich-Kwong equation, suggested by de Santis et al. (1974)
p = -R -T u-b
4T)
(3) T112u(u b) where, for any pure fluid, b is a constant and a ( T ) is, in general, a function of temperature. For water vapor, b = 14.6 cm3/mol; for carbon dioxide, b = 29.7 cm3/mol. For all other components considered here (see Table I), we obtain b from critical temperature T, and critical pressure pc 0.08664RTC b= (4) P C For components other than water and carbon dioxide, a(T) is a constant obtained from 0.4275R2T,2.5 a= (5) PC For hydrogen, we use effective critical constants in eq 4 and 5. For hydrogen we use T, = 43.6 K and P, = 20.3 atm. For water vapor
+
1.99798 X lo4
+
1.473169 X
T2
T where u is the molar volume of the gaseous mixture at T and P. To calculate hio,we use the method of Wilhoit (1975) as amplified by Harmens (1978). Since Harmens’ publication is not readily accessible, we present in the Appendix
Tj
For carbon dioxide gas 5.04354 X a ( T ) = (-7.97203 + T
* Chemical Engineering Department, University of California, Berkeley, CA 94720. 0196-4305/82/ 1 12 1-0695$0 1.2510
lo7 +
0 1982 American Chemical Society
lo4 - 9.77329 X Tz
lo6 +
698
Ind. Eng. Chem. Process Des. Dev., Vol. 21, No. 4, 1982
Table I. Constants for Harmens' Method
CPZ
gas
NO
s, K
water hydrogen nitrogen carbon monoxide carbon dioxide hydrogen sulfide methane ethane propane n-butane isobutane ethylene argon
3 2* 2* 2* 3* 3 5 8 11 14 14 6 b
370.0 120.0 400.0 400.0 140.0 300.0 240.0 190.0 160.0 130.0 150.0 160.0
CH,
a2
a1
0.930 36.938 3.543 2.816 -0.128 3.718 2.156 2.415 3.351 5.156 4.138 1.951 0.0
a3
0.050 -13.682 -21.524 -16.992 6.601 -17.193 -9.436 -9.786 -15.294 -29.220 -19.391 -7.702
1.639 5.163 64.727 56.921 -3.814 42.778 30.834 25.165 33.826 56.412 39.670 25.456 0.0
0.0
cs,
a4
cal/mol
cal/(mol K)
-8.868 46.040 -56.842 -54.294 -3.443 -33.232 -25.830 -19.026 -22.055 -32.440 -24.587 -20.004 0.0
-9.522 -41.425 -1.109 -1.337 -2.214 4.912 -1.303 7.210 19.090 65.215 39.343 0.164 0.0
-35.453 -13.984 -5.746 -4.303 -28.626 -29.978 -98.739 -180.081 -251.928 -328.872 -341.174 -114.348 8.672
Note: asterisk * in the column for N indicates that CPZ and DCP must be calculated for linear molecules. = 2.5 cal/( mol K); for S any value > 0 will do.
where the units are atm [cm3/mo1I2- [Kl1j2. For water and for carbon dioxide, we write
I
+
a ( T ) = a@) a'"(T)
For argon
Compos! l i o n
(8)
where a@),independent of temperature, represents nonpolar (dispersion-force) contributions to parameter a while ~("(7') represents the polar contributions; water has significant dipole and quadrupole moments while carbon dioxide had a significant quadrupole moment. Following de Santis et al., do)= 35 X loe for water and 46 X lo6 for carbon dioxide. To apply eq 3 to mixtures, we use bM
= Cyibz
(9)
200
1
300
P r e s s u r e Barr
and
Figure 1. Enthalpy departures and dew points at five temperatures. aM
=~C~LYJ~L]
(10)
1 1
For all components (other than water and carbon dioxide)
Compoti I i on
. Lwo -I -
Component
HOIC %
tH, 10,
50
2
a, = (a1a,)'/2
(11)
When component i is water (or carbon dioxide) and component j is any other component except carbon dioxide (or water) a , = (a,(0)a,) l / Z (12)
*Dew P O i n l
30
When component i is water and component j is carbon dioxide
I000 1
200
300
P r e s s u r r , bars
Where K, the equilibrium constant for the formation of a water-carbon dioxide complex, is given by 5953 2746 X lo3 + 464.6 X lo6 In K = -11.071 + --
T
T2
To
( 14)
T [K]; K [l/atm] When eq 3,9, and 10 are substituted into eq 2, we obtain
For mixtures which contain neither water nor carbon dioxide, daM/dT = 0. To use eq 15, it is first necessary to solve eq 3 for the molar volume of the mixture, using also eq 9 and 10. In
Figure 2. Enthalpy departures and dew points at five temperatures.
this work, eq 3 is applied only to the vapor phase; therefore, as used here, only one real root for u exists for given P, T , and y.
Results To illustrate our calculational method for some typical mixtures, Figures 1, 2, and 3 show some calculated isothermal enthalpy departures, while Figures 4 and 5 present isobaric plots of h vs. temperature. Solid points indicate calculated dew-point conditions, as discussed in the next section. Unfortunately, for water-containing gas mixtures, we cannot compare experimental with calculated enthalpies, because published experimental data are not available. (Experimental enthalpy measurements are now in progress at TU-Berlin.) However, the good agreement for PVT properties, reported by de Santis et al., (1974), and our reasonable, physically grounded mixing rules for a and b, suggest that the calculational procedure presented here
Ind. Eng. Chem. Process Des. Dev., Vol. 21, No. 4, 1982
Composi l i o n
i
Component
2
40
750 * D e w Point
20 50 10
H2
CO
897
in the vapor phase is given by cp,yJ' where cp, is the vapor-phase fugacity coefficient of water. At the same temperature and pressure, let the fugacity of liquid water be denoted by fwL. No condensation can occur as long as
'
fwL V W Y 2 (16) Upon cooling isobarically, fWL falls more rapidly than cp,yz; upon compressing isothermally, q , y z rises more rapidly than fWL.Therefore, upon cooling or compression, the inequality shown in eq 16 may become an equality. In that event, water condenses; a dew point has been attained. The fugacity of liquid water is given by
1
-250
200
IO0
300
Pressure. bots
Figure 3. Enthalpy departures and dew points at five temperatures.
I
I
Composition
-Component _ _ Mole
'/,
20
HlO
ri h:O
10
I
I bar
IO
3:
70
I = 150
when 1:P:O
L50
:
2:
, 500
5 :300
550
600
where fWuis the fugacity of pure water, saturated at its vapor pressure P,", and a, is the partial molar volume of liquid water. Since typical gases are slightly soluble in water, mole fraction x, is close to, but somewhat less, than unity while activity coefficient yw is also close to, but (usually) somewhat larger than unity. For our approximate purposes here, we set z,y, = 1and we assume that 0, is equal to the volume of pure saturated water. Further, we assume that water is incompressible over the range Pw8to P. The fugacity of pure saturated water is easily calculated from the steam tables; it is given by log f,S = 494.34 4.6173 X lo5 3.8535 X lo7 3.8926 - -(18) +
T
Tempemlure. I(
Figure 4. Enthalpy isobars for five pressures.
Further, from the steam tables 2.8696 X T
1
2
h:O
when T=P:O 150
, 500
!zQ
!P
550
:
I bar
= 30 3 : 70 b : 150 5 : 300
i 600
Temptrolure. K
Figure 5. Enthalpy isobars for five pressures.
should provide reliable estimates. In the absence of suitable data, it is difficult to estimate the accuracy of the proposed method of calculation. The ideal-gas contributions to enthalpy are certainly accurate since they follow from highly regarded specific heat data. Configurational contributions, calculated from the equation of state, are less accurate but, fortunately, they are often not important, as at low pressures. At pressures in the vicinity of 100-300 bar, we estimate that our calculated configurational enthalpies are accurate to better than f25 % for water-containing mixtures. For water-free mixtures the accuracy is better, probably in the range of *15%. Thermodynamic Framework for Dew-Point Calculations. Consider an aqueous gaseous mixture at absolute temperature T and total pressure P where T is less than the critical temperature of water. The mole fraction of water in the gaseous mixture is y,. The fugacity of water
lo3 + 4.4235 X lo5 T-2 7.6887 X 'Io
lo7
and uW8= (4.3257 - 3.3622 X 10-2T 1.2464 X 10-4P 2.0255 X 10-7!zQ 1.2549 X 10-'op) X 18.016 (20)
+
+
In these equations, fW8 and PWsare in atmospheres, uWsis in cm3/mol, and T i s in kelvins. The fits to the data are for the region 300-630 K. (The critical temperature of water is 647 K.) The fugacity coefficient for water is ,found from
(21)
where V is the total volume containing n, moles of water, nj moles of j , etc. (V = xiniu). When eq 9, 10, and 3 are substituted into eq 21, we obtain
698
Ind. Eng. Chem. Process Des. Dev., Vol. 21, No. 4, 1982
Table 11. Dew-Point Fugacity Coefficients ( P =150 bar)
%.oat
mixtures
H,O-H,-CO,
T,K
H20 - H 2
H,0-CO,
410 500 590
0.9183 0.8011 0.7062
0.5489 0.5995 0.6835
650
=
YH,/YCO,
0.7018 0.6866 0.6939
1
Acknowledgment For financial support, J.M.P. is grateful to the U.S. Department of Energy (Fossil Energy Program, Assistant Secretary of Energy Technology), to the National Science Foundation, and to the Alexander von Humboldt-Stifbung. Appendix Harmens’ Method for Calculating Ideal-Gas Enthalpies. For a pure ideal gas at absolute temperature T , the molar enthalpy ho is given by ho = CH
+ (CPnT + S(DCP)*f(y)
(All
t
+
fb) =
550 r
v
r
I l l f P U A l MOLAR P A R T S
,
,
02 01 06 H o l e Fractton W a t e r i n V o p o r
2y + l n ( i - y ) Y P +y3 -3+ - +y2 a 3 4 L
I OB
L
7
+
J
1
Figure 6. Dew-point temperatures for aqueous vapor mixtures.
For the cases considered here, calculated fugacity coefficients for water do not deviate much from unity, as shown in Table 11. Results Calculated dew points are indicated in Figures 1-5 and also in Figure 6. As expected, dew-point temperatures rise with gas-phase water content at constant pressure. At constant gas-phase water content and at low pressures, dew points are essentially independent of the nature of the other gaseous components. However, as pressure rises,dew points become increasingly sensitive to the nature of other species in the gas phase. Broadly speaking, at constant (high) pressure and at constant gas-phase water content, dew point temperatures fall as the average molecular weight of the nonaqueous components increases. The dew point of water is determined primarily by the vapor pressure of water, which is known with high accuracy. The fugacity coefficient, calculated from the equation of state, is less accurate. The dew-point calculations also ignore the solubilities of gases in liquid water. We expect that our dew-point calculations are accurate to &3 K and frequently much better. Conclusion This work presents a molecular-thermodynamic method for calculating enthalpies and dew points in compressed, water-containing gas mixtures. Such calculations may be useful for design of processes producing synthetic gases from coal or other heavy fossil fuel sources. All required parameters are given for water and for 12 other components commonly found in synthetic-gas manufacture. Computer programs are available upon request.
where
and S = a characteristic temperature (scaling factor); C H = a constant of integration; CPI = high-temperature limiting value of specific heat; and DCP = difference between CPI and the low-temperature limit of specific heat. Unfortunately, Harmens uses symbol y as defined by eq A3. This y is not to be confused with the mole fraction y used in the text. CPI = (3N - 1.5)R for linear molecules and CPI = (3N - 2)R for nonlinear molecules, where N is the number of atoms per molecule and R is the gas constant. The lowtemperature limit of specific heat is 3.5R for linear molecules and 4R for nonlinear molecules. Table I gives the seven constants required by eq AI for water and for 12 components commonly found in synthetic gases.
Literature Cited Harmens, A. “Proceedings of the Conference on Chemlcal Thermodynamic Data on Flulds and Fluid Mlxtures, Thelr Estimation, Comelation and Use”; National Physlcs Laboratory, Teddlngton, Middlesex, IPC Sclence and Technology Press: England. 1978. de Santls, R.; Breedveld, 0. J. F.; Prausnitz, J. M. I d . Chem. Process D e s . Dev. 1974, 13, 374. Wilholt, R. C. Thermodynamic Research Center, Texas A & M Unlversity, “Current Data News”, Vol. 3, 1975; pp 2-4.
Received for review September 3, 1981 Accepted March 25, 1982
