Ind. Eng. Chem. Process Des. Dev. 1084, 23, 226-234
228
S, = surface area of particle, cm2 t = time, s
U = transformed solid phase concentration V = reactor volume, cm3 V = volume of particle, cm3 d = total weight of adsorbent material, g x = dimensionless radial co-ordinate Creek Letters p = isotherm constant e = particle porosity p = particle density, g cm-3 = dimensionless time Literature Cited Abramowltz, M.; Stegun, 1. A. “Handbook of Mathematical Functions”; National Bureau of Standards: Washington, DC, 1964. Colwell, C. J.; Dranoff, J. S. AIChE J . 1866, 72, 304. Dryden, C. E.; Kay, W. B. Ind. Eng. Chem. 1854, 46, 2294. Eagle, S.; Scott,J. W. Ind. Eng. Chem. 1850. 42, 1287. H.M.S.O. “Notes on Applied Science No. 16: Modern Computing Methods”.
Mathews, A. P.; Weber, W. J. AICMSymp. Ser. 1876, 7 3 , 91. McKay, G.; McConvey, I . F. J. Chem. Technol. Blotechnol. 1881, 3 7 , 401. McKay, G.; Allen, S. J. Can. J . Chem. Eng. 1880, 58, 521. McKay, G.; Alexander, F.; Poots, V. J. P. Ind. Eng. Chem. Process D e s . Dev. 1878. 77, 406. McKay, G.; Otterburn, M. S.; Sweeney, A. G. Water Res. 1880, 74, 15. Miller, C. 0.; Clump, C. W. A I C M J. 1870, 76, 169. Natlonal Physical Laboratory Publlcation: Teddington. Middlesex, 1961. Neretnlelts, I . I . Ch. E . Symp. Ser. No. 54 1877, 49. Numerical Algorithms Group (U.K.) Ltd.; Central Office: 7 Banbury Road, Oxford OX2 6NN, England, 1959. Pwts, V. J. P.; McKay, G.; Healy. J. J. Water Res. 1976, 70, 1071. Rosen, J. B. J. Chem. Phys. 1852. 2 0 , 387. Rosen, J. B. I n d . Eng. Chem. 1854, 4 6 , 1590. Smith, S. 6.; Hlltgen, A. X.; Juhola, A. J. AIChE Symp. Ser. No. 24 1858, 55, 25. Tien, C. Can. J. Chem. Eng. 1860, 38, 25. Tien, C. AIChE J. 1881, 7 , 410. Weber, T. W.; Chakravorti, R. K. AIChE J. 1874, 2 0 , 224.
Received for review August 9, 1982 Revised manuscript received March 24, 1983 Accepted June 6, 1983
SolubHies of Heavy FogSil Fuels in Compressed Gases. Calculation of Dew Points in Tar-Containing Gas Streams Agustlne Mongot and John M. Prausnltr’ Chemical Engheering Department and Meterials and Mokcular Research Division, Lawrence Berkeley Laboratory, Universlty of Callfornia, Bericeky, Callfornk 94720
A molecular-thermodynamic model is used to establish a correlation for solubilities of heavy fossil fuels in dense gases (such as those from a coal gasifier) In the region ambient to 100 bar and 600 K. This model is then applied to calculate dew points in tarcontaining gas streams. The heavy fuel is fractionated in a spinning-band column at high reflux; each fraction is conskiered to be a pseudocomponent. Each fraction is characterized by one vaporpresswe datum (obtainedduring fractionation),elemental analysis, and proton NMR spectra (to determine aromaticity). Uqukl-phaseproperties are obtained from the SWAP equation for vapor pressure and from a density correlation. Vapor-phase properties are obtained with the virial equation of state with virlal coefficients from Kaul’s correlation. Experimental solubWy measurements have been made for two Lurgi coal-tar fractions in dry and moist methane. Calculated and experime~ntalsotubllities agree well. The correlation is used to establish a design-orbnted
computer program for calculating isobaric condensation as a function of temperature as required for design of a continuous-flow heat exchanger.
Introduction The high cost of energy has stimulated new process technologies toward more efficient utilization of energy resources; therefore, there has been growing interest in upgrading coal, heavy petroleum fractions, tar sands, shale oil, etc. Design of “downstream units” for emerging processes requires quantitative information for equilibrium properties of heavy fossil fuels at elevated temperatures and pressures. This work is concerned with the solubility of a heavy fossil fuel mixture in a compressed gas. This solubility is of interest in process design: e.g., for petroleum-reservoir pressurization with light gases, toward removal of high-molecular-weight hydrocarbons remaining after primary recovery; for design of coal-liquefaction reactors; for design of coal-gasification process steps (condensation and quenching) where product gas streams often contain high-boiling coal tars; and for design of heavyfossil-fuel/lighbgasseparation operations. Solubilities may
‘E.I. du Pont de Nemours and Co. Inc., P.O.Box 2o00, Laplace, LA 70068. 0196-4305/84/1123-0226$01.50/0
be of particular interest for calculating dew points as required in heat-exchanger design. Fossil fuel mixtures typically contain very many components. The wide range of properties and the analytical problem to identify these components makes phaseequilibrium predictions difficult. A common procedure is to separate the mixture into fractions with fewer components and smaller ranges of properties and to characterize each fraction. Phase-equlibrium predictions and process design are then based on average or effective (pseudocomponent) properties of the characterized fractions. In this work, we separate a heavy fuel by distillation into narrow-boiling fractions and we characterize each fraction. Characterization data are used with previously established physical-property correlations to determine required parameters in our molecular-thermodynamic model. Fossil Fuel Fractionation and Characterization To obtain narrow-boiling fractions, we use a PerkinElmer Model 251 annular still, operated at high reflux, as described by Macknick (1979) and Alexander and Prausnitz (1981). Each fraction has a boiling-point range of 0 1984 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 2, 1984 Table
I.
C h a r a c t e r i z a t i o n D a t a for
v a p o r pressure datum
-T , "C __
fract.
--
no. 1
2 3 4 5 6 7 8 9
10
Lurgi Coal T a r
wt %
0.45 1.2 1.8 1.6 4.1 17.5 20.8 10.8 15.7 26.1
-
__ ____--
P,torr
C
57 53 50 51 52 52 52 51 50
83 84 85 86 86 87 87 88 86 87
95 121 141 158 178 194 205 222 239
--
---
____-
e
a
d
k-Tot
~
e l e m e n t a l analysis, wt %
H 9.9 8.6 8.5 8.9 8.6 8.4 8.5 8.2 8.5 8.1
N 0.8 1.1 0.8 1.2 1.3 1.1 1.2 1.0 1.4 1.4
S 0.5 0.2 0.3 0.4 0.5 0.3 0.5 0.4 0.3 0.3
other
aromaticity
5.6 6.0 5.5 3.7 3.9 3.8 3.3 2.1 3.7 3.7
0.53 0.64 0.64 0.69 0.64 0.69 0.67 0.71 0.65 0.66
__________I
For the heavy-hydrocarbon mixtures of interest here, the liquid-phase fugacity of component i is given by
Condenser H
227
Vacuum
fiL = XiPi"(PC)i
(2)
where x i is the mole fraction of component i in the liquid, Pi"is the pure-component vapor pressure, and (PC), is the
-Receiver Flask
Poynting correction. The liquid-phase fugacity of a noncondensible (light-gas) component is here given by
f?
fiv
Figure 1. Fossil-fuel fractionation via spinning-band column.
about 20 K. Figure 1 shows a schematic of this spinning-band column and indicates operating conditions. During fractionation, the head temperature and pressure are recorded for each fraction at the beginning and end of collection. The average temperature and pressure provide a vapor-pressure datum for the fraction since the liquid fraction is in equilibrium with its vapor as it is collected. Each fraction is weighed. Further, each fraction is analyzed for carbon, hydrogen, nitrogen, and sulfur. Finally, proton NMR spectra are obtained as discussed elsewhere (Alexander and Prausnitz, 1981). The carbonto-hydrogen ratio, along with the NMR spectra, determines fractional aromaticity (fraction of carbon atoms which are aromatic), as briefly explained in Appendix A. Table I summarizes characterization results for a Lurgi creosote (coal tar)obtained from Sasol's coal-gasification plant in South Africa. A vapor-pressure datum for Lurgi fraction number 10 is not given because that part of the original sample could not be distilled overhead. Solidification of compounds (probably anthracene) in the head of the column limited the lowest column pressure to above 50 torr. Since the pot temperature was limited to 300 "C to minimize thermal decomposition,the heaviest overhead fraction that could be obtained has a normal boiling point of about 350 "C. Phase Equilibria: Molecular-Thermodynamic Framework Each fraction is considered to be a pseudocomponent. At equilibrium, for any component i, the fugacity of i in the liquid phase equals that in the vapor phase = fiV
(3)
where Hi is Henry's constant for light gas i, dissolved in the mixture of condensible components. The vapor-phase fugacity of component i is given by
S t i l l : Perkin-Elmer Model 251 Annular S t i l l m Monel Mesh Spinning Band: 0.91 ~ 0 . 0 1 Reflux Ratio: 1O:l Boilup Rate: - 3 x 10-sm3/s Operating Pressure: 0.067 bar absolute Maximum Head Temperature: 250°C Maximum Pot Temperature: 30OoC Boiling-Point Range of Fraction: -2OOC
fiL
= XiHi(PC),
(1)
= Yi4iP
(4)
where yi is the mole fraction of component i in the vapor, +i is the fugacity coefficient, and P is the total pressure. The solubility of a heavy component in a gas is determined primarily by that component's vapor pressure. Macknick and Prausnitz (1978) tested predictions of several vapor-pressure correlations for five representative heavy hydrocarbons; they found that the SWAP correlation (Smith et al., 1976) is likely to give the best results for typical heavy, fossil-fuel mixtures where the molecular structures of the heavy-hydrocarbon components are not well-known. The SWAP correlation requires only a single vapor-pressure datum and an estimate of the heavy hydrocarbon's fractional aromaticity. Edwards et al. (1981) extended the SWAP vapor-pressure correlation to include the effects of heteroatoms nitrogen and sulfur. Appendix B summarizes the procedure for applying Edwards' extension of SWAP to heavy, fossil-fuel fractions. For poorly defined mixtures, such as fossil-fuelfractions, there is little basis for prediction of the effect of liquidphase nonidealities (activity coefficients) on fugacity. However, liquid-phase nonidealities are probably at least partially taken into account through the "effective" pseudocomponent vapor-pressure datum which is used to characterize fractions and to predict "effectiven vapor pressures of pseudocomponents. An estimate of each fraction's molar liquid volume VL, is needed to calculate the Poynting correction (PC), in eq 2
To estimate ViL, we use a correlation that requires only a normal boiling point and fractional aromaticity, as discussed in Appendix B. To calculate mole fractions from weight fraction, we require the molecular weight for each fraction. Molecular
228
Id.Eng. Chem. Process Des. Dev., Vol. 23,No. 2, 1984 Table 11. Comparison of Predicted and Measured Molecular Weights for Four Lurgi Coal-Tar Fractions E i ptl _ Predicted Frcction C' __ _ -Point, 296
348
mol wt
Weigh1
187 221
t
1
fract. no.
pred.
measd
% error
6 I 8 9
184 192 201 218
187 207 209 227
1.6 6.8 3.8 4.0
av 4.0
T e m p e r a t u r e , "C
Figure 2. Solubilities of two Lurgi coal-tar fractions in methane: comparison of predicted and experimental resulta.
weights are estimated as shown in Appendix B. For water, the liquid-phase fugacity is given by f,L
= ~,YuPwB@,Bat(Pc)w
(6)
For our purposes here, we assume water condenses as a pure liquid and we neglect the solubility of light gases in liquid water; thus mole fraction x, and activity coefficient yw are set equal to unity. Pws,(PC), and the saturatedwater-vapor fugacity coefficient, @,#, are calculated with empirical relations based on literature data for water. These are given in Appendix B. Vapor-phase solubilities are not sensitive to Henry's constants when the light gases are only sparingly soluble in the liquid phase. Henry's constants for gases in fractions are estimated as shown in Appendix B. In a mixture containing m components, vapor-phase fugacity coefficients are calculated from (7)
where Bij is the cross second virial coefficient for components i and j , and for the gas-phase mixture
Virial coefficients are calculated from the square-well potential as discussed in Appendix C. Experimental Section To test the molecular-thermodynamic framework, we have used the total-vaporization technique (Monge and Prausnitz, 1983; Monge, 1982) to measure the solubilities of two Lurgi coal-tar fractions in compressed methane mixtures. Figure 2 compares experimental and predicted solubilities at 3.8,42, and 70 bar. Comparison at the lowest pressure, where vapor-phase nonidealities are small, provides an appropriate test of vapor-pressure prediction. As shown, agreement is good. Comparison at higher pressures, where gas-phase nonidealities and the Poynting correction are large, is also good.
The measurement for fraction 1at 42 bar and 200 "C has been repeated for a gas mixture containing 25 mol 5% water in methane. The effect of water on tar-fraction solubility in the gas was found to be negligible, as correctly predicted by the model. Molecular-weight predictions were also tested. Table I1 compares predicted molecular weights with those determined from freezing-point depression measurements (Alexander and Prausnitz, 1981) for four Lurgi coal-tar fractions. Calculation of Solubilities The proposed molecular-thermodynamic model, coupled with fossil-fuel-characterization data, has been incorporated into a design-oriented computer program. If a sample of the heavy fossil fuel has been fractionated and characterized, the computer program can: (1)predict the dew-point temperature of a superheated gas mixture containing the vaporized fossil fuel at specified pressure and composition, and (2) predict the change in gas-phase solubility as the temperature falls isobarically. Dew-Point Calculation. A fossil-fuel-containing gas is at specified pressure and composition. An iterative procedure is used to search for the temperature at which the gas becomes saturated and the heavy fossil fuel begins to condense. At this temperature, the fugacity of each component in the liquid, ft,equals its fugacity in the vapor, fiv; the objective function F equals zero within a specified tolerance
Solubility vs. Temperature. At constant pressure, as the temperature falls below the dew-point temperature, the gas-phase solubility of the heavy fossil fuel decreases. This decrease can be calculated by assuming either that the gas is maintained in contact with its condensing liquid or that the condensing liquid is removed after an incremental decrease in temperature. The first option can be used to generate isobaric, solubility vs. temperature curves. The second option provides the condensation characteristics of a saturated gas cooled in a continuous-flow heat exchanger. These calculations are useful for the design of heat exchangers for recovery of thermal energy from hot coal-gasifier effluents containing heavy tars, assuming, as we do here, that very heavy tars have been previously removed. Newton's method is used to determine iteratively the solubility of the fossil fuel in the gas after an incremental drop in the gas temperature. Flash calculations begin by determining if water condenses at the new temperature, i.e., by asking If the answer is yes, water does not condense. In that event, we iterate on the vapor-to-feed ratio a,using the objective function S, and its derivative with respect to CY,
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 2, 1984 229 I
I
In! t io1 Compos1 t Ion
-
Component Weight mole % % H20 40.0 45.8 Cop 32.0 15.0 co 15.0 11.0 CH, 5.0 6.4
210
230 /\
/ Colculoted Neglecting /
140
Figure 4. Predicted condensation in a continuous-flow heat exchanger for a typical Lurgi coal-gasifier effluent at 42.7 bar.
Fugacity Coefficient
,
!-
5x104
-I
I
I
1
200
220
240
I
I
160
170
190
Temperature, "C
180
Temperature,
1
10-2
I
I
I
A Experimental
"C
Figure 3. Solubility of coal tar in a typical Lurgi coal-gasifier effluent at 42.7 bar.
S', as given by Rachford and Rice (King, 1971) for a two-phase system m
s = i=l C(yi--Xi)
(11)
10-31 160
where xi
=Zi/@
@ = a(Ki - 1)
(13)
+1
(14) yi = KiXi (15) Here, zi is the mole fraction of component i in the feed and Ki is the equilibrium K factor ( K , = y i / x i ) . S and S', evaluated at aald (old estimate for a),are used to obtain a new estimate for a %ew = a o l d - s/s' (16) The iterative procedure is repeated until a,,, is found where S equals zero within a specified tolerance. However, if fw" fwL (17) water condenses. In that event, we use an objective function derived from material balances for a three-phase system, where one phase is pure (liquid water). The derivation of the three-phase objective function is given in Appendix D. At a given temperature, the gas-phase solubility of the fossil fuel is given by the sum of the converged gas-phase mole fractions for all fossil-fuel fractions. For isobaric condensation vs. temperature calculations, the total number of moles in the gas phase is adjusted after each incremental temperature decrease because the condensed liquid is removed from consideration (as in a flow heat exchanger). The vapor-to-feed ratio is used in the material balances to calculate the fraction of the vapor condensed as hydrocarbon-rich liquid and water. The calculations are repeated at incrementally lower temperatures (typically 5 "C). Figure 3 shows some solubility vs. temperature calculations for a typical coal-gasifier effluent containing all but
I
180
I
I
I
I
1
200
220
240
260
280
Temperature, ' C Figure 5. Solubility of Lurgi-tar fraction 6 in methane at 70 bar: effect of neglecting fugacity coefficient and Poynting correction. I Sample
I
I
'
I
i
I
'
1
L u r g i Creosote Fraction #6
'
8
6
4
2
0
Shift From Hexomethyldisiloxane, 6
Figure 6. Sample proton NMR spectra.
the heaviest parts of the Lurgi coal tar described in Table I. Figure 3 also shows the initial gas composition (heaviest tars previously removed). Figure 4 shows the results of condensation vs. temperature calculations for the same system. The computer program is available upon request from the authors. Discussion and Conclusions Vapor-phase nonidealities and Poynting corrections can have a significant effect on the solubility vs. temperature behavior of light-gas/ heavy-fossil-fuel systems, even at moderate pressures. Neglect of the fugacity coefficient and Poynting correction can cause solubility to be underpredicted by a fador of three. Figure 5 compares corrected (proposed model) and "uncorrected" solubility vs. tem-
230
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 2, 1984
Table 111. Constants for Approximate' Henry's Constant Correlation for Light Gases in Heavy Fractions (Pseudocomponents) (Eq B14)C light gas hydrogen nitrogen carbonmonoxide methane ethane carbon dioxide hydrogen sulfide propane butane
A
c
B
reduced temp rangeb
3.55 -0.936 0.524 0.4 < TR < 1.0 3.21 -0.591 0.567 0.4 < TR < 1.0 2.92 -0.348 0.50 0.4 < TR < 1.0 1.92 0.596 0.531 0.4 < TR < 0.8 2.40 0.0 0.531 0.8 < TR < 1.0 0.28 2.15 0.497 0.4 < TR < 0.8 2.00 0.0 0.497 0.8 < TR < 1.0 1.14 1.37 0.270 0.4 < TR < 0.8 2.23 0.0 0.270 0.8 < TR < 1.0 0.27 2.11 0.0 0.4 < TR < 1.0 -0.66 2.95 0.404 0.4 < TR < 0.8 2.78 0.0 0.404 0.8 < TR < 1.0 -1.88 4.27 0.40 0.4 < TR < 0.8 2.60 0.0 0.40 0.8 < TR < 1.0
While sufficiently accurate for our work, these approximate correlations may not be sufficiently accurate for other applications. TR = T / T , , , (T,,,, of the fraction). Data references: Chappelow, C. C.; Prausnitz, J. M. AIChB J. 1974, 20, 1097. Cukor, P. M.; Prausnitz, J. M. J. Phys. C h e m . 1972, 76, 598. Tremper, K. K.; Prausnitz, J. M. J. Chem. Eng. Data 1976, 21, 295. Table IV. Square-Well Parameters for Nine Light Gases (Well Width = 0.2 n m ) 1. 2. 3. 4. 5. 6. 7. 8. 9.
light gas hydrogen nitrogen carbon monoxide methane ethane carbon dioxide hydrogen sulfide propane butane
nm
Elk, K
0.245 0.327 0.325 0.335 0.403 0.357 0.387 0.465 0.514
18.7 89.1 92.6 141 259 211 272 3 46 425
0,
Table V. Square-Well Parameters for Light-Gas Pairs pair 1-2 1-3 1-4 1-5 1-6 1-7 1-8 1-9 2-3 2-4 2-5 2-6 2-7 2-8 2-9 3-4 3-5 3-6
Elllk, K
pair a
43.5 (43.5) 50.3 59.5 (58.0) (55.0) 79.7 84.0 (89.0) 106 151 147 127 178 18 2 (106) (151) 145
3-7 3-8 3-9 4- 5 4-6 4-7 4-8 4-9 5-6 5- 7 5-8 5- 9 6- 7 6-8 6-9 7-8 7-9 8- 9
El,lk,
K
(127) (178) (182) 197 171 154 231 258 222 237 295 331 245 251 272 (278) (310) 379
Table VI. Energy Interaction Parameters for Heavy-Fraction/Light-GasBinaries ( ~ i j / kK, and AH^, kcal/mol) hydrogen binaries E i j / k = 146 nitrogen and carbon monoxide binaries Ei$k = 266 - 6 0 3 exp(-0.294AHj) methane binaries Eij/k = 395 - 915 exp(-0.224AHj) ethane and hydrogen sulfide binaries ci,lk = 477 - 870 (exp(-0.255AHj) carbon dioxide binaries cijlk = 437 - 915 exp(-0.224AHj) propane binaries e;j/k = 532 - 870 exp(-0.255AHj) butane binaries Ei,/k = 576 - 870 exp(-0.255AHj) water binaries Eijlk = 420 - 91 5 exp(-0.224AHj)
error is 4.5% for 16 solubility data. On the basis of these results, it is likely that the proposed model provides useful predictions for process design. Acknowledgment The authors are grateful to S. H. Chough for molecular-weight measurements, and to A. I. El-Twaty for useful contributions to the early phases of this work, including some of the results shown in Tables IV, V, and VI.
Appendix A. Fractional Aromaticities from Proton NMR Spectra and Carbon-to-Hydrogen Ratio In hydrocarbons, the relative concentrations of aromatic and paraffinic hydrogen atoms are readily determined from proton NMR spectra where four types of hydrogen atoms yield distinct chemical shifts relative to the absorption for hydrogens of a reference substance, hexamethyldisiloxane, HMDS (Alexander and Prausnitz, 1981). Hydrogen atoms which are attached to aromatic carbon atoms H,,, shift in the range 6.0-9.0 6 relative to HMDS. Hydrogen atoms attached to carbons a to aromatic carbons H,, shift in the range 1.7-4.0 6 relative to HMDS. Hydrogen atoms attached to nonterminal, non-a, aliphatic carbons H,, shift in the range 0.9-1.7 6 relative to HMDS. Finally, hydrogens attached to terminal, non-a, aliphatic carbons H,, shift in the range 0.5-0.9 6 relative to HMDS. Fractional aromaticity FA, can be determined from proton NMR measurements as follows
L
a See Table IV. Quantities in parentheses are estimates.
perature curves for a Lurgi coal-tar fraction in methane a t 70 bar. In the solubility range 0.01 to 0.001, "uncorrected" predictions lead to errors of about 30 "C in the dew-point temperature. Figure 3 shows a similar comparison for the typical coal-gasifier effluent described earlier. In this case, "uncorrected" predictions lead to errors of about 15 "C in the dew-point temperature. The proposed molecular-thermodynamicmodel predicts solubilities which are in good agreement with measured solubilities at pressures to 70 bar and 275 "C. The average
where H , is the concentration of hydrogen atoms which are bonded to carbon atoms of type c and C, is the concentration of carbon atoms of type c. I , is the integral of the proton NMR spectra within the limits of type c. The subscript tot, refers to the sum (aro + a + (3 + y). If one assumes: no alkyl bridges, no naphthenic rings, no branching except at a-carbons, and no heteroatoms, then (C/H), = y3
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 2, 1984 231
and
F A =l - ( H / C ) [
I, I, 4 - + - + -Iy I, + I,, + I, + I,
]
(A2)
with the qualifier: if I, = 0 and I, = 0, then F A = 0. Figure 6 shows sample spectra for a Lurgi coal-tar fraction. The spectra are for a solution of coal-tar fraction in totally deuterated pyridine. The solvent must be periodically tested for purity as trace nondeuterated pyridine forms by reaction with atmospheric water. (Nondeuterated pyridine adds to the Ha shift.) Appendix B. Liquid-Phase Properties To estimate an effective or average property (molecular weight, molar liquid volume, Henry's constants for solutes, and square-well parameters) of a heavy fraction, we use its fractional aromaticity to interpolate between the appropriate property of a pure alkane and that of a pure aromatic, both having the same normal boiling point as that of the heavy fraction. Literature data have been used to correlate, with normal boiling point, the needed properties of pure alkanes and aromatics. We use the Edwards et al. (1981) extension of SWAP (Smith et al., 1976) to estimate the normal boiling point of a fraction. Vapor Pressures of Heavy Fractions. To apply Edwards' extension of SWAP, we need the normal boiling point, T,, of the homomorph of the heavy fraction. The homomorph is defined as the compound obtained by replacing heteroatoms (nitrogen and sulfur) with equivalent carbon atoms. For example, the homomorph of quinoline is naphthalene. The original SWAP correlation is used to estimate T7, of a heavy fraction's homomorph. To estimate the fractional aromaticity of the homomorph FAhomo (required to use SWAP correlation), we assume that all nitrogen and sulfur atoms in the heavy fraction are bound in fused rings, displacing aromatic carbons, as nitrogen does in quinoline FAhomo
= FA[
no. of C atoms no. of C +S + N atoms
]+
FN
+ F S (B1)
where F N and Fs are determined from elemental analysis no. of N atoms F N = (B2) no. of N + S + C atoms no. of S atoms Fs = 033) no. of N + S + C atoms and F A is the fractional aromaticity determined from elemental analysis and proton NMR spectra. Molecular Weights of Heavy Fractions. To estimate MW, the molecular weight of a heavy fraction, we interpolate between the molecular weight of the alkane and that of the aromatic, both having the same T760as that of the heavy fraction MW = (1- FA)(MW)*~
+ FA(MW)momatic
(B4)
and T7, data for the normal alkanes, C5 to C40, and for fused-ring aromatics, benzene, naphthalene, anthracene, and chrysene (Macknick, 1979). Molar Liquid Volumes of Heavy Fractions. To estimate molar volume as a function of temperature, we estimate the fraction's volumetric coefficient of expansion 0
Assuming that 8 is constant
We obtain VL(T = 300) from the molecular weight and from the specific gravity (Nokay, 1959). To obtain VLwe interpolate between corresponding values for the alkane and aromatic VL(T760) = (1- FA)VLalk(T760) +FAVLmo(T760) where v d k ( T 7 6 0 ) = 27.65NC - 34.2
(BW
= 83.86NR - 5.48
(B11)
VLm,(T760)
NC = exp[-0.128814 + 5.581 NR = -1.9256
X
(B9)
10-3T760- 9.40X 10-7T762] 4- 1 (B12)
+ 8.124 X 10-3T,60
(B13)
NC and NR are, respectively, the number of aliphatic carbons and the number of fused rings in the alkane and aromatic, with normal boiling point, T760.Equations B10 through B13 were obtained from predicted (Hankinson and Thomson, 1979) molar volumes at T7, for normal alkanes (C4to C,) and for fused-ring aromatics, benzene, naphthalene, anthracene, and chrysene. Henry's Constant and Poynting Correction for Light Gases. A rough approximation for Henry's constant Hij, for light gas i, in pseudocomponent j , is calculated from T log [Hij(atm)] = Ai + Bi+ CiFA (B14) T760
Table 111 gives constants Ai, Bi, and Ci for nine light gases. These approximate correlations, necessary to account for the relatively small effect of the solubility of light gases in the heavy liquids on vapor-phase solubility, are based on the data of Cukor and Prausnitz (1972),Chappelow and Prausnitz (1974), and Tremper and Prausnitz (1976). Henry's constant Hi, for a light gas in the heavy-fraction mixture is calculated using the mixing rule
Cxj
j=1
where n is the number of pseudocomponents. The Poynting correction in eq 3 is given by
where (MW)dkme= -385.01
+ 2.6371360 - 0.005019T76,2 + 4.0234
X
104T7,3 (B5)
and (MWImomatic = -68.28
+ 0.4062T760
(B6) Equations B5 and B6 were obtained from molecular-weight
vmi,,
The partial molar volume of gas i, at infinite dilution in pseudocomponent j , is estimated by the method of Lyckman et al. (1965). Gas-phase solubility results are not sensitive to inaccuracies in eq B14, B15, and B16.
232 Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 2, 1984
Fugacity of Liquid Water. Vapor pressure of water is calculated using expressions given in the NEL Steam Tables (Bain, 1964). Molar liquid volume is calculated with the COSTALD correlation (Hankinson and Thomson, is calcu1979). Saturated-vapor fugacity coefficient dWS, lated with the empirical relation
+ 5.7022 X lO-*T- 1.761 X 1 0 4 P
dWa(bar) = 1.0204
(B17) for T greater than 420 K. For T less than 420 K, $J,~ is set equal to unity. Appendix C. Virial Coefficients Virial coefficients are based on a square-well potential (Hirschfelder et al., 1954) as described by Kaul and Prausnitz (1978). The well width is fixed at 0.2 nm.
[
_ hBij i ; - 1 - kit - 1)
exp ( k9T - 1 1
(Cl)
where
+ 0.2 7 in nm)
In (Kwj)= -11.071
+ 5953/T - 2.746 X
106T2+ 4.646 X 10sT3 (C8) where Kwjis in atmospheres and T is in kelvins. The experimental data of Coan and King (1971) and equations C6, C7, and C8 were used to obtain for water/carbon dioxide twj _ -- 186.7K
k The size parameter was calculated by using 1 uwj = -(tw + U j ) (ClO) 2 Heavy-Fraction/Light-GasBinaries. Calculation of effective square-well parameters for heavy-fraction/ light-gas binaries is based on the correlation of Kaul and Prausnitz (1978). To account for molecular flexibility, Kaul calculated the effective size parameters of heavy hydrocarbons from their mean radius of gyration RG, relative to that of methane
ai;
gi; =
(u
1 2
a- = -(ai lJ
+ a;)
(C2)
where k is Boltzmann's constant, N is Avogadro's number, and uii and tij are size and energy parameters for molecular pair 11. Light Gases. For light-gas molecules and their mixtures, gi, and ti, have been obtained from reduction of second virial-coefficient data. Tables IV and V give parameters for nine light gases. Water and Water/Light-Gas Pairs. The energy parameter for water has been split into a nonpolar contribution two, and a polar contribution twl t,
=
two
+ tw'/T
(C3)
Reduction of pure-water second-virial-coefficientdata does not yield unique values of the three adjustable parameters u, to, and e l . However, reasonable values can be chosen such that a, is physically sensible and such that two/k gives good results for water-nonpolar mixtures (eq C5). The values chosen here are aw = 0.28 nm ewo/k = 186 K = 1.67 X lo5 K2
t,'/k
.=
W O eJJ ..)'/2
(C4)
((35)
The water/carbon dioxide binary 0' = carbon dioxide) is given special treatment to account for association. The cross virial coefficient is split into a chemical contribution, B .them, and a physical contribution, BwjPhYa,(Nothnagel etw/al., 1973) B WJ = B WJ.phys + B WJ.them (C6) ,
BWJ,them = -0.5RTKwj
(RG)he has been correlated with NC using the molecular-dynamics results of Bellemans (1973)
where NC = exp[-0.128814
5.581 x 10-3T760 - 9.40X 10-7T7602] ('214) (RG),, has been correlated with NR using values calculated from molecular structure data (Bowen, 1965) for benzene, naphthalene, anthracene, and chrysene (RG),omatic= 0.0794 O.O398(NR) (nm) ((215)
+
NR = -1.9256
For water/light-gas 0')mixtures, the cross energy parameter is calculated from EWJ
For methane, RG = 0.0443 nm (Moelwyn-Hughes, 1961) and u/2 = 0.1675 nm (Sherwood and Prausnitz, 1964). To estimate the effective RG for heavy fractions, we interpolate between values corresponding to a saturated alkane (RG)ke, and that corresponding to a fused-ring aromatic as that of the (RG)aromatic, when both have the same TTe0 heavy fraction (RG)i = (1- FA)(RG)dkane + Fa(RG),omatic (C12)
((37)
The equilibrium constant of association Kw,, has been fit (De Santis et al., 1974) to experimental data
+ 8.124 X 10-3T.,60
(C16) Kaul proposed a correlation of ti, with AH (Hildebrand enthalpy of vaporization of the heavy hydrocarbon) for calculating tijfor heavy-hydrocarbon/light-gaspairs. AH is defined as the enthalpy of vaporization at the temperature where the saturated-vapor volume is 49.5 L/g-mol. For heavy fractions, AH is obtained from Edwards' SWAP vapor-pressure curve using the Clausius-Clapeyron equation. Table VI gives correlations for tij, with AH for nine light gases. Appendix D. If vapor, hydrocarbon-rich liquid, and pure liquid are known to exist, we use an objective function derived from material balances for a three-phase system, where one phase is pure, liquid water. The overall material balance, based on one mole of feed, is l = a + v + p
01)
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 2, 1984 233
where q and @ are the fractions of the feed which condense as hydrocarbon-rich and pure-water phases, and a is the fraction of the feed that does not condense. The component balance for water is (D2) z, = ffYw+ @ where z, is the mole fraction of water in the feed. The component balance for component i, other than water, is (D3) zi = yia xi9 Eliminating /I yields 9 = (1- 2,) - 4 1 - Yw) (D4) Substituting eq D4 into eq D3,dividing by xi, and using the definition of Ki, we obtain
+
Xi
zi =Fi
where
ti = a(Ki - 1 + y,)
+1
This expression for x i and yi = K i ~ i are used in the objective function m ,.”
s = c(yi-xi) i=l
The derivative with respect to a is
where fwL
Yw = 4 2 Nomenclature Ai, Bi, Ci = constants in eq B14 B = second virial coefficient of the mixture Bij = second cross virial coefficient for components i and j c = type of carbon atom (aromatic, a,0, or y) C, = concentration of carbon atoms of type c F = objective function (eq 9) FA = fractional aromaticity FAhomo= fractional aromaticity of the homomorph (eq B1) FN = fractional heteroatomaticity with respect to nitrogen Fs = fractional heteroatomaticity with respect to sulfur f = fugacity Hi = Henry’s constant of component i in the liquid mixture H,= concentration of hydrogen atoms of type c H i . = Henry’s constant of component i in heavy fraction j H h D S = hexamethyldisiloxane I, = integral of proton NMR spectra withii the limits of type c hydrogen atoms k = Boltzmann’s constant Ki = equilibrium K factor K I z= equilibrium constant for association of water and carbon dioxide m = number of components in system MW = molecular weight MW-, = molecular weight of normal alkane having same normal boiling point as that of heavy fraction (eq B5) MW,? = molecular weight of aromatic having same normal boiling point as that of heavy fraction (eq B6) n = number of heavy fractions N = Avogadro’s number NC = number of aliphatic carbons in alkane having same normal boiling point as that of heavy fraction (eq B12) NMR = nuclear magnetic resonance NR = number of fused rings in aromatic having same normal boiling point as that of heavy fraction (eq B13)
P = total pressure
Pi”= vapor pressure of component i PwU = vapor pressure of water P = average pressure (torr) corresponding to vapol-preasure e%Jatumof heavy fraction (POi = Poynting correction for component i RG = radius of gyration of a molecule R = gas constant S = objective function (eq 11 and D8)) S’ = derivative of objective function with respect to a (eq 12 and D9) T = absolute temperature Texp= average temperature ( K ) corresponding to vaporpressure datum of heavy fraction TR = reduced temperature, T / T 7 , = normal boiling point 2P= molar liquid volume of component i V = molar liquid volume of water $(T = 300) = molar liquid volume at 300 K F(T7,) = molar liquid volume at the normal boiling point Vmi= partial molar volume of gas i in heavy liquid j at infiiite dilution = mole fraction of component i in the liquid yi = mole fraction of component i in the vapor zi = mole fraction of component i in feed Greek Letters a = fraction of feed that is vapor after flash 6 = chemical shift in NMR spectra, dimensionless y = activity coefficient AH = Hildebrand enthalpy of vaporization t i j = energy parameter (square-wellpotential) for molecules i and j E, = energy parameter of water two = nonpolar contribution to energy parameter of water cwl = polar contribution to energy parameter of water q, = size parameter (square-wellpotential) for molecules i and
i
9
= size parameter for water = fraction of feed which condenses as hydrocarbon-rich
p
= fraction of feed which condenses as pure water
0,
phase
ti = defined in eq D6
9 = fugacity coefficient = saturated-vapor fugacity coefficient Q = defined in eq 14 0 = volumetric coefficient of expansion Subscripts aro = aromatic i = component w = water w j = water/(light gas, j) tot = total R = reduced a = carbons a to aromatic carbons p = nonterminal, non-a, aliphatic carbons y = terminal, non-a, aliphatic carbons Superscripts chem = chemical L = liquid 0 = nonpolar contribution phys = physical s = saturated vapor V = vapor 1 = polar contribution Registry No. Water, 1132-18-5;methane, 14-82-8. Literature Cited Alexander, 0.; Prausnltr, J. M. American Institute of Chemical Engineers 1981 Annual Meetlng, New Orleans, LA, Nov 8-12, 1981;American Institute of Chemlcal Engineers: New York. Paper No. 44f. b i n , R. W. “N.E. L. Steam Tables 1964”;Her Majesty’s Stationery Offlce: Edinburgh, U.K., 1964. Bellemans. A. Physka 1973,68, 209. Bowen, H. J. M. “Tables of Interatomic Distances and Conflgwatlons in Molecules and Ions”, Special Publlcatlon l l and Supplement 18;Sutton, L.
234
Ind. Eng. Chem. Process Des. Dev. 1984,
E., Ed.; The Chemical Soclefy, London, 1958. De Santis, R.; Breedveld, G. J. F.; Prausnitz, J. M. I d . Eng. Chem. Process Des. D e v . 1974, 13, 347. Chappelow, C. C.; Prausnitz. J. M. A I C M J . 1974, 20, 1097. Coan, C. R.; King, A. D. J. Am. Chem. SIX. 1971, 93, 1857. Cukor, P. M.; Prausnitz, J. M. J. Phys. Chem. 1972, 76, 598. Edwards, D.; Van de Rostyne, C. G.; Winnlck. J.; Prausnitz, J. M. I n d . Eng. Chem. Process Des. Dev. 1981, 20, 138.
Gonzales, C. M.S. Thesis, University of California, Berkeley, CA, 1980. Hankinson, R. W.; Thomson, G. H. A I C M J. 1979. 25, 4. Hirschfekler, J. 0.;Curtiss, C. F.; Bird, R. B. “Molecular Theory of Gases and Liquid”, 1st ed.;WUey: New York, 1954; p 158. Kaui, B. K.; Prausnltz, J. M. AIChE J . 1978. 24, 223. Klng, C. J. “Separation Processes”, 1st ed.;McGraw-HIII: New York, 1971; p 513. Lyckman, E. W.; Eckert, C. A.; Prausnitz, J. M. Chem. Eng. Scl. WBS, 20, 685. Macknick, A. B.; Prausnltz. J. M. A I C M J . 1978, 2 4 , 4. Macknick, A. 8. Ph.D. Dissertation, University of California, Berkeley, CA, 1979. Moelwyn-Hughes, E. A. “Physical Chemistry”, 2nd ed.; Pergamon Press: New York, 1985; p 491. Monge. A.; Prausnitz, J. M. In “Chsmicai Engineering at SupercriticaCFluld Conditions”; Paulaitis, M. E.; Penninger, J. M. L.; Grey, R. D., Ed.; Ann
23,234-236
Arbor Science Pubiishers: Ann Arbor, MI, 1983. See also Ind. Eng. Chem. Fundem. 1983, 22, 505. Monge, A. Ph.D. Dissertation, University of California, Berkeley, CA, 1982. Nokay, R. Chem. Eng. 1959, 66, 4. Nothnagei, K. H.; Abrams, D. S.; Prausnitz, J. M. Ind. Eng. Chem. Process Des. Dev. 1973, 12, 25. Sherwood, A. E.; Prausnitz, J. M. J. Chem. Phys. 1984, 4 1 , 429. Smith, G.; Winnick, J.; Abrams, D. S.;Prausnitz, J. M. Can. J . Chem. Eng. 1976. 5 4 , 337. Tremper, K. K.; Prausnitz, J. M. J . Chem. Eng. Data 1978, 21, 295.
Received for review August 31, 1982 Accepted May 13, 1983 This work was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Chemical Sciences Division of the U.S.Department of Energy. For Financial support in the initial stages of this work, the authors are grateful to the Fossil Energy Program, Assistant Secretary of Energy Technology, United States Department of Energy, to the donors of the Petroleum Research Fund, administered by the American Chemical Society, and to the National Science Foundation.
Heat of Combustion of Green River Oil Shale Michael J. Muehlbauer and Alan K. Burnham’ Lawrence Livermore Natbnal Laboratory, Livermore, California 94550
We derive simple equations for estimating the heat of combustion of raw shale by thermochemical estimates and by linear regression of experimental data. We find that the heat c a n be estimated well by an exothermic term
that accounts for the combwtion of organic matter and a constant that accounts for pyrite combustion, carbonate decomposition, and glass formation. The net contribution of reactions included in the constant is endothermic for the standard state products of bomb calorimetry. As a sample application, we perform an energy balance on a modified Fischer assay of average Green River shale by using one of our formulas for raw shale along with previously derived formulas for pyrolysis products.
Introduction In making a heat balance for adiabatic oil shale retorting experiments, the sensible and chemical heat content of the raw shale and other reactants is compared to the sum of the heat contents of the products including the oil, retorted shale, and gas. A value for the heat of combustion of raw shale, (-AHc),, is frequently needed for this balance, especially for combustion retorting. If an experimental value for (-AHc)= is not available, a value must be estimated using thermochemical considerations. An expression whereby the heat of combustion of raw shale can be estimated quickly from shale composition would be useful. Burnham et al. (1982) have shown in previous work that the heat of combustion (kJ/kg) of retorted (spent) shale could be related to the organic carbon, total sulfur, and mineral C02 content by a simple linear equation. Coefficients for the equation were developed through thermochemical reasoning and by multiple linear regression. We expected that a similar expression could be developed for the heat of combustion of raw shale. In this report, we first derive an expression for the heat of combustion of raw shale based solely on thermochemical theory. Next, using available experimental data, we develop an expression for (-AHc)= by a multiple linear regression. The theoretical expression is compared to the regression equation to verify its applicability. Finally, to illustrate the use of the expression, we perform a heat balance to show the redistribution of combustion energy caused by a modified Fischer assay. Ol96-4305f84f 1123-0234$01.50/0
Thermochemical Expression for (-AH&, The expression for the heat of combustion of raw shale based on thermochemical theory is (-AE& = 496 (wt % org C) + 107 (wt % S) 18 (wt% acid C02) - 75 (1) The expression gives heat of combustion in units of kJ/kg. The first term on the right-hand side of the expression gives the contribution to (-AH&,by the combustion of the organic kerogen. The coefficient was calculated by estimating the heat of combustion of kerogen by the Boie formula (Ringen et al., 1979). The composition of the kerogen was taken to be as reported by Smith (1961): 80.5% C, 10.3% H, 2.39% N, 1.04% S, and 5.75% 0. The second term accounts for the heat of combustion of pyrite (FeSJ found in the raw shale. Typically 80% of the total sulfur in raw shale is in the form of pyrite, which burns with a heat of combustion of -830 kJ/mol of FeS2. Combustion products were taken to be Fe203and SOz, which are the standard-state products for a bomb calorimeter. The third term accounts for the heat of decomposition of carbonates in the shale. The carbonates typically consist of about 2 to 3 parts of dolomite (CaMg(C0s)2and one part calcite (CaCOS). Their decompositions are endothermic, hence the negative sign of the wt % acid COz coefficient. The final term in the expression accounts for the heat of glass formation. Approximately 67% of the initial weight of the raw shale is left as ash after combustion. 0 1984 American Chemical Society
