Ind. Eng. Chem. Process Des. Dev. 1002, 21, 559-564
559
Thermodynamic, Kinetic, and Mass Balance Aspects of Coal-Depolarized Water Electrolysis Robert W. Coughlln’ and Mohammed Farooque Department of Chemical Engineering, University of Connecticut, Storrs, Connecticut 06268
Thermodynamic considerations suggest that energy efficiencies greater than about 50 % should be attainable by reaction at operating potentials lower than about 0.7 Y. After the electrochemical oxidation of several coals slunied in aqueous H,SO, electrolyte, analysis of solid reactants and products indicates that the partially consumed (1 1-30%) solid residues are enriched in oxygen and depleted in hydrogen-rich volatile matter. Similar results indicate that the heating values of all samples are decreased by the reaction. Selectivity of the reaction for different components of the solid fuels seems to be influenced by the course or mode of reaction (Le.,potentiostatic or galvanostatic).
Introduction The production of hydrogen from carbonaceous materials can be traced back to a t least as early as 1780 when, according to Morgan (1945), Fontana produced water gas by reacting steam with incandescent carbon C(S) + H2O(g) CO(g) + Hz(g) (1) In subsequent years many improvements were developed in this process and in downstream processing such that, according to the Kirk-Othmer Encyclopedia (1963-70), at least 90% of world hydrogen production prior to 1940 was based on processes utilizing coal or coke. Production of hydrogen by water electrolysis 2H20(1) -* 2H2(g) + 02(g) (11) has been practiced on the industrial scale since the beginning of the 20th century according to Smith (1971), but the same author reports that it was as early as 1800 that Nicholson and Carlisle discovered that water could be decomposed electrolytically into hydrogen and oxygen. It appears that water electrolysis has never captured a large share of hydrogen production capacity due mainly to an economic barrier, viz., the higher cost of electrical energy necessary to split water endothermically vis-a-vis the cheaper cost of fossil fuel such as coal. Recently we reported a new method (Coughlin and Farooque, 1979a) of using coal and electricity in concert to split liquid water according to the following overall stoichiometrywritten to describe the reaction of the carbon in the coal 2H20(1) + C(S) CO2(g) + 2Hz(g) (111) In this electrochemical process the cathodic reaction is hydrogen liberation 2H2(g) 4H+ + 4e-
-
-
-
whereas the anodic reaction can be represented (at least stoichiometrically if not mechanistically) as 2H20(1) + C(s) C02(g) 4H+ + 4e-
-
+
We have dubbed the overall process “electrochemical gasification of coal” or “coal-assisted electrolysis of water”. Coal-depolarized water electrolysis is yet another possible descriptive name. Subsequent papers (Farooque and Coughlin, 1979a; Coughlin and Farooque, 1980) have presented additional data as to parametric studies and elementary economic considerations, as well as shown how 0196-4305/82/ 1121-0559$01.25/0
anodic oxidation of coal can be extended to electrodeposition of metals (Farooque and Coughlin, 1979b). In the present writing we explore some elementary practical thermodynamic aspects of this new reaction process and give data as to analyses of the coals before and after the electrochemical reaction; this permits assessment of carbon balance and some insight into the course of the reaction.
Experimental Section All experiments were conducted with stirred slurries of coal in aqueous electrolyte within the anode compartment of a cell such as that shown in Figure 1. The external emf was applied by a potentiostat (both Model PAR 371 and PAR 179A were used) made by Princeton Applied Research Corp. and the electrodes (both anode and cathode) were Pt mesh, gauge 52 (0.004 in. diameter wire) supplied by Matthey Bishop, Inc. Additional details of the experimental apparatus are given by Farooque and Coughlin (1979a) and Coughlin and Farooque (1980). The gas was analyzed by chromatography using a Spherocarb (100/120 mesh) separation column. Aqueous electrolytes were prepared with Baker analyzed reagent grade sulfuric acid. Coal samples in pulverized form were obtained from the US.Department of Energy Pittsburgh Energy Research Center; their ultimate analyses are given by Coughlin and Farooque (1980). Thermodynamic and Kinetic Considerations The reversible thermodynamic potential computed from the standard free energy change of reaction [Eo = AGO/ nF] is -0.21 V for the reaction (111)between carbon and liquid water, whereas the corresponding value for conventional water electrolysis (reaction 11)is -1.23 V. These values, together with the range of practical operating potentials for both electrochemical reactions, are shown graphically in Figure 2. The range of practical potentials is reasonably well established for conventional water electrolysis, whereas the range for electrochemical gasification of coal is a much more uncertain estimate, being based on only the experimental results reported in previous papers (Coughlin and Farooque, 1979,1980;Farooque and Coughlin, 1979a). The practical operating potentials are larger than the theoretical because they include the various irreversible phenomena inherent in conducting these reactions at practical and measurable rates under nonequilibrium conditions. Increasing temperature lowers the theoretical or “open circuit” potentials predicted from thermodynamics and usually also decreases the gap be0 1982 American Chemical Society
560
Ind. Eng. Chem. Process Des. Dev., Vol. 21, No. 4, 1982
'
COAL GASIFICATION CELL
ANODE COMPARTMENT G 4 S OUTLET THERMOMETER
,
CATHODE CCMPARTMENl GAS OUTLET
06
Above the thermoneutral voltoge waste heot i s evolved f r o m the excess electrical energy supplied t o the cell
-
a
-WORKING ELECTRODE
V
CATHODE COMPARTMENT
0-
-02;
FRITTED GLASS SEPARATCR
COAL SLURRY MAGNETIC STIRRING
'
Figure 1. Experimental apparatus.
rI - iI I
/
50
I
100
1
150
Temperature
SUPPORTING ELECTROLYTE
RANGE OF PRACTICAL OPE?.ATIXG PQTEZTIAL
I
01
CATHODE
I
zLECTRoLYSIS
.-
THEORETICAL THERMODYNAYIC POTENTIAL AT 25'C
I
I
200
250
300
1
i'C I
Figure 3. Influence of temperature on reversible open-circuit potential and on ideal, thermoneutral potential for coal-depolarized water electrolysis.
A thermodynamic efficiency for the process of reaction 111 conducted at potentials at or above the thermoneutral voltage may be defined as efficiency = (combustion energy of hydrogen produced) /(combustion energy of carbon consumed electrical energy consumed/electrical generation efficiency, q] = AHH2/(y&lc + nEF/q) = 136.6/[94.05 + 92.3(E/q)]
+
For operation at potentials lower than Em an additional term for the portion of the reaction enthalpy that must be supplied as thermal energy must be added to the denominator of the foregoing expression which then becomes efficiency = combustion energy of Hz/[(combustion energy of carbon consumed) + (electrical energy consumed/q) + thermal requirement] = AHHp/[l/AHc + nEF/q + ( A H A - AF)]
Figure 2. Comparison of the ideal, open-circuit potential and the range of practical operating potentials for conventional water electrolysis and coal-depolarized water electrolysis.
where AHAis the enthalpy change of reaction I11 and 1 4 = I n3El = AHH,/[l/pAHC + AHA+ nFE(l/T - l)]and efficiency = 136.6/[136.6 + 92.33(1 - q ) / q ]
tween the theoretical and the practical potentials by speeding the irreversible rate processes which take place in the electrolytic cell. Figure 3 provides further insight into the thermodynamic aspects of reaction I11 in the form of Eth= AGInF and E T N AHlnF plotted vs. temperature. Eth, the reversible thermodynamic potential, is seen to diminish with increased temperature, from about 0.21 V at room temperature to about zero at 250 OC, whereas ETN, the socalled thermoneutral voltage, is seen to be about 0.45 V and relatively insensitive to temperature. The thermoneutral voltage, ETN,is proportional to, and derived directly from, the enthalpy change of reaction, m when the electrochemical cell is operated at Em 5 AH/nF then the electrical energy supplied is just sufficient to provide the enthalpy of reaction. A t operating potentials lower than E T N the difference must be supplied as thermal energy to the reaction, whereas at operating potentials greater than Em electrical energy is thereby supplied in excess of the reaction enthalpy requirement and this excess must flow from the reactor in the form of heat.
Note that the higher heating value of Hzis used in these equations as is usually the practice for considerations of efficiency of water electrolysis; clearly, computed efficiencies would be somewhat lower if the lower heating value were used. Values of efficiency computed by these equations are plotted in Figure 3 vs. cell potential, for a typical value of q = 0.35 for conventional generation of electricity from fossil fuel. This graph clearly shows the strong incentive for conducting the electrochemical process at the lowest possible voltage consistent with a rate of reaction sufficiently rapid for practical purposes. Higher temperatures not only lower the thermodynamic energy barrier but also speed the irreversible transport processes, thereby also lowering these energy-consuming barriers as well; Figure 4 shows the increased efficiencies expected from lowering only the thermodynamic reversible potential by raising temperature. The additional favorable kinetic effects are not reflected in this figure. Mass Balance Considerations Our recent reports (Coughlin and Farooque, 1979,1980; Farooque and Coughlin, 1979a,b) of anodic oxidation of
0.0
Ind. Eng. Chem. Process Des. Dev., Vol. 21, No. 4, 1982 561 Table 11. Acetone Extraction of Anodically Oxidized North Dakota Lignitea 0.8
-
0.6
-
0.4
-
component C
H 0 N S FC VM ash
REVERSIBLE THEWlODYNAYIC POTENTIAL 0.1 V at 150°C 0.2
-
0.4
1.0
0.8
0.6
CELL POTENTIAL, E, VOLTS
Figure 4. Influence of operating cell potential on ideal thermodynamic efficiency of electrochemical gasification of coal. Efficiency of converting coal to electricity assumed equal to 35%. Table I. North Dakota Lignite before and after Reactiona
C (total)
H 0 N S ash fixed C volatile matter
w,,
loss:
w,- w,,
w,,
11.46 10.22 0.96
g 1.13 0.08 0.7 1
0.01
10.34 9.40 0.96
1.12 0.82
a Experimental conditions as in Table I. Weight loss due to acetone extraction = 23.85 - 22.65 = 1.20 g (TMBb); = 22.60 - 20.69 = 1.91 g (dry basis) TMB = total mass basis. 0.2
component
mass after mass after reaction before reaction and extraction, extraction g g 14.19 13.06 0.69 0.61 6.27 5.56 0.18 0.18 0.15 0.14
mass mass remainingb before after reaction, reaction, W,, g ?
w*
16.55 1.02 4.57 0.26 0.43 3.85 11.15 11.68
14.19 0.69 6.27 0.18 0.15 0.96 11.44 10.20
net loss g
gatoms
2.36 0.33 -1.70 0.08 0.28 2.89 -0.29 1.48
0.20 0.33 -0.11 0.006
0.008 0.02
Original particle s u e : < 4 3 pm; slurry concn = 0.069 g/cm3; original mass of coal = 26.68 g (dry basis), 32.9 g (total mass basis). Electrolyte: 5.6 M H,SO,; galvanostatic oxidation rate = 136 mA; potentials = 0.84 V (start), 1.98 V (final); temp = 114 “C;electrode area = 96.5 cmz (geometric guaze); charge passed = 1.38 X 10’ C; coal recovered after reaction: 23.85 g (total mass basis), 22.6 g (dry basis). The quantities in this column add to 22.4 g and not 22.6 g because each assay was done independently and none was estimated by difference. The discrepancy may be viewed as caused by random errors in assay as well as by round-off errors.
coal for the production of useful substances have focused mainly on the gaseous products of reaction and, until now, no information has been available as to the analyses of the residual solid material after the reaction. We now report this kind of information and interpret it by mass balance considerations to provide some insight into the reactivities and consumptions of the different chemical elements in the coal. a. Reaction of North Dakota Lignite. After reaction as described in previous papers, the partially reacted coal samples were filtered from the electrolyte, oven-dried at 110 “C for 1 h and cooled in air. Results of assay before and after reaction appear in Table I, where it is evident that the electrochemical oxidation consumes carbon and hydrogen but increases the oxygen content of the partially reacted coal. The increase in oxygen content is consistent with our previous hypothesis (Coughlin and Farooque, 1979,1980) that surface functional groups such as carbonyl, carboxyl, and hydroxyl oxygen are reaction intermediates
Table 111. Effect of Anodic Oxidation and Acetone Extraction o n Component Ratiosa (North Dakota Lignite)
specimen virgin NDL NDL, 26% consumed galvanostat ically , Table I conditions NDL, 29% consumed potentiostatically, 1.0 V; charge passed 1.54 X l o 5 C; other conditions as in Table I NDL, 26% consumed galvanostatically , acetone extracted; other conditions as in Table I
FC/O, dry basis
c/o, dry basis
VM/ FC
FC/ C
2.43 1.82
3.62 2.47
1.05 0.89
0.67 0.80
1.80
2.26
0.94
0.84
1.85
2.35
0.91
0.78
a All ratios are by weight; FC = fixed carbon; C = total carbon; VM = volatile matter.
that accumulate on the solid reactant. The results of Table I also show that hydrogen-rich volatile material is preferentially consumed and the reacted portion of the carbonaceous solid is enriched in fixed carbon as the result of the electrochemical reaction. The decrease in sulfur and ash content may be ascribed to reactions between the acidic electrolyte and noncarbonaceous coal minerals (e.g., basic oxides and sulfides) which liberate H2Sand dissolve metallic oxides. Table I also indicates that anodic oxidation produces a product with a higher proportion of fixed carbon. It has been found that (Coughlin and Farooque, 1979a) extracting a portion of the reacted coal with acetone can restore a significant portion of its virgin electrochemical activity. The effect of such leaching on composition is shown in Table 11. The H/C and O/C ratios of the extracted material indicate that this treatment seems to remove highly oxygenated compounds composed of all the components with the possible exception of nitrogen and ash. Some of the material extracted appeared to be colloidal and this may account for the removal of some fixed carbon by this treatment. We believe that the extracted materials are both tars and very small, peptized coal particles. Attempts are currently underway to better characterize these materials. Regarding the entry for “volatile matter” (VM) in Table 11, it should be recognized that this conventional pseudocomponent probably has only limited significance in the present work. As the coal is anodically oxidized, new VM is continually formed (e.g., as carboylic groups which get
562
Ind. Eng. Chem.
Process Des. Dev., Vol. 21, No. 4, 1982
Table IV. Mass Balance Data for NDL A. B. C.
D. E.
F. G.
Hydrogen Balance loss of hydrogen from coal 0.327 g a t o m hydrogen equivalent t o CO, (0.95)(0.196)(4)= 0.745 g a t o m produced (from 95% of C consumed) (0.05)(0.196)(2) = hydrogen equivalent t o CO 0.020 g-atom produced (from 5% C consumed) hydrogen equivalent to 0.212 g a t o m increased oxygen in coal 1.30 g a t o m total hydrogen (A + B + C (A+B+C+D) (1.38) ( 10-')/9.648 = total hydrogen equivalent t o charge passed 1.43 g-atom total hydrogen produced 1.42 g-atom (experimental measurement)
Carbon Balance 0.197 g-atom A. loss of carbon from coal 0.001 g a t o m B. organic carbon found in electrolyte by analysis 0.196 g-atom C. carbon expected in gaseous products ( A - B) 0.145 g a t o m D. carbon measured (as CO + CO,) in gaseous products
component
C H 0 N
24.94 1.7 1 2.86 0.48 0.39 1.80 17.79 11.87
Sb ash FC
VM
mass remaining after reaction.
w,,g
22.53 1.25 5.23 0.48 0.58 1.29 19.50 10.24
H 0 N S ash VM FC
w,,
w,,
loss =
w, w, -
0.05 0.05 0.06 0.03 0.08 0.05 0.06 -0.25
" Experimental conditions as in Table V. Weight loss due t o acetone extraction = 19.00 - 18.56 = 0.44 g (dry basis).
specimen
net loss g 2.41 0.46 -2.37
g-atoms
-0.19 0.51 -1.71 1.63
-0.01
0.20 0.45 0.15
-0.14
" Original particle size 12.5-149 Mm; slurry concn = 0.069 g/cm3; original mass of coal 32.9 g (TMB); 31.17 g (dry basis); electrolyte: 5.6 M H,SO,; galvanostatic current = 97.5 mA; potentials = 0.88 V (start), 1.98 (final); charge passed: 9.01 x lo4 C (11%of C reacted); coal recovered after reaction: 31.11 g (dry basis); other conditions as in Table I . The precision of sulfur analysis was i 2%. liberated as COPduring the VM test) from what was "fixed carbon Table 111summarizes the effects of anodic oxidation and of subsequent acetone leaching on the ratios of various components of NDL. This shows more emphatically the buildup of oxygen and the loss of hydrogen-rich volatile material as a result of anodic oxidation. The data of Table I for NDL can be assessed by mass balance as shown in Table IV. Given the various experimental uncertainties these mass balances are reasonably satisfactory. The measured hydrogen production agrees within about 10% with that based on the analyses of the coal before and after reaction. The ratio of hydrogen to carbon expected in the gaseous products based on the chemical analyses is 1.30/0.196 = 6.63 H/C atomic ratio. The corresponding ratio based on current measurement is 1.43/0.196 = 7.30, whereas the ratio observed experimentally was 1.42/0.145 = 9.79. The discrepancy may be attributed in part to errors in assay and volume measurement, but we believe the major portion arose from dissolution of COz in the water over which it was collected followed by diffusion into the atmosphere from the exposed surface of the water during experiments of many
.
component C
mass after mass after reaction before reaction and extraction, extract ion, g 13.75 13.70 0.77 0.72 3.19 3.13 0.27 0.30 0.37 0.29 0.79 0.84 6.19 6.25 11.57 11.32
Table VII. Effect of Anodic Oxidation and Acetone Extraction o n Component Ratios (Pittsburgh Seam C o d )
Table V. Pittsburgh Seam Coal before and after Reaction" mass before reaction.
Table VI. Acetone Extraction of Anodically Oxidized Pittsburgh Seam Coal"
A. virgin Pittsburgh coal B. coal 11%consumed by galvanostatic oxidation as in Table V C. coal 16.36% consumed potent ios tatically (1.0 V) other conditions as in Table V D. specimen C above after acetone ex traction
FC/O (dry)
C/) (dry)
VM/ FC
FCI C
7.96 3.73
11.16 4.30
0.67 0.53
0.71 0.87
1.38
1.53
1.26
0.90
3.69
4.37
0.54
0.84
hours duration; some loss of COPcould also have occurred by leakage at conduit joints. b. Reaction of Pittsburgh Seam Coal. Table V records the composition of this material before and after anodic oxidation. The results are similar to those obtained with the lignite of Table I in that the reaction increases oxygen content and decreases volatile material. The slight rise in sulfur content evident in Table V (but not in Table I for NDL) may have been caused by residual H2S04 electrolyte not removed by routine washing of the solid reaction product. The effect of extracting the solid reaction product with acetone is shown in Table VI. As in the case of the lignite, this leaching removes significant material and essentially each component of the leached sample is diminished. Table VI1 gives the ratios of various components in these samples; these ratios show that anodic oxidation increases oxygen content and preferentially collsumes volatile material during the galvanostatic process in which about 11% of the C is consumed. Such behavior parallels that observed for galvanostatic oxidation of the lignite (see Table 111). For potentiostatic oxidation, however, the results in Table VI1 indicate quite different behavior, viz.,increase in the ratio of volatile material to f i e d carbon (V,/FC) in the product; this suggests greater selectivity of the potentiostatic reaction for FC than for V,. It is also evident from Table VI1 that acetone extraction does not influence these ratios significantly except for an increase in FC/C which suggests acetone may remove some fixed carbon preferentially. c. Reaction of Minnesota Red Sedge Peat. The course of galvanostatic (70 mA) anodic oxidation of this material is shown in Figure 5 as potential and concentration of CO in the accumulated anode gas, both plotted against cumulative charge passed. The electrochemical behavior pattern appears rather similar to the corresponding observations with the North Dakota lignite
Ind. Eng. Chem. Process Des. Dev., Vol. 21, No. 4, 1982 563
Table VIII. Minnesota Red Sedge Peat before and after Reaction"
component
mass. mass remaining before after reaction, reaction, W,,g W2,g
g-atoms 0.66 0.65 0.18 0.07 -0.01
C H 0 N S
14.82 1.14 6.62 1.07 0.10
6.85 0.49 3.67 0.13 0.51
7.97 0.65 2.95 0.94 -0.41
ash
6.45 17.74 6.26
3.09 7.21 4.56
3.36 10.53 1.70
VM FC
i
net loss g
" Reaction conditions as for Figure 5.
r'i
1.6
/
4
c
Original mass: 16.00 g
i
a
I
'
1 1 ,
IO
Table IX. Acetone Extraction of Anodically Oxidized Minnesota Red Sedge Peat"
component C
WI,
loss: -w2, g
S
2.69 0.17 1.19 0.05 0.11
0.35 0.05 0.44 0.01 0.12
ash VM FC
1.38 3.21 2.03
1.39 2.48 1.77
-0.01
0
N
1
I
I
I
,
,
i i ,,-F
1 ,
c
L )
~
P
result of the anodic oxidation. As in the case of the PSC (but not NDL) there was a slight increase in sulfur concentration in the reacted solid material probably explainable as contamination from the electrolyte, although selective nonreactivity of the sulfur originally present cannot be ruled out. Table IX shows that acetone extraction of the reacted solid material removed volatile material, fixed carbon, and oxygen. The loss of oxygen is quite significant, as is the total amount of material (about 15% on a dry basis) loss as a result of acetone leaching; these values are substantially larger than in the cases of NDL and PSC. Changes in Heating Value Table X summarizes measured heating values (HV) of the coals before and after reaction, as well as after acetone extraction of the reacted materials. It appears that anodic oxidation increases the as-received heating value of the peat and the lignite whereas the opposite behavior is observed for the Pittsburgh bituminous coal. The observed increase in heating value of the peat and lignite might be due to extraction of components of low heating value by the electrolyte as well as to selective anodic oxidation of such components. Moreover, the acidic electrolyte could also have extracted some noncombustible mineral matter and the entire process could have changed the hydrophilic
0.73 0.26
" Experimental conditions as in Table VIII. Weight loss due to acetone extraction = 7.11 - 5.96 = 1.15 g (total mass); = 6.61 - 5.62 = 1.09 g (dry basis). (NDL) and the Pittsburgh seam coal (PSC). The CO composition in the accumulated anode gas displays a cyclic behavior different from the monotonic course of CO concentration observed with the NDL and PSC. The CO concentration is also larger in the case of the peat. Table W I gives the composition of a peat sample before and after reaction. The data indicate that some fixed carbon, but mostly volatile material, were consumed during the reaction. Far more carbon and hydrogen have been removed than the corresponding equivalents of current passed during the oxidation and this suggests that the unaccounted material dissolved or became dispersed as a sol in the electrolyte. Although there appears to be a decrease in oxygen content, the O/C ratio increases as a Table X. Heating Values of Reacted and Unreacted Materials
heating values, Btu/lb fuel North Dakota Lignite
Pittsburgh Seam Coal
Minnesota Red Sedge Peat
,
Figure 5. Potential vs. reaction extent during galvanostatic electrochemical gasification of Minnesota Red-Sedge Peat. Slurry concentration, 0.086 g/mL; current, 70 mA; temperature, 110 O C ; electrolyte, 5.6 M H2S04;total charge passed = 9.5 X lo4 C (19.3% consumed); electrode superficial area, 96.5 cm2 (geometrical Pt gauze).
WI
3.04 0.22 1.63 0.06 0.23
H
1
1
.O1 ~
mass after reaction and extraction, w,, g
L
.- 1 . 4
40.85 g (TMB), 30.44 g (dry basis); final mass: (TMB), 14.86 g (dry basis).
mass after reaction before extract ion,
t 3 0
t
history A. virgin B. 26% consumed galvanostatically; exptl conditions as in Table I C. 29% consumed potentiostatically (1.0 V); exptl conditions as in Table I D. sample of B above after acetone extraction A. virgin B. 11%consumed galvanostatically; exptl conditions as in Table V C. 16.36% consumed potentiostatically (1.0 V); exptl conditions as in Table V D. sample of B above after acetone extraction A. virgin B. 19.3% consumed galvanostatically; exptl conditions as in Figure 5
as recd, air dried
MAF
8 238 9 019
11870
9 770
9 920
8 780 13 740 11393
1 0 076 14 900 11957
6 047
7 453
11768 6 096 1006
12 635 10 380 9 737
9 497
Ind. Eng. Chem. Process Des. Dev. 1082, 2 1, 564-569
564
properties of the product coal, thereby lowering moisture content. A decreased MAF heating value was noted for all samples subjected to the electrochemical process. It should also be noted from Table X that acetone extraction of the solid residue from anodic oxidation of PSC caused an increase in its heating value, presumably by extraction of oxygenated components. As was shown elsewhere (Coughlin and Farooque 1979),such extraction by acetone restores partially the virgin electroactivity (which diminishes during the course of reaction) of these materials. Presumably less reactive, oxygenated materials are extracted.
Conclusions Thermodynamic considerations indicate that the energetic efficiency of coal-depolarized water electrolysis is rather sensitive to operating potential in the expected way. Encouragingly high efficiencies would seem to be attainable at potentials of about 0.4-0.5 V, i.e., about double the thermodynamic reversible (open circuit) potential. Analysis of coal, lignite, and peat residues partially consumed by anodic oxidation indicates that the oxygen content of these materials is increased and that the volatile matter and H2content is lowered. Potentiostatic reaction
seems to have lower selectivity for consumption of volatile matter over fixed carbon than does galvanostatic reaction. Oxidation of the peat seems to produce a greater proportion of CO (with respect to COz) than does similar reaction of the lignite or of the bituminous coal. The MAF heating value of all samples is lowered by anodic oxidation. It is not yet clear whether 100% conversion of the coal can be achieved by anodic oxidation. For this reason the chemical properties and calorific content of the partially consumed coal are significant. Literature Cited Coughlln, R. W.; Farooque, M. Ind. Eng. Chem. Process Des. Dev. 1980, 19, 211. CoughUn. R. W.; Farooque. M. Netwe (London)1979, 279, 301. Farooque. M.; CougMln R. W. Fuel 1979a, 58. 75. Farooque, M.; Coughlln R. W. Netwe (London)1979b. 280, 666. “Klrk-Othmer Encyclopedla of Chemlcal Technology”, 2nd ed.; Interscience Publishing Co.: New York, 1963-1970. Morgan, J. J. In “Chemistry of Coal Utlllzation”, Lowry, H. H.. Ed.; W h y : New York, 1945; Chepter 32, p 1675. Smith, D. H. "Industrial Electrochemical Processes”, Kyhns, A,, Ed.; Elsevier: New York, 1971; p 127. Welsr, P. B. Chem. Techno/. 1973, 3(8),498.
Received for review October 20, 1979 Revised manuscript received August 18, 1980 Accepted May 5 , 1982
ModlfOed RedHch-Kwong Equation of State for Phase Equilibrium Calculations Rlchard B. Steln Bechtei Civil and Minerals, Incorporated, San Francisco, California 94 119
The temperature-dependent parameters Q,, Q,,and ku of the Redlich-Kwong equation of state were evaluated first for pure components and then for binary mixtures. The coefficients of these parameters were generalized in terms of 1l T , and w by multiple regression. Calculation of VLE data for 1139 binary points predict K values with about half the average absolute deviation of the Soave or Peng-Robinson methods.
Introduction The twwonstant Redlich-Kwong equation of state (RK equation) is widely used for computerized calculation of K data employed in engineering process design. Besides acceptable accuracy for wide-boiling multicomponent mixtures (including noncondensables and supercritical conditions), this equation (eq 1) presents these computational advantages: (1)It requires only values of T,, P,, and w for each component. These are known for pure components and are computed for pseudo-components (petroleum fractions) by readily available correlations. (2) It converges to real roots for Zv and ZLin every case, even at or near the critical point, which is not always the case for other more complicated equations. (3) It requires minimum computer time for highly iterative proceases such as distillation when K values depend on liquid composition and vice versa. Variations on the RK equation have attempted to improve the accuracy by making some or all of the parameters into variables, generally as functions of T,. The better known of these are by Soave (1972), Peng and Robinson (1976), Graboski and Daubert (1978), and Zudkevitch and 0196-4305/82/1121-0564$01.25/0
Joffe (1970). While accuracy is sometimes improved, there is not always a favorable trade obtained in computer time nor certainity for convergence. The deficiency in the simple RK two-constant equation is that the number of variables in eq 1 is less than the number of degrees of freedom; hence the calculation system is underdefined. The RK equation is defined by a p = - -RT V - b F / 2 V ( V+ b ) b = R$tT,/P,
R, = 0.42747 Rb
= 0.08664
(5)
where the parameters R, and R b can be considered as implicit variables in eq 1. For a pure component V-L calculation there are three independent state variables when temperature is chosen as the dependent variable: preasure P, vapor volume V“ and liquid volume VL. From an 0 1982 American Chemical Society
