Ind. Eng. Chem. Process Des. Dev. 1980, 19, 51-59
trition rate of oil shale is not unlike that of limestones and dolomites. Conclusions Laboratory analyses suggest that the calcium in oil shales has a high reactivity with SOz and can be used in fluidized-bed coal combustors to reduce SOz emissions. It is predicted that more oil shale than limestone or dolomite would be required to meet the SOz emission standard since the calcium content of shales is relatively low. Also, the Green River shale contains approximately 1% sulfur, which may be released as SOz in a FBC. The use of shales may be desirable if the FBC is operated a t low superficial gas velocities (less than 3.8 m/s) or with low-sulfur coals (containing less than 3% sulfur). The oil shales should not be used in a FBC-CBC unless the shale elutriation rate is minimal, since at the temperature (1000-1100 "C) which a CBC operates, the CaS04 and the silicates in the elutriated shale react to release SO2. The geographic location of shale is a consideration. It may be desirable to use Western shale in FBC units in the Western United States in order to minimize transportation costs. The attrition rate of Green River oil shale was similar to that of Tymochtee dolomite, Greer limestone, and Germany Valley limestone when tested in a bubbling bed. Only one oil shale, Green River oil shale, was used in this evaluation. Since the SOz reactivity and attrition rates of limestones vary widely, a large variation is also expected for oil shales. Thus these results are not necessarily applicable to all oil shales. The Green River oil shale was not tested in an experimental FBC in which performance may differ from the results reported. Since all oil shales contain much less calcium than limestone, further investigation was not considered.
51
Acknowledgment This work was performed under the auspices of the U S . Department of Energy. We thank A. A. Jonke for his support and guidance and K. Jensen and his staff for their assistance in performing chemical analyses.
Nomenclature Ca/S = calcium to sulfur mole ratio K = average particle reaction rate constant, s-l U = calcium utilization, fraction V = superficial gas velocity, m/s e = bed voidage, assumed to be 0.5 H = fluidized-bed height, m
Literature Cited Field, M . A., Gill, D. W., Morgan, B. B., Hawksley, P. G. W., "Combustion of Putverized Fuel, Reaction Rate of Carbon Particles", Brit. Coal Mil. Res. Ass., Mon. Bull. 31(6), 295-311, Appendix 312-46 (1967). Fuchs, L. H., Nielsen, E. L. Hubble. B. R., presented at the 1977 Symposium on High Pressure Thermal Analysis and Combustion Process Studies at the 71 North American Thermal Analysis Conference, St. Louis, Mo., Sept 1977. Hendrickson, T. A., "Synthetic Fuels Data Handbood", p 7, Cameron Engineers, Inc., Denver, Colo., 1975. Keairns, D. L., Archer, D. H., Hamm, J. R., Jansson, S. A,, Lancaster, B. W. O'Neill, E. P., Peterson, C.H., Sun, C. C., Sverdrup, E. F., Vidt, E. J., Yang, W. G.,"Fluidized-Bed Combustion Process Evaluation, Phase 11, Pressurized Fluidized-Bed Coal Combustion Development", EPA-650/2-75-C, Westinghouse Research Laboratory, Pittsburgh, Pa., Sept 1975. Mazza, M., Morgantown Energy Research Center, Morgantown, W.Va., personal communicat'lon, Jan 11. 1978. Shapiro, R. N., Tekhnoi, K. I., Kinetics of H,S Absorption by Shale Coke", (Moscow-Leninarad: Khimiva) 1965. 108- 10 (in Russian). Snyder: R. B.,Wilsk, W. I., Johnson, I:, presented at the 1977 Symposium on High Pressure Thermal Analysis, St. Louis, Mo., Sept 1977a. Snyder, R. B., Wilson, W. I., Johnson, I., presented at the 5th International Conference on Fluidized-Bed Combustion, Washington, D.C., Dec 1977b. Svenke, J. E. (Akticbolzget Alomenergi. Stockholm), Proc. Int. Conf. Peaceful Uses At. Energy, P/784,8, 90-3 (1955).
Received for revieu; August 21, 1978 Accepted October 9, 1979
Estimation of Partial Molar Volume and Fugacity Coefficient of Components in Mixtures from the Soave and Peng-Robinson Equations of State Chung-Tong Lin and Thomas E. Daubert' Department o f Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania
16802
The Soave and Peng-Robinson equations of state are employed to calculate the liquid molar volume, partial molar volume, and the fugacity coefficient of components in nonpolar hydrocarbon mixtures. The predicted liquid molar volumes from the Soave equation have high errors and are not recommended to calculate partial molar volumes. The Peng-Robinson equation of state satisfactorily predicts both the liquid molar volume and partial molar volume. Over a wide range of temperature and pressure, the characteristic constants or interaction coefficients do not have significant effects on estimated partial molar volume from either equation. At low or moderate pressure, the fugacity coefficient of any component is predicted equally well by either equation, and the effect of the characteristic constant on the estimates of both equations is negligible. However, at high pressure the characteristic constant improves the predicted fugacity coefficients from either equation.
Introduction The partial molar volume of a component gives information on the effect of pressure on the liquid phase fugacity of that component in a mixture. This effect is negligible a t low or moderate pressure but becomes sig0019-7882/80/1119-0051$01.00/0
nificant a t high pressure. The fugacity coefficient of a component in a gas phase mixture shows the deviation of the behavior of the component from that of an ideal gas. Generally this deviation will increase as pressure increases. For this reason, the accuracy of the partial molar volume 0 1979
American Chemical Society
52
Ind. Eng. Chem. Process Des. Dev., Vol. 19, No. 1, 1980
and fugacity coefficient of a component in a mixture are very important in calculating vapor-liquid equilibria a t high pressure. Chueh and Prausnitz (1967) presented a method to predict the partial molar volume from their modified Redlich-Kwong equation; however, the predicted values a t high pressure are not satisfactory. The Lee-Kesler equation of state (Lee and Kesler, 1975) has also been applied to estimate the partial molar volume (Lin and Daubert, 1979) although the complexity of that equation requires more computer time and storage spaces. In this investigation, Soave’s modified Redlich-Kwong (Soave, 1972) and the Peng-Robinson (1976) equation of state are employed to predict partial molar volume and fugacity coefficient of each component in binary mixtures of nonpolar hydrocarbons. The effect of variation of coefficient a of these equations of state on the estimates has also been studied. Method of Calculation Soave’s Modified Redlich-Kwong Equation. Assuming that the coefficient a is a function of temperature, Soave (1972) rewrote the Redlich-Kwong equation as RT U (1)
both the Soave and Peng-Robinson equations of state. The estimated values of h,, are given for many binary systems and a correlation for estimating k,, for paraffinparaffin mixtures are recommended by Chueh and Prausnitz (1967). The fugacity coefficient of any component i in the mixture from Soave’s equation can be calculated by the equation
He then correlated values of a of the pure component with the reduced temperature and acentric factor.
The equation to estimate the partial molar volume of any component i in a mixture from Soave’s equation is
p==-m
(1
where = -pug
RT
vi
+ (0.480 + 1 . 5 7 4 ~ 0.1760~)-(1- T,O”)l2(2) -
While the coefficient b is given as R Tc b = 0.08664.-
PC
(3)
For a mixture, the following mixing rules are recommended by Soave (4)
bm = C x,b, (5) where the values of a, for hydrocarbon mixtures are recommended to be calculated by the following equation (Soave, 1972; Graboski and Daubert, 1978). a , = (a,a,)”z
(6)
A more generalized equation to calculate a,, is given as a,, = (ala,)l’z(l- K,,)
(7)
where KIIis an empirical factor, which must be determined from data on binary mixtures such as vapor-liquid equilibrium, critical properties, etc. The optimal values of K , for a particular system in different equations of state are not the same. Several authors (Soave, 1972; Graboski and Daubert, 1978) suggested that K,’s equal zero for nonpolar hydrocarbon mixtures. In order to test the effect of a small change of coefficient a on the values of predicted thermodynamic properties, a value of K,, for each binary mixture is necessary. A good approximation of the empirical K,, can be obtained from the so-called interaction coefficient, or characteristic constant, k , (Prausnitz, 1967) because both T , and a,, are related to the interaction energy between different molecules in mixtures. In this study, the values of k , suggested by Chueh and Prausnitz (1967) are applied in the calculation in testing the effect of the variation of coefficient a on the predicted values of the partial molar volumes and fugacity coefficients from
To study the effect of the characteristic constant on the estimates of partial molar volume and fugacity coefficient, both eq 6 and eq 7 are employed to calculate the values of a,, which are first used to obtain the gas phase molar volume, u , and liquid phase molar volume, ul, by solving eq 1 and t i e n substituting these parameters into eq 8 and 12, respectively, to calculate f, and VI. Although Soave’s equation accurately estimates the vapor-liquid equilibrium behavior of a wide variety of hydrocarbon mixtures (Graboski and Daubert, 1978), it overpredicts the liquid molar volume by 10 to 35% (Peng and Robinson, 1976). Therefore a modification of the liquid molar volume predicted by Soave’s equation would be necessary before it can be applied to calculate partial molar volume from eq 12. The liquid molar volume can be obtained by dividing the volume from eq 1 by a correction factor f C o R which is given as [T, > 1 or p , > p,,] fCoR = 1.1285 fCoR = 1 0.1668T, + ~ ( 0 . 9 6 1- 5.188T, + 6.025T:) + w2(6.895T, - 9.5032”:) [T, < 1 and p , < p,,] (13) where prc= 0.515 + 2 4 . 3 7 5 ~ (14) This correction is made for the purpose of calculating partial molal volume only and cannot be applied to calculate other properties as consistency could not be maintained.
Ind. Eng. Chern. Process Des. Dev., Vol. 19, No. 1, 1980 80
The mixing rules for the mixtures are
P, = (0.2905 - 0.085*~)RT,/V, W
=
I
I
1
I
I
53
/ I
(17) (18)
CXiW,
Peng-Robinson Equation. Peng and Robinson (1976) propose an equation of state as follows
Similar to Soave's equation, the coefficient a of eq 19 is correlated as
R2T,2 a = 0.4572411 + (0.37464 + 1.54226~PC 0.26992~')(1 - T,"2)}2(20)
: i 0 7
08
09
R8duc.d
I O
Ternp.ralur.
Figure 1. Liquid molar volumes of carbon dioxide a t 68 atm.
while coefficient b is given as
R T, B = 0.0778PC The mixing rules for a mixture are again given by eq 4, 5, 6, and 7. The fugacity coefficient of component i in a mixture predicted by the Peng-Robinson equation can be calculated from the equation
(2F:rLk :>
fi bi In - = - (2, - 1) - In (2, - B,) PYi b, ,
A, 2(2) l'*B,
--
-
-
-
In ( 2 , + 2.414Bm) 2, - 0.414Bm
where
The partial molar volume is estimated from the PengRobinson equation by
2Cx,a& k
UI(UI
2ambk(ul - bm)
ul(u1 + bm) .f bm(u1 - b m ) + bm) + bm(ul - bm)
]
/,,,
~
2am(u1 + bm)
-
[UI(UI
+ bm) + bm(ul - b m ) I 2
RT -
]
b,)'
(26)
Again both ug in eq 22 and V , in eq 26 are obtained by solving eq 19 directly. Equations 6 and 7 are also applied to study the effect of the characteristic constant on the estimates.
MDI.
fr..l,on
8."i."*
Figure 2. Predicted and experimental partial molar volumes of benzene-2,2,4-trimethylpentanea t 1 atm and 20 "C.
Results and Discussion Liquid Molar Volume. Figure 1 gives a comparison among the liquid molar volumes predicted by the Soave equation, corrected estimates of Soave's equation, the Peng-Robinson equation, and the measured liquid volume of carbon dioxide a t 68 atm. The original estimates from the Soave equation are 10 to 35% higher than the experimental measurements. The correction does reduce the error substantially; however, significant errors still exist in the corrected estimates for heavy hydrocarbons at high pressure. Table I presents the errors obtained using the corrected Soave equation and the Peng-Robinson equation for 17 different components over a wide range of temperature and pressure. The average error from the Peng-Robinson equation is within 11% of the experimental value. Also the estimates from the corrected Soave
Ind. Eng. Chem. Process Des. Dev., Vol. 19,
54
No. 1, 1980
I
soor.
t
I
M o l e Froc1,on f l h c n a
20
0
Figure 3. Predicted and experimental partial molar volumes of ethane and n-pentane at 408 atm and 4 "C. q,
I
t
I
1
I
I
I
I
1
I
I
1
,' , '
,/"'I 0,
""
I
I
I
02
03
0.
I
I
I
I
1
J
05
O b
0 1
08
0 9
IO
Molt F r o c m n Elhaw
Figure 5. Predicted and experimental partial molar volume of ethane in the mixture of ethane-n-decane at 136 atm and 171 "C.
=--,
3
1
/'
, ,
I
I
I
1
0 ,
c 2
0,
0. ~~~~8
f
I
I
I
1
I
1
31
5 ,
07
08
09
10
On
Figure 4. Predicted and experimental partial molar volume of benzene in the mixture of benzene-n-dodecane at 1 atm and 20 "C.
equation are accurate over the entire range of temperature when the reduced pressure is less than 1. The PengRobinson equation is superior to the Soave equation for hydrocarbons such as n-heptane, n-octane, etc. at reduced pressures greater than 2. For lighter hydrocarbons either method can be used to predict the liquid molar volumes. Finally, Soave's procedure gives slightly better results than the Peng-Robinson equation for gases such as N P ,H2S,etc. as shown in Table I. Partial Molar Volume. Experimental values of partial molar volume are calculated from data on volume change caused by variation of concentration in mixtures and are available in the literature for several different systems. Figure 2 compares estimates of both the Soave and Peng-Robinson equations with the experimental partial molar volumes of the mixture for the benzene-2,2,4-trimethylpentane system a t 1 atm. For high pressure systems, Figure 3 presents that of the mixture of ethane and n-pentane a t 408 atm. In either case, the estimates are close to the experimental values. It is interesting to find that the characteristic constant, h,j, does not have a significant effect on the predicted partial molar volume for
:--Ii 0 78
'? I 50
I
100
I
I
200
150 Pr.,>"r.
I
250
\
100
'.I uo
0,-
Figure 6. The effect of k,, on predicted fugacity coefficients of CO? at 15/85 mixture of CO,/n-butane at 340 O F .
either the Soave or the Peng-Robinson equation. Table I1 gives more evidence to support this conclusion by showing the estimates of ten more systems over a wide range of temperature and pressure. The Soave equation generally overpredicts the partial molar volumes and is not recommended for the calculation of partial molar volumes of heavy hydrocarbons such as n-octane, n-decane, etc. If the difference between the size
Ind. Eng. Chem. Process Des. Dev., Vol. 19, No. 1, 1980 55 Table I. Comparison of t h e Errors in Liquid Molar Volumes Predicted b y t h e Corrected Soave and t h e Peng-Robinson Equations no.
component
1
methane
2
ethane
3
propane
4
n-butane
5
is0 butane
6
n-pentane
7
isopentane
8
n - h e xane
9
n-heptane
10
n-octane
11
ethylene
12
propylene
13 14 15 16
H2S N*
17
n-decane
co
2
n-nonane
range of reduced t e m p
reduced pressure
0.582-1.048 0.582-1.747 0.582-2.7 37 0.399-0.799 0.399-1.054 0.399-1.745 0.399-1.745 0 . 3 30 -0.84 1 0.330-1.111 0.330-1.44 1 0.330-1.441 0 . 3 13-0.862 0.313-1.175 0.313-1.254 0.313-1.254 0.435-0 2 4 4 0.435-1.170 0.435-1.279 0.435-1.279 0.318-0.87 5 0.37 8-1.20 6 0.378-1.25 3 0.378-1.253 0.4 34 -0.8 68 0.434-1.230 0.434-1.278 0.434-1.27 8 0.438-0 3 9 7 0.438-1.248 0.438-1.269 0.438-1.269 0.47 3-0.905 0.473-1.192 0.473-1.192 0.449-0.9 1 8 0.449-1.133 0.449-1.133 0.4 33-0.7 87 0.433-1.062 0.433-1.888 0.433-1.888 0 , 3 3 5-0.82 2 0.335-1.09 6 0.335-1.461 0.335-1.461 0.505 -0.95 1 0.703-1.054 0.7 30-0.98 6 0.501-1.000 0.501-1.000 0.483-1.000 0.483-1.000
1.4974 5.989 11.979 0.2825 1.4138 5.651 11.303 0.3245 1.6226 6.4903 12.9807 0.3632 1.8158 7.2635 14.527 0.3780 1.890 7.560 15.120 0.4093 2.047 8.187 16.373 0.4078 2.0391 8.157 16.313 0.458 2.289 9.155 18.3108 0.5040 2.5202 10.0806 0.5546 2.7731 11.0926 0.274 1.3702 5.481 10.962 0.2989 1.4948 5.979 11.958 0.7657 2.0284 0.9341 0.008-1.327 3.541-26.559 0.096-1.450 3.867-29.00
no. of data points 9 11 20 12 10 20 20 18 14 20 20 12 18 19 19 16 15 17 17 12 19 20 20 19 18 19 19 12 20 20 20 12 19 19 13 19 19 10 9 20 20 9 14 20 20 16 5 8 28 26 28
2
error, %a cor Soave
Peng-Robinson
6.804 2.571 0.864 1.015 3.461 3.923 1.808 1.061 4.598 5.565 3.278 1.240 5.884 6.665 4.777 0.426 4.251 5.159 4.430 1.036 6.000 7.148 5.860 0.730 7.279 4.945 3.560 2.864 7.518 9.238 7 .87 2 1.251 9.908 9.923 3.068 11.271
8.31 7.868 8.615 7.07 3 0.319 6.399 8.844 6.710 6.055 6.005 7.429 4.541 4.887 5.053 6.2726 5.147 4.221 5.564 6.166 2.688 2.925 4.266 5.728 3.773 3.961 5.977 7.778 2.992 2.776 3.206 4.876 3.845 4.676 2.214 6.718 9.188 6.845 6.099 5.471 5.395 8.006 7.780 7.297 8.056 10.623 6.999 8.842 10.406 4.827 3.813 6.935 5.109
18.648 2.074 4.189 4.225 1.930 2.580 6.910 4.404 3.378 1.488 3.764 5.923 2.202 10.052 3.838 11.397
885 N
a
Error = [(c {[(calcd value
exptl vaIue)/(exptI value)] x 100
of the two components in the mixture is large, the Soave predictions of the partial molar volume of the light hydrocarbons a t dilute concentrations become unreliable. Figures 4 and 5 show two such cases for mixtures of benzene-n-dodecane and ethane-n-decane. Generally when the difference of the acentric factor is greater than 0.35, the errors in the estimates from the Soave equation for light hydrocarbons are very high. The predicted values from the Peng-Robinson equation are generally better than those of the Soave equation. The predicted partial molar volume from either equation is subject to error at conditions close to the bubble point or the critical point of the mixture. When the concentration of the mixture is within 5% of a pure component, the estimates of either equation cannot be justified because
) 2 ) / A ~ ] ” ? ,
where V . = number of data points.
the experimental partial molar volumes are either not available or subject to error. Fugacity Coefficients of Mixture Components. Figure 6 shows the effect of the characteristic constant on the predicted fugacity coefficients of carbon dioxide in a mixture of 85% n-butane and 15% carbon dioxide. The experimental fugacity coefficients are given by Prausnitz (1969). At low or moderate pressure, the effects of the characteristic constants on estimates from both the Soave and Peng-Robinson equations of state are negligible; however, more than 10% differences occur when the pressure of the system exceeds 60 atm. The percentage difference between estimated values with and without kij’s for 35 systems over a wide range of temperature and pressure are listed in Table I11 for both equations of state.
56
Ind. Eng. Chem. Process Des. Dev., Vol. 19, No. 1, 1980
IC0
Y
a X
ri
ri
:z
a c
j;. 0
E" Y
F
0
r
i
x
m
w
m
' 9
c-
5
a
0 ri
Ind. Eng. Chem. Process Des. Dev., Vol. 19, No. 1, 1980
57
N U
2a 0
E
8
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A 0 0 0 A 0 A
3R
t-
ririamrl
m w a 0 0 0 0 r i r i m m r -
*d
;o
rimm
emw
o o o o o ~ o o o ~ r i r l r i ~ r i r i r i r i ~ ~ r i m ~ m m m ~ e e a ~ a r - w m
999999999999999?9999999?99999?99?99
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
h
N
v h
2.
58
Ind. Eng. Chem. Process Des. Dev., Vol. 19, No. 1, 1980
i
C
m
w
~ m t -e
e
o
m
r
i o
N
u 3 m rict-cca mmrl 0 0 m * 0 ~ m a x - o ~ r i - o a ~r(m 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
doooodooo0ooooo0oooo~ooooooooo
Ind. Eng. Chem. Process Des. Dev. 1980, 19, 59-64
Again no significant difference is found at low or moderate pressure. As shown in Table IV, there is essentially no difference between the estimates from either equation with or without k,, a t low or moderate pressure although the difference exists a t high pressure. Generally the estimates from the Soave equation are greater than those of the Peng-Robinson equation. Nomenclature f, = fugacity of component i p = pressure p c = critical pressure pr = reduced pressure R = gas constant T = temperature T , = critical temperature T , = reduced temperature V, = partial molar volume of component i V, = critical volume ug = gas volume of the mixture u1 = liquid molar volume of the mixture w = acentric factor
59
xi = mole fraction of component i in liquid phase yi = mole fraction of component i in gas phase
Literature Cited Berry, V., Sage, B. H., J . Chem. Eng. Data, 4(3),204 (1959). Chueh, P. L., Prausnitz, J. M., Ind. Eng. Chem. Fundam., 6, 492 (1967). Chueh, P. L., Prausnitz, J. M., AIChE J . , l3(6),1099 (1967). Graboski, M. S.,M.S. Thesis, The Pennsylvania State University, University Park, Pa., 1970. Graboski, M. S.,Daubert, T. E., Ind. Eng. Chem. Process Des. Dev., 17,443
(1978). Grane, D. J.. Sage, 8. H., J . Chem. Eng. Data, 12(1),49 (1967). Lee, B. I., Kesler, M. G., AIChE J . , 21, 510 (1975). Lin, C.T., Daubert, T. E., AIChE J . , 25, 365 (1979). Peng, D. Y., Robinson, D. B., Ind. Eng. Chem. Fundam., 15, 59 (1976). Prausnitz, J. M., "Molecuhr Thermodynamics of Fluid-Phase Equilibrium", p 148, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1969. Reamer, H. H., Korpi, K. J., Sage, 8. H., Lacey. W. N., I n d . Eng. Chem., 39,
206 (1947). Reamer, H. H., Sage, B. H., J . Chem. Eng. Data, 4(2),98-102 (1959). Reamer, H. H.,Berry, V., Sage, B. H.. J . Chem. Eng. Data, 6(12),184 (1961). Reamer, H. H., Berry, V., Sage, 8. H., J . Chem. Eng. Data, 7(4), 486 (1962). Soave, G., Chem. Eng. Sci., 27, 1197 (1972).
Received for review July 20, 1978 Accepted July 11, 1979
Selectivity of Ion Transport in Desalination by Electrodialysis Kohel Urano," Masahiro Kawabata, Nobuhiko Yamada, and Yasunori Masaki Departnient of Safety and Environmental Engineering, Yokohama National University, Hodogaya-ku, Yokohama, Japan
Changes of selectivity of ion transport ( T ; ) with operating conditions such as electric current density ( I / S ) ,total concentration of desalting solution (C,) and linear flow velocity (,v) were studied in the electrodialysis desalination process. When IIS is very large, or when CT or vis very small, is equal to the ratio of the equivalent conductivities of j to iions in infinite dilute solution. When I I S is very small, or when CTor vis very large, T / seems to be equal to the ratio of the diffusion coefficients of j to i ions through the membrane. I n the transitional state, which is the The values of A most important state in practical use, T,/ can be given by the equation as r l = A(I/S)"CT'V'. and p vary according to systems of membranes and ion species, and the values of (Y seem to vary only with ion species. But the absolute values of y vary little according to the systems of membranes and ion species.
Introduction In many water-short areas, desalination processes of sea water or brackish water are needed to get potable water and water for industrial use. Desalination processes of wastewater are also applied to pollution control, recovery of valuable solute, and reuse of wastewater. The electrodialysis process is one of the most feasible processes for these purposes. The electrodialysis process has been under development since the 1950's, but the fundamental research for this process is still insufficient because the mechanism of multicomponent ion transport in the electrodialysis is very complicated. Making decisions of suitable operating conditions for selective removal or recovery of the objective ion in the application of this process is a very important problem. There are a few papers (Peers, 1958; Mandersloot, 1964; Tsunoda and Kato, 1967) that reported on changes of selective ion transport with several operating conditions, but the general relations between selectivity of ion transport and operating conditions have still not been clarified. Kitamoto and Takashima (1970) and Huang and Wang (1977) studied this problem, and they concluded that selectivity of ion transport of a certain ion to the other one can be generally evaluated by a dimensionless parameter, the Stanton 0019-7882/80/1119-0059$01.00/0
Table I. Type and Properties of Ion-Exchange Membranea
thickness, cm tensile strength, kg/cm? ion-exchangecapacity mequivig of dry resin a
anion-exchange membrane
cationexchange membrane
ACH- A V - AVS45T 4T 4T
CL- C6625T 5T
0.17 5 1.2
0.15 7 1.1
0.16 5 1.2
0.16 4 1.7
0.16 3 2.5
Commercial name: Neosepta.
number ( S t ) ,which is a function of operating conditions. It was found, however, that their conclusion could be applied only in specific cases. We then studied the detailed relation between the selective transport coefficient ( T i ) and operating conditions such as electric current density (Z/S), total concentration of desalting solution ( C T ) , and linear flow velocity ( u ) .
Experimental Section Materials. Types and properties of ion-exchange membranes which were used in this study are shown in C 1979 American Chemical Society
