boiler feed water treatment by means of an electrically operated pump. Prior t o the application of the hydrogen exchange process, the interpretation of the conductivity data would have indicated a serious boiler water carry-over problem. However, the ion exchange process eliminated this interference and indicated that good steam purity was being provided (Figure 7 ) . At plant 24, application of cycloCondensate hexylamine, morpholine, and ammonium chloride (Q), chemicals normally employed for condensate p H control hydrogen for corrosion preExchange vention, revealed Resin that the hydrogen exchange process plus reboil eliminated the interference provided by these chemicals (Figure 8). Preliminary tests on the effect of oc9’ ‘Ondensate A1la’J’zer Equipment tadecylamine ( 7 ) , a filming amine employed t o prevent condensate corrosion, indicate that t,his amine, apparently due t o its low solubility and ionization, does not appreciably influence the conductivity results. When these data mere discussed with F. G. Straub, a t the University of Illinois, he designed a small unit without temperature control for testing condensate to determine condenser leak__I
age in power plants employing ammonia or amines for condensate p H control (Figure 9). It was estimated t h a t immediately after installation the results detected a 0.01% condenser leakage (Lake Michigan water). CONCLUSION s
By combining the procedure of temperature control at the atmospheric boiling point and the hydrogen exchange process with reboiling, an easy foolproof method of testing steam purity has been developed. This method minimizes interference from carbon dioxide, ammonia, cyclohexylamine, and morpholine; provides a simple temperature control; and detects boiler water carry-over by continuous conductivity, pH, or redox measurement. LITERATURE CITED
(1) Ani. Soc. hlech. Engrs., 29 W. 39th St., Kew York, Power Test Code, ”Detexmination of Quality of Steam, Part 11,” 1940. ( 2 ) Am. Soc. Mech. Engrs., 29 W. 39th St., New York, Steam Contamination Subcommittee of the Joint Research Com-
mittee on Boiler Feedwater Studies, “Bibliography on Steam Contamination.” (3) Am. Soc. Testing - Materials. Committee D 1 0 6 M 9 T . “Tentative 8Iethod of Sampling Steam,” 1949. (4) Am. Soc. Testing Materials, Proc., 41, 1261 1340 (1941). (5) Lane, R. W., Larson, T. E., and Pankey, J. W., Proc. I 4 f h Ann. Water Conf., Eirg7s. Soc. Wesf. P e n n , 119-39 (1953). ( G ) Latimer, W. AI., “Osidation Potentials,” Prentice Hall, New York. 1952. ( 7 ) Xlaguire, J. J., IND.ENG.CIimI., 46, 994 (1954). ( 8 ) Place, P. B., Comb,ustion, 2 3 , 4 9 4 3 (-4pril 1951). (9) Proc. 14th Ann. W a t e r Conf., Eilgrs. SOC.W e s t . P a n . , “Panel Discussion on Corrosion and Deposits in Condensate and Feedwater Systems” (1953). RECEIVED for review March 29, 1054.
BCCEPTED
September 23, 1954.
Electrodialysis of ater Using Multiple Membrane Cell A. G. WINGER, G. F. BODARIER, R. KUNIN, C. J. PRIZER, AKD G. W. IIA4RRION,Rohm & Haas Co., Philadelphia, P a . T h e electrochemical properties of recently developed synthetic ion exchanger membranes and those of electrolytic solutions have been utilized to predict the performance of a multiple membrane electrodialysis cell in deionizing sodium chloride solutions. Equations were derived for the energy requirement and flow capacity of a cell of n unit cells with series flow connection, as a function of concentration change, concentration range, voltage per unit cell, cell geometry, and membrane and solution properties. A 50-unit mul.tiple membrane cell was built with Amberplex A-1 and Amberplex C - l membranes a1ternately separating the chambers. Agreement of results on energy requirements per unit volume of depleted effluent is satisfactory, that on the capacity of the cell. much less so. The results are analyzed to discover the probable reasons for discrepancy between predicted and actual performance.
I
N RIANY areas of the world, there exists so severe a shortage of potable water that means for recovering such water from brackish and sea water are being studied. The shorbages have become acute because of the incrcaFing population in cert,ain areas. increased demands of industry, poor conpervatmionpracticee. and pollution. Use of distillat,ion inet,hods. ion exchange 50
resins, and electrodialysis have received the major share of attention. The recent development of synthetic ion exchange membranes has greatly stimulated interest in the deionizat>ionof saline and brackich 11-atersby elcctrodial . Heretofore, thrpractical application of the well-lcno\l-nprii les of electroinigi.atiol1~t,i~i~ of ioiis had been greatly handicappctl by a lucli of suitable dia-
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 47, No. l
L
o
n Exchange
It is possible in principle to predict the flow characteristics, power require(ik . A N I O N E X C H A N G E M E M B R A N E \ ments, and efficiencies of any multiple DEPLETED EFFLUENT E L q E F F L U E N T C k *CATION EXCHANGE MEMBRANE membrane electrodialysis cell if the electrochemical properties of the membranes and solutions as well as the mechanical transport properties of the solutions through the membranes are known under a wide range of conditions. Langelier (8) has published a brief analysis of the problem of desalting sea water, which, however, contains no detailed scheme for predicting costs and kinetics of desalting under widely varied conditions. The Same is true of the recent publication ( 1 6 ) of the performance of a Briggs electrolytic cell operating in conjunction with ion exchange columns to deionize water The Briggs cell relevant t o this discussion is a three-chambered cell usFigure 1. Schematic Diagram of Multiple Ion Exchange Membrane ing nonpermselective diaphragms; its Electrodialysis Cell-10-Unit Cells principle of operation in deionizing Small horizontal arrows indicate movement of ions between compartments water is basically different from that of a multiple membrane electrodialysis phragms or membranes with which to separate the electrode cell, which would have practically no value if nonpermselecchambers from the central chambers undergoing deionization. tive membranes were used. Kollsman (6) has described in a "he principle defect of the known membranes was their lack of patent a multiple membrane electrodialysis cell without giving permselectivity-that is, their failure to possess, over a wide conexperimental values or theoretically predicted results of operacentration range of the surrounding solution, properties which tion. Since the characteristics of the new synthetic ion exwould cause the transport numbers of the ions within them to changer membranes have been published in some detail and differ from those of the same ions in the free solution surrounding those of the solutions have long been known with more or less the membrane and in equilibrium with it. The new synthetic accuracy depending on concentration range, it is desirable to membranes do possess such properties due principally to a high devise a scheme for predicting the performance of electrolytic concentration of fixed charge groups in the membrane. There is a deionization cells in order to evaluate this method for deionizconsiderable amount of literature ( 1 , 2, 4, 5, 7, 19, 15, 18, 19) ing saline and brackish waters. describing these membranes. In the positive type membrane the transport number of cations is less than in the surrounding soluDERIVATION O F ENERGY AND FLOW RATE EQUATIONS tion, while in the negative type, it is greater. As first clearly proposed and demonstrated by Meyer and When an electrical potential is applied across a membrane surStrauss ( 1 1 ) in 1940, an indefinite number of chambers may be rounded by two similar or dissimilar solutions, the solute will be alternately separated by positive and negative membranes in transported across the membrane by the migration of the ions series, and by passing current through, it is possible to deplete carrying current and by ordinary diffusion, the solvent by a mechthe solution in alternate chambers while concentrating that in anism commonly called electroendosmosis or electrokinetic transthe others. Onlv two electrodes are required, and the alternate port and by ordinary osmosis due to differences in the activity chambers can be connected in either a series flow connection or a of the solvent on either side of the membrane. All four mechaparallel flow connection ; both arrangements undoubtedly possess nisms will affect the operation of the multiple membrane cell certain practical advantages and disadvantages. Figure 1 and must be considered in a n analysis of its operation. The shows a schematic diagram of a multiple ion exchange membrane published transport numbers for the ions within the membranes electrodialysis (RIIEME) cell in which the series flow connection together with Faraday's laws of electrolysis enable a calculation is used. Membranes labeled a, are positive, that is, preferenof the transport of solute by electromigration of ions, but data on tially permeable to anions, w hile those labeled ct, are negative, the electroendosmotic, diffusion, and osmotic effects for the memor preferentially permeable to cations. Analysis will show that branes do not appear in the literature. Experimental data are under an applied potential the cations in compartments 1, 2,. 10 required for the electroendosmotic and osmotic effects, though the will migrate through the cation permeable membranes toward former could be approximated by the use of transport numbers the cathode into compartments l', 2',. . .lo'. Hence alternate in the membrane and hydration numbers of the ions involved. compartments will be depleted, and the others enriched as ilssume a multiple membrane cell as shown in Figure 1, conelectrical current flows. The alternate compartments may be sisting of n unit celh across which a potential E volts is impressed. joined as shoRn, and the solution flows through the cell continuA sodium chloride solution of concentration Cd equivalents per ously. The same current traverses either stream n times, where liter is fed countercurrentwise to both the depleted and enriched n is the number of unit cells. A unit cell is defined as consiststreams a t the identical flow rate of F liters per hour, producing a ing of a depleted chamber and an adjacent concentrated chamber depleted effluent of concentration COequivalents per liter. At nith the corresponding anion and cation permeable membranes. the steady state, the current passing through the cells will be The electrode chamberti are fed independently to keep the elec( E - e ) / R amperes, where R is the total ohmic resistance of the trode reaction products separate from the concentrated or decell including solution resistance and membrane resistance. and pleted electrolyte streams. If sodium chloride is the electrolyte, e is the sum of the end electrode potentials, the membrane potenchlorine and oxygen will be evolved in the anode chamber and tials which arise across each membrane due to the concentration its contents will become acidic, while hydrogen will be evolved a t differences on either side, and the diffusion potentials in the soluthe cathode, and sodium hydroxide will be formed in the catholyte. tions. From each depleted chamber, one faraday of electricity -INITIAL
\
SOLUTION
1-10 ; D E P L E T E D
CHAMBERS
l'-lO' = E N R I C H E D
CHAMBERS
I N I T I A L SOLUTION
-
.
January 1955
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
51
will remove one equivalent of salt, if the membranes are perfectly permselective, permitting only cations or only anions to migrate through. For an actual membrane (14), the current efficiency is equal to (2tr*
- 1) = Em,,./Eo
Then the equivalents of salt removed from the depleted stream and added to the concentrated stream of a multiple chamber cell per hour is
p(E
- e)nt
0.0374(E
I
- e)np R
R3
q =
The diffusion of salt through the membranes independent of electrical potential must also be considered. The introduction of the counterelectromotive force due to concentration potential in Equation 1 does not correct for the free diffusion of salt, since the major portion of the membrane potential arises from the Donnan potential within the membrane (9, 10, 17). Tf the diffusivity of electrolyte in the membrane is D sq. em. per hour, then the amount of salt diffusing from the concentrated into the depleted stream in equivalents per hour is q’
L-Zz
(2n
+ 1)ADZ 10001--
Then the total net transport of salt from depleted to concentrated stream in equivalents per hour is
Kow, the amount of salt removed from the depleted stream per liter of depleted effluent would be given by the concentration change Cj - CO = AC in the depleted stream if no water Tere gained or lost in that stream while traversing the cell. Actually the depleted stream loses water by osmosis and by electroendosmosis to the concentrated stream so that for every liter of depleted effluent f 01 liters of solution n’ere fed to the etream. As shown theoretically by Schmidt (Is),the amount of water transported across the membranes per faraday of electricity passed will be a nearly linear function of the concentration of the solutions suriounding the membrane. The total water transported by electroendosmosis from depleted to concentrated strcam per hour is
+
This equation assumes that all chambers of tlie multiple ion exchange membrane electrodialysis cell have equal volumes, so that the average concentration surrounding an individual membrane remains essentially constant during the desalting process. The maximum effluent flow rate liters per hour, in the depleted stream if no electroendosmosis or diffusion occurred n-ould have been
or
u is not exact, due to the neglect of diffusion in the Q used in Equation 5 . The actual salt removed from the depleted stream per liter of effluent is
52
and the actual flow rate of depleted effluent will be
Equation 7 for the flow rate of depleted emuent from the multiple membrane cell does not include the effect of ordinary osmosis, which would further decrease the flow rate. The avewge osmotic pressure across the membranes could be approximated from van’t Hoff’s lan., and from this value and experimental data on the hydraulic permeability of the membranes, the rate of transfer of water from depleted to concentrated stream could be estimated. The hydraulic permeability of the synthetic permselective membranes is very low (16, 1 8 ) ; hence, it can be safely assumed that the effect of ordinary osmotic transport of water in the multiple membrane cell is insignificant in practice, if these membranes are used. The electrical pon er supplied to the mriltiple membrane cell in its steady state operation is
W = ‘E 1000 - e)E R kilowatts Then the energy consumption of the process per liter of depleted effluent will be obtained by dividing Equation 8 by Equation 7, or
(9)
These equations permit a calculation of the performance characteristics of any multiple membrane electrodialysis cell from its geometry, the electrochemical properties of the solution to be dialyzed, and the membranes to be used. The effect of electroosmosis and diffusion are small compared with that of electrolytic transport of ions. If the electroosmotic and diffusion terms are omitted from the flow and average cost equations, simplified equations are obtained which facilitate the prediction of the influence of various factors on flow rate and costs. Thus, Elquation 7 becomes
and Equation 9 becomes
p = E-( A C ) kilowatt hour pw liter 37.4np
Equation 11, the simplified expression for the energy cost per unit volume of treated effluent, contains no unknown factors after a given depletion AC is arbitrarily chosen, and the energy cost is then directly proportional to the voltage applied per unit ceIl The range of concentration in which the depletion is affected vi11 affect the cost because of the dependence of current efficiency or membrane permselectivity on the concentration of the solution surrounding the membrane. At higher concentiations the current efficiency 4 ill be less, hence the cost per unit volume effluent for a given AC greater than at more dilute concentrations. Equation 9, the more exact one for energy cost, s h o m that the phenomenon of water transport across the membrane also causes the energy cost to depend on the concentration range treated, but in this case in the opposite Bense. The cost tends to decrease a t the higher concentrations for a given AC. Equation 10, the simplified one for the flow rate of the depleted stream contains two factors whose depcndence on the geometry of the cell, on the solution being treated, on the membrane properties, and on the amount and rate of depletion must be knovn before predictions of the flow rate can be made. Theae factors are
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 41,No. 1
J the counter electromotive force of the cell, which is the sum of all membrane potentials, concentration potentials, and endelectrode potentials, and the ohmic resistance of the cell. For any multiple membrane, flowing system cell, the ohmic resistance and counter electromotive force are necessarily exceedingly complex functions of all these variables and others as well, notably temperature. Neglect of one or more of these variables may cause large errors in the predicted flow rates even though energy cost estimates are quite accurate.
FEED T A N K S
FEED
FEED M A K E - U P DRUM
tion at membrane-solution interfaces, Equation 12 will permit satisfactory calculation of counter electromotive force in the cell. CALCULATION OF CELL RESISTANCE
The ohmic resistance of a cell can be broken in two parts, the membrane resistance and the solution resistance. The membrane specific resistance is a function of the nature of the ions involved, the average concentration of these ions in the solutions surrounding the membrane, and the temperature of the system (B,6,18). Similarly, the solution specific resistance is a function of the nature of the solute, the concentration of solute, and the temperature. If these functions were known and if a t steady state the distribution of concentrations in a cell of given geometry and number of unit cells were known along with the temperature at each point, then a point calculation could be made and the cell resistance calculated. Needless to say, this is not a convenient way to estimate cell resistance. Furthermore, the prediction of concentration distribution in a cell is difficult if not impossible. One approach t o the problem of predicting cell resistance and counter electromotive force is to make a number of simplifying assumptions, estimate cell performance, and then test these estimates by building and operating a cell. A great simplification is accomplished by considering the water solutions of a pure salt. For these studies sodium chloride was selected as the solute. Consider a cell of n unit cells assembled as shown in Figure 1 with the chambers connected in series. Each chamber in the cell has a face area, A , and thickness, 6.
WASTE
I STREAM
-OBSERVED PREDICTED
6.0-
DEPLETEDC O N C Flow Sheet of Multiple Ion Exchange Membrane Electrodialysis Cell
0 0
-----
---_ --
STREPM
a
Figure 2.
n Exchange
o
4.0-
0
-----____
\
$ The counter electromotive force set up in the multiple membrane cell under steady state conditions of electrical current flow and hydraulic flow is the sum of the end-electrode potentials, the membrane potentials, and the concentration or diffusion potentials in the solutions The size of the latter depends on the electrolyte in the cell and would be zero for potassium chloride with its nearly equal ionic transport numbers For sodium chlonde, the contribution of the diffusion potential would be very small compared to end-electrode potential and membrane potentials and will be neglected in this treatment. The net endelectrode potential would be about 2.5 volts for sodium chloride solutions using graphite electrodes and in practice has been found to be about 3 volts, the increased amount being due to the presence of hydroxyl or hydrogen ions in the end chambers and to the concentration differences between catholyte and anolyte. The numerical value of the membrane potential, Emem.,across a membrane separating tivo solutions of a uni-univalent electrolyte a t different concentrations C, and C2, neglecting activity coefficients is Emem.
= (2trf
- 1 RT) In Cr/C, ~
I
I
I
I
For any depleted chamber in the cell an element of solution whose area is s and whose thickness is, again, b may be selected. If it is assumed that no concentration gradients exist in the b direction, then
also
(12)
where t r f is the transport number of the ion to which the membrane is more permeable. The signs of the membrane potentials set up in a cell as shown in Figure 1 under steady state conditions are such that the sum of the membrane potentials is the sum of their numerical values and is in such a direction as to oppose the applied voltage across the cell. If the flowing streams in the cell are sufficiently turbulent to minimize concentration polarizaJanuary 1955
2.0:
Y
But
E = -rbS
and 7
-
B - (for short ranges of concentration) C
INDUSTRIAL AND ENGINEERING CHEMISTRY
53
.\ssuming that slug flow prevails in each chamber of a cell containing n unit cells, the total solution resistance Re map be Iound by summing the individual chamber resistances
Substihting
R, = Rd, + ad, $- . . .
let Ci,
=
Ed,, -t Re,
4-
Re2
+ . . . f n,,
concentration of element entering the kth chamber
when
C
=
CL;
t = 0 (iesidence time)
Integrating 16)
Thus, the concentriition of iliii solution in :in>- i~lementof ail). chamber depends on the concentr:rtion of the solut,ion in the element as it enters the chamber. the t,iriie the element has ?pent in the chamber (it,s age or resi(1ciice time)>and t h e voli,age drop across the (,hamher. It is tiicit,ly :issumed in perfolming t.his integration that the voltage drop i i c r o ~the ~ chamber is the mme a t all points in the chamber or that, the faces of the inc:iibranee bounding the chamber tire equipotential surfaces. The total resist,ance of thc solution in the chainher ticpeiids on the flow pat,tern in that cliamher or, better, on the rc.;iticnce time distribution of the elements i n thr chamber. For slug flow ( 3 ) ,the solution re;istance of a depleted c h a ~ n b e r is
On the other hand, lor perfrct miling of the holution in the chamber
For the chambers of the conceiitiated stieam the w n e treatment applies. For slug flon
For perfect mixing
54
If the current efficiency is the same in all chambers, then
here C, =
JI
C,(feed concentration)
Co =
= Jf, (feed concentration):
C,,, (effluent Concentration)
-If0
=
JE,
(effluent concentration)
Combining logarithms and wbstituting
Similarly, for the condition of complete mixing
As n heconies large or as (C, - C,/n)and (Mo - M % / n become ) %mall,E', approaches R,. For example, aheri (C, - Co/n) and (M, - illc/n) are in the range 0.001, the difference in R, and R', is negligible. Of course any flow pattexn in the chambers intermediate to slug flow and perfect mixing will give the same result. This is true only for the series connection of the chambers. If the cell chambers are connected in parallel-that is the feed
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 47, No. 1
i is split among all the chambers of either the depleted or concentrated set-then the flow pattern achieved in the chamber will markedly affect the chamber solution resistance. In this case, slug flow must be sought as that flow pattern which reduces the resistance to a minimum, This will be true regardless of t h e number of chambers.
n Exchange
o
and for perfect mixing
If the cells are numbered from the cathode, for the kth unit cell the membrane resistance may be estimated as follows: The kth cation permeable membrane will be surrounded by the solution in the kth depleted chamber and the (IC - 1)th concentrated chamber. The average Concentration may be found for either slug flow or perfect mixing by solving for C k and MI;- 1. The membrane specific resistance may then be evaluated a t
2
-OBSERVED
__---P R E D I C T E D
,
,
Similarly
Then
w
a 0
5 0
DEPLETED
Figure 4.
150
10 0
EFFLUENT
200
250
RATE- GPH
Depleted Effluent Flow Rate for Cell Operating on Brackish Water I570 p.p.m. NaCl as CaC03
-0 BS ERVED ----PREDICTED
100-
The constant B is affected by temperature
------------
_I
4
Bi
B
1
---7_1=:
a
+ 0.025(T - To)
where 0.025 is the temperature coefficient of resistance for sodium chloride solutions. Equations 22 and 23 can thus be generalized to a range of operating temperatures. The membrane specific resistance is a function of the average concentration of the solutions surrounding the membrane. Using several of the preceding assumptions, it is possible to estimate the membrane resistance of any cell Again, the flow pattern wil1 affect the estimates. For slug flow ( 3 ) , the average concentration of solution in a chamber is the log mean of the inlet and outlet concentration
30
'
I
I
Finally, the total membrane resistance R, can be found by summing the individual membrane resistances
+ . . . Rc, 4-
R m = Rq f Rcz,
For perfect mixing
Ck = G k + l ]?Ti,
Mk+i
Assuming, as before, that the current efficiency is the same in all chambers, then for slug flow
Ron
For concurrent flow of the two streams through the cell, the estimation of membrane resistance can be further simplified because the average concentration surrounding each membrane in the cell is the same. Hence R'm
=
4Rci
+ Baij
A similar approximation may be made if the range of concentrations in the cell is small. In this case, the variation of membrane resistance with average concentration may be assumed linear without significant error. The average concentration in the cell is the average of the inIet and outlet concentration of each stream, and the specific resistance of both cation and anion permeable membranes may be evaluated a t this concentration. The error in this approximation increases Kith increasing n. At any point on any membrane in the cell
E,,.
=
RT C -In 2 5
c1
Obviously, this potential will vary from point to point in any membrane because of the changing concentrations. If the conJanuary 1955
INDUSTRIAL AND ENGINEERING CHEMISTRY
55
centration a t each point in the cell is known, the niembrane potential a t each point may be calculated. With solution and membrane resistances, the cell may then be treated as a group of parallel circuits to estimate E e/R, hence, P, for any applied voltage.
-
I
0
I DEPLETED
2 3 EFFLUENT
When n = nmax., E = e, and the flow rate is zero. If n > nmax., the voltage applied cannot achieve the required depletion, AC. The energy consumption per liter effluent given by Equation 11 should now be a t the minimum value predicted thermodpnamically for reversible removal of dissolved electrolyte. EXPERIMEYTAL
I
4 RATE- G.PH
Figure 6. Depleted Emuelat Flow R a t e f c Cell Operating o n Sea Water 30,400 p.p.m. NaCl as CaCOi
.bother approach is to find the average membrane potential of each membrane in the cell and to add them. To do this. one may use the average concentrations that were employed to calculate the membrane resistance, C and and substitute in Equation 28. When n is large and when (Cc - Cc,o/n)and (Mo M d n ) are miall, the counter electromotive force calculated by this method approaches
n,
PROCEDURE
TOcheck the validity and usefulness of this analysis, a model cell was constructed and operated. The results predicted by the methods given were compared \1-ith aclual operating data. Scvcral concentrations of sodium chloride solution were employed as feed solutions. The cell used for this work was developed in the laboratory. Schemat'ically, it>follows closely Figure 1. The actual cell assembly is shown in the photographs. The dimension and arrangement of the cell were chosen primarily to facilitate experimental study. Little thought was given t o cell capacity. The cell consisted of 101 Plexiglas chambers whose iiiterna,i cross section was 1 square foot and whose thickness was 6 / 1 ~ inch. These were separated alternately by Amberplex C-1 and Ainberplex A-1 membranes, each approximately 25 mils thick. Plexiglas grids were used in each chamber to keep the membranes evenly spaced and to minimize concentration polarization a t the membrane solution interface by inducing turbulent flow. Each chamber hac! an inlet and outlet port. The chambers of each stream, depleted and concentrated, were connected in series. Electrode chambers a t each end of the cell were provided with individual feed and tlischarge ports and were fed independently. Anode and cathode xvere both of amorphous carbon and each had a face area of 1 square foot. Figure 2 shows the arrangement of accessory equipment, lced tanks, pumps, and meters. Direct current power was provided by rect,ifying alternating current in a dry plate, three phases, full wave recti-
fier.
-
e' =
-0SSERVED PREDICTED
_____
23
-
50 VOLTS ------
Regardless of the method used to estimat,e counterelectromotive force, the decomposition voltage plus any overvoltages (irreversible electrode effects) must be added to the counterelectromotive force to find the total voltage opposing that applied, The sum of membrane potentials developed in the cell during operation can thus be calculated using the average concentrations given by these equations. However, the actual average membrane potentials are likely to be higher than those calculated due to concentration gradients in each chamber in the direction of electrical current flow. In each depleted chamber, the concentration in the neighborhood of the membranes will be less than in the bulk solution, while in the concentrated chambers it will be greater. Thus the concentration ratio of solutions on either side of a membrane is greater than that calculated from average bulk concentrations, giving higher membrane potentials. The amount of this concentration polarization will be a complex function of current density, flow rate, and temperature, making a priori calculation of the true membrane potentials very difficult. The average membrane potential per unit cell, E , for a given depletion of a particular solution is independent of the number of unit cells, n, used to effect the depletion. This permits an estimate of the maximum number of unit cells, n m X , which can be used for given values of applied voltage, E, and concentration depletion, AC, that is
-
E eel. unit cells nmsr. = 56
-----
2 5 VOLTS
Y
1
20
I
1
I
40
60
80
I 0
DEPLETED
E F F L i l E Y T CONCENTRATION P P M h a c 1 A S CaCO,
Figure 7. Energy C o n m m p t i o n of Cell for Hard Water Deionization 640 p.p.m. KaC1 as CaCOr
Operation of the cell was generally as f o l l o ~ s : 1. Feed solutions were made from salt (Rfallinckrodt C.P. grade) and filtered plant water. After thorough mixing and testing for salt concentration, the solutions were pumped to the feed tanks. 2. From t h e feed tanks, the solutions were metered to the cells through rotameters. Care was taken to hold the rates constant. 3. After the feed rates were set, the rectifier mas started, and the voltage applied to the cell was adjusted t o the desired value. 4. The effluent streams were collected, weighed, and sampled every 30 minutes. Current was read every 30 minutes also. 5 . The voltage and the flow rates of the two streams Ryere held constant, and the concentration of the two effluent streams was recorded twice an hour. T h e n steady state operation wae reached as judged by the constancy of the effluent concentration, current, and flow rates for 2 to 3 hours, t h e cell was shut down.
I N D U S T R I A L AND E N G I N E E R I N G CHEMISTRY
Vol. 4.1. No. 1
Exchange
-.Ton Cell in Operation, Showing Rotameter Assembly to Measure Fed Rates
Four Cell Charnkrs Showing
+
Feed System
The salt concentration was determined by titration with standardized silver nitrate. A t concentrations below 0.002N the salt content waa determined by conductivity measurements. Since the temperature of the room and the feed solutions varied from day to day, a temperature correction was made to reduce all the data to an operating temperature of 18" C.
The variables studied were feed concentration, flow rate, and applied voltage. A comparison was then made of the predicted versus actual values of cell capacity (flow rate) and power usage per unit c ~ i pacity. These comparisons are shown in Figures 3-8. A sample calculation is: Feed concentration
FT
=1
+ 0.025(T - 18)
Ci = 0.010N;
Mi = 0.01N
Effluent concentration
i 2 0 r r
Co = 0.001N;
Mo = 0.019N
Applied voltage = 25 volts Cell characteristics No. of unit cells = 51 Area = 1sq. ft. = 144 sq. inches Chamber thickness = 6/la inch i Membrane thickness = 25 mils Cell resistance Solution resistance Depleted stream
Rd =
(51)(3.788)(5/16)(2.303)log 10 (144)(0.010 - O.OOl)--
Rd = 107.1 ohms Concentrated stream
L8
OO
DEPL.ETED
A
16 24 32 E F F L U E N T R A T E - G.P.H.
Ra =
Figure 8. Depleted Effluent Flow Rate for Cell Operating on Hard Water 540 p.p.m. NaCl a s CaCOi
January 1955
(51)(3.90)(5/16)(2.303) log 1.9 (144)(0.019 0.010)
-
R, = 30.8 ohms R, = R d
+ R , = 107.1 + 30.8 = 138 ohms
INDUSTRIAL AND ENGINEERING CHEMISTRY
57
Membrane resistance Since the membrane resistance does not vary greatly with concentration over the concentration ranges considered, the average resistance per mambrane will be very close to the membrane resistance at 0.010N.
R,, = 0.16 ohms/sq. ft. R., = 0.17 ohms/sq. ft. R, = (51)(0.16) (51)(0.17) R, = 17ohms
+
ciency is undoubtedly complex with the greater effect of diffusion arid osmosis under conditions producing high concentration gradients across the membranes being a partial explanation. Leakage of current through interchamber connections and other stray current paths would be experted t o increase as the resistance of the main current path increases, decreasing the apparent current efficiency of salt removal. The permselectivity of Amberplex membranes in a uni-univalent electrolyte, a function of the ionic transport numbers within the membrane (18) is a function of the average concentration of solution surrounding the membrane. I n the multiple membrane electrodialysis cell I'F" (under steady
Total cell resistance = 155 ohms Counterelectromotive force Membrane potentials
e'
(51)(0.0577) log 19 = 3.8 volts
=
Decomposition voltage is assumed equal to 2.5 volts Total counterelectromotive force = 6.3 volts Calculation of cell capacity
0.0374np(E
F =
-
e)
-
3.785 R A C [l
(2n
+looo I)ADRE
gallonszper-hour + mc] C%+
;dP n
3
I
60
100
DEPLETED
ZOO
300
400
500
EFFLUENT Q U A L I T Y - P P M
600
700
N & C L AS C A G 0 3
Figure 9.
Current Efficiency versus Effluent Quality in Operation of Cell on Brackish Water
P =
n = R = 2n+l= A = D = 1=
1570 p.p.m. NaCl as CaC08
@ = 0.275 liter/faraday
Ci = 0.010 equivalent/liter AC = 0.009 equivalent/!iter e = 6.3 volts E = 25 volts
Substituting
F = 6.70 ga!lons per hour DISCUSSION
Figures 3, 5, and 7 indicate that the energy consumption per unit volume of depleted effluent from the multiple ion exchange membrane electrodialysis cell can be predicted successfully using Equation 9. Over a wide range of effluent concentration the agreement between predicted and observed values for energy consumption is within 10% for treatment of brackish or sea water (Figures 3, 5 ) and within 15% for hard water deionization. The observed curves, showing the energy requirements per 1000 gallons of depleted effluent as a function of the depleted effluent concentration, begin to deviate from predicted curves when greater than 95% depletion of the initial feed solution is attained. The apparent current efficiency of the desalting process in equivalents of salt removed per faraday per depleted chamber is quite constant over a wide range of depleted effluent concentration but begins t o drop rapidly when greater than 95% depletion is attained, accounting for the deviation of the observed energy consumption curves from the calculated ones. Figure 9 shows a plot of the experimental current efficiency for treatment of brackish water, showing that the assumption of constant current efficiency regardless of depleted effluent concentration made in deriving the equations is valid until a high degree of depletion is reached. The current efficiencies, calculatpd from the initial and final concentration of the depleted stream and the effluent flow rate, are several per cent lower than the actual current efficiency due t o neglect of electroosmotic transport of water across the membranes. The cause of this drop in current effi-
58
state operating conditions) thie is closely approximated by the feed concentration for all membranes, since all chambers are of equal size, and the flow rates in both streams are held equal. Hence the perm3electivity of the membranes is constant regardless of effluent quality of the depleted stream. Cutting down the flow rate in the concentrated stream would be expected to reduce the permselectivity of the membranep, and therefore the apparent current efficiency of the desalting operation by a measureable amount. I n practice this is t r w , but the effect of over-all parformance of the cell is slight due to compensating effects of decreased 1 esistance of the concentrated stream. In view of the variation in resistive, permselective, and diffusion properties of individual membranes, the uncertainty introduced by corrections in these properties for temperatui e effects, and the neglect of osmotic effects, the agreement betwecn observed and calculated values of energy requirements is very satisfactory. The agreement between the experimental and calculated flow rates of the depleted stream is less satisfactory, as can be seen from Figures 4, 6, and 8, which give the flow late in the depleted stream as a function of depleted effluent quality for various applied voltages, for sea n-ater, brackish water, and hard water. Observed values range from 30 to 90% of the predicted values, calculated using Equation 7 , depending on the initial concentration of the feed waters, the degree of depletion achieved, and the applied voltage. Agreement is best for high initial concentration of the feed solution and foi runs in which less than 95% depletion of the dissolved electrolyte in the depleted stream is reached. Since the equation €or predicting flow rates is much less satisfactory than the equation for predicting energy consumption per unit volume of depleted effluent, important factors prc+ ent in the former and not the latter must be considered inaccurate and responsible for discrepancies between observed sad calculated values. The two factors fitting this description are the total cell resistance, R, and the total counterelectromotive force, e, including membrane, electrode, and diffusion potentials. The method used for calculating these two quantities apparently gives values for one or both which are too lorn.
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 47, No, 1
Ion Exchange The assumed resistance oi" the membranes is uncertain by at least lo%, and the presence of nonconducting grids or screens to separate the membranes could increase the actual resistance by another 10%. Together with other uncertainties due t o temperature effects and experimental errors, these could account for part of the difference between observed and predicted resistance or counterelectromotive force. Nevertheless, a much larger error must be accounted for. I n calculating the resistance of the solutions in the chambers, the assumption was implicitly made t h a t no concentration gradients existed in a single chamber
3001-- -1
',Ot
t-
I
An evident remedy for the production of a serious concentration polarization resistance in the cell was the creation of turbulent flow conditions in the cell. Piston flow conditions set by merely flowing solution through the chamber hardly affected the resistance-time curves. Figure 11 shows the effect of causing turbulent flow by insertion of a complex Plexiglas grid in the depleted chamber filled with 0.05N sodium chloride. As long as turbulent flow was maintained, the polarizing direct current produced no appreciable rise in resistance. Immediately on stopping the flow of solution t o end the turbulent state, the resistance-time curve followed the usual pattern of increase in resistance with time until inteiruption of current, flow. Aside from its effect on the total cell resistance, concentration polarization will increase the membrane potential acrose each membrane, which is proportional to the logarithm of the ratio of activities on either side of the membrane. T h e two consequences of concentration polarization taken together can evidently account for the discrepancy between observed and calculated values of the flow rate in the multiple ion exchange membrane electrodialysis cell. The experiments with this cell suggest production of turbulent flow as a means t o reduce concentration polarization and its unfavorable effect on cell performance. Under such conditions the equations developed can be expected to predict with considerable accuracy the performance characteristics of the cell.
100
16
TIME
. .
24
IN MINUTES
~
Iso
Figure 10. Resistance of Unit Cell with Time While Direct Polarizing Current Is Flowing Current density 1.44 amp./sq. ft. Electrolyte 0.02N NaCl
in the direction of current flow. Concentration polarization will develop in the solutions, producing a highly depleted layer of solution adjacent t o the membrane surface in chambers undergoing deionization and a more concentrated layer adjacent t o the membrane in the chambers of the concentrated stream. The net result is the development of a greater over-all resistance of the solution in the cell and a greater total membrane potential than that calculated using average solution concentrations in individual chambers. Neither the membrane resistance nor the current efficiency will be appreciably affected b y concentration polarization, since the average concentration surrounding each membrane will be unchanged by this effect, thus leaving permselectivity unchanged Preliminary measurements of the alternating current resistance of a unit cell in a model multiple membrane electrodialysis cell, made while a direct current polarizing current was flowing, indicate t h a t a n approximatelv 50% increase in resistance occurs due t o concent,ration polarization, a t current densities foundin a multiple membrane electrodialysis cell under normal operating conditions in solutions about 0.025N sodium chloride. Figure 10 shows the resistance-time cell in which a polarizing direct current density of 1.44 amperes per square foot was flowing. The ordinate values are proportional t o the total unit cell resistance. At zero time, before the application of the direct current potential, an initial resistance was recorded. After a short time lag following the application of the direct current potential, the alternating current resistance rose sharply t o a point almost 50y0 above the initial value. Thereafter the resistance increased slowly as the nonflowing chamber was depleted and more rapidly as high depletion was reached. After cutting the direct current potential, the resistance dropped sharply an amount approximately equal t o the initial resistance. The latter observation showed the chamber had undergone some depletion during the process. January 1955
50:
I
A
I
1I6
I
2I4
'
32
I
'
40
T I M E IN M I N U T E S
Figure 11. Effect of Turbulent Flow on Unit Cell Resistance Caused by Concentration Polarization Current density 2.16 amp./sq. ft. Electrolyte O.02N NaCl
The total cell resistance should be reduced t o the lowest possible value to achieve as high a capacity as possible for a cell. Two ways in which this can be done are by increasing the operating temperature and by decreasing chamber and membrane thicknesses. T h e temperature coefficient of resistance of the multiple ion exchange membrane electrodialysis cell using Amberplex membranes is about minus 2.5% of the resistance value a t 18" C. per degree rise in temperature. It follows t h a t every 10' C. rise in temperature of the feed stream over 18' C. would improve cell capacity by 25%, without appreciably affecting energy requirements per unit volume depleted effluent. The minimum chamber thickness that can be used is determined by the pressure drops that can be tolerated in the flowing stream without rupturing membranes and hy the design problems encountered in feeding the cell streams. The series flow connection adapted for the cell in this study has the disadvantage of producing high pressure drops in the streams; parallel flow connections would be superior in this respect and permit the use of thinner chambers, hence greater capacity per cubic foot of equipment. The derived
INDUSTRIAL AND ENGINEERING CHEMISTRY
59
equations for predicting cell performance are valid for either flow connection, though derived in this work with the aid of a series flow model. Equations 7 and 9 show t h a t both the energy requirements per unit volume effluent and the capacity of the multiple ion exchange membrane electrode cell are directly proportional to the voltage applied per unit cell. Consequently, in arriving at an optimum operating voltage from an economic standpoint, consideration must be given the rate of production required, the energy consumption per unit volume permitted, and the capital costs necessary t o achieve these. The power requirements predicted and obtained in this study demonatrate that electrodialysis of saline waters using permselective membranes is an economirally interesting approach to the problem of producing potable water from brackish or hard waters, and, in special applications, from sea water.
P
= energy consumption per unit volume depleted effluent,
Q
= net rate of salt transfer, equivalents/liter
kilowatt hr./1000 gal. or kilowatt hr./liter
R R,
Ra RO R* R, T
V
w b e eel.
e’ ACKNOWLEDGMENT
The authors wish to acknowledge the assistance of C. F. Ryan and J. Lirio of the Rohm & Haas Co. during the experimental program and the mechanical department of the Rohm & Haas Co., research laboratory, for their assistance in developing and fabricating the electrolytic cells. NOMENCLATURE
A B C Cr CO
= exposed membrane area, sq. cm. = a constant, ohm cm.4 = concentration, equivalents/liter = feed concentration, equivalents/’liter = depleted effluent concentration, equivalents/liter = concentration of t h e depleted stream entering the kth
n 1 t
q
q‘
r r. rc s
trf c p CY
electrical resistance of cell, ohm anion membrane resistance solution resistance of a single depleted chamber, ohm solution resistance of as ingle concentrated chamber, ohm solution resistance, ohm = total membrane resistance, ohm = temperature, ’ C. = total water transport by electroendosmosis, liiters/hr. = power, watts or kilowatt,s = chamber thickness, cm. = electrode potentials plus counterelectromotive force, volts = sum of electrode potential, volts = total counterelectromotive force, volts = number of unit cells between electrodes = membrane thickness, em. = time, see. = rate of Palt transfer, equivalents/liter = rate of salt transfer by diffusion, equivalents/liter = specific resistance, ohm-cm. = anion membrane specific resistance, ohm = cation membrane specific resistance, ohm = unit area, sq. cm. = transport number = average membrane potential/unit cell = current efficiency, equivalents/faraday = solvent transferred by osmosis and electroendosmoeis liters = average water transport, liters/faraday = = = = =
depleted chamber, equivalents/liter = average concentration of the solution in the kth depleted
D AC AT
chamber, equivalents/liter = diffusivity of electrolytes in membranes, sq. cm./hr. = Ci COchange in concentration of depleted stream in traversing a cell, equivalents/liter = average concentration gradient across membranes of a cell; equivaIents/Iiter = applied potential, volts = membrane potential, volts = perfect membrane potential, volts = volumetric flow rate (of depleted effluent), liter/hr. or gal./hr. = flow rate at operating temperature = flow rate a t 18’ C. = t h e faraday, coulombs = current in amperes passing through t h e element = concentration of concentrated stream, equivalents/liter = concentration of conc. stream entering kth concentrated chamber, equivalents/liter = feed concentration, equivalcnte/liter = concentrated effluent concentration, equivalents/Hter = average concentration of solution in t h e kth concentration chamber, equivalents/liter = average conoentration of t h e solutions surrounding a membrane, equivalents/liter
-
(ET),
60
LITERATURE CITED
(1) Bergsma, F., Chem. Weckblad, 48, 36 (1952). (2) Clarke, J. T., SIarinsky, J. A., Juda, W., Rosenberg, N . W., and Alexander, S., J . Phvs. Chem., 56, 100 (1952). (3) Dankwerts, P. V., Chem. Eng. Sci., 2, 1 (1963). (4) Ionics, Inc., 152 Sixth St., Cambridge, Mass., Bull., “Xepton Membranes,” 1952. (5) Juda, W., Rosenberg, N. W., hlarinsky, 9. A., and Kasper, -4. A., J . Am. Chem. Soc., 74, 3736 (1952). (6) Kollsman, P., Brit. Patent 694,223 (July 15, 1953). (7) Kressman, T. R. E., Nature, 165, 568 (1950). (8) Langelier, W. F., J. Am. Water Works Assoc., 44, 845 (1952). (9) Manecke, G., 2. Elektrochem., 55, 672 (1951). (IO) Jlanecke, G., and Bonhoeffer, K. F., Ibid., 55, 475 (1951). (11) hIeyer, K. E., and Strauss, W., HeZv. Chim. Acta, 23, 795 (1940). (12) Rohm & Haas Co., Washington Square, Phila., Bull., “Amborplex Ion Permeable Membranes,” 1952. (13) Schmidt, G., 2. Elektrochem., 55, 229 (1951). (14) Sollner, K., and Gregor, H. P., J . Phys. Chem., 61, 299 (1947). (15) Spiegler, K. S., J . Electrochem. SOC.,100, 303C (1953).
(le)
Streicher, L., Bowers, A. E., and Briggs, R. E., IND. ESQ. CHEM.,45, 2394 (1953). (17) Teorell, T., Z. Elektrochem., 55, 460 (1951). (18) Winger, A. G., Bodamer, G. W., and Kunin, R., J. Electrochem. Soc., 100, 178 (1953).
(19) Wyllie, M. R. J., and Patnode, H. W., J. Phus. Chem., 54, 204 (1950). R ~ C ~ I V for E Dreview March 29, 1964.
INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY
ACCEPTED October 9, 1954.
Vol. 47, No. 1
