Ind. Eng. Chem. Process Des. Dev. 1985, 2 4 , 444-450
444
Design and Anatysis of an Electrochemical Cell for Caustic Concentration and Power Generation Shl-Plng Ho' OccMental Research Corporation, Imine, Callfornla 927 14
An analysis was made for an electrochemical cell where concentrated caustic and electric power are produced in a hydrogen/air fuel cell with cation-exchange membranes. The cell is modeled as an electrochemical reactor with difute caustic from the chlor-alkali cell liquor added to the anode Compartment and concentrated caustic removed from the cathode compartment. Current density, caustic concentration, and temperature distributions across the cell were obtained as functions of membrane efticiency, water transport rate, and electrode polarization characteristlcs. Factors Invoked In the design and operation of a multistage cascade of cell modules in flow series for producing concentrated caustic were examined.
A novel concept which uses an electrochemical cell for improving the energy efficiency and reducing the cost of chlor-alkali product was recently patented by Occidental Research (Broniewski, 1981). The device, which is called the hybrid cell, is a hydrogen/air fuel cell with cationexchange membranes to allow electrodialysis of sodium hydroxide in chlor-alkali plants. Shown in Figure 1 is a schematic diagram illustrating the functioning of the hybrid cell. It is based on Alsthom-Atlantique's thin-element plastic fuel cell concept (Elzinga et al., 1977) with a cation-exchange membrane (such as Nafion) introduced between the two electrodes to block the transfer of chloride and other negatively charged ions (Koh and Silverman, 1982). The cell uses chlor-alkali hydrogen as fuel, supplies electric power to the chlor-alkali cells, and concentrates and purifies NaOH from the chlor-alkali cell liquor. Each unit cell is designed to contain a bipolar current collector made from nonconductive and conductive polypropylene comolded in a single operation. An anode is mounted on one side of the collector and a cathode on the other. A molded interframe positioned between the electrtode/membrane/collector assemblies provides the chambers for electrolyte. The interelectrode gap is small to minimize internal resistance and power loss. A hybrid cell stack or module consisting of a larger number of individual unit cells clamped together in a series array will be used in commercial manufacturing processes. The development and commercialization of the hybrid cell will result in significant cost and energy savings in chlor-alkali manufacturing. It was projected that electric energy savings of 1 5 2 0 % could be achieved together with steam savings of up to 70%. The total variable cost savings was estimated to be $20-40/ton chlorine over a conventional process with diaphragm cells (Emery et al., 1981). For process design and economics evaluations, studies have to be made of the factors affecting the performance of the hybrid cell. For example, electrode area, internal power consumption, and hydrogen fuel consumption are functions of current density and membrane efficiency for transferring sodium ions from the anode to the cathode compartment. Also, water transport across the membrane can affect makeup water requirements and it may limit the maximum caustic concentration attainable in the hybrid cell. An energy balance around the hybrid cell is b o *Present address: Amoco Oil Company, Naperville, IL 60566. 0196-4305/85/1124-0444$01.50/0
needed to determine the cell operating temperature under a variety of conditions. Frequently in electrolytic processes, the parameters describing the cell performance vary from point to point within the cell due to the change of flow conditions and the effect of electrode reactions on the properties of electrolytes (Grens and Tobias, 1961). This is particularly true for the hybrid cell system where the electrolytes flow concurrently in the thin channels of hybrid compartments. As it moves from the inlet end to the outlet end, the cell liquor becomes depleted in NaOH due to consumption of hydroxyl ions a t the hydrogen anode and transfer of sodium ions across a cationic membrane. This causes current density (or cell voltage) to change with position in the direction of electrolyte flow. Depending upon the mode of operation, the variation of these cell parameters can have a significant impact on the design and economics of the hybrid cell. For instance, operating at low current densities (but at high voltage) will increase capital costs for greater electrode and membrane area. On the other hand, maintaining high current densities a t low voltage will reduce the power output and result in generation of heat in the cell (Eisenberg, 1962; Keller, 1981). Only consideration of the electrochemical reactions and of the various transport phenomena involved can lead to maximization of the energy output and optimization of the hybrid cell design. In the design studies, it has been proposed that the dialysis of caustic be conducted in multiple stages of a cascade of the hybrid cell modules (Broniewski, 1981). In the cascade, the chlor-alkali cell liquor is introduced as the anolyte to the top stage while water or dilute caustic is added to the cathode compartment of the last stage. It is hoped in this manner that membrane efficiency (and power generation) could be maximized and that the NaOH concentration difference across the membrane could be minimized. However, the membrane efficiency (defined as the number of sodium ion equivalents transferred per Faraday of electricity passed through the cell) varies with the NaOH concentration on the more concentrated side (catholyte) in a fairly complex manner. The current density a t constant voltage (or vice versa) also varies strongly with the NaOH concentration on the more dilute side (anolyte). These variations in turn affect the cell temperature distribution as a result of heat generation from electrochemical reactions and ohmic potential losses. Hence, unless calculations are made of material and energy balances within the cascade, it is not clear that the mul0 1985 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 2, 1985 -1CHLOR-ALKALI CELL
CI2
ANOLYTE
CATHOLYTE
Chlor-Alkali Cell Liquor In
H3
Excess H2 Out
445
Water Or Dilute Caustic In
a
-
.Excess Air Out
26% NaCl Brine -E
@-
-0
HYBRID CELL
H2+20H%2H20+26
1 I
/2 02+H20+2e-+2OH: ~2 n I Depleted Anolyte Out
L-----;;;g Caustic Out
Figure 2. Hybrid cell model. Figure 1. Schematic of hybrid cell operation.
tistage cascade proposed for design and economic studies is anywhere near optimal. In the present study, a mathematical model has been developed for the prediction of hybrid cell performance under a variety of cell design and operating parameters. Specifically, the model is used to obtain current density distribution and electrolyte concentration profiles across the hybrid cell under constant cell voltage operation. Based on given cell polarization data, average current density and required electrode area can be calculated for a given caustic production. The temperature distribution within the cell is also calculated to determine if a uniform temperature in the stages can be maintained by evaporation of water into excess air. These results will give an indication as to the optimal number of stages required in a cascade for maximizing membrane efficiencies at high-energy output. This information should lead to the development of a more efficient design and operation of the hybrid cell for producing concentrated caustic in chlor-alkali plants. Model Development The hybrid cell model consisting of two thin compartments separated by a cationic membrane is schematically shown in Figure 2. Dilute caustic from the chlor-alkali cell liquor is added to the anode compartment, and concentrated caustic is removed from the cathode compartment. The membrane would allow transfer of sodium ions, but not chloride and other anions, from the anode to the cathode compartment. The membrane also restricts a limited rate of water leakage into the cathode compartment, resulting in a net increase of NaOH concentration from the anolyte to the catholyte. A net transfer of hydroxide from the anolyte to the catholyte occurs as hydroxyl ions are consumed a t the anode by the hydrogen reaction and generated a t the air cathode by the reaction of water with oxygen. The anodic and cathodic reactions are represented by H2 + 20H2H20 + 2e- at anode (1) H20
-+ -
+ 1/202 2e-
20H- a t cathode
(2)
Within a stage of hybrid cell modules, the anolyte cell liquor depleted in NaOH flows concurrently with the catholyte enriched in NaOH. In a multistage cascade, water or dilute caustic is added to the cathode compartment of the bottom stage and concentrated caustic is withdrawn from the top stage. This results in electrolyte flow that is concurrent in each stage but countercurrent between stages of a cascade (see Figures 3 and 4). The following assumptions are incorporated in the analysis of the hybrid cell model: (1)The cell is a t steady state and is considered as a plug-flow reactor with complete cross mixing in the direction of electrolyte flow. (2) The cathode concentration overpotential due to mass transfer limitations between the fluid bulk and the electrode is negligible compared to the anode concentration overpotential. (3) The temperature effect on the current density is negligible. (4) The amount of water transported across the membrane is independent of caustic concentration. (5) Water evaporation and cooling only occur in the catholyte in contact with air. Based on these assumptions, the current density, electrolyte concentration, and temperature distributions within the cell can be calculated from the following material, voltage, and energy balances. (I) Mass Balances. A differential mass balance for NaOH along the direction of electrolyte flow gives (3)
The water balance is related to the net transport rate of sodium ions and the electrochemical reactions 1 and 2; hence (4)
for water in the anolyte, and --d(qwpw) =
dz
--)-
dw, ( p - 0.5 ieibn - -
F
dz
(5)
446
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 2, 1985 -A
-----B 0,141
-40.0
Current Density Anolyte NaOH Conc Catholyte NaOH Conc.
----C
. @
T6'0
-----
.-re
- 35.0
- 30.0 s
A
- 25.0s
I '
0 - 20.02
-1
- 15.08
8 -10.0
- 5.0 0 6% NaOH
'0 0.16-
011
012
35% NaOH
014 015 016 017 Hybrid Cell Dimensionless Length, z/L
----- B --- C
013
Oh
019
-0.0 110
Anolyte NaOH Conc. Catholyte NaOH Conc.
for water in the catholyte, where Q, and q, = volumetric flow rates of water in the anolyte and catholyte, respectively, in liters/hour, C and c = NaOH concentration in the anolyte and catholyte, respectively, in gram mola/Eter of H20, i = current density a t distance z in amperes/ centimeters squared, ei = membrane efficiency as defined by the number of sodium ion equivalents transferred per Faraday of electricity passed through the cell, b = width of electrode or membrane in centimeters, n = number of cells per stage, F = Faraday constant in ampere-hours/ gram-mole of NaOH, p, = water molar density in gram moles/liter, p = water transport rate in moles of H 2 0 transported/mole of net Na+ ion transported, and w e = rate of water evaporation into air in gram-moles/hour. The initial NaOH and water flows are known variables a t the cell inlet z = 0. The selectivity of hybrid cell membranes in transferring the sodium ions is quantified
by the membrane efficiency (ei)as a function of the catholyte NaOH concentration in weight percent (y)
ei = 1 + a,y
+ af12 + a o 3
(6)
where ai's are constants determined from the membranes tested in the hybrid cell environment. The cubic equation repreaented the characteristicsof available membrane data; typical values of ai's to illustrate the performance of perfluorinated membranes are given in Table I. For design purposes, it is assumed that an equal number of cells be used in each stage of a cascade. Then the number of cells per stage is
n = (Mocec)F (i,ei)NbL
(7)
where Moc = total NaOH feed in the chlor-alkali cell liquor
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 2, 1985 447
Table I. Hybrid Cell Operating Conditions for a 100 Ton per Day Chlorine Plant anolyte input (Mo, and M',) = 35800 kg/h chlor-alkali cell liquor containing 12% NaOH and 13% NaCl catholyte input = 2400 kg/h of water; rate determined by water transport rate (0)and product caustic strength (35 w t %) and evaporation by air (we) catholyte output = 35 wt % NaOH and 96% caustic recovery efficiency (e,) membrane efficiency (ei)= varied as a function of catholyte being al NaOH concentration shown in eq 6 with constants = 0.025, a2 = 0.0015 and a3 = O.ooOo25 water transport rate (0)= constant at 4 mol of water transported/l mol of net Na+ transported cell voltage (E) = 0.63 V designed to provide approximately 20% of chlor-alkali power requirement cell open voltage ( E O ) = 1.065 V with bi's in eq 9 being bl = 0.45, b2 = 2.3, b3 = 11.7 and b, = 1.4 determined from cell performance curves cell dimension = 30-cm width by 30-cm length by 0.05-cm flow channel gap total cell resistance ( R ) and water evaporation rate (u,)are calculated from correlations shown in the Appendix section
in kilogram-moles/ hour, e, = caustic recovery efficiency, L = cell length in centimeters, N = number of stages in a cascade, and i, = average current density of a multistage cascade given by N
Ci; j=1 '
I,
=-
N
and ij = SoLi(z)dz/L is the average current density in the j t h stage of a cascade. (11) Voltage Balance. The current density at any point of the cell is related to the local electrolyte concentration and the cell operating voltage as given by
E = Eo - bli
-
bzi2 - b3ib4exp(-x) - iR
(9)
where bj's = constants, E = cell operating voltage in volts, E" = cell open potential for both anode and cathode in volts, x = local caustic concentration in the anolyte in weight percent, and R = total ohmic resistance including membrane and electrolytes in Q-cm2. In eq 9, the first three terms represent the combined anode and cathode overpotentials due to chemical polarization. The fourth term represents the anode overpotential due to concentration polarization and the last term is for the ohmic potential drops in the membrane and electrolytes. The exponential term generally indicates that the cell voltage decreases sharply as caustic concentration drops to a lower 1-2% range. Constants Eo and b;s in eq 9 have been determined from the electrode polarization data of Alsthom cells, and these values are given in Table I. Equation 9 is related to eq 3-5 through current density i and anolyte caustic concentration x x =
Q,C
+ (Q,P,)
QwC 08/40) + M0,(58.5/40)
(10)
where Moa is the inlet NaCl flow rate in kilogrammoles/hour and is constant throughout the cell. The total ohmic resistance R is given by
R = R,
+ Re + R, + R,
(11)
where R, is the membrane resistance, Re is the electrode resistance, and R, and R, are the respective anolyte and catholyte resistances depending upon the electrolyte conductivity and concentration. Under typical hybrid cell operating conditions, R, is the dominant factor in affecting
the overall ohmic losses and hence the cell voltage or the current density. Representative values of R,, Re, R,, and R, are given in the Appendix section. (111) Energy Balance. Assuming that there is no temperature gradient across the membrane, the overall energy balance per 1 g-mol of NaOH in the feed to the hybrid cell is out
in
CmkCpkTI - CmkCpkT - AHc 4k
k
(AHR- E
X
23.05)(e,ei) - ym,AHE = 0 (12)
where k = subscript referring to the kth component in the electrolyte, mk = molar ratio of the kth component to NaOH in the feed, C = average molar heat capacity of the kth component [:tween TI and T in in in kilocal/ gram-mole-OC,y = multiple of stoichiometric amount of air required for the Hz/Ozreaction, and m, = molar ratio of H 2 0 evaporated into air (stoichiometric amount) to NaOH in the feed. The first two terms in eq 12 represent the sensible heat change of all streams from inlet temperature T I to cell outlet temperature T. The third term AHc accounts for the enthalpy change resulting from NaOH concentration difference across the membrane. The fourth term is the parasitic heat generation resulting from the difference of heat of the Hz/Ozreaction (AHR)and cell power output at operating voltage E given by eq 9. The last term is the heat of vaporization of water into air (AHE)multiplied by molar ratio of water evaporated with excess air. The water evaporation rate is functions of caustic concentration and air humidity which can be determined from experimental data (see Appendix section). As seen from eq 9 and 12, an increase in electrode and concentration overpotential (or ohmic losses) will result in reduction of cell power output ( E )and more heat generation within the cell. To maintain a desirable operating temperature within the material of construction limitations of the hybrid cell, cooling must be provided by (i) reducing cell feed temperature, (ii) recirculating the electrolyte through an external exchanger between stages, and/or (iii) evaporating water through excess air flow. These options will be discussed in the sample case under consideration. To determine the temperature distribution within the cell, eq 12 can be applied over a small segment of cell length Az. In this case, the heat balance is written for the enthalpy effects of the electrochemical reaction and changing concentrations, sensible heats, vaporization of heat, and power output in section Az. Hence, in eq 12, TI denotes the inlet stream temperature a t upstream z and Tis the outlet stream temperature at the downstream end z Az. The enthalpy terms of AHc, AHR, and AHE are related to the incoming NaOH feed and are assumed constant within the increment Az. Method of Solution The differential mass balances (3)-(5) may be approximated by a series of algebraic equations by dividing the cell length into a number of small increments Az where the change of current within the increment can be assumed negligible (Grens and Tobias, 1961). By use of eq 3-12, the variables (currently density i, anolyte and catholyte NaOH concentration C's, and cell temperature T ) describing the cell performance can be determined for any desired cell operating parameters (applied cell potential E , cell liquor flow rate Q's, inlet concentration of NaCl and NaOH in cell liquor, air flow rate, number of stages N, cell dimensions, etc.). The procedure for numerical calculations is outlined as follows. (1)Assume an average current density in a cascade i, and
+
448
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 2, 1985
Table 11. Hybrid Cell Model Predictions for a 100 Ton of Cl,/Day Plant with a Multistage Cascade Operating at Constant Voltage of 0.63 V anolyte" output catholyteb output no. of av current av membrane flow rate/cell, flow ratelcell, no. of NaOH % g/ h NaOH % glh av temp, "C cells/stage stages density, A/cm2 efficiency, % One-Stage Cascade 1
0.106
90.9
0.6
1 2
0.113 0.105
90.8 91.5
6.9 0.6
1 2 3 4
0.113 0.113 0.113 0.094
89.7 91.5 92.3 89.7
9.4 6.7 3.6 0.6
372
35.0
163
74.9
31 642
35.0 28.9
345 204
53.2 76.0
14 786 14 786
35.0 33.1 29.3 20.8
671 526 386 250
46.6 57.5 68.7 77.0
7 622 7 622
Two-Stage Cascade 934 803
Four-Stage Cascade 1955 1810 1770 1547
7 622 7 622
"35800 kg/h of chlor-alkali cell liquor a t 12% NaOH, 13% NaCl, and 37 OC is added as anolyte input. b2400 kg/h of water is added as the catholyte to the last stage of the cascade to maintain 35% NaOH outlet concentration.
calculate the number of cells per stage, n, from eq 7. (2) Assume constant ohmic resistance in the catholyte and membrane efficiency eithroughout the cell. (3) Using given inlet concentrations (and other operating parameters), calculate i at z = 0 by trial and error solution of eq 9 and 10. Calculate changes in NaOH and HzO concentrations of the electrolytes over cell length Az from eq 3-5. (4) Calculate concentrations a t the downstream end of increment Az and find i from eq 9-10 a t the upstream end of the next increment. (5) Sum up all i's through the entire length of the cell to obtain the average current densities i. of the j t h stage. Calculate i, of the average current density for the cascade by use of eq 8. (6) Check i, calculated with i, assumed and repeat steps 2-5 until they agree. (7) For a given product caustic concentration, determine the amount of HzO added to the cathode compartment from the overall water balance which accounts for H 2 / 0 2reaction and water evaporation. (8) Calculate NaOH concentration in the catholyte by use of eq 3. Improve values of membrane efficiency and electrolyte resistances on the basis of new catholyte caustic concentration. (9) Repeat steps 3-8 several times to obtain new values of current densities. (10) Estimate the cell liquor inlet temperature from the overall energy balance eq 12 to give a desired average cell operating temperature. Also compute the cell temperature profile from eq 12 based on rates of reaction and water evaporation over an increment Az .
Discussion of Results On the basis of the computational procedures previously described, eq 3-12 can be readily solved to perform material and energy balance calculations for a cascade of hybrid cells in flow series for a given caustic production. Parameters required are water transport rate, caustic recovery efficiency, cell voltage, cell maximum temperature, air flow rate, desired caustic production concentration, and the number of stages in a hybrid cell cascade. In order to define a more optimal design of the hybrid cell system, an example is presented for the case of concentrating the chlor-alkali cell liquor from 1 2 % to 35% caustic in a 100 tons of C12/day plant. Typical values of cell operating parameters for design calculations are given in Table I. Constants ai's, hi's, and Eo in eq 6 and 9 were selected on the basis of preliminary electrode polarization data of Alsthom's cells by using perfluorinated membranes. The hybrid cells are arranged to maximize the effeciency of electric energy production to supply approximately 20% of the chlor-alkali cell power requirement. On the basis of these conditions, the average current density and the required number of hybrid cells in a multistage cascade
gob
'O0l
Chior-Alkali Cell /Liquor Inlet Temperature
20:
0'1
0'2
Hybrid Cell Liauor Outlet TI
013 014 015 016 017 0'8 Hybrid Cell Dimensionless Length, z/L
0'9
t
Figure 5. Electrolyte temperature profile in the hybrid cell.
have been determined. The results of calculations are summarized in Table I1 for the hybrid cell plant with one-, two-, and four-stage cascades. Figures 3-5 show the distributions of current density, caustic concentration, and electrolyte temperature within the cell. The following important observations can be made from Table 11: (1)Except for the last stage of a multistage cascade, the average current density does not change significantly from stage to stage. For a four-stage cascade system, the current density is constant for the top three stages and is about 17% lower in the bottom stage due to the concentration overpotential effect. However, the influence of this stage on the average current of the entire cascade is insignificant. (2) Since the effect of the bottom stage on the current is small, the total number of cells required for a given caustic production is only 4% less for a four-stage cascade than for a one-stage cascade. (3) The increase of catholyte NaOH concentration occurs mostly in the bottom stage where pure water is added. The catholyte NaOH concentration in the bottom stage increases from 0% to 21% for a four-stage cascade and from 0% to 29% for a two-stage cascade. The rate of increase becomes small in the rest of the stages as the catholyte approaches its final caustic concentration. (4)Even after one stage of a multistage cascade, the catholyte NaOH concentration is already high enough to depress the membrane efficiency to about 90% level. Increasing the number of stages in a cascade does not appear t o improve significantly the average membrane efficiency.
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 2, 1985
(5) The required inlet temperature of the cell liquor a t 3 times the stoichiometric amount of air flow is approximately 37 "C in order to maintain the electrolyte outlet temperature below 90 "C (also see Figure 5). This high temperature gradient across the hybrid cell may require interstage cooling of the electrolytes to maintain a more uniform temperature in the stages. Interstage cooling also allows for hotter feed from the chlor-alkali cells. (6) The flow rate in the cell increases proportionally with the increasing number of stages in a cascade. This could present pressure drop problems for multistage cell modules in the flow series. For a better illustration of the hybrid cell performance in one stage, the current density and the concentration of NaOH in the anolyte and the catholyte are plotted in Figure 3 as a function of cell length under constant voltage operation. As can be seen, the current density stays relatively constant throughout the major portion of the cell but starts to drop sharply at about 80% length of the cell. Since the electrochemical reaction rate depends upon the current density, the anolyte NaOH depletion rate is uniform throughout the cell, but it is gradually reduced near the cell exit. Figure 3 also shows that the catholyte becomes rapidly enriched in NaOH along the electrolyte flow direction due to formation of hydroxyl ions a t the cathode. Notice that there is a slight drop of current density near the cell entrance due to higher ohmic resistance of water added to the cathode compartment. Hence, rather than using water as the catholyte input, dilute caustic should be added to allow for maximization of current density. For comparison, Figure 4 gives the current density and electrolyte concentration distributions in a two-stage cascade system. Water is used as the catholyte input to the second (bottom) stage. The catholyte NaOH concentration reaches 29% at the bottom stage and increases to 35% in the top stage. For a two-stage cascade system, the current density is uniform throughout the top stage; however, it falls slightly near the entrance of the second stage due to pure water addition and it drops sharply toward the cell exit of that stage. However, the average current density of the twostage cascade system is about the same as that of the one-stage system. It has been speculated that the cell temperature may be controlled by flowing excess air through the cell to remove parasitic heat by water evaporation. It is hoped that this would eliminate the need of water cooling of the chlor-alkali cell liquor (normally a t about 90 "C) to the hybrid cell. Figure 5 shows the electrolyte temperature profiles in the cell and the required cell liquor inlet temperature to maintain a hybrid cell temperature under 90 "C at various air flow rates. At 3 times the stoichiometric amount of air, the cell liquor inlet temperature needs to be cooled to 37 "C to ensure a maximum of 75 "C cell temperature a t the cell outlet. Increasing the air flow rate to 9 times the stoichiometric will allow an increase in required cell liquor inlet temperature to 86 OC. Higher water evaporation through the cathode eliminates the need of a cell liquor cooler. However, the increased air flow would significantly add to pressure drop, and the air channels in the hybrid cell would need to be carefully designed to alleviate this problem. Furthermore, the calculations indicate that the cell temperature will not be uniformly distributed within the cell. In fact, the cell temperature goes through a minimum near the cell entrance before it reaches the maximum al-
449
lowable level at the cell exit. This initial temperature drop occurs because of higher water cooling from relatively dry inlet air in contact with the catholyte of lower NaOH concentration. The cell temperature starts to rise as evaporative cooling becomes less effective when air is saturated with water and the catholyte becomes enriched in NaOH concentration. The degree of temperature reduction is more pronounced with higher air flow rates. Hence, even with increasing air flow rates as a means to eliminate water cooling of the chlor-alkali cell liquor, it would be advantageous to remove heat between stages to obtain a more uniform temperature in the cell. This would have the added advantage of alllowing more heat removal through water evaporation in less saturated air and, hence, a higher caustic concentration in the product.
Conclusions A mathematical model has been developed for analysis of the hybrid cell where concentration of sodium hydroxide and generation of electric power occur through the use of chlor-alkali hydrogen as fuel. The model has been useful in identifying crucial experimental steps for the hybrid cell development program and in providing the design bases for process engineering studies. The development and commercialization of the hybrid cell can result in significant cost and energy savings in chlor-alkali manufacturing. It appears from the analysis of model simulations that a two-stage cascade will be close to optimal under the given voltage-current conditions. This arrangement will minimize the problems due to pressure drops in cell modules in flow series. It will also have the flexibility of providing an interstage cooler for heat removal to maintain a more uniform temperature across the hybrid cell system. Further increase of the stages does not appear to improve the membrane efficiency and power production nor will it reduce the total number of cells in a cascade. Appendix (I) Total Ohmic Resistance R = R, + Re R, R,. (i) Membrane and electrode resistance ( R , and Re) are constant at 2 and 0.5 Q-cm2,respectively. (ii) Anolyte and catholyte resistances (R, and R,) are calculated as
+ +
R, =
d
-
(-4-2)
AOHC
where xc1 and xOH are the respective weight fractions of NaCl and NaOH in the anolyte, d (centimeters) is the gap between the electrode and the membrane, and A's are the electrolyte specific conductivities in Q-' cm-'; Acf = 0.0024 + 1.52xcl - 2 . 5 ~ c t+ 0.005 (T - 20) (A-3)
+
AOH' = (3.47 - 27.6Xo~ 100XoHZ- X O H ~ ) - ~(A-4)
and A O His ~ given by eq (A-4) with xOH being replaced by the catholyte NaOH concentration, yOH,in weight fraction. For a typical hybrid cell with a gap d of 0.05 cm, the total ohmic resistance is mostly dominated by the membrane resistance. For example, at the cell entrance, xcl = 0.148, X O H = 0.138, and yOH= 0; hence Ra = 0.1, R , = 0.17, and R = 2.78 0-cm2. At the cell outlet, xcl = 0.192, xOH= 0.012, and YOH = 0.35; hence R , = 0.11, R, = 0.3, and R = 2.91 Q-cm2. Consequently, adding pure water to the catholyte feed will have small effect on the current density. This rate is de(11) Water Evaporation Rate (we).
Ind. Eng. Chem. Process Des. Dev. 1905, 2 4 , 450-454
450
termined from experimental data as we
(weq - wJy(23.14 + 0 . 4 6 5 ~+ 0 . 0 0 2 6 ~ ~ )
(A-5)
where ww and wi, in gram-mole/hour are, respectively, the water content of air in equilibrium with aqueous NaOH and that of incoming air. The terms of y and y have been defined in the main text. Nomenclature
b = width of electrode or membrane, cm C, c = NaOH concentration in the anolyte and catholyte, respectively, g-mol/L of HzO C, = average molar heat capacity, kcal/g-mol-"C e , = caustic recovery efficiency; g-equiv of NaOH in the catholyte/g-equiv of Clz produced in chlor-alkali cells ei = membrane efficiency; number of Na+ equivalents transferred/Faraday of electricity passed through the cell E = applied cell voltage, u E" = anode and cathode open voltage, V F = Faraday constant, A-h/g-mol of NaOH L = cell length, cm M",, M", = initial feed rate of NaOH and NaCl, respectively, in the chlor-alkali cell liquor, kg-mol/h AH,= enthalpy change due to resulting NaOH concentration difference across the membrane, 2.84 kcal/g-equiv NaOH for NaOH to go from 12% in anolyte to 40% in catholyte 'lHE= enthalpy of water evaporation, 10 kcal/g-mol of HzO AHR= enthalpy of the Hz/Ozreaction, 34.16 kcal/g-equiv H20 at 25 "C i = current density, A/cm2 i, = average current density of a multistage cascade, A/cm2 i, = average current density of a jth stage of a cascade, A/cm2 mk = molar ratio of the kth component to NaOH in the feed m, = molar ratio of H20evaporated into air (stoichiometric amount) to NaOH in the feed n = number of cells in a stage
N = number of stages in a cascade q,, Q, = volumetric flow rates of water in the catholyte and anolyte, respectively, L/h R,, R,, Re, R, = ohmic resistance of anolyte, catholyte, electrode, and membrane, respectively, %cm2 T = cell temperature, "C TI = inlet chlor-alkali cell liquor temperature, "C w e = rate of water evaporation into air, g-mol/h r = anolyte NaOH concentration, w t % y = catholyte NaOH concentration, w t % z = cell distance, cm /3 = water transport rate; mol of HzO/mol of net Na+ y = multiple of stoichiometric amount of air required for the H2/02 reaction p, = water molar density, g-mol/L L i t e r a t u r e Cited Eroniewski, E. M. US. Patent 4248078, 1981. Eroniewskl, 8 . M. U.S. Patent 4299873, 1981. Eisenberg, M. I n "Advances in Electrochemistry and Electrochemical Engineering": Tobias, C. W., Ed.: Interscience: New York, 1962; Vol. 2, Chapter 5. Elzlnga, E. R.; Eannochie, J. G.: Bellows, R. J.; Coma. J. H.; Horowitz, H. H.; Snyder, C. W. Electric Power Research Institute EM-384, 1977. Emery, A. T.; Silverman, H. P.; Warzawski, E. 159th Electrochemical Society Meetlng, Minneapolis, MN, May 10-15, 1981, Abstract No. 407. Grens, E. A,; Tobias, C. W. J. E k t r o c b m . SOC.1981, 108, 1063. Keller, R. AICHESymp. Ser.1981, No. 204, 77. Koh, W. H.; Silverman, H. P. Paper No. 36d, AICHE National Meeting, Orlando, FL, March 1. 1982.
Received for review February 17, 1983 Revised manuscript received June 18, 1984 Accepted July 30, 1984 Supplementary Material Available: Listings of the computer program to perform hybrid cell sample calculations (6 pages). Ordering information is given on any current masthead page.
Solar-Powered Dehumidifier Based on the Surface Diffusion Phenomenon Hajlme Tamon' and Ryozo Toel Department of Chemical Engineering, Kyoto University, Kyoto, 606 Japan
A new solar-powered dehumidifier based on the surface diffusion phenomenon using a desiccant, such as activated alumina, was proposed to decrease the latent heat bad in an air oooflng system. Two experiments were conducted, the first to investigate the physical properties of the activated alumina plate, the adsorption isotherm, and the effectivethermal conductivity and the second to test whether moisture was removed from air by using the proposed dehumidifier. It was found that the moisture was removed, and the rate of moisture removal was 0.03-0.29 kg.m-'-h-'. In addition, an analysis was made from the point of the simultaneous heat and mass transfer to explain the experimental results. The equations of heat and mass transfer were solved by taking into account the change of transport properties, and the temperature and adsorbed water distributions In activated alumina plate were calculated. The calculated rates of moisture removal agreed with the experimental values.
Introduction
The summer climate of Japan is very hot and humid. The consumption peak of electric power for air-conditioning equipment lies between 10 and 16 o'clock (Japan standard time). Solar energy has high radiation intensity during this time. A considerable amount of moisture in 0196-4305/85/1124-0450$01.50/0
air is taken off as condensation in the cooling equipment because the atmosphere had high humidity in summer, ranging from 0.02 to 0.025 kg/kg. About 40% of the energy consumption for air conditioning is the latent heat of condensed water in the air-conditioning equipment of an office building. It is necessary that the air is dehumidified 0 1985 American Chemical Soclety
