Study of Electrical Analogue for Electrodialysis
_r /
DOCUMENT:.-
Study of Electrical
Analogue for Electrodialysis
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United
States Department
of the Interior
iv. of Tutaa
Univ
Office of Saline Water
•
Research and Development
Ubrarr
Progress Report No. 238
196?
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Research and Development
Progress
Report No. 238
•
February 1967
Study of Electrical
Analogue for Electrodialysis
By C. Berger, G. A. Guter,
G. Belfort, Astropower Laboratory,
Douglas Aircraft Company, Inc., Newport Beach, California, for
Office of Saline Water; J. A. Hunter, Acting Director; K. C.
Channabasappa, Chief, Membrane Division, M. E. Mattson,
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Project Engineer
UNITED
STATES DEPARTMENT OF THE INTERIOR
•
Stewart
L Udall, Secretary
Frank C. Di Luzio, Assistant Secretary for Water Pollution Control
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Created in 1849,
the Department
of the Inter ior —
America's Department of Natural Resources—is concerned with
the management, conservation, and development of the Nation's
water, wildlife, mineral, forest, and park and recreational
resources.
It also has major responsibilities for Indian and
Territorial affairs.
As the Nation's principal conservation agency, the
of the Interior works to assure that nonrenewable
resources are developed and used wisely, that park and recrea
tional resources are conserved for the future, and that renewable
Department
resources
perity,
their full contribution to the progress, pros
security of the United States—now and in the future.
make
and
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FOREWORD
This is the two hundred and thirty eighth of a
series of reports designed to present accounts of progress
in saline water conversion with the expectation that the
exchange of such data will contribute to the long-range
development of economical processes applicable to largescale, low-cost demineralization of sea or other saline
water .
Except for minor editing, the data herein are as
contained in the reports submitted by the Astropower Laboratory,
Douglas Aircraft Company, Inc. under Contract No. 14-01-0001The data and conclusions given in this report are
676.
essentially those of the contractor and are not necessarily
endorsed by the Departmerit of the Interior.
ABSTRACT
The
highlight accomplishments of the program are as follows:
1.
This study is
a
first attempt to perform an analysis
of
electrodialysis by considering the process as an electrical network
composed of resistive elements representative of various electro
chemical subprocesses . The total effect of all subprocesses is
unified into the single mathematical equation for the network. This
study represents a step of major magnitude in understanding the
electrodialysis process because of the novel engineering equations
developed that can be used to quantitatively analyze the electrical
resistance of the stages in an electrodialysis plant. The treat
ment gives a breakdown of the various factors that contribute to
electrical resistance and pinpoints those factors that must be
improved to make technological improvements in the process.
2. Application of the analysis to the Webster, S. D. and
Buckeye, Arizona, plants enables the resistance of the separate
stages to be calculated.
The average calculated values for the
six stages of these plants agree to within 94% of the average
measured
values.
3.
The major resistive factors found in the operation of
the above plants are electrolyte resistance, ohmic polarization
Recommendations
(due primarily to scale) and membrane potentials.
are made to reduce the latter two factors.
resistive elements were found to be membrane
electrode polarization, and parasitic duct losses.
The membrane resistance in the first stage at Webster, S. D. ,
It
represents about two percent of the total stack resistance.
is recommended that polarization effects be reduced even at the
expense of increasing these minor resistive contributions, if
4.
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resistance,
The minor
necessary.
5.
The electrical characteristics of the Webster and
Buckeye plants were calculated based on assumed technological
advances which can be made in operating techniques, improved
hydrodynamics and use of exotic membranes.
was found that
It
reductions in electrical resistance of from 15 to
are possible using these advances.
45
percent
6. The resistive elements of a hypothetical sea water
plant were also calculated by the method developed in this study.
The results indicate that membrane resistance becomes an important
factor. In the future, development of membranes for sea water
use, low membrane resistance as well as reduction in ohmic
polarization is a justifiable goal.
11
TABLE OF CONTENTS
Page
1.0
INTRODUCTION
1
2. 0
PROGRAM OBJECTIVES AND SUMMARY
3
2. 1
2. 2
2.3
2.4
2. 5
3. 0
Program Objectives
Summary of Specific Accomplishments
Summary of Program Results
Recommendations
3
4
11
Personnel
14
ELECTRICAL ANALOGUE STUDIES
3. 1
15
Phase I — Subcomponent Analysis
3. 1. 1
3.1.2
3.1.2.2
3. 1. 2. 3
3. 1.2.4
3. 1. 2. 5
3.1.4
3.
1.4. 1
3. 1. 4. 3
34
34
35
35
38
38
42
R
Resistance Analogue of Electrical
Duct Losses
48
48
50
50
Discussion
50
Membrane Potential
Membrane Selectivity
55
58
Discussion
58
Selectivity
59
Terrmerature Effects
60
3. 1. 7. 1
3. 1. 7. 2
3. 1. 8
Concentration Overpotential
Chemical Overpotential
Ohmic Overpotential
Cathodic Resistance Analogue
Anodic Resistance Analogue
Total Channel Resistance,
Cell Pair Resistance, RD
15
27
32
Water Transfer Processes
3. 1. 5. 1
3.1.6
3.1.7
Concentration Polarization
Estimation of Ohmic Polarization
Composite Cell Pair Resistance
Parasitic Electrical Duct Losses
3.1.4.2
3. 1. 5
15
Electrode Polarization
3. 1. 2. 1
3. 1.3
15
Membrane Polarization
3. 1. 1. 1
3. 1. 1. 2
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3
Resistance Analogue of Membrane
iii
Page
3. 2
Phase II — Integration of Subcomponent Mathematical
Elements into a General Analytical Expression
3.2. 1
3.2.2
3. 3
Development of General Mathematical Analogue
Power Index
Phase III — Application of Generalized Mathematics
Solution to Specific Situations
3.3.1
Calculation of the Concentration Polarization
3.3.2
3.3.3
Estimation of Ohmic Polarization
Calculation of Electrode Polarization
Calculation of Resistance Due to the Overall
Cell Pair
Calculation of the Parasitic Duct Loss
3. 3. 4
3. 3. 5
at the Membrane Surfaces
Resistance
3. 3. 6
3. 3. 7
3. 3. 8
3.3.9
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67
74
86
89
94
104
109
3.3.9.1
111
Operating Characteristics
Mathematical Determination
of
109
110
111
..
Ill
Electrodialysis of Projected Plants
114
Concentration Polarization
Ohmic Polarization
Composite Cell Pair
3.3. 10.4 Membrane Polarization
3.3.10.5 Neglected Effects
114
115
115
115
115
Discussion of Calculated Values
115
3. 3. 10.
i
operating
1
3.3.10.2
3.3.10.3
3.3.11
62
62
Calculation of the Corrected Coulomb Efficiency
Based Solely on the Water Transfer Processes
Calculation of Resistance Due to Membrane
Selectivity
Calculation of Resistance Due to Membrane
Potential
Electrodialysis of Sea Water
3. 3. 9. 2
3.3. 10
62
STATEMENT OF INVENTION
118
REFERENCES
119
APPENDIX A
- Colloidal Coagulation
APPENDIX B — Theoretical Prediction of Membrane Resistance
Combining the Statistical Theory of Meares, et al. ,
and Spiegler's
Formation Factor
IV
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APPENDIX C
- Hydro dynamic Flow
APPENDIX D - Nomenclature
LIST OF ILLUSTRATIONS
Figure
1
2
3
4
Simplified Schematic of Cell Pair Resistive Network
Boundary Film Thickness as a Function of Volumetric
Rate of Flow
Diagram of the Concentration Profile and the Diffusion
Layer on Each Side of an Electrodialysis Ion Exchange
_
Membrane
/. ' \
Plot of the Correction Factor
I
( ^1
C. F. =7:
I
)
r
4-Of1
(him) 25 °C
17
19
I
J
Versus Temperature of Fluids at Various Product
5
6
7
22
Constants A and B (From Onsager Equation) Versus
Temperature °C
26
Relationship Between Rate of Resistance Change and
Reciprocal of Stack Current
29
Linear Relationship Between Rate of Resistance
Change and Stack Current
30
of Membrane Polarization
8
Development
9
Comparison of Resistances in Electrode Compartments
36
Various Overvoltages at Electrodes
39
10
11
12
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Concentrations
Representative Electrical Network of a Multicompartment
Electrodialysis Unit
"Reduced" Electrical Network of a Multicompartment
Electrodialysis Unit
13
Schematic View of Current Leakage
14
Plot of the Leakage Fractionl-: — I Versus the Normalized
Channel Resistance Ratio
15
16
17
18
19
(W)
o
33
43
44
45
46
Dimensions of Electrodialysis Unit Required for
Electrical Leakage Model
47a
Various Simultaneous Processes Occurring During
Electrodialytic Separation
51
Water Transfer From Dialysate to Brine per Gram
Equivalent of Salt Transport
52
Water Transfer as a Function of Current Density in a
Cationic Membrane
53
Ratio Tf/T/j.., for Various Values of Water Transferred
(W
)
and
Cproduct
Dialysate Concentration at Start, (C ,). when
=
°" 01 <drinking water>
56
VI
Figure
20
Equivalent Resistance Circuits for a Single Cell Pair
63
21
Equivalent Circuit for Electrodialysis Process
64
Electrical Schematic cf Current Resistance Losses
in a Membrane Cell Pair
Flow Sheet and Material Balance for Electrodialysis
66
22
23
24
25
26
27
28
29
30
31
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Page
32
33
34
35
36
37
Plant at Webster, So. Dakota
69
Flow Sheet and Material Balance for Electrodialysis
Plant at Buckeye, Arizona
70
Schematic of the Mark III (Ionics Inc. ) Spacer
75
Plot of Equivalent Conductance Versus Average
Solution Concentration for Various Temperatures.
Derived from the Onsager Equation
79
Plot of Equivalent Conductance Versus Average
Solution Concentration for Various Temperatures.
Derived from the Onsager Equation
80
Plot of Equivalent Conductance Versus Average Solution
Concentration for Various Temperatures. Derived from
the Onsager Equation
81
Plot of Equivalent Conductance Versus Average Solution
Concentration for Various Temperatures. Derived from
the Onsager Equation
82
Plot of Equivalent Conductance Versus Average Solution
Concentration for Various Temperatures. Derived from
the Onsager Equation
83
Plot of Equivalent Conductance Versus Average Solution
Concentration for Various Temperatures. Derived from
the Onsager Equation
84
Variation of Concentration Polarization With the
Normalised Operating Current Density for the
Electrodialysis Plants at Webster* S. D. and
Buckeye, Arizona
Concentration Profiles oi the Electrode, Buffer and
Adjacent Streams at Webster, South Dakota
88
90
Concentration Profiles of the Electrode and Adjacent
Streams at Buckeye, Arizona
91
Concentration Profiles of the Dialysate and Brine
Streams
98a
Resistivity of Ion Exchange Membranes and Sodium
Chloride Solutions
102
Mass Balance of the Dialysate and Brine Streams for
Stage IV, Webster, South Dakota
105
Figure
38
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39
Page
Channel Dimensions of Brine and Dialysate Streams
as Shown by a Dialysate Gasket, from the Stack at
Webster, South Dakota
108
Flow Sheet and Material Balance for Hypothetical Sea
Water Plant With Buckeye, Arizona,
Conditions
Equipment and
113
vin
LIST OF TABLES
Table
I
JJ
IV
Cell Pair Resistance of Webster Plant
Cell Pair Resistance of Buckeye Plant
Cell Pair Resistance of Projected Plants
Cell Pair Resistance of Sea Water Plants
10
V
Separator and Channel Dimensions
18
VI
Comparison of Calculated and Observed Ohmic
Resistance Change with Time
31
Summary of the Important Mathematical Relationships
Used in Phase III (Derived in Section 3. 1) — Application
of Generalized Mathematical Equations to Specific
Situations
68
III
VII
VIII
IX
X
XI
XII
XIII
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Page
XIV
XV
XVI
XVTI
XVIII
XIX
XX
7
8
9
Array of Data Used as Inputs for the Electrodialysis
Electrical Analogue Model for the Present Webster Plant
Array of Data Used as Inputs for the Electrodialysis
Electrical Analogue Model for the Present Buckeye Plant
Array of Data Used as Inputs for the Electrodialysis
Electrical Analogue Model for the Sea Water Plant
73
Concentration Polarization in the Brine and Dialysate
Streams Using the Computed Double Integration Method
77
Concentration Polarization Computed Using the
Double Integration Method
87
Detailed Brine, Catholyte, Anolyte and Buffer Material
Balances for the Electrodialysis Plant at Webster,
South Dakota
92
Detailed Electrode Material Balances for the
Electrodialysis Plant at Buckeye, Arizona
93
Resistance Analogue Evaluation for the Anode and
Cathode (Plus Buffer Stream at Webster, South
Dakota) Compartments
95
Detailed Dialysate Material Balances for the Electrodialysis Plant at Webster, South Dakota
Detailed Dialysate Material Balances for the Electrodialysis Plant at Buckeye, Arizona
Detailed Brine Material Balances for the Electrodialysis Plant at Buckeye, Arizona
71
72
96
97
98
Summary of the Solution and Membrane Resistances
Per Cell Pair
103
Major Constituents of Sea Water
112
ix
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1.0
INTRODUCTION
This is the final report of work under Contract 14-01-0001-676.
analytical engineering study of the electrodialysis
An
process was performed and
appropriate mathematical expressions were derived and applied to the calcu
lation of the resistance of electrodialysis
of conditions.
plants operating under
a
given set
The computed values are close to the actual plant operating
values and indicate for the first time a quantitative breakdown and relative
importance of the various factors which contribute to the electrical resistance.
Previous to this study no unified treatment of the electrodialysis
had been made.
There did exist a large number of theoretical and laboratory
studies on various subprocesses of electrodialysis.
Engineering studies had
also been made designed to give total operating costs of electrodialysis
and
process
costs of product water.
plants
In the latter studies, stack resistance assumed a
minor role and did not require an analytical treatment.
This study differs
from former studies in that it is centered on the many electrochemical proc
esses that constitute electrodialysis
teristics.
and
contribute to stack operating charac
This study constitutes a preliminary attempt to analyze the operation
of an electrodialysis
plant by reducing all associated factors to an electrical
resistance and unifies these factors by placing them in a network of resistive
elements
representative of the electrodialysis
process.
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The major objective of this study is to develop mathematical equations
of an electrical network that is analogous to the electrodialysis
process and
that can be applied to both projected and present electrodialysis
plants.
The
generalized equations contain parameters of operating plants and will facilitate
computing the processing costs for a given water supply and set of operating
parameters.
The equations describe the resistive elements
equivalent to
discrete phenomena or subprocesses such as concentration polarization, ohmic
polarization, bulk stream resistance, membrane resistance, electrical losses
through ducts,
water transfer processes,
and membrane
potentials.
This approach has provided a step of major magnitude in the under
standing of electrodialysis
analytical tod,
plant operation.
This study has resulted in an
applicable not only to the analysis of the operation of large
plants but the results pinpoint those technological advances in the processes
which are required to lower plant operating costs and expand the utility of the
process.
In this report each of the various resistive elements is discussed
separately, and a resistance analogue expression is derived for each.
area resistance equivalent for each factor is calculated.
The
The area resistances
are then combined to give a total area resistance of a single cell pair. This
procedure is applied to the electrodialysis plants at Webster, South Dakota;
Buckeye, Arizona;
technology.
a
sea water plant; and a plant using assumed advanced
Recommendations
concerning specific aspects of the electro-
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dialysis process are given as a result of the calculations for the various plants.
2. 0
PROGRAM OBJECTIVES AND SUMMARY
Program Objectives
2. 1
The objectives of this study are as follows:
Formulate a general mathematical equation for electrodialysis by developing a unified electrical analogy concept
in which critical component and subcomponent factors are
represented in terms of an electrical resistance network.
2.
Develop specific guidelines for future research and develop
ment work in improving electrodialysis technology by
applying the equation to specific situations and determining
how the variations in operating parameters and other vari
ables influence performance and operating costs.
Summary of Specific Accomplishments
2. 2
1.
the
1.
Engineering equations were derived that can be used to calculate
electrodialysis
stack resistance and
electrical operating costs if various
operating parameters are known such as, water compositions, temperature,
types of membranes, stack design, limiting current, operating current, flow
rates, etc.
2.
The use of the derived equations gives
a
breakdown
of and allows
comparison of separate resistive components of the total process.
This breakdown lists electrolyte resistance, resistance due to scale formation
a magnitude
and membrane polarization among the major resistive
membrane
resistance and membrane concentration polarization among the
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relatively unimportant factors.
of the total
elements and places
Electrolyte
resistance represents one-third
cell pair resistance for brackish water and two-thirds is due to a
number of various polarization
3.
effects.
This study resulted in a number of recommendations for directing
technical efforts to improve the electrodialysis
process.
These recommenda
tions are listed below in Section 2. 3.
4.
Most of the resistive elements were calculated by integrating
complex equations on a digital computer.
Consequently, highly refined values
were obtained and effects of changes in stack design can be readily evaluated.
operating
5. An
empirical correlation was made between ohmic polarization,
time
and
current
density.
Equations were derived and
applied to operating plants.
Estimates of ohmic polarization,
which may
involve phenomena such as scaling, fouling, and internal membrane changes,
are quite high and suggest ohmic polarization as one of the most important
and
least understood of the membrane
phenomena investigated.
Summary of Program Results
2. 3
The objectives of this program were achieved by a four-phase
study.
During Phase I, Subcomponent Analysis,
mathematical expressions
were developed based on electrical analogies for each of the subcomponent
factors influencing the operation of an electrodialysis
considered were concentration polarization,
selectivity,
membrane
polarization,
system.
The factors
ohmic polarization,
membrane
resistance, parasitic electrical losses,
water transfer processes,
membrane polarization,
and
electrode
and dialysate resistance,
concentrate
The effects of hydro -
electrode polarization.
dynamic factors and temperature were included.
The derivation of electrical
resistive equations for each of the above factors is given in Section 3. 0,
Electrical Analogue Studies. Membrane, concentrate and dialysate resistances
were combined into a single expression, designated as composite cell pair
resistance. This expression, as well as that developed for membrane con
parasitic duct losses,
centration polarization,
transfer, membrane polarization,
and
membrane
electrode polarization,
into computer language to facilitate computations
and to
grations over the cross-sectional area of a membrane
water
were translated
perform double inte
stack.
A tool for
studying design effects on these various resistive elements was thus intro
duced and successfully
employed.
During Phase II, Integration of Subcomponent Mathematical
Elements into
a General
Analytical Expression,
the
interrelationships
between
resistive elements was studied and their combination into a general ex
pression for a resistance network was accomplished. An expression for total
stack resistance was then written in terms of the separate resistive elements
the
and
their combination into a resistance network.
A simplified version of the
resistance network for a single cell pair is given in Figure 1.
current through an electrodialysis
currents
ift
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selectivity,
and
The total
stack is the sum of i , , i_, and i_.
The
i- represent processes that do not actually conduct a current,
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however, their effect is to lower the efficiency of the desalting current, i^;
parallel in the network.
cell pair
resistance is then easily obtained from the algebraic expression for the total
resistance of the network consisting of R, through R_. Resistances R0
consequently,
they are placed
in
through R, can be broken down to further series
The
or parallel networks.
A power index, P., for a given stack design was then defined
pi
•
iR AC
-V-
n)
where i is the stack current,
R
the stack resistance,
and
efficiency and AC is the change in dialysate concentration.
of the resistive elements
the
as
R? and
R~
in Figure
power cost required for electrodialysis
1.
r\
is the current
The latter consists
This index is proportional to
processing.
A comparison of
power indexes is possible for stacks of various designs, when product water
rate, feed water concentration, and amount of total dissolved solids removed
are held constant.
Under Phase III, Applications of Generalized Mathematical Solu
tion to Specific Situations, the expression for the derived resistance network
was applied to specific plant situations at Webster, South Dakota; Buckeye,
Arizona; a hypothetical sea water plant; and a projected plant based on assumed
advances in electrodialysis
technology.
A description of the calculation
and
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combination of the resistive elements is given in detail in Section 3. 3 of this
report.
A tabulation of results and comparison with the actual values are
given in Tables I,
II, III,
and
IV.
The separate
resistive component values
are listed as well as their combined values. The calculations using assumed
A
advanced technology is based on the Webster, South Dakota plant design.
comparison can thus be made of the present plant and what might be expected
if certain advances are made in membrane performance, scale elimination,
reduction of concentration polarization and membrane potentials.
Under Phase IV, recommendations on specific guidelines for
future research and development work in improving electrodialysis
were made.
These recommendations
technology
are based on the analysis of the Webster
and Buckeye plants, projected plants, and a hypothetical sea water plant.
Recommendations are given below.
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10
Recommendations
2. 4
As a result of this study a number of recommendations concerning
the electro'dialysis process can be made.
1 .
The elimination or substantial reduction of ohmic polariza
tion would significantly improve the economy of the process.
the least understood of all those subprocesses encountered
This factor is
in this study.
Although ohmic polarization is complex in nature, there appears to be no
theoretical reason for not expecting improvement in this area. Ohmic polari
zation is considered to be due to build up of hard and soft scale, flocs, and
opposing potentials that can build up within the membranes.
Improving the hydrodynamic flow at the membrane
surface would
reduce the diffusion layer concentration gradient and prevent formation of the
hydroxide ion responsible for precipitation of hydroxides in the concentrate
streams.
There appears to be a relationship between spacer design and scale
formation as indicated by an examination of used membranes which show
scale formation occuring at specific locations relative to the spacer mesh.
This relationship between local hydrodynamic flow and scale formation should
be
investigated.
Another approach for reducing ohmic polarization is to develop
selective anion membranes to lower or limit the conduction of scale and floc
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forming ions into the concentrate stream.
Work on cation membranes selec
tive for calcium and magnesium has been considered in the past and appears
feasible.
It is reasonable to extend this approach
The extremes to which membrane
to anion membranes
development
as
well.
for reduction of
ohmic polarization can be carried is indicated by the relative effects of mem
brane resistance and ohmic polarization.
Table I and Table IV give composite
cell pair resistance for the four stages at Webster,
S.
D.
The calculations
were based on the assumption that membrane resistance for the projected
plant (Table IV) was
50
percent of the membranes now in use (Table I).
How
ever, the composite cell pair resistance for Stage I differs only by two percent
because most of the resistance is offered by the electrolyte streams.
development
In the
of the selective membranes, it may be necessary to sacrifice
11
good membrane conductivity for specific selectivity provided advantages of
reducing polarization effects can be gained.
Methods of reducing membrane
2.
to_
potentials must be considered
gain significant reduction in_ electrical power costs.
Membrane potentials
arise due to concentration differences across the membrane coupled with
selective transport properties and are augmented by concentration gradients
in the diffusion layers adjacent to the membrane.
Elimination of the latter
concentration gradients was assumed in calculating membrane potentials for
the projected plants as given in Table IV.
The latter values can be considered
the lower limits obtainable with ideal flow conditions resulting in the elimina
tion of the diffusion layer.
A better understanding of the influence of spacer
design on local hydrodynamic flow is required as an initial step to more effec
tive spacer design.
Concentration gradients can also be discharged by intro
ducing pulsing and current
by
other investigators.
reversal techniques
as has
already been suggested
Studies, however, must be made to determine the
magnitude of the advantages gained because current reversal
will drastically
reduce current efficiency.
Analytic al studies to optimize plant design should be made.
3 .
The breakdown
of total stack resistance and capability to calculate separate
resistive elements can readily be adopted to optimization of plant design and
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operating procedures.
As was discussed above, the development of scale
resistant membranes may require sacrificing good membrane conductivity.
Once the characteristics of membranes are established, optimization of
Another obvious optimization is membrane
membrane
choice can be made.
potential.
The method of feeding a multistage plant
will influence both mem
in an opposite manner. The two
stages at the Buckeye plant use series feed for each of the inlet streams
brane potential and electrolyte resistance
giving a greater membrane potential in the last stage than in the first due to
larger concentration differences across the membrane. If series feed were
used for the dialysate stream and parallel feed for the concentrate, as is
done at Webster,
branes
lower concentration gradients would exist across the mem
resulting in lower membrane potentials.
Alterations in method of feed will also change electrolyte stream
resistance and scaling tendencies.
The latter is due to changes in calcium
12
and magnesium
ion concentration in the concentrate
when different feed patterns are introduced.
elements
have common factors,
stream which will occur
Because many of the resistive
design alterations optimum for one may not
necessarily guarantee optimization for the other factors, or their net result.
Optimization of design is possible, however, when all resistive factors are
considered simultaneously as can be done by the general network equation
derived in this study.
4.
Data from operating plants must be obtained to further
refine and develop more extensive and meaningful electrical analogue expres
sions.
Although OSW contractors were extremely helpful in providing data
presently available on the operations of their plants, it was found that a vast
amount of data remain unknown. Knowledge of water analyses and how it
varies with stack performance,
analyses
of electrode streams and water
transport data are few or lacking completely.
As discussed above, the
ohmic polarization factor is one of the most important resistive components.
However, only a two-parameter equation based on empirical correlations
was found to approximate this factor.
Certainly,
this phenomenon must be
influenced by several factors such as spacer design and hydrodynamics, tem
perature, nature of the membrane, the presence of certain anions and cations
in addition to calcium and magnesium, flow rate, pretreatment, feed method
and suspended solids.
There are far more variables that should be considered
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and which require much more plant operating data to more fully understand
the
ohmic polarization terms.
5.
Membrane research must be pursued from the standpoint
of reducing both short and long term polarization effects.
Membrane resist
ance is a minor consideration in seeking these improvements.
Polarization
effects determine cost factors exclusive of the electrical power costs.
and floc formation require special operating procedures,
Scale
pretreatment,
pulsing, acid backwashing, membrane breakage, and replacement. Advanced
membranes that can aid in the reduction of these costly factors need not
exhibit low membrane
resistance because of the insignificance of the latter
electrical power costs approxi
mate less than ten percent of the total cost picture for electrodialysis
factor compared to total operating cost.
processing.
The
Membrane resistance in the first stage at Webster,
13
South Dakota is about one percent of the total stack resistance.
Certainly,
sacrifices in membrane conductivity can justifiably be made
reduce the
to
scaling problems.
6.
The above recommendations
of an effective advanced study using the
of the
(3) and (4) can be the subjects
electrical analogue approach.
Much
required data for refinement of the study can be obtained using a
portable 1000 GPD test stack which can be operated at a number of sites
having different feed waters.
Completion and refinement of the optimization
equations could then be used to optimize a test stack design for each site or
water type.
Operation and testing the optimized designs at the various sites
would be a final phase of the program.
The use of any advanced electro-
dialysis technologies such as inorganic membranes,
procedures
and special operating
such as pulsing and current reversal should definitely be a part
of this program.
2. 5
Personnel
Astropower personnel who participated in this study are
Dr. C. Berger, principal investigator , Dr. G. A. Guter and Mr. G. Belfort.
Dr. K. S. Spiegler participated in this study as consultant to Astropower.
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Mr. Robert Hubata
of Astropower assisted with some of the calculations.
14
3. 0
ELECTRICAL ANALOGUE STUDIES
3. 1
Phase I — Subcomponent Analysis
A discussion and review of a number of subcomponent factors of
the electrodialysis process will be undertaken in this section. For each sub
component factor, the resistance-analogue (ohms-cm /cell pair), will be
preceded by a summary of the present state of the art.
These resistance
values are combined and calculated in Sections 3. Z and 3. 3 using data obtained
from the electrodialysis plants at Webster, South Dakota, and Buckeye,
Arizona.
3. 1. 1
Membrane Polarization
Extensive experimental work has been,
done to quantitatively
and
is being,
explain the phenomena of membrane polarization.
The
dialyzing current faces a two-fold polarization effect close to the membrane
surface.
A concentration gradient across the diffusion layer and scale for
mation are the respective causes of such polarization.
The former is termed
concentration polarization while the latter is called ohmic polarization.
Each
is separately discussed and evaluated below.
3. 1. 1.
1
Concentration Polarization
It is possible to estimate the approximate
resistance due to concentration polarization that the dialyzing current faces,
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provided two important system parameters can be calculated.
These are the
thickness (6) of and the concentration gradient and profile across the diffusion
layer.
Several empirical approaches,
use of the Chilton-Colburn
(4)
such as
transfer factors and the flux equation of Fick, are
able to predict the diffusion layer thickness for nonspace-filled
compartments.
Because in all practical electrodialysing plants spacers or turbulent promoters
are used, these theoretical equations are not applicable. H. P. Gregor,
et. al.
have studied and measured experimentally, using various size
spacers at different compartment flow rates and Reynolds numbers, the re
lation of the diffusion layer-thickness
relationship,
with flow rates.
Figure Z depicts this
while Table V provides the channel and spacer dimensions.
15
For flow rates greater than half a gallon per minute, 6 , the diffusion layer
thickness, can be predicted from the straight line relationship obtained from
the lower curve in Figure 2, viz,
6
=
30 - 10. 7 Q