WATER POLLUTION CONTROL RESEARCH SERIES • ORD-17O9OFTAO7/69
MATHEMATICAL MODEL OF
THE ELECTRODIALYSIS PROCESS
U.S. DEPARTMENT OF THE INTERIOR • FEDERAL WATER QUALITY ADMINISTRATION
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WAITER POLLUTION CONTROL RESEARCH SERIES
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Ihis report has been reviewed by the Federal Water
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Approval does not signify that the contents neces-
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MODEL OF THE
ELECTRODIALYSIS PROCESS
by
Kenneth T. Pruyn
Joseph J. Harrington
J. Douglas Smith
Process Research, Incorporated
Cambridge, Massachsettts 02142
for the
FEDERAL WATER QUALITY ADMINISTRATION
DEPARTMENT OF THE INTERIOR
Program #17090 FTA
Contract #14-12-410
FW3A Project Officer, J. F. Roesler
Advanced Waste Treatment Research Laboratory
Cincinnati/ Ohio
July, 1969
For sale by the Superintendent of Documents, U.S. Government Printing Office
Washington, D.C. 20402 - Price 70cents
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Table of Contents
Page No.
Table of Contents ................................. ii
List of Figures ................................... iii
List of Tables ................ . ................... iv
Electrodialysis Process Description ............... 1
Electrodialysis Equipment ......................... 7
Mathematical Model ................................ 11
Electrodialysis Performance Equations ............. 16
Electrodialysis Process Cost Functions ............ 19
Capital Costs ..................................... 20
Operating Costs ................................... 27
Flow Sheet and Sample Outputs ........... . ......... 30
Recommendations and Suggestions ................... 39
Pertinent References ...................... , ....... 40
Appendix A - Derivation of Electrodialysis
Design Equations ........ 42
Appendix B
Program Description ............................. 47
Program Organization ............................ 48
Nomenclature .................................... 49
Listings ........................................ 55
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List of Figures
Figure No. Title Page No.
1 Basic Ion and Water Flow in Electro-
dialysis Stack 6
2 Expanded View of Electrodialysis Stack .. 8
3 Electrodialysis Process Flow Sheet 12
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List of Tables
Table No. Title Page No.
1 Computer Output, 1 MGD Waste Treat-
ment Plant 35
2 Computer Output, 10 MGD Waste Treat-
ment Plant 36
3 Computer Output, 100 MGD Waste Treat-
ment Plant 37
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Electrodialysis Process Description
The electrodialysis process removes ionized salts and
minerals from water by the migration of ions through plastic
ion-transfer membranes, under the influence of a D. C.
electrical field. Commercially available electrodialysis
membranes are thin sheets (4-40 mils thick) of cross-linked
organic polymeric materials. These membranes are similar
in composition to granular ion exchange resins, except for
their physical form. They commonly contain 40-50%, by
weight, of water which is distributed in extremely fine
pores honeycombing the plastic structure. The size of these
pores has been estimated at 10-100 A°. For the salt concen-
trations common to advanced waste treatment applications,
water transfer through these membranes will be virtually
zero. Two types of membranes are necessary to the process:
1) Cation permeable membranes, which will permit the
passage of cations but, because of the Donnan
exclusion principle, will prevent the passage of
anions; and
2) Anion permeable membranes, which for the same reason
will allow the passage of anions but not cations.
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If two metal electrodes are placed in an aqueous salt
solution and electrical current is passed between them, all
of the negative ions will move toward the positive electrode
and all of the positive ions will move toward the negative
electrode. If, now, alternative cation and anion permeable
membranes are interposed between the electrodes, the move-
ment of the ions in the electrical field will be seriously
restricted. Half of the ions will be able to move through
one type of membrane barrier and half will not; no ion
will be able to move through more than one barrier. This
is illustrated in Figure 1. In this figure, cations from
compartments whose left boundary is a cation membrane
(compartments 2, 4, 6, 8, 10, etc.) will move one compart-
ment to the left but must then stop because the second
membrane to be encountered will be an anion membrane, which
is impermeable to cations. Conversely, anions from compart-
ments whose right boundary is an anion membrane (compartments
2, 4, 6, 8, 10, etc.) will move one compartment to the
right, but must then stop because the second membrane they
encounter will be a cation membrane and impermeable to anions,
The net result, therefore, of the interposition of the
alternating cation and anion permeable membranes between
the electrodes is the creation of two types of compartments:
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diluting compartments (i.e., 2, 4, 6, 8, 10) which will lose
ions; and concentrating compartments (i.e., 3, 5, 7, 9)
which will gain ions.
The extent of salt removal, or demineralization,
obtained in the diluting compartments will depend upon the
amount of electrical current passed, the concentration of
ions present in the feed solution, and the flow rate of the
feed solution through the equipment. All ions are not, how-
ever, removed at identical rates, some moving preferentially
faster than others. This preferential, or selective, removal
of certain ions is described here by a Separation Factor. The
Separation Factor for each ion is the ratio of its percentage
reduction to the total concentration reduction through the
process.
In compartments 1 and 11, electrode reactions take place.
Hydrogen gas and hydroxide ions (OH") are produced at the
cathode, or negative, electrode; oxygen or chlorine gas and
hydrogen ions (H+) are produced at the anode, or positive
electrode. The effluent from these electrode compartments
may, in some situations, be useful for chemical operations,
being sources, respectively, of base and acid. The gases
produced at the electrodes may be used for disinfection, or
as a source of fuel. For purposes of this model, the cathode
and anode waste streams will be mixed with the concentrated
brine and be considered a part of the total waste stream.
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The mathematical model developed here for the electro-
dialysis process represents an attempt to describe the
present, moderately well documented state of the art of
commercially available equipment and operating practice.
Current state of the art has been established from site
visits and discussions with operating personnel at various
electrodialysis installations in this country, i.e., Lebanon,
Ohio; Pomona, California; Port Mansfield, Texas; etc.; from
the literature and from our own experience.
The modeling of presently available equipment in no way
implies that such equipment is optimally designed or operated
for waste water treatment applications. Our own independent
studies, in fact, indicate rather the opposite. Our design
optimization programs, for instance, suggest that modifications
of flow path geometry, i.e., thickness and/or width, could
result in greatly reduced membrane area and D.C. power
requirements. Our membrane fouling studies have indicated
modes of operation, or pretreatments, which would further
reduce membrane area and maintenance requirements.
The potential cost reductions, on the order of one-half
of present cost estimates, to be gained through these various
design and operating modifications are sufficient to justify
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their further examination and documentation on something
larger than a laboratory scale.
Such modifications have not been included in the model
developed here, because inadequate field experience has
been obtained to warrant their inclusion as present "state
of the art". An attempt, however, has been made to express
this model in sufficiently general terms as to readily
facilitate their later inclusion.
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Saline
Hater Saline Hater
to to cl
"-jj Ion Gaining Ion losing 2 ,
f; 2 Compartments Compartments or Oj
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Cathode Concentrated Brine Product Anode
Waste or Haste Hater Waste
(7) Compartment Number (see text)
(N») Any Cation (Positive Ion) Like Sodium
(tr) Any Anion (Negative Ion) lake Chloride
C Cation Membrane
A Anion Membrane
FIGURE 1
BASIC ION AND HATER PLOW IN ELECTHODIALYSIS STACK
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Electrodialysis Equipment
The physical structure in which these demineralization
operations are carried out is called a membrane "stack".
Such a membrane stack is illustrated, in an expanded view,
in Figure 2. The stack consists of alternative anion and
cation permeable membranes, spacers, electrodes, end blocks
for making inlet and outlet manifold connections, heavy
steel end plates, and tie rods to provide uniform sealing
pressure.
The electrodes are thin metal sheets, stainless steel
or Hastelloy C being typical materials for the cathode.
Graphite, or platinum coated sheets of tantalum or titanium,
are typical materials for the anode.
The spacers are probably the most important component
in the electrodialysis stack, after the membranes them-
selves . They:
1) serve as gaskets, containing the water between the
membranes;
2) separate the thin, flexible membranes a constant
distance from each other; and
3) direct the flow of water across the surface of the
membranes.
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AJOUMULfll
00
I
Figure 2
Expanded view of Electrodialysis Stack
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A good spacer will be designed to provide an even distribution
of flow, and to promote sufficient turbulence at the membrane-
liquid interface to avoid the formation of polarization films
(to be discussed later). It has been suggested that by far
the greatest immediate process improvement, or cost reduction,
is to be found through optimal design of the geometry of
these spacers (see OSW R&D Report No. 325).
There are two general types of spacer designs used in
present commercially available equipment: the so-called
"sheet flow" design, as used in the Asahi Chemical electro-
dialysis plant at Webster, S. D.; and the so-called "tortuous-
path" design, as used in the Ionics, Inc., plant at Buckeye,
Arizona. The spacers shown in Figure 2 are of the tortuous-
path variety, the illustration being that of an earlv Ionics,
Inc. stack design.
Spacers are fabricated from sheets of electrical insulating,
plastic materials having good gasketing properties. Common
materials are plasticized polyvinyl chloride, polyethylene
or rubber-styrene compounds. In the tortuous-path type
spacer illustrated here, a flow path for the salt solution
is die-cut into one sheet of spacer material, along with
manifold holes and appropriate connections between manifold
holes and flow path. In the sheet-flow type spacer, a
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perimeter gasket containing the manifold holes and con-
nections to the flow path are die cut from sheets of gasket
material. Into the center of these perimeter gaskets, then,
are inserted plastic "screens", or mats, which provide the
necessary membrane support while still permitting hydraulic
flow through the compartments. Common insert support
materials have been expanded, or corrugated and perforated,
PVC or polypropylene.
Present commercially available electrodialysis stacks
contain approximately 500 membranes, or 250 anion-cation
membrane pairs. These stacks have hydraulic capacities of
the order of 250,000 gpd and conventionally provide a salt
reduction, or demineralization, or 40-60%. The concentrate,
or brine, stream is generally recirculated through the stack
at the same flow rate as the feed stream so as to minimize
pressure differentials across the somewhat fragile membranes.
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Mathematical^ Model
An electrodialysis process flow schematic, upon which
the mathematical model is based, is shown in Figure 3.
The development of the model follows the outline suggested
in Publication No. WP-20-9, "Preliminary Design and Simulation
of Conventional Waste Water Renovation Systems Using the
Digital Computer".
By writing material balances around the control volume
"A" in Figure 3, the following eguations can be derived
for flow and salt concentrations:
Q1 + Q9 = Q3 •»• Q? (1)
and:
Q1C1 * Q9C9 = Q3C3 + Q7C7
Assuming no water transport across the membranes, material
balances written around control volumes "B" and "C" will
establish'the following relationships:
Q2 * Q3 (3)
and:
Q5 « Q6. (4)
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FIGURE 3
Electrodialysis Process Flow Sheet
Fr-nri m
4«
r~
2
• --
*•
i
q
<
B,
1
1
^ np .... ,.,_ *
i
Uf^ J
T Cj
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1
R). ' .8
V \
1
1
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ACID
A
i
1
^aste
DC - Dilute Compartments
CC - Concentrate Compartments
CR - Concentrate Recycle
ACID - Acid Feed
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If FRACT equals the fraction of total influent salt transferred
from diluting to concentrating compartments:
C3 = C2 d-FHACT)
Q2
C6 * C5 "*"
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and:
C6 = C? = Cg (12)
The above equations, then, can be combined to yield:
Q. Q-FRACT QQ
C SB C (—— + —- ) + C —— (13)
In this model, the stream vectors include stream identi-
fication numbers, volume flow rates (MGD), and concentrations
of the various contaminants pertinent to the electrodialysis
process. In the latter regard, the classification scheme
for contaminants is somewhat different from those generally
pertinent to other waste stream processes, in that primary
emphasis is placed on the composition of inorganic, rather
than organic, materials. The concentrations of each ionic
species present are specified in the stream vectors. The
electrodialysis stream vector is:
Contents of Stream Vector for Electrodialysis
Row Fortran Variable
No. Descriptive Parameter Names
2 Volume Flow, MGD SMATX( 2,I),Q
18 Concentration of Dissolved Sodium SMATX(18,I),PNA
19 Concentration of Dissolved Potassium SMATX(19,I),PK
20 Concentration of Dissolved Calcium SMATX(20,I),PCA
21 Concentration of Dissolved Magnesium SMATX(21,I),PMG
22 Concentration of Dissolved Ammonium SMATX(22,I),PNH4
23 Concentration of Dissolved Chloride SMATX(23,I),PCL
24 Concentration of Dissolved Bicarbonate SMATX(24,I),PHCO3
25 Concentration of Dissolved Sulfate SMATX(25,I),PS04
26 Concentration of Dissolved Nitrate SMATX(26,I),PN03
27 Concentration of Dissolved Phosphate SMATX(27,I),PPO4
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The decision vector for the electrodialysis process
contains parameters describing:
1) spacer design geometry, i.e., flow path thickness;
2) membrane properties, i.e., resistivity, current
efficiency and separation factors (see WP-20-AWTR-18)
for each of the ions present in the feed stream; and
3) mode of operation of the stack, i.e., current
density, product stream concentration, waste/
product ratio, waste stream pH, etc.
The electrodialysis decision vector is:
Contents of Decision Vector for Electrodialysis
Row
No. Descriptive Parameter
1 Total Dissolved Inorganic Solids, Product
Stream, ppm
2 Membrane Spacer Thickness, cm
3 Ratio of Spacer Thickness to Mesh Spacing
4 Input Stream Temperature, Deg-P
5 Cation Membrane Resistivity, ohm-sq.cm
6 Anion Membrane Resistivity, ohm-sq.cm
7 Current Efficiency
8 Limiting Current Density Parameter
9 Desired Waste/Product Stream Volume Ratio
10 Maximum Allowable Waste/Product Stream
Volume Ratio
11 Max Allowable Hydrogen Ion Concentration
in Waste Stream
12 Cosine of Mesh Angle, Theta
13 Separation Factor, Sodium
14 Separation Factor, Potassium
15 Separation Factor, Calcium
16 Excess Capacity Factor
17 Separation Factor, Magnesium
18 Separation Factor, Ammonium
19 Separation Factor, Chloride
20 Separation Factor, Bicarbonate
21 Separation Factor, Sulfate
22 Separation Factor, Nitrate
23 Separation Factor, Phosphate
Fortran Variable
Names
DMATX(
DMATX(
DMATX(
DMATX(
DMATX(
DMATX(
DMATX(
DMATX(
DMATX(
1
2
3
4
5
6
7
8
9
,N)
,N)
,N)
,N)
,N)
,N)
,N)
,N)
,N)
r
t
t
t
t
i
t
t
,
PPMOU
TKNS
TDEL
T
RCM
RAM
E
CURK
GAMMA
DMATX(10,N),GMAX
DMATX(11,N),HMAX
DMATX(12,N),COTHE
DMATX(13,N),ANA
OMATX(14,N),AK
DMATX(15,N),ACA
DMATX(16,N),ECF
DMATX(17,N),AMG
DMATX(18,N),ANH4
DMATX(19,N),ACL
DMATX(20,N),AHCO3
DMATX(21,N),AS04
DMATX(22,N),AN03
DMATX(23,N),AP04
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Electrodialysis Performance Equations
The influent salt concentration at Station 1, and the
required effluent salt concentration at Station 3, are
supplied to the program as input. The waste stream salt
concentration at Station 7 is calculated as the maximum
concentration that can be achieved without precipitating
calcium (as carbonate or sulfate) , or as the concentration
resulting from the lowest desirable Q7 to CU ratio supplied
as input, whichever is the smaller.
The repetitive physical unit of an electrodialysis
stack is called a cell-pair and consists of a diluting
compartment, concentrating compartment, and two membranes.
2
The average areal resistivity (ohm-cm ) of the cell pair, as
derived in Appendix A, is:
TKNS 71
RPA = RM
PRACT*CLAMCI U-FRACT) (C7/C1
The areal resistivity (ohm-cm ) at the effluent end of
the cell-pair iss
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The total electrical resistance of one cell-pair (ohm)
is the average areal resistivity divided by the effective
transfer area per membrane:
__ RPA / , f- »
(16)
The D.C. current (amperes) required to remove a given
amount of salt is obtained from Faraday's Law:
96,500*(C,-C,)*Q.*43.9
1 - - E*NCP - <17>
where E is the current efficiency of the process and NCP
is the number of cell-pairs per stack.
The D.C. power (kw) requirement then is obtained from
Ohm's Law:
EOPWR - , (18)
where EP is the applied cell-pair voltage.
The number of electrodialysis stacks required is also
obtained from Ohm's Law:
NSTK = (19)
There, in general , is a limiting value assigned to EP,
that is a complex function of the hydrodynamic design and
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operation of the particular electrodialysis equipment being
used. The expression for the polarization parameter, XICD,
is derived in Appendix A; the appropriate design value for
EP is obtained from Ohm's Law:
XICD*C *RPO
EP im— <20>
The pumping head loss (ft H20) through the electro-
dialysis stacks is calculated:
STKHD = 30 + PGRAD*LENGTH (21)
where 30 ft is the contribution due to piping and manifold
losses, PGRAD is derived in Appendix A, and LENGTH is the
flow path length defined as the ratio of membrane area to
flow path width.
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Electrodiajffsis Process Cost Functions
The goal of this effort was to develop simple relation-
ships that give a good approximation to the cost of com-
mercially available equipment. Data on cost of actual
operating -electrodialysis plants were taken from OSW R&D
Progress Report No. 134, "An Engineering Evaluation of the
Electrodialysis Process Adapted for Computer Methods for
Water Desalination Plants", Mason-Rust, Webster, South
Dakota (1965). Relationships among the various cost
items, particularly relative magnitudes, which were useful
in making functional approximations were given by OSW
R&D Progress Report No. 325, "Hydraulic Design Optimization
of the Electrodialysis Process", by Process Research,
Incorporated (1967). Some values used were in accordance
with conventions recommended by the Office of Saline Water
and are so noted where used in this development. Capital
costs are assumed to be referred to the Engineering News -
Record Cost Index January 1965.
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Capital Costs*
It was generally convenient to divide electrodialysis
capital cost items into three related groups and develop
separate cost equations for each group. The groups are
stack related equipment, D.C. power related equipment, and
auxiliary equipment.
Stack related costs include:
Electrodialysis Stacks
Stack Piping
Distribution Piping
Pumps, Dilute Stream and Concentrate Recycle.
Pumps for delivering feed water from the source to the
plant, and pumps for carrying off product water and waste
water which are usually included in electrodialysis plant
cost calculations were not included here.
D.C. power costs include:
Rectifiers
Process Electrical.
Auxiliary costs include:
Acid Storage Tank
Acid Feed Pumps
Instruments
Miscellaneous Equipment.
*Publisher's Note: Estimates of capital and operating and
maintenance cost presented in this report are low compared
to other authoritative sources. For the most reliable
cost information equipment manufacturers should be consulted.
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The cost of a building to house the plant would be in-
cluded in the cost of an electrodialysis plant operating on
its own. As a part of a waste water treatment facility the
building space would be shared. The building area required
by the ED process itself is calculated and passed along
to the executive program so that it may be combined with all
other building area requirements. Engineering cost, con-
tractor's profit, contingencies and omissions, and cost of
land are not included because they are handled by the
executive system.
Electrodialysis stack materials costs were based on
the following:
Membrane Cost
Membrane Size
Membrane Pairs/Stack
Spacers
Anode
Cathode
End Plate/End Block
Stack Hardware
Manufacturers Assembly Cost
Stack Erection Labor
Erection Labor Cost
Payroll Extras
General & Administrative
$1.00-3.00/sg. ft.
5-10 sq/ ft.
250-300
$.60-1.00 sq. ft.
$26.00/sq. ft.
$4.43/sq. ft.
$114.60/sq. ft.
$72.20/sq. ft.
$4.00/sq. ft. Membrane Area
160 man-hrs.
$4.50/hr.
15%
30%
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The last two values, payroll extras and general adminis-
trative overhead follow OSW conventions.
Combining typical values from the foregoing table gives
an erected stack cost as:
(2 x 275 x (1.00 + 3.00 + 4.00) + 26.00 + 4.43 4 2 x
114.60 + 72.20) x 5.0 + 160 x 4.50 x 1.15 x 1.30 -
$24,700/stack
Stack piping * $750/stack
Distribution piping * $200/stack.
Cost of pumps depends on the capacity of the pumps.
Flow in both the dilute and concentrate stream are essen-
tially equal and are given by:
Ql - Q7
The following values enter into pump costs:
Minimum number of concentrate pumps
Minimum number of dilute stream pumps
Base cost, stainless steel pump
Base cost, cast iron pump
Power cost, stainless steel pump
Power cost, cast iron pump
Stack piping head loss
Pump size scale factor
(22)
2
2
$1800
$1400
$52.50/HP
$30.30/HP
30 ft.
9.1
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Cost of pumps is given by:
(2 x 1400 + 30.30 x STKHD x 03/5.7) x (2 x 9.1/03)°'2 +
(2 x 1800 + 52.50 x STKHD x Q./5.7) x (2 x 9.1/O.j)0'2 «
[6400 + 14.5 x Q3 x STKHD] x (18.2/Q3)0'2
where the exponent 0.2 is a scale factor for pump costs,
and STKHD is the head loss through the stack and its associ-
ated piping.
A factor of 1.4 is applied to each item other than
stacks to account for erection labor. A factor of 1.05 is
applied to account for miscellaneous equipment. Combining
all of the foregoing costs gives
CSTK - 1.05 X 24700 x XNSTK + 1.05 x 1.4 x (750 + 200)
XNSTK + 1.05 x 1.4 x [6400 + 14.5 x 03 x STKHD] x
(18.2/Q3)°-2 (23)
where XNSTK = the number of stacks in the required plant, and
CSTK = the total capital cost of stack related items.
Equation (23) reduces to
CSTK = 27330 x XNSTK + [16800 + 38.08 x Q3 x
STKHD] x Q3~°'2 (24)
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D.C. power related items include rectifiers and other
process electrical equipment. Rectifier cost is made up
of
Rectifier Base $2700
Rectifier Power Cost $63/KW
Number of Stacks/Rectifier 4
So that rectifier cost is:
(2700/4) x XNSTK + 63 x EDPWR
where EDPWR is electrodialysis power in kilowatts.
Process electrical cost is given as
$600/stack + $40/KW of D.C. power
Combining D.C. power items gives
CDC = 1.05 x 1.4 x [(2700/4 + 600) x XNSTK + (63 + 40)
x EDPWR] (25)
which reduces to
CDC • 1874.25 x XNSTK + 151.41 x EDPWR (26)
Auxiliary equipment includes acid feed pumps, storage
for acid and process instrumentation. Data given by Mason-
Rust for the cost of acid storage tanks as a function of
tank capacity lead to the following relationship:
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Tank Cost = .0013 x (TANK SIZE)'715
The size required to hold a 14 day supply is
14 x Qg x 106
Combining these two gives:
.0013 x (14 x 09 x 106)*715
or
167.3 x Q9*715
Acid feed pump costs are based on the following values:
Number of Pumps 2
Pump Base Cost $640
Pump Capacity $101.90/GAL/DAY
so that cost is given by
2 x 640 + 101.9 x 106 x 09
Mason-Rust suggests the following function for process
instrumentation:
9600 + 750 x XNSTK x (XNSTK/4)'*17
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where $9600 is the base cost and $750 is the cost per stack
for a small plant with 4 stacks and
(XNSTK/4)"'17
is a scale factor to adjust down the unit cost of stack
instrumentation in very large plants.
Total auxiliary equipment cost, CAUX, is given by
combining the previous three costs
CAUX = 1.05 x 1.4 x [167.3 x Qg*715 + 1280 + 101.9
x 106 x Qg + 9600 + 750 x XNSTK x (XNSTK/4)~*17 (27)
which reduces to
CAUX = 15993.6 -I- 149.79 x 106 x Qg + 245.9 x Qg*715
+ 1102.5 x XNSTK x (XNSTK/4)"'17 (28)
The total electrodialysis plant capital cost, then, is
the sum of the stack, D.C. power and auxiliary equipment
related costs,
CCAP = CSTK + CDC + CAUX (29)
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Operating Costs
Operating costs for the electrodialysis process consist
of electrical power, membrane replacement, and other costs.
Pumping power is
STKHD x (Q- + Q., x CKWH x 3.15 x 36S/.827
J D
2780.5 x STKHD x Q3 x CKWH
where
and electrodialysis power is
EDPWR x CKWH x 24 X 36S/.9
so that total power cost, CPWR, is:
CPWR - (2780.5 x STKHD x Q3 + 9733.33 x EDPWR)x CKWH (30)
Membrane replacement and stack tear-down costs are based on
a membrane life of five years and stack disassembly frequency
of six times per year. In waste water treatment applications
operating conditions could be such that these figures would
be very much different than would actually be experienced.
Based on a labor rate of $3.50/hr. and a stack dis-
assembly time of 8 hrs./stack teardown cost is:
3.50 x 8 x 6 x 1.15 x 1.30 x XNSTK
- 27 -
-------
and membrane cost is
6.00 X 5 x 275 x .2 x XNSTK
so that membrane replace cost, CREPf is
CREP = 1900 x XNSTK (31)
Other costs include:
Chemicals (Sulfuric Acid)
Operating Labor
Maintenance Materials
Using an acid cost of $30/ton, the cost of acid is:
30 x 7619.7 x Qg x 365 - 83.44 x 106 x Q
Operating labor is
79«;
1.15 x 1.30 x 3.50 x (5.9 x Q3 ) * 365 = 11268 x Q3
where the exponent 0.725 is a scaling factor for large
sized plants.
Conforming approximately to OSW suggested costing pro-
cedures, maintenance materials and supplies are estimated
as 0.35% of plant cost, or in this case
.0035 x (CSTK + CDC + CAUX)
- 28 -
-------
Combining the preceding expressions gives total other
costs, COT, as:
COT = 83.44 x 106 x Og + 11268 x Q3'725 -I- .0035
x [CSTK + CDC + CAUX] (32)
Electrodialysis plant operating costs are the sum of
electrical power, membrane replacement, and other related
costs,
CTOP = CPWR + CREP + COT (33)
Building area, ABLDG, required to include stacks,
pumps and piping, instruments, membrane and parts storage
and chemicals is based upon the following:
Chemicals
37 + (Q3 x ID6)'33
Membrane and parts storage
55 + (Q3 x 106)'4
Instruments
(Q3 x 106)'33
Pumps and- Piping
60 + 20.36 x Q3
and Stacks
127.5 x XNSTK
Combining the above gives
ABLDG • 152 4- 127.5 x XNSTK + 20.36 x Q3 + 2 x
(Q3 x 106)'33 + (Q3 x lO6)'4 (34)
- 29 -
-------
Flow Sheet and Sample Outputs
A flow sheet for the computer program ELECT is
presented in the following figures, 4 through 6.
Sample outputs from the stand-alone version of the
program are given in Tables 1, 2, and 3, for typical
secondary effluent compositions and plant capacities of 1,
10 and 100 MGD, respectively.
- 30 -
-------
FLOW DIAGRAM: SUBROUTINE ELECT
Initialize
SMATX,
IERR
Pick up
Input
Values
Convert
Units, Find
Sums, Etc.
( Electroneutrality
I Satisfied?
>feo
Yes
T
Set:
IBRR(l) =
Negative Separation
Factors Proper?
Yes
Set:
IERR (2)
= 1
-©
c
Positive Separation
Factors Proper?
I Yes
Set:
IERR (3) •
= 1
- 31 -
-------
Find
Solubility
Parameters
c
Sulfate Concen-
tration too High?
res
Set:
IERR(4) •
= 1
No
/HC03 Concentration
V Essentially = 0?
Yes
No
FG - FG at
Desired
Gamma and
Acid Feed=0
Find FG
at HMAX
C
Square Root
Negative?
JNo
T
Set:
IERR(5) = 1
-©
C
Acid Feed Required
at HMAX Negative?
No
Set:
IERR(6)
= 1
- 32 -
-------
c
FG Less at HMAX
at Desired GAMMA?
No
Find FG at
Desired
GAMMA
r
Acid Feed < 0?
Find FG
at HMAX
-©
Find Acid
Feed at
Current FG
'Yes
Set Acid
Feed = 0
f Sulf ate Constraint
V Satisfied?
Yes
No
Reduce
Current
FG
- 33 -
-------
c
FG Too Small?
Yes
Set:
IERR(7) = 1
Find ED
Plant
Design
Values
Find
Cost
Values
Put Output
Values in
SMATX
Print
Sub-
routine
Name
"ELECT"
Acid Feed = 0?
Yes
'No
- 34 -
-------
TABLE 1
Computer Output, I MGD Waste Treatment Plant
CONCENTRATION SEPARATION
IN
130.
.. J 5.
60.
25.
20.
165.
300.
100.
10.
25.
850.
OUT
86.
8*
28.
15.
10.
77.
20" 1 .""
53.
5.
1.7.
500.
FACTOR
.79 SODIUM
1 .14 POTASSIUM
1 .25 CALCIUM
.98 MAGNESIUM
1.15 AMMONIUM
_1 .25 CHLORIDE
.77 BICARBONATE
1.11 SULFATE
1 .22 NITRATE
.72 PHOSPHATE
*100 SPACER_ THJCKNESS'Cil
.100 RATIO OF THICKNESS TO MESH SPACING
70..000 T.a WATER TEMPERATURE*_pEG F.
40.000 RCM=CATION" MEMBRANE RESISTIVITY*OHM-SQ.CM.
40 ..000. _ RAM=ANLQN MJENB RANE RESISTIVIT Y * OHM-SQ•CM •
.900 E=CURRENT EFFICIENCY
.707 COSINE OF.MESH ANGLE.THETA
.083 GAMMA=DESIRED RATIO Q7/Q3
2.000 GMAX=MAXJMgM RATIO Q7/Q3
.001 MAX HYDROGEN ION CONCENTRATION*WASTE STREAM
82.000 LIMITING CURRENT DENSITY PARAMETER*CURK
.010 COST OF ELECTRICITY»$/KWHR
ED POUER-KW
STACK HEAD LOSS-FT.H20
NUMBER OF STACKS
_NUMB£R_ OF. SECJT IF IERS_ ..
BUILDING AREA-SQ.FT.
FLOW PATH WIDTH-IN.
STACK COSTS-S
DC E9PT COSTS .-$.
AUX E9PT COSTS-S
TOTAL CAPITAL-^
POWER COST-CENTS/KGAL
._WEJfflRAN£_ R EP UAC.EMENT.rCENTS /KGA L
OTHER OPERATING COST-CENTS/KGAL
TOTAL OPERATING COST-CENTS/KGAL
INPUT STREAM-MGD
PRODUCT STREAM-MGD
WASTE STREAM-MGD
ACID FEED-GAL/KGAL WASTE
29.9472
40*3505
3602.5841
4
I
if 10. 0871
6.0005
12783LS3481
12031 .3024
24756.3443
164619.9948
1 .0823
2.0822
3.9093
7.0738
1 .0000
.9231
.0769
.3778
*EX1T*
- 35 _
-------
TABLE 2
Computer Output, 10 MGD Waste Treatment Plant
CONCENTRATION
IN
130.
15.
60.
25.
20.
165.
300.
100.
10.
25.
850.
OUT
86.
8.
28.
15.
10.
77.
201 .
53.
5.
17.
500.
SEPARATION
FACTOR
.79
1.14
1 .25
.98
1 .15
1 .25
.77
1 .11
1 .22
.72
SODIUM
POTASSIUM
CALCIUM
MAGNESIUM
AMMONIUM
CHLORIDE
BICARBONATE
SULFATE
NITRATE
PHOSPHATE
-.100 SPACER THICKNESS*CM
.100 RATIO OF THICKNESS TO MESH SPACING
70.000 T=WATER TEMPERATURE* DEG F.
40.000 RCM=CATION MEMBRANE RESISTIVITY.OHM-SQ.CM.
.40_.000 RAM=AN10N MEMBRANE RESISTiyiTY*OHM-SQ .CM.
•900 E=CURRENT EFFICIENCY
.•707 COSINE OF MESH ANGLE.THETA
•083 GAMMA=DESIRED RATIO Q7/Q3
2.000 GMAX=MAXIMUM RATIO Q7/Q3
•001 MAX HYDROGEN ION CONCENTRATION.WASTE STREAM
82.003 LIMITING CURRENT DENSITY PARAMETER*CURK
•010 COST OF ELECTRICITY.S/KWHR
ED POWER-KW
STACK HEAD LOSS-FT.H20
_TQTAL .TRANSFER AREA -SQ.FT. ,,. „
NUMBER OF STACKS
._NIJMBER OF RECTIFIERS
BUILDING AREA-SQ.FT.
FLOW PATH WIDTH-IN.
STACK COSTS-S
DC EQPT COSTS-$ _ _
"A"UX" EQPT COSTS -$"
TOTAL CAPITAL-S
POWER COST-CENTS/KGAL
_MEMBRANE REPLACEMENT-CENTS/KGAL
OTHER OPERATING COST-CENTS/KGAL
jroTAL OPERATING COST-CENTS/KGAL
INPUT STREAM-MGD
_PRQD_UCT STREAM-MGD _
WASTE STREAM-MGD
ACID -FJIED-GAL/KGAL WASTE
299.4718
40.3505
3602.5.8406.
40
10
6448.7172
6.0005
1113064.7588
J 2031 3. 0242
89335.6271
1322713.4101
1 .0823
2.0822
2.4300
__ 5.5945
10.0000
9.2308
.7692
.3778
- 36 -
-------
TABLE 3
Computer Output, 100 MGD Waste Treatment Plant
CONCENTRATION
IN
130.
15.
60*
25.
20.
165.
300.
100.
10.
25.
850.
OUT
86.
8.
28'
15«
10.
7.7.
201 .
53.
5.
1 7.
500 <
SEPARATION
FACTOR
.79 SODIUM
.14 POTASSIUM
.25 CALCIUM
.98 MAGNESIUM
.15 AMMONIUM
.25 CHLORIDE
.77 BICARBONATE
.11 SULFATE
.22 NITRATE
.72 PHOSPHATE
.100 SPACER THICKNESS'CM
.100 RATIO OF THICKNESS TO MESH SPACING
70.000 T=WATER TEMPERATURE* DEG F.
40.000 RCM=CATION MEMBRANE RESISTIVITY»OHM-SQ-CM.
40.000 RAM=ANION MEMBRANE RESISTI VITY»OHM-SQ .'CM.
.900 E=CURRENT EFFICIENCY
.707 COSINE OF MESH ANGLE*THETA
.083 GAMMA-DESIRED RATIO Q7/Q3
2.000 GMAX=MAXIMUM RATIO 97/93
.001 MAX HYDROGEN ION CONCENTRATION*WASTE STREAM
JB2.000 .LIMITING C.UBRENJ DENSITY PARAM£TER*CURK
.010 COST OF ELECTRICITY*S/KWHR
ED POW5R-KW
STACK HEAD LOSS-FT.H20
TOTAL TRANSFER AREA-SQ.FT.
NUMBER OF STACKS
NUMBER OF RECTIFIERS
BUILDING AREA-SQ.FT.
FLOW PATH WIDTH-IN.
STACK "COSTS -$
DC EQPT COSTS-S
AUX EQPT COSTS-S
TOTAL CAPITAL-S
POWER COST-CENTS/KGAL
MEMBRANE REPLACEMENT-CENTS/KGAL
OTHER OPERATING COST-CENTS/KGAL
TOTAL OPERATING COST-CENTS/KGAL
INPUT STREAM-MGD
PRODUCT STREAM-MGD
WASTE STREAM-MGD
_M!D_FEED-GAL/KGAL WASTE
2994.7179
40.3505
360258.4065
393
98
54524.1120
6.1074
10804862.9849
1190010.4918
649901.3938
12644774.8704
1 .0823
2.0458
1 .6556
4.7837
100.0000
92.3077
7.6923
.3778
- 37 -
-------
RECOMMENDATIONS AND SUGGESTIONS
It is our recommendation that a program be promptly
initiated to establish the effects of varying degrees of
pretreatment and operating conditions upon the process
design, and for that matter to establish the optimal design
of electrodialysis equipment for waste water treatment
applications. Such a program should follow the outline
suggested in the Conclusions of our final report under
FWPCA Contract No. 14-12-91, "Membrane Fouling Mechanisms
in the Electrodialysis Process".
Specifically, this program should include but not
necessarily be limited to the following:
1. Quantification of the effects of high temperature
(50°C) operation on both fouling rates and membrane
area reductions;
2. Further examination of the effects of competetive
surface area, in the form of entrained microscopic
air bubbles, on membrane fouling rates;
3. Determination of the effects of length and frequency
of resting periods, both with and without the
addition of enzyme active agents, on stack fouling
rates;
4. Determination of operating voltages (above the
point of polarization) necessary to prevent fouling
and the required additional acid feed to control
scale problems.
- 38 -
-------
Finally, the results of this program should be used as the
basis for electrodialysis design and operating improvements
to be incorporated into the mathematical model presented
here.
- 39 -
-------
PERTINENT REFERENCES
Calvit, B. W. and J. J. Sloan, "Operation Experience of the
Webster, South Dakota, Electrodialysis Plant", Pro-
ceedings, 1st Intl. Symp. on Water Desalination,
Washington, D. C. (1965).
Cooke, B. A., "Some Phenomena Associated with Concentration
Polarization in Electrodialysis", 1st Intl. Symp. on
Water Desalination, Washington, D. C. (1965).
Cowan, D. A. and J. H. Brown, "Effect of Turbulence on
Limiting Current in Electrodialysis Cells", Ind. and
Engr. Chem. 51, 1445 (1959).
Helfferich, Friedrich, Ion Exchange, McGraw-Hill, New York
(1962).
Mandersloot, W. G. B., "The Limitations of Electrodialytic
Water Desalting with Permselective Membranes and the
Requirements for Electrodialytic Equipment", 1st
Intl. Symp. on Water Desalination, Washington, D. C.
(1965).
Mason, E. A. and T. A. Kirkham, "Design of Electrodialysis
Equipment", Chem. Engr. Progr. Symp. Series 5_5, No. 25,
71 (1959).
Mason-Rust, "An Engineering Evaluation of the Electrodialysi
Process Adapted for Computer Methods for Water Desali-
nation Plants", Office of Saline Water, R&D Report No.
134 (1965).
Mintz, M. S., "Electrodialysis—Principles of Process Design",
I&EC 55_, 18-28 (1963).
Ments, M. V., "Water Desalination by Electrodialysis", I&EC
5_2, 148-152 (1960).
Rosenberg, N. W. and C. E. Tirrell, "Limiting Currents
in Membrane Cells", Ind. and Engr. Chem. 49, 780 (1957).
Smith, J. D. and J. L. Eisenmann, "Limiting Current Densities
in Wastewater Electrodialysis", Proc. Fifth Ind. Water
and Waste Conf., 141-164 (1965).
Smith, J. D. and J. L. Eisenmann, "Electrodialysis in
Advanced Waste Treatment", U. S. Department of the
Interior, Federal Water Pollution and Control Adminis-
tration, Publication No. WP-20-AWTR-18 (1967).
- 40 -
-------
Smith, J. D. and J. J. Harrington, "Hydraulic Design
Optimization of the Electrodialysis Process", Office
of Saline Water, R&D Report No. 325 (1968).
Smith, J. D., "Membrane Fouling Mechanisms in the Electro-
dialysis Process", Final Report under FWPCA Contract
No. 14-12-91 (1968).
Smith, J. D. and J. J. Harrington, "An Effective Model for
Limiting Current Density Characteristics of Electro-
dialysis Equipment", presented at 133rd National Meeting
of the Electrochemical Society, Boston, Mass. (May 5-9,
1968).
Speigler, K. S., Ed., Principles of Desalination, Academic
Press, New York (1966).
Solt, G. S., "Influence of Membrane Phenomena on Electro-
dialysis Operation", 1st Intl. Symp. on Water Desali-
nation, Washington, D. C. (1965).
Wilson, J. R., Ed., Demineralization byElectrodialysis,
Butterworths, London (1960).'
- 41 -
-------
APPENDIX A
DERIVATION OP ELECTRODIALYSIS DESIGN EQUATIONS
The areal resistivity (ohm-cm2) of one cell-pair in an
electrodialysis stack is obtained from the summation of the
resistivities of the two membranes and a dilute and concen-
trating compartment, i.e.,
RP = Rm + Rd
The resistivity contribution of the membrane-solution inter-
face is included in the membrane resistance term in this
model. The resistivities of the two solution compartments
are expressed in terms of solution concentrations and compart-
ment thicknesses:
Rc ' (A-3)
where:
t = compartment thickness , cm
A = equivalent conductance, mho-L/cm-equiv.
C = solution concentration, equiv/L
and d, c, are subscripts referring to diluting and concen-
trating compartments, respectively.
- 42 -
-------
Solution concentrations, at any point along the flow
path (con-current flow) are described as a function of the
fractional salt removed at that point:
Cd = C^l-f) (A-4)
Cc - C5 + C^f (A-5)
As a general practice, the two compartmental thicknesses
are maintained equal and the flow rates through the two
compartments are the same:
t - t = TKNS (A-6)
a c
Q2 - Q5 (A-7)
The concentrating stream concentration then can be described
in terms of the total salt reduction obtained through the
process (PRACT) and the outlet concentrate stream concen-
tration (C7) :
C = C_ - C,*FRACT + C,f (A-8)
c / i i
The cell pair resistivity then is obtained by substituting
equations A-8, A-6, A-4, A-5 and A-2 into A-l:
JL - PRACT •«- f
Cl
(Note: The term CLAM is used in the program for A)
- 43 -
-------
At the effluent end of the process, f = FRACT and C.(l-FRACT)
C3. The cell-pair resistivity at this point becomes simply:
"PC - \ *
The averaged resistivity through the entire process is
obtained from the integration:
FRACT
df
(A-ii)
FRACT
£ df
Performing this integration results in the expression:
- Rm
(1-FRACT)
Generalized models for predicting the mass (salt)
transfer characteristics and pumping energy requirements
for electrodialysis systems have been developed by Process
Research, Incorporated, under previous contract with the
Office of Saline Water, U. S. Department of the Interior.
These models are described in OSW R&D Progress Report No. 325
Limiting mass transfer rates are described through a
so-called polarization parameter, (i/C,) , which in turn
d lira
is expressed as a function of fundamental solution and
membrane properties and standard hydrodynamic parameters:
- 44 -
-------
/ 0.6
*•»
2/3
where:
2
i = current density, ma/cm
C, =* dilute stream solution concentration, eq/L
F = Faraday's constant, 96,500 coulombs/equivalent
k' a» empirical constant
2
v = kinematic viscosity, cm /sec
t = distance (cm) between supporting strands of
membrane support material
t , = flow path thickness , cm
z", » electrochemical valence of ionic species j
t = transference number of species j in the membrane
t = transference number of species j in the solution
S3 2
D . =* Fickian diffusion coefficient of species j , cm /sec
e * void fraction of spacer flow path
e = angle between superficial and actual flow directions
V = superficial flow velocity, cm/sec
n * number of cell pairs
a = flow path width, cm
V t
In this model, the term (evcose> is the msiSS transfer
Reynolds Number for the electrodialysis process. The mem-
brane and solution properties and the various constant
coefficients can be lumped together into one term:
- 45 -
-------
CURKV = - — - (A- 14)
For present commerciallv available membranes and tvpical
waste water compositions, CURKV is about 1.3.
The polarization parameter then is described in terms
of hydrodynamic properties only:
V t °'6
1 » l'l ( - ?__) (A- 15)
;
(In the program, the term XICD is used for (i/C^) . Also,
lim
since P_/nat, is used for V , CURKV is modified to:
CURK » (103)°'6CURKV - 82).
Pumping energy requirements are obtained from the
head loss gradient through the electrodialysis process:
hr u2 2V
IT ' ^-^775 - f
(±^.) cose
where:
ht
r= * pressure drop across electrodialysis spacer, cm H20
n « wetted surface area per unit of flow path volume,
cm /cm .
2V
In this model, the terms (flvcOg9) and (jp) are the
hydraulic Reynolds Number and hydraulic diameter, respec-
hL
tively. In the program, the term PGRAD is used for sp.
- 46 -
-------
APPENDIX B
PROGRAM DESCRIPTION
The computer program is for modeling the electrodialysis
process as a unit process in the simulation of advanced
waste treatment plants. The program is not intended to
design a completely self-contained electrodialysis plant.
There are two versions of the program. One is a sub-
routine for use with the "Executive Digital Computer Program
for Preliminary Design of Wastewater Treatment Systems'*.
The second version is an independent program which is
completely self-contained. The two versions are essentially
equivalent except for the handling of input and output.
The subroutine version gets input values from the stream
matrix SMATX, the decision matrix, DMATX, and from other
variables in COMMON. Output values are placed in the
stream matrix and in variables in COMMON.
The self-contained version accepts input values from
an input file, which could be a punched card deck, and puts
output values in an output file, which could be a line
printer or other device as appropriate.
Listings of both versions are given below.
- 47 -
-------
Program Organi 2ation
The program is composed of six parts. Ksch part of
the program i headed by comment cards.
Part 1 picks up input parameters from the stream matrix,
SMATX, and from the decision matrix, DMATX.
Part 2 performs unit conversions such as from ppm to
moles/liter, finds summations of concentrations, and finds
concentrations of each species in the product water stream.
Input stream validity checks, described in detail in the
section on error conditions, are also made.
Part 3 finds allowable waste stream concentration and
required waste stream acid feed based on bicarbonate and
sulfate solubility limitations. The resulting product
stream volume is also found.
Part 4 computes the electrodialysis system design para-
meters required.
Part 5 computes the capital cost values and operating
cost values.
Part 6 puts output stream values in stream matrix.
- 48 -
-------
NOTATIONS
Fortran Name
Description
ABLDG
ACA
ACL
AH 003
AK
AMG
ANA
ANH4
AN03
APO4
AS04
CAC
CADI
CAUX or CCOST(3,N)
CDC or CCOST(2,N)
GDI
CLAM or -A-
CLDI
CPWR or COSTO(1,3)
CREP or COSTO(2,N)
O03K1
COTHE
Building area required, sq ft
Separation factor, calcium
Separation factor, chloride
Separation factor, bicarbonate
Separation factor, potassium
Separation factor, magnesium
Separation factor, sodium
Separation factor, ammonium
Separation factor, nitrate
Separation factor, phosphate
Separation factor, sulfate
Acid feed required, equivalent acid/1 waste
Calcium concentration, mole/1
Auxiliary capital costs, $
D.C. related capital costs, $
Input stream concentration, equivalent/1
Specific solution conductance, mhos/cm per
equivalent/1
Chloride concentration, mole/1
Power cost, $/yr
Membrane replacement, $/yr
Ratio XCAC03/(XK1*XK2) where
XCACO3 = calcium carbonate solubility product
XK2 = second bicarbonate protolysis constant
Cosine of mesh angle, theta
- 49 -
-------
NOTATIONS
Fortran Name
Description
COT or COSTO(3,N)
CSTK or CCOST(1,N)
CURK
EDPWR
E
PG
FGMAX
FGMIN
FRACT
GAMMA
GMAX
HOO
H003D
HMAX
IERR
Other operating cost, $/yr
Stack related capital costs, $
Limiting current density parameter
D.C. power required for electrodialysis
Current efficiency
FRACT/GAMMA (Variable)
FRACT/desired GAMMA
FRACT/maximum GAMMA
Fraction demineralized
Volume ratio of waste stream to product
stream
Maximum allowable waste/product stream
volume ratio
Hydrogen ion concentration, waste stream,
mole/1
Bicarbonate concentration, mole/1
Max allowable hydrogen ion concentration
in waste stream, mole/1
Error indicator array; values defined below
The following table defines the meaning of the various error indications.
If the element listed in the table below is set = 1, the error condition
corresponding to that item exists
ELEMENT
IBRR(l)
Meaning if IERR(I)=1
The difference betwen SMP and SMN exceeds 5%
of SMP. Electroneutrality is violated.
- 50 -
-------
NOTATIONS
Fortran Name
Description
IERR(2)
IERR(3)
IBRR(4)
IERR(5)
IERR(6)
IERR(7)
The difference between SMN and SMCAN is not
within 5% of SMN. Negative separation factors
are improper.
The difference between SMP and SMCAP is not
within 5% of SMP. Positive separation factors
are improper.
Calcium sulfate solubility product is exceeded
by input stream concentrations.
Negative square root was attempted in quadratic
solution for acid feed rate at limiting waste
hydrogen ion concentration.
Minimum brine stream pH (HMAX) is violated even
at zero acid feed.
Calcium sulfate solubility is exceeded even at
the minimum brine stream concentration (GMAX).
NSTK
NRECT
PCA
PCL
PHCO3
PK
PMG
PNA
PNH4
PNO3
PO4DI
POCA
Number of stacks
Number of rectifiers
Input stream concentration of calcium, ppm
Input stream concentration of chloride, ppm
Input stream concentration of bicarbonate, ppm
Input stream concentration of potassium, ppm
Input stream concentration of magnesium, ppm
Input stream concentration of sodium, ppm
Input stream concentration of ammonium, ppm
Input stream concentration of nitrate, ppm
Phosphate concentration, mole/1
Product stream concentration of calcium, ppm
- 51 -
-------
NOTATIONS
Fortran Name
Description
POCL
POHCO
POK
POMG
PONA
PONH4
PONO3
POPO4
POS04
PPND4
PP04
PSO4
Ql
Q3
Q7
Q9
RAM
ROM
SMCAN
Product stream concentration of chloride, ppm
Product stream concentration of bicarbonate,
ppm
Product stream concentration of potassium,
ppm
Product stream concentration of magnesium,
ppm
Product stream concentration of sodium, ppm
Product stream concentration of ammonia, ppm
Product stream concentration of nitrate, ppm
Product stream concentration of phosphate,
ppm
Product stream concentration of sulfate, ppm
Total dissolved inorganic solids, product
stream, ppm
Input stream concentration of phosphate, ppm
Input stream concentration of sulfate, ppm
Input stream flow, mgd
Product water flow, mgd
Waste stream flow, mgd
Acid feed rate, gal. acid/k gal. waste
Anion membrane resistivity ohm-sq cm
Cation membrane resistivity ohm-sq cm
Sum of the products of the equivalents of each
negative species with its separation factor
- 52 -
-------
NOTATIONS
Fortran Name
Description
SMCAP
SMN
SMP
SO4DI
STKHD
T
TDBL
TKNS
TTA
VISC or
WIDTH
WMCA
WMCL
WMHCO
WMK
WMMG
WMNA
WMNH4
WMNO3
WMP04
WMSO4
XCASO
Sum of the products of the equivalents of each
positive species with its separation factor
Sum of the equivalents of each negative species
Sum of the equivalents of each positive species
Sulfate concentration, mole/1
Stack headless, ft - HO (includes manifold
loss) 2
Input stream temperature, F
Ratio of spacer thickness to mesh spacing
Membrane spacing thickness, cm
Total membrane transfer area required, sq ft
Kinematic viscosity of water, sq cm/sec
Flow path width, in.
Molecular weight, calcium
Molecular weight, chloride
Molecular weight, bicarbonate
Molecular weight, potassium
Molecular weight, magnesium
Molecular weight, sodium
Molecular weight, ammonium ion
Molecular weight, nitrate
Molecular weight, phosphate
Molecular weight, sulfate
Calcium sulfate solubility product
- 53 -
-------
NOTATIONS
Fortran Name
Description
XFTNA
XK1
XKDI
XKW
XMGDI
XNH4D
XNADI
XN03D
Flow parameter, I/sec/cm
First bicarbonate protolysis constant
Potassium concentration, mole/1
Dissociation constant for water
Magnesium concentration, raole/1
Ammonium concentration, mole/1
Sodium concentration, mole/1
Nitrate concentration, mole/1
See CLAM
See VISC
- 54 -
-------
Listings
Following are listings of the source code for both
versions of the program and a listing of the data file used
for the sample cases.
- 55 -
-------
. SUBROUTINE ELECT
COMMON/EDERR/ XCASO, SMP,SMN,SMCAP*SMCAN» I ERR ( 7)
COMMON/EDJP/ ABLOG,NSTK,NRECT*EDPWR,STKHD*TTA,WIDTH,Q9
00 5 1=1,7
5 IERRU>=0
00 6 1 = 1 * NROWS
SMATX=SMATX(I,IS1 >
SMATX<2,OS1 >=0.
c
C PART 1- PICK UP INPUT PARAMETERS
C
Q1=3MATX<2,IS1 )*DMATXU6,N)
CKWH=OMATX(1
PPMOU=DMATX(
TKNS=DMATX( /N)
TDEL=OMATX(
T=DMATX( ,
RCM=DMATX<
RAM=DMATX(
E=OMATX< *N
CURK=DMATX<
GAMMA=DMATX<
GMAX=DMATX<
HMAX=DMATX<
COTHE=DMATXC
ANA=DMATXC
AK=DMATX<
ACA=DMATX(
AMG=DMATX(
ACL=DMATX(
AHC03=DMATX<
AS04=DMATX( »N)
AN03=OMATX< >N>
AP04=DMATX( »N)
PNA=SMATX( ,131)
PK=SMATX<
PCA=SMATX<
PMG=SMATX( ,131)
PNH4=SMATX<
PCL=SMATX(
PHC03=SMATX( ,131)
PS04=SMATX< *IS1>
PN03=SMATX( ,IS1 )
PP04=SMATX< ,IS1 )
C
C PART 2- PERFORM UNIT CONVERSIONS, PPM TO MOL/LTR, ETC.
C SUrt CONCENTRATION VALUES* ETC.
C
WMNA=22.9898E3
WMK=39.102E3
WMMG=24*312E3
- 56 -
-------
WMCL=35.453E3
WMNH4=18.03858E3
WMHCO =61 .0094E3
WMS04=96.0616E3
WMN03=62»0049E3
WMP04=84»949E3
XNADi=PNA/WMNA . . . .
XKDI=PK/WMK
CADI=PCA/WMCA .
XMGDI=PMG/WMMG
CLDI=PCL/WMCL
XNH4D=PNH4/WMNH4
HC03D =PHC03/WMHC.O. .............. _
S04DI=PSQ4/WMS04
XN03D -PN03/WMN03 ............................ . . . . ..
P04DI=PP04/WMP04
SMP=XNAni+XKQI+2.*CADI+2-*XMGPJ _ + XNH4D
SMN=CLOI+HC03D *2.*S040I +XN03D + P04DI * 1.5
_PPMT*PNA+P.K+PQA+PMG+PC,LtPliC03+PS04+PN03 + PP04 +PNH4
sijMCI=SMP-SMN+HCd30
SMCApaANA*XNApI+AJK*XKJ)I*ACA*CApI*2.+AMG*XMQOI*2.+ANH4*XNH4D
SMCAN=ACL*CLDI+AS04*S04DI*2.+
1 ANp3*XN03p+HC030*AHC03*AP04*P040I*l .5
GDI =.5*
RAC1*AK_)_
.-FRACT*A'MG>
.-FRACT*ANH4)
PQHCO =PHC03*U .-FRACT*AHCQ3>
POS04*PS04*U .-FR ACT'* AS 04)
___
POCA=PCA*<1 .-FRACTfAC'A) "
P QP 04rPPQ4*l L^jiFR AC T*AP 04 >
TPdUT»P6NA+PbK+POCA+P6MG+PONH4+POCL+POHCO+POS04*PON03+POP04
C_ _ _____
C ERROR CHECK INPUT "VALUES
C _______ __ .
IF(ABS(SMP-SMN)-.05*SMP)832*832*830
830 CONTINUE
IERRC1)»l
JB32 CONTINUE _
IF(ABS
-------
C
C
C
7110
WASTE STREAM ACID FEED BASED ON SULFATE AND
BICARBONATE CONCENTRATION.
IF7110*71 10*7120
XKW = .13E-14*(2.3>**«T-32.)/18.)
GO TO 7150
7120 IFC113.-T) 7130*7138*7143
7130 XKW = 4.0E-14*<4«0)**«T-1 13.)/45.)
GO TO 7150
7140 XKW = 1 .47£-14*<2.72>**«T-86.>/27.)
7150 CONTINUE
IFCT-70.) 7210*7210*7220
7210 XCASO * /l 36 • >**2
GO TO 7270
7220 IF(T-103.>7230*7230*7240
7230 XCASO = 2.4E-4
GO TO 7270
7240 IFCT-130.) 7250*7250*7260
7250 XCASO » (2 . 1 5* <0 • 7953488 ) **« T- 100 • ) /30 . )/l 36 . ) **2
GO TO 7270
7260 XCASO = (1 .71*<0.7427)**<(T-130.)/30.)/136.)**2
7270 CONTINUE
C03K1 =10.** «12343.5/
C
C
._ CL...
-_.417
. 619
505
C
__C
C
__51fl_
. 20 „
C
CHECK SULFATE CONSTRAINT TO SEE IF IT MAY BE BINDING
IF=t
GO TO 1000
CONTINUE ... ...
FGMIN=FRACT/GMAX
IF < CADI *HCQ3D-1 .£-30)505*505*510
FGsFGMAX
IACID=2
.CHECK, TO J5.EE IF.HMAX ..LIMITS. H C 03 _C_ONCE NT RATION
C2F2=ACA+AHC03
HCO=HMAX* FGAM FROM EQN 2
S = l .-(C3F2*HMAX*(XK1+HMAX)) _________ _ _______
S=C2F2**2-4.*C1F2*S
- 58 -
-------
IF (S) 110* 130* 130
110 IERR<5)=1
GO TO 1000
130 FGs(-C2F2+SQRT(S)>/C2.*ClF2>
CAC=SUMCI+FG*SMCIA -XK1*HC03D *(!•+
1 FG*AHC03>/CXK1+HMAX)+HMAX-XKW/HMAX
C
C IF CAC IS NEGATIVE'ERROR
C
IF 140.155*155
140 IERR(6)=1
GO TO 1000
155 IF(FG-FGMAX>520*520*515
515 FG=FGMAX
C
C FIND H TO SATISFY HC03 FOR CURRENT FG
C (THIS IS RE-ENTRY FROM 671.) FIND CAC REQUIRED.
C
520 B*XK1
C=-(FG*FG*ACA*AHC03+FG*+1•)*CADI*HC03D /C03K1
HCO»<-B+SQRT(B*B-4.*C»/2.
IFCHCO-1.£-35)640*640*630
.C . .
C IF HCO IS 'ESSENTIALLY' ZERO THIS CONSTRAINT CAN'T BIND
C
630 CONTINUE
CAC«SUMCI+FG*SMCIA -XK1*HC03D *(1.+FG*AHC03>/(XK1+HCO)
1 +HCO-XKW/HCO
IF(CAC>640*640*650
640 CAC*0.
IACID=2
650 CONTINUE
.C
C NOW HAVE FG*CAC DESIRED FOR HC03 CAND HMAX).
C MAY HAVE TO ADJUST DOWN TO SATISFY S04-
C (THIS IS FG RE-ENTRY FOR CAC=0.J
C _ .
XLM3FG*FG*ACA*AS04*CADI*S04DI+FG*«ACA+AS04>*CADI*S04DI
1 +CADI*ACA*CAC>+CADI*S04DI+CADI*CAC-XCASO
IF(XLM)470*470*660
C
C IF XLM IS NOT>0 S04 CONSTRAINT IS SATISFIED.
_C
C TRY REDUCING FG BUT NOT BELOW FGMIN
C
660 IF
Q3=Q1-Q7
- 59 -
-------
Q9=Q7*CAC/34.7
C THE CONSTANT ABOVE* 34.7* IS BASED ON 93ZH2S04
C
C
C PART 4- COMPUTE ELECTROOIALYSIS SYSTEM DESIGN VALUES
C
FT = Q3 * 43.8079
C XFTNA=FLOW PARAMETER- FT/NA> LTR/SEC/CM
XFTNA=2.412E-3
CLAM = 0.1*EXP(.01 l*(T-68.»
VISC = .01*EXPC-.011*CT-68.»
RM = *«1 .-.393*
1TDEL)*COTHE>**.6)
RN=XFTNA*1000/((1.+TDEL)*VISC*COTHE>
HDIAM=TKNS*<1 -3.14159265*TDEL/8)/( 1+TDEL)
PGRAD=VISC**2*C.023*RN+6«98E-5*RN**2>/
XIGD=CUHLI /'TKNS*XFTNA**.6
RPO=RM+TKNS/
XKPP=9.65E+07*(FRACT*RM+TKNS/(CLAM*CDI>*
1 ALOG <1 ./«! .-FRACT)*U .-FRACT*SOL) » )/C E*RPO*< 1 .-FRACT»
XKP=96.5*CDI**2*FRACT*U «-FRACT)/E
XNAP= XKPP/XICD+FT
EDPWR=XKP*RPO*XICD*FT/t000.
PMH20=PGRAD*XNAP/FT*XFTNA/100.
STKHD=3 .281*PMH20+30.
TTA = XNAP * 1.0764E-3
CURDE =96500.*CDI*FRACT*FT/E/TTA
ELL=TKNS/TDEL*.3937
XNA=FT/XFTNA
NSTK=TTA/917.+.9
XNSTK=NSTK
NRECT=XNSTK/4.+.5
IF(NRECT)13»13*14
13 NRECT = 1
14 CONTINUE
WIDTH=XNA*.3937/CXNSTK*275.)
C
C PART 5- COMPUTE COST VALUES
C
CCOST(1*N)=27330.*XNSTK+(16800.+38.08*Q3*(STKHD))*Q3**<-.2)
CCOSTC2/N)=1874.25*XNSTK+151.41*EDPWR
CCOST(3*N>=15993.6+1 49.79E6*Q9+245.9*G>9**.71 5
1 +1102.5*XNSTK*(XNSTK/4.)**(-•17)
COSTO(1*N)=(2780.5*STKHD*Q3+9733.3333*EDPWR)*CKWH
COSTO(2»N)=1900.*XNSTK
COSTO(3*N)=83.44E6*Q9+11268.*Q1**.725+.0035*CCCOST<1*N)+
.1 CCOST<2*N)+CCOST(3*N)>
A8LDG=152.+127.5*XNSTK+20.36*Q3+2.*(Q3*I.E6)**.33+(Q3*i.£6)**.4
GAMMA=FRACT/FG
C
C PART 6- PUT OUTPUT STREAM VALUES IN OUTPUT MATRIX*ETC.
C
- 60 -
-------
SMATX< ,OS1>=PONA
SMATXC *OS1>=POK
SMATXC *OS1)=POCA
SMATXC *OS1>=POMG
SMATX< »OSl>sPONH4
SMATX( *OSD=POCL
SMATXC *OS1>=POHC03
SMATXC *OS1>=POS04
SMATXC *OS1)=PON03
SMATXC *OS1)=POP04
SMATXC2»OSl)=Q3
SMATXC ,OS2)aCPNA-PONA)/GAMMA
SMATXC »OS2)=CPK-POK)/GAMMA
SMATXC »OS2)sCPGA-POCA)/GAMMA
SMATXC *OS2)=CPMG-POMG)/GAMMA
SMATXC ,OS2>=CPNH4-PONH4)/GAMMA
SMATXC *OS2)=CPCL-POCL)/GAMMA
SMATXC ,OS2>=CPHC03-POHC03)/GAMMA
SMATXC »OS2>=CPS04-POS04>/GAMMA+CAC*WMS04/2.
SMATXC *OS2)=CPN03-PON03)/GAMMA
SMATXC ,OS2)=CPP04-POP04)/GAMMA
SMATXC2,OS2)=Q7+Q9
Q9=CQ9/Q7)*1000.
1000 CONTINUE
199 FORMATC5X»5HELECT>
PRINT 199
RETURN
END
- 61 -
-------
L = b
IN = 2
READC IN/b>PNA*PK*FCA*PMG*PNH4,PCL*PHCG3»PS04>PN03*FP04
IF(PI\1A>4, 7, 4
READC iN>b >ANA* AK* ACA» AMG* ANH4* ACL* AHC03»Aii04» ANOS* AP04
"~ ........ IF(Q1)6,3*6
6 READC IN*b)GAI*iMA.» GMAX*HMAX*C01HE»PHM
b FORMATC 10F7. 1 )
999 FORMATC1H1)
WMNA=22.9898E3
tot"iCA-:40.08L3
IWfiMG=24. 312E.3
MCL=3b.4b3E3
WMNH4=18.038b8E3
WhHCO =61 .0094E3
WMS04=96.0616E3
WMN03=62.0049L3
WMP04=84.949E3
XNADI=PNA/WMNA
XKDI = PK/l'.;MK
CADI=PCA/^MCA
HC03D =PHC03/WMHCO
XN03D_=PNg3/>MNQ3.
P04Di=PPG4/WMP04
.. SMP_=XNADIt.XKD!_+2...*CADI+2.*Xtt.GPI . + XNH4D
SMN=CLDI+HC03D +2 . *S04DI +XN03D + F04DI * 1.5
PPM7SPNA + PK + PCA + PMG+PCL + PHCP3 + PS04 + PN03 + .P.P04... +PNH.4
SUMCI=SMP-SMN+HC03D
'
CDI = . b* ( 'SMP + SKN )
CIAI = ANA*PNA + AK*PK + ACA*PCA + . AM.G*PMG. +ANH4*PNH4 + .......
1 ACL*PGL + AHC03*PHC03 + AS04*PS04 + AN03*PN03+APO 4* PP04
SMCIA =SMCAP-S^CANj-HCjp3.P..*AHC.03 ...... .................. __________ ......... _„..._. ........ ._.,
"FRACT = VPPMT - PPMOU >/CIAI
FGMAX=FRACT/GAMMA ______________________ _______ ___________ ........ ...._ ..... .. __ ....... _..
PCJNA=PNA*"( 1. -FRACT*ANA )
POK=PK*( 1 .-FRAC1*AK) _ _ ...... . ...... .. ....... _______
"" POM~G=PMG* ( 1 ."-FRAC1 *AMG)
POCL = PCL*( 1 .-FRACT*ACL) ...... . ... __ ......... . _ .. ...... _______________________________________________
"" PNH4*c"i .-FRAC1*ANH4)
-. =PHCQ3*C 1 . -FRAC1*AHC03.) _____ ........ __________ ....... ______________________ ..... _________
POS04=PS04*( 1 . -FRACT*AS04)
= PCA*( 1 .-FH ACT* AC A)
POP04 = PP04*( 1 . -FKACT*AP04)
- 62 -
-------
C
C" EkhOK CHECK INPU'l VALUES
C
I F (ABS ( SNP -SfrN > - • 0 b* Stop )8 32 • B 32, 8 30
830 CONTINUE
WKI1L(L.»S31 >
831 FOKMATC44H ELECT KONEU1KAL IT Y IS NOT WITHIN 5% AS GIVEN) ....
832 CONTINUE
IF(Abi>(i3MN-SMCAN>-.05*StoN>83Sj83b>833
'833 iukiTE!SMN,SMCAN
834 FOKMAK34H SEPARATION FACTORS IMPROPER.SMN= E 1 2 . A, 7H .SMCA.N = E 1 2 . 4)
" 8 3S "I F ( ABS C sKiP - ShC AP ) - . 05* SMP ) 8 38 * 8 38 * 8 3 6
836 WMIECLjSSTJbMPjbfiCAP
837 FOftMAT(34H SEPAKA1ION FACTORS I MPF.OPER. SKP= E12.4,7H SMCAP = E12-4)
838 CONTINUE
IF(T-8b.)7110,7110i7120
7110 XKh = .13E-14*(2.3>**C(1-32. )/lg. )
GO TO 7150
7120 IFC113.-1) 7130*7130*7140
7130 XKVv = 4.fe)E-1 4*( 4.0)**( (T-l 13. )/45. )
GO TO 7lb0
"7140 XKW = 1.47E-14*(2.72)**((T-86. )/27. )
7150 CONTINUE
IFCT-70.) 7210.7210.7220
7210 XCASO = « 1 .9 + 0.2*(T-40.)/30.)/136.)**2
GO TO 7270
7220 IFO-103. )7230. 7230> 7240
7230 XCASO = 2.4E-4
GO TO 7270
"7240 IFU-130.) 72b0* 72b0, 7260
72b0 XCASO - (2.1b*C0.79b3488)**((1-100.)/30.)/136.)**2
GO 10 7270
7260 XCASO = (1.71*(0.7427>**((1-130.)/30.)/136.)**2
7270 CONTINUE
C03K1 =10.** ((12343.5/CT+491.7)>-26.7bSSb+.023568*
-------
C NOW HAVE FG*CAC DESIRED FOR HC03 (AND HMAX).
_C MAY HAVE TO ADJUST DOWN TO SATISFY SQ4.
C (THIS IS FG RE-ENTRY FOR CAC=0.)
_c ;
XLM=FG*FG*ACA*AS04*CADI*S04DI+FG*C(ACA+AS04)*CADI*S04DI
1 +CADI*ACA*CAC)-*-CADI*S04DI+CADI*CAC-XCASO
IF(XLM)470*470,660
_C
C IF XLM IS NOT>0 S04 CONSTRAINT IS SATISFIED.
C
C TRY REDUCING FG BUT NOT BELOW FGMIN
_C
660 IF(FG-FGMIN)665»665*670
665 WRITE(L*666)
666 FORMAT(53H SULFATE NOT SATISFIED AT MINIMUM WASTE CONCENTRATION)
GO TO 470
670 FG = FG*GMP
671 GO TO (520*650),IACID
470 CONTINUE
CMAX = GDI * ( l.+FG)
Q7=Q1/(FG/FRACT+1•)
Q3=Q1-Q7
Q9=Q7*CAC/34.7
C THE CONSTANT ABOVE* 34.7* IS BASED ON 93%H2S04
C
199 FORMAT(42H ERROR IN ELECTRODIALYSIS DESIGN PROBLEM )
FT = Q3 * 43.8079
_C XFTNA=FLOW PARAMETER- FT/NA, LTR/SEC/CM
XFTNA=2.412E-3
CLAM = 0.1*EXP(.011*(T-68.))
VISC = .01*EXP(-.01l*(T-68.>)
RM = (RAM»RCM)*EXP(-.01 l*(T-68. ))
SOL = CDI/CMAX
CURL I =_CU_RK_* T_PEL*_*. 4/ ( < VI SC** . 9 3) * ((1. -. 393*
1TDEL)*COTHE)**.6>
RN=XFTNA*1000/( C 1... -»-TDEL )*VI SC*COTHE )
HDIAM=TKNS*(1-3.14159265*TDEL/8)/(l+TDEL)~
PGRAD=VISC**2*( .023*RN-*-6.98E-5*RN**2)/(HDIAM**g.75»COTHE)
XICD=CURLI /TKNS*XFTNA**.6
-FRACT )+SOL)
= 9.65E+07*(FRACT*RM-»-TKNS/(CLAM*CDI)*
1 ALOG (1«/((1.-FRACT)*(1»-FRACT*SOL))))/(E*RPO*(^.-FRACT))
XKP=96.5*CDI**2*FRACT*(1.-FRACT)/E
XNAP= XKPP/XICD*FT
EDPWR=XKP*RPO*XICD*FT/1000.
PMH20=PGRAD*XNAP/FT*XFTNA/100 . ;
STKHD=3.281*PMH20+30.
TTA = XNAP * 1.0764E-3
CURDE =96500.*CDI*FRACT*FT/E/TTA
ELL=TKNS/TDEL*.3937 .
XNA=FT/XFTNA
NSTK=TTA/917.+.9
XNSTK=NSTK
NRECT=XNSTK/4.+.5
- 65 -
-------
13
14
IF(NRECT) 1 3* 13, 14
NRECT=1
CONTINUE
WIDTH=XNA* .3937/(XNSTK*275. )
CSTK-a7330« *XNSTK+( 1 6800 . +'JC) «08*Q3*( STKHD)) *( •'' * •* f -.2)
CDC=»°7/..2b*XNSTK+lbl .41*^ r >"'R
M 102. 5*XNSTK*(^'f TK/4. >**<-. 17)
CAPsCSTK+CDC+CAUX
CREP=1900.*XNSTK
COT=83. /i/'FM^o-* i j?68.*Ql**« 725+. 0035*
r
r
C
C
r
OPERATING COSTS IN CENTS/KGAL ARE. RA^n ov TN'pin; FLOW SO THAT.
COST IS PER I'IVTT n(r i-^FTE WATER TREATED. TO FIND COST PET: I 'N' T T
OF USABLE WATER PRODUCED REPLACE r' 1 T *• ^HF FOLLOWING EXPRESSIONS
COT=COT/Gl/3650.
" CREP=CREP/Q 1/3650.
ABLDG=152.+127.5*XNSTK+20.
1000 CONTINUE
Q9 = C&)9/Q7)*1000.
._IFCPRNT)30, 30*21
21 CONTINUE
950 FORMATC 30H CONCENTRATION
951
952
"953"
954
"955
956
957
958
"9b9
960
961
962
FORMATC
FORMATC
FORMATC
FORM AT C
FORMATC
FORMAT(
FORMATC
_FO,RMATC
FORMAT <
FORMATC
FORMATC
FORMATC
WRITECL
30H
F8
F8
F8
FB"
F8
F8
r.8.
F8
F8
F8
F8
* 9
9 9
•0'F.9
.0*F9
.0*F9
.0*F9
.0,F9
.0,F9
•0'F9
.0* F9
.0*F9
.0jF9
.0*F9
50)
IN
.0»F
i'0*F
.0*F
.0*F
.0,F
.0*F
.0*F,
.0, F
• 0*F
.0*F
•0.
1
0
•
10.
1
1
1
0
0
0
10
1
1
1
1
/
0
0
0
0
/
2*
2;
OUT
7H
10H
•_2*8H .
•
•
•
•
,
2*
2*
2>
2*
2,
10H
9.H
9H
J2H
8H
•2/8H
•
}
2>
10H
36*G3 + 2.*(Q3*1«E6>**.33+ 9 52 ) PNA* PONA, ANA
WRIjrECL*953>PKjPOK*AK .. _
WRITE"CL/954)PCA*POCA/ACA
__
WRI TEC L956 OPNH 4PONH4* ANH4
WRIJJLC Lj> 9 5 7 ) PCL ,, P.QCL *_A£L_
WRITE(L>958)PHC03*PbHCO>AHC03
WRITE(L,960)PN03*PON03>AN03
WKITE(L*961)P.P04»PP.PQ.4J!AP0.4_
WRITE(L,963)TKNS
- 66 -
-------
lvKITE(L,964)TDEL
WRITET
WRITE(L,966)HCM
lvkITE(L,?67)RAM
WRITECL,968)E
963
964
965
966
967
"968
969
970
971
'972
973
T74"
30
toKITEGAMMA
WRITECL,971 >GMAX
WRITECL,972)HMAX
WRITECL,973)CL'RK
toRITLCL,974>CKtoH
FORMATCF10.3,20H
FO'RMA'TC Fife). 3/35H "
FGKMATCFlia.3*28H
FGRMATCF10.3,43H
FORMAT(F10.3*43H
FORKATCF10.3,21H
FCRMAT
RCM=CATION MEMBRANE RESI STI V1T Y, OHM- SO . CM. )
RAM=ANIOl\ MEMBRANE RES I SI I VII Y, OHM-SQ . CM. )
E=CbKRENT EFFICIENCY )
COSINE OF MESH AN GLE, 1 HE! A- )
GAMMA = DESI RED RATIO Q7/Q3 )
GMAX=MAXIMUM RATIO Q7/Q3 )
"MAX HYDROGEN ION CONCENTRATION, WASTE STREAM
LIMITING CURRENT DENSITY PARAMETER, CURK )
COST OF ELECTRI CI TY, S/KVvHR //)
WRIJE904)NSTK
toRnENRECT
WRITE(L*920)ABLPG
WKl"TETL/906> WIDTH
UR1TE(L,908)CSTK
WRITE (1/909) CDC
WRnECL,910)CAUX
WR I_TE_(L * 9 1 1 ) CP WR
WRlfE(L,9l"2)CREP
WRITE(L.,913)COT
WRITYCL,919)OP
WRITE
-------
9f3 FORMAT<32H OTHER OPERATING COST-CENTS/KGAL F15.4)
91 ''
916
917
918
9 19
920
1001
7
FORMAT (32H
FORMAT ( 32H
FORMATC32H
FORMAT <32H
FORMATC32H
FORMAT ( 32H
FORMATC 32H
GO TO 8
CONTINUE
CALL "EXIT
END
INPUT STREAM-MGD
PRODUCT STREAM-MGD
WASTE STREAM-MGD
ACID FEED-GAL/KGAL WASTE
TOTAL CAPITAL- £
TOTAL OPERATING COST-CENTS/K GAL
BUILDING AREA-SO.FT.
Fl
Fl
Fl
Fl
Fl
Fl
Fl
b.
5.
b.
b.
5.
b.
5.
4)
4)
4)
4)
4)
4)
- 68 -
-------
THE FOLLOWING IS THE DATA FILE USED TO PRODUCE THE SAMPLE OUTPUTS*
130. 15.
• 79 1.14
10. 500.
.0833338.
100. S00.
.0833332*
1 . 500•
•0833332.
60.
1 .25
• 1
.001
.1
.001
.1
.001
25.
.98
.1
.707
.1
.707
• 1
.707
20.
1 .15
70.
1 .
70.
1 •
70.
1 .
165.
1 .25
40.
40.
40.
300.
.77
40.
40 .
40 <
100.
1 .11
.9
.9
.9
10.
1 .22
.01
.01
• 01
25.
.72
82.
82.
82.
- 69 -
-------
VARIABLE NAMES: DECISION MATRIX
THE FOLLOWING VARIABLES MUST BE PROVIDED AS INPUT TO THE
ELECTRODIALYSIS SUBROUTINE VIA THE DECISION MATRIX,DMATX.
THE NAMES LISTED HERE ARE THE FORTRAN VARIABLE NAMES USED WITHIN
THE SUBROUTINE.
TEXT PROGRAM
NAME NAME
PPMOU
TKNS TKNS
TDEL TDEL
T
RCM
RAM
E E
CURK CURK
GAMMA
GMAX
HMAX
COTHE
ANA
AK
ACA
AMG
ANH4
ACL
AH CO 3
AS04
AN03
AP04
NOMINAL
VALUE
500
. 1
. 1
70.
40 .
40.
.9
82.
.001
. 707
. 79
1.14
1.25
.98
1.15
1.25
.77
1.11
1 .22
.72
DESCRIPTION
TOTAL DISSOLVED INORGANIC SOLIDS*
PRODUCT STREAM.* PPM
MEMBRANE SPACER THICKNESS, CM.
RATIO OF SPACER THICKNESS TO MESH SPACING
INPUT STREAM TEMPERATURE, DEG-F .
CATION MEMBRANE RESI STI VI TY, OHM-SG . CM.
ANION MEMBRANE RESI STI V I TY, OHM- SQ . CM .
CURRENT EFFICIENCY
LIMITING CURRENT DENSITY PARAMETER
DESIRED WASTE/PRODUCT STREAM VOLUME RATIO
MAXIMUM ALLOWABLE WASTE/PRODUCT
STREAM VOLUME RATIO
MAX ALLOWABLE HYDROGEN ION CONCENTRATION
IN WASTE STREAM
COSINE OF MESH ANGLE,THETA
SEPARATION FACTOR, SODIUM
SEPARATION FACTOR* POTASSIUM
SEPARATION FACTOR, CALCI UM
SEPARATION FACTOR, MAGNESI UM
SEPARATION FACTOR, AMMONI UM
SEPARATION FACTOR, CHLORI DE
SEPARATION FACTOR, BI CARBONATE
SEPARATION FACTOR, SULFATE
SEPARATION FACTOR, NI TRATE
SEPARATION FACTOR, PHOSPHATE
t
- 70 -
U.S. GOVERNMENT PRINTING OFFICE:1970-0-408-309 516
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