Membranes - Principles of Chemical Separations with Environmental Applications - page 259

where I = current in amperes (A)

F = Faraday's constant (96,500 A · s / g equivalents removed)

E c = current efficiency (fraction).

The current efficiency and the electrolyte removal are determined experimentally, and
depend on the specific stack and feed conditions. The value of E c is typically 0.90 or
more, while E r usually ranges from 0.25 to 0.50.
Since the same electrical current is passed through all of the cells in a stack, it is used
n number of times ( n

= the number of cells). The current for the entire stack is:

FQNE r
nE c

I = . (9.19)

Two additional terms for an electrodialysis process are the current density and the
normality of the feed water:

current
membrane area

Current density =

equivalents
volume of solution .

Feed water normality =

The current density to normality ratio describes the capacity of an electrodialysis cell to
pass an electric current. This ratio may vary from 400 to 700 (when the current density is
expressed as mA

cm 2 ). If the ratio is too high, regions of low ionic concentration will form
near the membranes, which results in polarization. This causes high electrical resistance
and a higher electrical consumption.
The power ( W ) required for an electrodialysis stack for treatment of a particular feed
water is found from Ohm's Law:

/

RI 2 V = RI and W = VI = .

Here, V is the voltage, and R is the resistance, which must be obtained experimentally and
are specific for certain stack and feed water conditions.

Example 9.5: electrodialysis

Problem:
An electrodialysis stack having 100 cells is to be used to partially demineralize
100,000 L

L and the cation or
anion content is 0.066 gram equivalent weights per liter. Pilot-scale studies using a
multicellular stack have been made. It was found that the current efficiency, E c ,was
0.9, the efficiency of salt removal, E r , was 0.5, the resistance was 4.5 ohms, and the
current density/normality ratio was 500. Determine:
(a) the current, I , required; (b) the area of the membranes; (c) the power required.

/ day of wastewater. The salt content is 4000 mg /