Page 77 - Membranes for Industrial Wastewater Recovery and Re-Use

Membrane technology 57

hand, the trend is linear for constant flux operation. The trend in the
residual membrane permeability, that is the permeability of the “permanently
fouled” membrane as reflected in the trend in the minima for the backflush cycles
in Fig. 2.22, also tends to be exponential or pseudo-exponential. Whether
constant flux or constant pressure operation, the mean energy consumption
relates to the mean membrane permeability over a cleaning cycle.

Electrodialysis
In electrodialysis the total power consumption is the product of the voltage and
the current. Since the voltage relates directly to the current by the resistance
according to Ohm’s law, the specific energy demand is critically dependent upon
the current and electrical resistance. The applied current i is directly
proportional to the total equivalent quantity of counter-ions or co-ions
extracted:

(2.25)

where Q is the flow through the stack, F is the Faraday constant, AC is the
change in the diluate concentration in eq m-3 from inlet to outlet, N is
the number of cell pairs (the number of desalinating or concentrating cells in the
stack) and 6 is the current efficiency (normally 85-95%). The energy demand is
then given by:

E = i2R/OQ (2.26)

where R is the overall electrical resistance in ohms, and relates to the cell pair
resistance RCP:
R = RcpN (2.27)

If scaling can be overcome and the path length can be extended by staging the
principal constraint placed on the recovery 0 in Equation (2.26) is from
electrodialysis reversal (see below). Because there is no osmotic pressure
limitation in electrodialysis, and because the concentrate and diluate streams
can be completely segregated, further efficiencies are obtained by recycling of the
concentrate stream, which then decreases both the concentrate waste volume
and the electrical resistance across the stack. For large-scale systems, recoveries
in excess of 80% are normal.
The cell pair electrical resistance is given by:

(2.28)

where the subscripts conc and dil refer to the concentrate and diluate
compartments and CEM and AEM refer to the cation and anion exchanging
membranes. The concentrate resistance is normally no more than 20% of the