Page 76 - Membranes for Industrial Wastewater Recovery and Re-Use

56 Membranes for Industrial Wastewater Recovery and Re-use

(2.24)

where Q, is the feed flow rate to the module and fouling is ignored. In Equation
(2.24), the pressure losses per unit flow through the membrane channels on the
retentate side are represented by dP/dQ. This factor can be estimated from
the Hagen-Poiseulle equation, but is normally obtainable from the membrane
supplier. An allowance can be made for fouling through an empirical correction
factor. The rate of fouling in most reverse osmosis applications is normally low,
since fouling is routinely suppressed by appropriate pretreatment based on
chemical addition (Section 2.4.3).
In the case of filtration, the osmotic pressure term (the last term in Equation
(2.24)) does not apply but the effects of cake formation and fouling on operating
pressure cannot be ignored. Large-scale dead-end filtration plant operates with a
backflush cycle actuated either at fixed intervals or when the membrane
permeability has decreased to some pre-identified level. Since the backflush
invariably fails to entirely recover the original membrane permeability, a more
rigorous cleaning cycle, usually involving aggressive chemicals, is initiated
again either at fixed intervals or when once the permeability of the backflushed
membrane has declined to some other level. The calculation of energy
consumption per unit volume must therefore incorporate the effects of
downtime, specifically the energy consumption of the backflush and duration
of the backflush and cleaning cycles (Section 4.3.5). Since backflushing is
normally at 3-4 times the forward-flow flux, the energy expenditure per unit
time is commensurately higher.
Dead-end filtration plant may be operated at either constant pressure or at
constant flux (Fig. 2.23). In both cases trends in permeability decay over the
backflush cycle, as reflected by flux decline at constant pressure operation (Fig.
2.23a) or pressure increase at constant flux operation (Fig. 2.23b), is
exponential or pseudo-exponential, although the exact trend is dependent on
the relative contributions of cake filtration, pore blocking and adsorption
(Table 2.8). For filtration of solids forming an incompressible cake, on the other

1200
= 1000
2 800
600
g 400
I- 200
0
0 5 10 15 20 0 2 4 6 8 101214
Tlmo (mln) Time (hours)
(a) (W
Fzgure 2.23 Dead-end filtration: (a) constant pressure (declining flux over backflush cycle) and (b)
constantflux (incrensingpressure over backflush cycle)