Page 60 - Membranes for Industrial Wastewater Recovery and Re-Use

40 Membranes for Industrial Wastewater Recovery and Re-use

commences. The flux at this transition has been termed “secondary critical flux”
(Bouhabila et al., 1998). However, whilst potentially useful in providing a guide
value for the appropriate operating flux, the absolute value of the critical flux
obtained by this method is likely to be dependent on the exact method employed
and, specifically, the rate at which the flux is varied with time. A common
practice is to incrementally increase the flux for a fixed duration for each
increment, giving a stable TMP at low flux but an ever-increasing rate of TMP
increase at higher fluxes. This flux-step method defines the highest flux for which
TMP remains stable as the critical flux. This method is preferred over the TMP-step
method since the former provides a better control of the flow ofmaterial deposition
on the membrane surface, as the convective flow of solute towards the membrane
is constant during the run (Defrance and Jaffrin, 1999a). However, no single
protocol has been agreed for critical flux measurement, making comparison of
reported data difficult. It is also becoming apparent that irreversible fouling can
take place at operation below the critical flux (Cho and Fane, 2002).

2.3 The theory
There are essentially two approaches to describing mass transport in membrane
processes. The simplest is to add the hydraulic resistance of the membrane to that
of the cake or fouling layer to determine the relationship between the flux and
pressure through simple empirical Darcian relationships. This approach relies on
a knowledge of the resistance of both membrane and fouling/cake layer. The
membrane resistance can be determined either directly from ex situ experimental
measurements using pure water or, in the case of porous membranes, through
well-understood fluid physics relationships. Provided the cake or fouling layer
can be measured empirically, and assumptions can be made about the effect of
operation on the bulk membrane permeability, resistance theory can be usefully
applied to determine hydraulic relationships without recourse to further
theoretical development. It is, indeed, common practice to refer to the membrane
and cake or fouling layer resistance when defining filtration operation. Other
cake filtration empirical models are based on deposition of solids within the
membrane pores, thus accounting for the change in the permeability with time
but more as a diagnostic tool than for predictive purposes.
The development of predictive models for membrane mass transfer from first
principles is much more problematic and relies on mathematical description of
the system hydrodynamics, membrane structure and feedwater matrix. It is only
under specific limiting conditions that simple analytical expressions can be used
with complete impunity (for example dense, homogeneous, i.e. non-porous
membranes where the water content of the membrane is small, or isoporous,
non-adsorptive uncharged membranes). Hence, the combination of solution-
diffusion and sieving mechanisms (or more specifically capillary flow), as exists
in nanofiltration processes, substantially complicates the mathematical
description. Moreover, no simple fundamental analytical expressions can
account for fouling, in particular internal or permanent fouling where adhesive