Page 65 - Membranes for Industrial Wastewater Recovery and Re-Use

Membrane technology 45

adapted for cross-flow operation if the proportion of undeposited solute material
can be calculated.
The expressions listed in Table 2.10 illustrate a common difficulty in
describing filtration behaviour. Even for a supposedly generic matrix (mixed
liquor), the innate heterogeneity and diversity in composition of real feedwater
matrices forbids the formulation of general equations describing filtration
behaviour, even under steady-state conditions. Different key water quality
determinants (chemical oxygen demand, dissolved organic carbon and mixed
liquor (volatile) suspended solids) have been identified as the basis for
quantifying fouling propensity and dynamic behaviour. Most recent
publications of experimental studies of MBR processes make little or no reference
to dynamic modelling, with data interpretation being substantially limited to
reporting of hydraulic resistance values (Choo and Lee, 1996; Chang and Lee,
1998; Defrance and Jaffrin, 1999b). The more global semi-empirical models that
have been developed (Nagaoka et d., 1998), as with many other semi-empirical
models in this area, rely on specific hydraulic resistance data which is likely to be
specific to the system under investigation.
Dead-end filtration theory is thus to a very large extent limited by the accuracy
of the representation of the interaction between the solids and the membrane
material. The same also applies to cross-flow filtration. However, for dense
membrane processes where the water can be considered to be a continuum with
no complicating solid-liquid interactions, modelling from first principles of the
resistance offered by the membrane-solution interface, due to concentration
polarisation, is possible.

Classical concentration polarisation model
As already stated (Section 2.2.3), concentration polarisation describes the
tendency of the solute to build up in the membrane solution interfacial region,
and the extent to which this occurs depends on:

Table 2.8 Empirical dead-end filtration equations (from Chang et al.. 2002)
Approach Physical cause Description Equationa
Cake filtration Boundary layer Deposit of particles larger than t/V = AV i
R
resistance the membrane pore size onto
the membrane surface
Complete Pore blocking Occlusion of pores by particles -ln(J/]o) = At + I3
blocking with no particle
superimposition
Intermediate Long-term Occlusion ofpores by particles 1/J = At + R
blocking adsorption with particle superimposition
Standard Direct Deposit of particles smaller than t/V = At + B
blocking adsorption the membrane pore size onto
the pore walls, reducing the
pore size
a A, B, constants (value dependent upon cake and system characteristics): R cumulative volume of
permeate at time t; Jo 1, flux initially and at timet respectively.