Page 67 - Membranes for Industrial Wastewater Recovery and Re-Use

Membrane technology 47

Table 2.10 Empirical filtration expressions for activated sludge
_. _.
Application/derivation Expressiond Reference
AP
Protein I= Fane (1 986)
WI[R~+R/M,*(~ -e-klt) +RilMbl]
Fane (1 9 86)

A 1'
Classical cake liltration I= Changeful. (2001):
K(Rm + UCMMS) Shimizurf al. (1993)
Concentration J = a + b l0gCooc Ishiguro etnl. (1994)
polarisation
AP
Sidestream MBR I= Sat0 and Ishii (1 99 1)
w(Rm + 843AP~~~C~~~p0
32h)
)
k RdCMLss - CMLVSS)
Sidestream MBR 1 = 11) exp Krauth and Staab (1993)
CMLVSS
HF submerged MBR 1 = kUa@q&s Shimizuetal. (1996)
a, b, k, empirical constants; C, concentration: I(,, initial flux: kj 2.3, empirical first-order rate constants:
boundary layer cake deposit: AI&*. maximum cake deposit (mass per unit area): R'bl, specific
L&,
boundary layer resistance: Ua. approach velocity, air: rp, membrane geometric hindrance factor
(membrane geometry dependent). Subscripts: COD, chemical oxygen demand: DOC, dissolved organic
carbon: ML(V)SS. mixed liquor (volatile) suspended solids.
0 the physical properties of the liquid, which for most water treatment
processes change only marginally with chemical water quality and can
normally be accurately expressed as a function of temperature,
0 the shape and size of the flow channels within the module, and
0 the mean velocity of liquid flowing through the channels.

The rate at which ions accumulate in the stagnant film is simply determined
by the flux and the rejection. Therefore, provided the system is well defined,
the degree of concentration polarisation can be calculated and its effects on the
operation of the membrane process assessed. Mathematical description proceeds
by conducting a material balance at the membrane, where the build-up of solute
at the interface is countered by the diffusive flux of solute away from membrane.
This essentially entails the balancing of four fluxes:

0 back diffusion of solute away from the membrane by Fick's first law of
diffusion, which states that the diffusion rate is proportional to the
concentration gradient,
0 convective transport of the solute to the membrane,
0 convective diffusion of the solute through the membrane, and
0 convective diffusion of permeate through membrane.

Assuming a one-dimensional system (i.e. no Iongitudinal mass transfer) and a
constant value 6 for the boundary layer thickness (Fig. 2.1 8), the concentration
polarisation under steady-state conditions based on film theory can be defined as: