GPS-X Technical Reference

163 Suspended Growth Models
where:
qperm
= permeate flow rate (m 3 /d)
xliq = concentration of solids in bulk liquid phase within the MBR (kg/m 3 )
fcapture
= solids capture rate or fraction (dimensionless)
qbackw = backwash flow rate (m 3 /d)
xcake
= mass of solids in cake layer (kg)
fbw = backwash solids removal rate (1/m 3 )
qcross
= crossflow or air scour flow rate (m 3 /d)
Am = total membrane surface area (m 2 )
fcross
= cross-flow solids removal rate (kg/m)
Ks,cake = half-saturation coefficient for cross-flow air (kg)
The cake layer mass balance considers the bulk convection of solids to the surface of the
membrane, the solids removed due to backwashing, and the solids removed due to crossflow
aeration. Equation 6.45 ignores the diffusion away from the cake layer into the
bulk liquid as this term is assumed to be small compared to the other terms in the mass
balance. The half-saturation coefficient for cross-flow air and the switching function
based on the mass of cake solids is used to smoothly stop the solids removal as the cake
layer disappears.
The default density of a cake layer particle (see Equation 6.44) is equal to the density of
dry biofilm already used in the GPS-X fixed-film reactors. The default porosity of the
cake layer (see Equation 6.44) is given in the
Input Parameters > Physical – Membrane > More… form and is estimated using
information given in Chang et al. (1999). The membrane surface area (see Equation
6.44) is site-specific and should be selected to achieve a flux within the range normally
recommended by the manufacturer (e.g. a typical range for hollow fiber membranes is 17
to 25 L/m 2 /h; see Wallis-Lage et al., 2005).
The backwash solids removal rate (see Equation 6.45) is specified in the
Input Parameters > Physical – Membrane > More … form. It is multiplied in
Equation 6.45 by the backwash flow and the cake solids mass (term 2 in Equation
6.45) to give the mass of solids removed from the filter cake per unit time. The default
backwash solids removal rate was calibrated using data from Garcia and Kanj (2002).
The default backwash flow (see Equation 6.45) is entered in the Input Parameters >
Operational – Membrane form and is based on data provided by Garcia and Kanj
(2002).
GPS-X Technical Reference