GPS-X Technical Reference

271 Sand Filtration Models
The massbalance model accounts for the mass accumulated in the filter during the filter cycle
time. The accumulated mass is removed during backwash. Therefore, stoichiometric parameters
for the filter effluent and the backwash may be specified. The operational parameters for the
massbalance model are shown in Figure 9-2.
ONE-DIMENSIONAL MODEL
The basis for the simple1d model is the combination of the continuity (mass balance) and the
kinetic partial differential equations by Horner et al. (1986), which describe the removal of
suspended particles by a granular filter:
Equation 9.6
where:
C
u
d
t
= volume of deposited solids per unit bed volume
= filtration coefficient
= concentration of suspended particles at depth L and time t
= approach velocity (velocity of the fluid above the filter bed)
= porosity of deposited solids
= time
When combined with defining equations for the deposited (attached) solids (X= d) and the
unattached solids (X = C d) in the filter, the following equation is derived for the simple 1d
model:
Equation 9.7
where:
X
X d
δd
= unattached solids
= attached (deposited) solids
= density
GPS-X Technical Reference