Review of BAC Filtration Modeling in Drinking Water Treatment - Activated Carbon for Water and Wastewater Treatment - page 336

The model also calculates the attached and suspended biomass as a function of
time and filter depth. In the following equation, advective transport, biofilm shear,
and washout of suspended biomass due to filtration are taken into consideration,
whereas the effect of dispersion, growth, and decay of suspended biomass is
neglected:

@ X susp

@

v i @

X susp
@

þ a

X f s X susp b

¼

L f (11.10)

t z e ye B B

where
X susp

suspended biomass concentration (M x /L 3 ), ¼

density of biomass within biofilm (M x /L 3 ), X f ¼

L f ¼ biofilm thickness (L),

b¼ filtration efficiency (unitless),

y¼ EBCT (T),

e
B

¼

void ratio in the bed (unitless),

s¼ biofilm shear loss coefficient (1/T),

specific surface area of the media (surface area per reactor volume) (L 2 /L 3 ). a¼

The researchers also modeled the net accumulation of attached biomass at any
point of the biofilter due to growth, deposition, decay, and shear loss. The time-
dependent change in biofilm thickness was expressed as follows [20]:

b

@ L f

@

YJ f
X f þ

X susp

t ¼ ay

b tot L f (11.11)

X f

where

b tot ¼ overall loss rate of bacteria due to decay and fluid shear (1/T),

yield coefficient (M x /M s ).
The first term on the right-hand side of Eq. (11.11) shows that biofilm grows as a
result of substrate flux (J f ) into the biofilm. The term in the middle represents the
increase of biofilm thickness due to deposition of suspended biomass on filter
media. The last term is the loss of biofilm by decay and fluid shear.
The BIOFILT model was used in simulation of BOM removal in full-scale
biofilters. The effect of BOM composition, water temperature, and biomass
removal during backwashing was also examined. BOM removal was shown to
depend strongly on influent BOM composition [21]. The temperature decrease
resulted in the decline of pseudo-steady-state BOM removal and increase of bio-
filter startup time. One of the innovative features of this model is the ability to
simulate the effects of a sudden loss in attached biomass due to filter backwashing.
Biofilter performance was not affected unless biomass removal by backwashing
was less than 60%. Therefore, for practically oriented modeling the steady-state
approach was considered adequate [4].

Y ¼