Biofilters
5.4. Two-component diffusion
Biological removals are almost always redox-processes which require two substrates: an oxidant and a reductant; in this case oxygen and organic matter. One of
the most significant results of the biofilm kinetics is the determination as to which
substrate is limiting for the removal. This is regulated by the removal rate and the
diffusional rate for each of the two substrates:
Oxidant
d 2 Svf,ox ko,ox
dx 2
Dox
1 ko,ox 2
Sv£,ox=2 0 x +Kt,oxx+Kz,ox
ox
X = 0 Svf,ox = Sox = K2,ox
X=Xt
dSvf,ox _ O
K
_ ko,ox
-
'
lox-Xt
dx
'
D0 x
1 ko,ox 2 ko,ox
Svt,ox=- 2 -D x --D Xt·x+Sox
OX
OX
(5.30)
where the index" ox" stands for oxidant. x1 is the point in the biofilm beyond which
no removal takes place because one of the substrates has been used up. This is
illustrated in Fig 5.8.
By analogy we correspondingly get for:
Reductant
(5.31)
If it is assumed that there is sufficient reductant (Fig 5.8, left), the oxidant will be
used up for x = x1.
x=x1 Svf,ox=O
_A
. L- -vz DoxSox
Xt- t'OX
-
t;z
rA,ox = ...J2 Dox ko,ox ·(Sox)
ko,ox
as previously derived for a limiting substrate.
For the reductant we then get the removal per surface area of the biofilm
ko
ko
' -/2 Dox Sox
r A,red = ,red · Xl = ,red
ko,ox
157