Biofilters
A fully efficient biofilm:
rA = koA =kovt L
A partially efficient biofilm:
(5.17)
kY~A = --.12 kovt D
(5.18)
Amore detailed study of zero order kinetics in the biofilm can be found in /1/, /2/,
/3/ and /4/.
Example 5.1
At the top of a trickling filter there is a high concentration of a removable, dissolved organic matter and an oxygen concentration near saturation: 8 g/m 3 . Both substances
diffuse into the biofilms where the organic matter is mineralized while consuming oxygen at the rate of kot.o2 = 200,000 g/(m 3 · d). The diffusion coefficient of the oxygen is
set at
D02 = 1.7 · 1 o-4m 2 /d, see Tables 5.1 and 5.2.
How far does the oxygen penetrate the biofilm:
~ A/2•1,7•10- 4 •8
~L = kovt = 'I
200,000
= 117 ~-tm
It appears that if the biofilm is thinner than 117~-tm. the film will be fully penetrated.
Conversely, if the film is thicker than 117~-tm. the film will be partially penetrated and irrespective of the thickness it is a half order process, the reaction rate for oxygen being:
_/
-4
~
-1;, 1
k1J,A.02 = ..J2 kovt · D = -v2 · 200,000 · 1.7 · 10 = 8.2 g 2 m 2 d1;,
2
rA,02 = 8.2 · 8 = 23 g 02/(m ·d)
In practice, the biofilm in a trickling filter is considerably thicker than 117 IJ.m (of the order of 1 mm). Hence partial penetration and half order processes are dominant.
The overall reaction pattern for a biofilm can be summarized as follows:
r tanha.
first order: k 1 A = klVtL. E J E = ~a.
f
klVtL
la.= ---n(5.19)
zero order: { ~ > 1 koA = kovt L } R = - I 2 DS
~ < 1 k 1 ~zA = --.12 D kovf
" 'J kovt L2
An overview of the relationship between the three orders of reaction can be obtained
by substituting the following relation between the first and zero orders of reaction:
kovf = k1Vf Ks
(5.20)
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