Modeling of Biogas Reactors

174 6 Modeling of Biogas Reactors
formulating this kinetic equation one should understand more about the physicochemical
state of the fermentation broth.
Acetic acid is dissociated to a large extent in the relevant pH range between 6.6
and 7.4. The pH value is calculated on the basis of the activity of H + , which equals
ã 1·c H +.
The concentration of H + ions c H + can be calculated according to Eq. 3 which represents
the electroneutrality of the fermentation broth:
c OH –+ c Ac – +c Pro – +c HCO3 – +c HS – = c NH + 4 +c H + +Z
The amounts of negative and positive ions must be balanced.
The most important ion concentrations in this calculation are the concentrations
of dissociated acetic acid c –
Ac and propionic acid cPro –, OH – ion cOH –, hydrocarbon
ion c –, HCO3 and dissociated hydrogen sulfide cHS –. Besides the Hc ion, the ammonium
ion (concentration c c) NH4 has a positive charge. Z represents the pool of not extra
specified ions which are necessary to balance the equation and are assumed to be
constant during the different stages of fermentation.
The concentrations of these ions can be calculated according to Eqs. 4–14.
HAc I Ac – +H c c Ac = c HAc+c Ac – (4)
HProIPro – +H c c Pro = c HPro +c Pro – (5)
– +
H2O+CO2IHCO3 +H
– 2– c HCO3 ICO3 +H cC,tot = cCO2 +c –+c 2–
HCO3 CO3
H 2SIHS – +H c
HS – I S 2– +H c c S,tot = c H2 S +c HS –+c S 2–
c –
H2O+NH3INH4 +OH cN,tot = cNH3 +c c
NH4
(8)
c –
OH = ·10 –14 mol2 L –2
1
c H c
KD,Ac 2
KD,Ac+ c c
H ã1 c Ac – = c Ac (10)
KD,Pro 2
KD,Pro+ c c
H ã1 c Pro – = c Pro (11)
K I D,CO 2
c HCO – 3 = c C,tot (12)
K I D,CO+c H c ã 1 2
K I D,H 2 S
c HS – = c S,tot (13)
K I D,H 2 S+c H c ã 1 2
K
c c
NH4 = cN,tot (14)
I D,NH3 K I 2
D,NH + c P
OH ã1 3
(3)
(6)
(7)
(9)