Modeling of Biogas Reactors

198 6 Modeling of Biogas Reactors
sediments of lakes, or deeper parts of high technical biogas reactors, especially of
biogas tower reactors. Anaerobic reactors for the treatment of sewage sludge may
also have a height up to 50 m.
In the literature very little has been published on this important effect. The reason
may be found in the high complexity of performing experiments under steady-state
conditions and elevated pressure. A theoretical and experimental study was published
by Friedmann and Märkl (1993, 1994). It was shown that the most important effect of
elevated pressure is due to the higher solubility of the product gases, like CO 2, H 2S,
and NH 3. According to Eqs. 3–14 the pH may change because of a higher solubility of
these gases and, therefore, the equilibrium of dissociation of all the relevant substances
will shift, with a significant effect on the kinetics of biogas production.
If a higher percentage of the produced gases is dissolved in the liquid phase of the
reactor broth at higher pressures, a smaller amount of gas G will remain compared
to the gas volume at a usual pressure of 10 5 Pa G 0. Because this effect is different for
each gas component, the composition of the produced biogas will change when increasing
hydrostatic pressure.
Assuming the number of gas bubbles remains constant, increasing the pressure
leads to a smaller size of bubbles (bubble diameter: d B) according to Eq. 36.
;
3
dbF The bubble diameter decreases because the relative content of dissolved gas is
higher at higher pressures, which results in a smaller G; furthermore, the pressure
p hydrost itself reduces the bubble size. Highbie’s penetration theory (Eq. 37) and
Stoke’s theory (Eq. 39) of bubble rising velocity (w b) show the influence on the mass
transfer coefficient k L (Eq. 40).
D
kL = 2 (37)
� �
db wb ô = (38)
w bFd b 2
k LF (40)
It is assumed that the diffusion coefficient D in Eq. 37 is constant at the different
pressures and the boundary layer renewal time ô can be calculated according to
Eq. 38. Due to the fact that the interfacial contact area a between liquid and gas will
also be smaller according to Eq. 41, the k La value with respect to the hydrostatic pressure
p hydrost can be calculated by Eq. 42.
aFd b 2
k LaF
G
G 0
;
;d b
(
G
G 0
1
p hydrost
1
p hydrost
)
0.83
(36)
(39)
(41)
(42)