Environmental Engineering Reference
In-Depth Information
The biochemical processes involve disintegration, hydrolysis, acidogen-
esis, acetogenesis and methanogenesis. Initially, the feedstock is disinte-
grated into carbohydrates, proteins and lipids, which are subsequently
hydrolysed (Thamsiriroj and Murphy, 2011). A first-order function is used
to describe disintegration and hydrolysis and also the decay rate of microbes
(Thamsiriroj and Murphy, 2011). The Monod function models the growth
rate of microbes coupled with the uptake rate of monomers. Inhibition
terms are also added to the Monod function to allow the simulation of
reduced uptake rate caused by inhibitory effects.
The physico-chemical processes include liquid-liquid processes (i.e. ion
association/dissociation) and liquid-gas processes (Batstone et al., 2002;
Thamsiriroj and Murphy, 2011). pH is a liquid-liquid process; it is
determined in the ADM1 model by balancing cationic and anionic charges
that are present in the digester. Production of methane, carbon dioxide and
hydrogen is a liquid-gas process.
5.8.3 Mathematical model in ADM1
The digester model is built on a mass conservation basis. At steady state, the
balance of mass input and output for an ideal CSTR can be described by a
set of algebraic equations such as equation 5.4 (Nauman, 2002).
V
liq
X
j
r
j
n
i
;
j
¼
q
in
c
in
;
i
þ
q
out
c
liq
;
i
½
5
:
4
where q
in
and q
out
are volumetric inflow and outflow rate (m
3
/day); c
in,i
and
c
liq,i
are inflow and outflow concentration of component i (kg COD/m
3
); the
outflow concentration also represents the concentration within the digester;
V
liq
is the digester fermenting volume (m
3
);
ρ
j
is the kinetic rate function of
process j (kg COD/m
3
/day); and
ν
i,j
is the stoichiometric coefficient of
component i in process j.
However, since the conditions in an anaerobic digester are not usually in
steady state, algebraic equations are replaced by differential equations. In
the model, three categories of differential equations are formed and solved
simultaneously. These categories include: liquid phase equations, acid-base
equations and gas phase equations.
Liquid phase equations
Component i (c
i
) can be divided into soluble (liquid form, S
i
) and particulate
(solid form, X
i
) components. In total, there are 24 components in the liquid
phase, 12 soluble and 12 particulate components (Table 5.5), combining in
19 different processes (j=1-19) as shown in Table 5.6.
The differential equations describing these components are given by
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