Modeling of Biogas Reactors

186 6 Modeling of Biogas Reactors
6.4.1.2 Model B
Model B, which is simpler, consists of only one stirred vessel per module (Fig. 6.23).
This model is able to describe the mixing behavior of the whole reactor if the mixing
intensity within one module is high compared to the tracer transport from one module
to another. This assumption holds true in the real situation, as shown earlier.
Model B links the stirred vessels in the same way as model A. The intermixing
between two neighboring modules is again modeled by an exchange flow rate V · exchange
going up and down. Eq. 20 shows the material balance for one module i.
dc i
Vi = V · exchange,i–1 (ci –1–c i) + V · exchange,i (cic1–ci) + V · feed(ci –1–c i) (20)
dt
For describing the mixing of one compound in a BTR with model B, the number
of ordinary differential equations is equal to the number of modules. It is an initialvalue
problem which can be solved by the Runge–Kutta method. The only necessary
parameter for calculating the mixing behavior is the exchange flow rate V · exchange.
Experiments in both laboratory and pilot scale reactors are carried out at different
gas flow rates V · gas to investigate the dependence of the hydrodynamic parameters
on the gas loading. Although there are many investigations on airlift loop reactors
and bubble columns in general, the results cannot be applied to this type of reactor
because the gas and liquid loading of the BTR are far below those of the airlift loop
and bubble column reactors found in the literature. Since the present BTR has
unique characteristics, it was necessary to determine the exchange flow rates
V · exchange. Consequently, studies on the circulation velocity w m and the axial dispersion
D ax were carried out.
The characteristic parameters D ax, w m, V · exchange, are a function of the gas loading
of the system. The parameters can be obtained by using the least-squares method to
fit the simulation to the experimental data. The results are shown in Figures
6.24–6.26.
In Figure 6.24 the axial dispersion coefficient is plotted against the superficial gas
velocity of the riser u riser which is given by Eq. 21.
u riser =
This coefficient was only determined on the laboratory scale. Figure 6.25 shows
the mean circulation velocity w m of the laboratory scale and the pilot scale reactors
as a function of the superficial gas velocity of the riser u riser, From a momentum balance
the mean circulation velocity w m can be calculated on the basis of the difference
in gas holdup between riser and downcomer Äå and the knowledge of the total pressure
loss (friction) coefficient î according to Eq. 22.
;
V · gas
A riser
wm =
2 g L
Äå
(22)
�
(21)