Demand-oriented biogas production and biogas storage in digestate by flexibly feeding a full-scale biogas plant

Particularly, Eq. 
(8) 
approaches zero for an empty digester (h
*
=
0, 
no biogas can be stored/stirred out) and for a filled-up digester (h
*
=
h
R
, 
no biogas can be stored in the digestate since the smallest amount would 
lead to the overflow of the reactor). The optimum point of Eq. 
(8) 
con-
cerning h
*
,
h
*
opt
, is independant of A, T
0
,
T, and p
0 
and only weakly 
dependent on h
R
,
ϱ and
p in the limits of common full-scale digesters and 
is, roughly, somewhere in the range of h
*
opt
≈
0.40h
R
…
0.50h
R
. 
Relating Eq. 
(8) 
to Eq. 
(5) 
delivers the fraction ∊ which describes the 
useable stored biogas amount related to the wholly stored biogas 
amount: 
∊ =
1 − ln
(
ϱ
*
gh
*
p + 1
)
p
ϱ
*
gh
*
(9)
where especially ∊(h
*
=
0) = 0and lim
h
*
,
h
R
→∞
∊(
h
*
) =
1. Further, at 
constant h
R
, a completely filled-up digester would always have the 
highest stir-out efficiency ∊
max
, even if the absolute storable biogas 
amount vanishes. 
Fig. 1 
summarizes the introduced equations. 
Regarding generalization, Eqs. 
(5) and (7)-(9) 
can be de- 
dimensionalized by devision by Eq. 
(7) 
and introducing the dimen-
sioneless initial heigt, ̃h
*
=
h
*ϱ
*
g
p
, on which is dispensed with at this 
point. 
2.7. Determining the biogas storage in the digestate 
Several techniques for measuring the biogas storage in the digestate 
are conceivable. The most obvious one being to measure the increase of 
the liquid phase surface and claim that this rise is caused only by 
accumulating biogas. The relative growth of the fill level, related to the