360
Chapter 9
In figure9.4 A define
f = x j x < l ,
Now from (9.36):
(9.39)
while the substrate and product balances are
D{sf -s ) = YiaD f ^
or
xe =Ylx(sf - s ) = Ysx(sf - s e)
(9.40)
DP = Y*Pc> fy
or
P = Yy(Sf-s)
(9.41)
Equations (9.40) and (9.41) show that the overall mass balances forxe and
p = p eare
identical with
those of Eq. (9.24). The cell enrichment model differs from the basic model in one respect only: For
a given value of £> it is possible to obtain a specified effluent composition (^e
,xt ,pe)
by a suitable
choice o f/in Eq. (9.39).
We shall now relate / to the operating variables of a cell recirculation design. In Fig. 9.4 A a
hydrocyclone separates the effluent from the reactor into a product stream v and a recirculation
stream
Rv,
where
R
is the recirculation factor. The cell concentration is
xR
in the recirculation
stream, and
xR
- xß
}
with /? > 1. Neither product concentration nor substrate concentration are
affected by the hydrocyclone.
v, s,
i
1
v(R+I )
r
V
x, s,p
x,h P \
vR
X
fi, sfp
V
lfx,s,p
V2=V-V;
x= 0, s,
A
B
Figure 9.4 Biomass recirculation using a hydrocyclone (A) and an ultrafilter (B).
In (B) the permeate
v2
=
v - v; is cell free. The bleed stream
v,
is taken from the reactor.
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