4 Dynamic Simulation of Technical Precipitation Processes
125
Fig. 10 Process variables for the semi-batch process a and the equivalent circuit of PFR and BF b
the presence of only one solvent. The BF volume V BF is assumed to correspond to
the volume of pure solvent (V BF = x H 2 O,BF M
L
BF /ρ H 2 O ).
The streams, which are interconnecting BF and PFR are
S circ,1 (entering the PFR)
and
S circ,2 (leaving the PFR). The stream vector
S is defined by
S = ( ˙
M ξ
S x
L
j w
S
i )
T .
Corresponding to the BF, the variables for the stream vector are defined by
ξ
S
circ,1 = ˙
M
S
circ,1 / ˙
M circ,1 , ξ
L
circ,1 = ˙
M
L
circ,1 / ˙
M circ,1 , x
L
j,circ,1 = ˙
M
L
j,circ,1 / ˙
M
L
circ,1 and
w
S
i = ˙
m
S
i / ˙
M
S
circ,1 .
The balance equations for the BF can be derived with the variables given. M BF
will change due to the incoming and outgoing streams, according to Eq. (13).
d M BF
dt
= ˙
M sec + ˙
M circ,2 − ˙
M out − ˙
M circ,1
(13)
The temporal evolution of the solids phase fraction is described by Eq. (14). No
source term for solids formation must be considered for the BF balance equation, as
solids formation only takes place in the PFR.
dξ
S
BF
dt
+ ξ
S
BF
dln(M BF )
dt
=
1
M BF
·
˙
M sec ξ
S
sec + ˙
M circ,2 ξ
S
circ,2 −
˙
M out + ˙
M circ,1
ξ
S
BF
(14)
The component balances are given by Eq. (15).
dx
L
j,BF
dt
+ x
L
j,BF
dln
ξ
L
BF
dt
+ x
L
j,BF
dln(M BF )
dt
=
1
M BF ξ
L
BF
·
˙
M sec ξ
L
sec x
L
j,sec + ˙
M circ,2 ξ
L
circ,2 x
L
j,circ,2