Page 268 - Chiral Separation Techniques

246 9 Modeling and Simulation in SMB for Chiral Purification

met. On the other hand, the liquid flow rate in section I is the highest flow rate in a
four-section TMB system. For practical purposes, this flow rate will be limited by
the system pressure-drop. Taking into account the maximum system pressure-drop
accepted and the constraint considering the more retained component in section I,
we can fix the liquid flow rate in this zone, as well as the switch time interval for the
SMB system (related to the TMB solid flow rate). We will consider that the maxi-
–1
*
mum SMB liquid flow rate allowed is Q = 31.00 mL min .
I
The worst situation concerning the constraint in section I appears when dealing
with low concentrations of the two species because it leads to bigger retention times.
Since the function of section I is to regenerate completely the adsorbent phase, con-
centrations of both components at the beginning of this zone must be the lowest pos-
sible. Hence, the choice of the switch time interval must be made taking into account
the initial slope of the proposed isotherm. The linear retention time of a component
i in section j is given by the following equation:
ε V c  − ε 
t = Q  1 + 1 K i  (36)
ij
*
j ε
where K is the initial slope of the isotherm for component i. Considering that the
i
SMB system under study is constituted by 9.9 cm (length) × 2.6 cm (diameter)
columns (V = 52.56 mL), ε = 0.4, K = 1.35 + 7.32 × 0.163 = 2.543, and using the
c B
*
–1
maximum flow rate allowed in this SMB system, Q = 31.00 mL min , the retention
I
time of the more retained component in section I is t = 3.27 min. Hence, the switch
BI
time interval for the SMB operation must be greater than the retention time of the more
retained component in section I, if we want to fulfill the constraint previously pre-
*
sented for this zone. The value chosen for the switch time interval was t = 3.3 min,
which corresponds to a TMB solid flow rate of Q = 9.56 mL of solid per minute.
S
The function of section IV, located between the raffinate and eluent nodes, is to
regenerate the liquid phase, so that it can be recycled to section I as pure eluent. In
other words, both components A and B must move downwards, following the solid
phase. Because component A is the less-retained species, we have to consider only
the constraint considering this component; i.e., if the constraint is fulfilled for
species A, the constraint considering the more retained component B will be always
met.
The evaluation of the retention times in section IV and the choice of the liquid
flow rate for this zone (the recycling flow rate) are not straightforward as it was for
section I. The worst situation, concerning the constraint in section IV, appears when
dealing with nonlinear behavior because it leads to lower retention times, and we
must prevent the less-retained component reaching the end of this zone before the
jump of the inlet-outlet lines in the SMB operation. Since the switch time interval
was already chosen and, in a situation of an effective binary separation, the concen-
tration of the more retained component along the section IV is near zero, we suggest
the choice of the liquid flow rate in section IV by using the following equation:
ε V  1 − ε ∆ q * F 
c
Q * = *  1 + A F  (37)
IV
t  ε ∆ C 
A