Page 261 - Chiral Separation Techniques

9.5 The Steady State TMB Model 239

9.5.2 Prediction of the Separation Regions

The conditions for a complete separation of a binary mixture can be defined in terms
of the γ model parameters, which are directly related with the TMB (SMB) operat-
j
ing variables (fluid and solid velocities in the four sections of the TMB unit). From
the constraints presented, those related to sections II and III play the crucial role on
the separation performance of the TMB. It is in these central zones that the separa-
tion between the two species takes place. The role of the adjacent sections (I and IV)
is to prevent cross-contamination and to allow the improvement of the continuous
operation of the system by regenerating the solid and liquid phases. Taking into
account these considerations, a region of complete separation in a γ –γ plane can
III II
be defined. Considering that the constraints concerning sections I and IV are ful-
filled, the γ –γ plot is an important tool in the choice of best operating conditions.
III II
The first case studied concerns the situation where axial dispersion and mass
transfer resistances are slightly important. The value for mass transfer coefficient
used in this case was k = 0.5 s –1 (α = 180). Following the same methodology used
to study the effect of the operating conditions and model parameters on the SMB
performance, the γ –γ plot was built, keeping constant the recycling (flow rate in
III II
section IV) and solid flow rates, and so γ = 3.76. The total inlet or outlet flow rates
IV
–1
were also kept constant in all simulations and equal to 25.09 mL min . A TMB solid
flow rate of 11.15 mL min –1 corresponds to a switch time interval of 3 min in the
equivalent SMB unit; a recycling flow rate of 27.95 mL min –1 in the TMB corre-
–1
sponds to a recycling flow rate of 35.38 mL min in the SMB. Other model param-
eters were solid/fluid ratio equal to 1.5 and Pe = 2000. The configuration was
–1
2-2-2-2 with a section length of 21 cm. The feed concentration was 2.9 g L of each
enantiomer.
Figure 9-13 shows the γ –γ plot obtained for the first case where four regions
III II
are defined: a region of complete separation, two regions where only one outlet
stream is 100 % pure and a last region where neither of them is 100 % pure. The
closed circles are numerical results based on the equivalence between the TMB and
the SMB; the thick lines connect those results. The thin line in Fig. 9-13 has two
branches. The diagonal γ –γ corresponds to zero feed flow rate; therefore, γ must
III II III
be higher than γ . The horizontal branch γ ≈ 3.76 corresponds to zero raffinate flow
II III
–1
rate; in this case, the extract flow rate is 25.09 mL min .
In order to simplify the understanding of these plots, the relations between the
TMB or SMB flow rates and the γ model parameters can be developed. The rela-
j
tionship between the internal liquid flow rates in the TMB unit, Q , and the γ model
j
j
ε
parameters is given by Q = γ Q where Q is the volumetric solid flow rate in
j 1–ε j S s
the TMB system. The inlet and outlet flow rates can also be expressed in terms of the
ε ε
γ model parameters Q = (γ – γ )Q , Q = (γ – γ ) Q , ,
j E 1–ε I IV S X 1–ε I II S
ε ε
Q = (γ – γ ) Q , and Q = (γ – γ ) Q .
F 1–ε III II S R 1–ε III IV S