Page 285 - Chiral Separation Techniques

264 10 The Use of SMB for the Manufacture of Enantiopure Drug Substances: From …

Estimation of the pressure-drop: The system is designed to work within a given
pressure limit; thus, one needs a relation giving the pressure-drop in the column (per
unit length). Darcy’s law gives the relation of ∆P/L versus the mobile phase veloc-
ity u. However, the Kozeny-Carman equation is best adapted for laminar flows as
described:

∆P = h ⋅ 36 ⋅  1 −  ε 2 ⋅⋅ u = ϕ u ⋅ = Φ u ⋅ (8)
µ
L k d 2  ε  d 2
p p
where h is the Kozeny coefficient (close to 4.5), µ is the eluent viscosity, and u
k
is the linear velocity.

10.3.2.2 Step B: Calculation of TMB

For given feed composition, eluent, and stationary phase, the flowrates of a TMB to
allow processing a given flowrate of feed are calculated based on the knowledge of
the adsorption isotherms.
Optimum flowrates, resulting in high productivity and low eluent consumption,
are estimated first for an “ideal system”, which means that kinetic and hydrodynamic
dispersive effects are assumed to be negligible [46]. This procedure has recently
been improved [57].
In order to present the results in a normalized form, it is convenient to define the
reduced flowrates as:

m = Q i , i = to IV (9)
I
i
Q
–
where Q are the flowrates in zone i and Q is the solid flow rate.
i
Linear case: This case is met when the adsorption isotherm is considered linear,
which means operation under diluted conditions. Taking into account the saturation
capacities of the CSP, this behavior is usually met for concentrations around or
–1
below 1 g L for separation of enantiomers.
A more general criterion for linearity can be derived noting that the denominator
of the Langmuirian adsorption isotherms must approach 1, and consequently:

K ⋅ C + K ⋅ C ≤ . 01 (10)
˜
˜
F
F
A A B B
Assuming a linear behavior, the conditions that have to be fulfilled by the differ-
ent flowrates can be shown to be:
m IV ≤ K A m III ≤ K B
(11)
m ≥ K m ≥ K
II A I B