Page 249 - Chiral Separation Techniques

9.4 Simulation Results 227

The initial and boundary conditions are the same presented before and, for x = 0,
Equation (20) becomes:

c − 1 dc ij = c (27)
ij ij,0
Pe dx
j
The model parameters are similar to the ones presented for the SMB model, except
that Pe and α are expressed in terms of the length of the TMB sections and the ratio
j j
between fluid and solid interstitial velocities is γ = ν /u . The SMB and TMB mod-
j j s
els, defined by a set of partial differential equations, were numerically solved by
using the PDECOL software [16] based on the method of orthogonal collocation in
finite elements (OCFE). PDECOL implements the method of lines and uses a finite
element collocation procedure for the discretization of the spatial variable which
reduces the PDE system to an initial-value ODE system on the time variable. The
time integration is accomplished with the ODE solver STIFIB, which is a modified
version of the GEARIB ODE package developed by Hindmarsh [17]. The counter-
current motion of fluid and solid in the SMB operation is achieved with a discrete
jump of the injection (feed and eluent) and collection (extract and raffinate) points.
Due to this switch of the inlet and outlet points, the boundary conditions for each
column vary with time, changing at the end of each switch time interval. Hence, the
SMB model must take into account time-dependent boundary conditions.

9.4 Simulation Results

The chromatographic resolution of bi-naphthol enantiomers was considered for sim-
ulation purposes [18]. The chiral stationary phase is 3,5-dinitrobenzoyl phenyl-
glycine bonded to silica gel and a mixture of 72:28 (v/v) heptane/isopropanol was
used as eluent. The adsorption equilibrium isotherms, measured at 25 °C, are of bi-
Langmuir type and were proposed by the Separex group:

q = . 269 c A + . 010 c A (28a)
*
A
1 + . 0 0336 c + 0 .0466 c B 1 + c + 3 c B
A
A
q = . 373 c B + . 030 c B (28b)
*
B
1 + . 0 0336 c + 0 .0466 c B 1 + c + 3 c B
A
A
9.4.1 Equivalence Between TMB and SMB Modeling Strategies
The operating conditions and model parameters used in simulation for the TMB
approach are presented in Table 9-1. The feed concentration of each enantiomer is
2.9 g L –1 and columns were 2.6 cm wide and 10.5 cm long. The section length was