Zonal rate model for axial and radial flow membrane chromatography. Part I: knowledge transfer across operating conditions and scales

Abstract

The zonal rate model (ZRM) has previously been applied for analyzing the performance of axial flow membrane chromatography capsules by independently determining the impacts of flow and binding related non-idealities on measured breakthrough curves. In the present study, the ZRM is extended to radial flow configurations, which are commonly used at larger scales. The axial flow XT5 capsule and the radial flow XT140 capsule from Pall are rigorously analyzed under binding and non-binding conditions with bovine serum albumin (BSA) as test molecule. The binding data of this molecule is much better reproduced by the spreading model, which hypothesizes different binding orientations, than by the well-known Langmuir model. Moreover, a revised cleaning protocol with NaCl instead of NaOH and minimizing the storage time has been identified as most critical for quantitatively reproducing the measured breakthrough curves. The internal geometry of both capsules is visualized by magnetic resonance imaging (MRI). The flow in the external hold-up volumes of the XT140 capsule was found to be more homogeneous as in the previously studied XT5 capsule. An attempt for model-based scale-up was apparently impeded by irregular pleat structures in the used XT140 capsule, which might lead to local variations in the linear velocity through the membrane stack. However, the presented approach is universal and can be applied to different capsules. The ZRM is shown to potentially help save valuable material and time, as the experiments required for model calibration are much cheaper than the predicted large-scale experiment at binding conditions.

Figure 1

Traditional modeling of external hold-up volumes by a linear PFR and CSTR sequence Roper and Lightfoot model (Roper and Lightfoot, 1995).

Figure 2

Different flow paths in axial and radial flow configurations.

Figure 3

a: Virtual partitioning of hold-up volumes and of the membrane for an axial flow configuration with three membrane zones, (b) flow fractions for tanks downstream of the membrane, and (c) virtual partitioning of hold-up volumes and of the membrane for a radial flow configuration with three membrane zones.

Figure 4

Adsorption schemes in the (a) Langmuir and (b) spreading models.

Figure 5

Measured breakthrough curve of the axial flow XT5 capsule under non-binding conditions. a: Best fit of the symmetric Roper and Lightfoot model and of the symmetric zonal rate model (ZRM) with two membrane zones for XT5 capsule, (b): best fit of the symmetric and asymmetric ZRM with one membrane zone (Roper and Lightfoot model) for XT140 capsule.

Figure 6

Measured breakthrough curve of the axial flow XT5 capsule under binding conditions. a: Using 1 N NaOH for cleaning after each run, (b): using 1 M NaCl for cleaning after each run, (c): best fit of the ZRM combined with the Langmuir binding model and the spreading model, and (d): simulated concentrations of bound molecules in the end-on orientation (q1: red line) and in the sideways orientation (q2: black line) during the loading process over time.

Figure 7

a: Cross-sectional MRI scan through the center of the membrane stack of an axial flow XT5 capsule that has been cleaned using 1 N NaOH, (b): Cross-sectional MRI scan of the XT140 capsule. The membrane pleats are clearly visible in gray, due to their water content.

Figure 8

Measured breakthrough curve of the axial flow XT140 capsule under binding conditions. a: Using 1 N NaOH and (b): using 1 M NaCl for cleaning after each run.

Figure 9

Predicted and measured breakthrough curve of the axial flow XT140 capsule under binding conditions. The asymmetric ZRM with one membrane zone was solved with the flow related parameters from Table III and the binding related parameters from Table V.

Figure 10

a: Virtual partitioning of hold-up volumes and of the membrane for a radial flow configuration in which one axial membrane zone is splitted into three angular sectors with different linear velocities, (b): distribution of the volumetric flow relative to the total volumetric flow, f, over the linear velocity relative to the average linear velocity, v, in the respective sector.

Figure 11

Measured breakthrough curve of the axial flow XT140 capsule under binding conditions. Best fit of the ZRM with one axial membrane zone and (a) two, (b) three, (c) four, and (d) sixteen angular sectors.