Speedy standing wave design of size-exclusion simulated moving bed: Solvent consumption and sorbent productivity related to material properties and design parameters.

Size-exclusion simulated moving beds (SEC-SMB) have been used for large-scale separations of linear alkanes from branched alkanes. While SEC-SMBs are orders of magnitude more efficient than batch chromatography, they are not widely used. One key barrier is the complexity in design and optimization. A four-zone SEC-SMB for a binary separation has seven material properties and 14 design parameters (two yields, five operating parameters, and seven equipment parameters). Previous optimization studies using numerical methods do not guarantee global optima or explicitly express solvent consumption (D/F) or sorbent productivity (PR) as functions of the material properties and design parameters. The standing wave concept is used to develop analytical expressions for D/F and PR as functions of 14 dimensionless groups, which consist of 21 material and design parameters. The resulting speedy standing wave design (SSWD) solutions are simplified for two limiting cases: diffusion or dispersion controlled. An example of SEC-SMB for insulin purification is used to illustrate how D/F and PR change with the dimensionless groups. The results show that maximum PR for both diffusion and dispersion controlled systems is mainly determined by yields, equipment parameters, material properties, and two key dimensionless groups: (1) the ratio of step time to diffusion time and (2) the ratio of diffusion time to pressure-limited convection time. A sharp trade off of D/F and PR occurs when the yield is greater than 99%. The column configuration for maximum PR is analytically related to the diffusivity ratio and the selectivity. To achieve maximum sorbent productivity, one should match step time, diffusion time, and pressure-limited convection time for diffusion controlled systems. For dispersion controlled systems, the axial dispersion time should be about 10 times the step time and about 50 times the pressure-limited convection time. Its value can be estimated from given yields, material properties, and column configuration. Among the material properties, selectivity and particle size have the largest impact on D/F and PR. Particle size and 14 design parameters can be optimized for minimum D/F, maximum PR, or minimum cost on a laptop computer.