Speedy standing wave design, optimization, and scaling rules of simulated moving bed systems with linear isotherms

• Productivity (PR) and solvent efficiency (F/D) are related to key parameters.
• Productivity increases with the ratio of feed concentration to diffusion time.
• High selectivity (α) and low diffusivity ratio (η) give high PR and F/D.
• Configuration for maximum PR and F/D controlled by η/α2.
• Simple scaling rules based on two dimensionless groups are developed.

Simulated Moving Bed (SMB) systems with linear adsorption isotherms have been used for many different separations, including large-scale sugar separations. While SMBs are much more efficient than batch operations, they are not widely used for large-scale production because there are two key barriers. The methods for design, optimization, and scale-up are complex for non-ideal systems. The Speedy Standing Wave Design (SSWD) is developed here to reduce these barriers. The productivity (PR) and the solvent efficiency (F/D) are explicitly related to seven material properties and 13 design parameters. For diffusion-controlled systems, the maximum PR or F/D is controlled by two key dimensionless material properties, the selectivity (α) and the effective diffusivity ratio (η), and two key dimensionless design parameters, the ratios of step time/diffusion time and pressure-limited convection time/diffusion time. The optimum column configuration for maximum PR or F/D is controlled by the weighted diffusivity ratio (η/α2). In general, high α and low η/α2 favor high PR and F/D. The productivity is proportional to the ratio of the feed concentration to the diffusion time. Small particles and high diffusivities favor high productivity, but do not affect solvent efficiency. Simple scaling rules are derived from the two key dimensionless design parameters. The separation of acetic acid from glucose in biomass hydrolysate is used as an example to show how the productivity and the solvent efficiency are affected by the key dimensionless material and design parameters. Ten design parameters are optimized for maximum PR or minimum cost in one minute on a laptop computer. If the material properties are the same for different particle sizes and the dimensionless groups are kept constant, then lab-scale testing consumes less materials and can be done four times faster using particles with half the particle size.