Simulated Moving Bed (SMB) Design

Key Insight

Simulated Moving Bed (SMB) systems replicate true countercurrent moving beds (TMB) to achieve continuous chromatographic separation, typically using a four-zone configuration. Feed containing components A and B is introduced between Zones II and III. The less strongly retained species, A, is recovered between Zones III and IV, while the more strongly retained species, B, is recovered between Zones I and II. Adsorbent is recirculated from Zone I to Zone IV, and eluent is added to the fluid recycled from Zone IV, feeding Zone I. Each zone serves a specific purpose: Zone III adsorbs B while allowing A to pass, Zone II desorbs A while adsorbing B, Zone I desorbs B to regenerate the adsorbent, and Zone IV adsorbs A to recycle the mobile phase.

The design of operating conditions for SMB systems is guided by inequalities ensuring the net upward transport of each component in each zone, based on the TMB analogy. These inequalities translate into relationships involving Mj, the ratio of liquid phase to adsorbent velocities in zone j, which define the operating region for ideal separation (linear isotherms, constant modifier concentration) on an MIII-MII plane. This diagram features a triangular region for complete separation, with the vertex (mA, mB) representing minimum desorbent consumption. However, for robust operation in practice, especially with proteins where stationary phase degradation or fouling can alter equilibrium constants, it is necessary to operate away from this vertex, closer to the 45-degree line, even if it entails greater desorbent consumption.

A safety margin parameter, beta (>= 1), is introduced to define a robust operating point away from the ideal vertex, converting the inequality constraints into equalities for Mj. These equations enable the calculation of external and internal flow velocities within the SMB system, including adsorbent velocity (uS), extract (uE), raffinate (uR), and desorbent (uD) flows. For actual SMB systems, uS is adjusted by factors related to bed length (L) and switching period (p), and internal flow velocities are increased to account for extra-particle fluid carried during switching. SMB design also incorporates band-broadening factors. For preliminary design, a steady-state TMB analogy utilizing a linear driving force (LDF) model is often sufficient for protein chromatography, where mass transfer is typically the limiting factor. This approach involves solving a system of linear equations derived from steady-state material balances to determine productivity, specific desorbent consumption, and pressure drops across each zone, calculated using SMB internal velocities and hydraulic permeability.