Application of Membrane Residue Curve Maps to Batch and Continuous Processes

Membrane residue curve maps (M-RCMs) [Peters et al. Ind. Eng. Chem. Res. 2006. 45, 9080] plot the change, over time, of the retentate composition in a batch still. In this paper, the relevance of M-RCMs to both batch and continuous processes is investigated. A constant relative permeability model is used for demonstration purposes, and the theory is then extended to a real system of methanol/butene/methyl tertiary butyl ether (MTBE). It has been shown that the differential material balances over a continuously operated membrane unit are mathematically equivalent to those which describe the M-RCM. The time variable in the batch setup is analogous to the spatial variable in continuous units. The retentate composition in a nonreflux continuous unit, for example, will follow the residue curve that passes through the initial feed composition. The M-RCM, in conjunction with the necessary flux equations, allows a designer to determine permeation area (or time) required in a continuous (or batch) process. Membrane columns operating at total and infinite reflux are discussed. A novel approach in synthesizing and designing hybrid distillation−membrane processes emerges: using the M-RCM in conjunction with column profile maps (CPMs) allows one to graphically interpret hybrids in an efficient manner. The method generates the attainable region (AR) for a chosen configuration and informs the designer of parameters like membrane area and number of distillation stages required.