MIXING AND WORK OF SEPARATION IN COUNTERCURRENT RECYCLE CASCADES

The increased work of separation due to remixing partially separated s treams within countercurrent recycle cascades, W(unmix), was calculate d and compared with the absolute minimum thermodynamic work, W(min), r equired to effect a given separation. Remixing can occur in all counte rcurrent constant recycle cascades regardless of whether a separation process is potentially reversible, partially reversible, or irreversib le in nature, or whether the cascade is composed of double entry or si ngle entry stages. In an ideal cascade (IC), the remixing of materials with different compositions is eliminated and the sum of the stagewis e separative work, W(sep), is identically equal to W(min) based on the overall separation occurring across the cascade, or W(sep) = W(min). However, in the constant recycle cascade (CRC) the work of separation is greater than the thermodynamic minimum by an amount equal to W(mix) due to remixing of partially separated streams, or W(sep) = W(min) W(unmix). By comparison, the separative work due to remixing is lost o r wasted in the CRC. The lost work, W(unmix), can be a significant con tribution to the energy requirements of countercurrent recycle cascade s since it becomes infinite at both extremes of reflux; the minimum re cycle ratio, RR(min), and total recycle, RR(total). Consequently, W(un mix) goes through a minimum at some point in between the two limiting extremes of recycle ratio in a constant recycle cascade. For the examp les considered in this analysis, W(unmix) in the CRCs goes through a m inimum at recycle ratios of 1.32, 1.35, and 1.53 times the minimum rec ycle (RR(min)) for separation factors of alpha = 1.027, 1.067, and 1.2 0, respectively. At these ''Optimal'' recycle ratios (i.e.. minimum W( unmix)), the work of separation is increased by about 28 to 31% over t he thermodynamic minimum. Finally, many of the perceived differences i n the analysis of separation cascades for the partially reversible, po tentially reversible, and irreversible processes disappear when mixing within the CRC is taken into account.