(626a) New Insights Into The Ideal Cascade Theory For Membrane Separation Processes

Membrane separation processes have become increasingly popular in the last three decades. Most commercial membranes have finite permselectivity (ratio of the component permeabilities) values. The availability of modest permselectivity membranes has given impetus to the search for the most energy efficient design for a membrane process. Calculations show that considerable capital and energy savings can be made by cascading membrane stages together through recycle. To obtain specified high recoveries, the proper selection of cascade geometry and operating parameters, to minimize capital cost and energy consumption is an important problem. The analytical approaches to solve this problem were taken through the ?Ideal cascade? theory [1-3] discussed by Cohen and others. An Ideal cascade insures that streams that are mixed are of the same compositions, thereby avoiding the energy penalty associated with mixing dissimilar streams.

The optimality condition for the ?Classical ideal cascade design', termed IC-1 here, was derived under a set of operating conditions in which the components' permselectivity was nearly unity. However, for contemporary applications we need to optimize configurations operating with higher permselectivities, under constraints dictating that only a few recycle compressors be used. For moderate membrane permselectivity, an additional degree of freedom, in the stage separation factor, is available, the proper choice of which can lead to up to 50% energy savings. With this insight, the present work demonstrates the mathematical relationships extending the scope of the theory to such applications. The present work identifies an optimal regime of operation for a membrane cascade, which can lead to energy savings of up to a factor of two, while still under the IC-1 design. Detailed investigations were also made into a second operating condition proposed by Herbst and McCandless [4]. This condition identifies another operating regime, still retaining no mixing condition and employing a classical scheme. It will be referred to as the IC-2 design in this work. Rigorous derivations are made, in the current work, for the stage separation factor limits within which the IC-2 design can be operated. The present work provides useful results into what parameter values are optimal with respect to both, energy considerations and number of stages, to perform a prespecified separation task, when still working in the classical scheme.

It is expected that the current work, will provide a base for the construction of a much needed systematic framework for selection of the energy optimal cascade configuration. Future work will focus on optimization of the cascade using alternative no mixing schemes and then extending the theory to handle multicomponent systems.

References

1. Cohen, K., The Theory of Isotope Separation as Applied to Large-Scale production of U235. 1st ed. ed, ed. G.M. Murphy. 1951, New York: McGraw-Hill.

2. Benedict, M., T.H. Pigford, and H.W. Levi, Nuclear Chemical Engineering. 2nd ed. ed. 1981, New York: McGraw-Hill.

3. Pratt, H.R.C., Countercurrent Separation Processes. 1967, New York: Elsevier Publishing Co.

4. Herbst, R.S. and F.P. McCandless, No-Mix and Ideal Separation Cascades. Separation Science and Technology, 1994. 29(17): p. 2215 - 2226.