Multistage membrane separation processes for the continuous fractionation of solutes having similar permeabilities

Abstract

A new cascade configuration for the continuous membrane fractionation of solutes having similar permeabilities is proposed. In this scheme, solute selectivity is amplified by combining a concentrator and several mass exchangers (e.g., a reverse osmosis unit and hollow fiber dialyzers) to achieve a desired degree of separation. Separation efficiency of the new cascade is compared with that of a conventional counter‐current cascade.

Pseudo-sedimentation dialysis: an elliptic transmission problem

“…(It should be noted that, initially, Eqs. (14), (15), (18)- (25) are interpreted in a similar manner. Pointwise validity is verified a posteriori from bounds on \Amn\ and \Bmn\ and from the second part of Theorem 2, below.…”

“…This is not true of conventional dialysis, which works by bringing a separate flow stream into contact with the solution to be purified. Noda and Gryte [25] show that cascading of dialyzers alone does not change the selectivity. Thus, they consider how concentrators can be incorporated into the cascade to enhance separations.…”

“…Thus, the average concentration fx represents the degree of antisedimentation and serves as a measure of selectivity. The analogous quantity in the context of countercurrent dialysis is the fractional extraction E, which is related to the relevant membrane transport resistance R' by the equation (Noda and Gryte [25]) E = (1 + R')~l . This relation is also plotted in Fig.…”

“…But the enhancement of selectivity must be addressed in order for widespread industrial applications of dialysis to be possible. For this reason, Noda and Gryte [25] considered multistage processes, in which many dialyzers are combined with one or more concentrators into a cascade that yields higher selectivity than is possible with a single dialyzer. They noted that staging of dialyzers alone does not enhance selectivity; there must be at least one concentrator in the cascade.…”

“…Countercurrent dialysis is characterized primarily by diffusive transfer of certain chemical species from a flowing solution to be purified into the dialysate, which flows in the opposite direction. The crucial element is a semipermeable membrane interposed between the flow streams, which serves two purposes: (i) to separate the flow streams (i.e., prevent cross-stream permeation of solvent) by providing a large hydraulic resistance; and (ii) to allow selective removal of small molecules from the original solution while retaining the larger species, which are unable to diffuse through the membrane [13,15,17,25,28], It is well known [17,25] that large differences in membrane permeability between different species may yield only modest separation efficiencies. This fact does not hamper the widespread clinical use of hemodialysis, because the toxic metabolites to be removed (e.g., urea) are vastly smaller than other constituents of blood (cells, proteins, etc.)…”