Cocurrent membrane separators

We briefly describe cocurrent dialysis and gas permeation processes. 

In Section 4.3.1, we were introduced to a hemodialyzer with blood on one side of the membrane and the dialyzing solution on the other side. Solutes (metabolic waste products) from blood diffused through the liquid filled pores of the membrane to the dialysate side. Using a simple lumped analysis based on the overall solute mass-transfer coefficient Ku, we will develop an expression for the solute removal efficiency of a hemodialyzer in which blood as well as the dialyzing solution are in steady cocurrent flow (Section 8.1.7 treated countercurrent dia-lyzers). The analysis is valid for any other system, not just hemodialysis. 

Y+ (QflQd)) Cjfo Cifl) fri [(Ciyo Cido)I CifL — Cidl)] 

To that end, we carry out the following manipulations. From the mass balance relations (8.2.43), we get 

For a rectangular feed-gas flow channel of width W and length L, 

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We will first provide a very brief illustration of the governing equations for mass transport and the operating line for a two-phase continuous cocurrent separation system in a conventional chemical engineering context. This will be followed by a brief treatment of the multi-component separation capability of such a system. Cocurrent chromatographic separation in a two-phase system, where both phases are mobile and in cocurrent flow, will be introduced next. The systems of interest are micellar electrokinetic chromatography (MEKC) chromatography with two mobile phases, a gas phase and a liquid phase capillary electrochromatography, with mobile nanoparticles in the mobile liquid phase. Continuous separation of particles from a gas phase to a cocurrent liquid phase in a scrubber will then be illustrated. Finally, cocurrent membrane separators will be introduced. 

Walawender WP and Stem SA. Analysis of membrane separation parameters. 2. Countercurrent and cocurrent flow in a single permeation stage. Sep. Sci. 1972 7 553-584. 

Figure 13.3-4. Idea flow patterns in a membrane separator for gases (a) complete mixing, (h) cross-flow, (c) countercurrent flow, (d) cocurrent How.

FIGURE 18.6 (a) Countercurrent flow and (b) cocurrent flow membrane separators. 

Countercurrent and Cocurrent Plug Flows. The model equations for these flow patterns cannot be solved analytically. Oishi and coworkers first derived the general model eqnstions for a binary-component system with porous media.19 Walawenderand Stem,16 Blaisdell and Kammermeyer,1 and Pan and Habgood17 later reported solutions for similar membrane separators. The cocurrent-counteicurrent combiner inu flow pattern also lies been studied by Pen ned Habgood.17... 

W. P. Walawender and S. A. Stem, Analysis of Membrane Separation Parameters. II. Counter-cunent and Cocurrent Flow in a Single Permeation Process, Sep. Set., 1, 553 (1972). 

FIGURE 18.6 Countercurrent flow (a) and cocurrent flow (b) membrane separators. 

Hollow-fiber membranes may be run with shell-side or tube-side feed, cocurrent, countercurrent or in the case of shell-side feed and two end permeate collection, co- and countercurrent. Not shown is the scheme for feed inside the fiber, common practice in lower-pressure separations such as air. 

In Example 9.2, perfect mixing was assumed on both sides of the membrane. Three other idealized flow patterns, common to other mass-transfer processes, have been studied countercurrent flow, cocurrent flow, and crossflow. For a given cut, the flow pattern can significantly affect the degree of separation achieved and the membrane area required. For a given membrane module geometry, it is not always obvious which idealized flow pattern to assume. Hollow-fiber modules are the most versatile since they may be designed to approximate any of the three flow patterns mentioned above. 

Calculation of the degree of separation of a binary mixture in a membrane module for cocurrent or countercurrent flow patterns involves the numerical solution of a system of two nonlinear, coupled, ordinary differential equations (Walawender and Stem, 1972). For a given cut, the best separation is achieved with countercurrent flow, followed by crossflow, cocurrent flow, and perfect mixing, in that order. The crossflow case is considered to be a good, conservative estimate of module membrane performance (Seader and Henley, 2006). 

Microfluidic Microdialysis Systems Most microfluidic microdialysis systems consist of a two-compartment system with a sample flow channel and perfusion flow channel separated by the microdialysis membrane. A two-compartment cocurrent mass transport model of microdialysis is shown in Fig. 3. For this microdialysis system, molecules inside the sample channel are dialyzed across the membrane into the perfusion flow channel. Again, this system may be modeled by balancing the sample and perfusion convective fluxes with the diffusion of analyte across the membrane. Assuming the overall permeability... 

Similarly to partially overlapping channels, microchannels with mesh contactors (Figure 7.2h) are used to create the partial contact of fluids. The advantage of these contactors is that both modes of operation, cocurrent and countercurrent, can be apphed. Besides, the flow is stabilized because of the solid support between two fluids. The solid contactors are porous membrane [9, 10] and metal sheets with sieve-like structure [11]. Similarly to parallel flow, the mass transfer in both cases is only by diffusion and the flow is under laminar flow regime dominated by capillary forces. The membrane contactor has the advantage of being flexible with respect to the ratio of two fluids. In addition to flow velocities, the mass transfer is a function of membrane porosity and thickness. In another type of microextractor, two microchaimels are separated by a sieve-like wall architecture to achieve the separation of two continuous phases. However, the hydrodynamics in both types of contactors is more complex because of interfadal support and bursting of fluid... 

In general, it has been concluded by many parametric studies that at the same operating conditions the countercurrent flow pattern yields the best separation and requires the lowest membrane area. The order of efficiency is as follows countercurrent > cross-flow > cocurrent > complete mixing. 

The cross-flow model for reverse osmosis is similar to that for gas separation by membranes discussed in Section 13.6. Because of the small solute concentration, the permeate side acts as if completely mixed. Hence, even if the module is designed for countercurrent or cocurrent flow, the cross-flow model is valid. This is discussed in detail elsewhere (HI). 

In general, it has been concluded that countercurrent flow is the most efficient flow pattern, requiring the lowest membrane area and producing the highest degree of separation, at the same operating conditions. The order of efficiency for the other three flow patterns is crossflow > cocurrent flow > perfect mixing. 

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