Membrane systems staged/cascaded

Constant-volume batch diafiltration is the most efficient process mode. Sequential batch diafiltration is a series of dilution-concentration steps. Continuous diafiltration practiced in one or more stages of a cascade system has the same volume turnover relationship for overall recoveries as sequential batch diafiltration. The residence time however is dramatically reduced. If recovery of permeable solids is of primary importance, the permeate from the last stage may be used as diafiltration fluid for the previous stage. This countercurrent diafiltration arrangement results in higher permeate solids at the expense of increased membrane area. 

The principal stages in complement activation. Complement activation occurs exclusively on the microbial cell membrane, where it is triggered by bound antibody or microbial envelope polysaccharides, both of which activate early complement components. Two sets of early components belong to two distinct pathways of complement activation. Activation of each complement system involves a cascade of proteolytic reactions. Each component of the complement system is a proenzyme that is activated by the preceding component of the chain by a limited proteolytic cleavage. The ultimate result of this chain reaction is the development of a complex that attacks the cell membrane. 

Figure P3-10 shows a two-stage membrane cascade with recycling for producing ethylene product with a polymer-grade composition of 0.999 mol percent. The fresh feed pressure of2605 kPa and temperature of 28°C are identical to the conditions shown for stream 4 in the series configuration hybrid system presented in Fig. P3-8. The process conditions for this cascade contiguration are shown in the accompanying table.

Single membrane units can be evaluated based on their geometry and operation conditions. Zolandz and Fleming [4] provide a good description for gas permeation systems and models for design purposes. Sender [5] discusses the use of cascades (or staging) for various series and/or parallel sets of membrane modules. 

Operating Line and "Equilibrium" Curve. Both terms are of importance for the graphical solution of a separation problem, i.e., for the graphical determination of the number of stages of a cascade. This method has been developed for the design of distillation columns by MacCabe and Thiele and should be well known. For all cases, the operating line represents the mass and material balances. In distillation, the equilibrium curve represents the thermodynamical va-por/liquid equilibrium. For an ideal binary system, the equilibrium curve can be calculated from Raoult s law and the saturation-pressure curves of the pure components of the mixture. In all other cases, however, for example, for all membrane processes, the equilibrium curve does not represent a thermodynamical equilibrium at all but will represent the separation characteristics of the module or that of the stage. 

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