Mass transfer Through a membrane

As demonstrated by means of residue curve analysis, selective mass transfer through a membrane has a significant effect on the location of the singular points of a batch reactive separation process. The singular points are shifted, and thereby the topology of the residue curve maps can change dramatically. Depending on the structure of the matrix of effective membrane mass transfer coefficients, the attainable product compositions are shifted to a desired or to an undesired direction. 

Let us again consider the same problem of mass transfer through a membrane of Example 12.5 but this time we account for the fact that diffusivity is a function of the intramembrane concentration. The nondimensional equation can be written as... 

Thomas S, Schafer R, Caro J, Seidel-Morgenstem A. Investigation of mass transfer through inorganic membranes with several layers. Catal Today 2001 67 205-216. 

For effective mass transfer through the membrane, gas pressures far greater than those for PSA are needed. Metal membrane gas cleanup appears to be feasible only with a reformer system that is operating at a pressure of 20 atm194. 

Provided that the required information is available, based on Eqs. (26) and (27) several important questions can be answered in an early development stage - for example, how much membrane area must be provided per scale of the reaction zone and, more generally, whether a more detailed investigation of the coupling reaction and mass transfer through the membrane considered is justified. 

It is clear that the cyclohexane conversion increases with an increasing sweep ratio y- that is, with increasing driving forces for mass transfer through the membrane. In addition, the introduction of a more diluted feed leads to an enhanced conversion. Proof of an effect of the realized product removal via the Vycor glass membrane was the fact that the achieved conversions exceeded the equilibrium conversions (shown as dotted fines in Fig. 12.10). 

Poiseuille and Knudsen flow generally govern the mass transfer through the membrane in the above-defined nonseparative applications of membrane reactors. In this context, with special reference to the transition region from Poiseuille to the Knudsen flow (pore size = 0.1 1 p.m), the so-called Dusty-Gas Model [47], which combines a... 

A theory of gas diffusion and permeation has recently been proposed [56] for the interpretation of experimental data concerning molecular-sieve porous glass membranes. Other researchers [57,58], on the basis of experimental evidences, pointed out that a Stefan-Maxwell approach has to be preferred over a simple Pick one for the modeling of mass transfer through zeolite membranes. 

Mass transfer through the membrane can be adjusted by changing two major variables of the acceptor (upper) chamber. Thus, Xhe flow-rate of the acceptor fluid is a key to improved pervaporation this can be achieved through a displacement in the mass transfer equilibrium resulting from the continual use of fresh acceptor fluid — which maximizes the concentration gradient between both chambers. Keeping the fluid static facilitates attainment of an equilibrium or near-equilibrium state for mass transfer. 

The mass transfer through the membranes is achieved by application of an external driving force. The mass transport through porous membranes is enabled by a hydrostatic pressure difference (driving force) between the feed-side and the... 

M. Tasaka, T. Mizuta and O. Sekiguchi, Mass transfer through polymer membranes due to a temperature gradient, J. Membr. Sci., 1990, 54, 191-204. 

What is important to recognize from the discussion is that the boundary condition for mass transfer through a semipermeable membrane is directly analogous to that for a mixed heterogeneous reaction. A consequence of this is that what is said about the one problem can be translated to the other, despite the somewhat different physics and chemistry. The example of reverse osmosis is therefore used as an illustration of a mixed heterogeneous reaction. The major part of the discussion will, however, be confined to the developing layer, where... 

It is agreed that the permeabilities of the components may not be constant, but rather depend on a number of factors, such as the retentate and/or permeate composition(s), and mass transfer through the membrane can be quite complex. However, for demonstration purposes, a simplified approach will be followed. For this reason, constant relative permeabilities have been assumed, resulting in what is known as a Knudsen membrane [12]. 

Thomas, S., Schafer, R., Caro, J. and Seidel-Morgenstem, A., 2001. Investigation of Mass Transfer through Inorganic Membranes with Several Layers. Catalysis Today, 67(1 3) 205-216. 

Membrane distillation (MD) has been successfully applied and demonstrated for effective removal of ethanol from the fermentation broth. In MD, volatile feed components are evaporated through air-fiUed pores of a hydrophobic membrane. In the ethanol production, the aqueous solution containing ethanol is heated and vapors are formed, which go through the porous hydrophobic membrane that favors the transport of ethanol as compared with water vapor. Thus, the membranes in MD separate two aqueous solutions differing in temperature and composition. The driving force for the mass transfer through the membrane is the gradient of partial pressure caused by the temperature difference across the membrane. 

Looking at the schematic representation of the flow profile within the fiber shown in Figure 3.107, it becomes apparent that a further sensitivity increase can be accomplished by changing the parabolic flow profile. When the fiber is packed with inert Nafion beads, the translational diffusion of ions is favored over longitudinal diffusion. This, in turn, improves the mass transfer through the membrane, which leads to a further increase in sensitivity, particularly pronounced in the case of orthophosphate as the salt of a weak acid. 

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