Mass Transfer through the Membrane

In general, the Vycor glass membrane can be considered to be a membrane of the Knudsen type. Thus, the selectivity of transport of two gases i and j is approximately related to their molecular weights [27] according to  

A comparison is shown in Fig. 12.9 of the transient pressure difference between the two sides of the membrane after introducing a feed composition change at one side [30]. The good agreement between the predicted and measured 

By using the parameters detailed above, it could be estimated that for a partial pressure difference of 1 bar, hydrogen fluxes through the Vycor glass of ca. JHl = 5 x 10 7 mol cm-2 s could be achieved. 

in order to achieve interaction between the reaction process and the transport process the required membrane area per mass of catalyst must be in the following range  

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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... 

The rate of mass transfer through the membrane is proportional to the gradient of this curve, and thus decreases from an initial value to practically zero. The concentration enrichment factor value at equilibrium will be... 

The mass transfer smdies in AGMD suggest that, the transport of vapor through the membrane can be modeled by molecular diffusion mechanism [57], since the pore size of the membrane used is much bigger than the molecular mean free path of water vapor. Equations 19.23 and 19.27 can be used to calculate the mass transfer through the membrane. 

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 pertraction efficiency, E, is defined as the fraction of substances transported from the feed (donor) phase to the strip (acceptor) phase. It is the measure of the rate of mass transfer through the membrane and is constant at specified pertraction time, phase composition, and ionic strength. The pertraction is expressed as... 

In making the choice for an organic hquid membrane solvent, several aspects should be taken into consideration. First of all, the organic hquid should be hydrophobic enough to ensure immiscibihty with aqueous phases. Secondly, the solvent has to be characterized by low viscosity, which results in high mass transfer through the membrane. In this case, note that low viscosity decreases membrane stabihty. Surface tension... 

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... 

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]. 

The linear relationship between flux and vapor pressure differential indicates that mass transfer through the membrane was directly dependent on vapor pressure differential and concentration polarization effects are not changing with increases in flux. 

In this case, to describe the influence of the hydrodynamics in the cell and of the operating conditions on the mass transfer through the membrane, the following correlation can be used [80] ... 

The mass transfer through the membrane, during pervaporation with simultaneous polarizations of temperature and concentration, can be described using this system of three Equation (21.72)-Equation (21.74). 

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. 

The process of mass transfer through the membrane is determined by several factors ... 

If the fiber diameter varies either effect must taken into account. In case of a fiber diameter distribution within a module, small fibers could consume the product. If the whole feed stream entering a fiber permeates through the membrane, the pressure within the fibers will drop under the pressure of the retentate pressure, leaving larger fibers so that a backflow into the small fiber is induced. This results in a loss of product and will decrease the module recovery. The reduced pressure on the feed side also decreases the mass transfer through the membrane, which is indicated by eqn (5.19) ... 

Direct-Contact Membrane Distillation Configuration If the mean free path of the transported molecules is large in comparison with the membrane pore size (i.e., Kn > 1 or dp < X.,)> the molecule-pore wall collisions are dominant over the molecule-molecule collisions, and the Knudsen type of flow is responsible for mass transfer through the membrane pore. In this case the permeability through each pore in the Knudsen region was expressed as follows (Matsuura, 1994 Khayet et al., 2004a) ... 

Equation (12.22) seems simple and trivial. However, Ap, depends on both temperatures and concentrations at the membrane surfaces, which are not directly measurable and are different from those at bulk phases due to the simultaneous heat and mass transfers through the membrane. These phenomena are called temperature polarization and concentration polarization and are a major problem for MD. Therefore, the overall MD process rate... 

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