Membrane perfect mixing

Assuming perfect mixing in each compartment of the membrane pack and reservoir of the ED unit shown in Figure 9, the solute concentration in any of them is uniform and equal to that of the outlet stream. Therefore, by assuming pseudo-steady state conditions in any compartment, the differential solute and water mass balances in the diluted (D) and concentrated (C) reservoirs can be written as follows ... 

Several authors have already developed methodologies for the simulation of hybrid distillation-pervaporation processes. Short-cut methods were developed by Moganti et al. [95] and Stephan et al. [96]. Due to simplifications such as the use of constant relative volatility, one-phase sidestreams, perfect mixing on feed and permeate sides of the membrane, and simple membrane transport models, the results obtained should only be considered qualitative in nature. Verhoef et al. [97] used a quantitative approach for simulation, based on simplified calculations in Aspen Plus/Excel VBA. Hommerich and Rautenbach [98] describe the design and optimization of combined pervaporation-distillation processes, incorporating a user-written routine for pervaporation into the Aspen Plus simulation software. This is an improvement over most approaches with respect to accuracy, although the membrane model itself is still quite... 

Figure 3.9 Representation of the membrane filtration unit as an ensemble of three small perfect mixing filters.

Figure 10.3 Schematic diagram of a single cell or perfect mixing model for a packed-bed membrane shcll-and-tube reactor...

The flow conditions (e.g., co-cunent vs. counter-current and plug flow vs. perfect mixing) on both sides of the membrane can have significant effects on the conversion [Itoh et al., 1990] and will be discussed in Chapter 11. 

In those limited cases where the diffusion equation for the membrane/support composite is solved in conjunction with the governing mass transport equations for the tube and shell sides [Sun and Khang, 1988 and 1990 Agarwalla and Lund, 1992], Equation (10-5) applies with = 0 for catalytically inert membranes. In addition, either Equations (10-36) for plug flows or Equation (10-54) for perfect mixing needs to be solved for the... 

Figure 10.13 Yield and selectivity of C2 products in a perfectly mixed membrane reactor [Wang and Lin, 1995)...

None of the above studies, however, deals with the detailed hydrodynamics in a membrane reactor. It can be appreciated that detailed information on the hydrodynamics in a membrane enhances the understanding and prediction of the separation as well as reaction performances in a membrane reactor. All the reactor models presented in Chapter 10 assume very simple flow patterns in both the tube and annular regions. In almost all cases either plug flow or perfect mixing is used to represent the hydrodynamics in each reactor zone. No studies have yet been published linking detailed hydrodynamics inside a membrane reactor to reactor models. With the advent of CFD, this more complete rigorous description of a membrane reactor should become feasible in the near future. 

The above discussion pertains to dense membrane reactors. For the case of a semipermeable membrane reactor which has finite permselectivities for the various reaction components, isothermal operations favor the plug flow membrane reactor over the perfect mixing membrane reactor for both endothermic and exothermic reactions. In the case of exothermic reactions, the difference between the two flow patterns is rather small for low feed temperatures [Mohan and Govind, 1988b]. 

Preferred flow patterns in nonisothermal membrane reactors. The discussions so far focus on flow patterns in an isothermal membrane reactor. In many situations, however, the membrane reactor is not operated under a uniform temperature. The choice between a plug flow (PFMR) and a perfect mixing membrane reactor (PMMR) depends on a number of factors. First of all, it depends on whether the reaction is endothermic or exothermic. 

Figure 11.11 Difference in conversion between plug flow membrane reactor and perfect mixing membrane reactor as a function of permeation to reaction rate ratio for an exothermic reaction [Mohan and Govind, 1988b]...

They have also modeled a perfectly mixed membrane reactor for the same reaction. For this membrane configuration, the C2 selectivity is essentially 1(X)% for a jo value of less than 0.2 and drops off rapidly with increasing The yield becomes greater as the relative oxygen permeation rate increases. The yield reaches a maximum and then decreases with the permeation rate. There is only a limited range of Jo in which the yield can reach beyond 20%. 

Perfect-mixing membrane reactor. Mohan and Govind [1988b] have also analyzed the behavior of perfect-mixing membrane reactors (PMMR). Similar to the case of plug-flow membrane reactors, the reaction conversion in a PMMR is determined by the nature of the heat of reaction. 

Membrane reactor stability. Multiple steady states have been found in continuous stirred tank reactors (perfect-mixing reactors) or other reactors where mixing of process streams take place. This phenomenon is also evident in membrane reactors. The thermal management of a membrane reactor should be such that the reactor temperatures provide a stable range of operation. 

The flow directions (e.g., co-currcni, counter-current and flow-through) and flow patterns (e.g., plug flow, perfect mixing and fluidized bed) of feed, permeate and retentate streams in a membrane reactor can significantly affect the reaction conversion, yield and selectivity of the reaction involved in different ways. These variables have been widely investigated for both dense and porous membranes used to carry out various isothermal and non-isothermal catalytic reactions, particularly dehydrogenation and hydrogenation reactions. 

Same as above. The effect of plug flow or of perfect mixing behavior is investigated at both membrane sides. 

It may be added that the reject or retentate phase for a membrane cell forms a continuum with the feed—assuming perfect mixing at every point—albeit it will take on a different flow rate and composition as permeation proceeds. Moreover, this... 

Figure 19.15. Staged permeation cascade with rectification and stripping sections. The individual membrane modules may be operated concurrently or counterconcurrently, or perfect mixing may be assumed to occur.

Consider the schematic membrane stream juxtaposition, by analogy with a phase separation, as diagrammed in Figure 19.17. The conditions and compositions for each stream do not change with position, whereby the circumstance is called perfect mixing. Nor do the conditions and compositions change with time, signifying the steady-state. 

Figure 19.17. Single-stage membrane separation with perfect mixing.

In CO- and countercurrent operations, the feed and permeate stream flow co-currently or countercurrently along the membrane. In the cross-flow mode, it is assumed that mixing occurs so rapidly on the permeate side that the composition distributes equally. Among these modes, countercurrent flow gives the best results, and the perfect mixing gives the worst result. 

The equations derived in the previous section represent penneation rates and flux, and Examples 18.1 and 18.2 are apphcations to a speciflc model. The model assumes the fluid on each side of the membrane to have a constant composition parallel to the membrane. The compositions normal to the membrane are also assumed constant, with the possible exception of composition gradients in the films adjacent to the membrane. The bulk phase compositions on both sides of the membrane had to be given since no material balances were considered. The flow pattern implied in this model is that of perfect mixing (if the film resistances next to the membrane are neglected). Other flow patterns include cross flow, countercurrent flow, and cocurrent flow. 

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