Modeling and Design Considerations

As emphasized in the preceding sections, the successful application of membranes for separation purposes depends primarily on discovery of economically competitive membranes with high permselectivities and permeabilities. However, the ensuing considerations, such as membrane configurations and flow patterns of the feed and the permeant streams, are also very important in determining the performance of foe final separator system. 

The three major membrane configurations, flat sheet, spiral wound, and hollow fiber, each having advantages and limitations, will be reviewed briefly prior to considering the detailed analysis of these devices. Some of these issues include relative magnitudes of active membrane area per unit separator volume, minimization of pressure buildup in the permeant stream, membrane integrity, and the ease of module manufacture and membrane replacement. 

The permeability and selectivity of an asymmetric membrane are determined by its complex morphology 

If the hollow fiber is made of gla polymers, only small fiber deformation is tolerable over the possible operating pressure range to avoid rupture of the fiber wall. Since the selective dense layer on the outside region of the hollow fiber is normally very thin (less than 1500 A), it is understandable that the shell-feed mode, where the fiber is pressurized externally, is of most commercial interest since the dense layer may be ruptured by dilation if the fiber is pressurized internally. 

The inside and outside diameters of the fibers are in the ranges of 100-S(X) pm and 500-1000 pm, respectively, and the length has been rqiorted to be up to 16 ft. - When operated at high permeation rates, pressure buildup in the fiber bore can be substantial for small fibers (e.g., less than 1(X) pm). The increase in bore-side pressure will lower the overall production rate and undermine selectivities cranpared to cases with milder pressure profiles. Nevertheless, due to its large membrane area per separator volume and self-supporting feature, the hollow fiber is a vety desirable configuration as fer as the overall performance and economical feasibility of membrane processes are concerned. Optimization of fiber dimensions (diameter and length) becomes particularly important for these systems. 

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The innovative potential and the ingenuity which have gone into designing libraries, vectors and selection protocols are impressive. However, considerable input has come from structural modelling and design considerations, in the proliferation of phage-display scaffolds to provide constrained variable epitopes in different environments or contexts . In addition the method has been used to understand protein folding, protein-protein interactions and structure-function relationships in catalysis. I hope that, in this review,... 

A considerable literature exists dealing with Ihe potential benefits and eaergy requirements associated with these approaches. These techniqees typically are applied in cases where high recoveries are desired. There fore, the use of Eq. (20.2-1) to establish compositions for material halances is compromised somewhat, and rather mdinus calculations are required. Examples of the applications of these techniques are summarized in the section entitled Modeling and Design Considerations. ... 

The latest development is now to combine continuous photochemistry with microstmctured equipment. Only very recenfly photochemical conversions in microreactors have received a considerable amount of attention due to the problem often encountered in conventional photoreactors that the distribution of radiation is inhomogeneous in the reaction zone. During the scale-up process, such inhomogeneities often require intensive modeling and design considerations usually on the basis of photon transport models [66], and such models have been, for example, developed for biomedical and analytical purposes [67]. The problem of the intensity distribution in a reactor is illustrated in Figure 3.10. It is obvious that spatial restriction of the irradiation zone in a microphotoreactor to a... 

In this paper an overview of the developments in liquid membrane extraction of cephalosporin antibiotics has been presented. The principle of reactive extraction via the so-called liquid-liquid ion exchange extraction mechanism can be exploited to develop liquid membrane processes for extraction of cephalosporin antibiotics. The mathematical models that have been used to simulate experimental data have been discussed. Emulsion liquid membrane and supported liquid membrane could provide high extraction flux for cephalosporins, but stability problems need to be fully resolved for process application. Non-dispersive extraction in hollow fib er membrane is likely to offer an attractive alternative in this respect. The applicability of the liquid membrane process has been discussed from process engineering and design considerations. 

To design large scale supercritical desorption processes is necessary to understand in which way dynamic desorption is influenced by process variables as mass transfer effects and equilibrium considerations. The governing equilibrium in all desorption processes is the adsorption equilibrium and a description of this equilibrium is essential in all desorption models and design equations [3]. 

Figure 10.3 Considerations for process modeling and design of multienzyme systems. (Santacoloma, P.A. 2012 [41], Thesis. Reproduced with permission of the Technical University of Denmark, Lyngby/Denmark.)...

Several reported chemical systems of gas-liquid precipitation are first reviewed from the viewpoints of both experimental study and industrial application. The characteristic feature of gas-liquid mass transfer in terms of its effects on the crystallization process is then discussed theoretically together with a summary of experimental results. The secondary processes of particle agglomeration and disruption are then modelled and discussed in respect of the effect of reactor fluid dynamics. Finally, different types of gas-liquid contacting reactor and their respective design considerations are overviewed for application to controlled precipitate particle formation. 

Variational difference methods (the Ritz method and the Bubnov-Ga-lerkin method). The Ritz and the Bubnov-Galerkin variational methods have had considerable impact on complex numerical modeling problems and designs of difference schemes. 

An important difference between the statistical mixture design techniques popular in HPLC and the PRISMA model is that the former yields a computed optimum solvent composition id>ile the latter relies on a structured trial and error approach, which is readily adaptable to TLC. Solvent changes and re-equilibration in HPLC can be quite time consuming, so that it becomes attractive to ainimize the number of experiments, while for TLC, experiments can be performed in parallel and time constraints are less significant. Changes in solvent strength are also more rapidly adjusted empirically within the PRISMA model when theoretical considerations are found inadequate or require modification due to differences in the experimental approach. 

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