Mass-transport selectivity, description

Krishna and Paschek [91] employed the Maxwell-Stefan description for mass transport of alkanes through silicalite membranes, but did not consider more complex (e.g., unsaturated or branched) hydrocarbons. Kapteijn et al. [92] and Bakker et al. [93] applied the Maxwell-Stefan model for hydrocarbon permeation through silicalite membranes. Flanders et al. [94] studied separation of C6 isomers by pervaporation through ZSM-5 membranes and found that separation was due to shape selectivity. 

Studies with many types of porous media have shown that for the transport of a pure gas the Knudsen diffusion and viscous flow are additive (Present and DeBethune [52] and references therein). When more than one type of molecules is present at intermediate pressures there will also be momentum transfer from the light (fast) molecules to the heavy (slow) ones, which gives rise to non-selective mass transport. For the description of these combined mechanisms, sophisticated models have to be used for a proper description of mass transport, such as the model presented by Present and DeBethune or the Dusty Gas Model (DGM) [53], In the DGM the membrane is visualised as a collection of huge dust particles, held motionless in space. 

AH mass transport processes, which can be defined as the technology for moving one species in a mixture relative to another, depend ultimately upon diffusion as the basis for the desired selective motion. Diffusion takes many forms, and a general description is provided in Table 115.7 of Chapter 115 of previous edition. However, a great deal of information can often be obtained by carefully written statements of simple constraints, and that of conservation of mass is the most useful for our purposes. We shall begin with examples where this suffices and show how one can determine the vaUdity of such a simple approach. We then proceed to situations where more detailed analysis is needed. 

The measurement of partial pressures over a liquid or solid mixture of two metals is not as simple. Mostly, it is restricted to higher temperatures or even to the molten phase. The direct measurement can be done, for example, in high or ultra high vacuum, using a Knudsen cell and a mass spectrometer for selective pressure determination. Dynamic measurements were developed, e.g., transportation methods. A steady stream of a reactive gas is passed over the sample transporting the reactive component to a cooled region of the apparatus. From the measured mass of the transported metal and the flow rate the vapor pressure can be calculated. Kubaschewski et alP have given a detailed description of the experimental possibilities. 

The interactions between the chemical reaction and the simultaneously occurring transport processes for mass, energy, and impulse can be described by the fundamental conservation laws. At first the system boundaries must be specified. The volume enclosed by these boundaries is called system volume. The size of the system volume can be defined by natural boundaries, such as those of the phase boundary, the reactor, or by a small volume element of a phase through the defined limits of which mass, energy, and impulses can be exchanged (see Figure 2.1). For an unambiguous description, however, it is necessary to select the system volume in such a way that the conditions in it can be considered as uniform (e.g., constant temperature and concentrations). 

In these balance equations all terms should be described at the same level of accuracy. It certainly does not pay to have the finest description of one term in the balance equations if the others can only be very crudely described. Current demands for increased selectivity and volumetric productivity require more precise reactor models, and also force reactor operation to chum turbulent flow which to a great extent is uncharted territory. An improvement in accuracy and a more detailed description of the molecular scale events describing the rate of generation terms in the heat- and mass balance equations has in turn pushed forward a need for a more detailed description of the transport terms (i.e., in the convection/advection and dispersion/conduction terms in the basic mass- and heat balances). 

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