Dispersion mobile phase compressibility

In the above derivation of the mass balance equation, we assume that the column is radially homogeneous, the compressibility of the mobile phase is negligible, the axial dispersion coefficient is constant, and the temperature is unchanged. Furthermore, no diffusion in the stationary phase is assumed. 

Flow programming is not as effective in reducing the elution time of well-retained components and tends to cause increased band dispersion it is, however, more gentle than temperature programming and would be chosen when separating thermally labile materials. The complexity of the theoretical treatment depends on whether the mobile phase is compressible or not. In gas chromatography, the mobile phase is compressible, and this must be taken into account in the first theoretical treatment. 

All symbols have their usual meaning and only more important ones are defined here. Cj is the concentration of component j in the aqueous phase (e.g. polymer, tracer, etc.). The viscosity of the aqueous phase, rj, may depend on polymer or ionic concentrations, temperature, etc. Dj is the dispersion of component j in the aqueous phase Rj and qj are the source/sink terms for component j through chemical reaction and injection/production respectively. Polymer adsorption, as described by the Vj term in Equation 8.34, may feed back onto the mobility term in Equation 8.37 through permeability reduction as discussed above. In addition to the polymer/tracer transport equation above, a pressure equation must be solved (Bondor etai, 1972 Vela etai, 1974 Naiki, 1979 Scott etal, 1987), in order to find the velocity fields for each of the phases present, i.e. aqueous, oleic and micellar (if there is a surfactant present). This pressure equation will be rather more complex than that described earlier in this chapter (Equation 8.12). However, the overall idea is very similar except that when compressibility is included the pressure equation becomes parabolic rather than elliptic (as it is in Equation 8.12). This is discussed in detail elsewhere (Aziz and Settari, 1979 Peaceman, 1977). Various forms of the pressure equation for polymer and more general chemical flood simulators are presented in a number of references (Zeito, 1968 Bondor etal, 1972 Vela etal, 1974 Todd and Chase, 1979 Scott etal, 1987). 

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