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The four terms in the model describe the following phenomena in order: 1) axial dispersion 2) convective flow 3) gas phase accumulation 4) adsorption rate (i.e. solid phase accumulation). The adsorption rate is often described using a linear driving force (LDF) model expressed as: 25 where ni* is the equilibrium value of component i in the adsorbed phase at a given fluid phase concentration, and ni is the adsorbed phase concentration of component i, both averaged over an adsorbent particle. The mass transfer coefficient (MTC), ki, of a spherical particle is typically approximated as:24 where kf, is the film transfer coefficient, rp and rc are the particle and crystal radius respectivley, Dp and Dc are the macropore and micropore diffusivity of component i respectively, εp is the particle macroporosity, and K is the dimensionless equilibrium constant related to the Henry constant, KH, by K= KHRTρp. The three terms on the right side of the equation account for resistance to mass transfer in the film, macropore and micropore respectively. Equation 3.13 is defined from a flux equivalency through the three resistances in series and is exact for linear isotherms in the Henry’s law region. While only strictly applicable to linear isotherms, it is a useful approximation for non- linear isotherms, especially to understand the relative importance of different resistances. If the macropore term is considered controlling, equation 3.13 simplifies to: 42PDF Image | LIMITS OF SMALL SCALE PRESSURE SWING ADSORPTION
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