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Depending on the separation system, Freundlich model q∗ =qsbP1/n n>1, i=1,...,N iiii c or Langmuir-Freundlich model are occasionally used as adsorption isotherms. Both these models are empirical in nature with no sound theoretical basis, and both of these do not reduce to Henry’s Law in the low-concentration region. However, they can cogently represent the behavior of several systems over a wide range of conditions. 2.3.3 Material Balance PSA processes are generally carried out with packed adsorption columns. The dynamic be- havior of an adsorption column is governed by the coaction of adsorption kinetics, adsorption equilibrium, and fluid dynamics, and its understanding is vital for process modeling and anal- ysis [106, 156, 169, 206]. Assuming an axially dispersed plug flow pattern in a fixed bed adsorption column, the transient component material balance for the bulk gas phase is given by ε ∂Ci +(1−ε)ρ ∂qi +∂vCi =D ∂2Ci i=1,...,N (2.13) b∂t bs∂t∂xL∂x2 c We often omit the axial dispersion term from this equation while numerically integrating it because the numerical dispersion resulting from spatial discretization of the flux term always exists for any discretization scheme. Thus, considering physical dispersion, together with the inevitable numerical dispersion, causes additional smearing of the solution profiles. Hence, instead of a parabolic formulation, the following hyperbolic form is used for component material qsbiP1/n q∗ = i i i=1,...,N (2.11) (2.12) i 1+ bjP1/n c jj 2.3 PSA Modeling Chapter 2. Pressure Swing Adsorption 19PDF Image | Design and Operation of Pressure Swing Adsorption Processes
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