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balance in the bulk gas phase ε ∂Ci +(1−ε)ρ ∂qi +∂vCi =0 i=1,...,N (2.14) b∂t bs∂t∂x c Here we assume no radial dependence for concentration and solid loading. Thus, in the equa- tion above, Ci and qi represent cross-sectional average values. Numerical dispersion in such hyperbolic systems is generally mitigated by considering a large number of spatial discretization nodes or by utilizing high-resolution spatial discretization techniques. 2.3.4 Energy Balance As mentioned before, an adsorption process is accompanied by the evolution of heat, and temperature changes influence the adsorption equlibrium behavior. Thus, accounting for heat generation and transfer in adsorbent beds is essential for accurate modeling of PSA processes. The heat generated on the adsorbent surface is transported through conduction between ad- sorbent particles and through convection in the bulk gas phase. The extent of temperature variation in an adsorption chamber depends primarily on the heat of adsorption, bulk-phase transport properties, and heat transfer characteristics of the packed bed such as thermal con- ductivity and heat transfer coefficient [67]. In general, temperature difference is neglected and thermal equilibrium is assumed between the bulk gas phase and adsorbent particles. Moreover, heat transfer in the axial direction by thermal conduction is often negligible unless the operation is adiabatic at a very high flow rate. Based on these assumptions, the energy balance for the system is given by ε C(Ci −R)+ρC ∂T −ρ ∆Hads∂qi +∂vh+U (T−T )=0 b ipg bps∂tb i∂t∂xA w ii Ci =ai +biT +ciT2 +diT3 i=1,...,N pgcccc c h= CCidT i pg i (2.15a) (2.15b) (2.15c) 2.3 PSA Modeling Chapter 2. Pressure Swing Adsorption 20PDF Image | Design and Operation of Pressure Swing Adsorption Processes
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