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Chapter 3. Mathematical Modeling of PSA Systems effect of pressure dynamics (swings) on the adsorption behavior is taken into account. In fact, the primitive PSA design was labeled as a “heat less dryer” [137]. However, with PSA being employed for the bulk separation and purification operations handling multi-component mixtures, the heat of adsorption can be quite significant and neglecting heat effects inside the bed can seriously impact the model performance. Therefore, incorporating energy balance in the modeling framework, although amplifies the computational complexity for a given model, is of utmost importance, and is formulated in Eq. (3.7). (εb +(1−εb)εp) Ncomp Ncomp ∑ ∂T ∑ ∂T i=1 =λ∂2T ∂z2 ( ( i=1 ∆d 2 ) −1 Cpwρw (3.7) ∂T ∂t +Cpsρp(1−εb) ∂t Ncomp ∑∂Q ) ∂T ∂t Ci(Cpi −R) ∂t +ρp(1−εb) Ncomp i=1 Qi(Cpi −R) ∂t ∂T i=1 CiCpi ∂z −(εb +(1−εb)εp)RT Ncomp ∑ +U −ρp(1−εb) i (−∆Hi)+ i=1 ∂t ∑ ∂Ci 1+ w The above formulation is a combined gas/solid energy balance and incorpo- rates the contribution of solid phase, gas phase both in adsorbed and non adsorbed state, and the metal wall subsystems in a single expression and thus provides a single temperature value for the whole system (see also Appendix A). The main condition for the lumped energy balance to remain valid is the requirement of thermal equilibrium between the various subsystems, caused by fast rates of heat transfer among them. Furthermore, the beds are also assumed to be operating under adiabatic conditions. In the past, only few studies have considered applying separate energy balances for each sub system, however the results were found to be only marginally better than the results obtained from the lumped formulation [129]. 52 DPDF Image | Operation and Control of Pressure Swing Adsorption Systems
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