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Processes 2022, 10, 812 6 of 19 effective thermal conductivity of an adsorption bed, but this effect could be ignored under certain temperature conditions [47]. H=ρC w∂Ts (7) i spaii ∂t The rate of heat generation by the adsorption of each component i per unit mass of solid, depends on the local rate of mass transfer: HTi = ∂wi ∆Hi (8) ∂t These rates are held in vectors, HT, and summed for all components, to obtain the total rate of heat generation by adsorption per unit volume of solid: ρs ∑(−HTi) (9) i 2.4.2. Non-Isothermal Conditions and Thermal Equilibrium For non-isothermal conditions, an additional heat transfer coefficient resistance be- tween the adsorbent and gas introduces what can be calculated as follows: rate o f heat trans f erred per m3 o f bed = HTCapTg − Ts (10) When gas and solid are in thermal equilibrium, Tg = Ts. 2.4.3. Adiabatic, Thin-Wall, and Rigorous Models of Heat Transfer to Environment Adiabatic condition means no heat transfer occurs between the bed and the wall. For thin wall, the heat exchange between the gas in the bed and the environment is included in the gas-phase energy balance as: 4Hw Tg − Tamb (11) DB A rigorous model includes a wall-energy-balance equation that contains the following terms: heat transfer from the gas in the bed to the inner wall; heat transfer from the outer wall to the environment (including the influence of any insulating material); axial thermal conduction along the wall; and heat accumulation within the wall material. The governing equation is: ∂Tw 4DB 4(DB +WT)2 ∂2Tw −kw ∂z2 +ρwcpw ∂t −Hw(DB+WT)2−DB2 Tg−Tw +Hamb(DB+WT)2−DB2(Tw−Tamb)=0 (12) Abd et al. studied the three heat transfer models mentioned above on CO2 separation properties in a biomethane-upgrading system. The result showed that highest methane purity of 97% was presented in the rigorous model, followed by thin-wall (93%) and adiabatic (92%) systems. The rigorous model can help in the design of a new PSA system that can recuperate heat during the adsorption and desorption steps, for effective adsorption and regeneration. 2.5. One-Dimensional Process Model Usually, there are five basic cycle steps associated with any PSA process: adsorption, pressure equalization, purge/rinse, co-current or counter-current depressurization (blow- down) and re-pressurization steps, which can be scheduled in many different ways for a typical PSA process with multiple beds [48]. Many previous works reported approaches for a complex PSA-cycle scheduling, involving a priori specification of the cycle steps, their sequence, and the number of beds, and then following a systematic procedure basedPDF Image | Numerical Research on the Pressure Swing Adsorption Process
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