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3 PSA dynamic model 23 CTg+CvTg−k 2Tg+Pvg+ha(T−T)+4hw(T−T)=0 (Eq.3.1-5) B vg g t vg g g z i gz z2 z p g s D g a B T 2T T w C s −k s + (C w) s +Hk k −hap(Tg −Ts)=0 (Eq.3.1-6) pakk s ps s t sz z2 s t t kk Specifically, Eq. 3.1-5 includes terms of enthalpy accumulation in the gas phase, convection, axial thermal conduction, thermal effect of compression, and heat transfer between gas and solid phases. The variation of gas thermal conductivity kgz with the temperature is considered and calculated by empirical equation [75] as presented in Appendix 10.2. The gas-solid heat transfer coefficient h is implemented as a function of Reynolds and Prandtl numbers, according to the method presented in Appendix 10.3. Furthermore, the heat exchange between gas in the column and the environment is included in the gas phase energy balance. The equation involves the gas-wall heat transfer coefficient (HTC) hW which combines: (1) heat transfer resistances of the boundary layer between gas and wall on the inside of the column, (2) the material of the column wall, and (3) boundary layer between the outer column wall and the ambient. The specific particle surface ap is calculated according to Eq. 3.1-7. a =3(1−i) (Eq.3.1-7) Eq. 3.1-6 includes terms of enthalpy accumulation in the solid phase, axial thermal conduction, heat of adsorbed phase, thermal effect of the adsorption process, and heat transfer between gas and solid phases. The alteration of the adsorbed phase heat capacity Cpak with the temperature is considered and calculated by an empirical equation [75,76] as presented in Appendix 10.4. p rp Tab. 3.1-1 Parameters of the PSA dynamic model Packed bed diameter Average packing density Intra-particle voidage Average adsorbent particle radius Adsorbent thermal conductivity HTC between gas and adsorber wall Product receiver diameter Heat capacity of the product receiver shell HTC between product receiver shell and ambient Top-void volume Db [mm] 66 ρs [kg/m3] 711 εp [m3 void/m3 pellet] 0.234 rp [mm] 0.830 ksz [W/m/K] 0.675 hw [W/m2/K] 50 DR [mm] 220 CpR [J/kg/K] 500 hRa [W/m2/K] 20 VT [cm3] 35 Average packed bed length Hb [mm] 581 Inter-particle voidage εi [m3 void/m3 bed] 0.404 Total bed voidage εB [m3 (void+pore)/m3 bed] 0.543 Specific particle surface ap [m2 particle area/m3 pellet] 2155 Adsorbent specific heat capacity Cps [J/kg/K] 880 Product receiver volume VR [L] 12 Mass of product receiver shell mR [kg] 4.8 HTC between gas and product receiver shell hR [W/m2/K] 50 Bottom-void volume VB [cm3] 18.5 Mass and energy are accumulated within the product receiver tank (R) and adsorber voids (B_A1, B_A2, T_A1, T_A2). The ideal mixing of gas within each volume is assumed. In thisPDF Image | Modelling and Simulation of Twin-Bed Pressure Swing Adsorption Plants
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