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Table 2. Equations for vacuum swing adsorption model. Component material balance for i as CO2 or H2O ε∂Ci +ρs∂qi +∇·(⃗vCi)−DL∇2Ci =0 (1) ∂t ∂t Component balance for N2 through ideal gas equation of state CN = P −CCO −CH O (2) 2 RgT 2 2 Blake-Kozeny pressure flow relationship − dP = 150μv(1−ε)2 (3) dx Dp2 ε3 Linear driving force gas-to-solid mass transfer ρs∂qi =ki′(Ci−Ci∗) (4) ∂t Energy balance within a bed layer ρscp,s∂T +εcp,gC∇(⃗v·T)−K∇2T+hw,g(T−Tw,u)+hw,g(T−Tw,l)=ρs Ei∂qi (5) ∂t CO2 adsorption – Type I Toth isotherm representation i ∂t c◦ t=t◦ + T +r◦RH (6) (7) (8) aC∗ co2 E co2 E co2 a=a◦exp ReT qco2 = 1+(bCc∗o2)1/tt H2O adsorption – Type III Freundlich isotherm representation qH2O = αRH2 Superficial gas velocity within bed layer x xf−x Q = Qf xf + Q◦ xf b=b◦exp ReT Superficial gas velocity at layer boundaries during vacuum desorption (for Pi in atm and T in K) If Pd < 2 k/(k−1) flow is choked. P If d ≥ Pu v d (10) Acs SG·T vx , vx [m/s] = 235.116Cv Pu 1 1/2 (9) o f flowisnotchoked. vx ,vx [m/s]= o f Pu k+1 2 k/(k−1) k+1 Acs SG·T 277.236C Pu2−P2 1/2 6 of 15 American Institute of Aeronautics and AstronauticsPDF Image | Vacuum Swing Adsorption Units for Spacesuit Carbon Dioxide and Humidity Control
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