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M. Mofarahi, E. J. Shokroo/Petroleum & Coal 55(3) 216-225, 2013 218 ∂2y ∂u ⎛∂y ⎛1 ∂P 1 ∂T⎞⎞ −D i+y.+u.i+y..−. + L∂z2 i∂z ⎜∂z i⎜P∂zT∂z⎟⎟ ⎝⎝⎠⎠ (3) Another characteristic of adsorption process is temperature variations caused by heat of adsorption and desorption occur. In this system, energy balance for the gas phase and also heat transfer to the bed wall is included, [19]: −Kl ∂yi +y⎛1.∂P−1.∂T⎞+⎛ρp.R.T⎞.⎛1−ε⎞.∂qi =0 ∂t i⎜P∂tT∂t⎟⎜P⎟⎜ε⎟∂t ⎝⎠⎝⎠⎝⎠ ∂P ∂u ∂P ⎛∂⎛1⎞ ∂⎛1⎞⎞ ⎛1−ε⎞ N ∂t ∂z ∂z ⎝∂t⎝T⎠ ∂z⎝T⎠⎠ ⎝ ε ⎠i=1 ∂t ∂q +P +u +PT.⎜ ⎜ ⎟+u ⎜ ⎟⎟−ρp.R.T.⎜ ⎟.∑ i =0 (4) ∂2T ⎛∂T ∂u⎞ 2 +ε.ρg.cp,g.⎜u +T ⎟+(εt.ρg.cp,g +ρB.cp,s). ∂T N⎛∂q ⎞ −ρB. ⎜ i .(−ΔH )⎟+ ∑ ∂ti=1⎝∂t⎠ ∂z ⎝∂z∂z⎠ i (5) To evaluate heat loss through the walls and the accumulation of energy, (7) 2hi (T−Tw)=0 RB,i corresponding to an energy balance has also been used, [19]: ρ.c .A ∂Tw =2πR h(T−T)−2πR h(T −T ) (6) w p,w w ∂t B,i i w B,o o w atm where, The well-known Danckwerts boundary conditions are applied Pressurization and production step A=π(R2 −R2) w B,o B,i ⎛∂y ⎞ −Dl⎜ i⎟ ∂y +); i =0 =u.(yi =ρg.cp,g.u.(Tz=0− −Tz=0+ );∂z =0 (9) ⎝ ∂z ⎠ z=0 − −yi z=0 ∂z (8) z=0 ⎛ ∂T ⎞ −Kl⎜⎝∂z⎟⎠ z=L ∂T z=L Where yi z=0− means the feed composition for the component i. z=0 Counter current purge step ⎛∂y ⎞ −Dl⎜ i⎟ ∂y + −yi −); i =0 (10) =u.(yi =ρg.cp,g.u.(Tz=L+ −Tz=L− );∂z =0 (11) ⎝ ∂z ⎠ ∂z means a volume-averaged composition of the effluent stream during the z=L ⎛ ∂T ⎞ −Kl⎜⎝∂z⎟⎠ z=L Where yi z=L+ z=0 adsorption step for the purge step. Counter current blow down step z=L z=L z=0 ∂T ∂yi ∂z z=0 ∂T Pressurization and counter current blow down step = ∂yi ∂z z=L = 0 (12) (13) = ∂T = 0 Boundary conditions for the interstitial velocity ∂z z=0 ∂z z=L uz=L =0 (14) Pressurization and production step uz=0 =ufeed Counter current purge step (15)PDF Image | PRESSURE SWING ADSORPTION PROCESSES FOR AIR SEPARATION WITH ZEOLITE
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