Simulation of a radial flow rapid pressure swing adsorption process

r 2 − R02 Define a new dimensionl ess position η = 2 2 R − R0 R 2 ⇒ r 2 = R02{η[( ) 2 − 1] + 1} = R0 (aη + 1) R0 R0 , R : inner and outer radius (refered to Fig. 2), a = ( R / R0 ) 2 − 1, range of η is[0 : 1].
Utilize Blake − Kozeny equation ∂P ................................(5) 150(1 − ε ) µ ∂r d p : particle size of adsorbent , µ : viscosity. u=−
2 2 d2 pε
direction for the radial flow RPSA are shown in Fig. 2. MATHEMATICAL MODELING To simplify the calculation, the following assumptions were used to model RPSA processes: local equilibrium between the adsorbent and the adsorbate, ideal gas, extended Langmuir isotherm describing adsorption behavior, neglecting the concentration gradient and pressure-drop in the axial direction, the relation between velocity and pressure-drop described by Blake-Kozeny equation, isothermal, and radically dispersed plug flow describing the flow type. Based on these assumptions, the governing equations are:
Simulation of a radial flow rapid pressure swing adsorption process
Wen-Chun Huang (¶À¤å«T )
Department of Chemical Engineering, Kao Yuan Institute of Technology, Lu-Chu, Taiwan, R.O.C
Define t µ = 150(1 − ε ) 2 µL2 eff ε d P
2 2 p 0
, td =
L2 eff Dr
3) − ( 4) become ∂φ ∂ 1 ∂ ∂φ + ( N A + NB ) = [( aη + 1)φ ]...(6) ∂t ∂t t µ ∂η ∂η φ ∂y ∂N ∂N + (1 − y ) A − y B = ∂t ∂t ∂t 1 ∂φ ∂y 1 ∂ ∂( yφ ) ( aη + 1)φ + [( aη + 1) ].(7) tµ ∂η ∂η t d ∂η ∂η
For local equilibriu m model ∂N A ∂N * ∂N * A ∂N B B = ; = ........................(9) ∂t ∂t ∂t ∂t
Boundary conditions for pressure are tµ q ∂φ =− (η = 0©Î 1)..............(10) ∂η (aη + 1)Vbed εφ Boundary conditions for mole fraction are at inlet end t d ( y feed − y in ) q ∂y =− (η = 0©Î 1)...........(11) ∂η ( aη + 1)Vbedε at outlet end ∂y = 0. ∂η
Total mass balance ∂C 1 − ε ∂ 1 ∂ + ( nA + n B ) = − (Cur)...........(1) ∂t ε ∂t r ∂r Mass balance for component A ∂CA 1 − ε ∂n A 1 ∂ + =− (C Aur ) + ∂t ε ∂t r ∂r ∂C A 1 ∂ ( Dr r ).............(2) r ∂r ∂r where C : total molar concentration in the gas, C A : molar concentration for component A, n A , n B : amounts of adsorption on adsorbent , u : velocity, Dr : radial dispersion coefficien t, r : distance, t : time, ε : void fraction of adsorber. Apply the ideal gas law, C = P / RT ∂P 1 − ε ∂ 1 ∂ + RT (n A + nB ) = − ( Pur)....(3) ∂t ε ∂t r ∂r
and Cheng-tung Chou (©P¥¿°ó )
Department of Chemical Engineering, National Central University, Chung-Li, Taiwan, R.O.C
Abstract- Compared to axial flow pressure swing adsorption (PSA) processes, radial flow PSA processes can have the larger cross section for the same volume of adsorbers. Radial flow PSA processes, thus, may have the advantage of low pressure-drop for the same volume flow rate and small particle size of adsorbent can be use for the same pressure-drop. A simulation program has been developed to simulate the dynamic of the adsorbers for the radial flow and the axial flow rapid PSA processes. The simulation results of an axial rapid PSA were compared with the experimental data in the literary. The effects of particle size of adsorbent, feed pressure, production rate, and feed direction on purity and recovery were explored also. Keywords : radial flow, rapid pressure swing adsorption, simulation, air separation INTRODUCTION Pressure swing adsorption (PSA) processes may be divided into multi-bed and single-bed processes according to the number of adsorbers. Single-bed PSA usually has the shorter cycle time compared to multi-bed PSA and is called rapid pressure swing adsorption (RPSA) generally. The larger pressure-drop is another character of RPSA processes. Rota and Wankat (1991) proposed the radial flow PSA first. The radial flow RPSA could provide the larger flowing cross section for the same volume of adsorbers compared to axial flow RPSA and has, thus, the less pressure-drop for the same volume flow rate because of the slower velocity. That is, the smaller particles of adsorbent and the shorter cycle time can be applied to obtain the higher productivity, or the quantity of adsorbent and the volume of adsorbers can be reduced for the same productivity. In addition, the scale- up of a radial RPSA is easier because this kind of processes can remove the restriction of height. “As competitive pressures are driving companies to operate their PSA units with high superficial velocities and short mass-transfer zones, radial bed designs are becoming more and more popular.” (LaCava et al., 1998) The radial flow RPSA is a potential process, although, the studies about this kind of processes are few. Rota and Wanket (1991) proposed the idea of radial flow and Chiang and Hong (1995) do the experimental study of a radial RPSA process. A RPSA for separating air by 5A zeolite was studied. The mathematical modeling suited for both of the simulations of radial flow RPSA processes and axial flow RPSA processes was developed. The simulation results for the axial flow RPSA was compared to the experimental results of Pritchard and Simpson (1986). The RPSA studied is a three-step process, as shown in Fig. 1. The diagram of an adsorber and the flow