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410 P. BISWAS et al., Modeling and Simulation for Pressure Swing Adsorption System ..., Chem. Biochem. Eng. Q. 24 (4) 409–414 (2010) Due to increasing demand in industry for hydro- gen, there has been a growing need to recover hydro- gen from steam reformer off gas, catalytic reformer off gas ethylene plant effluent gas, and coke oven gas. H2 separation process was studied by many research- ers. Earlier studies were based on one-bed PSA sys- tems.4–6 Several adsorbents were studied for obtaining high purity hydrogen. In a study by Lee and co-work- ers7–9 it was found that zeolite 5A can well serve the purpose. The design and optimization of multi-bed PSA systems involves an adequate amount of com- plexity due to the interconnectivity of beds. The first numerical study on multi-bed systems was done by Kumar.10 He used internal stream to purge the used bed instead of product stream and optimized it. An experimental and theoretical study was performed by The energy balance for solid and gas phase, as- suming the temperature of the column wall is the same as the temperature of the gas and solid phase (this would decrease computational time) is given as ¶æ¶Tö ¶T ¶c çKl ÷-uctCm,p +eRT t - ¶zè ¶zø ¶z é ¶t -êëectcm,p +(1-e)(aåcicm,pi + n +rpåqlcm,ads +rpCm,ps)+ (2) i=1 +4rwcp,wù¶T+(1-e)aRT¶ct + ad úû¶t ¶t ww n i=1 Yang et al.11 on a 2-bed six-step PSA process using n zeolite 5A for bulk separation of binary gases. Several processes have been developed like multi-bed pro- cesses12–14 and more recently rapid PSA processes15 to serve the purpose. A paper by Jiang and Biegler (2004) published their simulation and optimization strategies to multiple-bed system which was an exten- sion to their previous work on a single-bed system. They previously studied PSA with parallel implemen- tation of beds. They used accurate sensitivities to de- termine cyclic steady states with design constraints. More recently, a paper by Biegler et al.16,17 in- troduces advanced methods involving non linear programming using IPOPT to solve the models for the units that operate in a periodic manner, such as PSA systems. Mathematical modeling The following assumptions were taken while modeling the PSA system: 1. The adsorption rate was considered to be following a linear driving force (LDF) model, with single lumped mass transfer parameter. 2. The flow pattern of gas is axially dispersed plug flow model. 3. Radial temperature and concentration gradi- ents are negligible. 4. Gas components are following ideal gas be- havior. 5. Constant porosity along the bed. The component mass balance equation assum- ing ideal gas is, (1) ¶ql 4awlU +rpåQi ¶t-ad (T-Tatm)=0 i=1 ww The pressure gradient across the bed was computed by steady state momentum balance or Ergun’s equation: ¶æ ¶xö ¶c ¶ çeDc i÷-e i- (uc)- ¶zè l t ¶zø ¶t ¶z i where and ¶z 150 e(1-e)2 ¶p - = amu + bru 2 (3) e3 (4) e 2 (1 - e ) 2 a= 4r2 p b=1.75 2rpe3 (5) Adsorption rate into solid phase was consid- ered following LDF model ¶ql =k(q*-q) (6) ¶t i i l where ki is the single lumped parameter for LDF model and q*i is the adsorbed amount at equilibrium. k =WcDc (7) Wc is the LDF factor, Wc = (ks +1)(ks + 3) where, ks (geometrical factor) is equal to 2, for spherical particles. Equilibrium adsorbed amount is computed from Multisite Langmuir model. Parameters in the model were determined previously by Lopes et al.18 a qi æqiöi ii ç÷ æ ¶c ¶q ö ç ÷ = a K p 1- å (8) -(1-e)a+rp =0 q iiç q÷ è ¶t ¶tø i,max è i,maxø ir2 cPDF Image | Modeling and Simulation for Pressure Swing Adsorption System
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