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Component mass balance Table 6.6: ROM for the hydrogen PSA process d2y M d2φ −D 0i+ a yij,φ + d 2 dy M dφ 0i+ a yij,φ L dx2 yij dx2 yik j=1 dx TR dx yij dx yik j=1 1 − εb M T Rφqij , φ daqij − 2 M T RyiRφqrj , φ s εb j=1 PR yik dt r=1j=1 PR daqrj yik dt (6.36) (6.37) (6.38) 6.5 Case Study - Hydrogen PSA +Rρ da dy M dφ +yik+u0i+ayij,φ=0∀k∈[1,M] dt dx j=1 yij dx yik Ergun equation 150μ (1 − εb)2 pb pb 1.75ρg 4R2 ε3 (u,φPk)+ 2R 1 − εb ε 2 (u ,φPk) + 0+ a Pj,φ =0 ∀k∈[1,M] dP M dφ dx PjdxPk j=1 LDF equation da M qik =k qR∗,φ −a − q ,φ ∀k∈[1,M] dti iqikqik0iqik j=1 Energy balance M da dT M dφ ε ρRCRφ,φ Tj+εuρRCR 0+ a Tj,φ b j=1 g pg Tk Tj dt b g pg dx Tj dx Tk j=1 da 2 M da Tk −ρ d2TMd2φ4h +ρC b ps dt b ∆Hads r φ ,φ qrj qrj Tk dt r=1 −K 0+a Tj,φ+wTR−T,φ=0∀k∈[1,M] j=1 Langmuir isotherm R ∗ a Ri y i R P R a Ri = α 1 i e α 2 i T R qi =1+2i=1bRiyiRPR bRi =β1ieβ2iTR Cyclic steady state M (6.39) (6.40) (6.41) Ldx2 Tjdx2Tk D wTk j=1 az,k(0) = pres j=1 az,j(tcycle) φz,j ,φz,k ∀k ∈ [1,M], z : yi,qi,T des des pres Chapter 6. Reduced-order Modeling for Optimization 118PDF Image | Design and Operation of Pressure Swing Adsorption Processes
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