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7.4 PSA Case Study - Post Combustion CO2 Capture Table 7.4: ROM for the isothermal PSA process M M Component mass balance ε dayik +uR dy0i + b dt RT a dφyij yij dx ,φ +yR i du0 + dx a dφuj ,φ uj dx yik + (7.26) (7.27) (7.28) (7.29) (7.30) P (1−εb)ρs Overall mass balance M j=1 daqij dx (φyik,φqij) dt =0 ∀k∈[1,M], i=1 qik =k qR∗,φ −a − q ,φ dti iqikqik0iqik ∀k∈[1,M] i=1,2 j=1 j=1 du0MdφujRT2M daqij dx + auj dx ,φuk + P (1−εb)ρs j=1 LDF equation j=1 Langmuir isotherm R∗ q1si b1i yiR P q2si b2i yiR P qi =1+2j=1b1jyjRP +1+2j=1b2jyjRP Cyclic steady state i=1 j=1 (φuk,φqij) dt =0 ∀k ∈ [1,M] da M yik M az,k(0) = pres j=1 az,j(tcycle) φz,j des des ,φz,k ∀k ∈ [1,M], z : yi,qi pres adsorption, depressurization and desorption steps. Moreover, we derive separate POD basis functions for gas phase mole fractions, solid phase loadings, and velocity. State variables are then expressed in terms of the corresponding POD basis as below R M yi (x,t)=y0i(x)+ j=1 M velocity respectively. It is noteworthy to mention that for the adsorption step, we use the ayij(t)φyij(x) aqij(t)φqij(x) for i=1 uR(x,t) = u0(x)+ Here y0i(x), q0i(x), and u0(x) are snapshot averages for mole fraction, solid loading, and qiR(x,t) = q0i(x)+ j=1 auj(t)φuj(x) M j=1 Chapter 7. Trust-region Framework for ROM-based Optimization 150PDF Image | Design and Operation of Pressure Swing Adsorption Processes
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