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purityH2 purityC H4 recoveryH2 recoveryC H4 6.5.2 Reduced-order Model = = OH2 (t) dt OH2(t)+OCH4 dt HpCH4 (t) dt (6.32) (6.33) (6.34) (6.35) HpH2 (t) + HpCH4 dt OH2 (t) dt − PgH2 (t) dt = 6.5 Case Study - Hydrogen PSA dependent adsorption isotherm parameters for hydrogen and methane on activated carbon (α1,α2 and β1,β2) are listed in Table 6.3 [108]. As suggested by Equations (6.24) and (6.25), PDE for the component mass balance is solved only for methane and mole fraction of hydrogen is evaluated by ensuring that the mole fractions sum up to one. We enforce this summation because the overall mass balance, which implicitly ensures such a summation, is not taken into account for superficial velocity calculation. We denote this model in Table 6.2 as the rigorous model for which we develop a reduced-order model. Tables 6.4 and 6.5 show the equations for molar flux variables, to calculate purities and recoveries, and the boundary conditions for each operating step, respectively. Based on the molar flux variables, purities and recoveries of hydrogen and methane are given by = FH2 (t) dt HpCH4 (t) dt FCH4 (t) dt We use the method of lines approach to convert PDAEs in Table 6.2 into a set of DAEs after spatial discretization, which is then simulated to generate snapshots for POD basis functions. For spatial discretization, we use an upwind-based finite volume scheme with Van Leer flux limiter for mole fraction and temperature in order to introduce additional numerical dispersion around steep adsorption fronts (cf. section 2.5.1). We utilize the Multibed approach and simulate both beds simultaneously for half the cycle (cf. section 2.4.3). Chapter 6. Reduced-order Modeling for Optimization 115PDF Image | Design and Operation of Pressure Swing Adsorption Processes
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