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p. The first equation represents the PDAE-based model for the PSA system, while the second equation is the cyclic steady state (CSS) condition (see Table 3.1). As mentioned before, the CSS condition is implemented by giving the final conditions of CoB as the initial condition for CnB and vice versa. Additional constraints for the optimization problem are given by the algebraic equations s and the inequalities g. The control variables α(t), β(t) and φ(t) are fractions bounded between 0 and 1. Other control variables, Pads(t) and Pdes(t), and decision variables p are bounded between their respective bounds bL and bU . It is important to note that although optimal 2-bed PSA configurations are construed from the optimal profiles of α(t), β(t), φ(t), Pads(t) and Pdes(t), multibed cycles (with more than two beds) follow immediately from these solutions. These are generated by staggering the steps over multiple beds and ensuring that a bed with a product flow step occurs at all points in time. 3.3 Model Equations We consider a detailed PDAE-based mathematical model for the optimal control problem. The model is fairly general and can also be extended beyond the following assumptions: 1. All of the gases follow the ideal gas law. 2. There are no radial variations in temperature, pressure and concentrations of the gases in the solid and the gas phase. 3. The gas and the solid phases are in thermal equilibrium and bulk density of the solid phase remains constant. 4. Pressure drop along the bed is calculated by the Ergun equation. 5. The adsorption behaviors are described by the dual-site Langmuir isotherm. 6. The adsorption rate is approximated by the linear driving force (LDF) expression. Sircar and Hufton [172] demonstrated that the LDF model is sufficient to capture the kinetics Chapter 3. PSA Superstructure 41 3.3 Model EquationsPDF Image | Design and Operation of Pressure Swing Adsorption Processes
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