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5.3 Case Studies and Computational Results To illustrate the generality of the superstructure approach, we consider two different cases. The first case involves superstructure optimization to obtain an optimal PSA configuration which maximizes CO2 recovery for a given lower bound on both CO2 and H2 purity, while the second case involves generating optimal cycle that minimizes overall power consumption for a given lower bound on CO2 purity and recovery. 5.3 Case Studies and Computational Results 5.3.1 Case I: Cycle synthesis to maximize CO2 recovery We solve the optimal control problem (3.1) to obtain an optimal cycle which maximizes CO2 recovery for a lower bound of 90% on both H2 and CO2 purity. Besides this, a lower bound on feed flux Qfeed is also imposed. In the absence of this bound, the optimizer may force the feed fraction φ(t) to zero in order to maximize CO2 recovery. Large-scale NLP that results after complete discretization of state and control variables in the optimal control problem is shown below. In the following problem, cycle time Tc is also a decision variable. Optimal values of the moving temporal finite elements together with optimal Tc give the optimal step times. max CO2 recovery (from Equation (3.14d)) s.t. c(w) = 0 (fully discretized Equations (3.2)-(3.13)) H2 purity ≥ 0.9 (from Equation (3.14a)) CO2 purity ≥ 0.9 (from Equation (3.14b)) Qfeed,L+Qfeed,H ≥35kgmolm−2hr−1 (fromEquation(3.14e)) Pads ≥ Pd Pdes ≤ Pfeed Pa ≥ Pfeed 0 ≤ α(ti), β(ti), φ(ti) ≤ 1 10 sec ≤ Tc ≤ 500 sec 101.32 kPa ≤ Pads(ti) ≤ 1000 kPa Pdes(ti) ≥ 50 kPa (5.1a) (5.1b) (5.1c) (5.1d) (5.1e) (5.1f) (5.1g) (5.1h) (5.1i) (5.1j) (5.1k) ∀ti Equation (5.1a) is the fully discretized PDAE system with the cyclic steady state condition. Constraint (5.1e) ensures that the pressure always decreases through the valve in the super- Chapter 5. Superstructure Case Study: Pre-combustion CO2 Capture 78 ∀ti ∀tiPDF Image | Design and Operation of Pressure Swing Adsorption Processes
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