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4.4 Case Studies and Computational Results properties for 13X and other model parameters are listed in Table 4.2 [111]. Usually a large number of spatially discretized nodes are required to capture steep adsorp- tion fronts. Such fine spatial discretization, together with temporal discretization, leads to a very large set of algebraic equations which becomes extremely expensive to solve. Although a large number of elements improve accuracy, it makes the problem computationally challenging to solve. Hence, to get the solution in a reasonable amount of time, we consider 20 spatial finite volumes and around 24-26 temporal finite elements for the optimization problem. NLP solution from IPOPT is verified with more accurate dynamic simulations in MATLAB at the optimum, as mentioned in section 3.4. We consider three different cases to explore different facets of the superstructure approach. The first case study optimizes the 2-bed 4-step Skarstrom configuration, obtained after fixing the control variables in the superstructure, and shows the ineffectiveness of such traditional cy- cles for high-purity CO2 separation. The second case then finds an optimal PSA configuration which separates CO2 at high purity and recovery. Finally, in the third case, we find an optimal configuration which achieves high-purity separation with minimal power requirements. 4.4 Case Studies and Computational Results 4.4.1 Case I: Optimization with a conventional configuration First, we explore the potential of the conventional 2-bed 4-step Skarstrom cycle (cf. section 2.4.1) for post-combustion CO2 capture. For this, we fix the profiles of α(t), β(t) and φ(t) over time, as shown in the Figure 3.3. While fβ is chosen as 0.3, fφ before tswitch is fixed to 0.35. This ensures that the superficial velocity is close to zero towards the light end of CoB during the FP step. In this case, Pads and Pdes remain constant for the entire cycle. The inlet pressure Pfeed is fixed to 300 kPa, as considered by Gomes et al. [85] as well. With this configuration we maximize CO2 recovery. Since the lack of any heavy reflux step in the configuration may not enable a high purity separation, a relatively low value of 40% Chapter 4. Superstructure Case Study: Post-combustion CO2 Capture 54PDF Image | Design and Operation of Pressure Swing Adsorption Processes
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