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Processes 2022, 10, 812 difficult to determine its optimal conditions through empirical methods. In addition, a PSA optimization is a typical multi-objective optimization problem, several objectiv functions may conflict with each other; for example, purity and recovery vary in the op posite direction [34,59,60]. Due to the mutual influence and tradeoff between differen tions (called the Pareto optimal set) rather than an optimal solution [61,62]. The projectio objective functions, a multi-objective optimization problem has a series of optimal solu the PSA process, or convert the multi-objective optimization problem into a single-objec objective optimization. Some researchers only focus on a single performance indicator of tive tohpe tPiSmAizparoticoenss,porocbolnevmertbtyhecmonusltir-oubcjteicntigveaospptiemcizfiactiofunnpcrtoibolnem[2in1t]o. a single-objective optimization problem by constructing a specific function [21]. A typical PSA-process optimization strategy is presented in Figure 2. In general, th A typical PSA-process optimization strategy is presented in Figure 2. In general, numerical optimization process of PSA includes two aspects: the process model and opti the numerical optimization process of PSA includes two aspects: the process model and mization algorithm. The former is the process of obtaining the process performanc optimization algorithm. The former is the process of obtaining the process performance through the input design and operation, while the latter is to determine the optimizatio 9 of 19 of the Pareto optimal set onto space is called the Pareto front, or the Pareto curve for dual (called the Pareto optimal set) rather than an optimal solution [61,62]. The projection of objective optimization. Some researchers only focus on a single performance indicator o the Pareto optimal set onto space is called the Pareto front, or the Pareto curve for dual- through the input design and operation, while the latter is to determine the optimization direction according to objectives and constraints. The process model can be divided int direction according to objectives and constraints. The process model can be divided into twotwmoaimnapinarptasr:tst:hteheddeteatailieled modellaannddsusrurorrgoagteamteomdeol,deealc,heoafctheomf tchoerrmespconrdresstpoonds t different optimization strategies and algorithms. different optimization strategies and algorithms. Figure 2. Typical PSA-process optimization strategies. Figure 2. Typical PSA-process optimization strategies. 3.1.1. CSS Definition 3.1.1. CSS Definition It is worth mentioning that the numerically optimized results only make sense when achieving the cyclic steady state (CSS). However, the number of such cycles depends on It is worth mentioning that the numerically optimized results only make sense whe the PSA set, operational sequence, and gas-adsorbent property, making it take a long achieving the cyclic steady state (CSS). However, the number of such cycles depends o time to be reached. Thus, a definition of an approximate CSS is employed, as shown in Equation (13) [63]. ecss = max yt=N·tcycle − yt=(N+1)·tcycle ≤ εcss (13) where y represents important PSA variables used for controlling the CSS, such as tempera- ture, concentration, pressure, purity, and recovery; εcss represents the solution accuracy of the definition of the cyclic steady state; and ecss is the absolute error of the definition of the cyclic steady state. 3.1.2. Detailed Model The detailed model is formed by a series of partial differential and algebraic equations (PDAEs) and periodic boundary conditions. According to different methods, the detailed models mainly include single discretization (SD) and complete discretization (CD). s e - t - n - f - e - e n o o n nPDF Image | Numerical Research on the Pressure Swing Adsorption Process
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