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Processes 2022, 10, 812 2 of 19 boundary conditions. The formation of a more complete model means an increase in the number of differential equations and functional dependencies by which the model coefficients are calculated [14]. Hence, to describe different PSA processes, some variants of mathematical models needed to be taken into account, such as heat transfer between a gas and adsorbent, gas intra-diffusion transfer in an adsorbent and mass and heat transfer coefficients during sorption. Considering that the reliability of simulation results is fundamentally determined by the description and establishment of the adsorption behavior and mathematical models, it is necessary to analyze the advantages and disadvantages of model assumptions and the scope of their use in this review. Various commercial numerical platforms have been applied for the modeling of the PSA process, such as Aspen Adsorption [15], gPROMS [16,17], MATLAB [18] and FLU- ENT [19]. The common approach used by the numerical calculations is the method of lines (MOL), which can discretize spatial derivatives to convert PDAEs to differential-algebraic equations (DAEs) or algebraic equations (AEs) and then solve them through different solvers. For the simulation and optimization of the PSA process with complex models and cyclic features, the solution of AEs is difficult to converge and will produce different calculation results. In addition, numerical integration of the DAEs system is complicated and time-consuming, to guarantee the performance accurately and capture the process’ dy- namic features simultaneously [20], especially dealing with highly nonlinear isotherms, due to numerical dispersion (smearing) and oscillation. All that has also greatly increased the difficulty of process optimization [21].To reduce the computation amounts for simulation and optimization, researchers have proposed a variety of different surrogate models, such as the polynomial surface response model (PRSM) [22], Kriging model [23], proper orthogo- nal decomposition [24–26], polynomial regression model (PNR), support vector regression, and artificial neural network (ANN) model [27,28]. The surrogate model is essentially a black-box model, which is built from a known sample of input–output data points, and can be used to predict the output response at untried points/configurations [25,29]. Limited by the number of samples, the accuracy and feasibility of the surrogate model still need further verification and benchmarking studies to extend its application. After determining the process model, it is also necessary to optimize the PSA process to find the best design parameters and operating variables to improve process efficiency. The optimization of the PSA process is a multi-objective optimization problem, which generally includes various process performance indicators, such as product purity, recovery rate, production capacity, process energy consumption, etc. For decades, various optimiza- tion strategies and algorithms have been continuously developed, which can be roughly divided into deterministic and metaheuristics algorithm. Gradient-based deterministic algorithms include sequential quadratic programming (SQP), reduced space sequential quadratic programming (rSQP), the interior point method, the efficient set method, the trust region efficient algorithm, etc. [30–32]. Novel metaheuristic and artificial-intelligence-based optimization algorithms, including the genetic algorithm (GA), particle swarm optimiza- tion (PSO), the ant colony algorithm, the annealing algorithm, etc. Among these, GA and PSO are typical metaheuristic algorithms, which have demonstrated superior performance and efficiency in multiple reports [31,33,34]. Currently, the research on PSA process opti- mization shows a clear trend toward a more intelligent, easier, and integrated direction. The combination of deep-learning technology with artificial-intelligence-based optimization algorithms will be new task for PSA industrial application. In addition, in actual industrial production, there are inevitably some uncertain factors that cause disturbance to the PSA process, such as feed flow, concentration and temperature deviating from the operation set, which make it take a long time to recover, resulting in suboptimal results of the entire process. Therefore, it is necessary to develop and design the control system to minimize impact and achieve stable operation. Researchers have actively explored the control system for a PSA unit, including the proportional-integral-derivative control strategy (PID) and model-predictive control strategy (MPC) [17,35].PDF Image | Numerical Research on the Pressure Swing Adsorption Process
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