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Processes 2022, 10, 812 3 of 19 To clarify the progress in the numerical research on PSA simulation, optimization and control, and promote the PSA technology in actual engineering applications, the paper is arranged as follows: In Section 2, some model assumptions and special treatments for energy balance are discussed, and then a complete one-dimensional mathematical model including adsorption bed, auxiliary devices, boundary conditions and performance indicators is summarized for a general PSA-process design. In Section 3, first, optimization strategies and algorithms for different process models, such as the single discrete model, fully discrete model, and surrogate model, are reviewed. Moreover, the PID controller and model predictive controller are introduced, respectively, when facing external disturbances or parameter fluctuations in the process. Finally, we summarize the whole work and point out some instructive future directions. 2. PSA Modeling At present, the numerical simulation based on adsorption theory is a promising method for PSA-process design. It can analyze the continuous distribution of physical quan- tities that is difficult to obtain through experiments and explore process-design variables more quickly. The fundamental of simulation is the mathematical model; as PSA is a peri- odic, cyclic, and dynamic process, its mathematical models are quite complex. Li et al. [12] summarized the mathematical modeling pathway map, which comprised the correspon- dence between the real physical scenario and mathematical model for carbon capture by adsorption (CCA). As Figure 1 shows, a typical mathematical model for the adsorption bed contains a mass-transfer model, energy-transfer model and momentum-transfer model to describe the transfer process that occurs between gas and adsorbent. In addition to the above three models, strict adsorption-bed models also include the adsorption-kinetics model and adsorption-equilibrium model. Among them, the mass-transfer model strictly includes diffusion in the axial and radial directions, but the radial diffusion coefficient is difficult to measure and estimate. Adsorption kinetics is to study the adsorption process of external diffusion, internal diffusion and surface-adsorption behavior; the adsorption- equilibrium model describes the static-adsorption equilibrium of a single component or multicomponent on the surface of a solid adsorbent after the external diffusion and internal diffusion of gas. Different adsorption-equilibrium-isotherm models will produce different predictions, and the selection of a suitable model can help to improve the accuracy of numerical calculations. A complete process simulation also needs to consider the auxiliary module models such as tank, the valve, pump, and pipeline and performance indicators such as purity, recovery and energy consumption. Exceptionally, for a system with simple cycle schedules such as air separation, the virtual moving-bed modeling methodology, which considers only mass and energy balances and adsorption isotherms, can be employed to describe the cyclic steady state [3]. To avoid complicated numerical computations, some key assumptions frequently used will be discussed, as follows. 2.1. Adsorption-Kinetics Model In the aspect of kinetic models, three representative adsorption-kinetic models are taken into consideration. First, a homogeneous-solid or pore-diffusion model (HSDM) has been used to describe intraparticle mass transfer [36]. This model assumes that the adsorbent is homogeneous and that the adsorption process occurs at the external surface, followed by the diffusion of the adsorbate into the interior of the adsorbent particles [37]. The mathematical expression for intraparticle diffusion is shown in Equation (1). ∂qi De ∂2∂qi ∂t = r2 ∂r r ∂r (1)PDF Image | Numerical Research on the Pressure Swing Adsorption Process
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