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Processes 2022, 10, 812 5 of 19 the intraparticle adsorbate, to eliminate the flaw of the conventional LDF concentration profile assumption, expressed as: ∂q15De −q ∂t= R2 qe+0.2789qee 2qe −q (4) 2.2. Pressure-Drop Model A continuous PSA process is implemented through circulating changes in pressure. Thus, a pressure drop in the adsorption bed will directly affect the recovery and purity of the product. However, in a situation of low adsorption pressure or short cycle time, several computational studies indicate that the pressure drop has a limited effect on the overall process performance. Aaron [42] experimentally confirmed that the effect of a pressure drop was negligible on process performance in the flow regime; namely, the pressure drop concerns were not reasonable for small-scale air separation processes using similar column lengths (9.8–19.6 cm) and particle sizes (0.5 mm). When considering the energy consumption of the process, the pressure drop model is a key concern, since a higher pressure drop leads to a lower energy-storage efficiency [43]. The Darcy model assumes that the pressure drop is proportional to the flow rate, as expressed by Equation (5). ∇p = −μv (5) α where μ is the kinetic viscosity and α is the permeability, which is an important considera- tion in this model. Furthermore, the Ergun equation combines the description of pressure drops by the Carman–Kozeny equation for laminar flow and the Burke–Plummer for tur- bulent flow, which is more appropriate in packed adsorbing columns, as expressed by Equation (6) [44]. 2.3. Fluid-Flow Model Fluid-flow models in a fixed bed include plug flow, plug flow with axial dispersion, and 2-dimensional (2D) radial dispersion flow, while the last term can be ignored because the adsorption bed diameter is much larger than that of particles. Currently, most PSA process numerical simulations are governed by 1-dimensional (1D) models, without radial variation in the gas concentration, temperature and pressure. As the development of available powerful computer resources raises, there is an interest in extending these 1D adsorption modeling approaches into 2D/3D configurations. Compared to the 1D model, the 2D/3D models seem to be more accurate in terms of heat- and mass- transfer results, as more flow directions are taken into consideration [45]. In addition, it is more intuitive to reflect the distribution of some parameters (mole fractions, temperature, pressure and so on) in the adsorption bed. Moreover, a 3D model can be used in complex bed geometries or perform research on the equipment in the column, such as gas distributor optimization [46]. However, with the increase in dimensions, the number of computations is increased, meaning that it should take a long time to run the required simulations. 2.4. Special Treatments for Energy Balance 2.4.1. Heat of Adsorbed Phases and the Heat of Adsorption The heat of the adsorbed phases for each component is a function of the loading and the temperature in the solid phases, the adsorbed phase heat capacity, and the solid density, as shown in Equation (7). Wang et al. found that the adsorbed phase would influence the ∂P 150μg(1 − εb)2u 1.75ρg(1 − εb)u2 −= 32 + 2 (6) ∂z εbdp εbdpPDF Image | Numerical Research on the Pressure Swing Adsorption Process
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