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Chapter 3. Mathematical Modeling of PSA Systems of PSA operation. In principle, accurate capturing of momentum transfer inside the packed bed requires the incorporation of full scale Navier Stokes equations in the PSA model. Here, it is important to note that inside a PSA bed both laminar and turbulent conditions can be active at the same time. For example, in the semi-batch pro- cessing steps of the PSA cycle, the flow conditions near the closed end of the column are laminar, while at the other end where the fluid is leaving the bed at high velocities, turbulent conditions are prevalent. In such a scenario, the usage of first principles based Navier Stokes equation is even more profound as it can handle both flow regimes. On the other hand, the actual solution of Navier Stokes equation, especially for turbulent regime requires further modeling information such as Eddy diffusion modeling, making its real implementation and solution a tough problem [19]. As an alternative, the quasi steady state [144] Ergun equation, as shown in Eq. (3.11), is widely used to approximate the pressure variations inside the packed bed, and is the option employed here as well. Ncomp 1.75(1 − εb) ∑ CiMWi i=1 |U|U (3.11) ε 3b d p ∂P 150μ(1 − ε )2 − = ∂ z b U+ ε 3b d 3p In the above equations (3.3)-(3.11), εb and εp are treated as constant pa- rameters, assuming that they remain unchanged for all hydrodynamic conditions encountered throughout the PSA cycle. In particular, constant εb assumption is under test during the start of any PSA processing step which is of semi-continuous flow nature. For example, it is not uncommon to observe momentary flow spikes during the re-pressurization or blowdown step which can slightly re-adjust the packed bed configuration. Furthermore, thermodynamic and transport proper- ties Cpi , μ, ρp and Cps are assumed to be constant at their feed conditions. 54PDF Image | Operation and Control of Pressure Swing Adsorption Systems
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