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domain thus converting them to a set of differential algebraic equations (DAEs). Next, DAEs are integrated using standard time integration routines. One of the advantages with MOL is that with a high-resolution spatial discretization as well as with the er- ror checking mechanisms present in the commercial time integration routines, we can achieve high order accuracy in both dimensions. A solution of the hyperbolic PDAEs defining PSA systems is usually characterized by steep adsorption fronts in the spa- tial domain, which is aggravated with higher adsorption pressure. In order to capture such steep fronts, it is essential to use a spatial discretization scheme which not only avoids physically unrealistic oscillations, but also ensures minimal numerical dispersion and negligible smearing (damping) with fewer discretization nodes. Moreover, it should also ensure extreme accuracy with mass, momentum, and energy conservation, which is vital for PSA-based separations. Because first- and second-order finite difference and finite element methods do not often mitigate such numerical noise with hyperbolic sys- tems, high-resolution schemes such as upwind-based finite volume methods are utilized for spatial discretization [57, 124, 125, 197]. • Complete Discretization (CD) In Complete Discretization approach, we discretize both spatial and temporal domains simultaneously, which leads to a large set of nonlinear algebraic equations. Such an approach allows seamless addition of the CSS condition to the discretized bed model, thus allowing entire system to be solved simultaneously by a Newton-based equation solver. Hence, CD is attractive and efficient for simpler PSA models. Nilchan and Pantelides [138, 139] successfully demonstrated this approach for small-scale PSA problems and solved the resulting algebraic system using a nonlinear equation solver inside gPROMS [2]. However, one of the drawbacks of CD is that in the absence of any error checking mechanism for temporal integration, pre-determined temporal discretization can lead to an inaccurate solution due to an insufficient number of temporal discretization nodes. While a large number of nodes can mitigate this drawback, it can consequently make the 2.5 Simulation Methodologies Chapter 2. Pressure Swing Adsorption 28PDF Image | Design and Operation of Pressure Swing Adsorption Processes
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