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Unibed and Multibed formulations are two different strategies to implement aforementioned boundary matchings. As shown in Figure 2.6(a), Unibed approach involves simulating a single bed for all the operating steps in a cycle. Since all the PSA beds follow same sequence of steps and demonstrate identical dynamic behavior, one bed is sufficient to simulate the entire PSA process. Hence, only one set of bed equations are solved with varying boundary conditions for all the steps. To simulate bed interactions and match boundary information for different beds, storage buffers are used in the model implementation. In contrast, in Multibed approach we simulate all the beds in the PSA flowsheet but only for a portion of the cycle. As illustrated in Figure 2.6(b) for a 2-bed 4-step process, this portion of the cycle is selected such that it covers all the operating steps of the cycle among all the beds. Thus, we solve bed equations for all the beds but only for one set of operating steps. Such an approach accurately simulates bed interactions by matching boundary information simultaneously. By imposing a bed profile match at the beginning of one bed and end of another bed, solution of the entire PSA cycle is eventually obtained. Ling Jiang [99] provides a detailed description of Unibed and Multibed approaches. 2.5 Simulation Methodologies As discussed in section 2.3, PSA processes are mathematically modeled by coupled hyperbolic partial differential and algebraic equations (PDAEs) distributed in both space and time. Ob- taining analytical solution without making any approximation is close to impossible for such a highly coupled set of PDAEs. Low dimensional PDAEs of this type (with simplifications) can be solved analytically or directly by the PDE package CLAWPACK [123]. However, for large-scale systems numerical methods employing discretization for the spatial or the temporal or both domains are essential. There are two distinct approaches to numerically simulate the set of PDAEs: • Method of Lines (MOL) Method of Lines is a two-step approach [160]. First, PDAEs are discretized in the spatial Chapter 2. Pressure Swing Adsorption 27 2.5 Simulation MethodologiesPDF Image | Design and Operation of Pressure Swing Adsorption Processes
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