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Chapter 3. Mathematical Modeling of PSA Systems differential variables in the PSA model represented by xp are measured at the start and end of each cycle. Here, the system is said to have reached CSS when all elements of CSS error, represented by eCSS, are identically zero. eCSS(t) = xp(t) − xp(t − tcycletime) = 0 (3.13) From the modeling perspective, since the number of such cycles necessary to reach CSS is not known in advance, the simulations need to be carried out for a arbitrarily long time period, assuming that CSS will be satisfied within this time frame. • Method 2 - Relaxed method Method 1, albeit quite rigorous, is time consuming in nature and difficult to implement for computationally intensive PSA system model. As an al- ternative, a relaxed version of Eq. 3.13 can also be followed, which is shown in Eq. 3.14, where the system is assumed to have reached CSS, when max- imum magnitude of the CSS error, denoted by eCSS max, reaches below a small positive number ε. eCSS(t) = xp(t) − xp(t − tcycletime) eCSS max(t) = max|eoCSS(t)| ≤ ε (3.14) • Method 3 - Lumped variables measurement In practice, it is difficult to track all PSA variables for the CSS condition, as required in Method 1 and 2. To tackle this, lumped variables can be defined, as shown in Eq. 3.15 and 3.16, which monitors the values of average bed 56PDF Image | Operation and Control of Pressure Swing Adsorption Systems
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