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Chapter 3. Mathematical Modeling of PSA Systems On one hand, incorporating system of equations to capture every mass transfer resistance mentioned above is expected to yield a rigorous model, while on the other hand, computation solution of such a formulation for multi-bed, multi-step PSA assembly can be a challenging task. In past PSA modeling studies, as shown in Table 3.1, linear driving force (LDF) model, which approximates the actual intra-particle diffusion rates with a semi-empirical lumped expression (see Eq. 3.2) has been very widely used [148, 26, 178]. ∂Qi =KLDFi(Q∗i −Qi) (3.2) ∂t The underlying assumption [133, 66, 156] for the applicability of this model is that the PSA cycletime stays considerably higher than the diffusional time constant for the given gas-solid system. For the case of very fast PSA cycles such as RPSA, addition of corrective terms have been considered to maintain its validity. 3.2.3 Mass Balance Mass balance formulation for each species in the gas phase, when applied on the packed bed system shown in Fig. 3.1 is given by the following Eq. (3.3). (ε +(1−ε)ε)∂Ci +∂UCi +ρ(1−ε)∂Qi =εD ∂2Ci (3.3) b bp∂t∂zpb∂tbz∂z2 Here, it is important to note that a given species is not only present in void space of the bed, but also in the void space of each pore in the non adsorbed state, inside the adsorbent. Furthermore, since this non adsorbed mass is completely inside the adsorbent pellet, it will only contribute to the accumulation term (first term of Eq. 3.3), and not towards other related terms. Another important feature of the formulation is the consideration of the dis- persion effects, which accounts for the effect of fluid-solid hydrodynamic interac- 50PDF Image | Operation and Control of Pressure Swing Adsorption Systems
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