Perturbation techniques for accelerated convergence of cyclic steady state (CSS) in oxygen VSA simulations

Abstract

Non-isothermal PSA bulk gas separations are notoriously slow to converge to cyclic steady state (CSS). Most numerical simulators that model the slow transient behaviour of these processes share this slow pace of convergence. This difficulty with numerical simulators has long been recognised, and has hampered the optimisation of oxygen VSA. This paper outlines the application of perturbation techniques to enable more rapid determination of CSS temperature profiles. A number of different techniques are proposed. The simplest approach based on experimental observations involves a two-time-scale decomposition of the adsorbent temperature profile. This decomposition of the temperature term enables the rapid numerical determination of the fast (or adsorptive) component of the temperature, followed by the direct determination of an estimated cyclic steady-state slow time-scale (or convective) temperature. It is demonstrated that this approach is the same as a zeroth-order multiple scale analysis (MSA) approach and a simple application of the Krylov–Bogoliubov (K–B) method of averaging. This study compares the results of this acceleration technique for determining CSS with a full numerical model. The results indicate that the proposed acceleration technique based on perturbation methods provides fast and reasonable estimates of the CSS temperature profile with some limitations. Recognising these limitations of the zeroth-order approach, a first-order MSA is developed. This compares better with full numerical simulations, and could be used to augment and complement existing acceleration techniques. It is shown that a first-order MSA approach can also be used to capture the dynamic temperature response of the oxygen VSA process, in addition to the CSS axial temperature profile. The perturbation techniques presented here are limited to a series expansion of the temperature term in the energy balance, and mass balance is ignored in this analysis. A procedure is outlined where a K–B approach can be used to incorporate a perturbation series expansion in the mass balance. We show that these perturbation techniques not only offer potential for simulation acceleration, but also offer useful insights into the thermal convergence to CSS in oxygen VSA.