An Improved Method to Calculate the Conservation of Mass in the Simulation of Rapid Pressurization and Depressurization in a Packed Bed

Abstract

The work described here forms part of a project to model rapid pressure swing adsorption (RPSA), which is a single-bed process used for air separation. We have earlier identified a form of model and boundary conditions for an axially dispersed plug flow model that conserves mass. We solve the RPSA models numerically by spatially discretizing the partial differential equations to a system of ordinary differential equations (ODEs), which are then integrated over time. Although the formulation of our models conserves mass, our numerical
simulations, however, do not perfectly conserve mass because of discretization error and rounding error. The discrepancy in the conservation of mass is computed as a guide to the numerical accuracy of the calculations. The computation of the conservation error requires the evaluation of time integrals of molar flowrates in and out of the bed. Since the velocity at the feed end of the bed changes
rapidly with time, the application of quadrature to evaluate the time integrals does not provide the accuracy required. In this paper, the inadequacy is
demonstrated using a simple problem, i.e. pressurization and depressurization into a non-adsorptive bed. An improved method is proposed. By transforming equations involving time integrals into ODEs, excellent accuracy is obtained. Further, this transformation minimizes the number of decision parameters that need to be specified by the users of the computer programs.