Dynamic simulation of reversible solid-fluid reactions in nonisothermal porous spheres with Stefan-Maxwell diffusion

Abstract

As is so often the case, an effort to apply numerical dynamic simulation to complicated physical phenomena must begin with overly simplified equations and overly powerful computers. Certainly, early models of the transient behavior of reacting porous solid/fluid pellets could represent special cases only and consumed up to a minute of CRAY-1 CPU time for one pellet. However, as the authors gained familiarity with the problem and applied better-suited methods to alternative forms of the original equations, simulation costs dropped two orders of magnitude. In this paper, the authors describe a common, second phase of numerical simulation: the exchange of solution efficiency for model enhancement. Porous solid/fluid reacting systems provide a vivid demonstration of the interdependence of the model features which can be accommodated and the available methods for numerical solution. The addition of Stefan-Maxwell diffusion, thereby eliminating the necessity to assume equimolar counter-diffusion transport, converts a set of time-dependent partial differential equations into a set of mixed time-dependent and time-independent partial differential equations. After the spatial operators are discretized by finite differences, one gets a system of differential-algebraic equations (DAEs) instead of ordinary differential equations (ODEs). The level of difficulty, and of potentially poor numerical behavior, of a DAE system is quantifiable by an integer called its index, with an ODE system having index 0. Solvers of generally good performance, e.g. DASSL and LSODI, are available for index 1 DAE systems, but are not reliable for the index 2 problems we obtain by direct approaches here. Thus alternative formulations of the models are derived having a lower index, and careful use and misuse of index 0 and index 1 solvers are presented in considerable detail. As a result, efficient simulations of nonequimolar counter-diffusion, nonisothermal, nonpseudosteady, reacting, porous solid/fluid pellets can be obtained using available, general purpose software solvers.