On the mathematical model simplification using constant Lewis number – Impact assessment on heterogeneous char conversion process

Centre for Sustainable Technologies, Indian Institute of Science,, India.

^* Corresponding author: mohmdasher@iisc.ac.in

Abstract

Reactive systems in a thermochemical conversion domain are modelled considering N-specie, 1-energy and 2-mass conservation equations assuming negligible pressure gradient resulting in N+3 non-linear coupled PDE system with dependency on thermodynamic and transport properties. Typically, simplistic temperature-dependent polynomials are chosen for estimating thermal conductivity and specific heat, however, the estimation of mass diffusion coefficient (D_i;mix) follows a complicated procedure involving kinetic theory culminating in Chapman-Enskog equation. This renders the solution computationally intensive. The complexity is simplified by assuming a constant Lewis (Le) number, a standard practice in the analytical solution for conventional reactive systems. In fixing Le, (D_i;mix) is equated to thermal diffusivity (a ratio of thermodynamic properties) resulting in the specie and energy equation yielding a similar solution and collapse of N+3 system of simultaneous equations to 3 equations. The current article explores the validity and limitation of assuming constant Le in the simulation of char conversion process in air and steam. Results of char conversion are compared for fixed Le and D estimated with Chapman{Enskog expresion. The analysis suggests that Le remains invariant only under a severely restricted set of conditions. Fixing Le influences, the conversion process either over-/under-predicting the conversion time scales and the product gas composition.