An incremental analytical solution for gas-solid reactions, application to the grain model

Abstract

Gas-solid reactions are very important in chemical and metallurgical process industries. The grain model is one of the most important models describing some of these reactions. This model gives two coupled partial differential equations. The governing equations of this model must be solved numerically. There are some analytical solutions that can be applied for very special and simplified cases. For rapid determination of conversion-time behavior, some approximate methods have also been proposed. In this work a new mathematical technique is applied for solution of the grain model equations. This technique makes it possible to solve the coupled partial differential equations for all physical shape of grains. The results of this technique are compared with existing numerical and approximate solutions. This technique is simple and rapid and fits numerical solution with reasonable accuracy. This solution also gives a mathematical expression which cannot be found in numerical solutions.