Transient chemical reaction analysis by orthogonal collocation

Abstract Models of packed-bed chemical reactors most frequently account for the diffusion of mass and energy within catalyst particles. The orthogonal collocation method is developed for transient, nonlinear problems of this type. A sequence of approximate solutions is proved to converge to the exact solution. A stability criterion is presented for estimating the maximum step size to use in the integration. The orthogonal collocation method is applied to linear transient diffusion and gives accuracy to six significant figures for dimensionless times greater than 0·1 using six expansion functions. The method is then applied to nonlinear diffusion and reaction problems which have multiple solutions. Eight to twelve expansion functions are required to give temperatures with accuracies from 0·03% to 0·1% and heat flux at the boundary of the catalyst pellet within 1%. Jacobi polynomials are preferred expansion functions for boundary conditions of the first kind and Legendre polynomials are recommended for boundary conditions of the third kind. Comparison to two finite difference methods indicates that the collocation method is from four to forty times as fast for comparable accuracy.