AN INTEGRAL-SPECTRAL FORMULATION FOR CONVECTIVE-DIFFUSIVE TRANSPORT IN A PACKED-BED WITH ADSORPTION AT THE WALL AND BULK REACTION

A solution for a convective-diffusive transport problem coupled with bulk reaction and adsorption at the wall in packed-bed reactor has been obtained. Such solution has been derived in terms of a particular solution that satisfies the non-homogeneous boundary conditions, at the wall, and the solution to the differential model with homogeneous boundary conditions. The latter is given in terms of integral equations whose kernel is the Green function of the parabolic differential operator of the transport problem. The Green function is expanded in terms of the eigenvalues and the eigenfunctions of the radial diffusion operator of the differential problems. This methodology allows a decoupling of the linear aspects of the problem (i.e., transport part) of the nonlinear source (i.e., kinetic of the reaction) and facilitates the convergence of the Fourier series involved in the spectral expansion in the case of a need for numerical solutions. Details about the solution methodology and the identification and solution of the eigenvalue problem, are given.