A family of discontinuous Galerkin (DG) methods are formulated and applied to chemical engineering problems. They are the four primal discontinuous Galerkin schemes for space discretization: symmetric interior penalty Galerkin, Oden-Babuška-Baumann DG formulation, nonsymmetric interior penalty Galerkin, and incomplete interior penalty Galerkin. Numerical examples of DG to solve typical chemical engineering problems, including a diffusion-convection-reaction system in a catalytic particle, a problem of heat transfer in a fixed bed, and flow and contaminant transport simulations in porous media, are presented. This article highlights the substantial advantages of DG on adaptive mesh modification over traditional methods. In particular, we propose and investigate the dynamic mesh modification strategy for DG guided by mathematically sound a posteriori error estimators.