This work is concerned with the simulation of two different convection-diffusion-reaction type partial differential equations. The first one is the one-dimensional heterogeneous gas-solid reaction model encountered in a variety of chemical engineering problems. The exothermic nature of such reactions enlarges the gradients of temperature and concentrations that generate steep reaction fronts. The second one is the two-dimensional Keller-Segel model of the chemotaxis that generates delta-type singularities in the solution during a finite time. In its simplest form, the model is a nonlinear-coupled system of the convection-diffusion equation for the cell density and the reaction-diffusion equation for the chemoattractant concentration. The space-time conservation element and solution element (CE/SE) method is proposed for approximating both systems. The method has capabilities to capture sharp discontinuities of the solutions without spurious oscillations. To validate the accuracy and efficiency of the method, several case studies are carried out. The results of the current method are compared with the staggered central schemes.