A one-dimensional model of reactive sedimentation in wastewater treatment is formulated. The model combines three main elements: the Activated Sludge Model No. 1 (ASM1) for the reactive part, a secondary sedimentation tank (SST) with a variable cross-sectional area, and a description with percentages of the solid phase. The final form of the model is a system of partial differential equations of the convection-diffusion-reaction type. Two new numerical methods are developed and compared for the proposed model, which differ in the discretization of the temporal variable. One method is explicit (method XPE) and the other is semi-implicit (method XPSI). In both cases, the Engquist-Osher numerical flux is used to approximate the nonlinear term of the convective flux of the solid particles. The numerical results demonstrate that the methods exhibit comparable accuracy in error estimation and that the semi-implicit scheme is more efficient.