A MATLAB model was developed for the smoldering combustion of wastewater in the context of a decentralized residential wastewater treatment appliance. Data from a batch process sewage smoldering experiment was simulated using implicit finite-difference approximations, assuming one-dimensional transient conductive heat transfer. The time-dependent temperature profiles within the column represented the main parameters of interest and were used to verify recoverable heat energy estimations. Given that the modeling method used for this thesis represents a unique approach, the assumptions and limitations of this model are thoroughly described in the context of reproducing results for other smoldering setups. A lack of convergence is seen in the model validation section of this report. Consequently, the practicality of this particular model contains significant limitations. Theoretical applications are also discussed and analyzed in terms of comparisons to modern alternatives and prototype feasibility.