Adverse impacts of drilling discharges on marine benthic environments have been observed since the advent of offshore drilling operations for exploration and production of oil and gas. This study utilizes a marine sediment model based on a system of equations that has been developed earlier to assess environmental impacts of drilling waste discharges. Bioturbation, bio-degradation and natural burial processes are included in the model. The model is based on the diagenetic equations, providing vertical concentration profiles of dissolved oxygen, naturally deposited substances and discharged substances in the marine sediment as a basis for marine risk assessment. The governing equations are solved by a random walk particle-tracking method for each constituent evaluated explicitly in time. The developed model is enhanced with a kernel smoothing method to obtain smooth concentration profiles. Simulation results reveal that the method demonstrates stable behavior for different model parameters, providing a promising alternative to finite difference approaches.