In this study, a one-dimensional model represented by Butler-Volmer-Monod (BVM) model was proposed to compute the anode overpotential and current density in a mediator-less MFC system. The system was fueled with various organic loadings of real field petroleum refinery oily sludge to optimize the favorable organic loading for biomass to operate the suggested system. The increase in each organic loading showed higher resistance to electrons transport to the anode represented by ohmic loss. On the contrary, both activation and mass transfer losses exhibited a noticeable decrement upon the increased organic loadings. However, current density was improved throughout all increased loads achieving a maximum current density of 5.2 A/m³. The BVM model perfectly expressed the bioelectrochemical reactions in the anodic-chamber. The experimental measurements for all the studied organic loadings agreed with the model predicted values by an estimated determination factor (R²) of 0.96, proving the validity of the proposed mathematical model to express the anodic bioelectrochemical reactions in the MFC. Also, the sustainable power generated from each cycle was evaluated, and it was found that higher sustainable energy can be harvested from higher organic loading 1000 g/L, which achieved maximum sustainable energy of 0.83 W/m³.