We present the algorithm and the source code of our numerical model to characterize the wettability of a three-phase system. Wettability is imperative in describing two-phase flow in subsurface geo-environmental applications, including storage of carbon dioxide in deep saline aquifers and groundwater remediation. Although the concept of contact angle is widely used to characterize the affinity of a fluid pair with a solid substrate, it does not accurately describe wettability alteration due to changes in pH and salinity. The latter arises from inter-molecular interactions, which are dominant in the three-phase contact region where the solid, wetting, and non-wetting fluids meet each other. We developed a physically-rooted lubrication model for thin films to model wettability alteration and replace the concept of contact angle. The model accounts for inter-molecular forces, including van der Waals, electric double layer, and hydration potential through a disjoining pressure. Unlike other approaches, we introduce a slope-dependent disjoining pressure. We present the implementation algorithm and the source code. The model has been thoroughly verified and used to investigate the role of salinity and pH on wettability. We find out that the slope-dependent disjoining pressure and the precursor film thickness alter the stability of the spreading.