Accurately modeling geochemical reactions in subsurface flow is essential for understanding processes such as CO2 sequestration and contaminant transport. This paper presents a new numerical subsurface simulator (MF3D-GC) that combines flow, geomechanics, and geochemistry in an integrated and fully coupled manner. The simulator's capabilities were benchmarked by comparing it with other reactive-transport simulators. An adaptive tolerance method was implemented in the geochemistry module which reduced computing time while maintaining accuracy. User-defined kinetic models were used and coupled with changes in specific surface area, fluid saturation, temperature, and pH. The unique abilities of the model to couple geomechanics with geochemistry are highlighted. Our results show the importance of carefully selecting minerals and models to balance accuracy and computational efficiency. The model is used to simulate 6 different classes of geochemical flow problems which include flow, dissolution, precipitation, redox reactions, and diffusion with increasing levels of complexity. The potential applications of the model to CO2 sequestration, solution mining, geothermal energy production, and contaminant transport are briefly discussed.