We present a unique microfluidics experimental system that uses geo-material (rock) micromodels and accommodates pressures and temperatures that are encountered in many fossil fuel operations. This system allows us to investigate a wide variety of fluid flow, transport, and chemistry processes that cannot be addressed with experiments at ambient conditions using typical micromodel materials (e.g., glass, silicon). We describe the experimental system in detail, including our versatile micromodel fabrication method that works for a variety of geo- and engineered materials. We present a shale fracture-matrix interaction experiment that shows the importance of imbibition in these systems. Additionally, we present a series of immiscible displacement experiments conducted in shale and glass involving supercritical-CO2 and water. The experiments and discussion highlight the advantages of using rock micromodels for applications involving fossil fuel operations.