Characterizing the faults and fractures that provide flow pathways for efficient geothermal energy production is critical for design of sustainable geothermal energy production. Both natural faults and stimulated fractures in enhanced geothermal systems (EGS) are difficult to image and map by seismic methods because hot brine filling the fractures and faults does not create a strong seismic property contrast relative to surrounding rock. We investigate here the technical feasibility of using supercritical CO2 (scCO(2)) injection into faults in a single-well push-pull scenario to characterize the hydraulic properties of the fault zone by emplacing scCO(2) that can serve as a contrast fluid for seismic monitoring. We develop a conceptual and numerical reservoir model of two intersecting faults based on the Dixie Valley geothermal system in Nevada, USA. The 2D conceptual model consists of a system with a main fault and an intersecting conjugate fault. The corresponding numerical model is discretized using irregular grid blocks with fine discretization around the slip plane, gouge, and damage zones. We perform forward modeling along with sensitivity and data-worth analyses of scCO(2) push-pull to investigate the CO2 distribution in the fault gouge during 30 days of push (injection) and 30 days of pull (production). Formal sensitivity analysis is conducted to determine the most controlling unknown parameters in the fault zones. Using the selected set of unknown parameters and output responses, we perform data-worth analysis to reveal the most valuable output response to be measured for the best prediction of CO2 distribution in the fault zones and its uncertainty. From the results of data-worth analysis, we determine the optimal properties to target in monitoring, their locations, and the minimum observation time. Our results provide information on the optimal design of scCO(2) push-pull testing in a conjugate fault system modeled after Dixie Valley that can be used to enhance monitoring by active seismic and well-logging methods to better characterize the transmissive fault(s).