CO_2 is now considered as a novel heat transmission fluid to extract geothermal energy. It can be used for both energy exploitation and CO_2 geological sequestration. Here, a 3-D, 'two-spot' pattern well model is developed to analyze the mechanism of CO_2-water displacement and heat extraction. To obtain a deeper understanding of CO_2-geothermal system under some more realistic conditions, heterogeneity of reservoir's hydrological properties is taken into account. Due to the fortissimo mobility of CO_2, as long as the existence of highly permeable zone between the two wells, it is more likely to flow through the highly permeable zone to reach the production well, even though the flow path is longer. The preferential flow shortens circulation time and reduces heat-exchange area, probably leading to early thermal breakthrough, which makes the production fluid temperature decrease rapidly. The analyses of flow dynamics of CO_2-water fluid and heat may be useful for future design of a CO_2-based geothermal development system.