Heterogeneous aperture distribution is very common in large faults or fracture connecting injection and production wells. Recently the effects of heterogeneity on the temperature drawdown and transmissivity alteration due to dissolution/precipitation and thermo-elastic deformation of silicate reservoir were studied. The previous results based on numerical modeling have indicated that energy production rate is affected by correlation length and standard deviation of initial heterogeneous aperture field. The formation of a preferential flow path or channel is one of the most important consequences of heterogeneity when aperture alteration due to thermo-chemical and thermo-mechanical effects is significant. Previous studies have shown significant differences between the aperture alteration patterns of initially uniform fractures in carbonate and silicate reservoirs. Retrograde solubility and fast reaction rate of calcite with water are responsible for this. This has motivated us to study the effect of heterogeneity in carbonate reservoir. We have shown that the heterogeneity has much stronger effect in carbonate reservoir than that in silicate reservoir. In some cases the nature of evolution is completely different from homogeneous case under same injection conditions.