Mathematical Modeling of Long-Term Productivity of Hydraulic- and HEG- Fractured Wells in Ultra-Low Permeability Reservoirs

摘要

Modern multi-fractured shale gas and oil wells are horizontal wells completed with Simul Frac, Zipper Frac, and particularly Modified Zipper Frac techniques. An analytical model was developed in this study for predicting the long-term productivity of these wells under pseudo steady state flow conditions, considering the cross-bilinear flow in the rock matrix and hydraulic fractures. Performance of the model was verified with the well productivity data obtained from a shale gas field and a shale oil field. Sensitivity analyses were performed to identify key parameters of hydraulic fracturing affecting well productivity. The conducted field case studies show that the analytical model over-predicts shale gas well productivity with an error of less than 5%, and over-predicts shale oil productivity with an error less than 10%. Results of sensitivity analysis with the model indicate that well productivity increases with reduced fracture spacing, increased fracture length, and increased fracture width, but not proportionally. Whenever operational restrictions permit, more fractures with high-density should be created in the hydraulic fracturing process to maximize well productivity. The benefit of increasing fracture width should diminish as the fracture width becomes larger. Thus, there is no need to pursue wide fractures in the hydraulic fracturing process. Increasing fracture length by pumping more fracturing fluid can increase well production rate nearly proportionally. Therefore, it is desirable to create long fractures by pumping a high volume of fracturing fluid in the hydraulic fracturing process.;The use of fresh water as a fracturing fluid has limitations such as limited water availability in arid areas and negative impacts of water on oil and gas production in formations with high clay content. Alternatives to water for well fracturing include tailored energetic materials such as novel explosives. High energy gas fracturing (HEGF) creates radial fractures with fracture-orientations independent of formation stress anisotropy and heterogeneity. This eliminates the requirement of in-situ stress orientation for designing multi-hydraulic water-fracturing horizontal wells. Assuming uniformly distributed radial fractures around wellbore, an analytical well productivity model was derived in this study to predict productivity of HEGF-completed oil wells under pseudo steady state flow condition. Field case studies and sensitivity analyses were performed with the analytical model. Results of field case studies indicate that the analytical model over-predicts productivity of HEGF-completed wells by about 10%. Sensitivity analysis with the analytical model shows that the productivity of HEGF-completed wells reaches a maximum value at an optimal number of radial fractures around the wellbore. The productivity of the HEGF-completed wells increases non-linearly with fracture conductivity. But the benefit of increasing fracture conductivity levels out beyond fracture conductivity 2000 md-inch for the typical case investigated in this study.