Hydraulic fracturing stimulation is one of the key technologies for shale gas development. The recent advances in micro-seismic data acquisition and processing suggest that hydraulic fracturing stimulation has often resulted in complex fracture network due to the pre-existing natural fractures. Modeling hydraulic fracturing processes needs to couple in-situ stress response and flow of engineered fluid that includes water, proppant and other chemicals. Moreover, the high Reynolds number indicates that the flow in the hydraulic fracturing processes is either in transition or turbulent flow regime. Consequently, the resulting mathematical model is complex and needs to be numerically solved.

In this paper, we have developed a hydraulic fracturing model considering the in-situ stress response to turbulent flow process. The mixed finite element method is employed for numerical solution of the resulting system of coupled nonlinear partial different equations. The proposed model has been validated with bi-wing hydraulic fracture model through regression tests. The preliminary numerical results show the significant differences in hydraulic fracture growth in comparison with the models that assume laminar flow in hydraulic fracturing processes. We have also integrated proposed hydraulic fracturing model into a numerical reservoir simulator and are currently conducting field-scale numerical simulation studies. The preliminary results also suggest that the proposed model is also capable of modeling the interactions between the hydraulic fracture and pre-existing natural fractures based on initial fracture mapping.

The proposed model provides an opportunity to optimize hydraulic fracturing stimulation design through numerical simulations, which is vital in unconventional reservoir production.

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