A quantitative model to predict hydraulic fracture propagating across cemented natural fracture

Abstract A quantitative model is proposed to predict hydraulic fracture propagating across cemented natural fracture based on the numerical simulation and statistical regression. The cohesive zone method is employed to capture fracture initiation and growth, and the model combining rock deformation and fluid flow is established to simulate hydraulic fracture propagation with pre-existing natural fracture. The numerical model is solved by using finite element method, and verified against the analytical solution on the classical fracture problem. The investigation of influencing factors on hydraulic fracture propagation shows that the horizontal principal stress difference, approaching angle, cementing strength of natural fracture, injection rate and fluid viscosity codetermine whether hydraulic fracture propagates across natural fracture. After identification of these influencing factors, a series of numerical cases are conducted based on different combination of factor levels. Then the logistic regression method is employed to get the quantitative relationship between the crossing result and the factors, and the accuracy of regression equation is above 99%. The crossing curves are drawn to give the threshold of injection rate for varying other influencing factors. The potential applications include the usage of crossing criterion in the numerical modeling of fracture network propagation and the optimization of injection rate in the real field.