Surrogate modeling and global sensitivity analysis for the simultaneous growth of multiple hydraulic fractures

Abstract

Hydraulic fracturing has been widely used in enhancing the conductivity of the rock formations and increasing the rate of extraction of unconventional resources. During hydraulic fracturing treatments, there are considerable uncertainties in the completion operations and measurement of the geomechanical parameters such as the perforation geometry and elastic modulus of the rock matrix, which may result in a large error in fracture pattern prediction and parameter optimization when deterministic models are implemented. Therefore, a good understanding of the impact of the input uncertainties on the output predictions, also referred to as uncertainty quantification, has become a major issue. In this paper, a non-intrusive stochastic model is developed by combining a fully coupled hydraulic fracturing model based on the dual boundary element method with a surrogate model using polynomial chaos expansion. The perforation geometry, mechanical parameters of the rock formation, orientation and magnitude of the in-situ stress are treated as random variables. The surrogate model is constructed using data from the hydraulic fracturing model and is capable of providing fast approximations of the objectives, thereby making Monte Carlo simulations and sensitivity studies feasible. The stochastic model is validated against the random responses predicted by semi-analytical solutions for the single fracture case and shows excellent agreements with a relative error less than 0.1% for the injection pressure and 1% for the maximum aperture. The impact of the geomechanical and geometric parameter randomness on the growth of multiple fractures is investigated. The results show that the randomness in the fracture toughness and Young’s modulus plays an important role in fracture growth among geomechanical parameters, and the uncertainty of the fracture pattern is mostly attributed to the randomness in the initial length and aperture of the inner fracture among geometric uncertainties.