Hydraulic fracturing technology is widely used to enhance the economic extraction of unconventional oil and gas resources. However, there is a lack of previous research on the hydraulic propagation behaviors of elliptical cracks under biaxial stress conditions. In this study, we combine laboratory experiments with a theoretical model to evaluate the influence of the viscosity of the fracture liquid, the external load, and the elastic modulus of the matrix on the propagation of an elliptical crack. Through experiments, we capture the development of the crack morphology and the evolution of the semi-major and semi-minor axes over time. The experimental observation reveals that the increase in the external loads and the liquid viscosity cause the crack to be more elliptical, while increasing the elastic modulus rounds the crack. Our theoretical model is built on the basis of a mechanical equilibrium between the critical pressure for the propagation of the crack determined by the properties of the material and the combined force of fluid pressure within the crack and external stress. Associated with two correction coefficients, the theoretical prediction is in good agreement with the experimental observation on the size of the crack. More importantly, we capture the systematic variation of the correction coefficient with key parameters, which provides a quantitative basis for parameter optimization based on formation characteristics in the practical hydraulic fracturing design.
Ning et al. (2026) studied this question.