Spatio-temporal evolution of a fluid-driven crack and its propagation: Insights from experiment and mathematical modelling

Article Type

Research Article

Publication Title

Journal of Earth System Science

Abstract

We present a complete numerical solution of a 3D transient, first-principle-based model for penny-shaped fluid-driven cracks, advancing from the existing scaling laws and extending beyond the previously produced (limiting) asymptotic profiles. Our mathematical analysis is complemented by experimental studies that explore fracture growth and the regime of the developed fracture. The study focuses on fracture toughness and viscous-dominated regimes, highlighting the applicability of our hydrodynamics-dominated penny-shaped fracture model predictions. The fracture experiments were carried out in a solid analogue material (gelatin) of dimensions 15 cm × 15 cm × 15 cm in a glass reservoir at a laboratory scale under simulated environments. Since the gelatin is transparent, tracking is feasible, and we track 3D crack formation and propagation in real time. We focus on the operational parameters that affect the evolution and propagation of cracks in an elastic medium dominated solely by hydrodynamic stress or in competition with the solid toughness. In our investigation, the injection rate and viscosity of the fracturing fluids are varied to study their influence on crack formation and propagation. To get an insight into the strain occurring in the gelatin, recorded strain displacement measurements are related to the dynamic evolution of the 3D fracture. The self-similar nature of the physical system of equations suggests that this problem is scale-independent and thus can be related to large-scale engineering applications such as hydraulic fracturing and CO2 geo-sequestration technologies.

DOI

10.1007/s12040-025-02611-4

Publication Date

9-1-2025

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