Propagation of Elongated Fluid-Driven Fractures: Rock Toughness vs. Fluid Viscosity
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916590878982144 |
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| author | Garagash, Dmitry I. |
| author_facet | Garagash, Dmitry I. |
| contents | This paper studies the effect of the rock fracture toughness on the propagation of elongated fluid-driven fractures. We use the `tough PKN' model of Sarvaramini and Garagash (2015), an extension of the classical PKN model(Perkins and Kern, 1961; Nordgren, 1972), which allows for a non-zero energy release rate into the advancing fracture front(s). We provide a self-consistent analysis of a `tough' elongated fracture driven by arbitrary fluid injection law under the assumption of negligible fluid leak-off. We use scaling considerations to identify the non-dimensional parameters governing the propagation regimes and their succession in time, provide a number of analytical solutions in the limiting regimes for an arbitrary power-law injection, and also posit a simplified, equation-of-motion, approach to solve a general elongated fracture propagation problem during the injection and shut-in periods. Finally, we use the developed solutions for a tough elongated fracture to surmise the relative importance of the viscous and toughness-related dissipation on the fracture dynamics and broach the implications of the possible toughness scale-dependence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18722 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Propagation of Elongated Fluid-Driven Fractures: Rock Toughness vs. Fluid Viscosity Garagash, Dmitry I. Geophysics This paper studies the effect of the rock fracture toughness on the propagation of elongated fluid-driven fractures. We use the `tough PKN' model of Sarvaramini and Garagash (2015), an extension of the classical PKN model(Perkins and Kern, 1961; Nordgren, 1972), which allows for a non-zero energy release rate into the advancing fracture front(s). We provide a self-consistent analysis of a `tough' elongated fracture driven by arbitrary fluid injection law under the assumption of negligible fluid leak-off. We use scaling considerations to identify the non-dimensional parameters governing the propagation regimes and their succession in time, provide a number of analytical solutions in the limiting regimes for an arbitrary power-law injection, and also posit a simplified, equation-of-motion, approach to solve a general elongated fracture propagation problem during the injection and shut-in periods. Finally, we use the developed solutions for a tough elongated fracture to surmise the relative importance of the viscous and toughness-related dissipation on the fracture dynamics and broach the implications of the possible toughness scale-dependence. |
| title | Propagation of Elongated Fluid-Driven Fractures: Rock Toughness vs. Fluid Viscosity |
| topic | Geophysics |
| url | https://arxiv.org/abs/2501.18722 |