We address questions that arose from studying gas and oil production from hydrofractured wells. Does past production predict the future? This depends on deducing from production as much as possible about the plausible geometries of the fracture network. We address the problem through a solvable model and use kinetic Monte Carlo and Green's function techniques to solve it. We have three main findings. First, at sufficiently long times, the production from all compact fracture networks is described by a universal function with two scaling parameters, one of which is the diffusivity of unbroken rock α and the second of which is a parameter Vext with units of volume. Second, for fracture networks where the power-law distribution of fracture spacings falls below a critical value (and this appears to be the case in practice), early-time production always scales as one over the square root of time. Third, the diffusivity α that sets the scale for late-time production is inherently difficult to estimate from production data, but the methods here provide the best hope of obtaining it and thus can determine the physics that will govern the decline of unconventional gas and oil wells.
Bibliographical noteKAUST Repository Item: Exported on 2021-12-13
Acknowledgements: Partial support for this work was provided by the US National Science Foundation through Award No. 1810196, Fracture and Transport Problems for Inhomogeneous Brittle Materials, and by a Competitive Research Grant from KAUST, “Numerical and Experimental Investigation of Gas Distribution, Complex Hydrofractures and the Associated Flow in the Jafurah Basin Shales: Fundamentals to Applications.” The opinions expressed in this work are not necessarily shared by the National Science Foundation.