Abstract
We consider single phase flow from an isolated fracture within a porous medium of finite vertical extent. The fracture is fully penetrating vertically and is of finite length in the horizontal direction. This problem is amenable to analysis with cylindrical elliptic coordinates in which the foci correspond to the ends of the fracture. With suitable boundary conditions, the solution is such that the gravity-adjusted pressure depends on only one of the elliptic coordinates, and the isobars in the horizontal plane are confocal ellipses. In this paper, we show that, contrary to the usual assumption made in transient testing, the material (fluid) fronts do not coincide with isobars. Rather, at early times the front exhibits a “dog-bone” appearance; at later times, the front shape is more oval, but is not an ellipse. To confirm the theoretical results, we present an experimental design capable of mapping material fronts. Tracer images of the displacing fluid agree with the theory, thus showing that injection test interpretation in fractured wells is not amenable to analysis with a single spatial coordinate, even for unit mobility ratio. The match with theory is also a partial validation of the continuum formulation of Darcy’s law.
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Research was supported by Schlumberger-Doll Research. There is no conflict of interest. TSR developed the theory and solutions, designed the experiments, and processed the data. MGS conducted the experiments. DJW collaborated on the analytical work with TSR.
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Ramakrishnan, T.S., Supp, M.G. & Wilkinson, D.J. Front Tracking of Flow from a Fracture. Transp Porous Med 139, 447–465 (2021). https://doi.org/10.1007/s11242-021-01664-5
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DOI: https://doi.org/10.1007/s11242-021-01664-5