The character of fluid flow in and around wellbores, cavities, and fractures in para-elastic media can significantly affect resource extraction operations in underground reservoirs. Reasonable estimations of hydraulic fracture profiles and propagation rates cannot be made without considering fluid exchange, especially for high leak-off; well production rates greatly depend on the flow rates into fractures; and reservoir properties are often strongly stress-sensitive.

In this paper, the fluid loss and the subsequent "backs tress" (i. e. induced reservoir stress) caused by it are characterized for stationary and propagating fractures, and the model is applied to three cases:

  1. a single fluid in the reservoir and fracture;

  2. two fluids: a reservoir fluid and a fracture fluid that has penetrated some distance into the reservoir;

  3. a production model where the crack has been propped and the reservoir fluid flows out of the well.

The fluid exchange between fracture and reservoir is found by solving an integral representation of the flow in the reservoir. Since the pressure distribution in the reservoir is governed by a diffusion process, the flow out of (or into) the fracture and the backstress are rather simply calculated by integrating along the fracture the influcence function for the pressure due to each component of fluid exchange, specifying the pressure at each point on the fracture or closing the system by some other means such as solving simultaneously the flow equations in the fracture, and solving for the fluid exchange inside the integral. Then backs tress can then be found from the fluid exchange. Preliminary computational results for plane fractures have been obtained that compare well with existing special analytical and numerical solutions (e.g.,those of Cinco and Samaniego). More general results are provided for moving fractures and induced stresses, and the broader capabilities of the methodology are outlined.

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