A review of hydraulic-fracture modeling is given. Equations governing pertinent fluid-flow, structural, and fracture-mechanics responses are presented. The finite-element method is used to discretize the field equations and to compute the fracture dimensions, fluid leakoff, and stress intensity factors. In addition, the effects of fracture-fluid properties, layered strata, and in-situ stresses are characterized, and numerical examples are presented.
Results from an on-going DOE sponsored program related to hydraulic fracture response modeling are presented. Finite element model formulations and the solution methodology associated with a pseudo-three-dimensional hydraulic fracture model coupling fracture fluid flow and leak-off on both horizontal and vertical cross-sections with the elastic response in vertical cross-sections are described. In addition, fracture geometry evaluations and selected comparisons with available results are revealed.
A numerical model to simulate step rate test (SRT) has been developed using finite element technology. This model accounts for the interaction of the fracture and the formation by coupling the fluid flow in both fracture and reservoir. Unlike the conventional models which utilize assumed values of fluid leak-off rate from the fracture into the formation, this coupled fluid flow model yields a realistic fluid leak-off rate. The model also incorporates the effects of rock mechanics on the fracture opening/closing and fracture extension and consequently, on the pressure behavior during a step rate test. This paper reviews the governing fluid flow and poroelastic equations both in the fracture and in the reservoir and also presents the associated finite element formulations. A procedure to history match the step rate test data, to estimate the horizontal in-situ stress and the fracture toughness of the reservoir rock, is also presented. This has been demonstrated by applying the procedure to actual field data.
The present work should be useful for investigating the fracturing mechanisms (opening/closing and propagation) so that a better understanding of the fracture behavior during a step rate test can be obtained. Proposed procedures also can be used to estimate both the horizontal in-situ stress and the fracture toughness of the reservoir rock.
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