Developed Regime of Motion in Hydraulic Fracture in a Double-Porosity Medium
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Journal of Engineering Physics and Thermophysics, Vol. 93, No. 6, November, 2020
DEVELOPED REGIME OF MOTION IN HYDRAULIC FRACTURE IN A DOUBLE-POROSITY MEDIUM A. V. Karakin
UDC 662.807.4
A study is made of a two-dimensional coupled problem on slow motions of a liquid in a hydraulic fracture and on deformations and filtration induced by these motions in a porous medium with double porosity that has two components: the porosity proper and the fracturing. The motions are produced by pumping the liquid into the well. Flow inside the fracture is described by hydrodynamics equations in a hydrostatic approximation. A certain ordered series of interdependent geomechanical processes occurring during the hydraulic fracturing is established. In the main space around the fracture, the liquid moves in the porous component of the two-phase medium. In the boundary layer, there are mixed processes: in addition to the motion of the liquid by the fractures, we have its crossflow between the fractures and the pores. These effects are investigated as a first approximation for a certain small parameter which is represented by the relative time. In contrast to the well-known classical problem with double porosity, in this case the indicated problem is rigorously solved with account of elastic deformations of the skeleton. In actual fact, the present paper is a continuation of the previous work of the author in an analogous formulation in a zero approximation, in which the boundary layer is trivial and is reduced to the boundary layer in a medium with ordinary porosity. Examples of solving concrete problems are given. Keywords: fracturing, porosity, poroelasticity, double porosity, hydraulic fracture. Introduction. The simplest variant of a poroelastic model is the Biot model [1]. For it, expressions for certain material parameters have been derived in [1–3] from simple thermodynamic considerations. Aifantis equations [4] generalize the Biot equation to the case of double porosity. In [5, 6], the indicated results (analogous to the results from [1–3]) have been obtained using rigorous transformations of the initial Biot equations of the mechanics of poroelastic media. The thermodynamic approach [3] guarantees the consistency of the obtained results. However, it is not always convenient in generalizations of various kinds, when the form of governing relations is found from certain additional considerations. Thus, in [7], the indicated heuristic approach to constructing the model of a porous medium with double porosity (with fractures and pores) is proposed. In the present work, we consider a hydraulic fracture (HF) in a double-porosity medium on the basis of the principles presented in [1–6]. The order of presentation is as follows. First, the existing Aifantis [4] and Barenblatt [7] models of a double-porosity medium are given, and thereafter the original model of an HF in a double-porosity medium is proposed by reproducing in general the line of reasoning from [5, 6]. Finally, a few examples of solving concrete problems in the indicat
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