Formation of Crack on Hydraulic Fracturing of Bed in a Medium with Double Porosity
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Journal of Engineering Physics and Thermophysics, Vol. 93, No. 4, July, 2020
FORMATION OF CRACK ON HYDRAULIC FRACTURING OF BED IN A MEDIUM WITH DOUBLE POROSITY A. V. Karakin
UDC 662.807.4
A study is made of a two-dimensional bound problem on slow motions of a liquid in a hydraulic fracturing crack and on deformations and filtration caused by these motions in a poroelastic medium with double porosity involving two components — the porosity proper and jointing. The motions are induced by the pumping of a liquid into a well. The motion inside the crack is described by hydrodynamics equations in hydrostatic approximation. Some ordered sequence of interdependent geomechanical processes occurring on hydraulic fracturing is established in conformity with the principle of incomplete connection. In the main space surrounding the crack, the liquid moves in the porous component of the two-phase medium. In the boundary layer the motion dominates in the jointy component. In distinction to the classical problem with double porosity, the indicated problem is solved rigorously with account for elastic deformations of the skeleton. The motion regimes in the main volume and in the boundary layer differ significantly due to the permeability of the medium. Keywords: jointing, porosity, poroelasticity, double porosity, hydraulic fracturing crack. Introduction. The simplest variant of the poroelastic model is the Biot model [1], for which expressions were derived in works [1–3] for some material parameters proceeding from thermodynamic considerations. The Aifantis equations [4] generalize the Biot equations to the case of double porosity. In work [5], with the aid of rather rigorous transformations of the input equations of the mechanics of Biot poroelastic media, results analogous to the results of works [1–3] were obtained. The thermodynamic approach guarantees the consistency of the results obtained. It is not always convenient, however, in the case of different kinds of generalizations, when the form of the determining relations is obtained from certain additional considerations. Thus, monograph [7] suggests the indicated heuristic approach to the construction of a model of a porous medium with double porosity (with cracks and pores). In the present work, we consider a crack (joint) of the hydraulic fracturing of a bed (HFB) in a medium with double porosity on the basis of the principles elucidated in [1–6]. The problem is solved in two stages. First, a model of a medium with double porosity is constructed that in general terms reproduces the line of reasoning presented in works [5, 6]. At the second stage, an equilibrium HFB crack is considered as an example at a constant pressure in it. The crack moves under the action of the pumped-in liquid. A characteristic feature of a multifactor model of the HFB crack is that this model involves a multitude of heterogeneous physical phenomena. The basic idea of investigation of the HFB crack model in the indicated medium (just as in an ordinary poroelastic medium) is associated with the p
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