[1] | Myasnikov A. V., Vershinin A. V., Sboychakov A. M. A generalization of geomechanical model for naturally fractured reservoirs // Proceedings - SPE Russian Petroleum Technology Conference and Exhibition, 24-26 October 2016, Moscow, Russia. — Vol. 2. — Moscow, 2016. — P. 1050–1092. The article discusses the generalization of the model proposed in [1] for the calculation of the effective properties of the rock sample (periodicity cell) made of an elastic material, dissected by groups of plane cracks. In the original version of the semianalytic mathematical model cracks are represented by elastic springs with different rigidities in the normal and tangential directions [2]. At the same time, the effects of dilatancy and shear deformations because of normal stresses acting on crack's boundaries are neglected in the crack's constitutive relation specified by a relationship between the components of the displacement vector and the vector of forces (stresses on the surface parallel to the crack) in the normal and tangential directions. Further, in accordance with the concept of an equivalent medium for the fractured rock samples proposed in [3], cracks' effective modules are calculated based on the spacing between the cracks and the stiffness of the elastic springs. In order to calculate the total effective elastic tensor of a fractured rock sample a small deformations assumption is introduced, according to which the full deformations are a sum of deformations of the matrix and the fractures. In this paper, by constructing a three-dimensional numerical model of the periodicity cell, we managed to remove both limitations of the original analytical model: a diagonal relationship between displacements and forces in the crack and small deformations. This generalization become possible by modeling a crack as a thin layer of elastic material with Young's modulus and shear modulus computed from the initial normal and tangential stiffness (the original simplified model is obtained by zeroing Poisson's ratio) and taking into account a geometric nonlinearity in the relationship between deformations and displacements of the fracture's boundaries. Based on the generalized numerical model a finite element model in CAE Fidesys is built capable of varying the parameters of the cracks: the number, spacing, thickness, hardness, etc. The results of averaging are presented for the periodicity cell, dissected by three groups of plane cracks - the first two groups are orthogonal to the third group of cracks and intersect at a predetermined angle. The results of numerical studies on grid convergence, the impact of the size of the periodicity cell and the thickness of the crack on the results of averaging are given. The coincidence of analytical and numerical solutions for a simplified model and the difference between them in the case of a generalized model, leading, in some cases, to the variation of the effective Young's modulus up to 30%, are presented. [ DOI ] |