Influence of spatial interactions of inclusions on the effective elastic tensor of cracked porous medium

Yu. A. Alkhimenkov ; I. O. Bayuk ; S. A. Tikhotskiy

Čebyševskij sbornik, Tome 18 (2017) no. 3, pp. 44-54

Résumé

The determination of effective stiffness tensor of microinhomogeneous and, in general, macroscopically homogeneous composite medium is related to so-called problem of many-body interaction. Solution to the problem can be found only as an approximation. In this paper we consider a solution to such a problem for porous-cracked medium that is a terrigenous rock having anisotropic elastic properties. The elastic anisotropy is a result of many factors including anisotropic properties of clay minerals and preferential orientation of non-isometric heterogeneities. Different Effective Medium Theories for calculating effective stiffness tensor of cracked porous medium use so called Effective Field Hypothesis (H1, H2 and H3). For example, T-matrix method, Mori-Tanaka method, General Singular Approximation method, and Effective Field Methods use the Effective Field Hypothesis. Thus, different methods produce similar results. When constructing models of rock's effective properties the rock is treated a composite “made by nature”. In this case of importance is a proper approximation of the real medium by a parametric model medium that reflects specific features of rock's microstructure. The microstructure is a result of rock evolution. Therefore, the model of the medium and the model parameters play very important roles in the modelling. To prove this statement, two models of a cracked-porous medium's properties were created using two different methods: the T-matrix method and General Singular Approximation Method. The methods were applied for two different parametric models of one and the same rock. The models were build based on visual analysis of rock's thin sections. Each of the constructed models has different number of parameters. The parameters are also different. However, a common feature of the two models is that for rocks of this type it is necessary to take into account a rigidity of contact between mineral grains and organic material. Besides, a connectivity of different heterogeneities should be also parametrized. For each model a set of parameters was found and a porosity interval where the models produce similar results in terms of elastic wave velocities is determined.

Détail

Keywords: pore-fractured media, effective properties, generalized singular approximation method.