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Applied Mathematics and Mechanics

, Volume 38, Issue 1, pp 15–28 | Cite as

Determination of elastic moduli of composite medium containing bimaterial matrix and non-uniform inclusion concentrations

  • Weitao SunEmail author
Article

Abstract

Reservoir porous rocks usually consist of more than two types of matrix materials, forming a randomly heterogeneous material. The determination of the bulk modulus of such a medium is critical to the elastic wave dispersion and attenuation. The elastic moduli for a simple matrix-inclusion model are theoretically analyzed. Most of the efforts assume a uniform inclusion concentration throughout the whole single-material matrix. However, the assumption is too strict in real-world rocks. A model is developed to estimate the moduli of a heterogeneous bimaterial skeleton, i.e., the host matrix and the patchy matrix. The elastic moduli, density, and permeability of the patchy matrix differ from those of the surrounding host matrix material. Both the matrices contain dispersed particle inclusions with different concentrations. By setting the elastic constant and density of the particles to be zero, a double-porosity medium is obtained. The bulk moduli for the whole system are derived with a multi-level effective modulus method based on Hashin’s work. The proposed model improves the elastic modulus calculation of reservoir rocks, and is used to predict the kerogen content based on the wave velocity measured in laboratory. The results show pretty good consistency between the inversed total organic carbon and the measured total organic carbon for two sets of rock samples.

Keywords

heterogeneous porous matrix composite material non-uniform inclusion concentration bulk modulus total organic carbon inversion 

Chinese Library Classification

O346.1 

2010 Mathematics Subject Classification

74R10 

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Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Zhou Pei-Yuan Center for Applied MathematicsTsinghua UniversityBeijingChina

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