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Applied Mathematics and Mechanics (English Edition) ›› 2017, Vol. 38 ›› Issue (1): 15-28.doi: https://doi.org/10.1007/s10483-017-2157-6

• 论文 • 上一篇    下一篇

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

Weitao SUN   

  1. Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing 100084, China
  • 收稿日期:2016-04-07 修回日期:2016-06-16 出版日期:2017-01-01 发布日期:2017-01-01
  • 通讯作者: Weitao SUN,E-mail:sunwt@tsinghua.edu.cn E-mail:sunwt@tsinghua.edu.cn
  • 基金资助:

    Project supported by the Open Project Program of Sinopec Key Laboratory of Multi-Component Seismic Technology (No. GSYKY-B09-33), the National Key Basic Research Program of China (973 Program) (No. 2014CB239006), and the Basic Research Program of Community Networks Program Centers (CNPC) (No. 2014A-3611)

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

Weitao SUN   

  1. Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing 100084, China
  • Received:2016-04-07 Revised:2016-06-16 Online:2017-01-01 Published:2017-01-01
  • Contact: Weitao SUN E-mail:sunwt@tsinghua.edu.cn
  • Supported by:

    Project supported by the Open Project Program of Sinopec Key Laboratory of Multi-Component Seismic Technology (No. GSYKY-B09-33), the National Key Basic Research Program of China (973 Program) (No. 2014CB239006), and the Basic Research Program of Community Networks Program Centers (CNPC) (No. 2014A-3611)

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摘要：

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.

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

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.

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

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