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Research Papers: Petroleum Engineering

Anisotropic Inhomogeneous Poroelastic Inclusions: With Application to Underground Energy-Related Problems

[+] Author and Article Information
Houman Bedayat

Bureau of Economic Geology,
University of Texas at Austin,
Austin, TX 78758
e-mail: houman.bedayat@gmail.com

Arash Dahi Taleghani

Department of Petroleum Engineering,
Louisiana State University,
Baton Rouge, LA 70803
e-mail: a_dahi@lsu.edu

1Corresponding author.

Contributed by the Petroleum Division of ASME for publication in the JOURNAL OF ENERGY RESOURCES TECHNOLOGY. Manuscript received November 30, 2015; final manuscript received December 21, 2015; published online January 21, 2016. Editor: Hameed Metghalchi.

J. Energy Resour. Technol 138(3), 032905 (Jan 21, 2016) (7 pages) Paper No: JERT-15-1455; doi: 10.1115/1.4032449 History: Received November 30, 2015; Revised December 21, 2015

Understanding the stress change in a reservoir generated by fluid production/injection is important for field development purposes. In this paper, we provide the Eshelby solution for stress and strain distribution inside and outside of an anisotropic poroelastic inhomogeneity due to pore pressure changes inside the inhomogeneity. The term anisotropic inhomogeneity refers to an inhomogeneity with anisotropic poroelastic constants. Some graphical results for strain and stress ratios for different material properties and geometries are presented as well. Anisotropy in elastic properties has been studied extensively in the last century; however, anisotropy in poroelastic properties, despite its potential significant impact in different engineering problems, has not been explored thoroughly. The results show how neglecting the effect of anisotropic poroelastic properties may result in large differences in calculated stresses. Due to the authors' primary interest in geomechanical problems, the discussions and examples are chosen for applications involving fluid withdrawal/injection into hydrocarbon reservoirs.

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Copyright © 2016 by ASME
Topics: Stress , Pressure
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Figures

Grahic Jump Location
Fig. 1

A single inclusion embedded in an infinite medium. Ω1 and C1 indicate inclusion domain and its elastic moduli tensor, respectively. Ω and C represent the surrounding matrix and its elasticity moduli tensor, respectively.

Grahic Jump Location
Fig. 2

(a) Strain ratio and (b) stress ratio due to a pressure change inside an isotropic poroelastic inhomogeneity. Both graphs are plotted against the inhomogeneity aspect ratio, e. It is assumed that g is a shear modulus ratio, G1/G; αij1=δij (isotropic case); and ν0=ν1=0.2. However, the dependence of the solution on ν0 is weak. These graphs are in exact agreement with Figs. 4 and 7 in Rudnicki [17].

Grahic Jump Location
Fig. 4

Stress ratio for different α331 values. g=(G1/G0);ν0=ν1=0.2;a1=a2=a3=1. (a) σ33/p if α331=0.1; (b) σ33/p if α331=1; (c) σ33d/p, difference of (a) and (b); (d) σ11/p if α331=0.1; (e) σ11/p if α331=1; and (f) σ11d/p, difference of (d) and (e).

Grahic Jump Location
Fig. 3

Stress ratio against inhomogeneity aspect ratio, e, for various shear modulus ratio (g=G1/G0) and Poisson's ratio. The solid lines indicate vertical stress ratio σ33/p, whereas the dotted lines indicate lateral stress ratio σ11/p.

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