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Research Papers

Theory and Analytical Solutions to Coupled Processes of Transport and Deformation in Dual-Porosity Dual-Permeability Poro-Chemo-Electro-Elastic Media

[+] Author and Article Information
Chao Liu

Aramco Research Center-Houston,
Aramco Services Company,
Houston, TX 77084
e-mail: Chao.Liu@Aramcoservices.com

Amin Mehrabian

Department of Energy and Mineral Engineering,
Earth and Mineral Sciences Energy Institute,
The Pennsylvania State University,
University Park, PA 16802
e-mail: amin.mehrabian@psu.edu

Younane N. Abousleiman

Integrated PoroMechanics Institute,
The University of Oklahoma,
Norman, OK 73019

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received May 25, 2018; final manuscript received June 30, 2018; published online August 1, 2018. Assoc. Editor: Shaoxing Qu.

J. Appl. Mech 85(11), 111006 (Aug 01, 2018) (13 pages) Paper No: JAM-18-1310; doi: 10.1115/1.4040890 History: Received May 25, 2018; Revised June 30, 2018

The linear theory of dual-porosity and dual-permeability poro-chemo-electro-elasticity is presented. The theory outlines the dual-continuum formulation of multiple coupled processes involving solid deformation, pore fluid flow, and electrically charged species transport, within and in between two coexisting porosity systems of a fluid-saturated, poro-elastic medium. The described formulation is used to derive the analytical solutions to the inclined wellbore problem and axisymmetric Mandel-Type problem of dual-porosity, dual-permeability poro-chemo-electro-elasticity. The effects of chemical and electrical potentials on the distributions of stress and pore pressure are demonstrated by numerical examples pertaining to the considered problems. It is shown that the fully coupled nature of the solutions rigorously captures the seemingly anomalous time variations of the effective stress as driven by the pore fluid pressure disturbances, as well as the distribution and movement of anions/cations within the dual-porosity porous medium. The existing subset of published solutions on the subject is successfully reproduced as special cases of the solutions presented in this paper.

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Figures

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Fig. 1

Submerged Woodford shale samples (a) heavily disintegrated when immersed in a solution with relatively low salinity; (b) milder reaction when immersed in a solution with relatively high salinity

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Fig. 2

Illustration of the fluid species flows for the poro-chemo-electro-elasticity

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Fig. 3

Schematic of wellbore drilling in a naturally fractured rock formation

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Fig. 4

During wellbore drilling, both matrix and fracture communicate with the wellbore fluid

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Fig. 5

Schematic of the axisymmetric Mandel-Type problem

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Fig. 6

Evolution of pore pressure distribution along the radial direction

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Fig. 15

Distribution of fracture pore pressure

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Fig. 14

Distribution of matrix pore pressure

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Fig. 13

Evolution of ions concentration at r = 0

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Fig. 12

Evolution of pore pressure at r = 0

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Fig. 11

Evolution of ions concentration at r/R = 1.05

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Fig. 10

Evolution of pore pressure at r/R = 1.05

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Fig. 9

Distributions of effective radial stress for different CEC at t = 10 min

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Fig. 8

Distribution of effective stress

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Fig. 7

Distribution of pore pressure (XI = 0; Da = 2.0 × 10−7, Dc = 6.0 × 10−7)

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Fig. 17

Reproduce Fig. 8 in Ref. [44] by the axisymmetric Mandel-Type solution presented in this paper

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Fig. 16

Reproduce Fig. 6 in Ref. [30] by the inclined wellbore solution presented in this paper

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