Foundations and Their Practical Implications for the Constitutive Coefficients of Poromechanical Dual-Continuum Models

Mark Ashworth, Florian Doster

Research output: Contribution to journalArticle

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Abstract

A dual-continuum model can offer a practical approach to understanding first-order behaviours of poromechanically coupled multiscale systems. To close the governing equations, constitutive equations with models to calculate effective constitutive coefficients are required. Several coefficient models have been proposed within the literature. However, a holistic overview of the different modelling concepts is still missing. To address this we first compare and contrast the dominant models existing within the literature. In terms of the constitutive relations themselves, early relations were indirectly postulated that implicitly neglected the effect of the mechanical interaction arising between continuum pressures. Further, recent users of complete constitutive systems that include inter-continuum pressure coupling have explicitly neglected these couplings as a means of providing direct relations between composite and constituent properties, and to simplify coefficient models. Within the framework of micromechanics, we show heuristically that these explicit decouplings are in fact coincident with bounds on the effective parameters themselves. Depending on the formulation, these bounds correspond to end-member states of isostress or isostrain. We show the impacts of using constitutive coefficient models, decoupling assumptions and parameter bounds on poromechanical behaviours using analytical solutions for a 2D model problem. Based on the findings herein, we offer recommendations for how and when to use different coefficient modelling concepts.
Original languageEnglish
Pages (from-to)699-730
Number of pages32
JournalTransport in Porous Media
Volume130
Issue number3
Early online date16 Sep 2019
DOIs
Publication statusPublished - Dec 2019

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Micromechanics
Constitutive equations
Composite materials

Keywords

  • Constitutive models
  • Dual-continuum
  • Micromechanics
  • Multiscale porous media
  • Poromechanics

ASJC Scopus subject areas

  • Catalysis
  • Chemical Engineering(all)

Cite this

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abstract = "A dual-continuum model can offer a practical approach to understanding first-order behaviours of poromechanically coupled multiscale systems. To close the governing equations, constitutive equations with models to calculate effective constitutive coefficients are required. Several coefficient models have been proposed within the literature. However, a holistic overview of the different modelling concepts is still missing. To address this we first compare and contrast the dominant models existing within the literature. In terms of the constitutive relations themselves, early relations were indirectly postulated that implicitly neglected the effect of the mechanical interaction arising between continuum pressures. Further, recent users of complete constitutive systems that include inter-continuum pressure coupling have explicitly neglected these couplings as a means of providing direct relations between composite and constituent properties, and to simplify coefficient models. Within the framework of micromechanics, we show heuristically that these explicit decouplings are in fact coincident with bounds on the effective parameters themselves. Depending on the formulation, these bounds correspond to end-member states of isostress or isostrain. We show the impacts of using constitutive coefficient models, decoupling assumptions and parameter bounds on poromechanical behaviours using analytical solutions for a 2D model problem. Based on the findings herein, we offer recommendations for how and when to use different coefficient modelling concepts.",
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Foundations and Their Practical Implications for the Constitutive Coefficients of Poromechanical Dual-Continuum Models. / Ashworth, Mark; Doster, Florian.

In: Transport in Porous Media, Vol. 130, No. 3, 12.2019, p. 699-730.

Research output: Contribution to journalArticle

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