Generalized solution to the anisotropic Mandel's problem

Solid deformation is always a crucial factor of gas transport in sedimentary rocks. While previous studies always adopt the assumption of isotropic poroelastic deformation, anisotropic poroelastoplastic deformation is rarely considered, despite anisotropy being a ubiquitous property of natural sedimentary rocks. In this work, an anisotropic poromechanical model is established to analyze the matrix porosity and apparent permeability evolutions during the process of gas migration. Using a thermodynamic formulation that treats the fluid–solid interface as an independent phase, we derive a rate form for matrix porosity and obtain the new dissipation function that contains three parts: dissipations from solid deformation, gas adsorption, and fluid flow. For gas adsorption, we justify the rationality of the adopted model; for fluid flow, the updated porosity can be substituted into sophisticated apparent permeability models for full‐scale analysis; and for solid deformation, a recently developed constitutive model appropriate for rocks exhibiting transverse isotropy in both the elastic and plastic responses is adopted in this work. Through the novel stress‐point simulation incorporating two effective stress measures and adsorption strain, new patterns of apparent permeability are obtained, which fit the experimental data quite well and cannot be reproduced from the assumption of isotropic poroelasticity. The advantages of our poromechanical model include thermodynamic consistency and the ability to employ finite‐element‐based formulation. Finally, an initial‐boundary value problem of gas production considering anisotropic plasticity is conducted, and the effects of the bedding plane and different adsorption models are highlighted.

“…These constants are directly measurable in laboratory experiments. Note that Poisson's ratios 𝜈 ℎ𝑣 and 𝜈 𝑣ℎ are not independent and are correlated through the equation 74…”

Section: Anisotropic Elastoplasticitymentioning

confidence: 99%

“…These constants are directly measurable in laboratory experiments. Note that Poisson's ratios

\nu _{hv}

and

\nu _{vh}

are not independent and are correlated through the equation 74

\begin{equation} \frac{\nu _{vh}}{E_v} = \frac{\nu _{hv}}{E_h}\,. \end{equation}

For a transversely isotropic material with positive elastic moduli (

E_h, E_v &gt; 0

) to be stable, the following inequality must be satisfied, as suggested by Ip et al 75 …”

Section: Constitutive Relationsmentioning

confidence: 99%

Anisotropic continuum framework of coupled gas flow – adsorption – deformation in sedimentary rocks

Zhang,

Yin,

Yan

2023

“…Transverse isotropy is a common type of anisotropy in which the material properties are symmetric about a bedding plane and anisotropic in the direction normal to this plane 19–23 . The effect of anisotropy on the stiffness and strength of various transversely isotropic rocks has been extensively investigated in the literature 24–31 . The stiffness and strength of transversely isotropic rocks depend on the direction of the load with respect to the orientation of the bedding plane, and are often different in the bed‐normal (BN) and bed‐parallel (BP) directions.…”

Section: Introductionmentioning

confidence: 99%

“…[19][20][21][22][23] The effect of anisotropy on the stiffness and strength of various transversely isotropic rocks has been extensively investigated in the literature. [24][25][26][27][28][29][30][31] The stiffness and strength of transversely isotropic rocks depend on the direction of the load with respect to the orientation of the bedding plane, and are often different in the bed-normal (BN) and bed-parallel (BP) directions. The maximum strength can occur in either direction, but the minimum strength typically occurs when the load is inclined with the bedding plane, often at an angle 𝜃 between 20 and 40 • .…”

Section: Introductionmentioning

confidence: 99%

Evolution of anisotropy with saturation and its implications for the elastoplastic responses of clay rocks

Borja

2021

Many clay rocks have distinct bedding planes. Experimental studies have shown that their mechanical properties evolve with the degree of saturation (DOS), often with higher stiffness and strength after drying. For transversely isotropic rocks, the effects of saturation can differ between the bed-normal (BN) and bedparallel (BP) directions, which gives rise to saturation-dependent stiffness and strength anisotropy. Accurate prediction of the mechanical behavior of clay rocks under partially saturated conditions requires numerical models that can capture the evolving elastic and plastic anisotropy with DOS. In this study, we present an anisotropy framework for coupled solid deformation-fluid flow in unsaturated elastoplastic media. We incorporate saturation-dependent strength anisotropy into an anisotropic modified Cam-Clay (MCC) model and consider the evolving anisotropy in both the elastic and plastic responses. The model was calibrated using experimental data from triaxial tests to demonstrate its capability in capturing strength anisotropy at various levels of saturation. Through numerical simulations, we demonstrate the role of evolving stiffness and strength anisotropy in the mechanical behavior of clay rocks. Plane strain simulations of triaxial compression tests were also conducted to demonstrate the impacts of material anisotropy and DOS on the mechanical and fluid flow responses.

“…extended Mandel's solution to account for material transverse isotropy. Later developments on the analytical solutions were presented to account for material dual‐porosity dual‐permeability poroelasticity 18,19 and anisotropy 20,21 . Analytical solutions to this problem have helped explain the coupled poroelasticity and validate poromechanics numerical algrorithms 22,23 .…”

Section: Introductionmentioning

confidence: 99%

Fundamental solutions to the transversely isotropic poroelastodynamics Mandel's problem

Liu

2021

Self Cite

Many geomaterials, such as shale, and biomaterials, including human bone and cartilage, are anisotropic. Understanding the dynamic responses of such anisotropic porous media is essential in field operations and laboratory measurements. This paper presents analytical solutions to the transversely isotropic poroelastodynamics Mandel's problem, using the Fourier transform method and Cardano formula to solve coupled six‐order partial differential equations. Potential applications of the solutions include explaining coupled fluid‐solid dynamics, validating numerical algorithms, and interpreting dynamic responses of anisotropic porous media. As an example, we apply the solutions to simulate a fluid‐saturated transversely isotropic Trafalgar shale specimen subjected to harmonic excitation. The simulation shows that pore pressure builds up as frequency increases. The buildup occurs at a lower frequency for a lower horizontal permeability. The amount of pore pressure buildup due to the Mandel‐Cryer effect is sensitive to material anisotropy. The porous material's effective stiffness reaches its periodic minimum and maximum at the resonant and anti‐resonant frequencies controlled by mechanical anisotropy and pore fluid.