The Elastic Coefficients of Double-Porosity Materials: A Revisit

Zheng, Pei; Gao, Zhe; Ding, B.Z.

doi:10.1007/s11242-015-0611-9

Cited by 10 publications

(4 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(Wilson & Aifantis, 1982) proposed effective parameters based on the Skempton coefficient:

b_{m} = \frac{K^{*}}{K} ((), 1 - \frac{K}{K_{s}}), b_{f} = 1 - \frac{K^{*}}{K},

where

K^{*}

K

, and

K_{s}

are the bulk moduli of fractured rock, intact porous matrix and solid grains, respectively (Bai, 1999). Alternative models to compute effective parameters for dual‐porosity poroelastic media haven been proposed by (Berryman & Pride, 2002) and by (Zheng et al., 2016).…”

Section: Background and Methodologymentioning

confidence: 99%

“…Continuum equivalent theories date back to Barenblatt's dual‐porosity concept (Barenblatt et al., 1960), in which the porous matrix blocks and the fractures are envisioned as two separate continua in terms of flow, but linked through the fluid exchange between the matrix blocks and secondary fractures. In the context of poroelasticity, this is the so‐called dual‐porosity poroelasticity (DPP) paradigm (Bai et al., 1993; Elsworth & Bai, 1992; Wilson & Aifantis, 1982), thoroughly analyzed by (Berryman & Wang, 1995), (Berryman & Pride, 2002), and (Bai, 1999), and recently revisited by (Mehrabian & Abousleiman, 2014), (Zheng et al., 2016), and (Presho et al., 2011). Analogous to the double‐porosity concept for solute and heat transfer, DPP recognizes nonequilibrium in deforming fractured media: the possibility that, over short timescales, pressures may be different in the rock matrix and fracture system.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Multirate Mass Transfer Approach for Double‐Porosity Poroelasticity in Fractured Media

Andrés

Dentz

Cueto‐Felgueroso

2021

Water Resources Research

View full text Add to dashboard Cite

Natural and anthropogenic fractured aquifers and reservoirs are dual porosity matrix‐fracture systems, where the fracture network provides highly–conductive flow pathways and the low–permeability matrix stores most of the fluid. The coupling between flow and mechanical deformation in fractured media is often modeled using the classical theory of dual‐porosity poroelasticity (DPP), based on Barenblatt's hypothesis of pressure equilibrium inside the rock matrix blocks. Equilibrium can be expected if the matrix blocks are small and the matrix diffusion time is comparable to the flow time scales along the fractures. In practice, matrix blocks may be large enough so that diffusion time scales are long, and the equilibrium hypothesis breaks down. Here, we study nonequilibrium effects in coupled flow and deformation in fractured media. We compare analytical predictions and modeling results of coupled flow and deformation in heterogeneous fractured porous media. The theoretical analysis is a nonequilibrium, dual‐porosity model. We use this theory to (a) Reveal the limitations of classical DPP formulations. (b) Obtain the scalings for drainage and displacement to be expected for coupled flow and deformation in highly heterogeneous, fractured media. (c) Identify what behavior to expect in fractured aquifers and reservoirs regarding flow and deformation. We observe strong tailing in fluid fluxes and land subsidence that cannot be captured by the classical DPP approach or a single porosity effective medium approach. We show that theoretical predictions from the multirate DPP model and high‐fidelity models agree, even for highly heterogeneous matrix‐fracture systems, and reproduce the observed nonequilibrium effects.

show abstract

“…(Wilson & Aifantis, 1982) proposed effective parameters based on the Skempton coefficient:

b_{m} = \frac{K^{*}}{K} ((), 1 - \frac{K}{K_{s}}), b_{f} = 1 - \frac{K^{*}}{K},

where

K^{*}

K

, and

K_{s}

Section: Background and Methodologymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multirate Mass Transfer Approach for Double‐Porosity Poroelasticity in Fractured Media

Andrés

Dentz

Cueto‐Felgueroso

2021

Water Resources Research

View full text Add to dashboard Cite

show abstract

“…The linear constitutive relations among stress, strain, fluid content, and pore pressure for isotropic materials with double‐porosity can be written in the form

σ_{ij} = ([],, ((),, b_{11} - 2 true/ 3 μ) e - b_{12} p^{1} - b_{13} p^{2}) δ_{ij} + 2 {με}_{ij},

ζ^{1} = b_{12} e + b_{22} p^{1} - b_{23} p^{2},

ζ^{2} = b_{13} e - b_{23} p^{1} + b_{33} p^{2},

where σ ij is the stress tensor; p 1 and p 2 are the pore pressures in the matrix and fracture; ζ 1 and ζ 2 are the increment of fluid content in the matrix and fracture; e ≡ ∂ V / V is the volume strain;

ε_{ij} \equiv \frac{1}{2} ((),, u_{i, j} + u_{j, i})

, with u i being solid displacement, is the stain tensor; μ is the shear modulus; b 11 , b 12 , b 13 , b 22 , b 23 , and b 33 are six independent coefficients, whose dependence on the material constants, such as the drained bulk modulus K and the pore fluid bulk modulus K f , are summarized in Appendix A.…”

Section: Governing Equationsmentioning

confidence: 99%

One-dimensional analytical solution for mesoscopic flow induced damping in a double-porosity dual-permeability material

Zheng

Cheng

2017

Int. J. Numer. Anal. Meth. Geomech.

View full text Add to dashboard Cite

Heterogeneities, such as fractures and cracks, are ubiquitous in porous rocks. Mesoscopic heterogeneities, that is, heterogeneities on length scales much larger than typical pore size but much smaller than the wavelength, are increasingly believed to be responsible for significant wave energy loss in the seismic frequency band. When a compressional wave stresses a material containing mesoscopic heterogeneities, the more compliant parts of the material (e.g., fractures and cracks) respond with a greater fluid pressure than the stiffer portions (e.g., matrix pores). The induced fluid flow, resulting from the pressure gradients developed on such scale, is called mesoscopic flow. In the present study, the double-porosity dual-permeability model is adopted to incorporate mesoscopic heterogeneities into rock models to account for the attenuation of wave energy. Based on the model, the damping effect due to mesoscopic flow in a one-dimensional porous structure is investigated. Analytical solutions for several boundary-value problems are obtained in the frequency domain. The dynamic responses of infinite and finite porous layer are examined. Numerical calculations show that the damping effect of mesoscopic flow is significant on the pore pressure response and the resulting effective stress. For the displacement, the effect is seen only at the very low frequency range or near the resonance frequencies.

show abstract

“…Poromechanic theories provide new ways to study porous materials whose mechanical behavior is influenced by the pore fluid (Coussy 2004). In fact, poromechanic methods have been successfully used to study most aspects of mechanical behavior and durability of CBPMs, e.g., multi-scale mechanical properties (Ulm et al 2004), drying shrinkages (Rougelot et al 2009), alkaline silica reactions (Multon and Sellier 2016), freezing-thawing swellings (Sun and Scherer 2010;Zeng 2011;Zeng et al 2011Zeng et al , 2014bZeng et al , 2014cZeng et al , 2016Wang et al 2014) and multiphase transport in other porous media (Boxberg et al 2015;Zheng et al 2016). Furthermore, poromechanic framework is robust to combine physical and/or chemical mechanisms, by which a porous material shows different properties (Coussy 2004).…”

Section: Introductionmentioning

confidence: 99%

Poroelastic Insights into Stress Dependence of Chloride Penetration into Saturated Cement-Based Porous Materials

Zeng

Wang

2019

ACT

View full text Add to dashboard Cite

Most concrete structures service under external loads and the studies of the external-loading effects on chloride diffusivity in these porous media remain insufficient. This paper reports a relationship between porosity variation and external load inspired by poroelastic theory. This porosity-load relationship, together with an empirical equation for chloride diffusivity versus porosity, provides an explicit diffusivity-load model for saturated porous media. Without the specific assumptions of geometries of the pores and the matrix phases, the present model shows flexible expressions. Comprehensive analyses are performed to demonstrate the effects of external load and initial porosity on the porosity variation, chloride diffusion coefficient, penetration depth and durable time of specific cement-based samples. Two models reported in the literature are employed for the purpose of comparison. Overall, initial porosity is a primarily dominative factor affecting the chloride diffusivity, penetration profile and durability of cement-based porous materials. Within the elastic regime, external loads only influence the outcomes in limited degrees.

show abstract

The Elastic Coefficients of Double-Porosity Materials: A Revisit

Cited by 10 publications

References 23 publications

Multirate Mass Transfer Approach for Double‐Porosity Poroelasticity in Fractured Media

Multirate Mass Transfer Approach for Double‐Porosity Poroelasticity in Fractured Media

One-dimensional analytical solution for mesoscopic flow induced damping in a double-porosity dual-permeability material

Poroelastic Insights into Stress Dependence of Chloride Penetration into Saturated Cement-Based Porous Materials

Contact Info

Product

Resources

About