Cascade Continuum Micromechanics model for the effective permeability of solids with distributed microcracks: Comparison with numerical homogenization

Leonhart, Dirk; Timothy, Jithender J.; Meschke, Günther

doi:10.1016/j.mechmat.2017.09.001

Cited by 5 publications

(5 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Third, the permeability was calculated by conducting a single-phase flow simulation in two perpendicular directions, using a computational homogenization (Leonhart et al, 2017) for an unperturbed and a perturbed fracture state. The permeability tensors of the deformed carbonates were obtained.…”

Section: Stress and Permeability Modellingmentioning

confidence: 99%

Impact of stress regime change on the permeability of a naturally fractured carbonate buildup (Latemar, The Dolomites, Northern Italy)

Igbokwe¹,

Timothy²,

Kumar³

et al. 2023

Preprint

View full text Add to dashboard Cite

Changing stress regimes control fracture network geometry and influence porosity and permeability in carbonate reservoirs. We investigate the impact of stress-regime change on fracture network permeability utilizing outcrop data analysis and a displacement-based linear elastic finite element method. The model is based on fracture networks, specifically, fracture sub-structures. The Latemar, predominantly affected by subsidence deformation and Alpine compression, is taken as an outcrop analogue for isolated (Mesozoic) carbonate buildups with fracture-dominated permeability. We apply a novel strategy involving two compressive boundary loading conditions, constrained by the NW-SE and N-S stress directions in the study area. Stress-dependent heterogeneous apertures and effective permeability were computed by: (i) using the local stress state within the fracture sub-structure and (ii) running a single-phase flow analysis considering the fracture apertures in each fracture sub-structure. Our results show that the impact of the modelled far-field stresses at: (i) subsidence deformation from the NW-SE, and (ii) Alpine deformation from N-S, increased the overall fracture aperture and permeability. In each case, increasing permeability is associated with open fractures parallel to the orientation of the loading stages and with fracture densities. The anisotropy of permeability is increased by the density and connectedness of the fracture network and affected by of shear dilation. The two far-field stresses simultaneously acting within the selected fracture sub-structure at a different magnitude and orientation do not necessarily cancel out each other in the mechanical deformation modelling. These stresses effect the overall aperture and permeability distributions. These effects, which may be ignored in simpler stress-dependent permeability, can result in significant inaccuracies in permeability estimation.

show abstract

Section: Stress and Permeability Modellingmentioning

confidence: 99%

Impact of stress regime change on the permeability of a naturally fractured carbonate buildup (Latemar, The Dolomites, Northern Italy)

Igbokwe¹,

Timothy²,

Kumar³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…The CCM model can predict the effect of the crack opening aspect ratio on the features of the conversion from a nonconnected solid to a completely connected solid, i.e., the percolation threshold depends on the crack opening aspect ratio (Leonhart et al 2015(Leonhart et al , 2017. The percolation scaling law deals with the crack clustering effect and takes the cracks no longer as homogeneous inclusions but as networks, i.e., the percolation threshold relies on the local crack clustering effect and the connectivity factor.…”

Section: Percolation Model For High Crack Clusteringmentioning

confidence: 99%

“…When cracks intersect to form a percolated path across the boundaries of the domain, the effective permeability will be significantly altered (Leonhart et al 2017;Renshaw et al 2020;Benkemoun et al 2018). After onset of percolation, the effective permeability is generally stable [Fig.…”

Section: Further Analysismentioning

confidence: 99%

Permeability of Microcracked Porous Solids: Modeling from Homogenization to Percolation

2022

J. Eng. Mech.

View full text Add to dashboard Cite

This paper establishes a comprehensive modeling for permeability of porous solids incorporating cracks with clustering extent ranging from nonoverlapping to percolation. The geometry of cracks is characterized through the crack density, orientation, connectivity, and fractal dimension of crack networks. The interaction direct derivative (IDD) model from effective medium theory is developed to predict the permeability of solids with nonoverlapping cracks and further extended by a two-step scheme to account for cracks with local clustering. The continuum percolation theory is adopted to build the permeability scaling law for crack networks approaching percolation. The comprehensive model thus established was validated against numerical simulations for crack networks with different geometry characteristics. The obtained results show that (1) the classical IDD model can predict satisfactorily the permeability for nonoverlapping cracks and the crack opening has nearly no impact on overall permeability, (2) the extended IDD model considers successfully the local clustering of cracks, the prediction range is greatly enhanced for overall permeability, and the impact of crack opening is still limited, and (3) as crack networks approachi percolation, the overall permeability observes a scaling law highlighting the importance of crack connectivity, and the impact of crack opening assumes a power law with the exponent related to the fractal dimension of crack networks.

show abstract

“…In the first localization level that refers to meso-to-micro localization, the strain at the microscale in both the rock matrix ( μ m ) and microcracks ( μ i (i = 1 ∶ )) is obtained via Equation (9). The total stress in the rock matrix ( μ m ) can then be calculated using Equation (22), from which the effective stress acting on each microcrack is obtained as:…”

Section: Algorithm Of Microstructure Updatementioning

confidence: 99%

“…In the second localization level that refers to micro-to-nano localization for the rock matrix, the strain at the nanolevel in both the rock mineral ( n s ) and nanopore space ( n f ) is calculated using Equation (9). Here, we neglect the shape change (change in aspect ratio) of nanopores and only calculate the change in their volume fraction (nanoporosity).…”

Section: Algorithm Of Microstructure Updatementioning

confidence: 99%

A three‐dimensional multiscale damage‐poroelasticity model for fractured porous media

Eghbalian

Pouragha

Wan

2020

Num Anal Meth Geomechanics

View full text Add to dashboard Cite

The paper investigates the failure of brittle rocks within a multiscale/multiphysics computational modeling framework so as to explicitly incorporate both microstructural and hydromechanical aspects in their overall (nonlinear) fracture behavior. Herein, the rock is idealized as a microfissured porous medium via a representative elementary volume (REV) containing distributed oblate spheroidal open microcracks and spheroidal nanopores at the lower scales. A two-scale analytical homogenization procedure is then performed on the REV, assuming a saturated pore space across the scales. The end result is a microstructurally enriched continuum damage-poroelasticity constitutive model within the generalized Biot's framework that inherits the underlying small-scale characteristics. A set of damage tensors is derived based on the directional density distribution of microcracks that operate on both the poromechanical and hydraulic properties. Microstructural evolution is modeled following changes in microcrack length, aperture, and number density, including nanoporosity. To this end, a robust localization procedure is used that accurately captures the macroscopic softening due to microcracking events, leading to a nonlinear (but path-independent) model. To investigate the baseline features of the model, including the salient effects of microcracking on induced anisotropy and deterioration of poroelastic properties, numerical results of material point-based computations are discussed in detail. Finally, predictions of the current model are validated against experiments on Fontainebleau sandstone.

show abstract

Cascade Continuum Micromechanics model for the effective permeability of solids with distributed microcracks: Comparison with numerical homogenization

Cited by 5 publications

References 18 publications

Impact of stress regime change on the permeability of a naturally fractured carbonate buildup (Latemar, The Dolomites, Northern Italy)

Impact of stress regime change on the permeability of a naturally fractured carbonate buildup (Latemar, The Dolomites, Northern Italy)

Permeability of Microcracked Porous Solids: Modeling from Homogenization to Percolation

A three‐dimensional multiscale damage‐poroelasticity model for fractured porous media

Contact Info

Product

Resources

About