Fractured porous media or double porosity media are common in nature. At the same time, accurate modeling remains a significant challenge due to bi-modal pore size distribution, anisotropy, multi-field coupling, and various flow patterns. This study aims to formulate a comprehensive coupled continuum framework that could adequately consider these critical characteristics. In our framework, fluid flow in the micro-fracture network is modeled with the generalized Darcy's law, in which the equivalent fracture permeability is upscaled from the detailed geological characterizations. The liquid in the much less permeable matrix follows a low-velocity non-Darcy flow characterized by threshold values and non-linearity. The fluid mass transfer is assumed to be a function of the shape factor, pressure difference, and (variable) interface permeability. The solid deformation relies on a thermodynamically consistent effective stress derived from the energy balance equation, and it is modeled following anisotropic poroelastic theory. The discussion revolves around generic double porosity media. Model applications reveal the capability of our framework to capture the crucial roles of coupling, poroelastic coefficients, anisotropy, and ultra-low matrix permeability in dictating the pressure and displacement fields.
A method is presented for the evaluation of the permeability-porosity relationship in a low-permeability porous material using the results of a single transient test. This method accounts for both elastic and non-elastic deformations of the sample during the test and is applied to a hardened class G oil well cement paste. An initial hydrostatic undrained loading is applied to the sample. The generated excess pore pressure is then released at one end of the sample while monitoring the pore pressure at the other end and the radial strain in the middle of the sample during the dissipation of the …
The permeability of a pore structure is typically described by stochastic representations of its geometrical attributes. Database-driven numerical solvers for large model domains can only accurately predict large-scale flow behaviour when they incorporate upscaled descriptions of that structure. The upscaling is particularly challenging for rocks with multimodal porosity structures such as carbonates, where several different types of structures are interacting. It is the connectivity both within and between these different structures that controls the porosity-permeability relationship at the …
Effects of heterogeneity of mineral distribution and reaction rate on the rock dissolution process are investigated using a pore-scale reactive transport model based on the lattice Boltzmann method. Coupled fluid flow, species transport, chemical reaction and solid structure alternation due to dissolution are simulated. Effects of mineral distributions and chemical heterogeneity on the dissolution behaviors and evolutions of hydrologic properties are studied under different reactive transport conditions. Simulation results show that the coupling between advection, diffusion and reaction as wel…
Porosity and permeability alteration due to the thermo-poro-elastic stress field disturbance from the cold fluid injection is a deciding factor for longer, economic and safer heat extraction from an enhanced geothermal system (EGS). In the Soultz-sous-Forêts geothermal system, faulted zones are the main flow paths and the resulting porosity-permeability development over time due to stress reorientation is more sensitive in comparison with the regions without faulted zones. Available operational and field data are combined through a validated numerical simulation model to examine the mechanical…
Modeling fluid flow in dual-porosity media with bi-modal pore size distributions has practical applications to understanding transport in multi-scale systems such as natural soils. Dual-porosity media are typically formed of two domains: (1) structure and (2) texture. The former mainly incorporates macropores, while the latter contains micropores. Although there exist models based on the series-parallel tubes approach, here we apply concepts from critical path analysis, a theoretical technique from statistical physics, to estimate water relative permeability (krw) in dual-porosity media. For t…
We present a microstructural model of permeability in fractured solids, where the fractures are described in terms of recursive families of parallel, equidistant cohesive faults. Faults originate upon the attainment of a tensile or shear resistance in the undamaged material. Secondary faults may form in a hierarchical orga- nization, creating a complex network of connected fractures that modify the permeability of the solid. The undamaged solid may possess initial porosity and permeability. The particular geometry of the superposed micro-faults lends itself to an explicit analytical quantifica…
A multiporosity extension of classical double and triple porosity fractured rock flow models for slightly compressible fluids is presented. The multiporosity model is an adaptation of the multirate solute transport model of Haggerty and Gorelick (1995) to viscous flow in fractured rock reservoirs. It is a generalization of both pseudo-steady-state and transient interporosity flow double porosity models. The model includes a fracture continuum and an overlapping distribution of multiple rock matrix continua, whose fracture-matrix exchange coefficients are specified through a discrete probabilit…
Predicting the permeability of porous media in saturated and partially saturated conditions is of crucial importance in many geo-engineering areas, from water resources to vadose zone hydrology or contaminant transport predictions. Many models have been proposed in the literature to estimate the permeability from properties of the porous media such as porosity, grain size or pore size. In this study, we develop a model of the permeability for porous media saturated by one or two fluid phases with all physically-based parameters using a fractal upscaling technique. The model is related to micro…
This paper discusses a continuum approach to track the evolution of permeability in granular rocks by accounting for the combined effect of porosity changes, grain breakage and cement bond damage. To account for such a broad range of microscopic processes under general loading paths, the Breakage Mechanics theory is used and the computed mechanical response is linked with the Kozeny equation, i.e. a permeability model able to evaluate the reduction of the hydraulic conductivity resulting from the simultaneous loss of porosity and growth of surface area. In particular, the evolution of the inte…
In this paper we present a constitutive model to describe unsaturated flow that considers the hysteresis phenomena. This constitutive model provides simple mathematical expressions for both saturation and hydraulic conductivity curves, and a relationship between permeability and porosity. The model is based on the assumption that the porous media can be represented by a bundle of capillary tubes with throats or "ink-bottles" and a fractal pore size distribution. Under these hypotheses, hysteretic curves are obtained for saturation and relative hydraulic conductivity in terms of pressure head. …
A reactive fluid dissolving the surrounding rock matrix can trigger an instability in the dissolution front, leading to spontaneous formation of pronounced channels or wormholes. Theoretical investigations of this instability have typically focused on a steadily propagating dissolution front that separates regions of high and low porosity. In this paper we show that this is not the only possible dissolutional instability in porous rocks; there is another instability that operates instantaneously on any initial porosity field, including an entirely uniform one. The relative importance of the tw…
Accurate estimation of single-phase permeability (k) has broad application in numerous areas, particularly modeling flow and transport in porous materials. Various techniques have been proposed in the literature to estimate k from other medium's properties, such as porosity, grain and/or pore size distribution, and pore connectivity. Among them critical path analysis (CPA) from statistical physics, first developed to model fluid flow in media with broad conductance distributions, has been successfully applied to heterogeneous soils and rocks. However, its application to uniform sphere and/or g…
We use helium released during mechanical deformation of shales as a signal to explore the effects of deformation and failure on material transport properties. A dynamic dual-permeability model with evolving pore and fracture networks is used to simulate gases released from shale during deformation and failure. Changes in material properties required to reproduce experimentally observed gas signals are explored. We model two different experiments of $^4$He flow rate measured from shale undergoing mechanical deformation, a core parallel to bedding and a core perpendicular to bedding. We find tha…
The current conceptual model of mineral dissolution in porous media is comprised of three dissolution patterns (wormhole, compact, and uniform) - or regimes - that develop depending on the relative dominance of flow, diffusion, and reaction rate. Here, we examine the evolution of pore structure during acid injection using numerical simulations on two porous media structures of increasing complexity. We examine the boundaries between regimes and characterise the existence of a fourth regime called channeling, where already existing fast flow pathways are preferentially widened by dissolution. C…
Gas slippage occurs when the mean free path of the gas molecules is in the order of the characteristic pore size of a porous medium. This phenomenon leads to the Klinkenberg's effect where the measured permeability of a gas (apparent permeability) is higher than that of the liquid (intrinsic permeability). A generalized lattice Boltzmann model is proposed for flow through porous media that includes Klinkenberg's effect, which is based on the model of Guo et al. (Z.L. Guo et al., Phys.Rev.E 65, 046308 (2002)). The second-order Beskok and Karniadakis-Civan's correlation (A. Beskok and G. Karniad…
Neural Networks for Predicting Permeability Tensors of 2D Porous Media: Comparison of Convolution- and Transformer-based Architectures
PoreLab, The Njord Centre, Department of Physics, University of Oslo（PoreLab、Njord中心、物理系、奥斯陆大学）；PoreLab, Department of Physics, Norwegian University of Science and Technology（PoreLab、物理系、挪威科学技术大学）；The Njord Centre, Department of Physics, University of Oslo（Njord中心、物理系、奥斯陆大学）
Shale gas recovery has seen a major boom in recent years due to the increasing global energy demands; but the extraction technologies are very expensive. It is therefore important to develop realistic transport modelling and simulation methods, for porous rocks and porous media, that can compliment the field work. Here, a new nonlinear transport model for single phase gas flow in tight porous media is derived, incorporating many important physical processes that occur in such porous systems: continuous flow, transition flow, slip flow, Knudsen diffusion, adsorption and desorption in to and out…
We investigate the possibility to extract information contained in seismic waveforms propagating in fluid-filled porous media by developing and using a full waveform inversion procedure valid for layered structures. To reach this objective, we first solve the forward problem by implementing the Biot theory in a reflectivity-type simulation program. We then study the sensitivity of the seismic response of stratified media to the poroelastic parameters. Our numerical tests indicate that the porosity and consolidation parameter are the most sensitive parameters in forward and inverse modeling, wh…
Investigating frictional instability due to pressurization in granular media: insights from coupled computational fluid dynamics discrete element method
