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 pore pressure. These measurements are back analysed to evaluate the permeability and its evolution with porosity change. The effect of creep of the sample during the test on the measured pore pressure and volume change is taken into account in the analysis. This approach permits to calibrate a power law permeability-porosity relationship for the tested hardened cement paste. The porosity sensitivity exponent of the power-law is evaluated equal to 11 and is shown to be mostly independent of the stress level and of the creep strains.
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 …
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…
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…
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…
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…
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…
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…
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. …
When a mass of saturated clay is heated, as in the case of host soils surrounding nuclear waste disposals at great depth, the thermal expansion of the constituents generates excess pore pressures. The mass of clay is submitted to gradients of pore pressure and temperature, to hydraulic and thermal flows, and to changes in its mechanical properties. In this work, some of these aspects were experimentally studied in the case of Boom clay, so as to help predicting the response of the soil, in relation with investigations made in the Belgian underground laboratory at Mol. Results of slow heating t…
Understanding gas transport in porous media and its mechanism has broad applications in various research areas, such as carbon sequestration in deep saline aquifers and gas explorations in reservoir rocks. Gas transport is mainly controlled by pore space geometrical and morphological characteristics. In this study, we apply a physically-based model developed using concepts from percolation theory (PT) and the effective-medium approximation (EMA) to better understand diffusion and permeability of gas in packings of angular and rounded sand grains as well as glass beads. Two average sizes of gra…
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…
Upscaling Klinkenberg-corrected gas permeability, k, in unconventional tight sandstones has numerous practical applications, particularly in gas exploration and production. In this study, we adapt the effective-medium approximation (EMA) model of Doyen - proposed first to estimate bulk electrical conductivity, σ_b, and permeability in sandstones from rock images - to scale up σ_b and k in tight-gas sandstones from pore to core. For this purpose, we calculate two characteristic pore sizes: an effective hydraulic and an effective electrical pore size from pore-throat size distributions - determi…
Investigating frictional instability due to pressurization in granular media: insights from coupled computational fluid dynamics discrete element method
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）
