Accurate modeling of gas relative permeability has practical applications in oil and gas exploration, production and recovery of unconventional reservoirs. In this study, we apply concepts from the effective-medium approximation (EMA) and universal power-law scaling from percolation theory. Although the EMA has been successfully used to estimate relative permeability in conventional porous media, to the best of our knowledge, its applications to unconventional reservoir rocks have not been addressed yet. The main objective of this study, therefore, is to evaluate the efficiency of EMA, in combination with universal power-law scaling from percolation theory, in estimating gas relative permeability from pore size distribution and pore connectivity. We presume that gas flow is mainly controlled by two main mechanisms contributing in parallel (1) hydraulic flow and (2) molecular flow. We then apply the EMA to determine effective conductances and, consequently, gas relative permeability at higher gas saturations, and the universal scaling from percolation theory at lower gas saturation values. Comparisons with two pore-network simulations and six experimental measurements from the literature show that, in the absence of microfractures, the proposed model estimates gas relative permeability reasonably well in shales and tight porous rocks. More specifically, we found that the crossover point, gas saturation at which transport crosses from percolation theory to the EMA, is non-universal. The value of crossover gas saturation is a function of pore space characteristics such as pore size distribution broadness and critical gas saturation. This means that one should expect the crossover gas saturation to vary from one rock sample to another.
A multi-step steady-state (MSSS) method is proposed here for the measurement of low permeability. This new method can accurately and easily measure very low permeabilities of rock samples using a new setup, where the targeted rock sample and ordinary apparatus components are connected with a reference rock sample to form a series circuit. Any conventional rock sample with high permeability could be used as a reference rock sample such that the traditional steady-state measurement is feasible to accurately determine its permeability as a reference value in the MSSS method. The challenging measu…
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…
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…
Skolkovo Institute of Science and Technology（斯科尔科沃科学技术学院）
We present a research study aimed at testing of applicability of machine learning techniques for prediction of permeability of digitized rock samples. We prepare a training set containing 3D images of sandstone samples imaged with X-ray microtomography and corresponding permeability values simulated with Pore Network approach. We also use Minkowski functionals and Deep Learning-based descriptors of 3D images and 2D slices as input features for predictive model training and prediction. We compare predictive power of various feature sets and methods. The later include Gradient Boosting and vario…
Permeability is the key parameter for quantifying fluid flow in porous rocks. Knowledge of the spatial distribution of the connected pore space allows, in principle, to predict the permeability of a rock sample. However, limitations in feature resolution and approximations at microscopic scales have so far precluded systematic upscaling of permeability predictions. Here, we report fluid flow simulations in capillary network representations designed to overcome such limitations. Performed with an unprecedented level of accuracy in geometric approximation at microscale, the pore scale flow simul…
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…
Permeability has a dominant influence on the flow properties of a natural fluid. Lattice Boltzmann simulator determines permeability from the nano and micropore network. The simulator holds millions of flow dynamics calculations with its accumulated errors and high consumption of computing power. To efficiently and consistently predict permeability, we propose a morphology decoder, a parallel and serial flow reconstruction of machine learning segmented heterogeneous Cretaceous texture from 3D micro computerized tomography and nuclear magnetic resonance images. For 3D vision, we introduce contr…
An extension of a previously developed rock physics model is made that quantifies the relationship between the ductile fraction of a brittle/ductile binary mixture and the isotropic seismic reflection response. By making a weak scattering (Born) approximation and plane wave (eikonal) approximation, with a subsequent ordering according to the angle of incidence, singular value decomposition analysis are done to understand the stack weightings, number of stacks, and the type of stacks that will optimally estimate the two fundamental rock physics parameters. Through this angle ordering, it is fou…
A new and fast Matlab algorithm for predicting absolute permeability is presented. The developed tool relies on measuring the connectivity of pores in a given three-dimensional (3D) micro-CT rock image. An index of pore connectivity is introduced. After a calibration step, the developed index is used to estimate permeability in a variety of rocks with challenging pore structures (e.g. complex carbonate formations). The developed algorithm was tested on sandstone and carbonate rock samples. It offers large computational and memory savings when compared with algorithms based on the Lattice Boltz…
Shear deformation of partially molten rock in laboratory experiments causes the emergence of melt-enriched sheets (bands in cross-section) that are aligned at about 15-20 degrees to the shear plane. Deformation and deviatoric stress also cause the coherent alignment of pores at the grain scale. This leads to a melt-preferred orientation that may, in turn, give rise to an anisotropic permeability. Here we develop a simple, general model of anisotropic permeability in partially molten rocks. We use linearised analysis and nonlinear numerical solutions to investigate its behaviour under simple-sh…
We present a new type of transducer capable of measuring local pore fluid pressure in jacketed rock samples under elevated confining pressure conditions. The transducers are passive (strain-gauge based), of small size (7 mm in diameter at the contact with the rock and around 10 mm in length), and have minimal dead volume (a few mm$^3$). The transducers measure the differential pressure between the confining fluid and the internal pore pressure. The design is easily adaptable to tune the sensitivity and working pressure range up to several hundred megapascals. An array of four such transducers …
Stony Brook University（石溪大学）；Halicioglu Data Science Institute, University of California, San Diego（加州大学圣地亚哥分校哈利西奥格鲁数据科学研究所）；Columbia University（哥伦比亚大学）
We present a SE(3)-equivariant graph neural network (GNN) approach that directly predicting the formation factor and effective permeability from micro-CT images. FFT solvers are established to compute both the formation factor and effective permeability, while the topology and geometry of the pore space are represented by a persistence-based Morse graph. Together, they constitute the database for training, validating, and testing the neural networks. While the graph and Euclidean convolutional approaches both employ neural networks to generate low-dimensional latent space to represent the feat…
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 presence of mesoscopic heterogeneities in fluid-saturated porous rocks can produce measurable seismoelectric signals due to wave-induced fluid flow between regions of differing compressibility. The dependence of these signals on the petrophysical and structural characteristics of the probed rock mass remains largely unexplored. In this work, we derive an analytical solution to describe the seismoelectric response of a rock sample, containing a horizontal layer at its center, that is subjected to an oscillatory compressibility test. We then adapt this general solution to compute the seismoe…
Apparent liquid permeability (ALP) in ultra-confined permeable media is primarily governed by the pore confinement and fluid-rock interactions. A new ALP model is required to predict the interactive effect of the above two on the flow in mixed-wet, heterogeneous nanoporous media. This study derives an ALP model and integrates the compiled results from molecular dynamics (MD) simulations, scanning electron microscopy, atomic force microscopy, and mercury injection capillary pressure. The ALP model assumes viscous forces, capillary forces, and liquid slippage in tortuous, rough pore throats. Pre…
The effective stress law for the permeability of a limestone is studied experimentally by performing constant head permeability tests in a triaxial cell with different conditions of confining pressure and pore pressure. Test results have shown that a pore pressure increase and a confining pressure decrease both result in an increase of the permeability, and that the effect of the pore pressure change on the variation of the permeability is more important than the effect of a change of the confining pressure. A power law is proposed for the variation of the permeability with the effective stres…
The interconnectivity of the porous space is an important characteristic in the study of porous media and their transport properties. Hence we propose a way to quantify it and relate it with the intrinsic permeability of rocks. We propose a measure of connectivity based on geometric and topological information of pore-throat network, which are models built from microtomographic images, and we obtain an analytical method to compute that property. The method is expanded to handle rocks that present a higher degree of heterogenity in the porous space, which characterization requires images from d…
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…
The Geothermal Battery Energy Storage concept has been proposed to provide large-scale heat storage when solar radiance is available, to be later recovered for economic benefit. The concept uses solar radiance to heat water on the surface which is then injected into a suitable subsurface formation. This hot water elevates the ambient formation temperature creating a high-temperature geothermal reservoir acceptable for geothermal electricity generation or direct heat applications. The process uses produced/injected, connate formation water and thus neither freshwater nor surface storage or disp…
A pore-scale numerical model for reactive transport processes based on the Lattice Boltzmann method is used to study the dissolution-induced changes in hydrologic properties of a fractured medium and a porous medium. The solid phase of both media consists of two minerals, and a structure reconstruction method called quartet structure generation set is employed to generate the distributions of both minerals. Emphasis is put on the effects of undissolved minerals on the changes of permeability and porosity under different Peclet and Damkohler numbers. The simulation results show porous layers fo…
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…
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…
A discretely fractured reservoir has the capability to support and sustain long term geothermal energy extraction operations. The process of injecting cold water to extract hot water from a fracture reservoir results in thermal and poroelastic stresses in the rock matrix. Therefore, these thermo-hydro-mechanical (THM) mechanisms govern the efficiency of an enhanced geothermal system (EGS) operation. However, THM mechanisms are governed by various rock and fluid parameters as well as on the initial and boundary conditions of the model set-up. In this paper, we have identified and analyzed 22 su…
Hydraulic stimulation of geothermal reservoirs in low-permeability basement and crystalline igneous rock can enhance permeability by reactivation and shear dilation of existing fractures. The process is characterized by interaction between fluid flow, deformation, and the fractured structure of the formation. The flow is highly affected by the fracture network, which in turn is deformed because of hydromechanical stress changes caused by the fluid injection. This process-structure interaction is decisive for the outcome of hydraulic stimulation, and, in analysis of governing mechanisms, physic…
Depleted oil fields in the Gulf of Suez (Egypt) can serve as geothermal reservoirs for power generation using a CO2-Plume Geothermal (CPG) system, while geologically sequestering CO2. This entails the injection of a substantial amount of CO2 into the highly permeable brine-saturated Nubian Sandstone. Numerical models of two-phase flow processes are indispensable for predicting the CO2-plume migration at a representative geological scale. Such models require reliable constitutive relationships, including relative permeability and capillary pressure curves. In this study, quasi-static pore-netwo…
