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Journal articles on the topic 'Transport in fractured porous media'

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Author: Grafiati

Published: 25 May 2024

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1

XU, PENG, HAICHENG LIU, AGUS PULUNG SASMITO, SHUXIA QIU, and CUIHONG LI. "EFFECTIVE PERMEABILITY OF FRACTURED POROUS MEDIA WITH FRACTAL DUAL-POROSITY MODEL." Fractals 25, no. 04 (July 25, 2017): 1740014. http://dx.doi.org/10.1142/s0218348x1740014x.

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As natural fractures show statistically fractal scaling laws, fractal geometry has been proposed and applied to model the fracture geometry and to study the hydraulic properties of fractured porous media. In this paper, a fractal dual-porosity model is developed to study the single-phase fluid flow through fractured porous media. An analytical expression for effective permeability of fractured porous media is derived, which depends on the fractal dimension and fracture aperture. The effect of fractal dimensions for fracture aperture distribution and tortuosity, the ratio of minimum to maximum fracture apertures and fracture fraction on the effective permeability have been discussed. In addition, a power law relationship between the effective permeability and fracture fraction is proposed to predict the equivalent hydraulic properties of fractured porous media. Compared with empirical formulas for effective permeability, the present fractal dual-porosity model can capture the statistical characteristics of fractures and shed light on the transport mechanism of fractured porous media.

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2

Fumagalli, Alessio, and Eirik Keilegavlen. "Dual Virtual Element Methods for Discrete Fracture Matrix models." Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles 74 (2019): 41. http://dx.doi.org/10.2516/ogst/2019008.

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The accurate description of fluid flow and transport in fractured porous media is of paramount importance to capture the macroscopic behavior of an oil reservoir, a geothermal system, or a CO2 sequestration site, to name few applications. The construction of accurate simulation models for flow in fractures is challenging due to the high ratio between a fracture’s length and width. In this paper, we present a mixed-dimensional Darcy problem which can represent the pressure and Darcy velocity in all the dimensions, i.e. in the rock matrix, in the fractures, and in their intersections. Moreover, we present a mixed-dimensional transport problem which, given the Darcy velocity, describes advection of a passive scalar into the fractured porous media. The approach can handle both conducting and blocking fractures. Our computational grids are created by coarsening of simplex tessellations that conform to the fracture’s surfaces. A suitable choice of the discrete approximation of the previous model, by virtual finite element and finite volume methods, allows us to simulate complex problems with a good balance of accuracy and computational cost. We illustrate the performance of our method by comparing to benchmark studies for two-dimensional fractured porous media, as well as a complex three-dimensional fracture geometry.

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3

XU, PENG, CUIHONG LI, SHUXIA QIU, and AGUS PULUNG SASMITO. "A FRACTAL NETWORK MODEL FOR FRACTURED POROUS MEDIA." Fractals 24, no. 02 (June 2016): 1650018. http://dx.doi.org/10.1142/s0218348x16500183.

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The transport properties and mechanisms of fractured porous media are very important for oil and gas reservoir engineering, hydraulics, environmental science, chemical engineering, etc. In this paper, a fractal dual-porosity model is developed to estimate the equivalent hydraulic properties of fractured porous media, where a fractal tree-like network model is used to characterize the fracture system according to its fractal scaling laws and topological structures. The analytical expressions for the effective permeability of fracture system and fractured porous media, tortuosity, fracture density and fraction are derived. The proposed fractal model has been validated by comparisons with available experimental data and numerical simulation. It has been shown that fractal dimensions for fracture length and aperture have significant effect on the equivalent hydraulic properties of fractured porous media. The effective permeability of fracture system can be increased with the increase of fractal dimensions for fracture length and aperture, while it can be remarkably lowered by introducing tortuosity at large branching angle. Also, a scaling law between the fracture density and fractal dimension for fracture length has been found, where the scaling exponent depends on the fracture number. The present fractal dual-porosity model may shed light on the transport physics of fractured porous media and provide theoretical basis for oil and gas exploitation, underground water, nuclear waste disposal and geothermal energy extraction as well as chemical engineering, etc.

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4

Shafabakhsh, Paiman, Marwan Fahs, Behzad Ataie-Ashtiani, and Craig T. Simmons. "Unstable Density-Driven Flow in Fractured Porous Media: The Fractured Elder Problem." Fluids 4, no. 3 (September 9, 2019): 168. http://dx.doi.org/10.3390/fluids4030168.

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The Elder problem is one of the well-known examples of an unstable density-driven flow (DDF) and solute transport in porous media. The goal of this research is to investigate the influence of fracture networks on this benchmark problem due to the great importance of the fractured heterogeneity effect on unstable DDF. For this aim, the fractured Elder problem is solved using COMSOL Multiphysics, which is a finite element method simulator. Uniform and orthogonal fracture networks are embedded to analyze free convective flow and development of unstable salt plumes. The results indicate that the mesh sensitivity of the fractured Elder problem is greater than the homogeneous case. Furthermore, it has been shown that in the fractured cases, the onset of instability and free convection occur with lower critical Rayleigh number, which means that fracture networks have a destabilizing effect. Also, we examined the structural properties of fracture networks that control convective flow patterns, and the simulation results show that the strength of convection and instability at the beginning of the intrusion is proportional to the aperture size of the fractures. Moreover, the increase of the fracture’s density leads different modes of transient convective modes, until a specific fracture density after which the transient convective modes become similar to the homogenous case.

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5

Song, Jing Wen, Ming Yu Wang, and Da Wei Tang. "Experiment on Water Infiltration and Solute Migration in Porous and Fractured Media." Advanced Materials Research 955-959 (June 2014): 1993–97. http://dx.doi.org/10.4028/www.scientific.net/amr.955-959.1993.

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The experiments were performed by considering the upper loose porous media and lower fractured media as a typical structure of vadose zones, and by constructing the corresponding physical model to simulate water flow and solute transport processes in order to investigate water flow features and migration mechanism. It has been indicated that in the porous and fractured complex media, if the lower fracture structure remains unchanged, the structure and permeability of the porous media offer considerable impact on infiltration processes. Additionally, if the structure and permeability of the porous media remain unchanged, the overall permeability and flow features of the fracture structure are significantly controlled by fracture configurations. Furthermore, for the fracture structures with different fracture configurations, it is indicated that increasing of the density of the vertical fractures results in much more enhancement of the solute concentration decay rate than that caused by increasing the density of the horizontal ones. This investigation was expected to be of scientific significance and practical value for effective groundwater protection.

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6

ZHENG, QIAN, JINTU FAN, XIANGPENG LI, and SHIFANG WANG. "FRACTAL MODEL OF GAS DIFFUSION IN FRACTURED POROUS MEDIA." Fractals 26, no. 03 (June 2018): 1850035. http://dx.doi.org/10.1142/s0218348x18500354.

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Understanding gas transport behavior though fractured porous media is essential in many fields including fiber science, energy science, soil science, environmental engineering, chemical engineering, etc. In this paper, a fractal model is developed to characterize gas diffusion through fractured porous media, where a bundle of fractal-like tree branching networks is used to represent the fracture system according to fractal scaling laws. The analytical expression for relative gas diffusion coefficient of fractured porous media is derived. The proposed fractal model has been validated by the available experimental data and empirical correlations. From the parametrical study, it can be seen that structural parameters of fractured porous media (for example porosity, the fractal dimension, the diameter ratio, the length ratio and the branching angle) have a significant effect on equivalent gas transport properties. Gas relative diffusion coefficient has a positive correlation with the porosity, the pore size fractal dimension, or the diameter ratio, whereas it has a negative correlation with the length ratio, the branching levels, or the branching angle. The proposed fractal model does not only shed light on gas transport physics of fractured porous media, but also reveals more mechanisms than experimental measurements.

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7

Novikov, Mikhail A., and Vadim V. Lisitsa. "NUMERICAL ALGORITHM OF SEISMIC ATTENUATION ESTIMATION IN ANISOTROPIC FRACTURED POROUS FLUID-SATURATED MEDIA." Interexpo GEO-Siberia 2, no. 2 (May 21, 2021): 186–95. http://dx.doi.org/10.33764/2618-981x-2021-2-2-186-195.

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In our work we investigate the effect of transport and elastic properties anisotropy on seismic attenuation due to fracture-to-fracture wave-induced fluid flow using numerical algorithm of estimation of seismic wave attenuation in anisotropic fractured porous fluid-saturated media. Algorithm is based on numerical solution of anisotropic Biot equations using finite-difference scheme on staggered grid. We perform a set of numerical experiments to model wave propagation in fractured media with anisotropic fractured-filling material providing wave-induced fluid flow within interconnected fractures. Recorded signals are used for numerical estimation of inverse quality factor. Results demonstrate the effect of fracture-filling material anisotropy on seismic wave attenuation.

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8

Nair, R. N., T. M. Krishnamoorthy, and K. C. Pillai. "Radionuclede Transport Through Fractured Porous Media." Isotopenpraxis Isotopes in Environmental and Health Studies 29, no. 3 (September 1993): 225–36. http://dx.doi.org/10.1080/00211919308046689.

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9

Schery, S. D., D. J. Holford, J. L. Wilson, and F. M. Phillips. "The Flow and Diffusion of Radon Isotopes in Fractured Porous Media: Part 1, Finite Slabs." Radiation Protection Dosimetry 24, no. 1-4 (August 1, 1988): 185–89. http://dx.doi.org/10.1093/oxfordjournals.rpd.a080267.

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Abstract In the conventional equations used to describe gaseous transport of radon isotopes through fractured porous media the two processes responsible for radon movement are diffusion and pressure-driven flow (advection). Fractures in a porous medium can be especially effective for pressure-driven transport but lateral diffusion can be a strong mitigating influence. The interplay of diffusion and flow is examined for a fractured concrete slab and a fractured, high-diffusivity layer between a house and an underlying radium-rich medium. For underpressures common in houses, fractures only a fraction of a millimetre wide in concrete are important and often big enough to ensure flow transport of radon with small diffusive loss. In contrast, fractures several millimetres wide through high-diffusivity layers several metres thick such as sand may be unimportant for radon transport due to large lateral diffusive losses.

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10

Owusu, Richard, Adu Sakyi, Peter Amoako-Yirenkyi, and Isaac Kwame Dontwi. "A New Multicontinuum Model for Advection-Diffusion Process of Single-Phase Nonlinear Flow in a Multiscale Fractured Porous Media." Journal of Applied Mathematics 2022 (March 31, 2022): 1–14. http://dx.doi.org/10.1155/2022/5731988.

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Fractured porous media modeling and simulation has seen significant development in the past decade but still pose a great challenge and difficulty due to the multiscale nature of fractures, domain heterogeneity, and the nonlinear flow fields due to the high flow velocity and permeability resulting from the presence of fractures. Therefore, modeling fluid transport that is influenced by both advection and diffusion in fractured porous media studies becomes a generic problem, which this study seeks to address. In this paper, we present a study on non-Darcian fluid transport in multiscale naturally fractured reservoirs via an upscaling technique. An averaged macroscopic equation representing pressure distribution in a three-phase multiscale fractured porous medium was developed, consisting of the matrix and a 2-scale fractured network of length-scales ℓ m and ℓ M . The resulting macroscopic model has cross-advective and diffusive terms that account for induced fluxes between the interacting domains, as well as a mass transfer function that is dependent on both physical and geometric properties of the domain, with both advective and diffusive properties. This model also has effective diffusive and advective coefficients that account for reservoir properties such as viscosity, fluid density, and flow velocity. From the numerical simulation, a radial, a horizontal-linear flow behavior, and a transient and quasi-steady-state flow regime that is typical of naturally fractured porous media was observed. The findings of this study will provide researchers a reliable tool to study fractured porous media and can also help for better understanding of the dynamics of flow in fractured reservoirs.

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11

Novikov, Mikhail, Vadim Lisitsa, and Tatiana Khachkova. "IMPACT OF FRACTURED-POROUS MEDIA TRANSPORT PROPERTIES CHANGE IN SEISMIC WAVEFIELDS." Interexpo GEO-Siberia 2, no. 2 (2019): 248–53. http://dx.doi.org/10.33764/2618-981x-2019-2-2-248-253.

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In this paper we research the response of carbonates dissolution when interacting with carbon dioxide in the seismic wave fields in a fractured-porous reservoir. We numerically estimate the change of limestone physical properties due to CO2 sequestration based on the analysis of samples CT-scans. Obtained estimations is then used to model a poroelastic material, which we use as fracture-filling material in statistically generated fractured porous fluid-saturated media models. A numerical modeling of wave propagation is performed to estimate a velocity dispersion and attenuation caused by a wave-induced fluid flow.

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12

Sharma, Pramod Kr, Nitin Joshi, Rajesh Srivastava, and C. S. P. Ojha. "Reactive Transport in Fractured Permeable Porous Media." Journal of Hydrologic Engineering 20, no. 7 (July 2015): 04014078. http://dx.doi.org/10.1061/(asce)he.1943-5584.0001096.

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13

Bai, Mao, Jean-Claude Roegiers, and Hilary I. Inyang. "Contaminant Transport in Nonisothermal Fractured Porous Media." Journal of Environmental Engineering 122, no. 5 (May 1996): 416–23. http://dx.doi.org/10.1061/(asce)0733-9372(1996)122:5(416).

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14

XU, PENG. "A DISCUSSION ON FRACTAL MODELS FOR TRANSPORT PHYSICS OF POROUS MEDIA." Fractals 23, no. 03 (July 31, 2015): 1530001. http://dx.doi.org/10.1142/s0218348x15300019.

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Fractal model provides an alternative and useful means for studying the transport phenomenon in porous media and analyzing the macroscopic transport properties of porous media, as fractal geometry can successfully characterize disordered and heterogeneous geometrical microstructures of porous media on multi scales. Recently, fractal models on porous media have attracted increasing interests from many different disciplines. In this mini-review paper, a review on fractal models for number-size distribution in porous media is made, and a unified fractal model to characterize pore and particle size distributions is proposed according to the statistical fractal property of the complex microstructure in porous media. Using the fractal scaling laws for pore and fracture size distributions, a fractal capillary bundle model and a fractal tree-like network model are presented and summarized for homogenous and fractured porous media, respectively. And the applications of the fractal capillary bundle model and fractal tree-like network model for analysis of transport physics in porous media are also reviewed.

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15

Wu, Tao, Qian Wang, and Shifang Wang. "An Apparent Gas Permeability Model for Real Gas Flow in Fractured Porous Media with Roughened Surfaces." Polymers 13, no. 12 (June 10, 2021): 1937. http://dx.doi.org/10.3390/polym13121937.

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The investigation of gas transport in fractured porous media is essential in most petroleum and chemical engineering. In this paper, an apparent gas permeability model for real gas flow in fractured porous media is derived with adequate consideration of real gas effect, the roughness of fracture surface, and Knudsen diffusion based on the fractal theory. The fractal apparent gas permeability model is obtained to be a function of micro-structural parameters of fractured porous media, relative roughness, the pressure, the temperature, and the properties of gas. The predictions from the apparent gas permeability model based on the fractal theory match well with the published permeability model and experimental data, which verifies the rationality of the present fractal apparent gas permeability model.

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16

YEH, LI-MING. "ON TWO-PHASE FLOW IN FRACTURED MEDIA." Mathematical Models and Methods in Applied Sciences 12, no. 08 (August 2002): 1075–107. http://dx.doi.org/10.1142/s0218202502002045.

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A model describing two-phase, incompressible, immiscible flow in fractured media is discussed. A fractured medium is regarded as a porous medium consisting of two superimposed continua, a continuous fracture system and a discontinuous system of medium-sized matrix blocks. Transport of fluids through the medium is primarily within the fracture system. No flow is allowed between blocks, and only matrix-fracture flow is possible. Matrix block system plays the role of a global source distributed over the entire medium. Two-phase flow in a fractured medium is strongly related to phase mobilities and capillary pressures. In this work, four relations for these functions are presented, and the existence of weak solutions under each relation will also be shown.

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17

Říha, Jakub, and Jiřina Královcová. "GENERATION OF TRANSPORT PATHS IN FRACTURED POROUS MEDIA." Acta Polytechnica 57, no. 5 (October 31, 2017): 348. http://dx.doi.org/10.14311/ap.2017.57.0348.

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In this article, a method for generation of transport paths in combined equivalent porous media / discrete fracture network computational meshes is proposed as an alternative to a particle tracking method. It is based on a computation of the functional of the velocity and concentration individually for each element of a mesh. Its functionality is demonstrated on two test cases.

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18

Fomin, Sergei A., Vladimir A. Chugunov, and Toshiyuki Hashida. "Non-Fickian mass transport in fractured porous media." Advances in Water Resources 34, no. 2 (February 2011): 205–14. http://dx.doi.org/10.1016/j.advwatres.2010.11.002.

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19

Schery, S. D., D. J. Holford, J. L. Wilson, and F. M. Phillips. "The Flow and Diffusion of Radon Isotopes in Fractured Porous Media: Part 2, Semi-infinite Media." Radiation Protection Dosimetry 24, no. 1-4 (August 1, 1988): 191–97. http://dx.doi.org/10.1093/oxfordjournals.rpd.a080268.

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Abstract The release of radon isotopes under conditions of combined diffusion and flow from a fractured, semi-infinite medium such as soil is analysed. Relations are developed to indicate when flow from fractures will dominate overall transport and when the radon released from fractures will have the concentration characteristic of great depths. The presence of pressure-driven flow from fractures can greatly enhance transport of radon, but narrow or shallow fractures are not necessarily important due to the strong diffusive exchange with the surrounding porous medium and a reduced vertical pressure gradient in the surrounding medium. Results should be of use in estimating whether fractures are important in transporting radon to air spaces where pollution from radon is a concern.

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20

Hoteit, Hussein, and Abbas Firoozabadi. "Compositional Modeling of Discrete-Fractured Media Without Transfer Functions by the Discontinuous Galerkin and Mixed Methods." SPE Journal 11, no. 03 (September 1, 2006): 341–52. http://dx.doi.org/10.2118/90277-pa.

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Summary In a recent work, we introduced a numerical approach that combines the mixed-finite-element (MFE) and the discontinuous Galerkin (DG) methods for compositional modeling in homogeneous and heterogeneous porous media. In this work, we extend our numerical approach to 2D fractured media. We use the discrete-fracture model (crossflow equilibrium) to approximate the two-phase flow with mass transfer in fractured media. The discrete-fracture model is numerically superior to the single-porosity model and overcomes limitations of the dual-porosity model including the use of a shape factor. The MFE method is used to solve the pressure equation where the concept of total velocity is invoked. The DG method associated with a slope limiter is used to approximate the species-balance equations. The cell-based finite-volume schemes that are adapted to a discrete-fracture model have deficiency in computing the fracture/fracture fluxes across three and higher intersecting-fracture branches. In our work, the problem is solved definitively because of the MFE formulation. Several numerical examples in fractured media are presented to demonstrate the superiority of our approach to the classical finite-difference method. Introduction Compositional modeling in fractured media has broad applications in CO2, nitrogen, and hydrocarbon-gas injection, and recycling in gas condensate reservoirs. In addition to species transfer, the compressibility effects should be also considered for such applications. Heterogeneities and fractures add complexity to the fluid-flow modeling. Several conceptually different models have been proposed in the literature for the simulation of flow and transport in fractured porous media. The single-porosity approach uses an explicit computational representation for fractures (Ghorayeb and Firoozabadi 2000; Rivière et al. 2000). It allows the geological parameters to vary sharply between the matrix and the fractures. However, the high contrast and different length scales in the matrix and fractures make the approach unpractical because of the ill conditionality of the matrix appearing in the numerical computations (Ghorayeb and Firoozabadi 2000).The small control volumes in the fracture grids also add a severe restriction on the timestep size because of the Courant-Freidricks-Levy (CFL) condition if an explicit temporal scheme is used.

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21

Natarajan, N., and G. Suresh Kumar. "Effect of fracture-skin on virus transport in fractured porous media." Geoscience Frontiers 3, no. 6 (November 2012): 893–900. http://dx.doi.org/10.1016/j.gsf.2012.03.004.

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22

Natarajan, N., and G. Suresh Kumar. "Numerical modelling of colloidal transport in fractured porous media with double layered fracture-skin." Journal of Geo-Engineering Sciences 1, no. 2 (2014): 83–94. http://dx.doi.org/10.3233/jgs-130016.

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A numerical model is developed for studying the transport of colloids in a coupled fracture-matrix system with double layer fracture-skin. The governing equations describing colloid transport along the fracture and diffusion into fracture-skin layers as well as rock-matrix, normal to the fracture axis are coupled with each other. The coupled non linear equations are solved numerically with fully implicit finite difference method. Sensitivity analysis is performed to investigate the effect of various colloid properties on the colloid concentration in the multiple porosity fractured system. Colloid remobilisation and filtration has been accounted in the model. Results suggest that the inclusion of a second fracture-skin layer has a marginal effect on the transport mechanism of colloids. As colloid velocity increases, the diffusion of colloids into the fracture-skin decreases due to the low residence time available for the colloids. High first layer fracture-skin thickness and porosity enhances the diffusion of colloids from the aqueous phase of the fracture into the skin considerably resulting in low colloidal concentration within the fracture. Variation in the porosity as well as thickness of the second layer of the fracture-skin has negligible effect on the colloidal concentration in the fracture. The colloid transport mechanism in fractured porous media is marginally affected by the multiple porosity system, or in other words additional layers of fracture skin. High filtration coefficient and low remobilisation coefficient result in low colloidal concentration within the fracture.

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23

Fan, Xiaolin, Shuyu Sun, Wei Wei, and Jisheng Kou. "Numerical Simulation of Pollutant Transport in Fractured Vuggy Porous Karstic Aquifers." Journal of Applied Mathematics 2011 (2011): 1–41. http://dx.doi.org/10.1155/2011/498098.

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This paper begins with presenting a mathematical model for contaminant transport in the fractured vuggy porous media of a species of contaminant (PCP). Two phases are numerically simulated for a process of contaminant and clean water infiltrated in the fractured vuggy porous media by coupling mixed finite element (MFE) method and finite volume method (FVM), both of which are locally conservative, to approximate the model. A hybrid mixed finite element (HMFE) method is applied to approximate the velocity field for the model. The convection and diffusion terms are approached by FVM and the standard MFE, respectively. The pressure distribution and temporary evolution of the concentration profiles are obtained for two phases. The average effluent concentration on the outflow boundary is obtained at different time and shows some different features from the matrix porous media. The temporal multiscale phenomena of the effluent concentration on the outlet are observed. The results show how the different distribution of the vugs and the fractures impacts on the contaminant transport and the effluent concentration on the outlet. This paper sheds light on certain features of karstic groundwater are obtained.

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24

Kfoury, Moussa, Rachid Ababou, Benoît Noetinger, and Michel Quintard. "Upscaling Fractured Heterogeneous Media: Permeability and Mass Exchange Coefficient." Journal of Applied Mechanics 73, no. 1 (May 8, 2005): 41–46. http://dx.doi.org/10.1115/1.1991864.

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In order to optimize oil recuperation, to secure waste storage, CO2 sequestration and describe more precisely many environmental problems in the underground, we need to improve some homogenization methods that calculate petrophysical parameters. In this paper, we discuss the upscaling of fluid transport equations in fractured heterogeneous media consisting of the fractures themselves and a heterogeneous porous matrix. Our goal is to estimate precisely the fluid flow parameters like permeability and fracture/matrix exchange coefficient at large scale. Two approaches are possible. The first approach consists in calculating the large-scale equivalent properties in one upscaling step, starting with a single continuum flow model at the local scale. The second approach is to perform upscaling in two sequential steps: first, calculate the equivalent properties at an intermediate scale called the ”unit scale,” and, second, average the flow equations up to the large scale. We have implemented the two approaches and applied them to randomly distributed fractured systems. The results allowed us to obtain valuable information in terms of sizes of representative elementary volume associated to a given fracture distribution.

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25

Mikhailov, Mikhail D., M. Ungs, and Renato M. Cotta. "HYBRID SOLUTIONS FOR CONTAMINANT TRANSPORT IN FRACTURED POROUS MEDIA." Hybrid Methods in Engineering 4, no. 1-2 (2002): 27. http://dx.doi.org/10.1615/hybmetheng.v4.i1-2.40.

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26

Sharma, P. K. "Temporal moments for solute transport through fractured porous media." ISH Journal of Hydraulic Engineering 19, no. 3 (September 2013): 235–43. http://dx.doi.org/10.1080/09715010.2013.798908.

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27

Toran, Laura, Andrea Sjoreen, and Max Morris. "Sensitivity analysis of solute transport in fractured porous media." Geophysical Research Letters 22, no. 11 (June 1, 1995): 1433–36. http://dx.doi.org/10.1029/95gl01096.

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28

Reynolds, David A., and Bernard H. Kueper. "Multiphase flow and transport through fractured heterogeneous porous media." Journal of Contaminant Hydrology 71, no. 1-4 (July 2004): 89–110. http://dx.doi.org/10.1016/j.jconhyd.2003.09.008.

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29

Kärger, J. "Flow and Transport in Porous Media and Fractured Rock." Zeitschrift für Physikalische Chemie 194, Part_1 (January 1996): 135–36. http://dx.doi.org/10.1524/zpch.1996.194.part_1.135a.

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30

Sharma, P. K., and Umang Dixit. "Contaminant transport through fractured-porous media: An experimental study." Journal of Hydro-environment Research 8, no. 3 (August 2014): 223–33. http://dx.doi.org/10.1016/j.jher.2013.08.003.

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31

Wu, Yu-Shu, Ming Ye, and E. A. Sudicky. "Fracture-Flow-Enhanced Matrix Diffusion in Solute Transport Through Fractured Porous Media." Transport in Porous Media 81, no. 1 (April 1, 2009): 21–34. http://dx.doi.org/10.1007/s11242-009-9383-4.

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32

Cherubini, Claudia, Nicola Pastore, Concetta I. Giasi, and Nicoletta Maria Allegretti. "Laboratory experimental investigation of heat transport in fractured media." Nonlinear Processes in Geophysics 24, no. 1 (January 26, 2017): 23–42. http://dx.doi.org/10.5194/npg-24-23-2017.

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Abstract. Low enthalpy geothermal energy is a renewable resource that is still underexploited nowadays in relation to its potential for development in society worldwide. Most of its applications have already been investigated, such as heating and cooling of private and public buildings, road defrosting, cooling of industrial processes, food drying systems or desalination. Geothermal power development is a long, risky and expensive process. It basically consists of successive development stages aimed at locating the resources (exploration), confirming the power generating capacity of the reservoir (confirmation) and building the power plant and associated structures (site development). Different factors intervene in influencing the length, difficulty and materials required for these phases, thereby affecting their cost. One of the major limitations related to the installation of low enthalpy geothermal power plants regards the initial development steps that are risky and the upfront capital costs that are huge. Most of the total cost of geothermal power is related to the reimbursement of invested capital and associated returns. In order to increase the optimal efficiency of installations which use groundwater as a geothermal resource, flow and heat transport dynamics in aquifers need to be well characterized. Especially in fractured rock aquifers these processes represent critical elements that are not well known. Therefore there is a tendency to oversize geothermal plants. In the literature there are very few studies on heat transport, especially on fractured media. This study is aimed at deepening the understanding of this topic through heat transport experiments in fractured networks and their interpretation. Heat transfer tests have been carried out on the experimental apparatus previously employed to perform flow and tracer transport experiments, which has been modified in order to analyze heat transport dynamics in a network of fractures. In order to model the obtained thermal breakthrough curves, the Explicit Network Model (ENM) has been used, which is based on an adaptation of Tang's solution for the transport of the solutes in a semi-infinite single fracture embedded in a porous matrix. Parameter estimation, time moment analysis, tailing character and other dimensionless parameters have permitted a better understanding of the dynamics of heat transport and the efficiency of heat exchange between the fractures and the matrix. The results have been compared with the previous experimental studies on solute transport.

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CAI, JIANCHAO, WEI WEI, XIANGYUN HU, RICHENG LIU, and JINJIE WANG. "FRACTAL CHARACTERIZATION OF DYNAMIC FRACTURE NETWORK EXTENSION IN POROUS MEDIA." Fractals 25, no. 02 (April 2017): 1750023. http://dx.doi.org/10.1142/s0218348x17500232.

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Fracture network and fractured porous media as well as their transport properties have received great attentions in many fields from engineering application and basic theoretical researches. Fracture will dynamically extend in length and aperture to form complex fracture network under some external conditions such as percussion drilling, wave propagation, desiccation and hydrofracturing. The complexity of fracture network can be well quantitatively characterized by fractal dimension. In this work, the dynamic characterization of fracture network extension in porous media under drying process is measured by the improved box-counting technique, and fractal dimensions of fracture network are respectively related to drying time, average aperture, moisture content and fracture porosity. The fractal dimension increases exponentially with drying time and average aperture, and decreases with moisture content in the form of power law. Specially, the fractal dimension is approximatively increased with porosity in the form of linearity in a narrow porosity range. The transport capacity of fracture network, described by seepage coefficient, is also related to the fractal dimension with drying time in the form of exponential function. The presented fractal analysis of fracture network could also shed light on the hydrofracturing application in subsurface unconventional oil and gas reservoirs.

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Li, Liyong, and Seong H. Lee. "Efficient Field-Scale Simulation of Black Oil in a Naturally Fractured Reservoir Through Discrete Fracture Networks and Homogenized Media." SPE Reservoir Evaluation & Engineering 11, no. 04 (August 1, 2008): 750–58. http://dx.doi.org/10.2118/103901-pa.

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Summary This paper describes a hybrid finite volume method, designed to simulate multiphase flow in a field-scale naturally fractured reservoir. Lee et al. (WRR 37:443-455, 2001) developed a hierarchical approach in which the permeability contribution from short fractures is derived in an analytical expression that from medium fractures is numerically solved using a boundary element method. The long fractures are modeled explicitly as major fluid conduits. Reservoirs with well-developed natural fractures include many complex fracture networks that cannot be easily modeled by simple long fracture formulation and/or homogenized single continuity model. We thus propose a numerically efficient hybrid method in which small and medium fractures are modeled by effective permeability, and large fractures are modeled by discrete fracture networks. A simple, systematic way is devised to calculate transport parameters between fracture networks and discretized, homogenized media. An efficient numerical algorithm is also devised to solve the dual system of fracture network and finite volume grid. Black oil formulation is implemented in the simulator to demonstrate practical applications of this hybrid finite volume method. Introduction Many reservoirs are highly fractured due to the complex tectonic movement and sedimentation process the formation has experienced. The permeability of a fracture is usually much larger than that of the rock matrix; as a result, the fluid will flow mostly through the fracture network, if the fractures are connected. This implies that the fracture connectivities and their distribution will determine fluid transport in a naturally fractured reservoir (Long and Witherspoon 1985). Because of statistically complex distribution of geological heterogeneity and multiple length and time scales in natural porous media, three approaches (Smith and Schwartz 1993) are commonly used in describing fluid flow and solute transport in naturally fractured formations:discrete fracture models;continuum models using effective properties for discrete grids; andhybrid models that combine discrete, large features and equivalent continuum. Currently, most reservoir simulators use dual continuum formulations (i.e., dual porosity/permeability) for naturally fractured reservoirs in which matrix blocks are divided by very regular fracture patterns (Kazemi et al. 1976, Van Golf-Racht 1982). Part of the primary input into these simulation models is the permeability of the fracture system assigned to the individual grid-blocks. This value can only be reasonably calculated if the fracture systems are regular and well connected. Field characterization studies have shown, however, that fracture systems are very irregular, often disconnected, and occur in swarms (Laubach 1991, Lorenz and Hill 1991, Narr et al. 2003). Most naturally fractured reservoirs include fractures of multiple- length scales. The effective grid-block permeability calculated by the boundary element method becomes expensive as the number of fractures increases. The calculated effective properties for grid-blocks also underestimates the properties for long fractures whose length scale is much larger than the grid-block size. Lee et al. (2001) proposed a hierarchical method to model fluid flow in a reservoir with multiple-length scaled fractures. They assumed that short fractures are randomly distributed and contribute to increasing the effective matrix permeability. An asymptotic solution representing the permeability contribution from short fractures was derived. With the short fracture contribution to permeability, the effective matrix permeability can be expressed in a general tensor form. Thus, they also developed a boundary element method for Darcy's equation with tensor permeability. For medium-length fractures in a grid-block, a coupled system of Poisson equations with tensor permeability was solved numerically using a boundary element method. The grid-block effective permeabilities were used with a finite difference simulator to compute flow through the fracture system. The simulator was enhanced to use a control-volume finite difference formulation (Lee et al. 1998, 2002) for general tensor permeability input (i.e., 9-point stencil for 2-D and 27-point stencil for 3-D). In addition, long fractures were explicitly modeled by using the transport index between fracture and matrix in a gridblock. In this paper we adopt their transport index concept and extend the hierarchical method:to include networks of long fractures;to model fracture as a two-dimensional plane; andto allow fractures to intersect with well bore. This generalization allows us to model a more realistic and complex fracture network that can be found in naturally fractured reservoirs. To demonstrate this new method for practical reservoir applications, we furthermore implement a black oil formulation in the simulator. We explicitly model long fractures as a two-dimensional plane that can penetrate several layers. The method, presented in this paper, allows a general description of fracture orientation in space. For simplicity of computational implementation however, both the medium-length and long fractures considered in this paper are assumed to be perpendicular to bedding boundaries. In addition, we derive a source/sink term to model the flux between matrix and long fracture networks. This source/sink allows for coupling multiphase flow equations in long fractures and matrix. The paper is organized as follows. In Section 2 black oil formulation is briefly summarized and the transport equations for three phase flow are presented. The fracture characterization and hierarchical modeling approach, based on fracture length, are discussed in Section 3. In Section 4 we review homogenization of short and medium fractures, which is part of our hierarchical approach to modeling flow in porous media with multiple length-scale fractures. In Section 5 we discuss a discrete network model of long fractures. We also derive transfer indices between fracture and effective matrix blocks. In Section 6 we present numerical examples for tracer transport in a model with simple fracture network, interactions of fractures and wells, and black oil production in a reservoir with a complex fracture network system. Finally, the summary of our main results and conclusion follows.

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Zhang, Wenjuan, Waleed Diab, Hadi Hajibeygi, and Mohammed Al Kobaisi. "A Computational Workflow for Flow and Transport in Fractured Porous Media Based on a Hierarchical Nonlinear Discrete Fracture Modeling Approach." Energies 13, no. 24 (December 17, 2020): 6667. http://dx.doi.org/10.3390/en13246667.

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Modeling flow and transport in fractured porous media has been a topic of intensive research for a number of energy- and environment-related industries. The presence of multiscale fractures makes it an extremely challenging task to resolve accurately and efficiently the flow dynamics at both the local and global scales. To tackle this challenge, we developed a computational workflow that adopts a two-level hierarchical strategy based on fracture length partitioning. This was achieved by specifying a partition length to split the discrete fracture network (DFN) into small-scale fractures and large-scale fractures. Flow-based numerical upscaling was then employed to homogenize the small-scale fractures and the porous matrix into an equivalent/effective single medium, whereas the large-scale fractures were modeled explicitly. As the effective medium properties can be fully tensorial, the developed hierarchical framework constructed the discrete systems for the explicit fracture–matrix sub-domains using the nonlinear two-point flux approximation (NTPFA) scheme. This led to a significant reduction of grid orientation effects, thus developing a robust, applicable, and field-relevant framework. To assess the efficacy of the proposed hierarchical workflow, several numerical simulations were carried out to systematically analyze the effects of the homogenized explicit cutoff length scale, as well as the fracture length and orientation distributions. The effect of different boundary conditions, namely, the constant pressure drop boundary condition and the linear pressure boundary condition, for the numerical upscaling on the accuracy of the workflow was investigated. The results show that when the partition length is much larger than the characteristic length of the grid block, and when the DFN has a predominant orientation that is often the case in practical simulations, the workflow employing linear pressure boundary conditions for numerical upscaling give closer results to the full-model reference solutions. Our findings shed new light on the development of meaningful computational frameworks for highly fractured, heterogeneous geological media where fractures are present at multiple scales.

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Younes, Anis, Marwan Fahs, and Philippe Ackerer. "Modeling of Flow and Transport in Saturated and Unsaturated Porous Media." Water 13, no. 8 (April 15, 2021): 1088. http://dx.doi.org/10.3390/w13081088.

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Modeling fluid flow and transport processes in porous media is a relevant topic for a wide range of applications. In water resources problems, this topic presents specific challenges related to the multiphysical processes, large time and space scales, heterogeneity and anisotropy of natural porous media, and complex mathematical models characterized by coupled nonlinear equations. This Special Issue aims at collecting papers presenting new developments in the field of flow and transport in porous media. The 25 published papers deal with different aspects of physical processes and applications such as unsaturated and saturated flow, flow in fractured porous media, landslide, reactive transport, seawater intrusion, and transport within hyporheic zones. Based on their objectives, we classified these papers into four categories: (i) improved numerical methods for flow and mass transport simulation, (ii) looking for reliable models and parameters, (iii) laboratory scale experiments and simulations, and (iv) modeling and simulations for improved process understanding. Current trends on modeling fluid flow and transport processes in porous media are discussed in the conclusion.

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Formaggia, Luca, Alessio Fumagalli, and Anna Scotti. "A multi-layer reactive transport model for fractured porous media." Mathematics in Engineering 4, no. 1 (2021): 1–32. http://dx.doi.org/10.3934/mine.2022008.

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Hakl, J., I. Csige, I. Hunyadi, A. Várhegyi, and G. Géczy. "Radon transport in fractured porous media — Experimental study in caves." Environment International 22 (January 1996): 433–37. http://dx.doi.org/10.1016/s0160-4120(96)00143-2.

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Battiato, Ilenia, Daniel M. Tartakovsky, Alexandre M. Tartakovsky, and T. D. Scheibe. "Hybrid models of reactive transport in porous and fractured media." Advances in Water Resources 34, no. 9 (September 2011): 1140–50. http://dx.doi.org/10.1016/j.advwatres.2011.01.012.

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Zhang, Dongxiao, and Qinjun Kang. "Pore scale simulation of solute transport in fractured porous media." Geophysical Research Letters 31, no. 12 (June 2004): n/a. http://dx.doi.org/10.1029/2004gl019886.

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Logan, J. D., V. A. Zlotnik, and S. Cohn. "Transport in fractured porous media with time-periodic boundary conditions." Mathematical and Computer Modelling 24, no. 9 (November 1996): 1–9. http://dx.doi.org/10.1016/0895-7177(96)00149-5.

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Leo, C. J., and J. R. Booker. "Boundary element analysis of contaminant transport in fractured porous media." International Journal for Numerical and Analytical Methods in Geomechanics 17, no. 7 (July 1993): 471–92. http://dx.doi.org/10.1002/nag.1610170704.

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Valliappan, S., W. Wang, and N. Khalili. "Contaminant transport under variable density flow in fractured porous media." International Journal for Numerical and Analytical Methods in Geomechanics 22, no. 7 (July 1998): 575–95. http://dx.doi.org/10.1002/(sici)1096-9853(199807)22:7<575::aid-nag928>3.0.co;2-x.

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Ibaraki, M., and E. A. Sudicky. "Colloid-facilitated contaminant transport in discretely fractured porous media: 2. Fracture network examples." Water Resources Research 31, no. 12 (December 1995): 2961–69. http://dx.doi.org/10.1029/95wr02181.

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Yang, Jianwen. "Reactive silica transport in fractured porous media: Analytical solution for a single fracture." Computers & Geosciences 38, no. 1 (January 2012): 80–86. http://dx.doi.org/10.1016/j.cageo.2011.05.008.

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Faybishenko, Boris. "A Concept of Fuzzy Dual Permeability of Fractured Porous Media." Water 15, no. 21 (October 27, 2023): 3752. http://dx.doi.org/10.3390/w15213752.

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The interpretation of the results of hydrogeological field observations and the modeling of fractured porous subsurface media is often conducted using dual-porosity and/or dual-permeability concepts. These concepts, however, do not consider the effects of spatial and temporal variations and uncertainties, or fuzziness, in the evaluation of the subsurface flow characteristics of fractured porous media. The goal of the paper is to introduce a concept of fuzzy dual permeability of fractured porous media based on the fuzzy system analysis of the results of ponded infiltration tests in fractured basalt. The author revisited the results of the tests conducted in areas close to the Idaho National Laboratory (INL), Idaho, USA: small-scale (approximately 0.5 m2) ponded tests at the Hell’s Half Acre site, mesoscale (56 m2) ponded tests at the Box Canyon site, and a large-scale infiltration test (31,416 m2) at the Radioactive Waste Management Complex at INL. Methods of fuzzy clustering and fuzzy regression were applied to describe the time-depth waterfront penetration and to characterize the phenomena of rapid flow through a predominantly fractured component and slow flow through a predominantly porous matrix component. The concept of fuzzy dual permeability is presented using a series of fuzzy membership functions of the waterfront propagation with depth and time. To describe the time variation of the flux, a fuzzy Horton’s model is presented. The developed concept can be used for the uncertainty quantification in flow and transport in geologic media.

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Blessent, Daniela, Peter R. Jørgensen, and René Therrien. "Comparing Discrete Fracture and Continuum Models to Predict Contaminant Transport in Fractured Porous Media." Groundwater 52, no. 1 (March 5, 2013): 84–95. http://dx.doi.org/10.1111/gwat.12032.

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Natarajan, N., and G. Suresh Kumar. "Numerical modeling of bacteria facilitated contaminant transport in fractured porous media." Colloids and Surfaces A: Physicochemical and Engineering Aspects 387, no. 1-3 (August 2011): 104–12. http://dx.doi.org/10.1016/j.colsurfa.2011.07.037.

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Grillo, Alfio, Dmitriy Logashenko, Sabine Stichel, and Gabriel Wittum. "Forchheimer’s correction in modelling flow and transport in fractured porous media." Computing and Visualization in Science 15, no. 4 (August 2012): 169–90. http://dx.doi.org/10.1007/s00791-013-0208-1.

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Ojha, C. S. P., Rao Y. Surampalli, Pramod Kumar Sharma, and Nitin Joshi. "Breakthrough Curves and Simulation of Virus Transport through Fractured Porous Media." Journal of Environmental Engineering 137, no. 8 (August 2011): 731–39. http://dx.doi.org/10.1061/(asce)ee.1943-7870.0000374.

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