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A G Hunt - One of the best experts on this subject based on the ideXlab platform.
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flow transport and reaction in porous media percolation scaling critical path analysis and effective medium approximation
Reviews of Geophysics, 2017Co-Authors: A G Hunt, Muhammad SahimiAbstract:We describe the most important developments in the application of three theoretical tools to modeling of the morphology of porous media and flow and transport processes in them. One tool is percolation theory. Although it was over 40 years ago that the possibility of using percolation theory to describe flow and transport processes in porous media was first raised, new models and concepts, as well as new variants of the original percolation model are still being developed for various applications to flow phenomena in porous media. The other two approaches, closely related to percolation theory, are the critical-path analysis, which is applicable when porous media are highly heterogeneous, and the effective-medium approximation - poor man's percolation - which provides a simple and, under certain conditions, quantitatively correct description of transport in porous media in which percolation-type disorder is relevant. Applications to topics in geosciences include predictions of the hydraulic conductivity and air permeability, solute and gas diffusion that are particularly important in ecohydrological applications and land-surface interactions, and multiphase flow in porous media, as well as non-Gaussian solute transport, and flow morphologies associated with imbibition into unsaturated fractures. We describe new applications of percolation theory of solute transport to chemical weathering and soil formation, geomorphology, and elemental cycling through the terrestrial Earth surface. Wherever quantitatively accurate predictions of such quantities are relevant, so are the techniques presented here. Whenever possible, the theoretical predictions are compared with the relevant experimental data. In practically all the cases, the agreement between the theoretical predictions and the data is excellent. Also discussed are possible future directions in the application of such concepts to many other phenomena in geosciences.
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saturation dependence of transport in porous media predicted by percolation and effective medium theories
Fractals, 2015Co-Authors: Behzad Ghanbarian, A G Hunt, Thomas E Skinner, Robert P EwingAbstract:Accurate prediction of the saturation dependence of different modes of transport in porous media, such as those due to conductivity, air permeability, and diffusion, is of broad interest in engineering and natural resources management. Most current predictions use a "bundle of capillary tubes" concept, which, despite its widespread use, is a severely distorted idealization of natural porous media. In contrast, percolation theory provides a reliable and powerful means to model interconnectivity of disordered networks and porous materials. In this study, we invoke scaling concepts from percolation theory and effective medium theory to predict the saturation dependence of modes of transport — hydraulic and electrical conductivity, air permeability, and gas diffusion — in two disturbed soils. Universal scaling from percolation theory predicts the saturation dependence of air permeability and gas diffusion accurately, even when the percolation threshold for airflow is estimated from the porosity. We also find that the non-universal scaling obtained from the critical path analysis (CPA) of percolation theory can make excellent predictions of hydraulic and electrical conductivity under partially saturated conditions.
M A Ioannidis - One of the best experts on this subject based on the ideXlab platform.
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a new approach for the characterization of the pore structure of dual porosity rocks
Chemical Engineering Science, 2009Co-Authors: Christos D. Tsakiroglou, M A Ioannidis, Edison Amirtharaj, Olga VizikaAbstract:Abstract For the realistic representation of the pore space of dual porosity rocks, a new method of pore structure characterization is developed by combining experimental Hg intrusion/retraction curves with back-scattered scanning electron microscope (BSEM) images and inverse modeling algorithms. The pore space autocorrelation function measured by processing the digitized BSEM images is combined with the surface fractal dimension estimated from the high pressure Hg intrusion (MIP) data to derive a synthetic small-angle neutron scattering (SANS) intensity function, the inversion of which provides a volume-based pore body radius distribution (PBRD). The volume-based PBRD is fitted with a multimodal number-based PBRD consisting of two component distributions: one representing the macroporosity and another one representing the microporosity. Based on arguments of percolation theory, analytical mathematical models are developed to describe the Hg intrusion in and retraction from dual pore networks in terms of the complete PBRD, pore throat radius distribution (PTRD) of macroporosity, drainage accessibility functions (DAFs) of both porosities, and imbibition accessibility functions (IAFs) of both porosities. Inverse modeling of the Hg intrusion data set enables us to estimate the PTRD and DAFs. Inverse modeling of the Hg retraction datasets enables us to estimate a set of primary and secondary IAFs. The method is demonstrated by the pore structure characterization of four outcrop samples of carbonate and sandstone rocks. Analytic approximate equations developed from the critical path analysis (CPA) of percolation theory enable us to calculate explicitly the absolute permeability and the formation factor of the porous rocks using the estimated parameters (PBRD, PTRD, DAF) of the macroporosity. The measured permeability of cores is predicted satisfactorily and observed discrepancies may be attributed to large length-scale macro-heterogeneities which are not evident in BSEM images and Hg porosimetry data.
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dual porosity modelling of the pore structure and transport properties of a contaminated soil
European Journal of Soil Science, 2008Co-Authors: C D Tsakiroglou, M A IoannidisAbstract:Summary We have developed a new method to characterize the pore structure of mineral soils. We combined data from the analysis of back-scattered scanning electron microscope (BSEM) images of resin-impregnated pore-casts, and mercury intrusion porosimetry (MIP) data, with analytical percolation models and inverse modeling algorithms. The pore space is regarded as a dual-pore network consisting of a primary Euclidean pore-and-throat network and a secondary, fractal, pore system that is accessed through primary pores. The digitized 2-D BSEM images of resin-impregnated soil samples are employed to determine the autocorrelation function. The Fourier transform of this function provides the small-angle neutron scattering (SANS) intensity function, which is extended by using the surface fractal dimension obtained from high-pressure MIP data. Inversion of the extended scattering intensity function produces the volume-based radius distribution function of spherical pore bodies (PBRD). The complete volume-based PBRD is fitted with a composite number-based PBRD composed of a lognormal primary PBRD and a power (fractal) secondary PBRD with upper and lower cut-offs. Based on the concepts of invasion percolation, an analytic mathematical model that describes Hg intrusion into dual pore networks is developed. The complete PBRD and pore-throat radius distribution (PTRD) functions of the primary network along with the drainage accessibility functions (DAFs) of the primary and secondary pore networks are estimated with inverse modelling of the Hg intrusion curve. Based on critical path analysis of percolation theory, approximate analytical relationships are developed to calculate explicitly the absolute permeability and electrical formation factor from the geometrical and topological parameters of the primary pore network. The method is demonstrated with application to four soil samples.
Behzad Ghanbarian - One of the best experts on this subject based on the ideXlab platform.
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gas permeability in unconventional tight sandstones scaling up from pore to core
Journal of Petroleum Science and Engineering, 2019Co-Authors: Behzad Ghanbarian, Carlos Torresverdin, Larry W Lake, Michael P MarderAbstract:Abstract 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 – determined from mercury intrusion capillary pressure (MICP) curves – and pore-throat connectivity. The latter is estimated from critical volume fraction (or percolation threshold) for macroscopic flow. Electrical conductivity and permeability are then scaled up from the two characteristic pore sizes, tortuosity, and porosity by assuming two different pore geometries: cylindrical and slit-shaped. Comparison of results obtained for eighteen tight-gas sandstones indicates that the EMA estimates σ b and k more accurately when pores are assumed to be cylindrical. We also estimate k from the pore-throat size distributions and the measured electrical conductivity using the EMA and critical path analysis (CPA), another upscaling technique borrowed from statistical physics. Theoretically, the former is valid in relatively heterogeneous porous media with narrow pore-throat size distribution, while the latter is valid in heterogeneous media with broad pore-throat size distribution. Results show that the EMA estimates k more accurately than CPA and arrives within a factor of two of the measurements on average.
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upscaling soil saturated hydraulic conductivity from pore throat characteristics
Advances in Water Resources, 2017Co-Authors: Behzad Ghanbarian, Allen G. Hunt, Todd H. Skaggs, Nicholas JarvisAbstract:Abstract Upscaling and/or estimating saturated hydraulic conductivity K sat at the core scale from microscopic/macroscopic soil characteristics has been actively under investigation in the hydrology and soil physics communities for several decades. Numerous models have been developed based on different approaches, such as the bundle of capillary tubes model, pedotransfer functions, etc. In this study, we apply concepts from critical path analysis, an upscaling technique first developed in the physics literature, to estimate saturated hydraulic conductivity at the core scale from microscopic pore throat characteristics reflected in capillary pressure data. With this new model, we find K sat estimations to be within a factor of 3 of the average measured saturated hydraulic conductivities reported by Rawls et al. (1982) for the eleven USDA soil texture classes.
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saturation dependence of transport in porous media predicted by percolation and effective medium theories
Fractals, 2015Co-Authors: Behzad Ghanbarian, A G Hunt, Thomas E Skinner, Robert P EwingAbstract:Accurate prediction of the saturation dependence of different modes of transport in porous media, such as those due to conductivity, air permeability, and diffusion, is of broad interest in engineering and natural resources management. Most current predictions use a "bundle of capillary tubes" concept, which, despite its widespread use, is a severely distorted idealization of natural porous media. In contrast, percolation theory provides a reliable and powerful means to model interconnectivity of disordered networks and porous materials. In this study, we invoke scaling concepts from percolation theory and effective medium theory to predict the saturation dependence of modes of transport — hydraulic and electrical conductivity, air permeability, and gas diffusion — in two disturbed soils. Universal scaling from percolation theory predicts the saturation dependence of air permeability and gas diffusion accurately, even when the percolation threshold for airflow is estimated from the porosity. We also find that the non-universal scaling obtained from the critical path analysis (CPA) of percolation theory can make excellent predictions of hydraulic and electrical conductivity under partially saturated conditions.
Muhammad Sahimi - One of the best experts on this subject based on the ideXlab platform.
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flow transport and reaction in porous media percolation scaling critical path analysis and effective medium approximation
Reviews of Geophysics, 2017Co-Authors: A G Hunt, Muhammad SahimiAbstract:We describe the most important developments in the application of three theoretical tools to modeling of the morphology of porous media and flow and transport processes in them. One tool is percolation theory. Although it was over 40 years ago that the possibility of using percolation theory to describe flow and transport processes in porous media was first raised, new models and concepts, as well as new variants of the original percolation model are still being developed for various applications to flow phenomena in porous media. The other two approaches, closely related to percolation theory, are the critical-path analysis, which is applicable when porous media are highly heterogeneous, and the effective-medium approximation - poor man's percolation - which provides a simple and, under certain conditions, quantitatively correct description of transport in porous media in which percolation-type disorder is relevant. Applications to topics in geosciences include predictions of the hydraulic conductivity and air permeability, solute and gas diffusion that are particularly important in ecohydrological applications and land-surface interactions, and multiphase flow in porous media, as well as non-Gaussian solute transport, and flow morphologies associated with imbibition into unsaturated fractures. We describe new applications of percolation theory of solute transport to chemical weathering and soil formation, geomorphology, and elemental cycling through the terrestrial Earth surface. Wherever quantitatively accurate predictions of such quantities are relevant, so are the techniques presented here. Whenever possible, the theoretical predictions are compared with the relevant experimental data. In practically all the cases, the agreement between the theoretical predictions and the data is excellent. Also discussed are possible future directions in the application of such concepts to many other phenomena in geosciences.
Yiju Hsueh - One of the best experts on this subject based on the ideXlab platform.
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a simple approach to fuzzy critical path analysis in project networks
Applied Mathematical Modelling, 2008Co-Authors: Shihpin Chen, Yiju HsuehAbstract:Abstract This paper develops a simple approach to critical path analysis in a project network with activity times being fuzzy numbers. The idea is based on the linear programming (LP) formulation and fuzzy number ranking method. The fuzzy critical path problem is formulated as an LP model with fuzzy coefficients of the objective function, and then on the basis of properties of linearity and additivity, the Yager’s ranking method is adopted to transform the fuzzy LP formulation to the crisp one which can be solved by using the conventional streamlined solution methods. Consequently, the critical path and total duration time can be obtained from the derived optimal solution. Moreover, in this paper we also define the most critical path and the relative path degree of criticality, which are theoretically sound and easy to use in practice. An example discussed in some previous studies illustrates that the proposed approach is able to find the most critical path, which is proved to be the same as that derived from an exhausted comparison of all possible paths. The proposed approach is very simple to apply, and it is not require knowing the explicit form of the membership functions of the fuzzy activity times.