Topological Characterization of Porous Media

Vogel, H. J.

doi:10.1007/3-540-45782-8_3

Cited by 87 publications

(74 citation statements)

References 36 publications

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“…[60] The connectivity of hydraulic conductivity and its effects on single-phase flow and solute transport have already been analyzed by Gomez-Hernandez and Wen [1997], Zinn andHarvey [2003], andVogel [2002]. Here we consider unsaturated flow, where the connectivity of the total permeability does not only depend on the distribution of soil materials but also on the capillary pressure, and the effect may be even more pronounced.…”

Section: Effective Relative Permeability Curves For Differently Connementioning

confidence: 99%

“…[61] Zinn and Harvey [2003] presented the absolute value transformation as a method to transform fields with high connectivity of medium parameter values to fields with high connectivity of either low or high parameter values [see also Vogel, 2002]:…”

Section: Effective Relative Permeability Curves For Differently Connementioning

confidence: 99%

“…Such concepts have been applied to soil fields by Western et al [2001]. Zinn and Harvey [2003] and Vogel [2002] introduced the absolute value transformation as an efficient method to generate fields with certain connectivity properties, providing the opportunity to investigate the impact of connectivity properties on effective flow behavior by Monte Carlo simulations. The result of the generator are fields with identical two-point correlation functions and probability distributions but differing in the parameter range forming continuous bands.…”

Section: Introductionmentioning

confidence: 99%

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Homogenization of Richards equation in permeability fields with different connectivities

Neuweiler

Cirpka

2005

Water Resources Research

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[1] Large-scale modeling of transient flow in the unsaturated zone is important for the estimation of the water budget and solute transport in the vadose zone. Upscaled flow models need to capture the impact of small-scale heterogeneities, which are not resolved by the model, on large-scale flow. We perform upscaling of the Richards equation in heterogeneous porous media with continuous distributions of the soil hydraulic parameters using homogenization theory and stochastic averaging techniques. We restrict the analysis to flow regimes in which the capillary-equilibrium assumption holds on the small scale. In order to account for effects of capillary entry pressure we apply the Brooks-Corey model for the soil retention and relative permeability curves and consider Leverett scaling for the coupling of intrinsic permeability and entry pressure. For this model we derive and analyze the ensemble-averaged parameter functions for the macroscopic flow equations. The effects of a definite entry pressure vanish with increasing variance of the log intrinsic permeability. We compare the statistically averaged parameter functions to numerically calculated effective functions for parameter fields with different connectivity properties. These results illustrate that soils with wellconnected coarse materials differ in the relative permeability from those with wellconnected fine materials or those without particular connectedness.

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Section: Effective Relative Permeability Curves For Differently Connementioning

confidence: 99%

Section: Effective Relative Permeability Curves For Differently Connementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Homogenization of Richards equation in permeability fields with different connectivities

Neuweiler

Cirpka

2005

Water Resources Research

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“…1). This procedure is usually called morphological granulometry and, following VOGEL (2002), in the study of porous media images the size criteria used almost perfectly reflects the idea of the hydraulic diameter of a pore. A functional measurement such as the volume, expressed in relation to the size of the structuring element d, provides a measure of the distribution of the functional in the set.…”

Section: Theory: Morphological Image Analysismentioning

confidence: 99%

Volume, Surface, Connectivity and Size Distribution of Soil Pore Space in CT Images: Comparison of Samples at Different Depths from Nearby Natural and Tillage Areas

Muñoz

Martínez

Monreal

2014

Pure Appl. Geophys.

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The study of soil structure, i.e., the pores, is of vital importance in different fields of science and technology. Total pore volume (porosity), pore surface, pore connectivity and pore size distribution are some (probably the most important) of the geometric measurements of pore space. The technology of X-ray computed tomography allows us to obtain 3D images of the inside of a soil sample enabling study of the pores without disturbing the samples. In this work we performed a set of geometrical measures, some of them from mathematical morphology, to assess and quantify any possible difference that tillage may have caused on the soil. We compared samples from tilled soil with samples from a soil with natural vegetation taken in a very close area. Our results show that the main differences between these two groups of samples are total surface area and pore connectivity per unit pore volume.

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“…These techniques give accurate results for specific types of heterogeneities and do not provide a thorough topological and geometrical analysis. Recently, the topology and geometry of the sub-scale structure has been recognized to be of crucial importance for the upscaled conductivity [21][22][23][24][25]. Knudby et al [26] developed a model for the estimation of K eq in random binary fields containing multiple inclusions.…”

Section: Introductionmentioning

confidence: 99%

Binary upscaling on complex heterogeneities: The role of geometry and connectivity

Oriani

Renard

2014

Advances in Water Resources

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a b s t r a c tThe equivalent conductivity (K eq ) of a binary medium is known to vary with the proportion of the two phases, but it also depends on the geometry and topology of the inclusions. In this paper, we analyze the role of connectivity and shape of the connected components through a correlation study between K eq and two topological and geometrical indicators: the Euler number and the Solidity indicator. We show that a local measure such as the Euler number is weakly correlated to K eq and therefore it is not suitable to quantify the influence of connectivity on the global flux; on the contrary the Solidity indicator, related to the convex hull of the connected components, presents a direct correlation with K eq . This result suggests that, in order to estimate K eq properly, one may consider the convex hull of each connected component as the area of influence of its spatial distribution on flow and make a correction of the proportion of the hydrofacies according to that. As a direct application of these principles, we propose a new method for the estimation of K eq using simple image analysis operations. In particular, we introduce a direct measure of the connected fraction and a non-parametric correction of the hydrofacies proportion to compensate for the influence of the connected components shape on flow. This model, tested on a large ensemble of isotropic media, provides a good K eq approximation even on complex heterogeneities without the need for calibration.

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Topological Characterization of Porous Media

Cited by 87 publications

References 36 publications

Homogenization of Richards equation in permeability fields with different connectivities

Homogenization of Richards equation in permeability fields with different connectivities

Volume, Surface, Connectivity and Size Distribution of Soil Pore Space in CT Images: Comparison of Samples at Different Depths from Nearby Natural and Tillage Areas

Binary upscaling on complex heterogeneities: The role of geometry and connectivity

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