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3D soil image characterization applied to hydraulic properties computation
Abstract
We propose a novel method to characterize the fluid-filled (usually air or water) space in images of porous media at the pore scale. First, an aperture map is created based on a skeleton process, to describe all local sizes in the pore space. Then the pore space is segmented in pores, defined as elementary objects that compose the pore space. Using this segmented image, a pore network is created, which is a graphic representation of the pore space that includes local sizes and direct information about connectivity at the pore scale. As an application of this method for pore space modelling, the equivalent hydraulic conductivity or permeability for a soil sample is computed.
... It is often necessary to measure from the image a quantity related to the physical property to be characterized. For example, transport phenomena and permeability in rocks can be studied through the distribution of the grains and the geometry of the pore phase [18]. In materials science, the anisotropy of a structure characterized by a Fabric tensor reflects the main poroelastic directions [17]. ...
... These porous objects are usually considered not only in industry but also in research as multiphase materials composed of several elements arranged in space as a complex, sometimes messy, network. The problems of porous media have raised considerable interest among the scientific community as they cover a wide range of applications and scales: the exploration of underground entities at the microscopic scale in geology, and the examination of soil structures [18], the degradation of monuments [27], or the analysis of bones and the synthesis of industrial materials [8]. In most of these problems, the challenge is to study the physical behavior of these objects by characterizing their complex geometry, in order to improve and enhance their performance (glass or carbon fiber), to avoid (or limit) weathering or deterioration (stones, metal oxidation), and to understand or predict their behaviors (soils, rock reservoir, concrete, bones). ...
Different image processing techniques have recently been investigated for the characterization of complex porous media, such as bones, stones and soils. Among these techniques, 3D thinning algorithms are generally used to extract a one-voxel-thick skeleton from 3D porous objects while preserving the topological information. Models based on simplified skeletons have been shown to be efficient in retrieving morphological information from large scale disordered objects not only at a global level but also at a local level. In this paper, we present a series of 3D skeleton-based image processing techniques for evaluating the micro-architecture of large scale disordered porous media. The proposed skeleton method combines curve and surface thinning methods with the help of an enhanced shape classification algorithm. Results on two different porous objects demonstrate the ability of the proposed method to provide significant topological and morphological information.
... However, tomography methods, due to the specifics of sample preparation and the lack of adapted techniques, have not been previously used for urban soils. For this reason, the present work is based on a general understanding of the soil structure as the physical arrangement of soil matter determined by the size, shape, quantitative ratio, nature of interaction, mutual arrangement of elementary soil particles and their aggregates (Voronin, 1984;Perret et al., 1999;Delerue et al., 2003;Al-Raoush and Willson, 2005;Lehmann and Stahr, 2007). This definition includes three main groups of indicators of the structural state of disperse systems: morphometric, spatial-geometric and energetic (Osipov et al., 1989;Korost, 2012). ...
Urban soils are exposed to transformations of physical properties which are not captured by the conventional approaches due to the presence of impurities that can distort the obtained data. Advanced visualization techniques such as X-ray computed tomography (CT) offer new opportunities of exploring heterogeneity of soil properties at horizon or aggregate scales. The studies of the structure and pore space of different types of urban soils formed on chernozems were carried out using a SkyScan 1172G tomograph. The tomographic study was carried out in the humus-accumulative horizons for six main types of urban soils. The volumetric parameters for the pore space were calculated, and pores orientation and shape parameters were calculated in 2D sections. The closed pore value was obtained as the most informative diagnostic indicator of the urban soils structural condition. A morphometric analysis of the shape and orientation of fine soil macropores with a diameter of 0.3–2.0 mm also showed significant structural differences between natural soils under woody or grassy vegetation and urban anthropogenically transformed soils. All studied soils at the aggregate scales slightly differ from each other in the value of the internal aggregate tomographic porosity. This shows that the compaction because of anthropogenic transformation occurs due to the interaggregate pore space. At the aggregate porous spaces, no changes can be traced.
... When the surface crack ratio increases over 4%, a dramatic increase in normalized infiltration capacity is observed. This is likely because when the surface crack ratio is smaller than a certain value, the degree of crack development inside the soil sample is relatively low and cracks may not penetrate the soil sample (Delerue et al., 2003;Tang et al., 2019). The connection of crack network is not well built. ...
Infiltration is of great concern in many fields like hydrology, agriculture as well as geotechnical and geological engineering. This study aims to investigate water infiltration in a cracked soil. Infiltration tests were conducted on compacted soil samples with different cracking degrees by drying to various water contents. Three drying-wetting cycles were applied. Experimental results show that no desiccation cracks are observed in the first drying process while cracks initiate and propagate in the second and third drying processes. Different from the infiltration curve of the non-cracked soil sample consisting of two distinct stages, that of the cracked soil consists of three distinct stages, representing constant, rapid reduction and gradual reduction in infiltration rate, respectively. A modified equation is proposed to describe the infiltration behavior of a cracked soil considering the prehealing time of cracks. Furthermore, it is found that for the tested soil, 4% of surface crack ratio is a critical value. When surface crack ratio is smaller than the critical value, its influence on infiltration capacity is insignificant. Afterwards, the infiltration capacity increases dramatically with increasing surface crack ratio. Based on this observation, a piecewise function is proposed to characterize the relationship between the normalized infiltration capacity of cracked soil and surface crack ratio. Infiltration capacity also increases with decreasing initial water content and increasing number of drying-wetting cycles. In terms of steady final infiltration rate, it increases with increasing initial water content as well as increasing number of drying-wetting cycles, but is not affected by desiccation cracking.
... This allows the prediction of root effects on SHP via the linkage between root-soil-K s . Moreover, several researchers developed a pore network model (e.g., Pore-Core) combining the pore size and connectivity parameters using soil water distribution images by advanced X-ray tomography, which enabled the calculation of the K s (Delerue et al., 2003;Holtham et al., 2007;Matthews et al., 2010). ...
Regional-scale hydrological investigations that involve vegetation change usually neglect root-induced modification (RIM) of soil hydraulic properties (SHP). However, there is evidence that root distributions may impart major control over SHP. A critical barrier to incorporating RIM of SHP in catchment hydrology models is the high uncertainty of root-effect parameterization. In response to this, the current article reviews available literature to summarize the key processes, measurement, prediction and implications of RIM of SHP. Previous studies found contrasting root effects (on SHP) depending on which processes are dominant, including root growth (or decay) and the density and diameter of roots. Based on data from laboratory experiments and field testing, RIM of SHP can be summarized as: (1) fine roots (root diameter <1 mm) at low density tend to block soil pores, leading to reduced saturated water content (θs), saturated hydraulic conductivity (Ks), and higher air entry potential (AEP); (2) fine roots at high density tend to eliminate macro-pores while increasing pore volume, leading to increased θs and AEP, and reduced Ks; (3) coarse roots (root diameter >2 mm) tend to cause small-scale compaction, particle re-orientation and macro-pore development, leading to increased θs and Ks, and decreased AEP. Root growth also tends to enhance soil moisture retention hysteresis. Root decay is expected to have the opposite effects to root growth due to the creation of continuous macro-pores, which may lead to Ks increases of up to two orders-of-magnitude. In general, the enhancement of Ks due to plant roots can be expected in fine-textured soils, whereas plants roots are known to reduce Ks and θs and increase soil water retention capacity in coarse-textured soils. An important aspect of RIM of SHP is the temporal variability that arises from seasonality and/or agricultural cycles. While neglecting RIM of SHP in hydrologic simulation may lead to high uncertainties, there remain significant knowledge gaps that impede the development of quantitative guidance on RIM of SHP at the catchment scale, at which variability in environmental conditions and human activities precludes the application of simple root-effect equations.
... All rights reserved. BULTREYS ET AL.: WATERFLOODING SIMULATIONS WITH MULTI-SCALE PNM X -5 Vogel and Roth, 2001;Al-Raoush and Willson, 2005;Delerue et al., 2003; Ngom et al., 2011]. These PNM can be plugged in to quasi-static simulators to investigate two-phase flow properties of natural rocks, soils and sediments displaying different wetttabilities [Øren et al., 1998;Blunt et al., 2002;Patzek , 2001]. ...
The two-phase flow properties of natural rocks depend strongly on their pore structure and wettability, both of which are often heterogeneous throughout the rock. To better understand and predict these properties, image-based models are being developed. Resulting simulations are however problematic in several important classes of rocks with broad pore size distributions. We present a new multi-scale pore network model to simulate secondary waterflooding in these rocks, which may undergo wettability alteration after primary drainage. This novel approach permits to include the effect of microporosity on the imbibition sequence without the need to describe each individual micropore. Instead, we show that fluid transport through unresolved pores can be taken into account in an upscaled fashion, by the inclusion of symbolic links between macropores, resulting in strongly decreased computational demands. Rules to describe the behaviour of these links in the quasi-static invasion sequence are derived from percolation theory. The model is validated by comparison to a fully detailed network representation, which takes each separate micropore into account. Strongly and weakly water-and oil-wet simulations show good results, as do mixed-wettability scenarios with different pore-scale wettability distributions. We also show simulations on a network extracted from a micro-CT scan of Estaillades limestone, which yields good agreement with water-wet and mixed-wet experimental results.
... During weathering, high-aperture fractures (or macrocracks) develop but fragment the rock, strongly diminishing its mechanical resistance, but greatly increasing its permeability (Røyne et al., 2008;Faulkner et al., 2011). The main solute transport process operating in macrocracks is flow (Beven and Germann, 1982;Moreau et al., 1996;Delerue et al., 2003). Microcracks and microporosity provide most of the reactive surface area made more available by macrofractures. ...
The progressive development of porosity during subsoil weathering of granodiorite clasts was studied at the Bishop Creek moraine chronosequence in east-central California. Fractures and other pores were examined using two complementary imaging techniques, X-ray computed tomography (XRCT) and a ¹⁴C-PMMA (¹⁴C-polymethylmethacrylate) method. The well-known XRCT method allows the investigation of three-dimensional (3-D) pore space. ¹⁴CPMMA is a less-known method based on the complete impregnation of pore space with ¹⁴C-doped PMMA, and subsequent autoradiograph of a rock section. These imaging methods allow us to decipher the evolution of pore space in the granodiorite during the 120 k.y. weathering period. The ¹⁴C-PMMA imaging technique was found to be more suitable for following the evolution of the whole sequence, from "intact" bedrock to saprock, in terms of crack density, porosity, and aperture. Working with hand specimens, this method was adapted to detect both the lowaperture fractures (microcracks) and macrocracks. Only a slight and progressive increase in total fracture density was observed during the whole weathering period. However, this trend does not hold if macrocracks and microcracks are separated: Microcrack density slightly decreases, whereas macrocrack density increases due to a progressive expansion of microcracks. The total porosity of the rock increases during weathering and is correlated to the progressive aperture increase of all types of cracks. This evolution is accompanied by a change of crack morphology and connectivity, and an overall increase in intragranular porosity of biotite and plagioclase aggregates.
... In their researches, Delerue et al. (2003) successfully developed a pore network directly from soil images by integrating pore size and connectivity parameters, which enabled calculation of the equivalent hydraulic conductivity from a 3D image of any porous soil. ...
In this paper we present a review of the application of X-ray computed tomography in soil science, a modern technique for structural analysis. The quantification of internal soil structure is the key in understanding the processes that lead to its development. The current analytical and traditional methods for exploring soil structure do not fully cover the needs of the researchers, in order to characterize the soil system and its properties. In the last decades, X-ray computed tomography has provided a non-destructive means in order to observe and quantify soils in 3D. It has been used in researches regarding the spatial distribution of soil pores, bulk density, macropore network structure, layer detection, permeability, calculated fractal properties, solute breakthrough, root system development etc. Compared to other analysis methods, the short time requiered for a CT scan (within the order of minutes) and the accuracy of the data provided, recommend this technique for the characterization of soil systems.
... X-ray computed tomography (CT) was initially developed as a 3-D medical imaging technique (Hounsfield, 1973). In the last ten years, X-ray computed tomography was used in several fields of the geosciences such as palaeontology (Brochu, 2000), metamorphic geology , soils (Delerue et al. 2003), meteorites (Kondo et al. 1997) or, more recently, economic geology (Barnes et al. 2007;Godel et al. 2006;Kyle and Ketcham, 2003;Kyle et al. 2004). Xray CT allows acquiring sequential series of images of rock samples of various sizes (< 1 cm up to several tens of centimetres). ...
The Merensky Reef of the Bushveld Complex (South Africa) and the J-M Reef of the Stillwater Complex (U.S.A.) are two layers enriched in platinum-group elements (PGE). In the last few years, several multidisciplinary studies were carried out on samples from these reefs. This includes: 3-D analysis by X-ray computed tomography, in-situ minerals (base-metal sulphide, chromite and primary silicate) or fluid inclusions analysis using laser-ablation ICP-MS, and detailed analysis of the platinum-group minerals (PGM). According to the results of these studies, in both reefs, the PGE are found either in solid-solution in the base-metal sulphides (BMS) or as PGM closely associated with the BMS. No PGE are present in the silicate or oxide lattices. Initially, the PGE were collected by a BMS sulphide liquid that interacted with silicate magma fertile in PGE. Then, the sulphide liquid may have percolated downward along vertical dilatancies formed during the compaction of the cumulate pile and may have stopped where the permeability is too low to allow it to further migrate. The PGE and base-metals were then redistributed either at a local scale (e.g. exsolution of the PGM from the BMS during cooling or partial desulphurization) or at a larger scale as observed in the J-M Reef. In this case, the Pd and to a lesser extent Pt may have been leached (possibly from the footwall) and then reprecipitated at the level of the reef by fluids (either liquid or vapour) during alteration and/or metamorphic events.
... ure, localized soil deformation and local strain analysis over very small spatial scales (<1 mm). Our understanding of these mechanisms at the microscale level is crucial to further understanding of the processes behind soil stabilization and structural development and support improvements in conceptual model development of geometric pore networks. Delerue et al . (2003) successfully developed a pore network directly from soil images by integrating pore size and connectivity parameters, which enabled calculation of the equivalent hydraulic conductivity from a 3D image of any porous soil. Likewise, Al-Raoush & Willson (2005) used skeletonization algorithms (thinning operations, which systematically remov ...
Soil systems are characterized by the spatial and temporal distribution of organic and mineral particles, water and air within a soil profile. Investigations into the complex interactions between soil constituents have greatly benefited from the advent of non‐invasive techniques for structural analysis. In this paper we present a review of the application of one such technique, X‐ray computed tomography (CT), for studies of undisturbed soil systems, focusing on research during the last 10 years in particular. The ability to undertake three‐dimensional imaging has provided valuable insights regarding the quantitative assessment of soil features, in a way previously unachievable because of the opaque nature of soil. A dynamic approach to the evaluation of soil pore networks, hydro‐physical characteristics and soil faunal behaviour has seen numerous scanning methodologies employed and a diverse range of image analysis protocols used. This has shed light on functional processes across multiple scales whilst also bringing its own challenges. In particular, much work has been carried out to link a soil's porous architecture with hydraulic function, although new technical improvements allowing the characterization of organic matter and the influence of soil biota on structural development are showing great promise. Here we summarize the development of X‐ray CT in soil science, highlight the major issues relating to its use, outline some of the applications for overcoming these challenges and describe the potential of future technological advances for non‐invasive soil characterization through integration with other complementary techniques.
... (b) Generalized stratigraphy of the Bushveld Complex (modified after Eales & Cawthorn, 1996).(Carlson & Denison, 1992;), sedimentary rocks (Flisch & Becker, 2003; Michaud et al., 2003), soils (Delerue et al., 2003), meteorites (Kondo et al., 1997), fossils (Brochu, 2000) or ores (Kyle & Ketcham, 2003; Kyle et al., 2004). The details of the principle and the functioning of X-ray CT have been developed in many papers ( Ketcham & Carlson, 2001; Mees et al., 2003; Ketcham & Iturrino, 2005) and only a brief description is given here. ...
Large mafic–ultramafic layered intrusions may contain layers enriched in platinum-group elements (PGE). In many cases, the PGE are hosted by disseminated sulphides. We have investigated the distribution of the sulphides in three dimensions in two oriented samples of the Merensky Reef and the J-M Reef. The aim of the study was to test the hypothesis that the sulphides crystallized from a base metal sulphide liquid that percolated through the cumulate pile during compaction. The distribution of sulphides was quantified using: (1) X-ray computed tomography; (2) microstructural analysis of polished thin sections oriented parallel to the paleovertical; (3) measurement of dihedral angles between sulphides and silicates or oxides. In the Merensky Reef and the J-M Reef, sulphides are connected in three dimensions and fill paleovertical dilatancies formed during compaction, which facilitated the downward migration of sulphide liquid in the cumulate. In the melanorite of the Merensky Reef, the sulphide content increases from top to bottom, reaching a maximum value above the underlying chromitite layer. In the chromitite layers sulphide melt connectivity is negligible. Thus, the chromitite may have acted as a filter, preventing extensive migration of sulphide melt downwards into the footwall. This could partially explain the enrichment in PGE of the chromitite layer and the observed paucity of sulphide in the footwall.
This study utilizes the capability of X-ray-computed tomography (CT) in the quantitative characterization of unconsolidated Quaternary sediments. Integrating CT scans with grain size endmember modeling (EMM) offers a novel approach to understanding sedimentological processes. The CT scans were analyzed to delineate Hounsfield Unit (HU) distributions, identifying four distinct density components reflective of varied sediment types. This classification, grounded in Gaussian mixture modeling, reveals intricate details of the sedimentary texture and its relation to depositional dynamics. The EMM further unraveled the textural complexity of the sediments, correlating CT-derived density variations with specific grain size fractions. This analysis illuminated the stratigraphic interplay between finer and coarser materials, indicative of alternating depositional energies within a dynamic fluvial-lacustrine setting. Principal Component Analysis (PCA) augmented this understanding, distilling the core’s complex sedimentology into principal factors that govern grain size distribution and density variations. Combining CT imaging with granulometric analysis provides a robust methodology for reconstructing depositional environments; this not only enhances our grasp of Quaternary sediment dynamics but also establishes a framework for future exploration in paleoenvironmental reconstruction.
The brine pore space in sea ice can form complex connected structures whose geometry is critical in the governance of important physical transport processes between the ocean, sea ice, and surface. Recent advances in three-dimensional imaging using X-ray micro-computed tomography have enabled the visualization and quantification of the brine network morphology and variability. Using imaging of first-year sea ice samples at in situ temperatures, we create a new mathematical network model to characterize the topology and connectivity of the brine channels. This model provides a statistical framework where we can characterize the pore networks via two parameters, depth and temperature, for use in dynamical sea ice models. Our approach advances the quantification of brine connectivity in sea ice, which can help investigations of bulk physical properties, such as fluid permeability, that are key in both global and regional sea ice models.
The brine network in sea ice is a complex labyrinth whose precise microstructure is critical in governing the movement of brine and gas between the ocean and the sea ice surface. Recent advances in three-dimensional imaging using x-ray micro-computed tomography have enabled the visualization and quantification of the brine network morphology and variability. Using imaging of first-year sea ice samples at in-situ temperatures, we create a new mathematical network model to characterize the topology and connectivity of the brine channels. This model provides a statistical framework where we can characterize the pore networks via two parameters, depth and temperature, for use in dynamical sea ice models. Our approach advances the quantification of brine connectivity in sea ice, which can help investigations of bulk physical properties, such as fluid permeability, that are key in both global and regional sea ice models.
The study of the spatial configuration of soil, in its complexity, requires an understanding of the interrelations and interactions between the diverse soil constituents, at various levels of organization. Investigations of the spatial arrangement of the mineral and organic components of soil have benefited from the development of techniques for structural analysis. X-ray computed tomography (CT) is a non-destructive and non-invasive technique that has been successfully used for three-dimensional (3D) examination of soil. Valuable information has been obtained by the application of CT for the description and quantitative measurements of soil structure elements, especially of soil pores and pore network features. In many studies, X-ray CT has been used to investigate the hydro-physical characteristics of the soil, in a functional and temporal manner. A dynamic approach has also been utilized in the evaluation of the biotic factor influence on soil. The analysis of soil solid phases, by X-ray CT, has been challenging due to the similar X-ray attenuation of different solid constituents. However, the use of multiple X-ray energy levels has facilitated the discrimination of minerals in soil. The aim of this review and synthesis is to offer a perspective on the major issues related to application of the technique, general attempted solutions and possible directions in the utilization of X-ray CT in soil research. Relevant scanning parameters, procedures for CT image reconstruction, algorithms for the quantification of soil characteristics and results are presented for each type of application.
The application of X-ray computed tomography (CT) in soil micromorphology has motivated researchers to quantify soil structure, particularly void space, for three dimensional analysis. The objective of this study was comparison of optical and a proposed CT method for void space determination, using a set of four thin section samples. The thin section samples were imaged for optical data using plain polarized, cross polarized and oblique incidental light. CT imaging used a D reconstruction to attain the average X-ray attenuation value of the thin section. After registering the two imagery types, an identical region of optical and CT imagery was extracted for analysis. Optical and CT imagery was classified as void or solid, from which simple characteristics of soil-voids were obtained. The characterization of voids indicated that the optical method was proficient in identifying continuous and linear void features, whereas CT readily identified a greater number of voids with higher circularity. The data also suggested that the CT method identified a greater degree of void space in thin section than was evident to the optical classification. The results of binary comparison imply that CT identified a category of void often overlooked by optical imagery classification and therefore would make an excellent complementary technique to the soil micromorphology tool set.
X-ray computed microtomography (μCT), a non-destructive analytical technique, was used to create volumetric three-dimensional (3D) models representing the internal composition and structure of undisturbed pro- and subglacial soft sediment sample plugs for the purposes of identifying and analysing kinematic indicators. The technique is introduced and a methodology is presented addressing specific issues relating to the investigation of unlithified, polymineralic sediments.Six samples were selected based on their proximity to ‘type’ brittle and ductile deformation structures, or because of their perceived suitability for successful application of the technique. Analysis of a proglacial ‘ideal’ specimen permitted the 3D geometry of a suite of micro-faults and folds to be investigated and the strain history of the sample reconstructed. The poor contrast achieved in scanning a diamicton of glaciomarine origin is attributable to overconsolidation under normal loading, the sediment demonstrated to have undergone subsequent subglacial deformation. Another overconsolidated diamicton contains an extensive, small scale (<20 μm) network of fractures delineating a ‘marble-bed’ structure, hitherto unknown at this scale. A volcanic lithic clast contrasts well with the surrounding matrix in a ‘lodgement’ till sample containing μCT (void) and thin-section evidence of clast ploughing. Initial ductile deformation was followed by dewatering of the matrix, which led to brittle failure and subsequent emplacement. Compelling evidence of clast rotation is located in the top of another sample, μCT analysis revealing that the grain has a proximal décollement surface orientated parallel to the plane of shear. The lenticular morphology of the rotational structure defined suggests an unequal distribution of forces along two of the principal stress axes. The excellent contrast between erratics contained within a sample and the enclosing till highlight the considerable potential of the technique in permitting the rapid (semi-)quantitative analysis of large datasets.The subglacial sample evidence indicates that complex, polyphase (brittle/ductile) deformation histories are common in such diamictic soft sediments and that the local (micro-scale) environment (composition, structure, shear forces and effective pressure) controls rheology. The sediment void ratio is a key indicator of strain. Three of the samples are tentatively placed at different points on the strain cycle for subglacially deforming soft sediment, based on their void ratio, characteristics and distribution.It has been demonstrated that μCT offers significant potential for elucidating glacial soft sediment kinematics. The ability of the technique to both test a variety of hypotheses pertaining to mechanisms operating within the subglacial environment and evaluate efforts to replicate those processes under controlled, laboratory conditions is therefore discussed along with solutions to the problems encountered within this project. μCT also permits the seamless linking of analytical techniques applied at the hand specimen (mm), micromorphological (μm-mm), scanning electron microscopy and X-ray diffraction/fluorescence (nm-μm) scales and the archiving, duplication and dissemination of sample volumetric 3D data.Highlights► The research has demonstrated that μCT is a highly effective, non-destructive technique. ► The kinematics of subglacial sediments are more complex than can be evaluated by 2D analysis. ► Void characteristics can be quantitatively and qualitatively evaluated using μCT. ► Local conditions are key to the rheological response of sediment to an applied shear stress. ► Subglacial soft sediment deformation is cyclical, the strain signature composite in nature.
A three-dimensional porous medium model that pertains to consolidated permeable porous rocks and similar structures is proposed. The porous medium is considered as a network of chambers connected through long narrow throats and it is approximated as a network of unit cells of the constricted tube type. The skeleton of the network can be either regular or randomized, and the throat-to-chamber coordination number can be varied by randomly removing a number of throats. The sizes of contiguous chambers and throats can be cither independent random variables, or they can be correlated. This correlation can be positive (large chambers preferring large throats), or negative (large chambers preferring small throats). The permeability of the network is found to be minimal when the chambers and throats are completely uncorrected. The degree of correlation also affects the throat-to-chamber size ratio, a parameter which is very important in two-phase flows through porous media. A substantial correlation between the local intensity of the flow field on one hand and the local porosity and throat diameter on the other is found. @KEYWORDS: Pore network model, Consolidated porous media.
A formal system is presented for the differentiation of mathematical formulas which can be implemented on a digital computer. The system departs in concept from others in that the programming language is nonprocedural, permitting the statement of the ...
The three-dimensional geometry and connectivity of pore space controls the hydraulic transport behavior of crustal rocks. We report on direct measurement of flow-relevant geometrical properties of the void space in a suite of 4 samples of Fontainebleau sandstone ranging from 7.5% to 22% porosity. The measurements are obtained from computer analysis of three dimensional, synchrotron X-ray computed microtomographic images. We present measured distributions of coordination number, channel length, throat size and pore volume, and of correlations between throat-size/pore-volume and nearest neighbor pore-volume/pore volume determined for these samples. We also present quantitative characterization of the distributions measured. The effects of finite sample volume are investigated. The accuracy of the numerical algorithms employed is investigated using a simulated image of hexagonal closed packed spheres.
In this paper, we present an efficient three-dimensional (3-D) parallel thinning algorithm for extracting both the medial surfaces and the medial axes of a 3-D object (given as a 3-D binary image). A new Euler table is derived to ensure the invariance of the Euler characteristic of the object, during thinning. An octree data structure of 3 × 3 × 3 lattice points is built to examine the local connectivity. The sets of "simple" points found by different researchers are compared with the constructed set. Different definitions of "surface" points including ours are given. By preserving the topological and the geometrical conditions, our algorithm produces desirable skeletons and performs better than others in terms of noise sensitivity and speed. Pre- and postprocessors can be used to remove additional noise spurs. Its use in defect analysis of objects produced by casting and forging is discussed.
Functional relationships for unsaturated flow in soils, including those between capillary pressure, saturation, and relative permeabilities, are often described using analytical models based on the bundle-of-tubes concept. These models are often limited by, for example, inherent difficulties in prediction of absolute permeabilities, and in incorporation of a discontinuous nonwetting phase. To overcome these difficulties, an alternative approach may be formulated using pore-scale network models. In this approach, the pore space of the network model is adjusted to match retention data, and absolute and relative permeabilities are then calculated. A new approach that allows more general assignments of pore sizes within the network model provides for greater flexibility to match measured data. This additional flexibility is especially important for simultaneous modeling of main imbibition and drainage branches. Through comparisons between the network model results, analytical model results, and measured data for a variety of both undisturbed and repacked soils, the network model is seen to match capillary pressure-saturation data nearly as well as the analytical model, to predict water phase relative permeabilities equally well, and to predict gas phase relative permeabilities significantly better than the analytical model. The network model also provides very good estimates for intrinsic permeability and thus for absolute permeabilities. Both the network model and the analytical model lost accuracy in predicting relative water permeabilities for soils characterized by a van Genuchten exponent n
The conduction of water by soil is fundamental to the way in which soils transport nutrients and pollutants into groundwater. The derivation of relations between water flow and void structure has relied on the implicit assumption that water flows through aligned unconnected cylindrical capillary tubes. We describe a three-dimensionally interconnected model of void structure, called Pore-Cor, which simulates the intrusion of a non-wetting fluid and drainage of a wetting fluid. The model is calibrated by fitting it to the water retention curves of a sandy soil at four depths. The experimental drainage pressures are related to the radii of the entries to the voids by the Laplace equation. The necessities of using this equation, and of employing a simplified void geometry, introduce major approximations into the modelling. Nevertheless, the model is sufficiently precise and versatile to predict trends in other properties usefully. It is illustrated in this work by a close correlation between a predicted and experimental change in saturated hydraulic conductivity with depth, and a realistic unsaturated hydraulic conductivity curve. The saturated and unsaturated hydraulic values are shown to be much more realistic than those predicted by the aligned cylinders model. In addition, the simulations by Pore-Cor indicate that the void network within the sandy soil is acting in a structured rather than a random manner. The Pore-Cor model is currently being used to explain the matrix-flow characteristics of tracers and pollutants.
A system, ANOPOR, has been developed which uses the Quantimet 720 image analyser to recognize and measure the different types of pores in impregnated soil blocks. The system is concerned with three types of pores: channels, planar voids (cracks and fissures) and vughs but is not suitable for highly interconnected pore patterns. Each of the three types has a different origin and function and presents a different two-dimensional (2-D) shape when sectioned.
A learning set consisting of these three pore classes was used to teach the system how to recognize statistically soil pores in images using measurements made by Quantimet. To describe the pore outlines in 2-D, shape factors giving the best class separation of the learning set in the pattern space were derived. Bayes equation was used to give the probability of a pore belonging to a particular class by comparing its position in the pattern space with the learning set. Class boundaries were determined which ANOPOR uses to allocate each pore in any image to the most likely class. The system measures the proportion of the pore space attributable to each class and the perimeter and intercept density for each. The system is used to measure the pore patterns in three soil horizons.
The wettability of a crude oil/brine/rock system is of central importance in determining the oil recovery efficiency of water displacement processes in oil reservoirs. Wettability of a rock sample has traditionally been measured using one of two experimental techniques, viz. the United States Bureau of Mines and Amott tests. The former gives the USBM index, I
USBM, and the latter yields the Amott–Harvey index, I
AH. As there is no well-established theoretical basis for either test, any relationship between the two indices remains unclear.Analytical relationships between I
AH and I
USBM for mixed-wet and fractionally-wet media have been based on a number of simplifying assumptions relating to the underlying pore-scale displacement mechanisms. This simple approach provides some guidelines regarding the influence of the distribution of oil-wet surfaces within the porous medium on I
AH and I
USBM. More detailed insight into the relationship between I
AH and I
USBM is provided by modelling the pore-scale displacement processes in a network of interconnected pores. The effects of pore size distribution, interconnectivity, displacement mechanisms, distribution of volume and of oil-wet pores within the pore space have all been investigated by means of the network model.The results of these analytical calculations and network simulations show that I
AH and I
USBM need not be identical. Moreover, the calculated indices and the relationship between them suggest explanations for some of the trends that appear in experimental data when both I
USBM and I
AH have been reported in the literature for tests with comparable fluids and solids. Such calculations should help with the design of more informative wettability tests in the future.
Recent research efforts have focused on using simple non-circular cross-sectional pore shapes to honour the physics observed at the pore scale. For example, there is evidence to suggest variations of wettability occur at this level. These pores can exhibit water-wet and oil-wet regions, depending on the physics of wetting films, and hence the porous medium maybe of mixed-wettability character. For low water saturations, electrical resistivity cannot be physically simulated at the pore scale using cylindrical tubes, even though wetting film thickness' and pore constrictions are taken into account.A three-dimensional network model that investigates the petrophysical characteristics, electrical resistivity and capillary pressure, is presented. The influence of saturation history is also modelled. Key pore geometrical attributes such as pore shape, aspect ratio, pore coordination number (pore connectivity) and pore size distribution are included in the model. In addition, pore constrictions are introduced which may result in phase trapping via snap-off within the tube itself.Analysis of our developing network model starting from representing the pore shape as circular is presented. Using a simple non-circular cross-sectional pore shape we show bulk water retained in the crevices give rise to predictions that are in close agreement with electrical resistivity and capillary pressure trends observed in experiments. Numerical results are presented and compared with experimental data.
We review the current status of modeling multiphase systems, including balance equation formulation, constitutive relations for both pressure-saturation-conductivity and interphase mass transfer, and stochastic and computational issues. We discuss weaknesses and inconsistencies of current approaches based on theoretical, computational, and experimental evidence. Where possible, we suggest new or evolving approaches.
Continuous filtration of fine particles involves filter cake formation and removal of surface moisture by drawing air through the pore structure network. Conventional network theory can be used to study the phenomena of flow through a porous structure by treating the pores as discrete volumes and connecting these with pore throats as resistances of zero volume. In this regard, analysis of the pore connectivity in a packed bed of particles should allow for a detailed description of fluid flow and transport in the filter cake structure. As the resolution and the techniques for 3-D geometric analysis have advanced in the last decade, it is now possible to specify in detail the pore structure in three-dimensional digital space using high-resolution X-ray microtomography to resolve features with micrometer resolution. This paper presents preliminary experimental findings of a filter cake pore structure in 3-D using X-ray microtomographic techniques.
Processes of fluid transport through underground reservoirs are closely related with microscopic properties of the pore structure. In the present work, a relatively simple method is developed for the determination of the topological and geometrical parameters of the pore space of sedimentary rocks, in terms of chamber-and-throat networks. Several parameters, such as the chamber-diameter distribution and the mean specific genus of the pore network are obtained from the serial sectioning analysis of double porecasts. This information is used in the computer-aided construction of a chamber-and-throat network which is to be used for further analysis. Mercury porosimetry curves are fitted to either 2-parameter or 5-parameter non-linear analytic functions which are identified by the median pressures, mean slopes and breakthrough pressures. A simulator of mercury intrusion/retraction, incorporating the results of serial tomography, in conjuction with the experimental mercury porosimetry curves of the porous solid are used iteratively to estimate the throat-diameter distribution, spatial correlation coefficients of pore sizes and parameters characterizing the pore-wall roughness. Estimation of the parameter values is performed by fitting the simulated mercury porosimetry curves to the experimental ones in terms of the macroscopic parameters of the analytic functions. The validity of the pore space characterization is evaluated through the correct prediction of the absolute permeability. The method is demonstrated with its application to an outcrop Grey-Vosgues sandstone.
Pore-network models are attractive to relate pore geometry and transport processes in soil. In this contribution a `morphological path' is presented to generate a network model based on quantitative morphological investigations of the 3D pore geometry in order to predict soil hydraulic properties. The 3D-geometry of pores larger than 0.04 mm in diameter is obtained using serial sections through impregnated samples. Beside pore-size distribution an important topological aspect of pore geometry is the spatial connectivity of the pore space which is difficult to measure. A connectivity function is proposed defined by the 3D-Euler number. The goodness in the estimation of the Euler number using serial sections is investigated in subsamples of different sizes and shapes. Then, a simple network model is generated which can be adapted to a predefined pore-size distribution and connectivity function. Network simulations of hydraulic properties are compared to independent measurements at the same soil material and the effect of topology on water flow and solute transport is investigated. It is concluded that a rough estimation of pore-size distribution and topology defined by the connectivity function might be sufficient to predict hydraulic properties.
Using large scale computer simulations and pore network models of porous rock, we investigate the effect of correlated heterogeneity on two-phase flow through porous media. First, we review and discuss the experimental evidence for correlated heterogeneity. We then employ the invasion percolation model of two-phase flow in porous media to study the effect of correlated heterogeneity on rate-controlled mercury porosimetry, the breakthrough and residual saturations, and the size distribution of clusters of trapped fluids that are formed during invasion of a porous medium by a fluid. For all the cases we compare the results with those for random (uncorrelated) systems, and show that the simulation results are consistent with the experimental data only if the heterogeneity of the pore space is correlated. In addition, we also describe a highly efficient algorithm for simulation of two-phase flow and invasion percolation that makes it possible to consider very large networks.
We present spatial distributions for pore path length and coordination number, pore throat size and nodal pore volume obtained for a 1.53 mm3 volume of 12.1% porosity Fontainebleau sandstone. The sandstone was imaged using Synchrotron X-Ray computed microtomography at 6 micron resolution. The spatial distributions were computed based upon three dimensional medial axis analysis of the void space in the image. We also present vesicle size and vesicle-vesicle contact surface area distributions for a 1.36 mm length of a 6.36 mm diameter core of basalt from a vesiculated lava flow imaged at 20 micron resolution.
We introduce a skeletization method based on the Voronoi diagram to determine local pore sizes in any porous medium. Using the skeleton of the pore space in a 3D image of the porous medium, a pore size value is assigned to each voxel and a reconstructed image of a spatialized local pore size distribution is created. The reconstructed image provides a means for calculating the global volume versus size pore distribution. It is also used to carry out fluid invasion simulation which take into account the connectivity of and constrictions in the pore network. As an example we simulate mercury intrusion in a 3D soil image.
A methodology is presented for the simultaneous prediction of absolute permeabilities, formation resistivity factors and drainage capillary pressure curves of sandstones by employing a network model of pore structure based on bond-correlated site percolation concepts. The model is a regular cubic lattice consisting of pore throats and pore bodies, having respective pore size distributions. Information about the pore structure, obtained from mercury porosimetry and photomicrographic analysis, is utilized to select the pore throat and pore body size distributions in a manner such that the resulting model (i) matches the porosity of the medium and (ii) satisfactorily simulates the drainage capillary pressure curve of the porous medium under consideration. Assumptions made about the cross-sectional shape of the pore throats and their effect on the network model predictions are discussed. Details of the methodology used in the simulation of transport properties with microscopic pore structure parameters are also presented and discussed. The problem of fluid and electric current flow through the simulated porous medium is reduced to an electric analogue-linear network problem and is numerically solved using a conjugate gradients method for computing the absolute permeability and the formation resistivity factor. Good agreement between the predicted and the measured values is observed for a number of sandstone samples having widely different transport properties.
Our goal is to implement skeletonization algorithms on distribution memory mechines. This implementation is not trivial, because we cannot apply locally thinning operators based on 26-neighborhood, sequentially or simultaneously on all the points of the image. After summarizing the problem, we describe two methodologies to implement these algorithms on MIMD machines, one based on the decomposition of the thinning operator into sub-operators, and the other based on the decomposition of the study domain (image) into sub-domains.
To study relationships between soil hydraulic properties and soil structural properties, a computer micro model of soil is constructed. We present first a general method of building a two-dimensional porous structure, including both pores and particles, with different levels of aggregation resulting from a fragmentation process. A fractal structure is obtained when self similarity is imposed over the successive scales of fragmentation. Emphasis is put upon the modeling of the retention curve. A classical capillary model and methods taken from percolation theory enable us to simulate qualitatively the primary and secondary loops of this hysteretic curve. In the fractal case, theoretical analytical expressions proposed for adjusting retention data are tested. The unsaturated hydraulic conductivity is also calculated on the same simulated soil by analogy with an electrical network. The soil structures are deformable and simulation proves to be a useful tool to investigate the behavior of swelling soils.
A comprehensive survey of thinning methodologies is presented. A wide range of thinning algorithms, including iterative deletion of pixels and nonpixel-based methods, is covered. Skeletonization algorithms based on medial axis and other distance transforms are not considered. An overview of the iterative thinning process and the pixel-deletion criteria needed to preserve the connectivity of the image pattern is given first. Thinning algorithms are then considered in terms of these criteria and their modes of operation. Nonpixel-based methods that usually produce a center line of the pattern directly in one pass without examining all the individual pixels are discussed. The algorithms are considered in great detail and scope, and the relationships among them are explored
Skeletons are useful shape abstractions and have varied applications in visualization. The complexity of the desired skeletal structure depends on the application. Current techniques for extracting skeletons do not allow control over the complexity. In this paper, we describe an algorithm which uses a thinness parameter to control the density of the skeleton. We present applications from CFD and medical visualization and show how the skeletal structure can be used in these domains. We also illustrate a technique which uses the skeleton to extract the centerline for surgical navigation. Keywords:Scientific Visualization, Medical Visualization, Skeleton, Volume Thinning, Centerline, Surgical Navigation ii Acknowledgement The research reported here was made possible through the support of the New Jersey Commission on Science and Technology and the CAIP Center's Industrial Members. The work for this paper was done at the Laboratory for Visiometrics and Modeling at Rutgers ...
A mathematical description and representation of 2D and 3D shape, capable of hierarchically decomposing complex objects, is at the focus of this paper. The development is based on a hierarchic extension to the Medial Axis Transformation (MAT). Our implementation of the hierarchic MAT (HMAT) combines full Voronoi tessellation generated by the set of border points with regularization procedures to obtain a hierarchy of geometrically and topologically correct medial manifolds. This hierarchy defines a skeleton pyramid allowing shape-driven decomposition in 2D and 3D. The proposed methodology is illustrated in 2D on a planar section through a 3D MRI data set of the human brain. The hierarchical decomposition indicates the process history of brain development. For further analysis, it is converted into a boundary representation. The 3D extension of the HMAT concept is tested and illustrated on synthetic objects. It is applied to the full 3D MRI data set to obtain a description of the sulci ...
Modelling of Transport Processes in Soils, A flexible and effective pre-correction algorithm for non medical applications with clinical X-ray CT scanners
- A Timmerman
- K Vandersteen
- T Fushs
- J V Cleynenbreuge
- J Feyen
Laboratory measurement of hydraulic conductivity of saturated soil Methods of Soil Analysis. Physical and Mineralogical Properties, including Statistics of Measurement and Sampling
- A Klute
- C A Black
- Klute A.