共查询到20条相似文献，搜索用时 15 毫秒
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Todd H. Skaggs 《Advances in water resources》2011,34(10):1335-1342
Critical path analysis (CPA) is a method for estimating macroscopic transport coefficients of heterogeneous materials that are highly disordered at the micro-scale. Developed originally to model conduction in semiconductors, numerous researchers have noted that CPA might also have relevance to flow and transport processes in porous media. However, the results of several numerical investigations of critical path analysis on pore network models raise questions about the applicability of CPA to porous media. Among other things, these studies found that (i) in well-connected 3D networks, CPA predictions were inaccurate and became worse when heterogeneity was increased; and (ii) CPA could not fully explain the transport properties of 2D networks. To better understand the applicability of CPA to porous media, we made numerical computations of permeability and electrical conductivity on 2D and 3D networks with differing pore-size distributions and geometries. A new CPA model for the relationship between the permeability and electrical conductivity was found to be in good agreement with numerical data, and to be a significant improvement over a classical CPA model. In sufficiently disordered 3D networks, the new CPA prediction was within ±20% of the true value, and was nearly optimal in terms of minimizing the squared prediction errors across differing network configurations. The agreement of CPA predictions with 2D network computations was similarly good, although 2D networks are in general not well-suited for evaluating CPA. Numerical transport coefficients derived for regular 3D networks of slit-shaped pores were found to be in better agreement with experimental data from rock samples than were coefficients derived for networks of cylindrical pores. 相似文献
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We present a model for pore spaces that consists of two parts related by duality: (1) a decomposition of an open polyhedral pore space into open contractible pore bodies separated by relatively open interfaces and (2) a pore network that is homotopy equivalent to the pore space. The dual model is unique and free of parameters, but it relies on regularity conditions for the pore space. We show how to approximate any pore space by the interior of a polyhedral complex such that the regularity conditions are fulfilled. Thus, we are able to calculate the dual model from synthetic porous media and images of real porous media. The pore bodies are unions of relatively open Delaunay cells with respect to the corners of the pore boundary, and the pore network consists of certain at most two-dimensional (2D) Voronoi cells with respect to the corners of the pore boundary. The pore network describes the neighborhood relations between the pore bodies. In particular, any relatively open 2D Delaunay face f separating two pore bodies has a unique (relatively open) dual network edge. In our model, f is a pore throat only if it is hit by its dual network edge. Thus, as opposed to widespread intuition, any pore throat is convex, and adjacent pore bodies are not necessarily separated by pore throats. Due to the duality between the pore network and the decomposition of the pore space into pore bodies it is straightforward to store the geometrical properties of the pore bodies [pore throats] as attributes of the dual network vertices [edges]. Such an attributed network is used to perform 2D drainage simulations. The results agree very well with those from a pore-morphology based modeling approach performed directly on the digital image of a porous medium. Contractibility of the pore bodies and homotopy equivalence of the pore space and the pore network is proven using discrete Morse theory and the nerve theorem from combinatorial topology. 相似文献
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The reconstruction of the architecture of void space in porous media is a challenging task, since porous media contain pore structures at multiple scales. Whereas past methods have been limited to producing samples with matching statistical behavior, the patterns of grey-level values in a measured sample actually say something about the unresolved details, thus we propose a statistical fusion framework for reconstructing high-resolution porous media images from low-resolution measurements. The proposed framework is based on a posterior sampling approach in which information obtained by low-resolution (MRI or X-ray) measurements is combined with prior models inferred from high-resolution microscopic data, typically 2D. In this paper, we focus on two-scale reconstruction tasks in which the measurements resolve only the large scale structures, leaving the small-scale to be inferred. The evaluation of the results generated by the proposed method shows the strong ability of the proposed method in reconstructing fine-scale structures positively correlated with the underlying ground truth. Comparing our method with the recent method of Okabe and Blunt [12], in which the measurements are also used in the reconstruction, we conclude that our method is more robust to the resolution of the measurement, and more closely matches the underlying fine-scale field. 相似文献
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《Advances in water resources》2007,30(6-7):1648-1667
A new simulator is developed for the prediction of the rate and pattern of growth of biofilms in granular porous media. The biofilm is considered as a heterogeneous porous material that exhibits a hierarchy of length scales. An effective-medium model is used to calculate the local hydraulic permeability and diffusion coefficient in the biofilm, as functions of the local geometric and physicochemical properties. The Navier–Stokes equations and the Brinkman equation are solved numerically to determine the velocity and pressure fields within the pore space and the biofilm, respectively. Biofilm fragments become detached if they are exposed to shear stress higher than a critical value. The detached fragments re-enter into the fluid stream and move within the pore space until they exit from the system or become reattached to downstream grain or biofilm surfaces. A Lagrangian-type simulation is used to determine the trajectories of detached fragments. The spatiotemporal distributions of a carbon source, an electron acceptor and a cell-to-cell signaling molecule are determined from the numerical solution of the governing convection–diffusion–reaction equations. The simulator incorporates growth and apoptosis kinetics for the bacterial cells and production and lysis kinetics for the EPS. The specific growth rate of active bacterial cells depends on the local concentrations of nutrients, mechanical stresses, and a quorum sensing mechanism. Growth-induced deformation of the biofilms is implemented with a cellular automaton approach. In this work, the spatiotemporal evolution of biofilms in the pore space of a 2D granular medium is simulated under high flow rate and nutrient-rich conditions. Transient changes in the pore geometry caused by biofilm growth lead to the formation of preferential flowpaths within the granular porous medium. The decrease of permeability caused by clogging of the porous medium is calculated and is found to be in qualitative agreement with published experimental results. 相似文献
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Transport in porous media is often characterized by the advection–dispersion equation, with the dispersion coefficient as the most important parameter that links the hydrodynamics to the transport processes. Morphological properties of any porous medium, such as pore size distribution, network topology, and correlation length control transport. In this study we explore the impact of correlation length on transport regime using pore-network modelling. Earlier direct simulation studies of dispersion in carbonate and sandstone rocks showed larger dispersion compared to granular homogenous sandpacks. However, in these studies, isolation of the impact of correlation length on transport regime was not possible due to the fundamentally different pore morphologies and pore-size distributions. Against this limitation, we simulate advection–dispersion transport for a wide range of Péclet numbers in unstructured irregular networks with “different” correlation lengths but “identical” pore size distributions and pore morphologies. Our simulation results show an increase in the magnitudes of the estimated dispersion coefficients in correlated networks compared to uncorrelated ones in the advection-controlled regime. The range of the Péclet numbers which dictate mixed advection–diffusion regime considerably reduces in the correlated networks. The findings emphasize the critical role of correlation length which is depicted in a conceptual transport phase diagram and the importance of accounting for the micro-scale correlation lengths into predictive stochastic pore-scale modelling. 相似文献
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This paper presents application of a series of algorithms used to extract pore network structure from high-resolution three-dimensional synchrotron microtomography images of unconsolidated porous media systems. These algorithms are based on the three-dimensional skeletonization that simplifies the pore space to networks in the form of nodes connected to paths. Dilation algorithms were developed to generate inscribed spheres on the nodes and paths of the medial axis to represent pore-bodies and pore-throats of the network, respectively. The end result is a physically representative pore network structure, i.e. three-dimensional spatial distribution (i.e. x-, y-, and z-coordinates) of pore-bodies and pore-throats, pore-body size distribution, pore-throat size distribution, and the connectivity. Systems analyzed in this study include different glass bead systems and natural marine sand. The media ranged in size from 0.123 to 1.0 mm, while the image volumes ranged between 7.7 and 108.9 mm3. In addition to extracting the pore network structure, the porosity, specific surface area, and representative elementary volume analysis on the porosity were calculated. Spatial correlation between pore-body sizes in the network was investigated using semivariograms and integral scale concepts. The impact of resolution on the calculated property was also investigated.
In this work, we show that microtomography is an effective tool to non-destructively extract the structure of many systems. The quality of the datasets depends on photon energy, photon flux, size of the sample, type of the sample, and size of the sample ‘features’. Results show that the developed method of extracting pore network structure is applicable to ideal and natural porous media systems. The impact of resolution on the quantification of the network structure properties varies in its significance based on feature size of the system and the properties being calculated. Therefore, a thorough resolution sensitivity analysis should be carried out to determine the degree of error associated with a system imaged at a given resolution. 相似文献
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Improved network flow models require the incorporation of increasingly accurate geometrical characterization of the microscale pore structure as well as greater information on fluid–fluid interaction (interfaces) at pore scales. We report on three dimensional (3D) pore scale medium characterization, absolute permeability computations for throat structures, and pore scale residual fluid distribution in a Berea core. X-ray computed microtomography combined with X-ray attenuating dopants is used to obtain 3D images of the pore network and to resolve phase distributions in the pore space. 相似文献
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In this work we propose a new methodology to calculate pore connectivity in granular rocks. This method is useful to characterize the pore networks of natural and laboratory compaction bands (CBs), and compare them with the host rock pore network.Data were collected using the synchrotron X-ray microtomography technique and quantitative analyses were carried out using the Pore3D software library. The porosity was calculated from segmented tridimensional images of deformed and pristine rocks. A process of skeletonization of the pore space was used to obtain the number of connected pores within the rock volume. By analyzing the skeletons the differences between natural and laboratory CBs were highlighted. The natural CB has a lower porosity than to the laboratory one. In natural CBs, the grain contacts appear welded, whereas laboratory CBs show irregular pore shape. Moreover, we assessed for the first time how pore connectivity evolves as a function of deformation, documenting the mechanism responsible for pore connectivity drop within the CBs. 相似文献
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Reconstruction of porous media using multiple-point statistics with data conditioning 总被引：1，自引：0，他引：1
Ting Zhang Yi Du Tao Huang Xue Li 《Stochastic Environmental Research and Risk Assessment (SERRA)》2015,29(3):727-738
The reconstruction of porous media is of great importance in predicting fluid transport properties, which are widely used in various fields such as catalysis, oil recovery, medicine and aging of building materials. The real three-dimensional structural data of porous media are helpful to describe the irregular topologic structures of porous media. By using multiple-point statistics (MPS) to extract the characteristics of real porous media acquired from micro computed tomography (micro-CT) scanning, the probabilities of structural characteristics of pore spaces are obtained first, and then reproduced in the reconstructed regions. One solution to overcome the anisotropy of training images is to use real 3D volume data as a training image (TI). The CPU cost and memory burden brought up by 3D simulations can be reduced greatly by selecting the optimal multiple-grid template size that is determined by the entropy of a TI. Moreover, both soft data and hard data are integrated in MPS simulation to improve the accuracy of reconstructed images. The variograms and permeabilities, computed by lattice Boltzmann method, of the reconstructed images and the target image obtained from real volume data are compared, showing that the structural characteristics of reconstructed porous media using our method are similar to those of real volume data. 相似文献
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Using Resin‐Based 3D Printing to Build Geometrically Accurate Proxies of Porous Sedimentary Rocks 
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下载免费PDF全文 Three‐dimensional (3D) printing is capable of transforming intricate digital models into tangible objects, allowing geoscientists to replicate the geometry of 3D pore networks of sedimentary rocks. We provide a refined method for building scalable pore‐network models (“proxies”) using stereolithography 3D printing that can be used in repeated flow experiments (e.g., core flooding, permeametry, porosimetry). Typically, this workflow involves two steps, model design and 3D printing. In this study, we explore how the addition of post‐processing and validation can reduce uncertainty in the 3D‐printed proxy accuracy (difference of proxy geometry from the digital model). Post‐processing is a multi‐step cleaning of porous proxies involving pressurized ethanol flushing and oven drying. Proxies are validated by: (1) helium porosimetry and (2) digital measurements of porosity from thin‐section images of 3D‐printed proxies. 3D printer resolution was determined by measuring the smallest open channel in 3D‐printed “gap test” wafers. This resolution (400 µm) was insufficient to build porosity of Fontainebleau sandstone (～13%) from computed tomography data at the sample's natural scale, so proxies were printed at 15‐, 23‐, and 30‐fold magnifications to validate the workflow. Helium porosities of the 3D‐printed proxies differed from digital calculations by up to 7% points. Results improved after pressurized flushing with ethanol (e.g., porosity difference reduced to ～1% point), though uncertainties remain regarding the nature of sub‐micron “artifact” pores imparted by the 3D printing process. This study shows the benefits of including post‐processing and validation in any workflow to produce porous rock proxies. 相似文献
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A multiple-point statistics algorithm for 3D pore space reconstruction from 2D images 总被引：1，自引：0，他引：1
Alireza HajizadehAliakbar Safekordi Farhad A. Farhadpour 《Advances in water resources》2011,34(10):1256-1267
Fluid flow behavior in a porous medium is a function of the geometry and topology of its pore space. The construction of a three dimensional pore space model of a porous medium is therefore an important first step in characterizing the medium and predicting its flow properties. A stochastic technique for reconstruction of the 3D pore structure of unstructured random porous media from a 2D thin section training image is presented. The proposed technique relies on successive 2D multiple point statistics simulations coupled to a multi-scale conditioning data extraction procedure. The Single Normal Equation Simulation Algorithm (SNESIM), originally developed as a tool for reproduction of long-range, curvilinear features of geological structures, serves as the simulation engine. Various validating criteria such as marginal distributions of pore and grain, directional variograms, multiple-point connectivity curves, single phase effective permeability and two phase relative permeability calculations are used to analyze the results. The method is tested on a sample of Berea sandstone for which a 3D micro-CT scanning image is available. The results confirm that the equi-probable 3D realizations obtained preserve the typical patterns of the pore space that exist in thin sections, reproduce the long-range connectivities, capture the characteristics of anisotropy in both horizontal and vertical directions and have single and two phase flow characteristics consistent with those of the measured 3D micro-CT image. 相似文献
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In porous media, the dynamics of the invading front between two immiscible fluids is often characterized by abrupt reconfigurations caused by local instabilities of the interface. As a prototype of these phenomena we consider the dynamics of a meniscus in a corner as it can be encountered in angular pores. We investigate this process in detail by means of direct numerical simulations that solve the Navier–Stokes equations in the pore space and employ the Volume of Fluid method (VOF) to track the evolution of the interface. We show that for a quasi-static displacement, the numerically calculated surface energy agrees well with the analytical solutions that we have derived for pores with circular and square cross sections. However, the spontaneous reconfigurations are irreversible and cannot be controlled by the injection rate: they are characterized by the amount of surface energy that is spontaneously released and transformed into kinetic energy. The resulting local velocities can be orders of magnitude larger than the injection velocity and they induce damped oscillations of the interface that possess their own time scales and depend only on fluid properties and pore geometry. In complex media (we consider a network of cubic pores) reconfigurations are so frequent and oscillations last long enough that increasing inertial effects leads to a different fluid distribution by influencing the selection of the next pore to be invaded. This calls into question simple pore-filling rules based only on capillary forces. Also, we demonstrate that inertial effects during irreversible reconfigurations can influence the work done by the external forces that is related to the pressure drop in Darcy’s law. This suggests that these phenomena have to be considered when upscaling multiphase flow because local oscillations of the menisci affect macroscopic quantities and modify the constitutive relationships to be used in macro-scale models. These results can be extrapolated to other interface instabilities that are at the origin of fast pore-scale events, such as Haines jumps, snap-off and coalescence. 相似文献
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The purpose of this study is to quantify the dispersivity in the longitudinal direction by upscaling pore scale mixing over a network domain and to verify the dispersivity with that obtained through the more rigorous upscaling technique, the Brownian particle tracking model (BPTM). We model a porous medium with a network of pore-units that are comprised of pore bodies and bonds of finite volume. Such a pore-unit is assumed to be a mixing cell with the steady state flow condition for a single fluid. Dispersivity can be obtained by solving the mixing cell model (MCM) for the concentration in each pore-unit and by averaging the concentrations for a large number of pore units (as a function of time and space). A minimal size of network that ascertains an asymptotic value of dispersivity was determined and verified with large size pore networks. This numerically computed dispersivity is compared with the results from the BPTM for the same porous medium and flow conditions. We show that the dispersivity obtained from the MCM is equally reliable for the heterogeneous pore-networks and can be estimated as a function of pore size heterogeneity. For homogeneous networks with the MCM, the iteration time step plays an important role. On the other hand, for networks with the BPTM, the assumption of intra-bond velocity profile affects the results. 相似文献
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Chaotic advection at the pore scale: Mechanisms,upscaling and implications for macroscopic transport
The macroscopic spreading and mixing of solute plumes in saturated porous media is ultimately controlled by processes operating at the pore scale. Whilst the conventional picture of pore-scale mechanical dispersion and molecular diffusion leading to persistent hydrodynamic dispersion is well accepted, this paradigm is inherently two-dimensional (2D) in nature and neglects important three-dimensional (3D) phenomena. We discuss how the kinematics of steady 3D flow at the pore scale generate chaotic advection—involving exponential stretching and folding of fluid elements—the mechanisms by which it arises and implications of microscopic chaos for macroscopic dispersion and mixing. Prohibited in steady 2D flow due to topological constraints, these phenomena are ubiquitous due to the topological complexity inherent to all 3D porous media. Consequently 3D porous media flows generate profoundly different fluid deformation and mixing processes to those of 2D flow. The interplay of chaotic advection and broad transit time distributions can be incorporated into a continuous-time random walk (CTRW) framework to predict macroscopic solute mixing and spreading. We show how these results may be generalised to real porous architectures via a CTRW model of fluid deformation, leading to stochastic models of macroscopic dispersion and mixing which both honour the pore-scale kinematics and are directly conditioned on the pore-scale architecture. 相似文献
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Characterizing the pore space of rock samples using three‐dimensional (3D) X‐ray computed tomography images is a crucial step in digital rock physics. Indeed, the quality of the pore network extracted has a high impact on the prediction of rock properties such as porosity, permeability and elastic moduli. In carbonate rocks, it is usually very difficult to find a single image resolution which fully captures the sample pore network because of the heterogeneities existing at different scales. Hence, to overcome this limitation a multiscale analysis of the pore space may be needed. In this paper, we present a method to estimate porosity and elastic properties of clean carbonate (without clay content) samples from 3D X‐ray microtomography images at multiple resolutions. We perform a three‐phase segmentation to separate grains, pores and unresolved porous phase using 19 μm resolution images of each core plug. Then, we use images with higher resolution (between 0.3 and 2 μm) of microplugs extracted from the core plug samples. These subsets of images are assumed to be representative of the unresolved phase. We estimate the porosity and elastic properties of each sample by extrapolating the microplug properties to the whole unresolved phase. In addition, we compute the absolute permeability using the lattice Boltzmann method on the microplug images due to the low resolution of the core plug images. In order to validate the results of the numerical simulations, we compare our results with available laboratory measurements at the core plug scale. Porosity average simulations for the eight samples agree within 13%. Permeability numerical predictions provide realistic values in the range of experimental data but with a higher relative error. Finally, elastic moduli show the highest disagreements, with simulation error values exceeding 150% for three samples. 相似文献
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ABSTRACTIn this paper, a mid- to long-term runoff forecast model is developed using an ideal point fuzzy neural network–Markov (NFNN-MKV) hybrid algorithm to improve the forecasting precision. Combining the advantages of the new fuzzy neural network and the Markov prediction model, this model can solve the problem of stationary or volatile strong random processes. Defined error statistics algorithms are used to evaluate the performance of models. A runoff prediction for the Si Quan Reservoir is made by utilizing the modelling method and the historical runoff data, with a comprehensive consideration of various runoff-impacting factors such as rainfall. Compared with the traditional fuzzy neural networks and Markov prediction models, the results show that the NFNN-MKV hybrid algorithm has good performance in faster convergence, better forecasting accuracy and significant improvement of neural network generalization. The absolute percentage error of the NFNN-MKV hybrid algorithm is less than 7.0%, MSE is less than 3.9, and qualification rate reaches 100%. For further comparison of the proposed model, the NFNN-MKV model is employed to estimate (training and testing for 120-month-ahead prediction) and predict river discharge for 156 months at Weijiabao on the Weihe River in China. Comparisons among the results of the NFNN-MKV model, the WNN model and the SVR model indicate that the NFNN-MKV model is able to significantly increase prediction accuracy.
Editor D. Koutsoyiannis; Associate editor Y. Gyasi-Agyei 相似文献