Dissertations / Theses on the topic 'Pore-scale simulations'

Transport phenomena in heterogeneous media play a crucial role in numerous engineering applications such as hydrocarbon recovery from shales and material processing. Understanding and predicting these phenomena is critical for the success of these applications. In this dissertation, nanoscale transport phenomena in porous media are studied through physics-based simulations, and the effective solution of forward and inverse transport phenomena problems in heterogeneous media is tackled using data-driven, deep learning approaches. For nanoscale transport in porous media, the storage and recovery of gas from ultra-tight shale formations are investigated at the single-pore scale using molecular dynamics simulations. In the single-component gas recovery, a super-diffusive scaling law was found for the gas production due to the strong gas adsorption-desorption effects. For binary gas (methane/ethane) mixtures, surface adsorption contributes greatly to the storage of both gas in nanopores, with ethane enriched compared to methane. Ethane is produced from nanopores as effectively as the lighter methane despite its slower self-diffusion than the methane, and this phenomenon is traced to the strong couplings between the transport of the two species in the nanopore. The dying of solvent-loaded nanoporous filtration cakes by a purge gas flowing through them is next studied. The novelty and challenge of this problem lie in the fact that the drainage and evaporation can occur simultaneously. Using pore-network modeling, three distinct drying stages are identified. While drainage contributes less and less as drying proceeds through the first two stages, it can still contribute considerably to the net drying rate because of the strong coupling between the drainage and evaporation processes in the filtration cake. For the solution of transport phenomena problems using deep learning, first, convolutional neural networks with various architectures are trained to predict the effective diffusivity of two-dimensional (2D) porous media with complex and realistic structures from their images. Next, the inverse problem of reconstructing the structure of 2D heterogeneous composites featuring high-conductivity, circular fillers from the composites' temperature field is studied. This problem is challenging because of the high dimensionality of the temperature and conductivity fields. A deep-learning model based on convolutional neural networks with a U-shape architecture and the encoding-decoding processes is developed. The trained model can predict the distribution of fillers with good accuracy even when coarse-grained temperature data (less than 1% of the full data) are used as an input. Incorporating the temperature measurements in regions where the deep learning model has low prediction confidence can improve the model's prediction accuracy.
Doctor of Philosophy
Multiphysics transport phenomena inside structures with non-uniform pores or properties are common in engineering applications, e.g., gas recovery from shale reservoirs and drying of porous materials. Research on these transport phenomena can help improve related applications. In this dissertation, multiphysics transport in several types of structures is studied using physics-based simulations and data-driven deep learning models. In physics-based simulations, the multicomponent and multiphase transport phenomena in porous media are solved at the pore scale. The recovery of methane and methane-ethane mixtures from nanopores is studied using simulations to track motions and interactions of methane and ethane molecules inside the nanopores. The strong gas-pore wall interactions lead to significant adsorption of gas near the pore wall and contribute greatly to the gas storage in these pores. Because of strong gas adsorption and couplings between the transport of different gas species, several interesting and practically important observations have been found during the gas recovery process. For example, lighter methane and heavier ethane are recovered at similar rates. Pore-scale modeling are applied to study the drying of nanoporous filtration cakes, during which drainage and evaporation can occur concurrently. The drying is found to proceed in three distinct stages and the drainage-evaporation coupling greatly affects the drying rate. In deep learning modeling, convolutional neural networks are trained to predict the diffusivity of two-dimensional porous media by taking the image of their structures as input. The model can predict the diffusivity of the porous media accurately with computational cost orders of magnitude lower than physics-based simulations. A deep learning model is also developed to reconstruct the structure of fillers inside a two-dimensional matrix from its temperature field. The trained model can predict the structure of fillers accurately using full-scale and coarse-grained temperature input data. The predictions of the deep learning model can be improved by adding additional true temperature data in regions where the model has low prediction confidence.

Fuel cells and hydrogen are two key components for building a competitive, secure, and sustainable clean energy economy, due to possibility to convert diverse fuels directly into electrical power without combustion and a carbon-free fuel that can be produced from renewable resources. However, to become competitive in a market, fuel cells should overcome the issues by improvements in durability and performance as well as reductions in manufacturing cost. Recent advances in fuel cell technology has been made by development of the high temperature (HT) polymeric electrolyte membrane (PEM) fuel cells (FC). Owing to combination of the advantages of two types of fuel cells, namely polymeric electrolyte membrane and phosphoric acid, it is considered as one of the best technological solutions. Further improvements cannot be done without deep understanding of the major causes and underlying physico-chemical phenomena for specific degradation mechanisms of different compartments of HT-PEMFC, especially porous electrodes, which are the most vulnerable part prone to degradation processes, and predicting the impact of these degradation effects. Modeling can provide insight into the mechanisms that lead to irreversible or reversible performance loss and the relation between these mechanisms and the operating conditions, based on the changes in materials properties that can be observed. Moreover, another important issue of modeling is understanding the interaction between different specific membrane degradation mechanisms and their complex and mixed effects due to their simultaneously occurrence in real fuel cell operation, which requires multi-scale analysis of undergoing phenomena. This work represents a step towards reliable algorithms for reconstructing micro-morphology of electrode materials of high-temperature proton-exchange membrane fuel cells and for performing pore-scale simulations of fluid flow (including rarefaction effects). In particular, we developed a deterministic model for a woven gas diffusion layer (GDL) and the stochastic model for a non-woven GDL and a carbon- supported catalyst layer (CL) based on clusterization of carbon particles. We verified that both developed models accurately recover the experimental values of permeability, without any special ad-hoc tuning. Moreover, we investigated the effect of catalyst particle distributions inside the CL on the degree of clusterization and on the microscopic fluid flow, which is relevant for degradation modeling (e.g. loss of phosphoric acid). The three-dimensional pore-scale simulations of fluid flow for the direct numerical calculation of macroscopic transport parameters, like permeability, were performed by the Lattice Boltzmann Method (LBM). Within framework of this thesis, we investigate how distribution of catalyst (Pt) particles can affect gas dynamics, electro-chemistry and consequently performance in high temperature proton exchange membrane fuel cells. Optimal distribution of catalyst can be used as a mitigation strategy for phosphoric acid loss and crossover of reagents through membrane. The main idea is that one of the reasons of degradation is the gas dynamic pulling stress at the interface between the catalyst and the membrane. This stress can be highly reduced by tuning the main morphological parameters of the catalyst layer, like distribution of catalyst particles and clusterization. We have performed direct numerical pore-scale simulations of the gas flow through catalyst layer for different distributions of catalyst particles, in order to minimize this stress and hence to improve durability. The results of pore-scale simulation for exponential decay distribution show more than one order of magnitude reduction of the pulling stress, compared to the homogeneous (conventional) distribution. Moreover, a simplified three-dimensional macroscopic model of the membrane electrode assembly (MEA) with catalyst layer comprised of three sublayers with different catalyst loadings, has been developed to analyze how the proposed mitigation strategy affects the polarization curve and hence the performance. This macroscopic model presents 67% reduction in pulling stress for feasible mitigation strategy, at the price of only 9.3% reduction in efficiency at high current densities.

Rock properties are usually predicted using 3D images of the rockÂ’s microstructure. While single-phase rock properties can be computed directly on these images, twophase properties are usually predicted using networks extracted from these images. To make accurate predictions with networks, they must be topologically similar to the porous medium of interest. In this work, NMR response is simulated using a random walk method. The simulations were performed on 3D images obtained from micro-CT scanning and in topologically equivalent networks extracted from these images using a maximal ball algorithm. A comparison of the NMR simulations on a 3D image and an extracted network helps to ascertain if the network is representative of the underlying 3D image. Single-phase NMR simulations are performed on 3D images and extracted networks for different porous media including sand packs, poorly consolidated sandstones, consolidated sandstones and carbonates, and are compared successfully with experimental measurements. The algorithm developed for the simulation of NMR response in networks was validated using a tuned Berea network that reproduced experimental capillary pressure data in Bentheimer sandstone. Simulation results of the sand packs and poorly consolidated media show that the T2 distributions of the networks are narrower than those of the corresponding micro-CT images and experimental data. This is attributed to the loss of some fine details of the pore structure in the network extraction algorithm. The algorithm developed for singlephase NMR response in networks was extended to two-phase fluids in order to study the effect of wettability on simulated NMR response in networks. While NMR behaviour is influenced pore structure, wettability and phase saturation, it is not possible to determine each of these influences uniquely. The ultimate goal is to have a two-phase simulator that predicts relative permeability, electrical resistivity, NMR response and capillary pressure which will be used to determine the wettability of a porous medium.

I present a new finite element (FE) simulation method to simulate pore-scale flow. Within the pore-space, I solve a simplified form of the incompressible Navier-Stoke’s equation, yielding the velocity field in a two-step solution approach. First, Poisson’s equation is solved with homogeneous boundary conditions, and then the pore pressure is computed and the velocity field obtained for no slip conditions at the grain boundaries. From the computed velocity field I estimate the effective permeability of porous media samples characterized by thin section micrographs, micro-CT scans and synthetically generated grain packings. This two-step process is much simpler than solving the full Navier Stokes equation and therefore provides the opportunity to study pore geometries with hundreds of thousands of pores in a computationally more cost effective manner than solving the full Navier-Stoke’s equation. My numerical model is verified with an analytical solution and validated on samples whose permeabilities and porosities had been measured in laboratory experiments (Akanji and Matthai, 2010). Comparisons were also made with Stokes solver, published experimental, approximate and exact permeability data. Starting with a numerically constructed synthetic grain packings, I also investigated the extent to which the details of pore micro-structure affect the hydraulic permeability (Garcia et al., 2009). I then estimate the hydraulic anisotropy of unconsolidated granular packings. With the future aim to simulate multiphase flow within the pore-space, I also compute the radii and derive capillary pressure from the Young-Laplace equation (Akanji and Matthai,2010)

In the last decade, the fundamental understanding of pore-scale flow in porous media has been undergoing a revolution through the recent development of new pore-scale imaging techniques, reconstruction of three-dimensional pore space images, and advances in the computational methods for solving complex fluid flow equations directly or indirectly on the reconstructed three-dimensional pore space images. Important applications include hydrocarbon recovery from - and CO2 storage in - reservoir rock formations. Of particular importance is the consideration of carbonate reservoirs, as our understanding of carbonates with respect to geometry and fluid flow processes is still very limited in comparison with sandstone reservoirs. This thesis consists of work mainly performed within the Qatar Carbonates and Carbon Storage Research Centre (QCCSRC) project, focusing on development of three dimensional imaging techniques for accurately characterizing and predicting flow/transport properties in both complex benchmark carbonate and sandstone rock samples. Firstly, the thesis presents advances in the application of Confocal Laser Scanning Microscopy (CLSM), including the improvement of existing sample preparation techniques and a step-by step guide for imaging heterogeneous rock samples exhibiting sub-micron resolution pores. A novel method has been developed combining CLSM with sequential grinding and polishing to obtain deep 3D pore-scale images. This overcomes a traditional limitation of CLSM, where the depth information in a single slice is limited by attenuation of the laser light. Other features of this new method include a wide field of view at high resolution to arbitrary depth; fewer grinding steps than conventional serial sectioning using 2D microscopy; the image quality does not degrade with sample size, as e.g. in micro-computed tomography (micro- CT) imaging. Secondly, it presents two fundamental issues - Representative Element of Volume (REV) and scale dependency which are addressed with qualitative and quantitative solutions for rocks increasing in heterogeneity from beadpacks to sandpacks to sandstone to carbonate rocks. The REV is predicted using the mathematical concept of the Convex Hull, CH, and the Lorenz coefficient, LC, to investigate the relation between two macroscopic properties simultaneously, in this case porosity and absolute permeability. The effect of voxel resolution is then studied on the segmented macro-pore phase (macro-porosity) and intermediate phase (micro-porosity) and the fluid flow properties of the connected macro-pore space using lattice-Boltzmann (LB) and pore network (PN) modelling methods. A numerical coarsening (up-scaling) algorithm have also been applied to reduce the computational power and time required to accurately predict the flow properties using the LB and PN methods. Finally, a quantitative methodology has been developed to predict petrophysical properties, including porosity and absolute permeability for X-ray medical computed tomography (CT) carbonate core images of length 120 meters using image based analysis. The porosity is calculated using a simple segmentation based on intensity grey values and the absolute permeability using the Kozeny-Carman equation. The calculated petrophysical properties were validated with the experimental plug data.

The transport and deposition of colloidal particles in saturated porous media are processes of considerable importance in many fields of science and engineering, including the propagation of contaminants and of microorganisms in aquifer systems and the use of micro- and nano-particles as reagents for groundwater remediation interventions. Colloid transport is a peculiar multi-scale problem: pore-scale phenomena and inter granular dynamics have an important impact on the larger-scale transport. In this thesis a microscale approach was used to gain a better understanding of the mechanisms underlying colloidal processes, such as deposition and aggregation. The research activity was carried out by performing numerical simulations through the FEM software, COMSOL Multiphysics®. The first part of the study focuses on the development of a new correlation equation to predict single collector efficiency, a key concept in filtration theory, which allows predicting particle deposition on a single spherical collector. By performing Eulerian and Lagrangian simulations in a simple geometry and by using an innovative approach to interpret the results, a new correlation equation to predict single collector efficiency has been formulated. A hierarchical approach to interpret the results was exploited. The proposed correlation equation presents innovative features, such as the validity for a wide range of parameters (also at very small Peclet numbers), the prediction of efficiency values always lower than unity, the total flux normalization and the analysis of the mutual interactions between the main transport mechanisms (advection, gravity and diffusion) and the steric effect. The final formula was also extended to include porosity and a reduced model was proposed. The second part of the study focuses on more realistic systems, characterized by a column of spherical collectors in series. The numerical simulations performed show the limits of the existing models to interpret the experimental data. Therefore, a more rigorous procedure to evaluate the filtration processes in presence of a series of collectors was developed.

Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2017.
Thesis: S.M., Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2017.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 57-60).
Fluid flow and particle transport through porous media are determined by the geometry of the host medium itself. Despite the fundamental importance of the velocity distribution in controlling early-time and late-time transport properties (e.g., early breakthrough and superdiffusive spreading), direct relations linking velocity distribution with the statistics of pore structure in 3D porous media have not been established yet. High velocities are controlled by the formation of channels, while low velocities are dominated by stagnation zones. Recent studies have proposed phenomenological models for the distribution of high velocities including stretched exponential and power-exponential distributions but without an underlying mechanistic or statistical physics theory. Here, we investigate the relationship between the structure of the host medium and the resulting fluid flow in random dense spherical packs. We simulate flow at low Reynolds numbers by solving the Stokes equations with the finite volume method and imposing a no-slip boundary condition at the boundary of each sphere. High fidelity numerical simulations of Stokes flow are facilitated with the assist of open source Computational Fluid Dynamics (CFD) tools such as OpenFOAM. We show that the distribution of low velocities in 3D porous media is described by a Gamma distribution, which is robust to variations in the geometry of the porous media. We develop a simple model that predicts the parameters of the gamma distribution in terms of the porosity of the host medium. Despite its simplicity, the analytical predictions from the model agree well with high-resolution simulations in terms of velocity distribution.
by Mohammad S Kh F Sh AlAdwani.
S.M.

Carbon Capture and Storage (CCS) is one of the effective methods to manage CO2 emissions to mitigate global warming and associated environmental changes. This thesis provide insight into this aspects emphasising on investigating the two-phase (brine and scCO2) flow behaviour, and advanced understanding on residual saturation, relative permeability, and capillary trapping capacity under various drainage and imbibition conditions using pore-scale numerical simulations based upon computational fluid dynamics (CFD).

Ce travail est motivé par la nécessité de mieux comprendre la technique de récupération du pétrole par injection de polymères à l'échelle du pore. On considère deux fluides immiscibles dans un réseau de microcanaux. A cette échelle, le diamètre des canaux est de l'ordre de quelques dizaines de micromètres tandis que la vitesse est de l'ordre du centimètre par seconde. Cela nous permet d'utiliser les équations de Stokes incompressible pour décrire l'écoulement des fluides. Le modèle Olroyd-B est utilisé pour décrire l'écoulement du fluide viscoélastique. Afin d'effectuer des simulations numériques dans une géométrie complexe comme un réseau de microcanaux, une méthode de pénalisation est utilisée. Pour suivre l'interface entre les deux fluides, la méthode Level-Set est employée. Le modèle pour la dynamique de la ligne triple est basé sur les la loi de Cox. Enfin, on présente des résultats de simulations numériques avec des paramètres physiques réalistes
This work is motivated by the need for better understanding the polymer Enhanced Oil Recovery (EOR) technique at the pore-scale. We consider two phase immiscible fluids in a microchannel network. In microfluidics, the diameter of the channels is of the order of a few tens of micrometers and the flow velocity is of the order of one centimeter per second. The incompressible Stokes equations are used to describe the fluid flow. The Oldroyd-B rheological model is used to capture the viscoelastic behavior. In order to perform numerical simulations in a complex geometry like a microchannel network, a penalization method is implemented. To follow the interface between the two fluids, the Level-Set method is employed. The dynamic contact line model used in this work is based on the Cox law. Finally, we perform simulations with realistic parameters

Understanding flow and transport in porous media is critical as it plays a central role in many biological, natural, and industrial processes. Such processes are not limited to one length or time scale; they occur over a wide span of scales from micron to Kilometers and microseconds to years. While field-scale simulation relies on a continuum description of the flow and transport, one must take into account transport processes occurring on much smaller scales. In doing so, pore-scale modeling is a powerful tool for shedding light on processes at small length and time scales.

In this work, we look into the multi-phase flow and transport through porous media at two different scales, namely pore- and Darcy scales. First, using direct numerical simulations, we study pore-scale Eulerian and Lagrangian statistics. We study the evolution of Lagrangian velocities for uniform injection of particles and numerically verify their relationship with the Eulerian velocity field. We show that for three porous media velocity, probability distributions change over a range of porosities from an exponential distribution to a Gaussian distribution. We thus model this behavior by using a power-exponential function and show that it can accurately represent the velocity distributions. Finally, using fully resolved velocity field and pore-geometry, we show that despite the randomness in the flow and pore space distributions, their two-point correlation functions decay extremely similarly.

Next, we extend our previous study to investigate the effect of viscoelastic fluids on particle dispersion, velocity distributions, and flow resistance in porous media. We show that long-term particle dispersion could not be modulated by using viscoelastic fluids in random porous media. However, flow resistance compared to the Newtonian case goes through three distinct regions depending on the strength of fluid elasticity. We also show that when elastic effects are strong, flow thickens and strongly fluctuates even in the absence of inertial forces.

Next, we focused our attention on flow and transport at the Darcy scale. In particular, we study a tertiary improved oil recovery technique called surfactant-polymer flooding. In this work, which has been done in collaboration with Purdue enhanced oil recovery lab, we aim at modeling coreflood experiments using 1D numerical simulations. To do so, we propose a framework in which various experiments need to be done to quantity surfactant phase behavior, polymer rheology, polymer effects on rock permeability, dispersion, and etc. Then, via a sensitivity study, we further reduce the parameter space of the problem to facilitate the model calibration process. Finally, we propose a multi-stage calibration algorithm in which two critically important parameters, namely peak pressure drop, and cumulative oil recovery factor, are matched with experimental data. To show the predictive capabilities of our framework, we numerically simulate two additional coreflood experiments and show good agreement with experimental data for both of our quantities of interest.

Lastly, we study the unstable displacement of non-aqueous phase liquids (e.g., oil) via a finite-size injection of surfactant-polymer slug in a 2-D domain with homogeneous and heterogeneous permeability fields. Unstable displacement could be detrimental to surfactant-polymer flood and thus is critically important to design it in a way that a piston-like displacement is achieved for maximum recovery. We study the effects of mobility ratio, finite-size length of surfactant-polymer slug, and heterogeneity on the effectiveness of such process by looking into recovery rate and breakthrough and removal times.

Many engineering and scientific applications of flow in porous media are characterized by transport phenomena at multiple spatial scales, including pollutant transport, groundwater remediation, and acid injection to enhance well production. Carbon sequestration in particular is a multiscale problem, because the trapping and leakage mechanisms of CO2 in the subsurface occur from the sub-pore level to the basin scale. Quantitative and predictive pore-scale modeling has long shown to be a valuable tool for studying fluid-rock interactions in porous media. However, due to the size limitation of the pore-scale models (10-4-10-2m), it is impossible to model an entire reservoir at the pore scale. A straightforward multiscale approach would be to upscale macroscopic parameters (e.g. permeability) directly from pore-scale models and then input them into a continuum-scale simulator. However, it has been found that the large-scale models do not predict in many cases. One possible reason for the inaccuracies is oversimplified boundary conditions used in this direct upscaling approach. The hypothesis of this work is that pore-level flow and upscaled macroscopic parameters depends on surrounding flow behavior manifested in the form of boundary conditions. The detailed heterogeneity captured by the pore-scale models may be partially lost if oversimplified boundary conditions are employed in a direct upscaling approach. As a result, extracted macroscopic properties may be inaccurate. Coupling the model to surrounding media (using finite element mortars to ensure continuity between subdomains) would result in more realistic boundary conditions, and can thus improve the accuracy of the upscaled parameters. To test the hypothesis, mortar coupling is employed to couple pore-scale models and also couple pore-scale models to continuum models. Flow field derived from mortar coupling and direct upscaling are compared, preferably against a true solution if one exists. It is found in this dissertation that pore-scale flow and upscaled parameters can be significantly affected by the surrounding media. Therefore, using arbitrary boundary conditions such as constant pressure and no-flow boundaries may yield misleading results. Mortar coupling captures the detailed variation on the interface and imposes realistic boundary conditions, thus estimating more accurate upscaled values and flow fields. An advanced upscaling tool, a Super Permeability Tensor (SPT) is developed that contains pore-scale heterogeneity in greater detail than a conventional permeability tensor. Furthermore, a multiscale simulator is developed taking advantage of mortar coupling to substitute continuum grids directly with pore-scale models where needed. The findings from this dissertation can significantly benefit the understanding of fluid flow in porous media, and, in particular, CO2 storage in geological formations which requires accurate modeling across multiple scales. The fine-scale models are sensitive to the boundary conditions, and the large scale modeling of CO2 transport is sensitive to the CO2 behavior affected by the pore-scale heterogeneity. Using direct upscaling might cause significant errors in both the fine-scale and the large-scale model. The multiscale simulator developed in this dissertation could integrate modeling of CO2 physics at all relevant scales, which span the sub-pore or pore level to the basin scale, into one single simulator with effective and accurate communication between the scales. The multiscale simulator provides realistic boundary conditions for the fine scales, accurate upscaled information to continuum-scale, and allows for the distribution of computational power where needed, thus maintaining high accuracy with relatively low computational cost.
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The increasing complexity of oil and gas reservoirs has led to the need of a better understanding of the processes governing the rock properties. Traditional theoretical and empirical models often fail to predict the behavior of carbonates, tight gas sands and shale gas, for example. An essential part of the necessary investigation is the study of the phenomena occurring at the pore scale. In this direction, the so-called digital rock physics is emerging as a research field that offers the possibility of imaging the rock pore space and simulating the processes therein directly. This report describes our work on developing algorithms to simulate viscous and electric flow through a three dimensional Cartesian representation of the porous space, such as those available through X-ray microtomography. We use finite differences to discretize the governing equations and also propose a new method to enforce the incompressible flow constraint under natural boundary conditions. Parallel computational codes are written targeting performance and computer memory optimization, allowing the use of bigger and more representative samples. Results are reported with an estimate of the error bars in order to help on the simulation appraisal. Tests performed using benchmark samples show good agreement with experimental/theoretical values. Example of application on digital modeling of cement growth and on multiphase fluid distribution are also provided. The final test is done on Bentheimer, Buff Berea and Idaho Brown sandstone samples with available laboratory measurements. Some limitations need to be investigated in future work. First, the computer potential fields show anomalous border effects at the open boundaries. Second, a minor problem arises with the decreased convergence rate for the velocity field due to the increased number of operations, leading to the need of a more sophisticated preconditioner. We intend to expand the algorithms to handle microporosity (e.g. carbonates) and multiphase fluid flow.
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Contamination of ground water by non-aqueous phase liquids (NAPLs) has received increasing attention. The most common approach to numerical modeling of NAPL movement through the unsaturated zone is the use of the finite difference or finite element methods to solve a set of partial differential equations derived from Darcy's law and the continuity equations (Abriola and Pinder, 1985; Kaluarachchi and Parker, 1989). These methods work well in many settings, but have given little insights as to why certain non-ideal flow phenomena will occur. The network modeling method, which considers flow at the pore-scale, was used in this study to better understand macroscopic flow phenomena in porous media. Pore-scale network models approximate porous medium as a connected network of pores and channels. Two and three-dimensional pore-scale network models were constructed in this study. A uniform statistical distribution was assumed to represent the random arrangement of pore and tube sizes. Both hysteristic scanning curves and intermediate fluid distribution are studied. The simulation results suggested that network models may be used to predict the characteristic curves of three-phase systems. The results also suggested that three-dimensional models are necessary to study the three-phase problems. Two-dimensional models do not provide realistic results as evidenced by their inability to provide scale-invariant representation of flow processes. The network sizes used in this study ranged from 10 x 5 (50) to 156 x 78 (12168) pores for two-dimensional and from 10 x 5 x 5 (250) to 100 x 50 x 5 (25000) pores for three-dimensional domains. The domain size of 100 x 50 x 5 pores was large enough to provide descriptions independent of the domain scale. The one important limitation of network models is the considerable computational requirements. The use of very high speed computers is essential. Except for this limitation, the network model provides an invaluable technique to study fluid transport mechanisms in the vadose zone.
Graduation date: 1996