Carbonate rocks are of global importance as they contain about 50% of the world’s remaining hydrocarbon reserves and are also a major host to the world’s groundwater resources. Therefore, understanding and modelling the fluid flow processes in carbonates are of great importance. A critical problem is that, unlike homogenous media (such as sandstones), carbonates often show features, including porosity, that span across a wide spatial range, from sub-micron porosity to fractures of meters length-scale. In this study X-ray computed micro-tomography (μCT) has been utilised as a tool to monitor two phase (oil-brine) flow in porous carbonate (dolomite) plugs at ambient temperature and pressures smaller than 690 kPa. A simple, low-cost and highly X-ray transparent core-holder was utilised for which the design is introduced. Capillary end effects were recognised and avoided in data analysis. Displacement processes that occur in the dolomite under water-wet, oil-wet, and partially mixed-wet states were investigated. The experiments consisted of a series of drainage and imbibition processes occurring under capillary and viscous dominated flow regimes. Pore-scale mechanisms of piston-like displacement and snap-off (or at least clear results of them), that were previously observed in sandstones and 2D micro-models, were observed in the dolomite under study. In addition, a new pore-scale mechanism was identified which occurred at high capillary numbers, referred to as droplet-fragmentation. This new pore-scale mechanism may provide an explanation to the capillary-desaturation process for heterogeneous media. In the experiments performed on the oil-wet plug formation of a stable water in oil emulsion was observed which appears to be the first 3D observation of in situ emulsion formation made using μCT. Direct visualisation of the oil-brine-rock configurations and measurement of the contact angles are presented. A comparison was made for the contact angle distributions measured for the water-wet and oil-wet conditions. Observation of fluid displacement processes as well as oil-brine-rock contact angle distributions demonstrate that pore-scale imaging provides a promising tool for wettability characterisation on both pore and core scales. Such detailed wettability data can also be used in pore-scale flow models. For the dolomite under study multiple-scale pore network models were constructed by integrating single-scale networks extracted from μCT images acquired at different length-scales. Mercury injection capillary pressure laboratory measurements were used to evaluate the capillary pressure (vs. saturation) curves calculated using single, two-scale, and three-scale network models of this dolomite. The integrated networks displayed an improved match to the laboratory measurements in comparison with the single-scale network model. The three-scale network provided the closest simulated curve, this result confirms that a more representative model displays closer properties. While simulated capillary pressure curves are close (converging) for the integrated networks the calculated relative permeability curves show variability for different multiple-scale networks. The present work demonstrates that the pore-scale fluid displacement processes occurring in heterogeneous porous media are more complex than those occurring in homogeneous media. In addition, successful fluid flow simulations require construction of multiple-scale models as well as consideration of the pore-scale processes (such as droplet-fragmentation) that are specific to such complex pore systems.

This research addresses a number of fundamental issues concerning convective mass transfer across fluid-fluid interfaces in porous media. Mass transfer to/from distributed sinks/sources is considered for i) the slow dissolution of liquid filaments of a wetting non-aqueous phase liquid (NAPL) held in the corners of angular pores or throats and ii) the fate of gas bubbles generated during the flow of a supersaturated aqueous phase in porous media. 1. Effects of the stability of NAPL films on wetting NAPL dissolution Wettability profoundly affects the distribution of residual NAPL contaminants in natural soils. Under conditions of preferential NAPL wettability, NAPL is retained within small pores and in the form of thick films (liquid filaments) along the corners and crevices of the pore walls. NAPL films in pore corners provide capillary continuity between NAPL-filled pores, dramatically influencing the behaviour of NAPL dissolution to the flowing aqueous phase by convection and diffusion. A pore network model is developed to explore the dissolution behaviour of wetting NAPL in porous media. The effects of initial NAPL distribution and NAPL film stability on dissolution behaviour are studied using the simulator. NAPL phase loses continuity and splits into disconnected clusters of NAPL-filled pores due to rupture of NAPL films. Quasi-state drainage and fingering of the aqueous phase into NAPL-filled pores is treated as an invasion percolation process and a stepwise procedure is adopted for the solution of flow and solute concentration fields. NAPL film stability is shown to critically affect the rate of mass transfer as such that stable NAPL films provide for more rapid dissolution. The network simulator reproduces the essential physics of wetting NAPL dissolution in porous media and explains the concentration-tailing behaviour observed in experiments, suggesting also new possibilities for experimental investigation. 2. Convective Mass Transfer across Fluid Interfaces in Straight Angular Pores Steady convective mass transfer to or from fluid interfaces in pores of angular cross-section is theoretically investigated. The model incorporates the essential physics of capillarity and solute mass transfer by convection and diffusion in corner fluid filaments. The geometry of the corner filaments, characterized by the fluid-fluid contact angle, the corner half-angle and the interface meniscus curvature, is accounted for. Boundary conditions of zero surface shear (‘perfect-slip’) and infinite surface shear (‘no-slip’) at the fluid-fluid interface are considered. The governing equations for laminar flow within the corner filament and convective diffusion to or from the fluid-fluid interface are solved using finite-element methods. Flow computations are verified by comparing the dimensionless resistance factor and hydraulic conductance of corner filaments against recent numerical solutions by Patzek and Kristensen [2001]. Novel results are obtained for the average effluent concentration as a function of flow geometry and pore-scale Peclet number. These results are correlated to a characteristic corner length and local pore-scale Peclet number using empirical equations appropriate for implementation in pore network models. Finally, a previously published “2D-slit” approximation to the problem at hand is checked and found to be in considerable error. 3. Bubble evolution driven by solute diffusion during the process of supersaturated carbonated water flooding In situ bubble growth in porous media is simulated using a pore network model that idealizes the pore space as a lattice of cubic chambers connected by square tubes. Evolution of the gas phase from nucleation sites is driven by the solute mass transfer from the flowing supersaturated water solution to the bubble clusters. Effects of viscous aqueous phase flow and convective diffusion in pore corners are explicitly accounted for. Growth of bubble clusters is characterised by a pattern of quasi-static drainage and fingering in the gas phase, an invasion percolation process controlled by capillary and gravitational forces. A stepwise solution procedure is followed to determine the aqueous flow field and the solute concentration field in the model by solving the conservation equations. Mobilization of bubbles driven by buoyancy forces is also studied. Results of bubble growth pattern, relative permeability and macroscopic mass transfer coefficient are obtained under different gas saturations and aqueous flow conditions.

Carbonate rocks contain most of the world&rsquo / s proven hydrocarbon reserves. It is essential to predict flow properties and understand flow mechanisms in carbonates for estimating hydrocarbon recovery accurately. Pore network modeling is an effective tool in determination of flow properties and investigation of flow mechanisms. Topologically equivalent pore network models yield accurate results for flow properties. Due to their simple pore structure, sandstones are generally considered in pore scale studies and studies involving carbonates are limited. In this study, in order to understand flow mechanisms and wettability effects in heterogeneous carbonate rocks, a novel pore network model was developed for simulating two-phase flow. The constructed model was composed of matrix, fissure and vug sub domains and the sequence of fluid displacements was simulated typical by primary drainage followed by water flooding. Main mechanisms of imbibition, snap-off, piston like advance and pore body filling, were also considered. All the physically possible fluid configurations in the pores, vugs and fissures for all wettability types were examined. For configurations with a fluid layer sandwiched between other phases, the range of capillary pressures for the existence of such a layer was also evaluated. Then, results of the proposed model were compared with data available in literature. Finally, effects of wettability and pore structure on flow properties were examined by assigning different wettability conditions and porosity features. It was concluded that the proposed pore network model successfully represented two phase flow in fissured and vuggy carbonate rocks.

This thesis presents an investigation of reactive transport of species in porous media, with the aim to understand better and predict the fate of radionuclide in engineered and natural barriers of future deep geological disposal facilities for nuclear waste. The work involves developments of several pore-scale models for simulating reactive transport by coupling convective, adsorptive and diffusive processes. Pore network models (PNM) are amongst the appealing approaches that provide a suitable description for dealing with mutable pore space structures. Such models have been used to describe conservative as well as reactive transport in saturated and unsaturated porous media. In the present thesis, pore network models based on a regular tessellation of truncated octahedral cells are proposed and developed to simulate mass transport in porous media with incomplete pore space information due to limitation of existing characterisation techniques. Bentonite and Opalinus Clay are selected to illustrate the methodology. The micro- and meso-structure of these clays and their effects on the transport behaviour are investigated. The research shows that the clays are anisotropic and heterogeneous with fast diffusion parallel to the bedding plane and slow diffusion perpendicular to the bedding plane. In addition, different types of species have different accessible porosity and macroscopic diffusion coefficients. The anisotropy and heterogeneity of clays are achieved by different length scales and percentage of pores in different directions in the pore network models. The transport behaviour of various species, including sorption and anion exclusion, is simulated and analyzed. The effect of sorption is simulated via changing the pore radii by a coarse grained mathematical formula or by a formula directly in each pore. The results are in good agreement with experimentally measured macroscopic (bulk) diffusivities for the materials studied, including anisotropic diffusion coefficients. This lends strong support to the physical realism of the proposed models. The developed methodology can be used for any micro and meso-porous material with known distribution of pore sizes. It can be extended to other pore space changing mechanisms, in addition to sorption, to derive mechanism-based evolution laws for the transport parameters of porous media.

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.

[pt] A microtomografia computadorizada de uma amostra de rocha possibilita uma caracterização do meio poroso e pode ser utilizada para estimar propriedades da rocha em macroescala, isto é, em escala de reservatório. Métodos baseados em mapas de distâncias e em algoritmos de erosão são as principais abordagens utilizadas para extração de uma rede de poros e gargantas a partir de imagens microtomográficas de rocha. Este trabalho propõe um método híbrido para a construção da rede, de modo que, durante o processo de modelagem na escala de poros, obtemos um esqueleto do espaço poroso por meio de um algoritmo de erosão e utilizamos um mapa de distâncias para construir uma rede de poros e gargantas. A determinação dos poros e gargantas a partir do esqueleto adota uma abordagem não-determinística possibilitando a geração de múltiplas redes com configurações distintas a partir de um mesmo esqueleto. Avaliamos a variabilidade dos cenários gerados e comparamos as estimativas para as propriedades petrofísicas com as obtidas pelo método de Bolas Máximas por meio dos resultados de uma simulação de fluxo monofásica na rede. / [en] Computerized microtomography of a rock sample enables a characterization of the porous medium and can be used to estimate rock properties at the macro-scale, i.e., reservoir-scale. Methods based on distance maps and thinning algorithms are the main approaches used for extracting a pore and throats network from microtomographic rock images. This paper proposes a hybrid method for constructing the network. So that during the pore-scale modeling process, we obtain a skeleton of the pore space by using a thinning algorithm and a distance map to build a network of pores and throats. The determination of pores and throats from the skeleton assumes a non-deterministic approach enabling the generation of multiple networks with distinct configurations from the same skeleton. We evaluate the variability of the generated scenarios and compare the estimates for the petrophysical properties with those obtained by the Maximum Ball Method through the results of a single-phase flow simulation on the network.

Ce travail concerne principalement la détermination des propriétés acoustiques de mousses. Il s’agit d’un projet mené dans le cadre d’une collaboration entre une équipe de physico-chimie des mousses chargée de l’élaboration de matériaux modèles (laboratoire Navier UMR 8205 CNRS) et une équipe d’acousticiens chargée de l’étude de leurs propriétés acoustiques (laboratoire MSME UMR 8208 CNRS). Cette thèse s’articule essentiellement autour de trois parties principales, dont le contenu est résumé ci-dessous. 1) La première partie porte sur la génération de surfaces de réponse par des approximations polynomiales, dans le but de disposer d'un modèle intermédiaire entre le modèle éléments finis micro-macro et la réponse macroscopique. Au lieu d'appeler le modèle éléments finis systématiquement dans un travail d'optimisation, on a recourt à la surface de réponse qui contient l'information associée aux points de calcul éléments finis ainsi que les interpolations correspondantes. Ce manuscrit a été publié dans le journal AAA sous forme de communication rapide. 2) La deuxième partie porte sur la mise au point d'un modèle semi-analytique définit à partir d'une formule disponible pour prédire la perméabilité d'une plaque infinie percée par un trou de surface connue. Ce modèle, utilisé de manière appropriée, permet de calculer la perméabilité de mousses dont la taille de bulles est constante et le taux de fermeture de membranes variable. Des validations numériques par éléments finis et expérimentales sont proposées. L'article a été accepté pour publication dans la revue Physical Review E. 3) La troisième partie, porte sur un calcul éléments finis dans lequel un grand nombre de réalisations sont menées de manière à prendre en compte l'ensemble des combinaisons possibles lorsque on dispose de caractérisation expérimentales fines à l'échelle de la microstructure et que l'on souhaite connaitre la réponse de la mousse avec précision. Le manuscrit est en préparation et la revue visée pour ce dernier manuscrit est le journal Materials and Design. Une introduction et une conclusion générale complètent ces trois parties, et permettent de mettre en perspectives ces contributions par rapport à la littérature existante sur le sujet / This work mainly concerns the determination of the acoustic properties of foams. This is a project carried out as part of a collaboration between a team of physico-chemistry of foams in charge of the development of model materials (Navier laboratory UMR 8205 CNRS) and a team of acousticians responsible for the study of their acoustic properties (MSME laboratory UMR 8208 CNRS). This thesis is structured around three main parts, the content of which is summarized below. 1) The first part deals with the generation of response surfaces by polynomial approximations, in order to have an intermediate model between the micro-macro finite element model and the macroscopic response. Instead of calling the finite element model systematically in an optimization work, we use the response surface that contains the information associated with finite element calculation points and the corresponding interpolations. This manuscript was published in the AAA journal as a fast track publication. 2) The second part focuses on the development of a semi-analytical model defined from an available formula to predict the permeability of a circular orifice in a thin plate. This model, used in an appropriate way, makes it possible to calculate the permeability of foams with a constant bubble size but a tuned membrane content. Numerical validations by finite element computations are proposed. The article has been accepted for publication in the journal Physical Review E. 3) The third part deals with a finite element calculation in which a large number of realizations are carried out in order to take into account all the possible combinations when one has fine experimental characterization at the microstructure scale and that one seek to determine the properties of the foam with precision. The manuscript is in preparation and a possible journal for the publication of this manuscript is the journal Materials and Design. An introduction and a general conclusion complete these three parts, and make it possible to discuss these contributions

The understanding of multiphase flow properties is essential for the exploitation of hydrocarbon reserves in a reservoir; these properties in turn are dependent on the geometric properties and connectivity of the pore space. The determination of the pore size distribution in carbonate reservoirs remains challenging; carbonates exhibit complex pore structures comprising length scales from nanometers to several centimeters. A major challenge to the accurate evaluation of these reservoirs is accounting for pore scale heterogeneity on multiple scales. This is the topic of this thesis. Conventionally, this micron scale information is achieved either by building stochastic models using 2D images or by combining log and laboratory data to classify pore types and their behaviour. None of these capture the true 3D connectivity vital for flow characterisation. We present here an approach to build realistic 3D network models across a range of scales to improve property estimation through employment of X-ray micro-Computed Tomography (μCT) and Focussed Ion Beam Tomography (FIBT). The submicron, or microporous, regions are delineated through a differential imaging technique undertaken on x-ray CT providing a qualitative description of microporosity. Various 3-Phase segmentation methods are then applied for quantitative characterisation of those regions utilising the attenuation coefficient values from the 3D tomographic images. X-ray micro-CT is resolution limited and can not resolve the detailed geometrical features of the submicron pores. FIB tomography is used to image the 3D pore structure of submicron pores down to a scale of tens of nanometers. We describe the experimental development and subsequent image processing including issues and difficulties resolved at various stages. The developed methodology is implemented on cores from producing wackstone and grainstone reservoirs. Pore network models are generated to characterise the 3D interconnectivity of pores. We perform the simulations of petrophysical properties (permeability and formation resistivity) directly on the submicron scale image data. Simulated drainage capillary pressure curves are matched with the experimental data. We also present some preliminary results for the integration of multiscale pore information to build dual-scale network models. The integration of multiscale data allows one to select appropriate effective medium theories to incorporate sub-micron structure into property calculations at macro scale giving a more realistic estimation of properties.

No description available.

The understanding of multiphase flow properties is essential for the exploitation of hydrocarbon reserves in a reservoir; these properties in turn are dependent on the geometric properties and connectivity of the pore space. The determination of the pore size distribution in carbonate reservoirs remains challenging; carbonates exhibit complex pore structures comprising length scales from nanometers to several centimeters. A major challenge to the accurate evaluation of these reservoirs is accounting for pore scale heterogeneity on multiple scales. This is the topic of this thesis. Conventionally, this micron scale information is achieved either by building stochastic models using 2D images or by combining log and laboratory data to classify pore types and their behaviour. None of these capture the true 3D connectivity vital for flow characterisation. We present here an approach to build realistic 3D network models across a range of scales to improve property estimation through employment of X-ray micro-Computed Tomography (μCT) and Focussed Ion Beam Tomography (FIBT). The submicron, or microporous, regions are delineated through a differential imaging technique undertaken on x-ray CT providing a qualitative description of microporosity. Various 3-Phase segmentation methods are then applied for quantitative characterisation of those regions utilising the attenuation coefficient values from the 3D tomographic images. X-ray micro-CT is resolution limited and can not resolve the detailed geometrical features of the submicron pores. FIB tomography is used to image the 3D pore structure of submicron pores down to a scale of tens of nanometers. We describe the experimental development and subsequent image processing including issues and difficulties resolved at various stages. The developed methodology is implemented on cores from producing wackstone and grainstone reservoirs. Pore network models are generated to characterise the 3D interconnectivity of pores. We perform the simulations of petrophysical properties (permeability and formation resistivity) directly on the submicron scale image data. Simulated drainage capillary pressure curves are matched with the experimental data. We also present some preliminary results for the integration of multiscale pore information to build dual-scale network models. The integration of multiscale data allows one to select appropriate effective medium theories to incorporate sub-micron structure into property calculations at macro scale giving a more realistic estimation of properties.