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 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.

En vue de contrôler les émissions de gaz à effet de serre, il est envisagé d’injecter du CO2 dans des réservoirs géologiques. Or le CO2 n'est pas un gaz inerte. En modifiant la composition chimique de l'eau in situ, il est à l'origine d'interactions roche/fluide. Ces réactions géochimiques impactent les propriétés d'écoulement. Aussi, pour s'assurer de la viabilité et de la pérennité du stockage, les opérateurs ont besoin de simulations tenant compte de ces écoulements réactifs. Cependant les paramètres de l'équation macroscopique de transport utilisée sont affectés par les réactions surfaciques. Or, ces spécificités dues au transfert de masse ne sont pas prises en compte actuellement. De même, la loi perméabilité-porosité (K-F) n’est estimée que semi-empiriquement. Le but de cette thèse a été de développer une méthode pour obtenir les coefficients macroscopiques précédents et les relations K-F, en résolvant les équations gouvernant les phénomènes à l'échelle du pore. Pour ce faire, nous avons utilisé l'approche réseau de pores. L'avantage du modèle réseau est qu'il prend en compte explicitement la structure tout en conceptualisant cette dernière à un ensemble de pores et de canaux à la morphologie simplifiée (sphères, cylindres). L'étude est basée sur deux changements d'échelles successifs : du local au pore, puis du pore à la carotte. Le problème de transport réactif est résolu pour des éléments basiques, analytiquement ou numériquement. Puis, en faisant appel aux solutions précédemment trouvées, le transport réactif est traité sur l'ensemble du réseau. Notre model fut validé par des observations sur micromodèles, puis à l'aide d'une expérience d'altération acide / The geological storage of CO2 is considered as an attractive option to reduce the greenhouse gas emissions in the atmosphere. CO2 is not an inert gas, however. Its dissolution in brine forms a weak acid that has the potential to react with the host rock formation. The induced pores structure modification impacts the flow properties. Thus, to ensure the viability and sustainability of CO2 storage, operators need simulations that take into account the specificities of reactive transport. However, the macroscopic coefficients of the reactive transport equation are modified from the values of an inert tracer by surface reactions. These specificities due to mass transfer are currently not considered. Similarly, the permeability-porosity (K-F) relationship is only estimated semi-empirically. The aim of this thesis was to develop a method to obtain the macroscopic coefficients and the K-F laws, by solving the equations governing the pore-scale phenomena. To do this, we used the Pore Network Modelling approach (PNM). The advantage of the PNM is that it explicitly takes into account the pore structure, while conceptualizing the latter to a set of pores and throats whose morphology is simplified into spheres or cylinders for instance. The study is based into two successive upscalings: from local-scale to pore-scale, then from pore-scale to core-scale. The reactive transport problem is solved for basic elements, analytically or numerically. Then, using the solutions previously found at the pore scale, the reactive transport phenomena are treated throughout the network. Our model was validated by observations on micromodels and by a comparison with an acid-induced alteration experiment