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. / text

Pore-scale simulation has become increasingly important in recent years as a tool to understand multiphase flow behavior. Wettability affects aspects of flow such as capillary-pressure saturation curves, residual saturation of each phase, and relative permeability. Simulation of wettability at the pore-scale is still a non-trivial problem, and many different approaches exist to model it. In this work, we implement a variational level set formulation to impose different contact angles at the solid-fluid-fluid contact line for two-phase flow in simple rhomboidal pore geometries, and calculate the maximum mean curvature (equivalently capillary pressure) for each case. We compare our results with a detailed set of analytical and experimental results in a range of pore geometries of varying wettability from Mason and Morrow (1994), and demonstrate the accuracy of this method. While the simulations shown are for relatively simple geometries, the method has the ability to handle arbitrarily complex geometry (such as input from X-ray microtomography imaging). / text

Accurate predictions of macroscopic multiphase flow properties, such as relative permeability and capillary pressure, are necessary for making key decisions in reservoir engineering. These properties are usually measured experimentally, but pore-scale network modeling has become an efficient alternative for understanding fundamental flow behavior and prediction of macroscopic properties. In many cases network modeling gives excellent agreement with experiment by using models physically representative of real media. Void space within a rock sample can be extracted from high resolution images and converted to a topologically equivalent network of pores and throats. Multiphase fluid transport is then modeled by imposing mass conservation at each pore and implementing the Young-Laplace equation in pore throats; the resulting pressure field and phase distributions are used to extract macroscopic properties. Advancements continue to be made in making network modeling predictive, but one limitation is that artificial (e.g. constant pressure gradient) boundary conditions are usually assumed; they do not reflect the local saturations and pressure distributions that are affected by flow and transport in the surrounding media. In this work we demonstrate that flow behavior at the pore scale, and therefore macroscopic properties, is directly affected by the boundary conditions. Pore-scale drainage is modeled here by direct coupling to other pore-scale models so that the boundary conditions reflect flow behavior in the surrounding media. Saturation couples are used as the mathematical tool to ensure continuity of saturations between adjacent models. Network simulations obtained using the accurate, coupled boundary conditions are compared to traditional approach and the resulting macroscopic petrophysical properties are shown to be largely dependent upon the specified boundary conditions. The predictive ability of network simulations is improved using the novel network coupling scheme. Our results give important insight into upscaling as well as approaches for including pore-scale models directly into reservoir simulators. / text

Macroscopic transport properties of porous media depend on textural rock parameters such as porosity, grain size and grain shape distributions, surface-to-volume ratios, and spatial distributions of cement. Although porosity is routinely measured in the laboratory, direct measurements of other textural rock properties can be tedious, time-consuming, or impossible to obtain without special methods such as X-ray microtomography and scanning electron microscopy. However, by using digital three-dimensional pore-scale rock models and physics-based algorithms researchers can calculate both geometrical and transport properties of porous media. Therefore, pore-scale modeling techniques provide a unique opportunity to explore explicit relationships between pore-scale geometry and fluid and electric flow properties. The primary objective of this dissertation is to investigate at the pore-scale level the effects of grain shapes and spatial cement distribution on macroscopic rock properties for improved understanding of various petrophysical correlations. Deposition and compaction of grains having arbitrary angular shapes and various sizes is modeled using novel sedimentation and cementation pore-scale algorithms. Additionally, the algorithms implement numerical quartz precipitation to describe preferential cement growth in pore-throats, pore-bodies, or uniform layers. Subsequently, petrophysical properties such as geometrical pore-size distribution, primary drainage capillary pressure, absolute permeability, streamline-based throat size distribution, and apparent electrical formation factor are calculated for several digital rock models to evaluate petrophysical correlations. Furthermore, two geometrical approximation methods are introduced to model irreducible (connate) water saturation at the pore scale. Consolidated grain packs having comparable porosities and grain size distributions but various grain shapes indicate that realistic angular grain shape distribution gives the best agreement of petrophysical properties with experimental measurements. Cement volume and its spatial distribution significantly affect pore-space geometry and connectivity, and subsequently, macroscopic petrophysical properties of the porous media. For example, low-porosity rocks having similar grain structure but different cement spatial distribution could differ in absolute permeability by two orders of magnitude and in capillary trapped water saturation by a factor of three. For clastic rocks with porosity much higher than percolation threshold porosity, pore-scale modeling results confirm that surface-to-volume ratio and porosity provide sufficient rock-structure character to describe absolute permeability correlations. In comparison to surface-to-volume ratio, capillary trapped (irreducible) water saturation exhibits better correlation with absolute permeability due to weak pore space connectivity in low-porosity samples near the percolation threshold. Furthermore, in grain packs with fine laminations and permeability anisotropy, pore-scale analysis reveals anisotropy in directional drainage capillary- pressure curves and corresponding amounts of capillary-trapped wetting fluid. Finally, results presented in this dissertation indicate that pore-scale modeling methods can competently capture the effects of porous media geometry on macroscopic rock properties. Pore-scale two- and three-phase transport calculations with fast computers can predict petrophysical properties and provide sensitivity analysis of petrophysical properties for accurate reservoir characterization and subsequent field development planning. / text

Geological Carbon Storage (GCS) is considered as one of the key techniques to reduce the rate of atmospheric emissions of CO2 and thereby to contribute to controlling the global warming. A successful application of a GCS project requires the capability of the formation to trap CO2 for a long term. In this context, processes related to CO2 trapping and also possible leakage of CO2 to the near surface environment need to be understood. The overall aim of this thesis is to understand the flow and transport of CO2 through porous media in the context of geological storage of CO2. The entire range of scales, including the pore scale, the laboratory scale, the field experiment scale and the industrial scale of CO2 injection operation are addressed, and some of the key processes investigated by means of experiments and modeling.  First, a numerical model and laboratory experimental setup were developed to investigate the CO2 gas flow, mimicking the system in the near-surface conditions in case a leak from the storage formation should occur. The system specifically addressed the coupled flow and mass transport of gaseous CO2 both in the porous domain as well as the free flow domain above it. The comparison of experiments and modelling results showed a very good agreement indicating that the model developed can be applied to evaluate monitoring and surface detection of potential CO2 leakage. Second, the field scale CO2 injection test carried out in a shallow aquifer in Maguelone, France was analyzed and modeled. The results showed that Monte Carlo simulations accounting for the heterogeneity effects of the permeability field did capture the key observations of the monitoring data, while a homogeneous model could not represent them. Third, a numerical model based on phase-field method was developed and model simulations carried out addressing the effect of wettability on CO2-brine displacement at the pore-scale. The results show that strongly water-wet reservoirs provide a better potential for the dissolution trapping, due to the increase of interface between CO2 and brine with very low contact angles. The results further showed that strong water-wet conditions also imply a strong capillary effect, which is important for residual trapping of CO2. Finally, numerical model development and model simulations were carried out to address the large scale geological storage of CO2 in the presence of impurity gases in the CO2 rich phase. The results showed that impurity gases N2 and CH4 affected the spatial distribution of the gas (the supercritical CO2 rich phase), and a larger volume of reservoir is needed in comparison to the pure CO2 injection scenario. In addition, the solubility trapping significantly increased in the presence of N2 and CH4.

Les situations où deux fluides non miscibles sont présents dans un matériau granulaire déformable sont largement rencontrées dans la nature et dans de nombreux domaines de l'ingénierie et de la science. Comprendre l'évolution de tels systèmes multiphases nécessite la connaissance de toutes les phases, leur distribution et interactions. Un modèle micro-hydromécanique couplé est présenté dans cette thèse sur la base de travaux précédents, visant à simuler le drainage quasi-statique de matériaux granulaires déformables. Il combine une approche de type réseau de pores et la méthode des éléments discrets (DEM) pour les fluides et les grains respectivement. Un critère local de mouvement d'interfaces fluides est établi, afin d'approximer au mieux le rôle de la géométrie porale sur les phénomènes capillaires et notamment les forces exercées sur les grains solides à l'intérieur de chaque pore. Une attention particulière est dédiée aux événements de piégeage du fluide drainé et à l'invasion préférentielle le long des bords du domaines. Le modèle est valide par la comparaison avec des résultats expérimentaux (courbes de rétention d'eau). Nous appliquons le modèle pour étudier deux questions: (1) les effets de taille finie et à la question du volume élémentaire représentatif (REV); (2) le paramètre de contrainte effective de Bishop et la relation entre contrainte effective macroscopique contrainte de contact micromécanique. Finalement, une extension du modèle au régime pendulaire est présentée et des premiers résultats sont présentés et discutés. / The situation of two immiscible fluids through a deformable granular material is widely encountered in nature and in many areas of engineering and science. To understand the physical evolution of the multiphase system is of great importance for the applications. It requires the knowledge of all component phases, their distribution and interactions. A pore-scale coupled hydromechanical model is presented in this thesis based on previous work, aiming at simulating the quasi-static drainage of a deformable granular materials. The model combines a pore network approach and the discrete element method (DEM) for the fluids and grains, respectively. A local criterion for determining the local movements of the fluids interfaces established to approximate the role of the local pore geometry on capillarity and namely on the forces exerted on the solid grains inside each pore. Special attentions have been paid to the entrapment events of the receding fluid and to the preferential invasion along the boundaries. The model is validated through comparisons with experimental results (water retention curves). We apply the model for examining two issues: (1) finite size effects and the concept of representative elementary volume (REV); (2) Bishop's effective stress parameter and to the relationship between macro-scale effective stress and micro-scale contact stress. Finally, an extension to the pendular regimes is proposed and first results are presented and analyzed.