Multiscale descriptions of density-driven flow instabilities in porous media

Les instabilités engendrées par des gradients de densité interviennent dans une variété d'écoulements. Un exemple est celui de la séquestration géologique du dioxyde de carbone en milieux poreux. Ce gaz est injecté à haute pression dans des aquifères salines et profondes. La différence de densité entre la saumure saturée en CO2 dissous et la saumure environnante induit des courants favorables qui le transportent vers les couches géologiques profondes. Les gradients de densité peuvent aussi être la cause du transport indésirable de matières toxiques, ce qui peut éventuellement conduire à la pollution des sols et des eaux. La gamme d'échelles intervenant dans ce type de phénomènes est très large. Elle s'étend de l'échelle poreuse où les phénomènes de croissance des instabilités s'opèrent, jusqu'à l'échelle des aquifères à laquelle interviennent les phénomènes à temps long. Une reproduction fiable de la physique par la simulation numérique demeure donc un défi en raison du caractère multi-échelles aussi bien au niveau spatial et temporel de ces phénomènes. Il requiert donc le développement d'algorithmes performants et l'utilisation d'outils de calculs modernes. En conjugaison avec les méthodes de résolution itératives, les méthodes multi-échelles permettent de résoudre les grands systèmes d'équations algébriques de manière efficace. Ces méthodes ont été introduites comme méthodes d'upscaling et de downscaling pour la simulation d'écoulements en milieux poreux afin de traiter de fortes hétérogénéités du champ de perméabilité. Le principe repose sur l'utilisation parallèle de deux maillages, le premier est choisi en fonction de la résolution du champ de perméabilité (grille fine), alors que le second (grille grossière) est utilisé pour approximer le problème fin à moindre coût. La qualité de la solution multi-échelles peut être améliorée de manière itérative pour empêcher des erreurs trop importantes si le champ de perméabilité est complexe. Les méthodes adaptatives qui restreignent les procédures de mise à jour aux régions à forts gradients permettent de limiter les coûts de calculs additionnels. Dans le cas d'instabilités induites par des gradients de densité, l'échelle des phénomènes varie au cours du temps. En conséquence, des méthodes multi-échelles adaptatives sont requises pour tenir compte de cette dynamique. L'objectif de cette thèse est de développer des algorithmes multi-échelles adaptatifs et efficaces pour la simulation des instabilités induites par des gradients de densité. Pour cela, nous nous basons sur la méthode des volumes finis multi-échelles (MsFV) qui offre l'avantage de résoudre les phénomènes de transport tout en conservant la masse de manière exacte. Dans la première partie, nous pouvons démontrer que les approximations de la méthode MsFV engendrent des phénomènes de digitation non-physiques dont la suppression requiert des opérations de correction itératives. Les coûts de calculs additionnels de ces opérations peuvent toutefois être compensés par des méthodes adaptatives. Nous proposons aussi l'utilisation de la méthode MsFV comme méthode de downscaling: la grille grossière étant utilisée dans les zones où l'écoulement est relativement homogène alors que la grille plus fine est utilisée pour résoudre les forts gradients. Dans la seconde partie, la méthode multi-échelle est étendue à un nombre arbitraire de niveaux. Nous prouvons que la méthode généralisée est performante pour la résolution de grands systèmes d'équations algébriques. Dans la dernière partie, nous focalisons notre étude sur les échelles qui déterminent l'évolution des instabilités engendrées par des gradients de densité. L'identification de la structure locale ainsi que globale de l'écoulement permet de procéder à un upscaling des instabilités à temps long alors que les structures à petite échelle sont conservées lors du déclenchement de l'instabilité. Les résultats présentés dans ce travail permettent d'étendre les connaissances des méthodes MsFV et offrent des formulations multi-échelles efficaces pour la simulation des instabilités engendrées par des gradients de densité. - Density-driven instabilities in porous media are of interest for a wide range of applications, for instance, for geological sequestration of CO2, during which CO2 is injected at high pressure into deep saline aquifers. Due to the density difference between the C02-saturated brine and the surrounding brine, a downward migration of CO2 into deeper regions, where the risk of leakage is reduced, takes place. Similarly, undesired spontaneous mobilization of potentially hazardous substances that might endanger groundwater quality can be triggered by density differences. Over the last years, these effects have been investigated with the help of numerical groundwater models. Major challenges in simulating density-driven instabilities arise from the different scales of interest involved, i.e., the scale at which instabilities are triggered and the aquifer scale over which long-term processes take place. An accurate numerical reproduction is possible, only if the finest scale is captured. For large aquifers, this leads to problems with a large number of unknowns. Advanced numerical methods are required to efficiently solve these problems with today's available computational resources. Beside efficient iterative solvers, multiscale methods are available to solve large numerical systems. Originally, multiscale methods have been developed as upscaling-downscaling techniques to resolve strong permeability contrasts. In this case, two static grids are used: one is chosen with respect to the resolution of the permeability field (fine grid); the other (coarse grid) is used to approximate the fine-scale problem at low computational costs. The quality of the multiscale solution can be iteratively improved to avoid large errors in case of complex permeability structures. Adaptive formulations, which restrict the iterative update to domains with large gradients, enable limiting the additional computational costs of the iterations. In case of density-driven instabilities, additional spatial scales appear which change with time. Flexible adaptive methods are required to account for these emerging dynamic scales. The objective of this work is to develop an adaptive multiscale formulation for the efficient and accurate simulation of density-driven instabilities. We consider the Multiscale Finite-Volume (MsFV) method, which is well suited for simulations including the solution of transport problems as it guarantees a conservative velocity field. In the first part of this thesis, we investigate the applicability of the standard MsFV method to density- driven flow problems. We demonstrate that approximations in MsFV may trigger unphysical fingers and iterative corrections are necessary. Adaptive formulations (e.g., limiting a refined solution to domains with large concentration gradients where fingers form) can be used to balance the extra costs. We also propose to use the MsFV method as downscaling technique: the coarse discretization is used in areas without significant change in the flow field whereas the problem is refined in the zones of interest. This enables accounting for the dynamic change in scales of density-driven instabilities. In the second part of the thesis the MsFV algorithm, which originally employs one coarse level, is extended to an arbitrary number of coarse levels. We prove that this keeps the MsFV method efficient for problems with a large number of unknowns. In the last part of this thesis, we focus on the scales that control the evolution of density fingers. The identification of local and global flow patterns allows a coarse description at late times while conserving fine-scale details during onset stage. Results presented in this work advance the understanding of the Multiscale Finite-Volume method and offer efficient dynamic multiscale formulations to simulate density-driven instabilities. - Les nappes phréatiques caractérisées par des structures poreuses et des fractures très perméables représentent un intérêt particulier pour les hydrogéologues et ingénieurs environnementaux. Dans ces milieux, une large variété d'écoulements peut être observée. Les plus communs sont le transport de contaminants par les eaux souterraines, le transport réactif ou l'écoulement simultané de plusieurs phases non miscibles, comme le pétrole et l'eau. L'échelle qui caractérise ces écoulements est définie par l'interaction de l'hétérogénéité géologique et des processus physiques. Un fluide au repos dans l'espace interstitiel d'un milieu poreux peut être déstabilisé par des gradients de densité. Ils peuvent être induits par des changements locaux de température ou par dissolution d'un composé chimique. Les instabilités engendrées par des gradients de densité revêtent un intérêt particulier puisque qu'elles peuvent éventuellement compromettre la qualité des eaux. Un exemple frappant est la salinisation de l'eau douce dans les nappes phréatiques par pénétration d'eau salée plus dense dans les régions profondes. Dans le cas des écoulements gouvernés par les gradients de densité, les échelles caractéristiques de l'écoulement s'étendent de l'échelle poreuse où les phénomènes de croissance des instabilités s'opèrent, jusqu'à l'échelle des aquifères sur laquelle interviennent les phénomènes à temps long. Etant donné que les investigations in-situ sont pratiquement impossibles, les modèles numériques sont utilisés pour prédire et évaluer les risques liés aux instabilités engendrées par les gradients de densité. Une description correcte de ces phénomènes repose sur la description de toutes les échelles de l'écoulement dont la gamme peut s'étendre sur huit à dix ordres de grandeur dans le cas de grands aquifères. Il en résulte des problèmes numériques de grande taille qui sont très couteux à résoudre. Des schémas numériques sophistiqués sont donc nécessaires pour effectuer des simulations précises d'instabilités hydro-dynamiques à grande échelle. Dans ce travail, nous présentons différentes méthodes numériques qui permettent de simuler efficacement et avec précision les instabilités dues aux gradients de densité. Ces nouvelles méthodes sont basées sur les volumes finis multi-échelles. L'idée est de projeter le problème original à une échelle plus grande où il est moins coûteux à résoudre puis de relever la solution grossière vers l'échelle de départ. Cette technique est particulièrement adaptée pour résoudre des problèmes où une large gamme d'échelle intervient et évolue de manière spatio-temporelle. Ceci permet de réduire les coûts de calculs en limitant la description détaillée du problème aux régions qui contiennent un front de concentration mobile. Les aboutissements sont illustrés par la simulation de phénomènes tels que l'intrusion d'eau salée ou la séquestration de dioxyde de carbone.

Fertility discourse in parental leave policies' media coverage : a frame analysis of French-speaking Swiss press articles from 1999 to 2009

This paper analyses the media coverage of parental leave policies (parental and paternity leaves) in Swiss French-speaking press articles from 1999 to 2009. Switzerland is one of the rare European countries which has no statutory parental or paternity leave. The aim is to describe the mediatisation of these policies and to analyse the arguments in favour and against their implementation. We investigate the status of a fertility frame - the mobilisation of discourse relating to fertility issues - among the various arguments used to justify or reject parental leave policies. We proceed with a content analysis of 579 press articles, as well as a frame analysis on a subset in which parental leave policies are the central theme (N=206). Results show that paternity leave is the predominant public issue addressed in the dataset. A mediatisation peak was reached in 2007, following an initiative of a member of the Federal executive to implement a short paternity leave. Parental leave policies are predominantly represented in a positive light. The main positive frame is economic, in which leaves are represented as serving the interests of companies. Involved fatherhood and gender equality are also frequently mentioned as positive frames. The fertility frame is only moderately used in articles covering Swiss news on paternity leaves. Conversely, the fertility frame is largely mobilised in articles covering parental leave in other countries. We discuss some interpretations of this discrepancy and suggest future avenues of research on parental leave policies in Switzerland.

Secondhand smoke exposure in children is associated with common carotid artery intima-media thickness

Objective: To investigate the association between common carotid artery intima-media thickness (cIMT) and exposure to secondhand smoke (SHS) in children. Methods: Data were available at baseline in the Quebec Adiposity and Lifestyle investigation in Youth (QUALITY) study, an ongoing longitudinal investigation of Caucasian children aged 8e10 years at cohort inception, who had at least one obese parent. Data on exposure to parents, siblings and friends smoking were collected in interviewer-administered child, and self-report parent questionnaires. Blood cotinine was measured with a high sensitivity ELISA. cIMTwas measured by ultrasound. The association between blood cotinine and cIMT was investigated in multivariable linear regression analyses controlling for age, body mass index, and child smoking status. Results: Mean (SD) cIMT (0.5803 (0.04602)) did not differ across age or sex. Overall 26%, 6% and 3% of children were exposed to parents, siblings and friends smoking, respectively. Cotinine ranged from 0.13 ng/ml to 7.38 ng/ml (median (IQR)¼0.18 ng/ml)). Multivariately, a 1 ng/ml increase in cotinine was associated with a 0.090 mm increase in cIMT (p¼0.034). Conclusion: In children as young as age 8e10 years, exposure to SHS relates to cIMT, a marker of pre-clinical atherosclerosis. Given the wide range of health effects of SHS, increased public health efforts are needed to reduced exposure among children in homes an private vehicles.

Characterization of surface functional groups present on laboratory-generated and ambient aerosol particles by means of heterogeneous titration reactions

A Knudsen flow reactor has been used to quantify surface functional groups on aerosols collected in the field. This technique is based on a heterogeneous titration reaction between a probe gas and a specific functional group on the particle surface. In the first part of this work, the reactivity of different probe gases on laboratory-generated aerosols (limonene SOA, Pb(NO3)2, Cd(NO3)2) and diesel reference soot (SRM 2975) has been studied. Five probe gases have been selected for the quantitative determination of important functional groups: N(CH3)3 (for the titration of acidic sites), NH2OH (for carbonyl functions), CF3COOH and HCl (for basic sites of different strength), and O3 (for oxidizable groups). The second part describes a field campaign that has been undertaken in several bus depots in Switzerland, where ambient fine and ultrafine particles were collected on suitable filters and quantitatively investigated using the Knudsen flow reactor. Results point to important differences in the surface reactivity of ambient particles, depending on the sampling site and season. The particle surface appears to be multi-functional, with the simultaneous presence of antagonistic functional groups which do not undergo internal chemical reactions, such as acid-base neutralization. Results also indicate that the surface of ambient particles was characterized by a high density of carbonyl functions (reactivity towards NH2OH probe in the range 0.26-6 formal molecular monolayers) and a low density of acidic sites (reactivity towards N(CH3)3 probe in the range 0.01-0.20 formal molecular monolayer). Kinetic parameters point to fast redox reactions (uptake coefficient ?0>10-3 for O3 probe) and slow acid-base reactions (?0<10-4 for N(CH3)3 probe) on the particle surface. [Authors]

Diabetes and pre-diabetes are associated with cardiovascular risk factors and carotid/femoral intima-media thickness independently of markers of insuline resistance and adiposity

Background Impaired glucose regulation (IGR) is associated with detrimental cardiovascular outcomes such as cardiovascular disease risk factors (CVD risk factors) or intima-media thickness (IMT). Our aim was to examine whether these associations are mediated by body mass index (BMI), waist circumference (waist) or fasting serum insulin (insulin) in a population in the African region. Methods Major CVD risk factors (systolic blood pressure, smoking, LDL-cholesterol, HDL-cholesterol,) were measured in a random sample of adults aged 25-64 in the Seychelles (n=1255, participation rate: 80.2%). According to the criteria of the American Diabetes Association, IGR was divided in four ordered categories: 1) normal fasting glucose (NFG), 2) impaired fasting glucose (IFG) and normal glucose tolerance (IFG/NGT), 3) IFG and impaired glucose tolerance (IFG/IGT), and 4) diabetes mellitus (DM). Carotid and femoral IMT was assessed by ultrasound (n=496). Results Age-adjusted levels of the major CVD risk factors worsened gradually across IGR categories (NFG < IFG/NGT < IFG/IGT < DM), particularly HDL-cholesterol and blood pressure (p for trend <0.001). These relationships were marginally attenuated upon further adjustment for waist, BMI or insulin (whether considered alone or combined) and most of these relationships remained significant. With regards to IMT, the association was null with IFG/NGT, weak with IFG/IGT and stronger with DM (all more markedly at femoral than carotid levels). The associations between IMT and IFG/IGT or DM (adjusted by age and major CVD risk factors) decreased only marginally upon further adjustment for BMI, waist or insulin. Further adjustment for family history of diabetes did not alter the results. Conclusions We found graded relationships between IGR categories and both major CVD risk factors and carotid/femoral IMT. These relationships were only partly accounted for by BMI, waist and insulin. This suggests that increased CVD-risk associated with IGR is also mediated by factors other than the considered markers of adiposity and insulin resistance. The results also imply that IGR and associated major CVD risk factors should be systematically screened and appropriately managed.

Self-potentials in partially saturated media: the importance of explicit modeling of electrode effects

Self-potential (SP) data are of interest to vadose zone hydrology because of their direct sensitivity to water flow and ionic transport. There is unfortunately little consensus in the literature about how to best model SP data under partially saturated conditions, and different approaches (often supported by one laboratory data set alone) have been proposed. We argue that this lack of agreement can largely be traced to electrode effects that have not been properly taken into account. A series of drainage and imbibition experiments were considered in which we found that previously proposed approaches to remove electrode effects were unlikely to provide adequate corrections. Instead, we explicitly modeled the electrode effects together with classical SP contributions using a flow and transport model. The simulated data agreed overall with the observed SP signals and allowed decomposing the different signal contributions to analyze them separately. After reviewing other published experimental data, we suggest that most of them include electrode effects that have not been properly taken into account. Our results suggest that previously presented SP theory works well when considering the modeling uncertainties presently associated with electrode effects. Additional work is warranted to not only develop suitable electrodes for laboratory experiments but also to assure that associated electrode effects that appear inevitable in longer term experiments are predictable, so that they can be incorporated into the modeling framework.

A framework for hybrid simulations of two-phase flow in porous media

Rough a global coarse problem. Although these techniques are usually employed for problems in which the fine-scale processes are described by Darcy's law, they can also be applied to pore-scale simulations and used as a mathematical framework for hybrid methods that couples a Darcy and pore scales. In this work, we consider a pore-scale description of fine-scale processes. The Navier-Stokes equations are numerically solved in the pore geometry to compute the velocity field and obtain generalized permeabilities. In the case of two-phase flow, the dynamics of the phase interface is described by the volume of fluid method with the continuum surface force model. The MsFV method is employed to construct an algorithm that couples a Darcy macro-scale description with a pore-scale description at the fine scale. The hybrid simulations results presented are in good agreement with the fine-scale reference solutions. As the reconstruction of the fine-scale details can be done adaptively, the presented method offers a flexible framework for hybrid modeling.

Quantitative comparison between simulations of seismic wave propagation in heterogeneous poro-elastic media and equivalent visco-elastic solids for marine-type environments

There is increasing evidence to suggest that the presence of mesoscopic heterogeneities constitutes an important seismic attenuation mechanism in porous rocks. As a consequence, centimetre-scale perturbations of the rock physical properties should be taken into account for seismic modelling whenever detailed and accurate responses of specific target structures are desired, which is, however, computationally prohibitive. A convenient way to circumvent this problem is to use an upscaling procedure to replace each of the heterogeneous porous media composing the geological model by corresponding equivalent visco-elastic solids and to solve the visco-elastic equations of motion for the inferred equivalent model. While the overall qualitative validity of this procedure is well established, there are as of yet no quantitative analyses regarding the equivalence of the seismograms resulting from the original poro-elastic and the corresponding upscaled visco-elastic models. To address this issue, we compare poro-elastic and visco-elastic solutions for a range of marine-type models of increasing complexity. We found that despite the identical dispersion and attenuation behaviour of the heterogeneous poro-elastic and the equivalent visco-elastic media, the seismograms may differ substantially due to diverging boundary conditions, where there exist additional options for the poro-elastic case. In particular, we observe that at the fluid/porous-solid interface, the poro- and visco-elastic seismograms agree for closed-pore boundary conditions, but differ significantly for open-pore boundary conditions. This is an important result which has potentially far-reaching implications for wave-equation-based algorithms in exploration geophysics involving fluid/porous-solid interfaces, such as, for example, wavefield decomposition.

The Implied Book and the Narrative Text. On a Blind Spot in Narratological Theory - from a Media Studies Perspective

The article is concerned with the formal definition of a largely unnoticed factor in narrative structure. Based on the assumptions that (1) the semantics of a written text depend, among other factors, directly on its visual alignment in space, that (2) the formal structure of a text has to meet that of its spatial presentation and that (3) these assumptions hold true also for narrative texts (which, however, in modern times typically conceal their spatial dimensions by a low-key linear layout), it is argued that, how ever low-key, the expected material shape of a given narrative determines the configuration of its plot by its author. The ,implied book' thus denotes an author's historically assumable, not necessarily conscious idea of how his text, which is still in the process of creation, will be dimensionally presented and under these circumstances visually absorbed. Assuming that an author's knowledge of this later (potentially) substantiated material form influences the composition, the implied book is to be understood as a text-genetically determined, structuring moment of the text. Historically reconstructed, it thus serves the methodical analysis of structural characteristics of a completed text.

Pore-scale modeling of two-phase flow instabilities in porous media

Les problèmes d'écoulements multiphasiques en média poreux sont d'un grand intérêt pour de nombreuses applications scientifiques et techniques ; comme la séquestration de C02, l'extraction de pétrole et la dépollution des aquifères. La complexité intrinsèque des systèmes multiphasiques et l'hétérogénéité des formations géologiques sur des échelles multiples représentent un challenge majeur pour comprendre et modéliser les déplacements immiscibles dans les milieux poreux. Les descriptions à l'échelle supérieure basées sur la généralisation de l'équation de Darcy sont largement utilisées, mais ces méthodes sont sujettes à limitations pour les écoulements présentant de l'hystérèse. Les avancées récentes en terme de performances computationnelles et le développement de méthodes précises pour caractériser l'espace interstitiel ainsi que la distribution des phases ont favorisé l'utilisation de modèles qui permettent une résolution fine à l'échelle du pore. Ces modèles offrent un aperçu des caractéristiques de l'écoulement qui ne peuvent pas être facilement observées en laboratoire et peuvent être utilisé pour expliquer la différence entre les processus physiques et les modèles à l'échelle macroscopique existants. L'objet premier de la thèse se porte sur la simulation numérique directe : les équations de Navier-Stokes sont résolues dans l'espace interstitiel et la méthode du volume de fluide (VOF) est employée pour suivre l'évolution de l'interface. Dans VOF, la distribution des phases est décrite par une fonction fluide pour l'ensemble du domaine et des conditions aux bords particulières permettent la prise en compte des propriétés de mouillage du milieu poreux. Dans la première partie de la thèse, nous simulons le drainage dans une cellule Hele-Shaw 2D avec des obstacles cylindriques. Nous montrons que l'approche proposée est applicable même pour des ratios de densité et de viscosité très importants et permet de modéliser la transition entre déplacement stable et digitation visqueuse. Nous intéressons ensuite à l'interprétation de la pression capillaire à l'échelle macroscopique. Nous montrons que les techniques basées sur la moyenne spatiale de la pression présentent plusieurs limitations et sont imprécises en présence d'effets visqueux et de piégeage. Au contraire, une définition basée sur l'énergie permet de séparer les contributions capillaires des effets visqueux. La seconde partie de la thèse est consacrée à l'investigation des effets d'inertie associés aux reconfigurations irréversibles du ménisque causé par l'interface des instabilités. Comme prototype pour ces phénomènes, nous étudions d'abord la dynamique d'un ménisque dans un pore angulaire. Nous montrons que, dans un réseau de pores cubiques, les sauts et reconfigurations sont si fréquents que les effets d'inertie mènent à différentes configurations des fluides. A cause de la non-linéarité du problème, la distribution des fluides influence le travail des forces de pression, qui, à son tour, provoque une chute de pression dans la loi de Darcy. Cela suggère que ces phénomènes devraient être pris en compte lorsque que l'on décrit l'écoulement multiphasique en média poreux à l'échelle macroscopique. La dernière partie de la thèse s'attache à démontrer la validité de notre approche par une comparaison avec des expériences en laboratoire : un drainage instable dans un milieu poreux quasi 2D (une cellule Hele-Shaw avec des obstacles cylindriques). Plusieurs simulations sont tournées sous différentes conditions aux bords et en utilisant différents modèles (modèle intégré 2D et modèle 3D) afin de comparer certaines quantités macroscopiques avec les observations au laboratoire correspondantes. Malgré le challenge de modéliser des déplacements instables, où, par définition, de petites perturbations peuvent grandir sans fin, notre approche numérique apporte de résultats satisfaisants pour tous les cas étudiés. - Problems involving multiphase flow in porous media are of great interest in many scientific and engineering applications including Carbon Capture and Storage, oil recovery and groundwater remediation. The intrinsic complexity of multiphase systems and the multi scale heterogeneity of geological formations represent the major challenges to understand and model immiscible displacement in porous media. Upscaled descriptions based on generalization of Darcy's law are widely used, but they are subject to several limitations for flow that exhibit hysteric and history- dependent behaviors. Recent advances in high performance computing and the development of accurate methods to characterize pore space and phase distribution have fostered the use of models that allow sub-pore resolution. These models provide an insight on flow characteristics that cannot be easily achieved by laboratory experiments and can be used to explain the gap between physical processes and existing macro-scale models. We focus on direct numerical simulations: we solve the Navier-Stokes equations for mass and momentum conservation in the pore space and employ the Volume Of Fluid (VOF) method to track the evolution of the interface. In the VOF the distribution of the phases is described by a fluid function (whole-domain formulation) and special boundary conditions account for the wetting properties of the porous medium. In the first part of this thesis we simulate drainage in a 2-D Hele-Shaw cell filled with cylindrical obstacles. We show that the proposed approach can handle very large density and viscosity ratios and it is able to model the transition from stable displacement to viscous fingering. We then focus on the interpretation of the macroscopic capillary pressure showing that pressure average techniques are subject to several limitations and they are not accurate in presence of viscous effects and trapping. On the contrary an energy-based definition allows separating viscous and capillary contributions. In the second part of the thesis we investigate inertia effects associated with abrupt and irreversible reconfigurations of the menisci caused by interface instabilities. As a prototype of these phenomena we first consider the dynamics of a meniscus in an angular pore. We show that in a network of cubic pores, jumps and reconfigurations are so frequent that inertia effects lead to different fluid configurations. Due to the non-linearity of the problem, the distribution of the fluids influences the work done by pressure forces, which is in turn related to the pressure drop in Darcy's law. This suggests that these phenomena should be taken into account when upscaling multiphase flow in porous media. The last part of the thesis is devoted to proving the accuracy of the numerical approach by validation with experiments of unstable primary drainage in a quasi-2D porous medium (i.e., Hele-Shaw cell filled with cylindrical obstacles). We perform simulations under different boundary conditions and using different models (2-D integrated and full 3-D) and we compare several macroscopic quantities with the corresponding experiment. Despite the intrinsic challenges of modeling unstable displacement, where by definition small perturbations can grow without bounds, the numerical method gives satisfactory results for all the cases studied.