Growth activity during fingering in a porous Hele Shaw cell

We present in this paper an experimental study of the invasion activity during unstable drainage in a 2D random porous medium, when the (wetting) displaced fluid has a high viscosity with respect to that of the (non-wetting) displacing fluid, and for a range of almost two decades in capillary numbers corresponding to the transition between capillary and viscous fingering. We show that the invasion process takes place in an active zone within a characteristic screening length from the tip of the most advanced finger. The invasion probability density is found to only depend on the distance to the latter tip, and to be independent of the value for the capillary number Ca. The mass density along the flow direction is related analytically to the invasion probability density, and the scaling with respect to the capillary number is consistent with a power law. Other quantities characteristic of the displacement process, such as the speed of the most advanced finger tip or the characteristic finger width, are also consistent with power laws of the capillary number. The link between the growth probability and the pressure field is studied analytically and an expression for the pressure in the defending fluid along the cluster is derived. The measured pressure are then compared with the corresponding simulated pressure field using this expression for the boundary condition on the cluster.Comment: 11 pages 10 figure

Spontaneous and guided self-assembly of clay nanoplatelets

この論文は国立情報学研究所の電子図書館事業により電子化されました。研究会報

Ecoulements dans les fractures ouvertes

La 1 re partie de cette thèse présent une étude de la géométrie de surfaces rugueuses obtenues en laboratoire par fracturation de blocs de granite et de grès . Ces surfaces sont enregistrées à l'aide d'un rugosimètre à mesure mécanique et optique, développé pour cet usage. Les enregistrements sont bien décrits par un modèle auto-affine isotrope. La persistance des corrélations spatiales est sensiblement moins importante pour le grès que pour le granite. Dans un 2 e partie , on étudie comment l'écoulement à travers une fracture ouverte est influencé par la rugosité de ses parois, lorsque les effets inertiels peuvent être négligés. Une étude expérimentale met en évidence une sensibilité importante de la perméabilité de la fracture vis-à-vis de l'orientation du gradient de pression effectif. Un modèle numérique confirme ces observations, et permet d'interpréter cette " anisotropie " hydraulique en termes de chenalisation de l'écoulement...The first part of this thesis addresses a study of the geometry of rough fractures that have been obtained through controlled fracturing of granite and sandstone blocks. The surfaces are recorded using a specially deviced profiler, which allows mechanical and optical measurement. The recordings are well described by an isotropic self-affine model. The persistence of the correlations is significantly smaller for sandstone than it is for granite. In a second part, we study how the flow through a rough fracture is influenced by the roughness of the fracture walls, when inertial effects can be neglected. An experimental setup allows to observe a significant dependence of the of the fracture permeability on the orientation of the effective pressure gradient. A numerical model confirms these observations, and allows to interpret this " hydraulic anisotropy " in terms of flow channeling. Channeling is controlled by large scale heterogeneities in the aperture field; the importance of theseheterogeneities is greatly dependent on the matching of the two walls at large scales...ORSAY-PARIS 11-BU Sciences (914712101) / SudocSudocFranceF

Depth-integrated Two-dimensional Model for Immiscible Two-phase Flow in Open Rough-walled Fractures with Smoothly Varying Aperture

International audienceTwo-phase flow in geological fractures holds significant relevance in various applications, including subsurface fluid storage and oil and gas exploitation. The pore-scale modelling of such flows is a challenging task influenced by many factors, such as the complex interplay between the viscous, capillary, gravitational and inertial forces, intricate geometries, as well as molecular scale phenomena such as moving contact lines and thin wetting films. Although various modelling approaches have been used to tackle these challenges, the high computational demands required to accurately capture the three-dimensional fluid-fluid interfacial dynamics often render these models impractical for real-world applications. Consequently, from a practical point of view, the simplification of these 3D models may become imperative to facilitate efficient and reasonably accurate predictions of flow quantities.Depth-integrated two-dimensional modelling is one such approach which enables saving computational time and effort at the expense of not resolving the third dimension. Here, the governing equations are solved in two dimensions, the influence of the third dimension being incorporated through appropriate additional terms. While such models have been used previously, they have so far been restricted to either permanent single-phase flow in rough fractures or two-phase flow in 2D porous media of homogeneous depth. In a rough fracture, the fluid-fluid interface possesses not only an in-plane curvature but also an out-of-plane curvature, which must be accommodated in the 2D depth-integrated model. Therefore, to address the immiscible flows in rough fractures it is essential to reformulate the 2-D depth-integrated approach from the first principles.To perform the depth integration, we proceed from the traditional direct numerical simulation (DNS) approach, where the Navier-Stokes equations, coupled with an interface capturing technique, which in our case is the Volume of Fluid (VOF), are solved numerically. We integrate the governing flow equations in the vertical direction while expressing the flow fields in terms of 2D depth-averaged flow quantities. To account for the out-of-plane curvature and the wall shear stress arising from the no-slip conditions on the fracture walls, we assume locally a plane Poiseuille configuration (Hele-Shaw). The derived 2D depth-integrated model is implemented in the open-source CFD code OpenFOAM. We validate our model using the Saffman-Taylor instability case, comparing predictions with experiments and full 3D model results. We then extend our study to two numerically generated rough fractures with (a) smoothly and periodically varying aperture and (b) a more realistic aperture field with a larger roughness. We investigate drainage (i.e., the displacement of the wetting fluid by the non-wetting fluid) over a range of Capillary numbers spanning more than three orders of magnitude. We compare our 2D model predictions of both, pore-scale and macroscopic flow variables, with those obtained using 3D simulations. Our 2D model accurately estimates key statistical indicators with a tenfold reduction in computation time, offering an excellent compromise between solution accuracy and computational efficiency. We also discuss the limitations of the depth-averaged model depending on flow ranges

Étude numérique de l'impact des effets densitaires et inertiels sur le transport en milieu chenalisé

L'écoulement et le transport dans les milieux hétérogènes a principalement lieu dans des chenaux d'écoulement préférentiels. Il est donc crucial d'y caractériser au mieux les processus de transport. Pourtant, les techniques actuelles ne permettent pas de décrire le transport à l'échelle d'un site par les équations valides à l'échelle hydrodynamique, il est donc nécessaire d'effectuer un changement d'échelle pour décrire le transport à une échelle où la complexité du milieu n'apparaît plus directement. Les principaux objectifs de cette thèse ont été de caractériser l'impact à l'échelle du chenal de deux effets négligés dans la plupart des études hydrogéologiques. (i) Le premier survient lorsque la présence du soluté modifie significativement la masse volumique du fluide. Ce contraste densitaire modifie le chemin emprunté par le nuage de soluté. Dans un chenal horizontal lisse, le régime pré-asymptotique de dispersion est modifié et le nuage de soluté subit un retard. (ii) L'autre effet classiquement négligé survient lorsque l'écoulement est rapide (ou la viscosité du fluide faible). Les effets inertiels qui entrent alors en jeu sont étudiés dans un chenal d'ouverture variable et périodique. Des zones de recirculation apparaissent dans les cavités. Un soluté peut y pénétrer par diffusion et y rester piégé durant un temps long, tandis que l'écoulement principal est réduit à un chenal central d'ouverture moins hétérogène. (iii) Enfin, la combinaison des effets (i) et (ii) est abordée. Chacune des trois études est menée à l'échelle hydrodynamique en fonction du nombre de Reynolds, du nombre de Péclet et d'un nombre adimensionnel quantifiant l'impact du contraste densitaire.In heterogeneous media, flow and transport usually take place in preferential flow channels. Thus, it is of prime interest to take the associated physical processes into account. However, we are limited by current technology and cannot compute the transport of solute at the field scale using the equations of hydrodynamic. Thus, in order to describe solute transport at the field scale, upscaling is required. In this thesis, we study at the scale of the channels the impact of two effects usually neglected. (i) The first effect occurs when a sufficiently concentrated solute is diluted so that the density of the fluid increase significantly. As the density gradient of the solute plume locally modifies the flow field, the solute transport is impacted. In a horizontal smooth channel, the pre-asymptotic regime of dispersion is impacted and the plume is delayed. (ii) Second, when flow is fast enough (or fluid viscosity low enough), inertial effects can dramatically alter the flow field. We study their impact in channels with periodically varying apertures. When the inertial effects increase, recirculation zones grow at the location of the maximum aperture. Solute can then enter by diffusion into these zones and be trapped for a significant duration. (iii) Finally, the coupling of the effects (i) and (ii) is addressed. We reproduce numerically each effect at the hydrodynamic scale and characterize their impact as a function of the Reynolds number, the Péclet number and a dimensionless number that quantify the impact of the density gradients.RENNES1-BU Sciences Philo (352382102) / SudocSudocFranceF

Coupled electro-hydrodynamic transport in geological fractures

by Uddipta Ghosh, Tanguy Le Borgne and Yves Meheus

Transport en fracture et interaction avec la matrice (une expérience analogique)

Nous caractérisons en laboratoire le transport de solutés dans une fracture unique et l interaction fracture-matrice durant ce transport. Notre dispositif expérimental en Plexiglas est constitué d une fracture synthétique (100 cm de long, 5 cm de large, 0,5 cm de haut) présentant une interface inférieure imperméable (Plexiglas) ou perméable (couche de billes de verre) selon les configurations choisies. Un flux d eau est imposé à travers la fracture à des vitesses moyennes contrôlées (~1 mm/s). Un système d injection de colorant simule au centre de la fracture une source ponctuelle de contaminant, dont la migration est décrite par l évolution spatio-temporelle de la concentration grâce à un système de mesures optiques. Le dispositif se révèle bien adapté à l étude du couplage densitaire entre écoulement et transport dans une fracture imperméable en régime pré-asymptotique. La mesure à intervalles réguliers du flux massique advectif bidimensionnel associé au panache de soluté permet d établir des profils de la masse m(x)qui traverse une section de fracture transverse à l écoulement à la position longitudinale x. Une quantité de soluté piégée à la surface du milieu poreux, même sans réelle diffusion dans le milieu, est vue par le dispositif de mesure comme de la masse perdue, et donc échangée. Des pertes de masses significatives par rapport à notre incertitude expérimentales sont mesurées pour une fracture dont la paroi inférieure poreuse présente une rugosité ondulée. Cette configuration géométrique crée des zones de faibles vitesses permettant le piégeage superficiel d une partie du soluté (jusqu à 30 %). Les effets gravitaires jouent un rôle prépondérant dans ce processus.We characterize in the laboratory the solute transport in a single fracture, as well as the fracture-matrix interaction during transport. Our experimental setup consists in a 100x5x0,5 cm3 synthetic plexiglass fracture, the lower wall of which is either an impervious plane, or the top boundary of a glass bead piling. A controlled volumetric rate corresponding to fluid velocities in the mm/s range is imposed through the fracture. A localized source of contaminant is simulated in the setup using a custom-made injection setup, and an optical measurement system is used to monitor in time the two-dimensional concentration field inside the fracture. This setup proves to be well-suited to the study of the coupling between flow and transport through density effects in the pre-asymptotic regime. Measuring at regular time intervals the advective mass flux field inside the fracture allows us to determine the mass m(x) that passes through a section of the fracture transverse to the flow, at position x along the fracture. An amount of solute that is trapped at the piling s surface, even without penetration of the solute inside the porous medium, is seen by the measurement system as lost-, and therefore, exchanged-, solute mass. Mass losses significant compared to our experimental uncertainty are measured in a geometrical configuration for which the porous wall exhibits a quasi-sinusoidal roughness: in such a configuration, low velocity zones make superficial solute trapping (up to 30% of it) possible. Gravity plays a major role in this process.RENNES1-BU Sciences Philo (352382102) / SudocRENNES-Géosciences (352382209) / SudocSudocFranceF