[1] Alteration and dissolution resulting from reactive fluid flows in vertical fracture are investigated from numerical and laboratory experiments. Due to fluid density contrast, buoyancy effects are observed leading to significant changes in fracture geometry. Buoyant and forced convection forces act here in the same direction. The experiments were carried out at two different flow rates. When buoyancy forces are preponderant (low injection flow rate), the dissolution rate increases with the vertical distance. By contrast, for convectiondominated transport (high injection flow rate), a uniform dissolution is observed. Using numerical simulations, four dissolution regimes were identified. The fracture patterns observed strongly depend on the characteristic dimensionless numbers of the process, respectively, the Richardson, Damköhler, and Péclet numbers. The good agreement between numerical simulations and experimental results in terms of fracture patterns highlights the capability of the numerical model to describe the complex coupling between flow dynamics, buoyancy, and chemical reaction. Finally, a 3-D behavior diagram is constructed to illustrate these interactions and as a means of relating the appropriate dimensionless parameters to the morphological changes observed.Citation: Olte´an, C., F. Golfier, and M. A. Bue`s (2013), Numerical and experimental investigation of buoyancy-driven dissolution in vertical fracture,

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In this paper, we present a two-dimensional pore-scale numerical model to investigate the main mechanisms governing biofilm growth in porous media. The fluid flow and solute transport equations are coupled with a biofilm evolution model. Fluid flow is simulated with an immersed boundary-lattice Boltzmann model while solute transport is described with a volume-of-fluid-type approach. A cellular automaton algorithm combined with immersed boundary methods was developed to describe the spreading and distribution of biomass. Bacterial attachment and detachment mechanisms are also taken into account.The capability of this model to describe correctly the couplings involved between fluid circulation, nutrient transport and bacterial growth is tested under different hydrostatic and hydrodynamic conditions (i) on a flat medium and (ii) for a complex porous medium. For the second case, different regimes of biofilm growth are identified and are found to be related to the dimensionless parameters of the model, Damköhler and Péclet numbers and dimensionless shear stress. Finally, the impact of biofilm growth on the macroscopic properties of the porous medium is investigated and we discuss the unicity of the relationships between hydraulic conductivity and biofilm volume fraction.

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Predicting the instabilities that occur during the chemical reaction between a percolating fluid and a soluble rock leading to the development of macroscopic channels called wormholes is a key for understanding many geological processes. Their shape and their spatial distribution depend on two dimensionless numbers, namely Damköhler (Da) and Péclet (Pe) numbers. Although the dissolution phenomenon has been extensively studied both in the context of acid stimulation of oil wells in carbonate rocks and carbon capture and storage, few works have focused on the influence of the physical properties of fluids on wormhole patterns. Consequently, through interpretation of images acquired during the injection of pure water into a 2-D reconstituted salt massif and considering different configurations of injection, we illustrate the buoyancy effects on wormhole formation. Contrarily to observation in fractures, experimental results suggest that dissolution regimes can still be described by the classical dimensionless numbers Da and Pe. As for the regime diagram, it remains practically unchanged for strong Péclet and weak Damköhler and undergoes a slowdown of the propagation of the dissolution front when the number of Richardson's increases. Analysis of morphological descriptors such as area, interface, and tortuosity shows that density contrast has an influence on intermediate-to high-Richardson dissolution regimes that may be explained by the existence of buoyancy effects.

We develop a Darcy-scale model for multiphase transport in porous media colonized by biofilms. We start with the pore scale description of mass transfer within and between the phases (water, biofilm, and NAPL phases) and biologically mediated reactions. The macroscale mass balance equations under local mass equilibrium condition at the fluidbiofilm interface are derived from the pore scale problem, obtained by the method of volume averaging. The case of local mass equilibrium considered here finally provides one mass balance equation for the fluid and biological phases coupled with the NAPL-phase equation. We predict the effective dispersion tensor and the mass exchange coefficient that appear in the upscaled equation by solving closure problems on representative unit cells. The results of this model have been compared with pore scale simulations. Based on these comparisons, the validity domain of this model has been identified in terms of hydrodynamic and biochemical conditions of transport (i.e., Péclet and Damköhler numbers). This study should provide a better insight on the impact of biofilm dynamics near NAPL sources through the upscaling process. Keywords Porous media • Biofilm • NAPL • Upscaling • Volume averaging List of Symbols A i j Interface between the i-phase and j-phase (i, j: ω, β, γ, k) b β Closure variable that maps ∇ c Aβ β ontoc Aβ (m) b ω Closure variable that maps ∇ c Aω ω ontoc Aω (m) b β Dimensionless form of the closure variable b β (-) b ω Dimensionless form of the closure variable b ω (-)

The radial Navier–Stokes flow in a fracture bounded by impermeable corrugated rock surfaces is significantly different from the commonly used creeping flow model between two parallel surfaces, described by Darcy's law on the macroscale. Continuous variations in the Reynolds number along the radial coordinate determine the important role of the nonlinear inertial effects, which are reinforced by local oscillations of the velocity field caused by wall corrugation. The system behaviour is studied both analytically and numerically. A solution for the full system of Navier–Stokes equations in a thin cylindrical domain with oscillating walls is developed as a biparametric and two-scale asymptotic expansion with respect to fracture aperture and corrugation period. The numerical solution is derived based on the finite volume method. A new macroscale flow equation is obtained, which explicitly displays the relative roles of viscous dissipation caused by corrugation, local and global inertia, and cross inertia–viscous effects. The effective flow parameters are defined using analytical relationships.