Fabrice Golfier

On the ability of a Darcy-scale model to capture wormhole formation during the dissolution of a porous medium

Dissolution of a porous medium creates, under certain conditions, some highly conductive channels called wormholes. The mechanism of propagation is an unstable phenomenon depending on the microscopic properties at the pore scale and is controlled by the injection rate. The aim of this work is to test the ability of a Darcy-scale model to describe the different dissolution regimes and to characterize the influence of the flow parameters on the wormhole development. The numerical approach is validated by model experiments reflecting dissolution processes occurring during acid injection in limestone. Flow and transport macroscopic equations are written under the assumption of local mass non-equilibrium. The coupled system of equations is solved numerically in two dimensions using a finite volume method. Results are discussed in terms of wormhole propagation rate and pore volume injected.

Core-scale description of porous media dissolution during acid injection - Part I: theoretical development

Dissolution mechanisms in porous media may lead to unstable dissolution fronts (wormholing). It has been shown in the literature that Darcy-scale models may reproduce all the characteristics of such dissolution patterns. This paper considers the core-scale averaged behavior of these Darcy-scale dissolution models. The form of core-scale equations is discussed based on the volume averaging of the Darcy-scale equations. The uncertainty about the choice of the unit cell (and boundary conditions) to solve the closure problems and the impact of the dissolution history on the core-scale properties is emphasized.

Investigation of the effective permeability of vuggy or fractured porous media from a Darcy-Brinkman approach

In this paper, the macroscopic representation of one-phase incompressible flow in fractured and cavity (or vuggy) porous media is studied from theoretical and numerical points of view. A single-domain (or equivalently a Darcy-Brinkman) type of approach is followed to describe the momentum transport at Darcy scale where the fracture or cavity region and porous matrix region are well identified. The Darcy scale model is upscaled yielding a macroscopic momentum equation operating on the equivalent homogeneous medium. Numerical solution to the associated closure problem is proposed in order to compute the effective permeability. Numerical results on some model fractured and cavity media are discussed and compared to some analytical results.

Numerical Efficiency Assessment of IB–LB Method for 3D Pore-Scale Modeling of Flow and Transport

In many earth science and environmental problems, the fluid–structure interactions can affect the hydrodynamics properties of the porous medium via the spatial evolution of its solid matrix. A significant insight into these properties can be obtained from pore-scale simulations. Using a 3D pore-scale domain with moving walls, we proposed in this paper a comparison of the numerical accuracy between different approaches in regard to flow and reactive transport. Two direct-forcing immersed boundary (IB) models coupled with lattice Boltzmann method (LBM) are evaluated for the flow calculation against an analytical solution. The IB–LBM showed improvement compared to the classical and interpolated bounce-back lattice Boltzmann model. Concerning the reactive transport, the most accurate IB–LB method was coupled with two non-boundary conforming finite volume methods (volume of fluid and reconstruction). The comparative study performed with different mesh sizes and Damköhler numbers demonstrates better results for the reconstruction method.

Dispersive transport in porous media with biofilms: local mass equilibrium in simple unit cells

In this work, we continue our study of upscaling biofilm processes in porous media from the pore scale to the Darcy scale. We adopt a continuum-level description of biofilms at the pore scale on the basis of work reported in Wood et al. (2002b). We upscale from the pore scale to the Darcy scale using the method of volume averaging and we predict the effective dispersion tensor with two- and three-dimensional closure problems. Our results indicate that, for a one-equation local mass equilibrium theory, the primary influence of the biofilm is that the effective diffusion coefficient is smaller than it would be without the presence of biofilm. This effect is important primarily at low Peclet numbers.

Core-scale description of porous media dissolution during acid injection - part II: calculation of the effective properties

Acid injection in porous medium is a process widely used for stimulation of petroleum wells and leads to the formation of highly conductive channels called wormholes. Two different transport-reaction models have been developed in Part I to describe the phenomenon at the core-scale. The possible existence of core-scale effective properties which appear in these models is discussed here on the basis of Darcy-scale numerical experiments. The advantages and drawbacks of one-equation and two-equation models are investigated by reference to averaged fields computed from Darcy-scale simulations.

Gravity-driven fingers in fractures: experimental study and dispersion analysis by moment method for a point-source injection.

In this study, we investigate the behavior of a dense contaminant injected from a point-source in a fracture. Our experimental model is a transparent Hele-Shaw cell, 0.5 mm of aperture. A saline solution is injected locally representing the point-source pollution. A Laser Induced Fluorescence (LIF) method provides concentration measurement of the pollution plume. Two propagation patterns have been observed: one and two-finger plumes. If the upper part of the plume is stable over time regardless of the second configuration, the moment when the plume separates into two fingers is highly dependent on both injection flow-rate and contaminant concentration. To further investigate the dispersion process inside the fracture, experimental results are interpreted by the spatial and time moment methods. Resulting dispersivities and plume propagation mean velocity are compared to theoretical values derived from a modified Taylor-Aris dispersion tensor. The longitudinal macro-dispersion obtained suggests an asymptotical behavior of the plume spread regardless of the studied configurations. Experimental local dispersivities derived from time and space moments proved to be close at large times to theoretical values predicted by the density-dependent dispersion tensor (Oltéan et al., 2004). Based on those observations the mechanism behind the separation of the plume into two fingers is believed to be significantly impacted by the pre-asymptotic behavior of the dispersion tensor.

Upscaling of transport processes in porous media with biofilms in equilibrium and non-equilibrium conditions

Transport of biologically reactive dissolved solutes in a saturated porous medium including a biofilm-phase occurs in various technological applications such as in biochemical or environmental engineering. It is a complex process involving a wide variety of scales (from the bacteria-scale to the aquifer-heterogeneities-scale in the case of groundwater remediation) and processes (hydrodynamic, physicochemical and biochemical). This work is devoted to the upscaling of the pore-scale description of such processes. Firstly, one-equation macroscopic models for bio-reactive transport at the Darcy-scale have been developed by using the volume averaging method; they will be presented below. These one-equation models are valid for different limit cases of transport; their validity domains in terms of hydrodynamic and biochemical conditions will also be discussed. Finally, in order to illustrate such a theoretical development, an example of application to the operation of a packed bed reactor will be studied.

An Upscaled Model for Bio-Enhanced NAPL Dissolution in Porous Media

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 fluid–biofilm 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.

Impact of biofilm‐induced heterogeneities on solute transport in porous media

In subsurface systems, biofilm may degrade organic or organometallic pollutants contributing to natural attenuation and soil bioremediation techniques. This increase of microbial activity leads to change the hydrodynamic properties of aquifers. The purpose of this work was to investigate the influence of biofilm-induced heterogeneities on solute transport in porous media and more specifically on dispersivity. We pursued this goal by (i) monitoring both spatial concentration fields and solute breakthrough curves from conservative tracer experiments in a biofilm-supporting porous medium, (ii) characterizing in situ the changes in biovolume and visualizing the dynamics of the biological material at the mesoscale. A series of experiments was carried out in a flow cell system (60 cm(3)) with a silica sand (Phi = 50-70 mesh) as solid carrier and Shewanella oneidensis MR-1 as bacterial strain. Biofilm growth was monitored by image acquisition with a digital camera. The biofilm volume fraction was estimated through tracer experiments with the Blue Dextran macromolecule as in size-exclusion chromatography, leading to a fair picture of the biocolonization within the flow cell. Biofilm growth was achieved in the whole flow cell in 29 days and up to 50% of void space volume was plugged. The influence of biofilm maturation on porous medium transport properties was evaluated from tracer experiments using Brilliant Blue FCF. An experimental correlation was found between effective (i.e., nonbiocolonized) porosity and biofilm-affected dispersivity. Comparison with values given by the theoretical model of Taylor and Jaffe (1990b) yields a fair agreement.