Michel Quintard

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.

Transport in ordered and disordered porous media III: Closure and comparison between theory and experiment

In this paper we examine the closure problem associated with the volume averaged form of the Stokes equations presented in Part II. For both ordered and disordered porous media, we make use of a spatially periodic model of a porous medium. Under these circumstances the closure problem, in terms of theclosure variables, is independent of the weighting functions used in the spatial smoothing process. Comparison between theory and experiment suggests that the geometrical characteristics of the unit cell dominate the calculated value of the Darcys law permeability tensor, whereas the periodic conditions required for thelocal form of the closure problem play only a minor role.

Transport in ordered and disordered porous media V: Geometrical results for two-dimensional systems

In this paper we continue the geometrical studies of computer generated two-phase systems that were presented in Part IV. In order to reduce the computational time associated with the previous three-dimensional studies, the calculations presented in this work are restricted to two dimensions. This allows us to explore more thoroughly the influence of the size of the averaging volume and to learn something about the use of anon-representative region in the determination of averaged quantities.

Transport in Ordered and Disordered Porous Media IV: Computer Generated Porous Media for Three-Dimensional Systems

In the method of volume averaging, the difference between ordered and disordered porous media appears at two distinct points in the analysis, i.e. in the process of spatial smoothing and in the closure problem. In theclosure problem, the use of spatially periodic boundary conditions isconsistent with ordered porous media and the fields under consideration when the length-scale constraint,r0≪L is satisfied. For disordered porous media, spatially periodic boundary conditions are an approximation in need of further study.In theprocess of spatial smoothing, average quantities must be removed from area and volume integrals in order to extractlocal transport equations fromnonlocal equations. This leads to a series of geometrical integrals that need to be evaluated. In Part II we indicated that these integrals were constants for ordered porous media provided that the weighting function used in the averaging process contained thecellular average. We also indicated that these integrals were constrained by certain order of magnitude estimates for disordered porous media. In this paper we verify these characteristics of the geometrical integrals, and we examine their values for pseudo-periodic and uniformly random systems through the use of computer generated porous media.

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.

Effective surface and boundary conditions for heterogeneous surfaces with mixed boundary conditions

To deal with multi-scale problems involving transport from a heterogeneous and rough surface characterized by a mixed boundary condition, an effective surface theory is developed, which replaces the original surface by a homogeneous and smooth surface with specific boundary conditions. A typical example corresponds to a laminar flow over a soluble salt medium which contains insoluble material. To develop the concept of effective surface, a multi-domain decomposition approach is applied. In this framework, velocity and concentration at micro-scale are estimated with an asymptotic expansion of deviation terms with respect to macro-scale velocity and concentration fields. Closure problems for the deviations are obtained and used to define the effective surface position and the related boundary conditions. The evolution of some effective properties and the impact of surface geometry, Peclet, Schmidt and Damkohler numbers are investigated. Finally, comparisons are made between the numerical results obtained with the effective models and those from direct numerical simulations with the original rough surface, for two kinds of configurations.

A Numerical Model Of Hydrocarbon ContaminantFlow In Soil And Aquifers

We present a numerical model which can be used to design remediation strategies for cleaning up soils and aquifers in both the saturated and unsaturated zones. This three-phase (air, water and pollutants) flow model takes into account the advective and the dispersive mass-transport, and includes local non-equilibrium mass transfer. The simulator is based on a finite-volume method. Several innovative techniques have been introduced to improve the efficiency and accuracy of the numerical model. In particular, for each time step the splitting method is used to solve the equations in two stages: (i) the first stage deals with transport and dispersion, (ii) the second stage deals with the mass exchange between the phases. The validity of the model has been tested against experimental studies in the following two cases 1 . A two-dimensional physical model representing the flow in an aquifer with pollutant injection, 2. A history matching of dissolved hydrocarbon in core samples. The results of the oneand two-dimensional simulations agree very well with the experimental data.

Determination of Chlorinated Solvent Sorption by Porous Material—Application to Trichloroethene Vapor on Cement Mortar

Experiments have been performed to investigate the sorption of trichloroethene (TCE) vapor by concrete material or, more specifically, the cement mortar component. Gas-flow experiments were conducted using columns packed with small pieces of cement mortar obtained from the grinding of typical concrete material. Transport and retardation of TCE at high vapor concentrations (500xa0mgxa0L