Understanding and Modelling Turbulence Over and Inside Porous Media

To understand turbulence over porous media, a series of PIV measurements were carried out in porous-walled channel flows. The porous walls were made of three types of foamed ceramics which had the same porosity but different permeability. For turbulence inside porous media, LES studies of fully developed flows in three different model porous media were performed. Referring to these databases, a multi-scale k ? ε four equation eddy viscosity model for turbulence around and/or inside porous media was developed. Through the comparison to the experimental results, the proposed model was validated with satisfactory accuracy.     

Experimental Investigation and Modelling of Colloidal Release in Porous Media

Gas production from underground storage reservoirs is sometimes associated with solid particles eroded from the rock matrix. This phenomenon often called sand production can cause damage to the storage equipments, leading the operator to choke the wells and prevent them from producing at full capacity. Colloid release is often associated as a precursor of larger solid production. Indeed, in sandstone storage sites, clay release induced by the presence of condensed water associated with the gas production in the near-wellbore region can be a forecast of intergranular cement erosion. The objective of this work is twofold: firstly to experimentally investigate colloidal particle detachment through ionic strength reduction (absence of salinity of the condensed water) in porous media and secondly to determine its evolution with time and to model it. Laboratory experiments with model systems are developed to reproduce the particle generation and their transport in porous media. The model porous medium is a packed column of two powders: silicon carbide particles of 50 μm and silica particles of 0.5 μm (3% by weight) initially mixed together. Brine flows at different concentrations are imposed through the porous sample and, at very low salt concentration, colloid silica particles are massively released from the medium. Experimental evolutions of the particle concentration with time are compared to solutions of the advection–dispersion equation including first-order source terms for colloid release. The dispersion coefficients of the porous medium have been determined with tracer tests. The experimental results exhibit a different behaviour at short- and long-time intervals and a model has been built to predict the colloid production evolution with the introduction of two different time scales for the eroded rate. The model can be used in a core test to evaluate the amount of detachable fines and the rate of erosion.     

The Effects of Periodicity Assumptions in Porous Media Modelling

Transport in Porous Media - The effects of periodicity assumptions on the macroscopic properties of packed porous beds are evaluated using a cascaded Lattice-Boltzmann method model. The porous bed...     

Modelling the Flow of Yield-Stress Fluids in Porous Media

Yield-stress is a problematic and controversial non-Newtonian flow phenomenon. In this article, we investigate the flow of yield-stress substances through porous media within the framework of pore-scale network modelling. We also investigate the validity of the Minimum Threshold Path (MTP) algorithms to predict the pressure yield point of a network depicting random or regular porous media. Percolation theory as a basis for predicting the yield point of a network is briefly presented and assessed. In the course of this study, a yield-stress flow simulation model alongside several numerical algorithms related to yield-stress in porous media were developed, implemented and assessed. The general conclusion is that modelling the flow of yield-stress fluids in porous media is too difficult and problematic. More fundamental modelling strategies are required to tackle this problem in the future.     

A Micropolar Theory of Porous Media: Constitutive Modelling

The extension of the classical mixture theory by the concept of volume fractions leads to the theory of porous media. In this article, the theory of porous media is generalised to micropolar constituents. The kinematic relations and the balance equations for a porous medium are developed without restricting the number of constituents. Based on the entropy inequality, the general form of the constitutive equations are derived for a binary medium consisting of a porous elastic skeleton saturated by a viscous pore-fluid. Both constituents are assumed to be compressible. Handling the saturation constraint by a Lagrangian multiplier leads to a compatibility of the proposed model to so-called hybrid and incompressible models.     

Hydromechanical Modelling of Experimentally Compacted Saturated Argillaceous Porous Media

In order to model the experimental compaction of clays as completely as possible, it is necessary to use the hydromechanical coupled three-dimensional theory for saturated porous media. The proposed formulation is based on elastoplasticity, more precisely on modified Cam-clay model. The identification of the parameters of the model is made by special oedometric experiments at steady state. The compaction experiments are simulated with accuracy in transient and steady states and complement those obtained in a recent study based only on steady state.     

Some Pitfalls in the Modelling of Convective Flows in Porous Media

Some modelling deficiencies in various recent papers, on convective flows in porous media, are pointed out and discussed. These deficiencies are related to the Forchheimer coefficient, mixed double-diffusive convection, magnetohydrodynamic mixed convection, convection in a rarefied gas, and geophysical phenomena.     

Macroscale Thermodynamics and the Chemical Potential for Swelling Porous Media

The thermodynamical relations for a two-phase, N-constituent, swelling porous medium are derived using a hybridization of averaging and the mixture-theoretic approach of Bowen. Examples of such media include 2-1 lattice clays and lyophilic polymers. A novel, scalar definition for the macroscale chemical potential for porous media is introduced, and it is shown how the properties of this chemical potential can be derived by slightly expanding the usual Coleman and Noll approach for exploiting the entropy inequality to obtain near-equilibrium results. The relationship between this novel scalar chemical potential and the tensorial chemical potential of Bowen is discussed. The tensorial chemical potential may be discontinuous between the solid and fluid phases at equilibrium; a result in clear contrast to Gibbsian theories. It is shown that the macroscopic scalar chemical potential is completely analogous with the Gibbsian chemical potential. The relation between the two potentials is illustrated in three examples.     

Numerical Modelling of Swelling Pressure in Unsaturated Expansive Elasto-Plastic Porous Media

The focus of this work is to provide a new concept for accessing the swelling stress in expansive porous media, especially in highly compacted bentonite. The key to the new approach is the simulation with a chemical swelling model of an infinitesimal volume change followed by a back compaction Process. Free extension is allowed in the first step, to calculate the interlayer porosity change (micro) and the induced volume change potential (macro). The object-oriented FEM simulator GeoSys/RockFlow allows the combination of different processes. The hydro-mechanic/chemical (H²M/C) model takes into consideration two phase flow and deformation, as well as chemical swelling effects. The negative displacements on each boundary after the free extension simulation are taken as Dirichlet boundary conditions of the back compaction problem. The deformation step is simulated in the context of elasto-plasticity using the modified Cam-Clay model. The stresses obtained by back compaction represent the swelling pressure. A 2D example of compacted bentonite is analyzed with the new H²M/C model.     

Dispersion Phenomena in Thermal Diffusion and Modelling of Thermogravitational Experiments in Porous Media

In a TIPM paper published in 1992, the authors presented a simple model of thermogravitational diffusion in packed columns (TPC). Though qualitatively in agreement with the experimental results, this model exhibited a systematic discrepancy with respect to the magnitude of the permeability of maximum separation in the TPC experiments. Here, the results of a re-examination of the classical phenomenology of irreversible thermodynamics in porous media, applied to TPC, are described. Through the interpretation of additional TPC experiments, we show that the effective thermal diffusion coefficient in TPC includes a dependency upon the fluid velocity. This dependency is consistent with a nonlinear extension of irreversible thermodynamics, and the model so amended accounts for a correct re-interpretation of the experiments.     

Poromechanical Modelling and Inverse Approach of Drying Tests on Weakly Permeable Porous Rocks

The present paper deals with the determination of permeability in partially saturated conditions for weakly permeable porous rocks such as argillites or deep clayey formations. The level of permeability can be obtained via the measurements of transient weight loss of a sample submitted to a decrease in relative humidity imposed by saline solution in a hermetic chamber. An identification method based on simplified uncoupled 1D-linear and 1D-non-linear modelling was presented in a previous paper (Giraud et al. Trans Porous Media 69(2):259–280, 2006). The present paper takes into account generalized mass transfer phenomena such as Darcean advective transport of liquid and gas mixtures and Fickean diffusive transport of the vapour specie inside a gas mixture. Poromechanical coupling as well as 3D effects due to the geometry and finite dimensions of the tested samples are also covered by this approach. The coupled THM finite element computer code Code_Aster is then used to model the forward problem. The parameter identification procedure is based upon the solution of an inverse problem. The Levenberg–Marquardt algorithm was used for the problem of minimization. Comparisons between previous simplified 1D modelling and 2D-axisymmetrical coupled modelling show that the former method efficiently provides the correct order of magnitude of the level of permeability or the equivalent storage coefficients. Due to the boundary condition, the real 2D-axisymmetrical geometry of the sample must not be neglected if we are to obtain accurate results.     

Modelling of Power-law Fluid Flow Through Porous Media Using Smoothed Particle Hydrodynamics

The flow of non-Newtonian fluids through two-dimensional porous media is analyzed at the pore scale using the smoothed particle hydrodynamics (SPH) method. A fully explicit projection method is used to simulate incompressible flow. This study focuses on a shear-thinning power-law model (n < 1), though the method is sufficiently general to include other stress-shear rate relationships. The capabilities of the proposed method are demonstrated by analyzing a Poiseuille problem at low Reynolds numbers. Two test cases are also solved to evaluate validity of Darcy’s law for power-law fluids and to investigate the effect of anisotropy at the pore scale. Results show that the proposed algorithm can accurately simulate non-Newtonian fluid flows in porous media.     

Computation of the Longitudinal and Transverse Dispersion Coefficient in an Adsorbing Porous Medium Using Homogenization

This article compares for the first time, local longitudinal and transverse dispersion coefficients obtained by homogenization with experimental data of dispersion coefficients in porous media, using the correct porosity dependence. It is shown that the longitudinal dispersion coefficient can be reasonably represented by a simple periodic unit cell (PUC), which consists of a single sphere in a cube. We present a slightly modified and simplified approach to derive the homogenized equations, which emphasizes physical aspects of homogenization. Subsequently, we give full dimensional expressions for the dispersion tensor based on a comparison with the convective dispersion equation used for contaminant transport, inclusive the correct dependence on porosity. For the PUC of choice, the dispersion relations are identical to the relations obtained for periodic media. We show that commercial finite element software can be readily used to compute longitudinal and transverse dispersion coefficients in 2D and 3D. The 3D results are for the first time obtained at relevant Peclet numbers. There is good agreement for longitudinal dispersion. The computed transverse dispersion coefficients for a single sphere in a cube are much too low. The effect of adsorption on the dispersion coefficient is also studied. Adsorption does not affect the transverse dispersion coefficient. However, adsorption enhances the longitudinal dispersion coefficient in agreement with an analysis of homogenization applied to Taylor dispersion discussed in the literature.     

Reliability of Algorithms Interpreting Topological and Geometric Properties of Porous Media for Pore Network Modelling

Pore network models (PNMs) offer a computationally efficient way to analyse transport in porous media. Their effectiveness depends on how well they represent the topology and geometry of real pore systems, for example as imaged by X-ray CT. The performance of two popular algorithms, maximum ball and watershed, is evaluated for three porous systems: an idealised medium with known pore throat properties and two rocks with different morphogenesis—carbonate and sandstone. It is demonstrated that while the extracted PNM simulates simple flow (permeability) with acceptable accuracy, their topological and geometric properties are significantly different. This suggests that such PNM may not serve more complex studies, such as reactive/convective transport of contaminants or bacteria, and further research is necessary to improve the interpretation of real pore spaces with networks. Linear topology–geometry relations are derived and presented to stimulate development of more realistic PNM.

     

Modelling of Advection-Dominated Transport in a Porous Column with a Time-Decaying Flow Field

This paper examines the problem of the advective-dispersive movement of a non-decaying, inert chemical dye solution through the pore space of a fluid saturated porous column. The objective of the paper is to present a complete study of the one-dimensional advective-dispersive transport problem by considering certain analytical solutions, experimental results and their comparisons with specific computational simulations. Dye concentrations obtained by means of an image processing method are used in conjunction with an analytical solution to identify the hydrodynamic dispersion coefficient that governs the advective-dispersive transport problem. The experimental results and identified parameters are also used to assess the computational estimates derived from several stabilized computational schemes available in the literature, for examining advection-dominated transport processes in porous media.