Showing papers in "Transport in Porous Media in 2004"

Drawdown Induced Changes in Permeability of Coalbeds: A New Interpretation of the Reservoir Response to Primary Recovery

Abstract: A model for pore pressure-dependent cleat permeability is presented for gas-desorbing, linear elastic coalbeds under uniaxial strain conditions experienced in producing reservoirs. In the model, changes in the cleat permeability of coalbeds, which are idealised to have a bundled matchstick geometry, is controlled by the prevailing effective horizontal stresses normal to the cleats. Variations in the effective horizontal stresses under uniaxial strain conditions are expressed as a function of pore pressure reduction during drawdown, which includes a cleat compression term and a matrix shrinkage term that have competing effects on cleat permeability. A comprehensive analysis has revealed that the shape of the stress – pore pressure curve is predominantly determined by the magnitude of recovery pressure and rebound pressure relative to the initial reservoir pressure. A total of five possible scenarios have been identified with regard to response of the horizontal stress function to reservoir drawdown. When applied to four coalbed wells at two separate sites in the fairway of the San Juan basin, the model predictions at one site, where the three wells have shown increased absolute permeability during gas production, are in excellent agreement with the published pore pressure dependent permeability changes that were obtained independently from history matching the field production data. At a separate site the model correctly predicts, at least qualitatively, a strong permeability rebound at lower drawdown pressures that has been inferred through history matching the production data. An analysis of the effects of initial reservoir pressure on the response of effective horizontal stress to drawdown was carried out, with reference to the range of pressure likely to be encountered in the San Juan basin. The implications of this in terms of pore pressure dependent permeability are discussed.

An Improved IMPES Method for Two-Phase Flow in Porous Media

Abstract: In this paper we develop and numerically study an improved IMPES method for solving a partial differential coupled system for two-phase flow in a three-dimensional porous medium. This improved method utilizes an adaptive control strategy on the choice of a time step for saturation and takes a much larger time step for pressure than for the saturation. Through a stability analysis and a comparison with a simultaneous solution method, we show that this improved IMPES method is effective and efficient for the numerical simulation of two-phase flow and it is capable of solving two-phase coning problems.

Application of a n-Phase Model to the Diffusion Coefficient of Chloride in Mortar

Abstract: The determination of the chloride diffusion coefficient of a concrete is needed to help the prediction of the service life of concrete structure. In this paper, we propose first a critical review of models for chloride diffusion coefficients already used in literature at different scales and then we develop an analytical model, which takes into account the characteristics of the different phases of concrete. These materials are treated as a three-phase composite, consisting of a cement continuous phase, of an aggregates dispersed phase and of an interface transition zone. Chloride diffusion coefficient using an n-layered inclusion-based micromechanical modeling is predicted. The details of calculations are summarized hereafter and experimental measurements obtained on mortars are compared with predicted results.

Effects of viscous dissipation and flow work on forced convection in a channel filled by a saturated porous medium

Abstract: Fully developed forced convection in a parallel plate channel filled by a saturated porous medium, with walls held either at uniform temperature or at uniform heat flux, with the effects of viscous dissipation and flow work included, is treated analytically. The Brinkman model is employed. The analysis leads to expressions for the Nusselt number, as a function of the Darcy number and Brinkman number.

Effect of Network Topology on Relative Permeability

Abstract: We consider the role of topology on drainage relative permeabilities derived from network models. We describe the topological properties of rock networks derived from a suite of tomographic images of Fontainbleau sandstone (Lindquist et al., 2000, J. Geophys. Res.105B, 21508). All rock networks display a broad distribution of coordination number and the presence of long-range topological bonds. We show the importance of accurately reproducing sample topology when deriving relative permeability curves from the model networks. Comparisons between the relative permeability curves for the rock networks and those computed on a regular cubic lattice with identical geometric characteristics (pore and throat size distributions) show poor agreement. Relative permeabilities computed on regular lattices and on diluted lattices with a similar average coordination number to the rock networks also display poor agreement. We find that relative permeability curves computed on stochastic networks which honour the full coordination number distribution of the rock networks produce reasonable agreement with the rock networks. We show that random and regular lattices with the same coordination number distribution produce similar relative permeabilities and that the introduction of longer-range topological bonds has only a small effect. We show that relative permeabilities for networks exhibiting pore–throat size correlations and sizes up to the core-scale still exhibit a significant dependence on network topology. The results show the importance of incorporating realistic 3D topologies in network models for predicting multiphase flow properties.

On Barenblatt's model of spontaneous countercurrent imbibition

Abstract: Water imbibition is a critical mechanism of secondary oil recovery from fractured reservoirs. Spontaneous imbibition also plays a significant role in storage of liquid waste by controlling the extent of rock invasion. In the present paper, we extend a model of countercurrent imbibition based on Barenblatt's theory of non-equilibrium two-phase flow by allowing the model's relaxation time to be a function of the wetting fluid saturation. We obtain two asymptotic self-similar solutions, valid at early and late times, respectively. At a very early stage, the time scale characterizing the cumulative volume of imbibed (and expelled) fluid is a power function with exponent between 1.5 and 1. At a later stage, the time scaling for this volume approaches asymptotically classical square root of time, whereas the saturation profile asymptotically converges to Ryzhik's self-similar solution. Our conclusions are verified against experiments. By fitting the laboratory data, we estimate the characteristic relaxation times for different pairs of liquids.

Heat and mass transfer in MHD micropolar flow over a vertical moving porous plate in a porous medium

Abstract: An analysis is presented for the problem of free convection with mass transfer flow for a micropolar fluid via a porous medium bounded by a semi-infinite vertical porous plate in the presence of a transverse magnetic field. The plate moves with constant velocity in the longitudinal direction, and the free stream velocity follows an exponentially small perturbation law. A uniform magnetic field acts perpendicularly to the porous surface in which absorbs the micropolar fluid with a suction velocity varying with time. Numerical results of velocity distribution of micropolar fluids are compared with the corresponding flow problems for a Newtonian fluid. Also, the results of the skin-friction coefficient, the couple stress coefficient, the rate of the heat and mass transfers at the wall are prepared with various values of fluid properties and flow conditions.

A steady-state upscaling approach for immiscible two-phase flow

Abstract: The paper presents a model for computing rate-dependent effective capillary pressure and relative permeabilities for two-phase flow, in 2 and 3 space-dimensions. The model is based on solving the equations for immiscible two-phase flow at steady-state, accounting for viscous and capillary forces, at a given external pressure drop. The computational performance of the steady-state model and its accuracy is evaluated through comparison with a commercial simulator ECLIPSE. The properties of the rate-dependent effective relative permeabilities are studied by way of computations using the developed steady-state model. Examples presented show the dependence of the effective relative permeabilities and capillary pressures, which incorporate the effects of fine scale wettability heterogeneity, on the external pressure drop, and thereby on the dimensionless macro-scale capillary number. The effective relative permeabilities converge towards the viscous limit functions as the capillary number tends to infinity. Special cases, when the effective relative permeabilities are rate-invariant, are also studied. The applicability of the steady-state upscaling algorithm in dynamic displacement situations is validated by comparing fine-gridded simulations in heterogeneous reservoirs against their homogenized counterparts. It is concluded that the steady-state upscaling method is able to accurately predict the dynamic behavior of a heterogeneous reservoir, including small scale heterogeneities in both the absolute permeability and the wettability.

Stability of Convection in a Gravity Modulated Porous Layer Heated from Below

Abstract: The linear stability theory is used to investigate analytically the effects of gravity modulation on convection in a homogenous porous layer heated from below. The gravitational field consists of a constant part and a sinusoidally varying part, which is tantamount to a vertically oscillating porous layer subjected to constant gravity. The linear stability results are presented for the specific case of low amplitude vibration for which it is shown that increasing the frequency of vibration stabilises the convection.

Nonlinear Coupled Mathematical Model for Solid Deformation and Gas Seepage in Fractured Media

Abstract: Based on detailed investigation into the interactional physical mechanism of solid deformations and gas seepage in rock matrix and fracture, a nonlinear coupled mathematical model of solid deformation and gas seepage is put forward and the FEM model is built up to carry out numerical analysis. The coupled interaction laws between solid deformations and gas seepage in rock matrix and fractures has been emphasized in the model, which is a vital progress for coupled mathematical model of solid deformation and gas seepage of rock mass media. As an example, the methane extraction in fractured coal seam has been numerically simulated. By analyzing the simulation results, the law of methane migration and exchange in rock matrix and fractures is interpreted.

The Onset of Oscillatory Convection in a Horizontal Porous Layer Saturated with Viscoelastic Liquid

Abstract: The onset of thermal convection in an isothermally heated, horizontal porous layer saturated with viscoelastic liquid was analyzed analytically under the linear theory. An existing constitutive model, which is rather simple, was employed to examine the effects of relaxation times. It is shown clearly that oscillatory instabilities can set in before stationary modes are exhibited. The peculiar behavior of the frequency at the critical state was discussed in connection to polymeric liquids.

Steady flows in unsaturated soils are stable

Abstract: The stability of steady, vertically upward and downward flow of water in a homogeneous layer of soil is analyzed. Three equivalent dimensionless forms of the Richards equation are introduced, namely the pressure head, saturation, and matric flux potential forms. To illustrate general results and derive special results, use is made of several representative classes of soils. For all classes of soils with a Lipschitz continuous relationship between the hydraulic conductivity and the matric flux potential, steady flows are shown to be unique. In addition, linear stability of these steady flows is proved. To this end, use is made of the energy method, in which one considers (weighted) L2-norms of the perturbations of the steady flows. This gives a general restriction of the dependence of the hydraulic conductivity upon the matric flux potential, yielding linear stability and exponential decay with time of a specific weighted L2-norm. It is shown that for other norms the ultimate decay towards the steady-solution is preceded by transient growth. An extension of the Richards equation to take into account dynamic memory effects is also considered. It is shown that the stability condition for the standard Richards equation implies linear stability of the steady solution of the extended model.

Theoretical Analysis of Anion Exclusion and Diffusive Transport Through Platy-Clay Soils

Abstract: Diffusive transport through geosynthetic clay liners and engineered compacted clay landfill liners is the primary mechanism for mass transport from well-engineered modern landfills. For this reason, accurate estimates of diffusion coefficients for clay soils are essential for the design of engineered liner systems. A long-standing theoretical problem is the role of anion exclusion on the estimation of diffusion coefficients for ionic solutes migrating through charged porous media. This paper describes the steady-state solution of a fully coupled set of transport equations modeling ion movement through a permanently charged platy-clay soil. The microscale analysis takes into account the actual diffusion coefficient for each ion species, ion-pairing (as required by electroneutrality of the solution), as well as anion exclusion and cation inclusion ,arising from the permanent charge on clay particles. To render the problem tractable, the theoretical analysis focuses on an extremely small two-dimensional unit cell in an ideal, saturated, two-phase porous medium. The analysis presented here is limited to a particular geometrical example, but this example is sufficiently general for characteristic behaviours of systems of this kind to be identified. Most importantly, new insight is gained into the mechanism of ion migration through a charged platy-clay soil. The numerical results obtained from this study show that the identification of macroscopic transport quantities such as effective diffusion coefficients and membrane potentials from diffusion cell tests using standard diffusion theory only hold for a specific system. While ion exclusion behaviours are often referred to in the literature, as far as the authors are aware there has been no previous detailed microscale analysis of their role in steady-state diffusion through a charged platy-clay soil.

An Experimental Study of Miscible Displacements in Porous Media with Variation of Fluid Density and Viscosity

Abstract: The effect of fluid density and viscosity on dispersion in miscible displacements in porous media is examined. Miscible displacement experiments with fluid pairs having density and viscosity differences are carried out in a Plexiglas column containing a homogeneous and isotropic sand pack. Tracer tests and tests of both stable and unstable miscible displacement are conducted using NaCl and glycerine solutions. Concentration breakthrough curves are measured through an electrical monitoring technique. Following the conventional convection–dispersion formulation, the dispersion coefficient is determined by performing a least squares fit to the measured concentration breakthrough curves. It is found that for stable displacements dispersion coefficients drop continually when density differences increase or when viscosity ratios of the displaced and displacing fluid decrease. In the unstable case the dispersion coefficients increase with both density and viscosity differences.

Three Pressures in Porous Media

Abstract: In a thermodynamic setting for a single phase (usually fluid), the thermodynamically defined pressure, involving the change in energy with respect to volume, is often assumed to be equal to the physically measurable pressure, related to the trace of the stress tensor. This assumption holds under certain conditions such as a small rate of deformation tensor for a fluid. For a two-phase porous medium, an additional thermodynamic pressure has been previously defined for each phase, relating the change in energy with respect to volume fraction. Within the framework of Hybrid Mixture Theory and hence the Coleman and Noll technique of exploiting the entropy inequality, we show how these three macroscopic pressures (the two thermodynamically defined pressures and the pressure relating to the trace of the stress tensor) are related and discuss the physical interpretation of each of them. In the process, we show how one can convert directly between different combinations of independent variables without re-exploiting the entropy inequality. The physical interpretation of these three pressures is investigated by examining four media: a single solid phase, a porous solid saturated with a fluid which has negligible physico-chemical interaction with the solid phase, a swelling porous medium with a non-interacting solid phase, such as well-layered clay, and a swelling porous medium with an interacting solid phase such as swelling polymers.

Relative Permeabilities for Strictly Hyperbolic Models of Three-Phase Flow in Porous Media

Abstract: Traditional mathematical models of multiphase flow in porous media use a straightforward extension of Darcy’s equation. The key element of these models is the appropriate formulation of the relative permeability functions. It is well known that for one-dimensional flow of three immiscible incompressible fluids, when capillarity is neglected, most relative permeability models used today give rise to regions in the saturation space with elliptic behavior (the so-called elliptic regions). We believe that this behavior is not physical, but rather the result of an incomplete mathematical model. In this paper we identify necessary conditions that must be satisfied by the relative permeability functions, so that the system of equations describing three-phase flow is strictly hyperbolic everywhere in the saturation triangle. These conditions seem to be in good agreement with pore-scale physics and experimental data.

Effect of Wetting on the Dynamics of Drainage in Porous Media

Abstract: We examine the consequences of the wettability properties on the dynamics of gravity drainage in porous media. The relation between the wetting properties at the pore scale and the macroscale hydrodynamics is studied. Model porous media consisting of hydrophilic and hydrophobic glass beads or sand with well defined wetting properties, are prepared for this study. Gravity drainage experiments with air displacing water (two-phase flow), are performed for different Bond numbers, and using different techniques such as gamma-ray densitometry, magnetic resonance imaging (MRI) and weight measurements. The dynamics of drainage is found to be different for hydrophilic and hydrophobic porous media in the transition zone (funicular regime). Moreover, for hydrophilic (water-wet) porous media, MRI experiments reveal the importance of drainage through the continuous water film, which leads to an increase of the residual quantity of water in the transition zone with time.

Unsteady Flow Through a Highly Porous Medium in the Presence of Radiation

Abstract: The unsteady natural convection flow of a viscous and incompressible fluid through a porous medium with high porosity bounded by a vertical infinite stationary plate in the presence of radiation has been investigated. The fluid is assumed to be a gray, emitting and absorbing radiation, but non-scattering medium. The effects of the radiation parameter, Grashof number and permeability parameter of the medium on the velocity field as well as the effects of the radiation parameter and Prandtl number on the temperature field have been included in the analysis.

Analytical Solution to the Riemann Problem of Three-Phase Flow in Porous Media

Abstract: In this paper we study one-dimensional three-phase flow through porous media of immiscible, incompressible fluids. The model uses the common multiphase flow extension of Darcy's equation, and does not include gravity and capillarity effects. Under these conditions, the mathematical problem reduces to a 2 x 2 system of conservation laws whose essential features are: (1) the system is strictly hyperbolic; (2) both characteristic fields are nongenuinely nonlinear, with single, connected inflection loci. These properties, which are natural extensions of the two-phase flow model, ensure that the solution is physically sensible. We present the complete analytical solution to the Riemann problem (constant initial and injected states) in detail, and describe the characteristic waves that may arise, concluding that only nine combinations of rarefactions, shocks and rarefaction-shocks are possible. We demonstrate that assuming the saturation paths of the solution are straightlines may result in inaccurate predictions for some realistic systems. Efficient algorithms for computing the exact solution are also given, making the analytical developments presented here readily applicable to interpretation of lab displacement experiments, and implementation of streamline simulators.

Multiresolution Wavelet Scale Up of Unstable Miscible Displacements in Flow Through Heterogeneous Porous Media

Abstract: We describe scale up of geological models of field-scale porous media using a new method based on the wavelet transformations. The porous media of interest contain broadly-distributed and correlated permeabilities. Wavelet transformation of the permeability field of such porous media coarsens the geological model from smallest to largest length scales, drastically reduces the number of equations to be solved, preserves the important information on the permeability field at all the relevant length scales, and yields numerical results for any fluid flow property that are as accurate as those that are obtained with the highly detailed geological model of the same porous media. To test this method, we carry out extensive computer simulations of unstable miscible displacement processes and the associated viscous fingering phenomenon in highly heterogeneous porous media, both with the fine-scale geological model and the coarsened model. Excellent agreement is found between the results of the two sets of simulations.

Flow Through a Two-Scale Porosity, Oriented Fibre Porous Medium

Abstract: A model is described for the meso- and micro-flow through an array of oriented fibre tows with meso-channels between the tows. Axial Stokes's flow was considered in the meso-channels and Darcy's law was applied within the porous fibre tows, taking into account injection pressure and capillary pressures in both types of flow. Transverse flow transfer was modelled from the leading flow front to the lagging flow and a partial-slip boundary condition was applied at the permeable boundaries of meso-channels. Flow visualisation experiments and microstructural characterisation of laminates provided appropriate experimental data for model validation. In this, the predictions for the progress of the leading meso-flow were in excellent agreement with the experimental data. Parametric studies followed including the effects of injection pressure and meso-channel size.

Dual Mesh Method for Upscaling in Waterflood Simulation

Abstract: Detailed geological models typically contain many more cells than can be accommodated by reservoir simulation due to computer time and memory constraints. However, recovery predictions performed on a coarser upscaled mesh are inevitably less accurate than those performed on the initial fine mesh. Recent studies have shown how to use both coarse and fine mesh information during waterflooding simulations. In this paper, we present an extension of the dual mesh method (Verdiere and Guerillot, 1996) which simulates water flooding injection using both the coarse and the original fine mesh information. The pressure field is first calculated on the coarse mesh. This information is used to estimate the pressure field within each coarse cell and then phase saturations are updated on the fine mesh. This method avoids the most time consuming step of reservoir simulation, namely solving for the pressure field on the fine grid. A conventional finite difference IMPES scheme is used considering a two phase fluid with gravity and vertical wells. Two upscaling methodologies are used and compared for averaging the coarse grid properties: geometric average and the pressure solve method. A series of test cases show that the method provides predictions similar to those of full fine grid simulations but using less computer time.

One- and Two-Phase Permeabilities of Vugular Porous Media

Abstract: The single and double phase macroscopic permeabilities of bimodal reconstructed porous media have been studied. The structure of these bimodal media is characterized by the micro and macroporosities (vug system) and by the micro and macrocorrelation lengths l p and l v. For a single phase, if the vugular system does not percolate, it is shown that the absolute permeability K mainly depends on l p and very little on the other parameters. However, when the vugs percolate, K is also influenced by the density of vugs. For double phase calculations (in strong wettability conditions), it is shown that a vuggy percolating system affects mainly the nonwetting phase permeability. Moreover, the relative permeabilities for a nonpercolating vuggy system are only slightly influenced by the porosity distribution. These predictions are in good agreement with some experimental data obtained with limestones.

A Numerical Study of Micro-Heterogeneity Effects on Upscaled Properties of Two-Phase Flow in Porous Media

Abstract: Commonly, capillary pressure–saturation–relative permeability (P c–S–K r) relationships are obtained by means of laboratory experiments carried out on soil samples that are up to 10–12 cm long. In obtaining these relationships, it is implicitly assumed that the soil sample is homogeneous. However, it is well known that even at such scales, some micro-heterogeneities may exist. These heterogeneous regions will have distinct multiphase flow properties and will affect saturation and distribution of wetting and non-wetting phases within the soil sample. This, in turn, may affect the measured two-phase flow relationships. In the present work, numerical simulations have been carried out to investigate how the variations in nature, amount, and distribution of sub-sample scale heterogeneities affect P c–S–K r relationships for dense non-aqueous phase liquid (DNAPL) and water flow. Fourteen combinations of sand types and heterogeneous patterns have been defined. These include binary combinations of coarse sand imbedded in fine sand and vice versa. The domains size is chosen so that it represents typical laboratory samples used in the measurements of P c–S–K r curves. Upscaled drainage and imbibition P c–S–K r relationships for various heterogeneity patterns have been obtained and compared in order to determine the relative significance of the heterogeneity patterns. Our results show that for micro-heterogeneities of the type shown here, the upscaled P c–S curve mainly follows the corresponding curve for the background sand. Only irreducible water saturation (in drainage) and residual DNAPL saturation (in imbibition) are affected by the presence and intensity of heterogeneities.

Absorption Rate and Volume Dependency on the Complexity of Porous Network Structures

Abstract: Results of simulated supersource imbibition into model network structures are compared with experimental observations of real network structures determined by dynamical gravimetric fluid uptake. A computer model, Pore-Cor, has been used previously to simulate the imbibition of fluid into porous structures by applying an imbibition algorithm for fluids undergoing both inertial and viscous dynamical absorption (Schoelkopf et al., 2000). The structures comprise cubic pores connected by cylindrical throats on a three-dimensional 10 × 10 × 10 position matrix. The absorption curves for model structures with monosized pore and throat size ranges and for polydisperse pore and throat size distributions centred around 0.1 µm, increasing from 0.1 µm as a lower limit, and decreasing from 0.1 µm as an upper limit, respectively, are analysed. A relevant observable porosity and 50% volume intrusion radius (r50) are obtained using simulated mercury intrusion. Experimental network pore structures were made using compressed tablets, formed under a series of pressures, of two finely ground calcium carbonates with defined differences in skeletal particle size distribution. The surface chemical, particulate and morphological pore characteristics were maintained constant over a range of porosities using controlled wet grinding and careful use of dispersant levels such that the ratio of dispersant to BET surface area was held constant. The experimental porosities were determined by mercury intrusion porosimetry applying corrections for mercury compression and penetrometer expansion together with a correction for sample skeletal compression (Gane et al., 1996). The applicability of the Lucas–Washburn equation is examined by defining two equivalent hydraulic radii, one based on a Darcy absorption length (rehcDarcy) and the other on a volume uptake (rehc), respectively. The results from the model structures having distributions of pores and throats, which contain either small or large pores, respectively, follow the experimental results qualitatively. Both approaches show a long timescale macroscopic absorption rate depending approximately, but not exactly, on the square root of time. The two experimental series, however, fail to scale with each other via the Lucas–Washburn equation in accordance with pore size, r50. Porosity is shown to be the main factor determining the volume absorption rate, and, when used as a weighting factor, gives linear correlation-scaling between r50 and a derived volume-based r′ehc equivalent hydraulic radius, obtained from an analytical expression of the observed Darcy-based rehcDarcy. The experimental samples showed that the directly observed rehc and the calculated r′ehc, derived from Darcy length, were equal, but this was not the case for the model values. A factor β = r′ehc/r50 is shown to be a possible descriptor of the sample network complexity and an indicator for the probability level of pore filling during the absorption dynamic.

Dynamics of the Water–Oil Front for Two-Phase, Immiscible Flow in Heterogeneous Porous Media. 2 – Isotropic Media

Abstract: We study the evolution of the water–oil front for two-phase, immiscible flow in heterogeneous porous media. Our analysis takes into account the viscous coupling between the pressure field and the saturation map. Although most of previously published stochastic homogenization approaches for upscaling two-phase flow in heterogeneous porous media neglect this viscous coupling, we show that it plays a crucial role in the dynamics of the front. In particular, when the mobility ratio is favorable, it induces a transverse flux that stabilizes the water–oil front, which follows a stationary behavior, at least in a statistical sense. Calculations are based on a double perturbation expansion of equations at first order: the local velocity fluctuation is defined as the sum of a viscous term related to perturbations of the saturation map, on one hand, plus the perturbation induced by the heterogeneity of the permeability field with a base-state saturation map, on the other hand. In this companion paper, we focus on flows in isotropic media. Our results predict the dynamics of the water–oil front for favorable mobility ratios. We show that the statistics of the front reach a stationary limit, as a function of the geostatistics of the permeability field and of the mobility ratio evaluated across the front. Results of numerical experiments and Monte-Carlo analysis confirm our predictions.

Mixing of Stably Stratified Gases in Subsurface Reservoirs: A Comparison of Diffusion Models

Abstract: Numerical simulations of the mixing of carbon dioxide (CO2) and methane (CH4) in a gravitationally stable configuration have been carried out using the multicomponent flow and transport simulator TOUGH2/EOS7C. The purpose of the simulations is to compare and test the appropriateness of the advective–diffusive model (ADM) relative to the more accurate dusty-gas model (DGM). The configuration is relevant to carbon sequestration in depleted natural gas reservoirs, where injected CO2 will migrate to low levels of the reservoir by buoyancy flow. Once a gravitationally stable configuration is attained, mixing will continue on a longer time scale by molecular diffusion. However, diffusive mixing of real gas components CO2 and CH4 can give rise to pressure gradients that can induce pressurization and flow that may affect the mixing process. Understanding this coupled response of diffusion and flow to concentration gradients is important for predicting mixing times in stratified gas reservoirs used for carbon sequestration. Motivated by prior studies that have shown that the ADM and DGM deviate from one another in low permeability systems, we have compared the ADM and DGM for the case of permeability equal to 10−15 m2 and 10−18 m2. At representative reservoir conditions of 40 bar and 40°C, gas transport by advection and diffusion using the ADM is slightly overpredicted for permeability equal to 10−15 m2, and substantially overpredicted for permeability equal to 10−18 m2 compared to DGM predictions. This result suggests that gas reservoirs with permeabilities larger than approximately 10−15 m2 can be adequately simulated using the ADM. For simulations of gas transport in the cap rock, or other very low permeability layers, the DGM is recommended.

Removal of small particles from a porous material by ultrasonic irradiation

Abstract: A study has been made of the removal of small particles from a porous material by means of ultrasonic irradiation. To that purpose a microscopic theoretical model has been developed to calculate the force of a traveling acoustic wave on a spherical particle attached to the wall of a smooth, cylindrical pore inside the porous material. This force was compared with the adhesion force between a small particle and a pore wall. From the comparison between the two forces the conditions were found, at which particles are detached from pore walls and removed from the porous material. The transformation of the results gained from the microscopic model to macroscopic property (permeability) of the porous material was made by means of the Kozeny relation. The aim is to be able to understand and predict qualitatively the influence of relevant parameters on the ultrasonic cleaning process. Predictions made with the theoretical model were compared with data from experiments carried out with ultrasound to remove particles from Berea sandstone. The agreement is reasonable.

Free flow at the interface of porous surfaces: A generalization of the taylor brush configuration

Abstract: A solution to the problem of shallow laminar water flow above a porous surface is essential when modeling phenomena such as erosion, resuspension, and mass transfer between the porous media and the flow above it. Previous studies proposed theoretical, experimental, and numerical insight with no single general solution to the problem. Many studies have used the Brinkman equation, while others showed that it does not represent the actual interface flow conditions. In this paper we show that the interface macroscopic velocity can be accurately modeled by introducing a modification to the Brinkman equation. A moving average approach was proved to be successful when choosing the correct representative elementary volume and comparing the macroscopic solution with the average microscopic flow. As the size of the representative elementary volume was found to be equal to the product of the square root of the permeability and an exponential function of the porosity, a general solution is now available for any brush configuration. Given the properties of the porous media (porosity and permeability), the flow height and its driving force, a complete macroscopic solution of the interface flow is obtained.