F. Delay

Transport and retention of clay particles in saturated porous media. Influence of ionic strength and pore velocity.

The aim of this work was to experimentally evaluate the role of ionic strength and pore velocity on clay suspension transport and retention through a saturated porous medium. A smectite suspension was injected into columns filled with a very fine quartz sand. Experiments were carried out at constant pore velocity with increasing ionic strength adjusted with a divalent electrolyte (CaCl2) and at constant ionic strength (using three chemical conditions) with decreasing pore velocity. Typical colloid breakthrough curves show two important behaviors: a constant outlet concentration value after a transient phase, and a pronounced tailing effect at the end of the injection step. No differences were observed between the mean travel time of a solute tracer and that of the clay suspension. The classical advection-dispersion equation coupled with a first-order two-site kinetics model was used to reproduce the experimental breakthrough curves. The kinetic model consisted in a site with irreversible deposition and a reversible site used to reproduce the transient phase preceding the plateau of the experimental breakthrough curves. The particle fraction kept by the porous medium increases with ionic strength; consequently the kinetic parameters of the numerical model vary with chemistry. The irreversible sorption rate (Kirr: equivalent to a clean-bed filter coefficient) increases with ionic strength and was directly determined from experimental data. With increasing ionic strength, the deposition rate (Kd) for the reversible sorption increases whereas the release rate (Kr) decreases. The kinetic parameters of the reversible site show an evolution with pore velocity similar to that observed in kinetics model used for modeling solute transport in double porosity media. With decreasing pore velocities, the retention of clay particles increases but the kinetic deposition coefficient of the irreversible site decreases. Particle deposition can also be described and reinterpreted in terms of collector efficiency using the concept of the sphere-in-cell model. The collector efficiency, which adds a correction to the kinetic parameter with the residence time, is a more consistent way to represent particle retention. Its value increases with increasing ionic strength and decreasing pore velocity.

Predicting solute transport in heterogeneous media from results obtained in homogeneous ones: an experimental approach

Abstract The aim of this paper is to show that the hydrodispersive transport parameters of a solute in a heterogeneous medium can be predicted using parameters determined by several experiments with the different homogeneous media that constitute together the heterogeneous one. Elementary rules for predicting these parameters are defined. Three types of experiments were carried out. (1) Homogeneous medium transport experiments in 1-D columns. They were fitted with the help of a new numerical particle tracking method, including advection-dispersion and exchange between mobile and immobile water with first-order kinetics. (2) Layered heterogeneous media. The experiments were simulated by the numerical model without fitting, using the parameters of each of the layers of the homogeneous media included in the heterogeneous one. The results prove that, in such layered media, the global transport problem can be considered as the convolution of elementary transports in homogeneous blocks. We will therefore conclude that the reservoir simulation methods which represent the heterogeneous reservoir as a random set of elementary homogeneous blocks can be used to represent transport if each elementary block is given its appropriate hydrodispersive parameters. (3) Homogeneous mixtures of two pure components. The experiments produced three interesting results. The immobile water volume is the direct linear combination of its equivalent in the two components, weighted by the volumetric fraction of the component in the mixture. The dispersivity of the medium also evolves linearly, but is affected by an initial sharp rise due to a strong increase in local flow path heterogeneities whenever a “foreign body” is introduced into a pure component. The exchange rate between mobile and immobile water is also perturbed by mixing. In a binary mixture of one component with dual porosity and another one without, the exchange rate decreases with the increase of the volumetric fraction of the medium without dual porosity. It seems that, even if it does not modify the volumes of immobile and mobile water, it reduces the surface/volume ratio of the solid medium and consequently the exchange rate. Mixing rules could be adopted in order to modify the values of the hydrodispersive parameters that need to be introduced for the elementary blocks of heterogeneous reservoirs.

Transmissivity and morphological features in a chalk aquifer: a geostatistical approach of their relationship

Abstract Whether for the management of an aquifer or to locate new wells, hydrogeologists have always tried to establish transmissivity maps of regional aquifers with the highest possible accuracy. Classically, the transmissivity is obtained from well tests and/or from calibrating a groundwater flow model on the piezometric data. In this paper, we investigate the possibility of adding new information to improve the estimates of the transmissivity in a shallow chalk aquifer, i.e. the characteristics of certain morphological features, here referred to as ‘lynchets’, which are short lineaments that can be seen on aerial photographs or on topographic maps and represent a sudden breach in slope of the ground surface. We implicitly associate the density of these features with the density of vertical fracturing of the chalk, which is linked to the transmissivity. We selected the chalk aquifer of Northern France to test this approach. Using numerical and geostatistical techniques to construct maps of the density of the lynchets, we compared them with transmissivity maps produced either by calibrating a groundwater flow model with piezometric data or by kriging the transmissivity values obtained with well tests. We conclude that the lynchet information is clearly correlated with the transmissivity, and that this information can best be used by cokriging as a second variable associated with the well test data. Incidentally, to fit our geostatistical models of spatial variability (variogram), we use a new technique called the ‘integral semi-variogram’, which is ideally suited to cases such as this where the spatial distribution of the data is such that the data points cannot easily be grouped into pairs of increasing lag distance. This new technique is described briefly.

The integral of the semivariogram: A powerful method for adjusting the semivariogram in geostatistics

A good fining of the structural junction that describes the variability of a spatial phenomenon is an essential stage in the building of an accurate estimator by kriging. The technique of the integral of the semivariogram (ISV) makes it possible to find this structural function while overcoming the problem of grouping together the pairs of experimental points into classes of distances when the data are not sampled on a regular grid. The ISV is particularly useful when the dispersion of the values of the classical Semivariogram (SV) makes it difficult to fit a model. Since the ISV is composed of a large number of values, it is more continuous than a SV and therefore easier to fit analytically. In fact, when the general shape of the SV is known, the ISV method proves its worth in finding the parameters that best fit a given variogram model. The analytical models of ISV which will be used, are the integral expressions of the traditional analytical SV. In this paper and on the basis of hydrogeological examples, we propose a method to adjust all the parameters of each model. The first derivative of a filled ISV, used in the kriging equations, appears to be systematically the best SV for a cross-validation on the data. This is why we think that the ISV technique should be used when the strong spatial variability of a parameter spreads out the values of the experimental SV.

Comparison of transport simulations and equivalent dispersion coefficients in heterogeneous media generated by different numerical methods: A genesis model and a simple geostatistical sequential Gaussian simulator

This article presents a genesis method for characterizing heterogeneous media representing alluvial deposits. This method simulates the main steps of the medium genesis for meandering, braided, and incising streams and generates facies, which are then translated into hydraulic conductivities to simulate fl ow and transport. In order to compare this “genetic” model with other methods commonly used to characterize heterogeneous media, a basic sequential Gaussian indicator method was applied to the same site: a 5200-m-long reach of the Aube River fl oodplain (France). Ten different geostatistical realizations were generated. An equivalent homogeneous representation was also included. Flow and transport simulations in the different heterogeneous numerical media were conducted with Visual MODFLOW. The results were analyzed and compared in terms of permeability fi elds, plume spreading, and equivalent longitudinal dispersion. Emphasis is on the ability of the genetic model to represent continuous channels that can serve either as conduits or as barriers to fl ow, which, we think, is unique.

Simulation algorithm of time-dependent tracer test systems in hydrogeology

Abstract Artificial tracer tests contribute to the knowledge of the transfer time for a pollutant between the inlets and the outlets. This transfer time however is time-dependent and changes according to the hydrodynamic conditions (transit time velocity) and the state of the system during the experiments (periods of rising or high flows). The transformation of a point injection of a tracer into a system under pressure, considered as a “black box” depends, in particular, on the hydrodynamic conditions prevailing during the experiment. The properties of linearity of the system and the assumption of steady state allow the extrapolation in time of the response of a system where a constant flowrate is imposed. In this situation, the convolution operator predicts the result at the outlet from complex inputs of tracers or pollutants at the inlet. To carry out these operations in transient flow conditions, we propose a model taking into consideration the influence of the discharge on the concentration time distribution in a system. This model is built for a system under pressure with one input and one output from relations established between the impulse responses and the discharge. The use of this model requires a reference tracer test made under known hydrodynamic conditions.

A new algorithm for representing transport in porous media in one dimension, including convection, dispersion, and interaction with the immobile phase with first-order kinetics

The model uses, in one-dimensional flow, the random-walk method on particles and integrates them into a discretized representation of space which eliminates the individual management of each particle. The method of computing allows a simulation of mass transfer in adsorbing media by dissociating the roles of convection, dispersion, and the exchange occurring between the mobile and immobile phases. This gives the parameters that have to be fitted, such as the dispersivity or the exchange rate, a meaning which is closer to their physical reality than that defined by global models (e.g., apparent dispersivity without considering exchange between phases). The model was tested first on analytical solutions and also on data from laboratory experiments on a double porosity chalk column and showed that, with the same limited set of parameters, it could fit concentration/time restitutions at different distances from the injection point. Because of its structure, the algorithm can easily be modified so as to simulate distributed injections and transfers in a regime of variable flow rates.

Coupling of the time domain random walk method with the finite fragment method to simulate flow and transport in 1-D heterogeneous media

Abstract A new method to simulate flow and solute transport in 1-D heterogeneous media is presented. This method integrates the time domain random walk method (TDRW) and the finite fragment method (FFM). The TDRW, similar in concept to the classical random walk method, calculates the arrival time of a particle cloud at a given location and provides the solute breakthrough curve. The FFM, which can be seen as an enhancement of the finite difference scheme, allows a heterogenous media to be divided into homogeneous zones to which the TDRW can be applied. The main advantage of the resulting coupling is that the restrictions can be avoided on the space increments and the time steps which exist with the classical methods of finite differences and random walk. In a homogeneous zone of soil, the breakthrough curve can be calculated directly at a given distance with a reasonable number of particles. A 1-D heterogeneous domain to be simulated is then split into homogeneous zones in which the hydraulic heads and the velocities are calculated by the FFM and at the end of which the temporal solute distributions are calculated by the TDRW. A few hundred particles are generally sufficient to clearly define the breakthrough curve. Comparisons with analytical and numerical solutions and experimental data shows the reliability and advantages of this new method.

One-dimensional solution of the transport equation in porous media in transient state by a new numerical method for the management of particle track

Abstract For the last fifteen years or so, the random-walk methods have proved their worth in solving the transport equation in porous and fractured media. Their principal shortcomings remain their relatively slow calculation speed and their lack of precision at low concentrations. This paper proposes a new code which eliminates these disadvantages by managing the particles not individually but in the form of numerical values (representing the number of particles in each phase, mobile and immobile) assigned to each cell in a 1-D system. The calculation time then is short, and it is possible to introduce as many particles as desired into the model without increasing the calculation time. A large number of injection types can be simulated, and to the classical convection-dispersion phenomenon can be added a process of exchange between the mobile and immobile phase according to first-order kinetics. Because the particles are managed as numbers, the analytical solution obtained for the exchange during a time step reduces the calculation to a simple assignation of numerical values to two variables, one of which represents the mobile and the other the immobile phase; the calculation is then almost instantaneous. Because the program is developed in C, it leaves much room for graphic interaction which greatly facilitates the fitting of tracer experiments with a limited set of parameters.

A vectorial method for the study of the spatial distribution or morphological features applied to the needs of hydrogeology

Abstract The purpose of this computerized processing is to create a database of morphological features in vectorial form with an access by index. The file system is independent of the type and format of the initial documents. It allows work both with objects of various sizes and recomposition of maps by superposing and juxtaposing the information. A practical example showing maps of major directions or frequencies of orientations by mesh, explains how heterogeneous data are linked together and managed dynamically in memory. The methodology used here, can be transposed easily to any other type of counting, for example in order to determine the fractal dimension of a river network.