.[1] A normalized clay-water isotherm model based on BET theory and describing the sorption and desorption of the bound water in clays, sand-clay mixtures, and shales is presented. Clay-water sorption isotherms (sorption and desorption) of clayey materials are normalized by their cation exchange capacity (CEC) accounting for a correction factor depending on the type of counterion sorbed on the mineral surface in the so-called Stern layer. With such normalizations, all the data collapse into two master curves, one for sorption and one for desorption, independent of the clay mineralogy, crystallographic considerations, and bound cation type; therefore, neglecting the true heterogeneity of water sorption/ desorption in smectite. The two master curves show the general hysteretic behavior of the capillary pressure curve at low relative humidity (below 70%). The model is validated against several data sets obtained from the literature comprising a broad range of clay types and clay mineralogies. The CEC values, derived by inverting the sorption/adsorption curves using a Markov chain Monte Carlo approach, are consistent with the CEC associated with the clay mineralogy.

International audienceInduced polarization (more precisely the magnitude and phase of impedance of the subsurface) is measured using a network of electrodes located at the ground surface or in boreholes. This method yields important information related to the distribution of permeability and contaminants in the shallow subsurface. We propose a new time-lapse 3-D modelling and inversion algorithm to image the evolution of complex conductivity over time. We discretize the subsurface using hexahedron cells. Each cell is assigned a complex resistivity or conductivity value. Using the finite-element approach, we model the in-phase and out-of-phase (quadrature) electrical potentials on the 3-D grid, which are then transformed into apparent complex resistivity. Inhomogeneous Dirichlet boundary conditions are used at the boundary of the domain. The calculation of the Jacobian matrix is based on the principles of reciprocity. The goal of time-lapse inversion is to determine the change in the complex resistivity of each cell of the spatial grid as a function of time. Each model along the time axis is called a 'reference space model'. This approach can be simplified into an inverse problem looking for the optimum of several reference space models using the approximation that the material properties vary linearly in time between two subsequent reference models. Regularizations in both space domain and time domain reduce inversion artefacts and improve the stability of the inversion problem. In addition, the use of the time-lapse equations allows the simultaneous inversion of data obtained at different times in just one inversion step (4-D inversion). The advantages of this new inversion algorithm are demonstrated on synthetic time-lapse data resulting from the simulation of a salt tracer test in a heterogeneous random material described by an anisotropic semi-variogram

[1] We first upscale the local transport (Stokes and Nernst-Planck) equations to the scale of a single capillary saturated by a binary 1:1 electrolyte. These equations are then upscaled to the scale of a network of tortuous capillaries embedded in a homogeneous and continuous mineral matrix, including the influence of the distribution of pore sizes but excluding the effect of connectivity between the pores. One of the features of our theory is to account for transport along the mineral surface in the so-called Stern layer because of recent evidence that this mechanism is effective in describing frequency-dependent electrical conductivity. Real clay materials are, however, not described by a set of capillaries, so we have to modify the model to include the effect of transversal dispersivity, for example. We found no evidence for transport in the Stern layer because of the discontinuity of the solid phase at the scale of a representative elementary volume in clay materials. The effect of the diffuse layer is accounted for through the use of a Donnan equilibrium approach to determine the effective concentrations of the ions in the pore space, which are different from the ionic concentrations of an ionic reservoir in local equilibrium with the porous material. We found that the diffuse layer controls various transport properties, including, for example, the DC electrical conductivity, the osmotic efficiency coefficient, the streaming potential coupling coefficient, and the macroscopic Hittorf numbers. Comparison to a large data set of experimental data, mainly on clay materials, confirms the validity of the derived relationships used to describe the material properties entering into the constitutive equations.

A model was recently introduced to describe the complex electrical conductivity and high-frequency dielectric constant of isotropic clayey porous materials. We generalized that approach to the case of anisotropic and tight hydrocarbon-bearing shales and mudrocks by introducing tensorial versions of formation factor and tortuosity. In-phase and quadrature conductivity tensors have common eigenvectors, but the eigenvectors of the dielectric tensor may be different due to influence of the solid phase at high frequencies. In-phase and quadrature contributions to complex electrical conductivity depend on saturation, salinity, porosity, temperature, and cation exchange capacity (alternatively, specific surface area) of the porous material. Kerogen is likely to have a negligible contribution to the cation exchange capacity of the material because all exchangeable sites in the functional groups of organic matter may have been polymerized during diagenesis. An anisotropic experiment is performed to validate some of the properties described by the proposed model, especially to verify that the electrical anisotropy factor is the same for in-phase and quadrature conductivities. We used two samples from the Bakken formation. Experimental data confirm the validity of the model. Also, the range of values for cation exchange capacity determined when implementing the new model with experimental data agree with the known range of cation exchange capacity for the Bakken shale. Measurements indicate that the bulk-space tortuosity in the direction normal to bedding plane can be higher than 100.

[1] A method is proposed to localize preferential fluid flow pathways in porous media on the basis of time-lapse self-potential measurements associated with salt tracer injection upstream. This method is first tested using laboratory data. A network of nonpolarizing electrodes located is connected to a highly sensitive voltmeter used to record the resulting electrical field fluctuations occurring over time at the surface of the tank. The transport of the conductive salt plume through the permeable porous materials changes the localized streaming potential coupling coefficient associated with the advective drag of the excess charge of the pore water and is also responsible for a diffusion current associated with the salinity gradient. Monitoring of the electrical potential distribution at the ground surface can be used to localize the pulse of saline water over time and to determine its velocity. This method applies in real time and can be used to track highly localized flow pathways characterized by high permeability. Our sandbox experiment demonstrates the applicability of this new method under well-controlled conditions with a coarse-sand channel embedded between fine-sand banks. A finite element model allows us to reproduce the time-lapse electrical potential distribution over the channel, but some discrepancies were observed on the banks. Finally, we performed a numerical simulation for a synthetic case study inspired by a recently published field case study. A Markov chain Monte Carlo sampler is used to determine the permeability and the porosity of the preferential fluid flow pathway of this synthetic case study.