ALBERT

Description: A new approach of seismoelectric imaging has been recently proposed to detect saturation fronts in which seismic waves are focused in the subsurface to scan its heterogeneous nature and determine saturation fronts. Such type of imaging requires however a complete modelling of the seismoelectric properties of porous media saturated by two immiscible fluid phases, one being usually electrically insulating (for instance water and oil). We combine an extension of Biot dynamic theory, valid for porous media containing two immiscible Newtonian fluids, with an extension of the electrokinetic theory based on the notion of effective volumetric charge densities dragged by the flow of each fluid phase. These effective charge densities can be related directly to the permeability and saturation of each fluid phase. The coupled partial differential equations are solved with the finite element method. We also derive analytically the transfer function connecting the macroscopic electrical field to the acceleration of the fast P wave (coseismic electrical field) and we study the influence of the water content on this coupling. We observe that the amplitude of the co-seismic electrical disturbance is very sensitive to the water content with an increase in amplitude with water saturation. We also investigate the seismoelectric conversions (interface effect) occurring at the water table. We show that the conversion response at the water table can be identifiable only when the saturation contrasts between the vadose and saturated zones are sharp enough. A relatively dry vadose zone represents the best condition to identify the water table through seismoelectric measurements. Indeed, in this case, the coseismic electrical disturbances are vanishingly small compared to the seismoelectric interface response.

Description: Pumping tests can be used to estimate the hydraulic conductivity field from the inversion of hydraulic head data taken intrusively in a set of piezometers. Nevertheless, the inverse problem is strongly underdetermined. We propose to add more information by adding (non-intrusive) self-potential data taken at the ground surface during pumping tests. These self-potential data correspond to perturbations of the electrical field caused directly by the flow of the ground water. The coupling is electrokinetic in nature that is due to the drag of the excess of electrical charges existing in the pore water. These self-potential signals can be easily measured in field conditions with a set of the non-polarizing electrodes installed at the ground surface. We used the adjoint-state method for the estimation of the hydraulic conductivity field from measurements of both hydraulic heads and self-potential during pumping tests. In addition, we use a recently developed petrophysical formulation of the streaming potential problem using an effective charge density of the pore water derived directly from the hydraulic conductivity. The geostatistical inverse framework is applied to five synthetic case studies with different number of wells and electrodes and thickness of the confining unit. To evaluate the benefits of incorporating the self-potential data in the inverse problem, we compare the cases in which the data are combined or not. Incorporating the self-potential information improves the estimate of hydraulic conductivity field in the case where the number of piezometers is limited. However, the uncertainty of the characterization of the hydraulic conductivity from the inversion of the self-potential data is dependent on the quality of the distribution of the electrical conductivity used to solve the Poisson equation. Consequently, the approach discussed in this paper requires a precise estimate of the electrical conductivity distribution of the subsurface and requires therefore new strategies to be developed for the joint inversion of the hydraulic and electrical conductivity distributions.

Description: Electromagnetic signals have been observed in association with fracking experiments in the laboratory, and in the field. We have developed a seismoelectric forward modeling approach to produce synthetic seismograms and electrograms generated by fracking events using the finite-element method with perfect matched-layer boundary conditions. The poroelastodynamic equations are solved in the frequency domain using a formulation based on the solid phase displacement and the pore pressure. These results are used to compute the electrical field disturbances of electrokinetic nature. Three types of electrical signals are generated: Type I disturbance is associated with the seismic source itself, Type II disturbance corresponds to seismoelectric conversions, and Type III corresponds to coseismic signals. This model is applied to simulate the seismic and electrical signals corresponding to the occurrence of a fracking event in a two-layers system. We perform a stochastic joint inversion of the seismograms and electrograms using the adaptive Metropolis algorithm (AMA) to obtain the posterior probability density functions of the parameters characterizing the seismic source assuming that the velocity model is perfectly known. The joint waveform inversion is performed on synthetic noise-free data and the AMA algorithm is successful in retrieving the true values of the unknown parameters. The proposed approach is then tested on the same synthetic data after being contaminated with 15% random noise with respect to the maximum amplitude of the signals. The model parameters are better determined for the joint inversion of seismic and electrical data by comparison with the inversion of the seismic time-series alone. We also propose a deterministic tomographic algorithm that is successful in locating the in situ source current density distribution for Types I and II anomalies from the electrical data alone.

Description: The flow of the ground water in an aquifer or during pumping test generates an electrical current (called the streaming current), which is of advective nature. The resulting electrical field (streaming potential field, one of the components of the self-potential field) can be remotely measured at the ground surface or in boreholes. We first discuss the underlying physics of this electrokinetic effect and the role of the electrical double layer coating the surface of the grains. We show how the drag of the excess of electrical charge of the pore water by the flow is equivalent to a source current density. Then, we discuss the metrological aspects, the type of voltmeter and electrodes required to carry out good measurements in field conditions. Two applications are discussed in steady-state conditions. The first is dedicated to the flow of water in shallow aquifers. In this case, the streaming current and the conduction current are nearly balanced and, inside the aquifer, the electrical equipotentials mimic the hydraulic equipotentials. They have, however, the advantage to extend the shape of these hydraulic equipotentials up to the ground surface. The second case is related to the flow of water in the vadose zone, here again investigated in steady-state conditions. In this situation, the vadose zone is polarized and the ground surface electrical potential map reflects essentially the depth of the vadose zone. A case study is shown for a small watershed in the South of France. The resistivity tomography shows no contrast in resistivity between the vadose zone and the aquifer and the observed self-potential data are observed to be linearly correlated to the depth of the water table.

Description: Harmonic pumping tests consist in stimulating an aquifer by the means of hydraulic stimulations at some discrete frequencies. The inverse problem consisting in retrieving the hydraulic properties is inherently ill-posed and is usually underdetermined when considering the number of well head data available in field conditions. To better constrain this inverse problem, we add self-potential data recorded at the ground surface to the head data. The self-potential method is a passive geophysical method. Its signals are generated by the groundwater flow through an electrokinetic coupling. We showed, using a 3D saturated unconfined synthetic aquifer, that the self-potential method significantly improves the results of the harmonic hydraulic tomography. The hydroelectric forward problem is obtained by solving first the Richards equation, describing the groundwater flow, and then using the result in an electrical Poisson equation describing the self-potential problem. The joint inversion problem is solved using a reduction model based on the principal component geostatistical approach. In this method, the large prior covariance matrix is truncated and replaced by its low-rank approximation, allowing thus for notable computational time and storage savings. Three test cases are studied, to assess the validity of our approach. In the first test, we show that when the number of harmonic stimulations is low, combining the harmonic hydraulic and self-potential data does not improve the inversion results. In the second test, where enough harmonic stimulations are performed, a significant improvement of the hydraulic parameters is observed. In the last synthetic test, we show that the electrical conductivity field required to invert the self-potential data can be determined with enough accuracy using an electrical resistivity tomography survey using the same electrodes configuration as used for the self-potential investigation. This article is protected by copyright. All rights reserved.

Description: The seismoelectric method is based on the interpretation of the electrical field associated with the conversion of mechanical to electromagnetic energy during the propagation of seismic waves in heterogeneous porous media. We propose an extension of a poroacoustic model that takes into account fluid flow and the effect of saturation. This model is coupled with an electrokinetic model accounting for the effect of saturation and in agreement with available experimental data in sands and carbonate rocks. We also developed new scaling laws for the permeability, the streaming potential coupling coefficient and the capillary entry pressure of porous media. The theory is developed for frequencies much below the critical frequency at which inertial effects starts to dominate in the Navier–Stokes equation (〉10 kHz). The equations used to compute the propagation of the P waves and the seismoelectric effect in unsaturated condition are solved with finite elements using triangular meshing. We demonstrate the usefulness of a recently developed technique, seismoelectric beamforming, to localize saturation fronts by focusing seismic waves and looking at the resulting seismoelectric conversions. This method is applied to a cross-hole problem showing how a saturation front characterized by a drop in the electrical conductivity and compressibility is responsible for seismoelectric conversions. These conversions can be used, in turn, to determine the position of the front over time.