Quantitative characterization of solute transport processes in the laboratory using electrical resistivity tomography

Abstract

The shallow subsurface is an important zone from a social, economical, and environmental point of view. The increased use of the shallow subsurface together with the call for its protection and sustainable exploitation have increased the need for tools to monitor and characterize the subsurface, as well as for an improved understanding of the hydrogeological processes taking place in this zone. The limitations of traditional point sampling techniques have led to the field of hydrogeophysics, in which geophysical methods are employed to characterize the subsurface at a relatively high spatial resolution but with minimal disturbance. A common geophysical method used for hydrogeological characterization is electrical resistivity tomography (ERT). ERT uses the injection of electrical currents and the measurement of the resulting voltages to obtain a spatial distribution of the electrical conductivity, which is related, among other things, to volumetric moisture content and ionic strength of the pore water. Although ERT is an established tool for qualitative visualization of hydrogeological processes in the subsurface, its quantitative application is relatively new and constitutes an active area of research. The main aim of this study is to explore the quantitative characterization of solute transport processes in porous media in the laboratory using ERT. For this purpose a flexible, high-speed, and modular ERT measurement system was developed in collaboration with the Electronic and Mechanical Support Division. The new system can perform measurements with a much higher temporal resolution than commercially available field equipment. The ERT system uses a pulsed direct current source and eight channels for simultaneous voltage measurement, and can be connected to a total of 128 electrodes. An error analysis for the ERT system shows that the measurement noise of a transfer resistance measurement (the ratio of injected current and measured voltage) in the used laboratory setup is described by a Gaussian probability distribution with e ? N(e ?,se ). The standard deviation of the measurement errors (se ) can be estimated from repeatability measurements, while the mean (e ?, representing systematic errors) can be estimated from reciprocity measurements. The ERT setup (ERT measurement system, electrodes, and experimental tank) has been used to perform a set of relatively simple, well-defined, static experiments. For these experiments the experimental tank was filled with an aqueous solution into which a solid plastic cylinder was placed. The collected ERT measurements have been used in uncoupled as well as coupled inverse approaches to estimate parameters such as the location and radius of the plastic cylinder. The statistical inversion algorithm DREAM(ZS), based on the Markov Chain Monte Carlo method, was used to estimate the model parameters. The reconstructed electrical conductivity images required in the uncoupled inversion were obtained using an algorithm based on Occam’s inversion. The model parameters estimated with the uncoupled inverse approach are corrupted due to the regularization bias introduced into the reconstructed electrical conductivity image. This bias particularly affects the estimates of the plastic cylinder’s electrical conductivity and radius. The poor performance of the uncoupled inverse approach is mainly caused by the use of a smoothness prior in the image reconstruction. Obviously, such a prior is not in agreement with the sharp conductivity contrast between the plastic cylinder and the aqueous solution. Conversely, the model parameters estimated in the coupled inverse approach are in close agreement with the measured values. The residual between the measured and simulated transfer resistances in the coupled inversion suggest that the model errors are larger than the measurement noise. The model errors are mainly attributed to errors in electrode position or shape and errors in the shape of the experimental tank. Even though the model errors are statistically significant, the total data errors are too small to significantly affect the estimated parameters values. The results show that when accurate forward models are used in a coupled inverse approach, ERT measurements can provide accurate and precise parameter estimates. Subsequently, the feasibility of ERT to quantitatively characterize solute transport processes in our laboratory setup was explored. For this purpose, a straightforward solute transport experiment was performed, consisting of a series of three single-step tracer injections into a saturated homogeneous sand column. The use of ERT to quantify processes in porous media introduces additional uncertainty since a petrophysical relationship is required to relate the bulk electrical conductivity modelled with ERT to the properties of the porous medium. In addition, the solute transport model is subject to uncertainty in porous medium parameters as well as petrophysical parameters, uncertainty in boundary and initial conditions, and model structural errors (e.g. caused by assuming a homogeneous porous medium while in reality the medium is heterogeneous). The reconstructed electrical conductivity images for the tracer injection experiments clearly were affected by the spatially variable resolution of the smoothness-constrained image reconstruction as well as by inversion artefacts. The applied smoothing primarily caused overestimation of the dispersion of the tracer front. The reconstructed electrical conductivities could be improved by the use of a process-based prior which includes specific information about the solute transport process in the regularized inversion. However, the success of this prior is dependent on the accuracy of the solute transport model and petrophysical relationship used to generate the set of feasible electrical conductivity models. The ERT measurements collected during the tracer injections were also used to estimate the parameters of a one-dimensional solute transport model in an uncoupled as well as a coupled inverse approach. In both inverse approaches, the solute transport parameters could be estimated to a high precision. Moreover, the estimated values were physically realistic and agreed relatively well with the expected values. Surprisingly, the results obtained in the uncoupled and coupled inversions were comparable, despite the fact that the reconstructed electrical conductivities were clearly affected by regularization. An explanation for this observation was found in the variable sizes of the elements used in the ERT mesh. The smaller elements near the electrodes, where ERT spatial resolution was high, relatively contributed more to the objective function in the uncoupled inversion than the larger elements towards the centre of the domain, where ERT spatial resolution was low. As a result, the uncoupled inversion was biased towards areas with good data quality. Although the solute transport parameters estimated with the coupled inversion are physically realistic and agree relatively well with the expected values, the (mis)fit between the observed and simulated transfer resistances suggests that significant model errors in the solute transport and/or petrophysical model must have been present. These model errors likely are the result of heterogeneities in the solute transport caused by small-scale preferential flow (cm or less). Possible causes for small-scale preferential flow are unsaturated conditions in the sand column, the periodic invasive sampling of water at the sampling ports, or non-uniform tracer injection at the sand column’s bottom boundary. Overall, the results presented in this thesis show that ERT can be used to quantitatively characterize a solute transport process in a laboratory sand column, given that a coupled inverse framework is used and the forward models are accurate enough representations of reality. In general, the success of quantitative characterization using ERT measurements is highly dependent on the information available in addition to the ERT measurements, such as information about the dominant flow and transport processes, porous medium properties, heterogeneities, and initial and boundary conditions. When little or no information is available, ERT is best used in a standard image reconstruction using a smoothness prior or other general prior. Although the resulting images will only provide qualitative information, this information could still be beneficial for the construction of an appropriate hydrogeological model. Once a hydrogeological model is constructed, its unknown parameters could be estimated using the ERT measurements in a coupled inverse approach. In a controlled laboratory experiment additional information is readily available, which increases the feasibility of ERT for quantitative characterization. Additional information may come from imposed boundary and initial conditions and the experimental design, as well as from independent measurements of the soil’s properties (e.g., porosity, water content) and petrophysical parameters. Alternatively, additional information may come from other geophysical datatypes as well as hydrological measurements. Since the success of quantitative characterization of hydrogeological processes using ERT is highly dependent on the information available in addition to the ERT measurements, future research should focus on the integration of multiple types of geophysical data (e.g., electrical resistivity tomography, ground-penetrating radar, induced potential, self potential, electromagnetics, time-domain reflectometry) and local hydrological data (e.g., concentration, hydraulic head, flowrates).