Three-dimensional hydrogeological parametrization using sparse piezometric data

When modelling contamination transport in the subsurface and aquifers, it is crucial to assess the heterogeneities of the porous medium, including the vertical distribution of the aquifer parameter. This issue is generally addressed thanks to geophysical investigations. As an alternative, a method is proposed using estimated hydraulic parameters from a 2D calibrated flow model (solely reliant on piezometric series) as parametrization constraints for a 3D hydrogeological model. The methodology is tested via a synthetic model, ensuring full knowledge and control of its structure. The synthetic aquifer is composed of five lithofacies, distributed according to a sedimentary pattern, and functions in an unconfined regime. The level of heterogeneity for hydraulic conductivity spans 3 orders of magnitude. It provides the piezometric chronicles used to inverse 2D flow parameter fields and the lithological logs used to interpolate the 3D lithological model. Finally, the parameters of each facies (hydraulic conductivity and porosity) are obtained through an optimization loop, which minimizes the difference between the 2D calibrated transmissivity and the transmissivity computed with the estimated 3D facies parameters. The method estimates values close to the known parameters, even with sparse piezometric and lithological data sampling. The maximal discrepancy is 45 % of the known value for the hydraulic conductivity and 6 % for the porosity (mean error 26 % and 3 %, respectively). Although the methodology does not prevent interpolation errors, it succeeds in reconstructing flow and transport dynamics close to the control data. Due to the inherent limitations of the 2D inversion approach, the method only applies to the saturated zone at this point.</p

Numerical error in groundwater flow and solute transport simulation

Models of groundwater flow and solute transport may be affected by numerical error, leading to quantitative and qualitative changes in behavior. In this paper we compare and combine three methods of assessing the extent of numerical error: grid refinement, mathematical analysis, and benchmark test problems. In particular, we assess the popular solute transport code SUTRA [ Voss, 1984 ] as being a typical finite element code. Our numerical analysis suggests that SUTRA incorporates a numerical dispersion error and that its mass-lumped numerical scheme increases the numerical error. This is confirmed using a Gaussian test problem. A modified SUTRA code, in which the numerical dispersion is calculated and subtracted, produces better results. The much more challenging Elder problem [ Elder, 1967 ; Voss and Souza, 1987 ] is then considered. Calculation of its numerical dispersion coefficients and numerical stability show that the Elder problem is prone to error. We confirm that Elder problem results are extremely sensitive to the simulation method used.Juliette A. Woods, Michael D. Teubner, Craig T. Simmons and Kumar A. Naraya

On the measurement of solute concentrations in 2-D flow tank experiments

In this study we describe and compare photometric and resistivity measurement methodologies to determine solute concentrations in porous media flow tank experiments. The first method is the photometric method, which directly relates digitally measured intensities of a tracer dye to solute concentrations, without first converting the intensities to optical densities. This enables an effective processing of a large number of images in order to compute concentration time series at various points of the flow tank and concentration contour lines. This paper investigates perturbations of the measurements; it was found both lens flare effects and image resolution were a major source of error. Attaching a mask minimizes the lens flare. The second method for in situ measurement of salt concentrations in porous media experiments is the resistivity method. The resistivity measurement system uses two different input voltages at gilded electrode sticks to enable the measurement of salt concentrations from 0 to 300 g/l. The method is highly precise and the major perturbations are caused by temperature changes, which can be controlled in the laboratory. The two measurement approaches are compared with regard to their usefulness in providing data for benchmark experiments aimed at improving process understanding and testing numerical codes. Due to the unknown measurement volume of the electrodes, we consider the image analysis method more appropriate for intermediate scale 2D laboratory benchmark experiments for the purpose of evaluating numerical codes

Statistical Description of Calcite Surface Roughness Resulting from Dissolution at Close-to-Equilibrium Conditions

Linking the evolution of the surface area (as quantified, e.g., through its spatial roughness) of minerals to their dissolution rate is a key aspect of mineral reactivity. Unraveling the nature of their main features requires relying on approaches yielding a quantitative characterization of the temporal evolution of surface topography/roughness. Here, a mechanically polished {104} calcite surface was dissolved at room temperature and at close-to-equilibrium conditions (ω = 0.6) with an alkaline solution (pH = 8) across a temporal window of 8 days. Surface topography images were acquired daily using vertical scanning interferometry, the ensuing topography data being then embedded within a statistical analysis framework aimed at describing comprehensively the surface roughness evolution. The strongest system variations were observed after 1 day: the probability density function of surface roughness was observed to transition from being approximately Gaussian to being left-skewed and leptokurtic, exhibiting a dramatic increase in the variance and a significant change in the semi-variogram structure. After a relaxation time of approximately 2 days, the reacting surface appeared to attain a steady-state configuration, being characterized by the values of the statistical moments characterizing surface roughness that become virtually independent of time. Attempting to unravel the underlying dissolution mechanism, an original numerical model able to reproduce satisfactorily the statistical behavior observed experimentally was developed and tested. Our results suggest that under the investigated conditions, dissolution may be characterized as a spatially correlated random process, with the areas most exposed to the flowing fluid being prone to preferential dissolution. The numerical model was also used to obtain insights into the influences of the initial surface roughness and of the fluid composition on the steady-state statistical characterization of the surface roughness. Our results suggest that the influence of the initial surface roughness is limited. The present study suggests that potential empirical relations linking the surface roughness of the reacted crystals to the saturation state at which they dissolved may be developed, which would allow to back-estimate the reacting conditions only based on topography data

Generalized Sub-Gaussian Processes: Theory and Application to Hydrogeological and Geochemical Data

We start from the well-documented scale dependence displayed by the probability distribution and associated statistical moments of a variety of hydrogeological and soil science variables and their spatial or temporal increments. These features can be captured by a Generalized Sub-Gaussian (GSG) model, according to which a given variable, Y, is subordinated to a (typically spatially correlated) Gaussian random field, G, through a subordinator, U. This study extends the theoretical framework originally proposed by Riva et al. (2015, 10.1002/2015WR016998) to include the possibility of selecting a general form of the subordinator, thus enhancing the flexibility of the GSG framework for data interpretation and modeling. Analytical expressions for the GSG process associated with lognormal, Pareto, and Gamma subordinator distributions are then derived. We demonstrate the ability of the GSG modeling framework to capture the way key features of the statistics associated with two data sets transition across scales. The latter correspond to variables, which are typical of a geochemical and a hydrogeological setting, that is, (i) data characterizing the micrometer-scale surface roughness of a crystal of calcite, collected within a laboratory-scale setting, resulting from induced mineral dissolution, and (ii) a vertical distribution of decimeter-scale porosity data, collected along a deep kilometer-scale borehole within a sandstone formation and typically used in hydrogeological and geophysical characterization of aquifer systems. The theoretical developments and the successful applications of the approach we propose provide a unique framework within which one can interpret a broad range of scaling behaviors displayed by a variety of Earth and environmental variables in various scenarios

Reply to 'No substantial long-term bias in the Cenozoic benthic foraminifera oxygen-isotope record'

International audienc

Burial-induced oxygen-isotope re-equilibration of fossil foraminifera explains ocean paleotemperature paradoxes

The oxygen-isotope composition of fossil foraminifera tests is an established proxy for ocean paleotemperatures. Here, the authors show that isotope re-equilibration can occur during sediment burial without structural modification of the tests and cause a substantial overestimation of ocean paleotemperatures

Regolith evolution on the millennial timescale from combined U–Th–Ra isotopes and in situ cosmogenic 10 Be analysis in a weathering profile (Strengbach catchment, France)

International audienc

Experimental Study of Dissolution Kinetics of K-feldspar as a Function of Crystal Structure Anisotropy under Hydrothermal Conditions

International audienc