Bayesian inversion of laboratory experiments of transport through limestone fractures.

In this study, a novel experimental setup is proposed for which a column filled with glass beads and parallelepiped-shaped limestone beams is used to reconstruct a multiple fracture limestone media. The proposed setup produces asymmetric breakthrough curves (BTCs) that are consistent with the shape expected from the past field and lab-scale studies. Three transport experiments have been conducted under fast, medium, and slow flow velocity conditions. The research focuses on parameter and state estimation using Bayesian inference via Markov Chain Monte Carlo (MCMC) sampler, investigating the degree to which three models of transport through fractured media can reproduce the experimental results under the three flow conditions. The first transport model, named ADE, is based on the equivalent porous medium (EPM) approach and corresponds to the linear advection dispersion equation (ADE). The second model, named FOMIM (first-order mobile immobile), is based on the mobile/immobile approach and uses the dual porosity model with a linear first-order transfer between mobile and immobile regions. The third model, named NLMIM (non-linear mobile-immobile), uses a nonlinear transfer function between these two regions. The results of the three models show that almost all the unknown model input parameters can be well-estimated with narrow confidence intervals using the MCMC method. With respect to state estimation, the ADE model fails to reproduce correctly the tail of the BTCs observed under slow and medium flow conditions. The FOMIM model improves the tailing of the BTCs, but significant discrepancies remain between simulated and measured concentrations. The NLMIM model with velocity-dependent parameters is the only model that captures BTCs under all three conditions of slow, medium, and fast flow velocities.

Benchmarking numerical codes for tracer transport with the aid of laboratory-scale experiments in 2D heterogeneous porous media.

We present a combined experimental and numerical modeling study that addresses two principal questions: (i) is any particular Eulerian-based method used to solve the classical advection-dispersion equation (ADE) clearly superior (relative to the others), in terms of yielding solutions that reproduce BTCs of the kind that are typically sampled at the outlet of a laboratory cell? and (ii) in the presence of matches of comparable quality against such BTCs, do any of these methods render different (or similar) numerical BTCs at locations within the domain? To address these questions, we obtained measurements from carefully controlled laboratory experiments, and employ them as a reference against which numerical results are benchmarked and compared. The experiments measure solute transport breakthrough curves (BTCs) through a square domain containing various configurations of coarse, medium, and fine quartz sand. The approaches to solve the ADE involve Eulerian-Lagrangian and Eulerian (finite volume, finite elements, mixed and discontinuous finite elements) numerical methods. Model calibration is not examined; permeability and porosity of each sand were determined previously through separate, standard laboratory tests, while dispersivities are assigned values proportional to mean grain size. We find that the spatial discretization of the flow field is of critical importance, due to the non-uniformity of the domain. Although simulated BTCs at the system outlet are observed to be very similar for these various numerical methods, computed local (point-wise, inside the domain) BTCs can be very different. We find that none of the numerical methods is able to fully reproduce the measured BTCs. The impact of model parameter uncertainty on the calculated BTCs is characterized through a set of numerical Monte Carlo simulations; in cases where the impact is significant, assessment of simulation matches to the experimental data can be ambiguous.

Modeling the effects of water content on TiO2 nanoparticles transport in porous media.

The transport of manufactured titanium dioxide (TiO2, rutile) nanoparticles (NP) in porous media was investigated by metric scale column experiments under different water saturation and ionic strength (IS) conditions. The NP breakthrough curves showed that TiO2 NP retention on the interface between air and water (AWI) and the interface between the solid and the fluid (SWI) is insignificant for an IS equal to or smaller than 3mM KCl. For larger IS, the retention is depending on the water content and the fluid velocity. The experiments, conducted with an IS of 5mM KCl, showed a significantly higher retention of NP than that observed under saturated conditions and very similar experimental conditions. Water flow was simulated using the standard Richards equation. The hydrodynamic model parameters for unsaturated flow were estimated through independent drainage experiments. A new mathematical model was developed to describe TiO2 NP transport and retention on SWI and AWI. The model accounts for the variation of water content and water velocity as a function of depth and takes into account the presence of the AWI and its role as a NP collector. Comparisons with experimental data showed that the suggested modeled processes can be used to quantify the NPs retentions at the AWI and SWI. The suggested model can be used for both saturated and unsaturated conditions and for a rather large range of velocities.

Modeling the effects of water velocity on TiO2 nanoparticles transport in saturated porous media.

The transport of manufactured titanium dioxide (TiO2, rutile) nanoparticles (NP) in porous media was investigated under saturated conditions. Experiments were carried out with different fluid velocities, with values in the range of observed velocities in alluvial aquifers. As reported on the literature for different kinds of NPs, the amount of retained NPs decreased when the water velocity increased. Moreover, no retention was observed for ionic strength values smaller than 5mM. A transport model coupling convective-dispersive transport with a Langmuirian kinetic deposition was used to fit the BTCs. Empirical linear equations were developed to estimate the attachment rate ka and the maximal solid phase concentration smax. Both parameters were found to be linearly depending on the collector efficiency (η0). It was also observed that attachment efficiency (α) did not change with increase of water velocity under the given experimental conditions and that the model had a low sensitivity to α. Based on these estimates of the retention parameters, the classical dispersion-convection model coupled with a Langmuir type adsorption model was able to reproduce quite well the observed TiO2 breakthrough curves for every fluid velocity used in the experiments.

Acid/base front propagation in saturated porous media: 2D laboratory experiments and modeling.

We perform laboratory scale reactive transport experiments involving acid-basic reactions between nitric acid and sodium hydroxide. A two-dimensional experimental setup is designed to provide continuous on-line measurements of physico-chemical parameters such as pH, redox potential (Eh) and electrical conductivity (EC) inside the system under saturated flow through conditions. The electrodes provide reliable values of pH and EC, while sharp fronts associated with redox potential dynamics could not be captured. Care should be taken to properly incorporate within a numerical model the mixing processes occurring inside the electrodes. The available observations are modeled through a numerical code based on the advection-dispersion equation. In this framework, EC is considered as a variable behaving as a conservative tracer and pH and Eh require solving the advection dispersion equation only once. The agreement between the computed and measured pH and EC is good even without recurring to parameters calibration on the basis of the experiments. Our findings suggest that the classical advection-dispersion equation can be used to interpret these kinds of experiments if mixing inside the electrodes is adequately considered.

Identification of groundwater parameters using an adaptative multiscale method.

The identification of groundwater parameters in heterogeneous systems is a major challenge in groundwater modeling. Flexible parameterization methods are needed to assess the complexity of the spatial distributions of these parameters in real aquifers. In this article, we introduce an adaptative parameterization to identify the distribution of hydraulic conductivity within the large-scale (4400 km(2) ) Upper Rhine aquifer. The method is based on adaptative multiscale triangulation (AMT) coupled with an inverse problem procedure that identifies the parameters' distributions by reducing the error between measured and simulated heads. The AMT method has the advantage of combining both zonation and interpolation approaches. The AMT method uses area-based interpolation rather than an interpolation based on stochastic features. The method is applied to a standard 2D groundwater model that takes into account the interactions between the aquifer and surface water bodies, groundwater recharge, and pumping wells. The simulation period covers 204 months, from January 1986 to December 2002. Recordings at 109 piezometers are used for model calibration. The simulated heads are globally quite accurate and reproduce the main dynamics of the system. The local hydraulic conductivities resulting from the AMT method agree qualitatively with existing local experimental observations across the Rhine aquifer.

Detection of advected, reacting redox fronts from self-potential measurements.

We report on an experiment aimed at testing the use of self-potential measurements to monitor the motion and mixing of redox reactants advected through a well-controlled, laboratory-scale, artificial aquifer system. A rectangular, plastic tank was filled up with water-saturated sand and an array of unpolarizable electrodes was installed in the sand body. A nearly uniform, steady-state flow was established by tilting the tank and controlling the water level in reservoirs at both ends. Then, we simultaneously injected a known quantity of KMnO(4) and FeCl(2), respectively, into two separate compartments forming the upstream reservoir. We thus generated two abrupt fronts, one oxidizing and the other reducing, which subsequently travelled in parallel by advection through the sand body. The KMnO(4) and FeCl(2) solutions were in contact and reacted with each other in a region located along the median vertical plane parallel to the flow direction. During flow, the electrical potential differences between each electrode and a reference located in the downstream reservoir were recorded. In the unreacted FeCl(2) region the electric potential showed sudden variations successively occurring at increasing distances in the flow direction, associated with the passage of the FeCl(2) front. These signals essentially corresponded to the junction potential produced by the difference in ionic mobility of Fe(2+) and Cl(-). In the unreacted KMnO(4) region sharp signals, but with much smaller amplitudes, were also observed. Near the vertical median plane on the FeCl(2) side, we observed a second front associated with the spreading of the reaction zone. The shape and evolution of the reaction zone was largely controlled by the precipitation of Fe(OH)(3).