Stochastic modelling of groundwater flow and solute transport in aquifers

This paper presents an introductory overview of recently developed stochastic theories for tackling spatial variability problems in predicting groundwater flow and solute transport. Advantages and limitations of the theories are discussed. Lastly, strategies based on the stochastic approaches to predict solute transport in aquifers are recommended.     

Screening model for volatile pollutants in dual porosity soils

This paper develops mass fraction models for transport and fate of agricultural pollutants in structured two-region soils. Mass fraction index models, based on a semi-infinite domain solution, are derived that describe leaching at depth, vapor losses through soil surface, absorption, and degradation in the dynamic- and stagnant-water soil regions. The models predict that leaching is the result of the combined effect of the upward vapor-phase transport relative to downward advection, residence time relative to half-life, dispersion, and lateral diffusive mass transfer. Simulations show that leached fraction of volatile compounds does not always decrease monotonically with increased residence time relative to the pollutant half-life, as a result of complex interactions among the different physical and biochemical processes. The results show that leaching, volatilization, and degradation losses can be affected significantly by lateral diffusive mass transfer into immobile-water regions and advection relative to dispersion (i.e. Peclet number) in the mobile-water regions. It is shown that solute diffusion into the immobile phase and subsequent biochemical decay reduces leaching and vapor losses through soil surface. Potential use of the modified leaching index for the screening of selected pesticides is illustrated for different soil textures and infiltration rates. The analysis may be useful to the management of pesticides and the design of landfills.     

Transport of dissolved methoxy-nonafluorobutane through a saturated column

Solute transport experiments were conducted in a one-dimensional saturated column using dissolved methoxy-nonafluorobutane (HFE-7100), a Novec engineered fluid developed by the 3M Corporation, as the solute. Novec engineered fluids are considered dense non-aqueous phase liquids (DNAPLs) because they are immiscible with water and have a specific gravity greater than one. The HFE-7100 fluid is safer and environmentally friendlier than common DNAPL contaminants such as tetrachloroethylene (PCE) or trichloroethylene (TCE); thus, it is an ideal substitute DNAPL for laboratory groundwater contamination research. Three sets of solute transport experiments were conducted. The first set of experiments was conducted in a glass-bead-packed column using dissolved HFE-7100 as the solute. The second set of experiments was conducted in a sand-packed column using dissolved HFE-7100 as the solute. The third set of experiments was conducted in a sand-packed column using dissolved PCE as the solute. The dissolved HFE-7100 column breakthrough concentrations were compared with dissolved PCE breakthrough concentrations. Results show that the one-dimensional solute transport equation was successful in describing the transport behavior of dissolved HFE-7100. This study demonstrates that the HFE-7100 fluid can be used as a safer substitute DNAPL for groundwater contaminant dissolution and transport research.     

Flow and transport predictions during multi-borehole tests in fractured chalk using discrete fracture network models

Multi-borehole pumping and tracer tests on the 10 to 100-m scale were conducted in a fractured chalk aquitard in the Negev Desert, Israel. Outcrop and core fracture surveys, as well as slug tests in packed-off intervals, were carried out at this site to obtain the parameters needed for construction of a stochastic discrete fracture network (DFN). Calibration of stochastic DFNs directly to the multiple borehole test data was inadequate. Instead, two equivalent deterministic DFN flow models were used: the vertical-fractures (VF) model, consisting of only vertical fractures, and the fractures’ intersections (INT) model, consisting of vertical and horizontal fractures with enhanced transmissivity at their intersections. Both models were calibrated against the multi-borehole response of one pumping test and their predictions were tested against three other independent pumping tests. The average accuracies of all transient drawdown predictions of the VF and INT models were 65 and 66%, respectively. In contrast to this equality in average drawdown predictions of both models, the INT model predicted better important breakthrough curve features (e.g., first and peak arrival times), than the VF model. This result is in line with previously assumed channeled flow, derived from analytical analysis of these pumping and tracer tests. Ronit Nativ, deceased, may her memory be blessed.     

Solute and isotope constraint of groundwater recharge simulation in an arid environment,Abu Dhabi Emirate,United Arab Emirates

A simple, well-constrained simulation of solute increases in a downgradient direction was used in the shallow unconfined aquifer of eastern Abu Dhabi Emirate (United Arab Emirates). The simulation indicates that the observed exponential increase in solute concentrations results from a combination of upward transport of solutes from underlying mudstones and evaporites, and groundwater losses by evaporation. Groundwater recharge and discharge flux in unconfined regional aquifers in arid regions commonly are difficult to estimate because there are few constraints on the flux of water lost or gained from the system. Total dissolved solids (TDS) and deuterium isotopes (δ²H) in groundwater are used to constrain estimated fluxes to the shallow aquifer of eastern Abu Dhabi Emirate. Vertical upward transport of solutes from underlying mudstones and evaporites accounts for solute increases along approximately the first 80 km of the simulated flow path, but a combination of upward solute transport and evaporation is necessary to explain observed solute concentrations beyond 80 km. Mobilization and transport of solutes in the unsaturated zone by recharging precipitation is not a significant factor.

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Résumé Une simulation simple et bien contrainte de l’augmentation des solutés dans la direction de l’écoulement a été réalisée sur l’aquifère phréatique et libre de l’Est de l’émirat d’Abu Dhabi (émirats Arabes Unis). La simulation indique que l’augmentation observée de solutés, de forme exponentielle, est le produit de la combinaison du transport ascendant de solutés provenant des mudstones et des évaporites sous-jacents, et de l’évaporation des eaux souterraines. La recharge des eaux souterraines et les flux de vidange dans les aquifères régionaux libres des régions arides sont habituellement difficiles à estimer du fait du peu de contraintes agissant sur la perte ou le gain d’eau dans le système. La charge dissoute totale (TDS, en anglais) et les isotopes deutérium (δ²H) des eaux souterraines sont utilisés pour contraindre l’estimation des flux en direction de l’aquifère phréatique de l’Est de l’émirat d’Abu Dhabi. Le transport vertical ascendant des solutés à partir des mudstones et des évaporites fait parti des processus qui concentrent les solutés approximativement le long des 80 premiers kilomètres du trajet des écoulements simulés, mais une combinaison du transport ascendant des solutés et de l’évaporation est nécessaire pour expliquer les concentrations observées en soluté au delà des 80 km. La mobilisation et le transport des solutés par les précipitations efficaces dans la zone non saturée ne représentent pas des facteurs significatifs.

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Resumen Se utilizó una simulación simple y muy restringida, de incrementos de soluto en la dirección del flujo, en el acuífero libre poco profundo del Emirato oriental de Abu Dhabi, (Emiratos árabes Unidos). La simulación indica que el aumento exponencial observado en las concentraciones del soluto, resulta de una combinación de transporte ascendente de solutos desde las evaporitas y lodolitas subyacentes, y por pérdidas del agua subterránea por evaporación. Los flujos de recarga y descarga de agua subterránea, en los acuíferos libres regionales en regiones áridas, normalmente son difíciles estimar, porque hay algunas restricciones en el flujo de agua perdido o ganado por el sistema. Los sólidos disueltos totales (TDS) y los isótopos de deuterio (δ²H) en el agua subterránea, se usan para forzar los flujos estimados hacia el acuífero poco profundo del Emirato oriental de Abu Dhabi. El transporte ascendente vertical de solutos desde las lodolitas y evaporitas subyacentes, involucra los aumentos del soluto a lo largo de aproximadamente los primeros 80 Km. de la dirección de flujo simulada, pero es necesaria una combinación de transporte ascendente del soluto y la evaporación para explicar las concentraciones del soluto observadas más allá de 80 Km. La movilización y transporte de solutos en la zona no saturada, por recarga debida a precipitación, no es un factor significante.

     

Effects of intraborehole flow on groundwater age distribution

Environmental tracers are used to estimate groundwater ages and travel times, but the strongly heterogeneous nature of many subsurface environments can cause mixing between waters of highly disparate ages, adding additional complexity to the age-estimation process. Mixing may be exacerbated by the presence of wells because long open intervals or long screens with openings at multiple depths can transport water and solutes rapidly over a large vertical distance. The effect of intraborehole flow on groundwater age was examined numerically using direct age transport simulation coupled with the Multi-Node Well Package of MODFLOW. Ages in a homogeneous, anisotropic aquifer reached a predevelopment steady state possessing strong depth dependence. A nonpumping multi-node well was then introduced in one of three locations within the system. In all three cases, vertical transport along the well resulted in substantial changes in age distributions within the system. After a pumping well was added near the nonpumping multi-node well, ages were further perturbed by a flow reversal in the nonpumping multi-node well. Results indicated that intraborehole flow can substantially alter groundwater ages, but the effects are highly dependent on local or regional flow conditions and may change with time.     

Density-dependent dispersion in heterogeneous porous media Part I: A numerical study

In this paper, we describe carefully conducted numerical experiments, in which a dense salt solution vertically displaces fresh water in a stable manner. The two-dimensional porous media are weakly heterogeneous at a small scale. The purpose of these simulations, conducted for a range of density differences, is to obtain accurate concentration profiles that can be used to validate nonlinear models for high-concentration-gradient dispersion. In this part we focus on convergence of the computations, in numerical and statistical sense, to ensure that the uncertainty in the results is small enough.Concentration variances are computed, which give estimates of the uncertainty in local concentration values. These local variations decrease with increasing density contrast. For tracer transport, obtained longitudinal dispersivities are in accordance with analytical findings. In the case of high-density contrasts, stabilizing gravity forces counteract the growth of dispersive fingers, decreasing the effective width of the transition zone. For small log-permeability variances, the decrease of the apparent dispersivity that is found is in agreement with laboratory results for homogeneous columns.     

A field study of the coupled effects of aquifer stratification,fluid density,and groundwater fluctuations on dispersivity assessments

A number of experimental studies have tackled the issue of solute transport parameter assessments either in the laboratory or in the field. But yet, the behavior of a plume in the field under density driven forces, is not well known due to possible development of instabilities. Some field tracer tests on the fate of plumes denser than native groundwater such as those encountered under waste disposal facilities, have pointed out the processes of sinking and splitting at the early stage of migration. The process of dispersion was widely investigated, but the range of dispersivity values obtained from either experimental tests, or numerical and theoretical calculations is still very large, even for the same type of aquifers. These discrepancies were considered to be essentially caused by soil heterogeneities and scale effects. In the meantime, studies on the influence of sinking and fingering have remained more scarce. The objective of the work is to analyze how transport parameters such as dispersivities can be affected by unstable conditions, which lead to plume sinking and fingering. A series of tracer tests were carried out to study under natural conditions, the transport of a dense chloride solution injected in a shallow two-layered aquifer. Two types of experiments were performed: in the first type, source injection was such that the plume could travel downward from one layer to the other of higher pore velocity, and in the second one, the migration took place only in the faster layer. The results suggest some new insights in the processes occurring at the early stages of a dense plume migration moving in a stratified aquifer under groundwater fluctuations, which can be summarized through the following points: (i) Above a stability criterion threshold, a fingering process and a multi modal plume transport take place, but local dispersivities can be cautiously derived, using breakthrough curves matching. (ii) When water table is subject to some cycling or rising, the plume can be significantly distorted in the transverse direction, leading to unusual values of the ratio between longitudinal and transverse dispersivities. (iii) Under stable conditions, for example in the case of straightforward injection in the faster aquifer layer, longitudinal dispersivity is greater than the transverse component as usually encountered, and the obtained transport parameters are closed to macro dispersivity values, which reach their asymptotic limit at very short distances. (iv) The classical scale effect about the varying dispersivity at short distances could be a process mainly due to the distance required for a plume stabilization.     

Finite difference modeling of contaminant transport using analytic element flow solutions

The two-dimensional implementation of the analytic element method (AEM) is commonly used to simulate steady-state saturated groundwater flow phenomena at regional and local scales. However, unlike alternative groundwater flow simulation methods, AEM results are not ordinarily used as the basis for simulation of reactive solute transport. The use of AEM-simulated flow fields is impeded by the discrepancy between a continuous representation of flow and a typically discrete representation of transport, and requires translation of the flow solution to a discrete analog. This paper presents a variety of methods for analytically calculating conservative discrete water fluxes and integrated components of the dispersion tensor across cell interfaces. An Eulerian finite difference method based on these AEM-derived parameters is implemented for use in simulation of 2D (vertically averaged) solute transport. This implementation is first benchmarked against existing methods that use standard finite difference flow solutions, then used to investigate the effects of an inaccurate discrete water balance. It is shown that improper translation of AEM fluxes leads to significant water balance errors and inaccurate simulation of contaminant transport.