Andreas Englert

Mixing, spreading and reaction in heterogeneous media: A brief review

Geological media exhibit heterogeneities in their hydraulic and chemical properties, which can lead to enhanced spreading and mixing of the transported species and induce an effective reaction behavior that is different from the one for a homogeneous medium. Chemical heterogeneities such as spatially varying adsorption properties and specific reactive surface areas can act directly on the chemical reaction dynamics and lead to different effective reaction laws. Physical heterogeneities affect mixing-limited chemical reactions in an indirect way by their impact on spreading and mixing of dissolved species. To understand and model large-scale reactive transport the interactions of these coupled processes need to be understood and quantified. This paper provides a brief review on approaches of non-reactive and reactive transport modeling in geological media.

Effects of physical and geochemical heterogeneities on mineral transformation and biomass accumulation during biostimulation experiments at Rifle, Colorado

Electron donor amendment for bioremediation often results in precipitation of secondary minerals and the growth of biomass, both of which can potentially change flow paths and the efficacy of bioremediation. Quantitative estimation of precipitate and biomass distribution has remained challenging, partly due to the intrinsic heterogeneities of natural porous media and the scarcity of field data. In this work, we examine the effects of physical and geochemical heterogeneities on the spatial distributions of mineral precipitates and biomass accumulated during a biostimulation field experiment near Rifle, Colorado. Field bromide breakthrough data were used to infer a heterogeneous distribution of hydraulic conductivity through inverse transport modeling, while the solid phase Fe(III) content was determined by assuming a negative correlation with hydraulic conductivity. Validated by field aqueous geochemical data, reactive transport modeling was used to explicitly keep track of the growth of the biomass and to estimate the spatial distribution of precipitates and biomass. The results show that the maximum mineral precipitation and biomass accumulation occurs in the vicinity of the injection wells, occupying up to 5.4vol.% of the pore space, and is dominated by reaction products of sulfate reduction. Accumulation near the injection wells is not strongly affected by heterogeneities present in the system due to the ubiquitous presence of sulfate in the groundwater. However, accumulation in the down-gradient regions is dominated by the iron-reducing reaction products, whose spatial patterns are strongly controlled by both physical and geochemical heterogeneities. Heterogeneities can lead to localized large accumulation of mineral precipitates and biomass, increasing the possibility of pore clogging. Although ignoring the heterogeneities of the system can lead to adequate prediction of the average behavior of sulfate-reducing related products, it can also lead to an overestimation of the overall accumulation of iron-reducing bacteria, as well as the rate and extent of iron reduction. Surprisingly, the model predicts that the total amount of uranium being reduced in the heterogeneous 2D system was similar to that in the 1D homogeneous system, suggesting that the overall uranium bioremediation efficacy may not be significantly affected by the heterogeneities of Fe(III) content in the down-gradient regions. Rather, the characteristics close to the vicinity of the injection wells might be crucial in determining the overall efficacy of uranium bioremediation. These findings have important implications not only for uranium bioremediation at the Rifle site and for bioremediation of other redox sensitive contaminants at sites with similar characteristics, but also for the development of optimal amendment delivery strategies in other settings.

Three-Dimensional Geostatistical Inversion of Flowmeter and Pumping Test Data

We jointly invert field data of flowmeter and multiple pumping tests in fully screened wells to estimate hydraulic conductivity using a geostatistical method. We use the steady-state drawdowns of pumping tests and the discharge profiles of flowmeter tests as our data in the inference. The discharge profiles need not be converted to absolute hydraulic conductivities. Consequently, we do not need measurements of depth-averaged hydraulic conductivity at well locations. The flowmeter profiles contain information about relative vertical distributions of hydraulic conductivity, while drawdown measurements of pumping tests provide information about horizontal fluctuation of the depth-averaged hydraulic conductivity. We apply the method to data obtained at the Krauthausen test site of the Forschungszentrum Jülich, Germany. The resulting estimate of our joint three-dimensional (3D) geostatistical inversion shows an improved 3D structure in comparison to the inversion of pumping test data only.

Electrode-based approach for monitoring in situ microbial activity during subsurface bioremediation.

Current production by microorganisms colonizing subsurface electrodes and its relationship to substrate availability and microbial activity was evaluated in an aquifer undergoing bioremediation. Borehole graphite anodes were installed downgradient from a region of acetate injection designed to stimulate bioreduction of U(VI); cathodes consisted of graphite electrodes embedded at the ground surface. Significant increases in current density (< or =50 mA/m2) tracked delivery of acetate to the electrodes, dropping rapidly when acetate inputs were discontinued. An upgradient control electrode not exposed to acetate produced low, steady currents (< or =0.2 mA/m2). Elevated current was strongly correlated with uranium removal but minimal correlation existed with elevated Fe(II). Confocal laser scanning microscopy of electrodes revealed firmly attached biofilms, and analysis of 16S rRNA gene sequences indicated the electrode surfaces were dominated (67-80%) by Geobacter species. This is the first demonstration that electrodes can produce readily detectable currents despite long-range (6 m) separation of anode and cathode, and these results suggest that oxidation of acetate coupled to electron transfer to electrodes by Geobacter species was the primary source of current. Thus it is expected that current production may serve as an effective proxy for monitoring in situ microbial activity in a variety of subsurface anoxic environments.

A SUCCESSIVE LINEAR ESTIMATOR FOR ELECTRICAL RESISTIVITY TOMOGRAPHY

A dc resistivity survey is an inexpensive and widely used technique for investigation of near surface resistivity anomalies. It recently has become popular for the investigation of subsurface pollution problems (NRC, 2000). In principle, it measures the electric potential field generated by a transmission of dc electric current between electrodes implanted at the ground surface. Then, an apparent (bulk or effective) electrical resistivity for a particular set of measurement electrodes is calculated using formulas that assume homogeneous earth. Many pairs of current transmission and electric potential measurements are used to “map” subsurface electrical resistivity anomalies. This conventional resistivity survey is analogous to classical aquifer test in which an aquifer is excited by pumping at one well and the response of the aquifer (e.g. drawdown-time relation or well hydrograph) is observed at another well. The theoretical well hydrograph from an analytical solution that assumes aquifer homogeneity and infinite domain (e.g. Theis’ solution, 1935) is then used to match the observed hydrograph to obtain apparent or effective aquifer transmissivity and storage coefficient. Due to the homogeneity assumption, the theoretical drawdown represents a spatially averaged drawdown in a heterogeneous aquifer. This average drawdown is unequivocally different from the one observed at a well in a heterogeneous aquifer, although the difference may be small due to diffusive nature of the flow process. Thus, applying Theis’ solution to aquifer tests in a heterogeneous aquifer is tantamount to comparing apples to oranges (Wu et al., 2005). They suggested that the apparent transmissivity represents a weighted average of transmissivity anomalies over the cone of depression. High weights are given to transmissivity anomalies near the observation and the pumping well. The apparent transmissivity reflects, as a consequence, local geology but it can also be affected by significant geologic anomalies within the cone of depression. In other words, the physical meaning of the apparent transmissivity can be highly dubious. The strong similarity between traditional aquifer and apparent resistivity analysis leads us to conclude that conventional analysis of electrical resistivity

High resolution aquifer characterization using crosshole GPR full‐waveform tomography: Comparison with direct‐push and tracer test data

Limited knowledge about the spatial distribution of aquifer properties typically constrains our ability to predict subsurface flow and transport. Here we investigate the value of using high resolution full-waveform inversion of cross-borehole ground penetrating radar (GPR) data for aquifer characterization. By stitching together GPR tomograms from multiple adjacent crosshole planes, we are able to image, with a decimeter scale resolution, the dielectric permittivity and electrical conductivity of an alluvial aquifer along cross sections of 50 m length and 10 m depth. A logistic regression model is employed to predict the spatial distribution of lithological facies on the basis of the GPR results. Vertical profiles of porosity and hydraulic conductivity from direct-push, flowmeter and grain size data suggest that the GPR predicted facies classification is meaningful with regard to porosity and hydraulic conductivity, even though the distributions of individual facies show some overlap and the absolute hydraulic conductivities from the different methods (direct-push, flowmeter, grain size) differ up to approximately one order of magnitude. Comparison of the GPR predicted facies architecture with tracer test data suggests that the plume splitting observed in a tracer experiment was caused by a hydraulically low-conductive sand layer with a thickness of only a few decimeters. Because this sand layer is identified by GPR full-waveform inversion but not by conventional GPR ray-based inversion we conclude that the improvement in spatial resolution due to full-waveform inversion is crucial to detect small-scale aquifer structures that are highly relevant for solute transport.

Contribution of the Finite Volume Point Dilution Method for measurement of groundwater fluxes in a fractured aquifer

Measurement of groundwater fluxes is the basis of all hydrogeological study, from hydraulic characterization to the most advanced reactive transport modeling. Usual groundwater flux estimation with Darcys law may lead to cumulated errors on spatial variability, especially in fractured aquifers where local direct measurement of groundwater fluxes becomes necessary. In the present study, both classical point dilution method (PDM) and finite volume point dilution method (FVPDM) are compared on the fractured crystalline aquifer of Ploemeur, France. The manipulation includes the first use of the FVPDM in a fractured aquifer using a double packer. This configuration limits the vertical extent of the tested zone to target a precise fracture zone of the aquifer. The result of this experiment is a continuous monitoring of groundwater fluxes that lasted for more than 4 days. Measurements of groundwater flow rate in the fracture (Q(t)) by PDM provide good estimates only if the mixing volume (V(w)) (volume of water in which the tracer is mixed) is precisely known. Conversely, the FVPDM allows for an independent estimation of V(w) and Q(t), leading to better precision in case of complex experimental setup such as the one used. The precision of a PDM does not rely on the duration of the experiment while a FVPDM may require long experimental duration to guarantees a good precision. Classical PDM should then be used for rapid estimation of groundwater flux using simple experimental setup. On the other hand, the FVPDM is a more precise method that has a great potential for development but may require longer duration experiment to achieve a good precision if the groundwater fluxes investigated are low and/or the mixing volume is large.

Reconstruction of Three-Dimensional Aquifer Heterogeneity from Two-Dimensional Geophysical Data

Suitable training images (TIs) for multiple-point statistics (MPS) are difficult to identify in real-case three-dimensional applications, posing challenges for modelers trying to develop realistic subsurface models. This study demonstrates that two-dimensional geophysical images, when employed as training and conditioning data, can provide sufficient information for three-dimensional MPS simulations. The advantage of such a data-driven approach is that it does not rely on any external (possibly inappropriate) TI. The disadvantage is that three-dimensional MPS simulations must be carried out based on two-dimensional information. Three different approaches (two existing, one new) are tested to overcome this problem. The two existing approaches rely on three-dimensional reconstruction of incomplete datasets and on sequential two-dimensional simulations, respectively. The third approach is a newly proposed combination of the two former approaches. The three approaches are applied to model the three-dimensional facies structure of an alluvial aquifer based on high-resolution ground-penetrating radar cross-sections. The quality of each simulation outcome is evaluated based on the similarity of its multiple-point histogram (MPH) to reference MPHs derived from geophysical images. This evaluation reveals that the first approach (three-dimensional reconstruction) performs well close to conditioning data, but farther away from the data the simulation results deteriorate. Quite conversely, the second approach (sequential two-dimensional) performs well when only few conditioning data exist, but with increasing simulation sequence the quality decreases. The newly proposed third approach integrates the benefits of both approaches and is found to reproduce the reference MPHs significantly better than either of the two other approaches alone.

Multi-scale characterization of joint surface roughness

Recent studies provided detailed characterizations of fault (i.e. shear fracture) roughness at different length scales. Similar investigation for joints (i.e. tensile fractures) are seldom and not as detailed. The present study aims at characterizing joint plumose patterns. We investigated the scale-dependent surface roughness properties of S-type plumoses. Joint surface measurements at relatively large scales were carried out with Light Detection And Ranging (LiDAR) technology. Joint surface measurements at the microscopic scale were carried out based on a non-contact optical method, using a Keyence VHX-2000D microscope. Three parameters were used to characterize fracture surface elevation, standard deviation, Hurst exponent and correlation length through three scale-length orders of magnitude. Our study showed that standard deviation and correlation length decrease with scale, similarly to previous findings on faults. In addition, the range of Hurst exponents as a function of scale for the studied joint surface agrees well with those previously found for faults. However, directional analysis showed that correlation length and Hurst exponent of joint surfaces at scales smaller than 1 dm differ significantly from the ones of fault surfaces. In contrast to fault surface ornaments, that are mainly characterized by linear structures, plumose structures show marked variability in orientation and anisotropy as a function of position on the joint surface.

Three-dimensional flow characterization in a joint with plumose pattern

This work numerically simulates fracture flow in natural fractures, specifically in a joint with plumose pattern. A natural fracture surface, previously measured in the field using LiDAR scanning, was used to rebuild an open fracture geometry, assuming mode 1 fracture opening. Three-dimensional fracture flow was modeled by solving Stokes equation in a stationary regime using the finite element method. Three different pressure gradients and apertures were numerically investigated to better understand the impact of plumose patterns with different degrees of roughness. Resulting fracture flow fields were characterized by hydraulic aperture and by statistics on the directional components of the three-dimensional velocity vector. The results show that the hydraulic aperture and the longitudinal component of the velocity vector decrease with increasing roughness. Beyond this classical finding, the study shows that the variance of the longitudinal component of the flow velocity vector also decreases with increasing roughness. This behavior can be predicted based on variance estimates connected to the parabolic profile. The results further revealed that the variances of the transverse components of the velocity vector increase with fracture surface roughness. These findings suggest that the roughness-induced reduction in the mean and the variance of the longitudinal component of the velocity vector in joints with rough surfaces is accompanied with a simultaneous increase of the transverse components of the three-dimensional velocity vector.RésuméCe travail simule numériquement les écoulements dans des fractures naturelles, en particulier dans des joints avec des caractéristiques morphologiques de plumose. Une surface de fracture naturelle, initialement mesurée sur le terrain à l’aide d’une imagerie LiDAR, a été utilisée pour reconstituer la géométrie d’une fracture ouverte en supposant une ouverture de fracture en mode 1. L’écoulement tridimensionnel dans la fracture a été modélisé en résolvant l’équation de Stokes en régime permanent et en utilisant la méthode des éléments finis. Trois gradients de pression et trois ouvertures ont été étudiés numériquement afin de mieux comprendre l’impact des plumoses avec différents degrés de rugosité sur les écoulements. Les champs d’écoulement résultant dans la fracture ont été caractérisés à l’aide de l’ouverture hydraulique et de l’analyse statistique des composantes directionnelles du vecteur tridimensionnel de la vitesse. Les résultats montrent que l’ouverture hydraulique et la composante longitudinale du vecteur de la vitesse décroissent avec l’augmentation de la rugosité. Au-delà de ces résultats classiques, cette étude montre que la variance de la composante longitudinale du vecteur de vitesse diminue également avec l’augmentation de la rugosité. Ce comportement peut être prédit en fonction des estimations de variance liées au profil parabolique des vitesses dans la fracture. Les résultats ont montré que les variances des composantes transversales du vecteur de vitesse augmentent avec la rugosité des surfaces de fracture. Ces résultats suggèrent que la réduction de la moyenne et de la variance de la composante longitudinale du vecteur de vitesse induite par la rugosité dans les joints est accompagnée d’une augmentation simultanée des composantes transversales du vecteur de la vitesse tridimensionnelle.ResumenEste trabajo simula numéricamente el flujo de fractura en fracturas naturales, específicamente en una diaclasa con patrón plumoso. Se usó una superficie de fractura natural, previamente medida en el campo utilizando el escaneo LiDAR, para reconstruir una geometría de fractura abierta asumiendo la apertura de fractura en modo 1. El flujo de fractura tridimensional se modeló mediante la resolución de la ecuación de Stokes en un régimen estacionario utilizando el método de elementos finitos. Se investigaron numéricamente tres diferentes gradientes de presión y aperturas para comprender mejor el impacto de los patrones plumosos con diferentes grados de rugosidad. Los campos de flujo de fractura resultantes se caracterizaron por la apertura hidráulica y por las estadísticas sobre las componentes direccionales del vector de velocidad tridimensional. Los resultados muestran que la apertura hidráulica y la componente longitudinal del vector de velocidad disminuyen con el aumento de la rugosidad. Más allá de este hallazgo clásico, el estudio muestra que la varianza de la componente longitudinal del vector de velocidad de flujo también disminuye al aumentar la rugosidad. Este comportamiento se puede predecir a partir de las estimaciones de varianza relacionadas con el perfil parabólico. Los resultados revelaron además que las varianzas de las componentes transversales del vector de velocidad aumentan con la rugosidad superficial de la fractura. Estos hallazgos sugieren que la reducción inducida por la rugosidad en la media y la varianza del componente longitudinal del vector de velocidad en las diaclasas con superficies rugosas se acompaña con un aumento simultáneo de las componentes transversales del vector de la velocidad tridimensional.摘要本研究工作数值模拟了天然断裂中、特别是羽状模式节理中的断裂水流。过去在野外采用LiDAR扫描测量的天然断裂面用来重建假定模式1 断裂缝隙的开放的断裂几何形状。采用有限元方法依靠稳定状态下求解Stokes方程模拟了三维断裂水流。数值上调查了三个不同的压力梯度和缝隙以便更好地了解不同粗糙程度的羽状模式的影响。通过水力缝隙以及对三维速度矢量方向性成分的统计学计算,描述了断裂水流场的特征。结果显示,水力缝隙及速度矢量纵向成分随着粗糙度增加而减少。除了这个经典的发现, 研究还显示,水流速度矢量纵向成分的方差也随着粗糙度的增加而减少。这种状况可根据与抛物线剖面相连的方差估算值预测。结果进一步揭示,速度矢量的横向成分方差随着断裂面的粗糙度的增加而增加。这些发现表明,粗糙度引起的带有粗糙面节理中速度矢量纵向成分平均值和方差的减少伴随着三维速度矢量横向成分的同时增加。ResumoEste trabalho simula numericamente o fluxo fraturado em fraturas naturais, especificamente em uma diaclase com padrão plumoso. Uma superfície de fratura natural, previamente medida no campo utilizando a varredura LiDAR foi utilizada para reconstruir uma geometria de fratura aberta assumindo como abertura de fratura o modo 1. O fluxo de fratura tridimensional foi modelado aplicando-se a equação de Stokes em um regime estacionário utilizando o método de elementos finitos. Três diferentes gradientes de pressão e aberturas foram numericamente investigados para melhor entender o impacto do padrão plumoso com diferentes graus de rugosidade. Os campos de fraturas resultantes foram caracterizados por abertura hidráulica e estatísticas nos componentes direcionais do vetor de velocidade tridimensional. Os resultados mostram que a abertura hidráulica e o componente longitudinal do vetor de velocidade diminuem com o aumento da rugosidade. Além deste achado clássico, o estudo mostra que a variância do componente longitudinal do vetor de velocidade de fluxo também diminui com o aumento da rugosidade. Este comportamento pode ser previsto baseado nas estimativas de variância conectadas ao perfil parabólico. Os resultados revelaram ainda que as variâncias dos componentes transversais do vetor velocidade aumentam com a rugosidade da superfície da fratura. Isto sugere que a redução da média e da variância da componente longitudinal do vetor velocidade em articulações com superfícies irregulares induzidas pela rugosidade é acompanhada de um aumento simultâneo dos componentes transversais do vetor de velocidade tridimensional.