An adaptive finite element model for wellbore breakout simulation

A finite element formulation is proposed and implemented for analysing the stability of excavated wells using the DiMaggio-Sandler constitutive elastoplastic model with a typical carbonate reservoir configuration. The quality of the finite element approximation is ensured by applying smooth curved elements adapted to the wellbore geometry, and h − p adaptive finite element meshes in the plastic zone. General purpose procedures are defined to transfer the elastoplastic deformation history to newly created integration points. A breakout damage criterion is proposed based on the second invariant of the deviatoric plastic deformation tensor. This damage criterion is used to apply a mesh movement algorithm to represent material collapse. The automatic successive application of the breakout damage criterion results in elliptical realistically looking geometries obtained in experiments reported in the literature.     

A methodology for regionalizing 3‐D effective porosity at watershed scale in crystalline aquifers

An innovative approach for regionalizing the 3‐D effective porosity field is presented and applied to two large, overexploited, and deeply weathered crystalline aquifers located in southern India. The method derives from earlier work on regionalizing a 2‐D effective porosity field in that part of an aquifer where the water table fluctuates, which is now extended over the entire aquifer using a 3‐D approach. A method based on geological and geophysical surveys has also been developed for mapping the weathering profile layers (saprolite and fractured layers). The method for regionalizing 3‐D effective porosity combines water table fluctuation and groundwater budget techniques at various cell sizes with the use of satellite‐based data (for groundwater abstraction), the structure of the weathering profile, and geostatistical techniques. The approach is presented in detail for the Kudaliar watershed (983 km²) and tested on the 730 km² Anantapur watershed. At watershed scale, the effective porosity of the aquifer ranges from 0.5% to 2% in Kudaliar and between 0.3% and 1% in Anantapur, which agrees with earlier works. Results show that (a) depending on the geology and on the structure of the weathering profile, the vertical distribution of effective porosity can be very different and that the fractured layers in crystalline aquifers are not necessarily characterized by a rapid decrease in effective porosity and (b) that the lateral variations in effective porosity can be larger than the vertical ones. These variations suggest that within a same weathering profile, the density of open fractures and/or degree of weathering in the fractured zone may significantly vary from a place to another. The proposed method provides information on the spatial distribution of effective porosity that is of prime interest in terms of flux and contaminant transport in crystalline aquifers. Implications for mapping groundwater storage and scarcity are also discussed, which should help in improving groundwater resource management strategies.     

A GLUE‐based uncertainty assessment framework for tritium‐inferred transit time estimations under baseflow conditions

The last decade has seen major technical and scientific improvements in the study of water transfer time through catchments. Nevertheless, it has been argued that most of these developments used conservative tracers that may disregard the oldest component of water transfer, which often has transit times greater than 5 years. Indeed, although the analytical reproducibility of tracers limits the detection of the older flow components associated with the most dampened seasonal fluctuations, this is very rarely taken into account in modelling applications. Tritium is the only environmental tracer at hand to investigate transfer times in the 5‐ to 50‐year range in surface waters, as dissolved gases are not suitable due to the degassing process. Water dating with tritium has often been difficult because of the complex history of its atmospheric concentration, but its current stabilization together with recent analytical improvements open promising perspectives. In this context, the innovative contribution of this study lies in the development of a generalized likelihood uncertainty estimation‐based approach for analysing the uncertainties associated with the modelling of transit time due to both parameter identification and tracer analytical precision issues. A coupled resampling procedure allows assessment of the statistical significance of the transfer time differences found in diverse waters. This approach was developed for tritium and the exponential‐piston model but can be implemented for virtually any tracer and model. Stream baseflow, spring and shallow aquifer waters from the Vallcebre research catchments, analysed for tritium in different years with different analytical precisions, were investigated by using this approach and taking into account other sources of uncertainty. The results showed three groups of waters of different mean transit times, with all the stream baseflow and spring waters older than the 5‐year threshold needing tritium. Low sensitivity of the results to the model structure was also demonstrated. Dual solutions were found for the waters sampled in 2013, but these results may be disambiguated when additional analyses will be made in a few years. Copyright © 2016 John Wiley & Sons, Ltd.     

Towards more systematic perceptual model development: a case study using 3 Luxembourgish catchments

The synthesis of experimental understanding of catchment behaviour and its translation into qualitative perceptual models is an important objective of hydrological sciences. We explore this challenge by examining the cumulative understanding of the hydrology of three experimental catchments and how it evolves through the application of different investigation techniques. The case study considers the Huewelerbach, Weierbach and Wollefsbach headwater catchments of the Attert basin in Luxembourg. Subsurface investigations including bore holes and pits, analysis of soil samples and Electrical Resistivity Tomography measurements are presented and discussed. Streamflow and tracer data are used to gain further insights into the streamflow dynamics of the catchments, using end‐member mixing analysis and hydrograph separation based on dissolved silica and electrical conductivity. We show that the streamflow generating processes in all three catchments are controlled primarily by the subsolum and underlying bedrock. In the Huewelerbach, the permeable sandstone formation supports a stable groundwater component with little seasonality, which reaches the stream through a series of sources at the contact zone with the impermeable marls formation. In the Weierbach, the schist formation is relatively impermeable and supports a ‘fill and spill’‐type of flow mechanism; during wet conditions, it produces a delayed response dominated by pre‐event water. In the Wollefsbach, the impermeable marls formation is responsible for a saturation‐excess runoff generating process, producing a fast and highly seasonal response dominated by event water. The distinct streamflow generating processes of the three catchments are represented qualitatively using perceptual models. The perceptual models are in turn translated into quantitative conceptual models, which simulate the hydrological processes using networks of connected reservoirs and transfer functions. More generally, the paper illustrates the evolution of perceptual models based on experimental fieldwork data, the translation of perceptual models into conceptual models and the value of different types of data for processes understanding and model representation. Copyright © 2014 John Wiley & Sons, Ltd.     

A probabilistic approach for computing water retention of particulate systems from statistics of grain size and tessellated pore network

The paper offers an analytical determination of the hydraulic properties of an unsaturated soil with reference to its retention curve, which describes the relationship between the volumetric water content and capillarity through matric suction. The analysis combines a particulate approach focused on the physics at the pore scale, including microstructural aspects, with a probabilistic approach where the void space and grain size are considered as random variables. In the end, the soil water characteristic curve of an unsaturated granular medium along a drying path can be derived analytically based on the sole information of particle size distribution. The analysis hinges on the tessellation of a wet granular system into an assemblage of tetrahedral unit cells revealing a pore network upon which capillary physics are computed with respect to pore throat invasion by a non-wetting fluid with evolving pendular capillary bridges. The crux of the paper is to pass from particle size probability distribution to a matching void space distribution to eventually reveal key information such as void cell and solid volume statistics. Making reasonable statistically based assumptions to render calculations tractable, the water retention curve can be readily constructed. Model predictions compare quite favourably with experimental data available for actual soils, especially in the high saturation range. Having a sound scientific basis, the model can be made amenable to address a variety of soils with a wider range of particle sizes.     

Spatio‐temporal variability of the isotopic input signal in a partly forested catchment: Implications for hydrograph separation

The isotopic composition of precipitation (D and ¹⁸O) has been widely used as an input signal in water tracer studies. Whereas much recent effort has been put into developing methodologies to improve our understanding and modelling of hydrological processes (e.g., transit‐time distributions or young water fractions), less attention has been paid to the spatio‐temporal variability of the isotopic composition of precipitation, used as input signal in these studies. Here, we investigated the uncertainty in isotope‐based hydrograph separation due to the spatio‐temporal variability of the isotopic composition of precipitation. The study was carried out in a Mediterranean headwater catchment (0.56 km²). Rainfall and throughfall samples were collected at three locations across this relatively small catchment, and stream water samples were collected at the outlet. Results showed that throughout an event, the spatial variability of the input signal had a higher impact on hydrograph separation results than its temporal variability. However, differences in isotope‐based hydrograph separation determined preevent water due to the spatio‐temporal variability were different between events and ranged between 1 and 14%. Based on catchment‐scale isoscapes, the most representative sampling location could also be identified. This study confirms that even in small headwater catchments, spatio‐temporal variability can be significant. Therefore, it is important to characterize this variability and identify the best sampling strategy to reduce the uncertainty in our understanding of catchment hydrological processes.     

Analysis of Physical and Chemical Parameters for Discrimination of Water Origin in a Hydroelectric Reservoir

Seventeen physical and chemical parameters were obtained from a hydroelectric reservoir located in a tropical region in the south of Brazil. Multivariate Principal Component Analysis (PCA) and Hierarchical Group Analysis (HGA) were used to identify the parameters discriminating the origin of water from the Tibagi and the Primeiro de Maio River, after it has passed the mixing region. The study was conducted during the dry and rainy seasons in July 2002 and February 2003 at three depths and three sampling sites located 0, 5, and 10 km away from the mixing region. The statistical methods showed to be appropriate for identifying the contribution of each tributary in the water mixing site of a complex water system. The most important discriminating parameter was the absorbance relation A(253 nm)/A(203 nm), followed by the concentrations of Fe(III), Mn(III), and Ni(II). An anthropogenic interference was found in the reservoir due to high Ni(II) and orthophosphate concentrations caused by a nearby town sewage discharge. The interference was more important during the dry periods due to the lower dispersion of the pollutants. Urgent initiatives should be taken from the state government to build treatment stations for the wastewater of the small cities around the Capivara hydroelectric reservoir to prevent the drinking water quality from deteriorating.