Review of the use of Péclet numbers to determine the relative importance of advection and diffusion in low permeability environments

In low permeability environments, transport by advection is often neglected based on a Péclet number criterion. Such a criterion usually states that if the Péclet number (Pe) is much smaller than 1, diffusion dominates over advection and transport may be modeled considering diffusion only. Unfortunately, up to 10 different Péclet number definitions exist and for a particular case these different definitions lead to very diverse Péclet number values, differing several orders of magnitude from each other. In this paper, the different Péclet number definitions are therefore evaluated on their ability to determine the relative importance of transport by advection and by diffusion in low permeability environments. This is done by comparing the results of the analytical solution for pure diffusion with the analytical solution for diffusion, advection and dispersion for a large number of different input parameter values. The relation between the different Péclet numbers and the difference between the calculated concentration considering diffusion only and the calculated concentration considering both diffusion and advection is studied. These calculations show that some Péclet number definitions are not well suited to decide whether advection may be neglected in low permeability media.

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Resumen Frecuentemente se descuida el transporte por avección en ambientes de baja permeabilidad sobre la base del criterio del número de Péclet. Dicho criterio usualmente sostiene que si el número de Péclet (Pe) es mucho menor a 1, la difusión domina sobre la avección y es posible modelar el transporte considerando la difusión únicamente. Desafortunadamente existen 10 definiciones diferentes del número de Péclet y para un caso en particular estas diferentes definiciones conducen a valores de número de Péclet muy diversos los cuales difieren entre sí en varias magnitudes. Por lo tanto, en este artículo se evalúan las diferentes definiciones en base a su habilidad para determinar la importancia relativa del transporte por avección y difusión en ambientes de baja permeabilidad. Esto se lleva a cabo mediante la comparación de los resultados de la solución analítica para difusión pura con los de la solución analítica por difusión, avección y dispersión para un número amplio de diferentes valores como parámetro. Se ha estudiado la relación entre los diferentes números de Péclet y las diferencias entre la concentración calculada considerando difusión únicamente y considerando tanto difusión como avección. Estos cálculos muestran que algunas de las definiciones de los números de Péclet no son muy apropiadas par decidir si se puede descuidar la avección en medios de baja permeabilidad.

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Résumé Dans les milieux à faible perméabilité, le transport par advection est souvent négligeable lorsquon se base sur le critère du nombre de Péclet. Un tel critère suggère habituellement que pour un nombre de Péclet beaucoup plus petit que 1, la diffusion domine sur ladvection et que le transport peut être modélisé par diffusion seulement. Malheureusement, il existe jusquà environ dix définitions du nombre de Péclet et pour un cas spécifique, ces différentes définitions mènent à des valeurs du nombre de Péclet très différentes, et qui varient entre elles de plusieurs ordres de grandeur. Dans cet article, les différentes définitions du nombre de Péclet sont évaluées en fonction de leur habileté à déterminer limportance relative du transport par advection et par diffusion dans les milieux à faible perméabilité. Ceci est fait en comparant les résultats de la solution analytique pour la diffusion pure à la solution analytique pour la diffusion, ladvection et la dispersion, et ce, pour un grand nombre de valeurs différentes comme paramètre dentrée. La relation entre les différents nombres de Péclet et la différence entre la concentration calculée en considérant la diffusion seulement et la concentration calculée considérant simultanément la diffusion et ladvection est étudiée. Ces calculs prouvent que certaines définitions de nombre de Péclet ne sont pas appropriées afin de décider si ladvection peut être négligée dans les milieux à faible perméabilité.

     

Influence of injection conditions on field tracer experiments

Calibration of ground water transport models is often performed using results of field tracer experiments. However, little attention is usually paid to the influence, on resulting breakthrough curves, of injection conditions and well-aquifer interactions, more particularly of the influence of the possible trapping of the tracer in the injection wellbore. Recently, a new mathematical and numerical approach has been developed to model injection conditions and well-aquifer interactions in a very accurate way. Using an analytical solution derived from this model, a detailed analysis is made of the evolution of the tracer input function in the aquifer. By varying injection conditions from one simulation to another, synthetic breakthrough curves are generated with the SUFT3D ground water flow and transport finite-element simulator. These tests show clearly that the shape of the breakthrough curves can be dramatically affected by injection conditions. Using generated breakthrough curves as "actual" field results, a calibration of hydrodispersive parameters is performed, neglecting the influence of injection conditions. This shows that neglecting the influence of actual injection conditions can lead to (1) errors on fitted parameters and (2) misleading identification of the active transport processes. Conclusions and guidelines are drawn in terms of proposed methodologies for better controlling the tracer injection in the field, in order to minimize risk of misinterpretation of results.     

Estimating the Depth of Stratigraphic Units from Marine Seismic Profiles Using Nonstationary Geostatistics

The object of this study is to build a three-dimensional (3D) geometric model of the stratigraphicunits of the margin of the Rhone River on the basis of geophysical investigations by a networkof seismic profiles at sea. The geometry of these units is described by depth charts of eachsurface identified by seismic profiling, which is done by geostatistics. The modeling starts bya statistical analysis by which we determine the parameters that enable us to calculate thevariograms of the identified surfaces. After having determined the statistical parameters, wecalculate the variograms of the variable Depth. By analyzing the behavior of the variogramwe then can deduce whether the situation is stationary and if the variable has an anisotropicbehavior. We tried the following two nonstationary methods to obtain our estimates: (a) Themethod of universal kriging if the underlying variogram was directly accessible. (b) Themethod of increments if the underlying variogram was not directly accessible. After havingmodeled the variograms of the increments and of the variable itself, we calculated the surfacesby kriging the variable Depth on a small-mesh estimation grid. The two methods then arecompared and their respective advantages and disadvantages are discussed, as well as theirfields of application. These methods are capable of being used widely in earthsciences forautomatic mapping of geometric surfaces or for variables such as a piezometricsurface or aconcentration, which are not stationary, that is, essentially, possess a gradient or a tendencyto develop systematically in space.     

Origin and formation pathways of kerogen-like organic matter in recent sediments off the Danube delta (northwestern Black Sea)

The chemical structure, source(s), and formation pathway(s) of kerogen-like organic matter (KL) were investigated in recent sediments from the northwestern Black Sea, off the Danube delta. Three sections from a sediment core collected at the mouth of the Sulina branch of the delta, under an oxic water column, were examined: S₀ (0–0.5 cm bsf), S₁₀ (10–13 cm bsf), and S₂₀ (20–25 cm bsf). The bulk geochemical features of these sediments (total organic carbon, organic C/N atomic ratio, δ¹³C_org) were determined. Thereafter, KL was isolated from the samples, as the insoluble residue obtained after HF/HCl treatment. KL chemical composition was investigated via spectroscopic (FTIR, solid state ¹³C and ¹⁵N NMR) and pyrolytic (Curie point pyrolysis–gas chromatography–mass spectrometry) methods, and the morphological features were examined by scanning and transmission electron microscopy. Similar morphological features and chemical composition were observed for the three KLs and they suggested that the selective preservation of land-plant derived material as well as of resistant aliphatic biomacromolecules (probably derived from cell walls of freshwater microalgae) was the main process involved in KL formation. Besides, some melanoidin-type macromolecules (formed via the degradation-recondensation of products mainly derived from proteinaceous material) and/or some encapsulated proteins also contributed to the KL chemical structure.     

1D complete calculation for electrostatic soundings interpretation

Soundings achieved with the electrostatic method cannot be interpreted correctly with 1D electrical programs if the extension of the array or the conductivity of the ground are too large. A complete calculation taking into account the induction effect due to the frequency must be performed. This paper presents the solutions for overcoming the difficulties encountered in this calculation: the iterative processes which make it possible to determine the kernel functions of the Hankel transforms and the analytic integration of the terms of the electric field. Application to practical cases first illustrates the distortion of the electrostatic curves by reference to DC sounding curves. The limitation in depth of investigation is then emphasized: in practice, the investigation is limited by the skin depth corresponding to the frequency used. The examples of the soundings obtained in the city of Alexandria (Egypt) demonstrate the importance of using the complete calculation for very conductive grounds.     

Sources of Cd, Cu, Ni and Zn in Portuguese coastal waters

In order to identify the major sources of trace metals (TM) in the Portuguese coastal waters, 58 surface water samples were collected during September 1988. The area sampled extended from the Tagus Estuary (down to a salinity of 25) to cape Ste Marie on the southern coast of Portugal. Dissolved metal concentrations in the fully marine waters ranged from 30 to 250 pM for Cd, 0.7–15 nM for Cu, 0.9–20 nM for Zn and 1.8–4.5 nM for Ni. Within the Tagus Estuary (salinity 25), concentrations increased to 3400 pM for Cd, 26 nM for Cu, 14 nM for Ni and 230 nM for Zn.The large-scale distribution of these metals is dominated by two strong continental sources, both probably linked to the exploitation of pyrite ores. In the Tagus Estuary, TM enrichments can be mostly attributed to a pyrite roasting plant located on the shore in front of Lisbon. Concerning the south Portuguese shelf waters, several hypotheses are proposed to explain their elevated metal concentrations. We particularly discussed the likely influence of the Tinto/Odiel rivers located 100 km eastward, an influence well known in the shelf waters of the Gulf of Cadiz. These rivers are extremely metal-rich because of acid mine tailings originating from their catchment. Between these two regions, upwelling of relatively metal-poor water largely contributes to the dilution of the continental inputs. Indeed, water exchanges on the shelf linked to the upwelling involve water fluxes 500 times higher than the Tagus River flow, and renew the coastal waters that are thus cleaned from terrestrial contamination. Contrary to many other upwelling systems in non-contaminated areas, the Portuguese upwelling does not act as a source of trace-metal enrichment of the continental margin waters.     

A multimodel comparison for assessing water temperatures under changing climate conditions via the equilibrium temperature concept: case study of the Middle Loire River,France

This paper investigates three categories of models that are derived from the equilibrium temperature concept to estimate water temperatures in the Loire River in France and the sensitivity to changes in hydrology and climate. We test the models' individual performances for simulating water temperatures and assess the variability of the thermal responses under the extreme changing climate scenarios that are projected for 2081–2100. We attempt to identify the most reliable models for studying the impact of climate change on river temperature (T_w). Six models are based on a linear relationship between air temperatures (T_a) and equilibrium temperatures (T_e), six depend on a logistic relationship, and six rely on the closure of heat budgets. For each category, three approaches that account for the river's thermal exchange coefficient are tested. In addition to air temperatures, an index of day length is incorporated to compute equilibrium temperatures. Each model is analysed in terms of its ability to simulate the seasonal patterns of river temperatures and heat peaks. We found that including the day length as a covariate in regression‐based approaches improves the performance in comparison with classical approaches that use only T_a. Moreover, the regression‐based models that rely on the logistic relationship between T_e and T_a exhibit root mean square errors comparable (0.90 °C) with those obtained with a classical five‐term heat budget model (0.82 °C), despite a small number of required forcing variables. In contrast, the regressive models that are based on a linear relationship T_e = f(T_a) fail to simulate the heat peaks and are not advisable for climate change studies. The regression‐based approaches that are based on a logistic relationship and the heat balance approaches generate notably similar responses to the projected climate changes scenarios. This similarity suggests that sophisticated thermal models are not preferable to cruder ones, which are less time‐consuming and require fewer input data. Copyright © 2012 John Wiley & Sons, Ltd.     

Using land cover changes and demographic data to improve hydrological modeling in the Sahel

At the beginning of the drought in the Sahel in the 1970s and 1980s, rainfall decreased markedly, but runoff coefficients and in some cases, absolute runoff increased. This situation was due to the conversion of the land cover from natural vegetation with a low annual runoff coefficient, to cropland and bare soils, whose runoff coefficients are higher. Unless they are adapted, hydrological conceptual models, such as GR2M, are unable to reproduce this increase in runoff. Despite the varying environmental and climatic conditions of the West African Sahel, we show that it is possible to increase the performance of the GR2M model simulations by elaborating a time‐varying soil water holding capacity and to incorporate this value in the annual maximum amount of water to be stored in reservoir A of the model. We looked for interactions between climate, rural society, and the environment. These interactions drive land‐cover changes in the Sahel, which in turn drive the distribution of rainfall between infiltration, evaporation, and runoff and hence the water resources, which are vital in this region. We elaborated several time series of key indicators linked to these interactions. We then integrated these changes in the runoff conditions of the GR2M model through the maximum value of the reservoir capacity. We calculated annual values of water holding capacity using the annual values of four classes of land cover, natural vegetation, cultivated area, bare soil, and surface water. We then used the hydrological model with and without this time‐varying soil value of A and compared the performances of the model under the two scenarios. Whatever the calibration period used, the Nash–Sutcliffe index was always greater in the case of the time‐varying A time series.     

Suspended sediment and dissolved load budgets of two Amazonian rivers from the Guiana Shield: Maroni River at Langa Tabiki and Oyapock River at Saut Maripa (French Guiana)

This study presents the data collected within the framework of an Observatory of Research in Environment on the Amazonian Basin—the ORE HYBAM. It relates to the dissolved and solid loads of the two main rivers of French Guiana, the Maroni and Oyapock rivers, running on the Guiana Shield and draining respectively 64 230 and 24 630 km². The low coefficient of variation of the average annual flows of the two rivers indicates an inter‐annual hydrological stability probably related to the immediate vicinity of the Atlantic Ocean. The sedimentary load is mainly composed of quartz and kaolinite. The total suspended solid (TSS) concentrations are among the world's lowest values; they range from 1 to 130 mg l⁻¹ during the hydrological cycle, with averages of 22 and 12 mg l⁻¹, for the Maroni and Oyapock rivers, respectively. The seasonal variability of these values is significantly higher than that of hydrologic flows, but without simple relationship with the discharge. Water chemical composition of the two rivers indicates a very weak mineralization, very similar to that found in the Amazonian rivers running on the Brazilian and Guianese shields, and in the Congo River and its tributaries in the Central African Shield. Seasonal variations are observed in both basins; they correspond to higher concentrations during low water stage (from October to February) and to more diluted water during the flood, from April to July. A signature enriched in Cl⁻ is present at the Saut Maripa station on the Oyapock River indicating a more marked influence of the trade winds in this basin. The computation of atmospheric contributions to ions budget indicated a weak contribution for Ca²⁺ and Mg²⁺, which originates mainly from water‐rock interactions in both stations, while more than half of Na⁺ is derived from atmospheric inputs. Copyright © 2010 John Wiley & Sons, Ltd.