Effective porosity and dispersion in stratified aquifers: closed-form solutions

Résumé: Ce Rapport Technique présente des solutions analytiques inédites pour la migration d’un traceur non réactif par écoulement plan ou radial dans un aquifère idéal stratifié, dans le cas d’une distribution lognormale de la conductivité hydraulique K. Des solutions sont obtenues pour la porosité effective et la dispersivité longitudinale de l’aquifère homogène hydrauliquement équivalent. La recherche conduisant à ces nouvelles solutions a été motivée par le fait que l’équation classique d’advection–dispersion n’explique pas trois caractéristiques des courbes de restitution des essais in situ de traceurs non réactifs: (1) arrivée précoce, (2) effet d’échelle pour la dispersion longitudinale, et (3) courbe avec une longue queue. Les problèmes de traceurs sont résolus d’abord pour un nombre fini de souscouches afin de bien illustrer les résultats clés, et ensuite pour une distribution lognormale de K. Pour une injection soutenue du traceur, la nouvelle équation de la courbe de restitution ressemble à l’équation d’advection–dispersion d’un aquifère homogène, mais avec une arrivée précoce et plus de distorsion. Des distributions, normale et lognormale, de K donnent des courbes de restitution similaires seulement dans le cas d’une faible variance. Une nouvelle équation est obtenue pour la dispersivité longitudinale : elle explique les résultats de terrain collectés par divers auteurs, leur variation avec la distance ainsi qu’avec la variance de ln (K). Pour une injection temporaire de traceur, la courbe de restitution théorique, obtenue pour une distribution lognormale de K, présente elle aussi une arrivée précoce, une distorsion et une longue queue, qui sont les trois caractéristiques des essais de traceurs in situ. ---------- Abstract: This Technical Report provides original closed-form solutions for the migration of a non-reactive tracer due to either plane or radial seepage in an ideally stratified aquifer, in the case of a lognormal K distribution. New solutions are obtained for the effective porosity and longitudinal dispersivity of the hydraulically equivalent homogenous aquifer. The research leading to these new solutions was initiated because the classical advection-dispersion equation does not explain three features of break-through curves of field non-reactive tracer tests: (1) early arrival, (2) scale-dependent longitudinal dispersion, and (3) long tail. Initially, the tracer test problems are solved for a finite number of sub-layers to illustrate the key findings, then for a lognormal distribution of the hydraulic conductivity, K. For steady tracer injection and a lognormal K distribution, the new break-through curve equation looks like the advection-diffusion equation in a homogenous aquifer, but with an earlier arrival and more distortion. The normal and lognormal K distributions yield similar break-through curves only for a case of small variance. The new equation for the longitudinal dispersivity explains field values which have been collected by various authors, their variation with distance and also with the variance of ln (K). For a tracer injection of limited duration, the predicted break-through curve for a lognormal K distribution also yields the early arrival, a BTC distortion and long tail, which are the three features of field tracer tests

Predicting the coefficient of permeability of soils using the Kozeny-Carman equation

Résumé: La conductivité hydraulique saturée d'un sol peut être prédite par des relations empiriques, des modèles capillaires, des modèles statistiques et des théories de rayon hydraulique. Une relation bien connue entre perméabilité et propriétés des pores fut proposée par Kozeny et modifiée par Carman. L'équation résultante est largement connue sous le nom Kozeny-Carman (KC), bien que ces auteurs n'aient jamais publié ensemble. Dans la littérature géotechnique, il existe un large consensus à l'effet que l'équation de Kozeny-Carman s'applique aux sables mais pas aux argiles. Cependant, cette opinion n'est appuyée que par une démonstration partielle. Cet article examine les fondements et la validité de l'équation KC à l'aide d'essais de perméabilité en laboratoire. Les résultats d'essais proviennent de diverses publications qui ont fourni toute l'information requise pour faire une prédiction : indice des vides et soit la surface spécifique mesurée pour les sols cohérents, soit la courbe granulométrique pour les sols pulvérulents. L'article montre comment calculer la surface spécifique d'un sol pulvérulent à partir de sa courbe granulométrique. Les résultats présentés ici indiquent qu'en général, l'équation de Kozeny-Carman prédit assez bien la conductivité hydraulique saturée de la plupart des sols. Plusieurs des divergences constatées peuvent être reliées soit à des raisons pratiques (e.g. valeur imprécise de la surface spécifique, régime permanent pas établi, échantillons non saturés, etc.) soit à des raisons théoriques (une partie de l'eau est immobile, et l'équation de prédiction est isotrope alors que la conductivité hydraulique est une propriété anisotrope). Ces aspects sont discutés dans l'article en relation avec la capacité de prédiction de l'équation de Kozeny-Carman. --------- Abstract: The saturated hydraulic conductivity of a soil can be predicted using empirical relationships, capillary models, statistical models and hydraulic radius theories. A well-known relationship between permeability and properties of pores was proposed by Kozeny and later modified by Carman. The resulting equation is largely known under the name of Kozeny-Carman, although these authors never published together. In the geotechnical literature, there is a large consensus that the Kozeny-Carman (KC) equation applies to sands but not to clays. Such opinion, however, is supported only by partial demonstration. This report evaluates the background and the validity of the KC equation with laboratory permeability tests. Considered test results were taken from publications that provided all information needed to make a prediction: void ratio, and either the measured specific surface for cohesive soils, or the gradation curve for non-cohesive soils. This report shows how to estimate the specific surface of a non-cohesive soil from its gradation curve. The results presented here show that, as a general rule, the KC equation predicts fairly well the saturated hydraulic conductivity of most soils. Many of the observed discrepancies can be related to either practical reasons (e.g. inaccurate specific surface value, steady flow not reached, unsaturated specimens, etc.) or theoretical reasons (some water is motionless, and the predictive equation is isotropic whereas hydraulic conductivity is an anisotropic property). Theses issues are discussed in relation to the predictive capabilities of the KC equation

What maximum permeability can be measured with a monitoring well?

The PVC screens of recentmonitoringwells (MWs) have thin slots and a lowopen area, usually in the 2–8% range. The MW screen and filter pack may cause important head losses which are not taken into account when interpreting the data of permeability tests performed using the MW. The equivalent hydraulic conductivity K of usual PVC screens was defined by hydraulic tests in a water tank, which have shown that gas microbubbles, a common problem in MWs and filter packs, contribute to increase the parasitic head losses. Closedform equations and numerical models are used to explain by how much a field permeability test in a MW under evaluates an aquifer K value due to parasitic head losses in the screen and filter pack. TheMWcan properly measure the local soil K value only if it is markedly lower than the maximum MWvalue as obtained in a water tank. TheMWmeasuring capacity can reach 5 × 10−3 m/s for large slots and deairedwater, but ismost often between 10−5 and 10−4 m/s for small slots in field conditions, and it can be only 10−6 m/s for poorly designed and installedMWs. The limitedmeasuring capacitymay yield artificial permeability scale effects as often registered in environmental studies

Practical Considerations when Using the Swedish Fall Cone

This paper presents the results of Swedish fall cone tests and Casagrande liquid limit tests conducted on saline Champlain Sea clay samples from Lachenaie, Quebec. The main objective was to study a few hitherto unanswered practical questions regarding these testing methods. Penetration range is found to affect the Hansbo’s relationship used in fall cone experiments, while the mass and the bluntness degree of the cone have no effect on it. A direct relationship between thixotropic regain in shear strength and sensitivity is found. When measuring the liquid limit, if only the first penetration depth is recorded, results are up to 5% smaller than those obtained when following the standard procedure of CAN/BNQ-2501-092. With this standard, the average of the first two penetration depths within 0.3 mm of each other is recorded. These penetrations usually follow the bulk of the thixotropic shear strength regain. The Swedish fall cone was compared to the traditional Casagrande apparatus for liquid limit determinations. The two methods yielded identical results in the studied conditions (saline Lachenaie clay with liquid limit between 44% and 75%). An incorrect calibration of the height-of-drop of 1.4 mm led to a mean error of 6 liquid limit points. This error is greater than the theoretical error obtained by assuming that the number of blows is proportional to the square of the height-of-drop

Development of a model to predict the water retention curve using basic geotechnical properties

Résumé: La courbe de rétention d’eau (CRE) est devenue une fonction clé pour définir le comportement non saturé des sols et d'autres matériaux meubles. Dans beaucoup de cas, il peut être très utile d'avoir une évaluation de la CRE dans les pr emières phases d’un projet, lorsque peu ou pas de résultats d'essais sont disponibles. Des modèles prédictifs, basés sur les propriétés géotechniques de base, peuvent aussi être utilisés pour évaluer comment le changement des paramètres (en termes de porosité ou de granulométrie) affecte la CRE. Dans cet article, les auteurs présentent un ensemble d'équations développées pour prédire la relation entre la teneur en eau volumique θ (et le degré de saturation S r correspondant) et la succion ψ . Le modèle proposé pour la prédiction de la CRE est une version modifiée du modèle de Kovács (1981), qui fait une distinction entre la rétention d’eau due aux forces capillaires et celle par adhésion. Ce jeu d'équations est donné avec des relations complémentaires développées pour des applications spécifiques sur des matériaux granulaires et sur des sols (argileux) plastiques/c ohérents. Il est montré que le modèle constitue un moyen simple et pratique pour estimer la courbe de rétention d’eau à partir des propriétés géotechniques de base. Une discussion suit sur les capacités et les limitations du modèle. ---------- Abstract: The water retention curve (WRC) has become a key material function to define the unsaturated behavior of soils and of other particulate media. In many instances, it can be very useful to have an estimate of the WRC early in a project, when little or no test results are available. Predictive models, based on easy to obtain geotechnical prope rties, can also be employed to evaluate how changing parameters (e.g. porosity or grain size) affect the WRC. In this paper, the authors present a general set of equations developed for predicting the relationship between volumetric water content θ (and the corresponding degree of saturation S r ) and suction ψ . The proposed WRC model is a modified version of the Kovács (1981) model, which makes a distinction between water retention due to capillary forces and retention by adhesion. The complete set of equations is given together with complementary relationships developed for specific applications on granular materials and on plastic/cohesive (clayey) soils. It is shown that the model provides a simple and practical means to estimate the water retention curve from basic properties. A discussion follows on the capabilities and limitations of the model

Simulating water flow and reactive transport in waste rock piles using stochastic properties

Résumé: Ce rapport présente une approche de modélisation numérique visant à évaluer l’écoulement d'eau et le transport géochimique dans une halde à stériles réactifs, en utilisant des propriétés stochastiques pour les matériaux sulfureux. De telles simulations peuvent servir à mieux comprendre la réponse à long terme d'une halde à stériles typique. La courbe de rétention d'eau et la fonction de conductivité hydraulique non saturée sont utilisées pour représenter la variabilité spatiale de l'écoulement de l'eau ; une distribution des paramètres géochimiques sert pour l’analyse du transport réactif. Les résultats illustrent comment la corrélation spatiale des propriétés hydrauliques affecte la distribution et la circulation de l'eau au sein de l’empilement, produisant, dans certains cas des chemins d’écoulement préférentiels dans la direction de la plus forte corrélation des propriétés hydrauliques. Les simulations numériques montrent également que les taux d'oxydation des minéraux sulfureux sont influencés par la taille des grains, la proportion de sulfure et la distribution de l’eau, qui peuvent être la cause de grandes variations spatiales dans la composition des eaux de drainage. ---------- Abstract: This report presents a numerical modeling approach to assess unsaturated water flow and geochemical transport in a sulphidic waste rock pile using selected realizations of stochastically distributed material properties. Such simulations can serve to better understand the long-term response of a typical waste rock pile. The water retention curve and hydraulic conductivity function are used to represent spatial variability for water flow, while distributed geochemical parameters are used for reactive transport. The results illustrate how the spatial correlation of hydraulic properties directly affects the moisture distribution and flow within the pile, which in some cases creates local preferential flow paths along the direction of the strongest correlation of hydraulic properties. The numerical simulations also show how sulphide mineral oxidation rates can be influenced by the grain size, sulphide fraction and moisture content distribution, which may explain large observed spatial variations in the composition of drainage water

Quality of Life and Costs in Parkinson's Disease: A Cross Sectional Study in Hungary.

BACKGROUND: Patient reported outcomes and costs of illness are useful to capture some of the multiple effects of a disease and its treatments. Our aim was to assess quality of life (QoL) and costs of Parkinson's disease (PD) in Hungary, and to analyze their associations. METHODS: A cross-sectional questionnaire survey was conducted in one neurology university clinic. Clinical characteristics, PD related resource utilizations and productivity loss in the past 12 months were recorded; the Hoehn&Yahr (HY) scale, PDQ-39 and EQ-5D questionnaires were applied. Cost calculation was performed from the societal perspective. RESULTS: 110 patients (34.5% female) were involved with mean age of 63.3 (SD = 11.3) and disease duration of 8.2 (SD = 5.8) years. PDQ-39 summary score was 48.1 (SD = 13.4). The average EQ-5D score was 0.59 (SD = 0.28), and was significantly lower than the population norm in age-groups 45-74. The correlation was significant between EQ-5D and PDQ-39 (-0.47, p = 0.000), the HY scale and EQ-5D (-0.3416, p = 0.0008) and PDQ-39 (0.3419, p = 0.0006) scores. The total mean cost was euro6030.2 (SD = 6163.0)/patient/year (direct medical 35.7%, direct non-medical 29.4%, indirect cost 34.9%). A one year increase in disease duration and 0.1 decrease of the EQ-5D utility score increase the yearly costs by 8 to 10%, and 7.8%, respectively. The effect of the PDQ-39 score on total cost was not significant. CONCLUSIONS: Disease severity and public health importance of PD are clearly demonstrated by the magnitude of QoL loss. PD-related costs are substantial, but are much lower in Hungary than in Western European countries. Disease duration and EQ-5D score are significant proxy of costs

Population Genetic Differences along a Latitudinal Cline between Original and Recently Colonized Habitat in a Butterfly

BACKGROUND: Past and current range or spatial expansions have important consequences on population genetic structure. Habitat-use expansion, i.e. changing habitat associations, may also influence genetic population parameters, but has been less studied. Here we examined the genetic population structure of a Palaeartic woodland butterfly Pararge aegeria (Nymphalidae) which has recently colonized agricultural landscapes in NW-Europe. Butterflies from woodland and agricultural landscapes differ in several phenotypic traits (including morphology, behavior and life history). We investigated whether phenotypic divergence is accompanied by genetic divergence between populations of different landscapes along a 700 km latitudinal gradient. METHODOLOGY/PRINCIPAL FINDINGS: Populations (23) along the latitudinal gradient in both landscape types were analyzed using microsatellite and allozyme markers. A general decrease in genetic diversity with latitude was detected, likely due to post-glacial colonization effects. Contrary to expectations, agricultural landscapes were not less diverse and no significant bottlenecks were detected. Nonetheless, a genetic signature of recent colonization is reflected in the absence of clinal genetic differentiation within the agricultural landscape, significantly lower gene flow between agricultural populations (3.494) than between woodland populations (4.183), and significantly higher genetic differentiation between agricultural (0.050) than woodland (0.034) pairwise comparisons, likely due to multiple founder events. Globally, the genetic data suggest multiple long distance dispersal/colonization events and subsequent high intra- and inter-landscape gene flow in this species. Phosphoglucomutase deviated from other enzymes and microsatellite markers, and hence may be under selection along the latitudinal gradient but not between landscape types. Phenotypic divergence was greater than genetic divergence, indicating directional selection on some flight morphology traits. MAIN CONCLUSIONS/SIGNIFICANCE: Clinal differentiation characterizes the population structure within the original woodland habitat. Genetic signatures of recent habitat expansion remain, notwithstanding high gene flow. After differentiation through drift was excluded, both latitude and landscape were significant factors inducing spatially variable phenotypic variation