Multiscale descriptions of density-driven flow instabilities in porous media

Les instabilités engendrées par des gradients de densité interviennent dans une variété d'écoulements. Un exemple est celui de la séquestration géologique du dioxyde de carbone en milieux poreux. Ce gaz est injecté à haute pression dans des aquifères salines et profondes. La différence de densité entre la saumure saturée en CO2 dissous et la saumure environnante induit des courants favorables qui le transportent vers les couches géologiques profondes. Les gradients de densité peuvent aussi être la cause du transport indésirable de matières toxiques, ce qui peut éventuellement conduire à la pollution des sols et des eaux. La gamme d'échelles intervenant dans ce type de phénomènes est très large. Elle s'étend de l'échelle poreuse où les phénomènes de croissance des instabilités s'opèrent, jusqu'à l'échelle des aquifères à laquelle interviennent les phénomènes à temps long. Une reproduction fiable de la physique par la simulation numérique demeure donc un défi en raison du caractère multi-échelles aussi bien au niveau spatial et temporel de ces phénomènes. Il requiert donc le développement d'algorithmes performants et l'utilisation d'outils de calculs modernes. En conjugaison avec les méthodes de résolution itératives, les méthodes multi-échelles permettent de résoudre les grands systèmes d'équations algébriques de manière efficace. Ces méthodes ont été introduites comme méthodes d'upscaling et de downscaling pour la simulation d'écoulements en milieux poreux afin de traiter de fortes hétérogénéités du champ de perméabilité. Le principe repose sur l'utilisation parallèle de deux maillages, le premier est choisi en fonction de la résolution du champ de perméabilité (grille fine), alors que le second (grille grossière) est utilisé pour approximer le problème fin à moindre coût. La qualité de la solution multi-échelles peut être améliorée de manière itérative pour empêcher des erreurs trop importantes si le champ de perméabilité est complexe. Les méthodes adaptatives qui restreignent les procédures de mise à jour aux régions à forts gradients permettent de limiter les coûts de calculs additionnels. Dans le cas d'instabilités induites par des gradients de densité, l'échelle des phénomènes varie au cours du temps. En conséquence, des méthodes multi-échelles adaptatives sont requises pour tenir compte de cette dynamique. L'objectif de cette thèse est de développer des algorithmes multi-échelles adaptatifs et efficaces pour la simulation des instabilités induites par des gradients de densité. Pour cela, nous nous basons sur la méthode des volumes finis multi-échelles (MsFV) qui offre l'avantage de résoudre les phénomènes de transport tout en conservant la masse de manière exacte. Dans la première partie, nous pouvons démontrer que les approximations de la méthode MsFV engendrent des phénomènes de digitation non-physiques dont la suppression requiert des opérations de correction itératives. Les coûts de calculs additionnels de ces opérations peuvent toutefois être compensés par des méthodes adaptatives. Nous proposons aussi l'utilisation de la méthode MsFV comme méthode de downscaling: la grille grossière étant utilisée dans les zones où l'écoulement est relativement homogène alors que la grille plus fine est utilisée pour résoudre les forts gradients. Dans la seconde partie, la méthode multi-échelle est étendue à un nombre arbitraire de niveaux. Nous prouvons que la méthode généralisée est performante pour la résolution de grands systèmes d'équations algébriques. Dans la dernière partie, nous focalisons notre étude sur les échelles qui déterminent l'évolution des instabilités engendrées par des gradients de densité. L'identification de la structure locale ainsi que globale de l'écoulement permet de procéder à un upscaling des instabilités à temps long alors que les structures à petite échelle sont conservées lors du déclenchement de l'instabilité. Les résultats présentés dans ce travail permettent d'étendre les connaissances des méthodes MsFV et offrent des formulations multi-échelles efficaces pour la simulation des instabilités engendrées par des gradients de densité. - Density-driven instabilities in porous media are of interest for a wide range of applications, for instance, for geological sequestration of CO2, during which CO2 is injected at high pressure into deep saline aquifers. Due to the density difference between the C02-saturated brine and the surrounding brine, a downward migration of CO2 into deeper regions, where the risk of leakage is reduced, takes place. Similarly, undesired spontaneous mobilization of potentially hazardous substances that might endanger groundwater quality can be triggered by density differences. Over the last years, these effects have been investigated with the help of numerical groundwater models. Major challenges in simulating density-driven instabilities arise from the different scales of interest involved, i.e., the scale at which instabilities are triggered and the aquifer scale over which long-term processes take place. An accurate numerical reproduction is possible, only if the finest scale is captured. For large aquifers, this leads to problems with a large number of unknowns. Advanced numerical methods are required to efficiently solve these problems with today's available computational resources. Beside efficient iterative solvers, multiscale methods are available to solve large numerical systems. Originally, multiscale methods have been developed as upscaling-downscaling techniques to resolve strong permeability contrasts. In this case, two static grids are used: one is chosen with respect to the resolution of the permeability field (fine grid); the other (coarse grid) is used to approximate the fine-scale problem at low computational costs. The quality of the multiscale solution can be iteratively improved to avoid large errors in case of complex permeability structures. Adaptive formulations, which restrict the iterative update to domains with large gradients, enable limiting the additional computational costs of the iterations. In case of density-driven instabilities, additional spatial scales appear which change with time. Flexible adaptive methods are required to account for these emerging dynamic scales. The objective of this work is to develop an adaptive multiscale formulation for the efficient and accurate simulation of density-driven instabilities. We consider the Multiscale Finite-Volume (MsFV) method, which is well suited for simulations including the solution of transport problems as it guarantees a conservative velocity field. In the first part of this thesis, we investigate the applicability of the standard MsFV method to density- driven flow problems. We demonstrate that approximations in MsFV may trigger unphysical fingers and iterative corrections are necessary. Adaptive formulations (e.g., limiting a refined solution to domains with large concentration gradients where fingers form) can be used to balance the extra costs. We also propose to use the MsFV method as downscaling technique: the coarse discretization is used in areas without significant change in the flow field whereas the problem is refined in the zones of interest. This enables accounting for the dynamic change in scales of density-driven instabilities. In the second part of the thesis the MsFV algorithm, which originally employs one coarse level, is extended to an arbitrary number of coarse levels. We prove that this keeps the MsFV method efficient for problems with a large number of unknowns. In the last part of this thesis, we focus on the scales that control the evolution of density fingers. The identification of local and global flow patterns allows a coarse description at late times while conserving fine-scale details during onset stage. Results presented in this work advance the understanding of the Multiscale Finite-Volume method and offer efficient dynamic multiscale formulations to simulate density-driven instabilities. - Les nappes phréatiques caractérisées par des structures poreuses et des fractures très perméables représentent un intérêt particulier pour les hydrogéologues et ingénieurs environnementaux. Dans ces milieux, une large variété d'écoulements peut être observée. Les plus communs sont le transport de contaminants par les eaux souterraines, le transport réactif ou l'écoulement simultané de plusieurs phases non miscibles, comme le pétrole et l'eau. L'échelle qui caractérise ces écoulements est définie par l'interaction de l'hétérogénéité géologique et des processus physiques. Un fluide au repos dans l'espace interstitiel d'un milieu poreux peut être déstabilisé par des gradients de densité. Ils peuvent être induits par des changements locaux de température ou par dissolution d'un composé chimique. Les instabilités engendrées par des gradients de densité revêtent un intérêt particulier puisque qu'elles peuvent éventuellement compromettre la qualité des eaux. Un exemple frappant est la salinisation de l'eau douce dans les nappes phréatiques par pénétration d'eau salée plus dense dans les régions profondes. Dans le cas des écoulements gouvernés par les gradients de densité, les échelles caractéristiques de l'écoulement s'étendent de l'échelle poreuse où les phénomènes de croissance des instabilités s'opèrent, jusqu'à l'échelle des aquifères sur laquelle interviennent les phénomènes à temps long. Etant donné que les investigations in-situ sont pratiquement impossibles, les modèles numériques sont utilisés pour prédire et évaluer les risques liés aux instabilités engendrées par les gradients de densité. Une description correcte de ces phénomènes repose sur la description de toutes les échelles de l'écoulement dont la gamme peut s'étendre sur huit à dix ordres de grandeur dans le cas de grands aquifères. Il en résulte des problèmes numériques de grande taille qui sont très couteux à résoudre. Des schémas numériques sophistiqués sont donc nécessaires pour effectuer des simulations précises d'instabilités hydro-dynamiques à grande échelle. Dans ce travail, nous présentons différentes méthodes numériques qui permettent de simuler efficacement et avec précision les instabilités dues aux gradients de densité. Ces nouvelles méthodes sont basées sur les volumes finis multi-échelles. L'idée est de projeter le problème original à une échelle plus grande où il est moins coûteux à résoudre puis de relever la solution grossière vers l'échelle de départ. Cette technique est particulièrement adaptée pour résoudre des problèmes où une large gamme d'échelle intervient et évolue de manière spatio-temporelle. Ceci permet de réduire les coûts de calculs en limitant la description détaillée du problème aux régions qui contiennent un front de concentration mobile. Les aboutissements sont illustrés par la simulation de phénomènes tels que l'intrusion d'eau salée ou la séquestration de dioxyde de carbone.

Static structure and dynamics of the liquid Li-Na and Li-Mg alloys

We present calculations for the static structure and ordering properties of two lithium-based s-p bonded liquid alloys, Li-Na and Li-Mg. Our theoretical approach is based on the neutral pseudoatom method to derive the interatomic pair potentials, and on the modified-hypernetted-chain theory of liquids to obtain the liquid static structure, leading to a whole combination that is free of adjustable parameters. The study is complemented by performing molecular dynamics simulations which, besides checking the theoretical static structural results, also allow a calculation of some dynamical properties. The obtained results are compared with the available experimental data.

Static and dynamic structure of liquid metals: Role of the different parts of the interaction potential

The influence of different parts of the interaction potential on the microscopic behavior of simple liquid metals is investigated by molecular dynamics simulation. The role of the soft-core repulsive, short-range attractive, and long-range oscillatory forces on the properties of liquid lithium close to the triple point is analyzed by comparing the results from simulations of identical systems but truncating the potential at different distances. Special attention is paid to dynamic collective properties such as the dynamic structure factors, transverse current correlation functions, and transport coefficients. It is observed that, in general, the effects of the short-range attractive forces are important. On the contrary, the influence of the oscillatory long-range interactions is considerably less, being the most pronounced for the dynamic structure factor at long wavelengths. The results of this work suggest that the influence of the attractive forces becomes less significant when temperature and density increase.

FERTILIZER RECOMMENDATION SYSTEM FOR MELON BASED ON NUTRITIONAL BALANCE

Melon is one of the most demanding cucurbits regarding fertilization, requiring knowledge of soils, crop nutritional requirements, time of application, and nutrient use efficiency for proper fertilization. Developing support systems for decision-making for fertilization that considers these variables in nutrient requirement and supply is necessary. The objective of this study was parameterization of a fertilizer recommendation system for melon (Ferticalc-melon) based on nutritional balance. To estimate fertilizer recommendation, the system considers the requirement subsystem (REQ), which includes the demand for nutrients by the plant, and the supply subsystem (SUP), which corresponds to the supply of nutrients through the soil and irrigation water. After determining the REQtotal and SUPtotal, the system calculates the nutrient balances for N, P, K, Ca, Mg, and S, recommending fertilizer application if the balance is negative (SUP < REQ), but not if the balance is positive or zero (SUP ≥ REQ). Simulations were made for different melon types (Yellow, Cantaloupe, Galia and Piel-de-sapo), with expected yield of 45 t ha-1. The system estimated that Galia type was the least demanding in P, while Piel-de-sapo was the most demanding. Cantaloupe was the least demanding for N and Ca, while the Yellow type required less K, Mg, and S. As compared to other fertilizer recommendation methods adopted in Brazil, the Ferticalc system was more dynamic and flexible. Although the system has shown satisfactory results, it needs to be evaluated under field conditions to improve its recommendations.

Striking a Balance, Presentation to the Justice System Appropriations Subcommittee, February 2011

This presentation covers the rise in prison and cbc populations while at the same time seeing a decrease in appropriations. Staffing has not kept up with growth of the corrections population either.

Water Balance Components in Covered and Uncovered Soil Growing Irrigated Muskmelon

ABSTRACT Knowledge of the terms (or processes) of the soil water balance equation or simply the components of the soil water balance over the cycle of an agricultural crop is essential for soil and water management. Thus, the aim of this study was to analyze these components in a Cambissolo Háplico (Haplocambids) growing muskmelon (Cucumis melo L.) under drip irrigation, with covered and uncovered soil, in the municipality of Baraúna, State of Rio Grande do Norte, Brazil (05º 04’ 48” S, 37º 37’ 00” W). Muskmelon, variety AF-646, was cultivated in a flat experimental area (20 × 50 m). The crop was spaced at 2.00 m between rows and 0.35 m between plants, in a total of ten 50-m-long plant rows. At points corresponding to ⅓ and ⅔ of each plant row, four tensiometers (at a distance of 0.1 m from each other) were set up at the depths of 0.1, 0.2, 0.3, and 0.4 m, adjacent to the irrigation line (0.1 m from the plant row), between two selected plants. Five random plant rows were mulched using dry leaves of banana (Musa sp.) along the drip line, forming a 0.5-m-wide strip, which covered an area of 25 m2 per of plant row with covered soil. In the other five rows, there was no covering. Thus, the experiment consisted of two treatments, with 10 replicates, in four phenological stages: initial (7-22 DAS - days after sowing), growing (22-40 DAS), fruiting (40-58 DAS) and maturation (58-70 DAS). Rainfall was measured with a rain gauge and water storage was estimated by the trapezoidal method, based on tensiometer readings and soil water retention curves. For soil water flux densities at 0.3 m, the tensiometers at the depths of 0.2, 0.3, and 0.4 m were considered; the tensiometer at 0.3 m was used to estimate soil water content from the soil water retention curve at this depth, and the other two to calculate the total potential gradient. Flux densities were calculated through use of the Darcy-Buckingham equation, with hydraulic conductivity determined by the instantaneous profile method. Crop actual evapotranspiration was calculated as the unknown of the soil water balance equation. The soil water balance method is effective in estimating the actual evapotranspiration of irrigated muskmelon; there was no significant effect of soil coverage on capillary rise, internal drainage, crop actual evapotranspiration, and muskmelon yield compared with the uncovered soil; the transport of water caused by evaporation in the uncovered soil was controlled by the break in capillarity at the soil-atmosphere interface, which caused similar water dynamics for both management practices applied.

Estimate of Groundwater Recharge Based on Water Balance in The Unsaturated Soil Zone

ABSTRACT Groundwater management depends on the knowledge on recharge rates and water fluxes within aquifers. The recharge is one of the water cycle components most difficult to estimate. As a result, despite the chosen method, the estimates are subject to uncertainties that can be identified by means of comparison with other approaches. In this study, groundwater recharge estimates based on the water balance in the unsaturated zone is assessed. Firstly, the approach is evaluated by comparing the results with those of another method. Then, the estimates are used as inputs in a transient groundwater flow model in order to assess how the water table would respond to the obtained recharges rates compared to measured levels. The results suggest a good performance of the adopted approach and, despite some inherent limitations, it has advantages over other methods since the data required are easier to obtain.

Classical predictive electrodynamics of two charges with radiation: Energy and 3. momentum balance and scattering crossections-II

We deal with a classical predictive mechanical system of two spinless charges where radiation is considered and there are no external fields. The terms (2,2)Paa of the expansion in the charges of the HamiltonJacobi momenta are calculated. Using these, together with known previous results, we can obtain the paa up to the fourth order. Then we have calculated the radiated energy and the 3-momentum in a scattering process as functions of the impact parameter and the incident energy for the former and 3-momentum for the latter. Scattering cross-sections are also calculated. Good agreement with well known results, including those of quantum electrodynamics, has been found.

Antagonistes de l'angiotensine II et cancer: un bilan rassurant [Angiotensin II receptor blockers (ARBs) and cancer: a reassuring balance].

The effects of drugs on new cancer and cancer-related death are a major concern. Recently, a meta-analysis raised the possibility that ARBs might have an adverse impact in this respect. This point of view was highly debated until the publication of two other meta-analyses which did not demonstrate any increased risk of new cancer occurrence as well as of cancer related-death with the use of ARBs in patients with hypertension, heart failure and/or nephropathy. This illustrates that the results of meta-analyses should be interpreted cautiously and critically in order to avoid biased conclusions. Overall the bulk of evidence today indicates that ARBs are not associated with an increased cancer risk.

Intestinal and hepatic nitrogen balance in the rat after the administration of an oral protein load

The fate of a small oral dose of protein given to overnight-starved rats was studied. After 3 h, 62 per cent of the protein amino acids had been absorbed. Most of the absorbed N went into the bloodstream through the portal in the form of amino acids, but urea and ammonia were also present. About one-quarter of all absorbed N was carried as lymph amino acids. The liver was able to take all portal free ammonia and a large proportion of portal amino acids, releasing urea. The hepatic N balance was negative, indicating active proteolysis and net loss of liver protein.

Balance del siglo XIX: la medicina

Amb motiu del Quart Congrés d'Història de la Medicina Catalana, es publica aquest recull d'articles del Doctor Robert, aparescuts a La Vanguardia a partir del 1901 i que aporten un testimoni directe d'un moment àlgid de la medicina catalana. Els recopil·ladors, en Josep M. Calbet i en Jacint Corbella, pretenen també destacar la implicació política d'aquest personatge tan rellevant.

Energy balance, physical activity, and thermogenic effect of feeding in premature infants.

In order to assess the contribution of the thermogenic effect of feeding and muscular activity to total energy expenditure, nine premature infants were studied for 2 consecutive days during which time repeated measurements of energy expenditure by indirect calorimetry were performed throughout the day, combined with a visual activity score based on body movement. The infants were growing at 16.6 +/- 4.0 g/kg/day (mean +/- SD) and received 110 +/- 8 kcal/kg/day metabolizable energy (milk formula) and 522 +/- 40 mgN/kg/day. Their total energy expenditure was 68 +/- 4 kcal/kg/day indicating that 41 +/- 7 kcal/kg/day was retained for growth. Based on the combination of energy + N balances it was estimated that 80% of the weight gain was fat-free tissue and 20% was fat tissue. The rate of energy expenditure measured minute-by-minute was significantly and linearly correlated with the activity score in both the premeal (r = 0.75;p less than 0.001) and the postmeal periods (r = 0.74; p less than 0.001) with no difference in the regression slope, but with a significant difference in intercept. In preset feeding schedules the latter allowed an estimation of the thermogenic effect without the confounding effect of activity. This was found to be 3.1 +/- 1.8% when expressed as a percentage of metabolizable energy intake. However when the "classical" approach was used as a comparison (integration of extra energy expenditure induced by the meal), the thermogenic effect was found to be greater, i.e. 9.5 +/- 3.8% of the meal's metabolizable energy, due to the superimposed effect of physical activity in the postprandial state.(ABSTRACT TRUNCATED AT 250 WORDS)