Instability of Buckley-Leverett flow in a heterogeneous medium

We study the simultaneous one-dimensional flow of water and oil in a heterogeneous medium modelled by the Buckley-Leverett equation. It is shown both by analytical solutions and by numerical experiments that this hyperbolic model is unstable in the following sense: Perturbations in physical parameters in a tiny region of the reservoir may lead to a totally different picture of the flow. This means that simulation results obtained by solving the hyperbolic Buckley-Leverett equation may be unreliable.Symbols and Notation f fractional flow function varying withs andx - value off outsideI - value off insideI - local approximation off around¯x - f ^–,f ⁺ values of - f _j ⁿ value off atS _j ⁿ andx _j - g acceleration due to gravity [ms^–2] - I interval containing a low permeable rock - k dimensionless absolute permeability - k ^* absolute permeability [m²] - k _c ^* characteristic absolute permeability [m²] - k _ro relative oil permeability - k _rw relative water permeability - L ^* characteristic length [m] - L ₁ the space of absolutely integrable functions - L the space of bounded functions - P _c dimensionless capillary pressure function - P _c ^* capillary pressure function [Pa] - P _c ^* characteristic pressure [Pa] - S similarity solution - S _j ⁿ numerical approximation tos(x_j, t_n) - S ₁, S₂,S ₃ constant values ofs - s water saturation - value ofs at - s ^L left state ofs (wrt. ) - s ^R right state ofs (wrt. ) - s s for a fixed value of in Section 3 - T value oft - t dimensionless time coordinate - t ^* time coordinate [s] - t _c ^* characteristic time [s] - t _n temporal grid point,t _n=n t - v ^* total filtration (Darcy) velocity [ms^–1] - W, , v dimensionless numbers defined by Equations (4), (5) and (6) - x dimensionless spatial coordinate [m] - x ^* spatial coordinate [m] - x _j spatial grid piont,x _j=j x - discontinuity curve in (x, t) space - right limiting value of¯x - left limiting value of¯x - angle between flow direction and horizontal direction - t temporal grid spacing - x spatial grid spacing - length ofI - parameter measuring the capillary effects - argument ofS - _o dimensionless dynamic oil viscosity - _w dimensionless dynamic water viscosity - _c ^* characteristic viscosity [kg m^–1s^–1] - _o ^* dynamic oil viscosity [kg m^–1s^–1] - _w ^* dynamic water viscosity [k gm^–1s^–1] - _o dimensionless density of oil - _w dimensionless density of water - _c ^* characteristic density [kgm^–3] - _o ^* density of oil [kgm^–3] - _w ^* density of water [kgm^–3] - porosity - dimensionless diffusion function varying withs andx - ^* dimensionless function varying with s andx ^* [kg^–1m³s] - _j ⁿ value of atS _j ⁿ andx _j This research has been supported by VISTA, a research cooperation between the Norwegian Academy of Science and Letters and Den norske stats oljeselskap a.s. (Statoil).     

Quantitative aspects of analyzing small molecules – monitoring singly or doubly charged ions? A case study of ximelagatran

Precision, reproducibility and lower limit of quantitation (LLOQ) are important characteristics of a quantitative method. We have investigated these properties for Ximelagatran (Xi), which has a high tendency to form doubly charged ions in electrospray ionization (ESI), by studying the percentage of doubly charged species formed when varying the formic acid (FA) concentration, analyte concentration, amount of organic modifier and flow rate. It was found that the percentage of [Xi + 2H]²⁺ can be controlled to be more than 90% or less than 10% by varying the amount of FA present, and that the change between these values is dramatic. Furthermore, the percentage of [Xi + 2H]²⁺ formed decreases with increased analyte concentration and increased flow rate. No apparent relationship with the amount of organic modifier was found. The results have the implication that, by carefully controlling the selected parameters, the LLOQ, precision and reproducibility can be improved. We have compared the fragmentation of the singly and doubly charged species and concluded that the [Xi + 2H]²⁺ ion is more inclined to undergo fragmentation than [Xi + H]⁺. As a consequence, unusual instrumental settings had to be used for the experiments. The fragmentation patterns are to a great extent similar, but the doubly charged species is more inclined to generate low‐mass product ions. Copyright © 2010 John Wiley & Sons, Ltd.     

Microdetermination of lead in biological material

Summary Two photometric methods for the microdetermination of lead are described. The first is based on a one-color dithizone procedure and the accuracy is mostly sufficient for analyses of biological material such as urine. A more sensitive and accurate determination can be made with the reagent di--naphthylthiocarbazone.The samples are mineralized with the aid of nitric acid, hydrogen peroxide and potassium chlorate. Urine samples are concentrated through evaporation in vacuum before decomposition.

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Zusammenfassung Es werden zwei photometrische Methoden zur Mikrobestimmung von Blei beschrieben. Die erste beruht auf der Farbreaktion mit Dithizon unter Ausschaltung von dessen Eigenfarbe. Ihre Genauigkeit ist in der Regel für die Untersuchung von biologischem Material (wie etwa Harn) ausreichend. Ein empfindlicheres und genaueres Verfahren kann mit Hilfe von Di--naphthylthiocarbazon durchgeführt werden.Das Untersuchungsmaterial wird mittels Salpetersäure, Wasserstoffperoxyd und Kaliumchlorat mineralisiert. Harn wird vor der Mineralisierung im Vakuum eingedampft.

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Résumé On décrit deux méthodes colorimétriques pour le microdosage du plomb. La première repose sur la réaction colorée avec la dithizone par élimination de sa couleur propre. En général, la précision est suffisante pour la recherche dans les substances biologiques (comme l'urine). Un procédé plus sensible et plus précis peut s'effectuer à l'aide de la di--naphthylthiocarbazone. La prise d'essai est minéralisée au moyen de l'acide azotique, de l'eau oxygénée et du chlorate de potassium. L'urine est évaporisée dans le vide avant la minéralisation.

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With 2 figures.     

Spectroelectrochemical cell for in situ studies of solid oxide fuel cells

Solid oxide fuel cells (SOFCs) are able to produce electricity and heat from hydrogen‐ or carbon‐containing fuels with high efficiencies and are considered important cornerstones for future sustainable energy systems. Performance, activation and degradation processes are crucial parameters to control before the technology can achieve breakthrough. They have been widely studied, predominately by electrochemical testing with subsequent micro‐structural analysis. In order to be able to develop better SOFCs, it is important to understand how the measured electrochemical performance depends on materials and structural properties, preferably at the atomic level. A characterization of these properties under operation is desired. As SOFCs operate at temperatures around 1073 K, this is a challenge. A spectroelectrochemical cell was designed that is able to study SOFCs at operating temperatures and in the presence of relevant gases. Simultaneous spectroscopic and electrochemical evaluation by using X‐ray absorption spectroscopy and electrochemical impedance spectroscopy is possible.     

Robust convergence of multi point flux approximation on rough grids

This paper establishes the convergence of a multi point flux approximation control volume method on rough quadrilateral grids. By rough grids we refer to a family of refined quadrilateral grids where the cells are not required to approach parallelograms in the asymptotic limit. In contrast to previous convergence results for these methods we consider here a version where the flux approximation is derived directly in the physical space, and not on a reference cell. As a consequence, less regular grids are allowed. However, the extra cost is that the symmetry of the method is lost.