Monotonicity for MPFA methods on triangular grids

Flow in a porous medium can be described by a set of non-linear partial differential equations. The pressure variable satisfies a maximum principle, which guarantees that the solution will have no oscillations. A discretisation of the pressure equation should preserve this monotonicity property. Whether a numerical method is monotone will depend both on the medium and on the grid. We study monotonicity of Multi-point Flux Approximation methods on triangular grids. We derive necessary conditions for monotonicity on uniform grids. Further, we study the robustness of the methods on rough grids, and quantify the violations of the maximum principle. These investigations are done for single phase flow, however, they are supported by two-phase simulations.     

Tropospheric ozone chemistry. The impact of cloud chemistry

The effect of clouds and cloud chemistry on tropospheric ozone chemistry is tested out in a two-dimensional channel model covering a latitudinal band from 30 to 60° N. Three different methods describing how clouds affect gaseous species are applied, and the results are compared. The three methods are:

?A first order parameterization scheme for the removal of sulphur and other soluble gases by liquid droplets.

?A parameterization scheme for SO₂, O₃, and H₂O₂ removal is constructed. The scheme is based on the solubility of gases in liquid droplets, cycling times of air masses between clouds and cloud free areas and on the chemical interaction of SO₂ with H₂O₂ and O₃ in the liquid phase.

?Gas-aqueous-phase interactions and aqueous-phase chemical reactions are included in the reaction scheme for a number of components in areas where clouds are present.

In all three methods, a full gas-phase chemistry scheme is used. Particular emphasis is given to the study of how the ozone and hydrogen peroxide levels are affected. Significant changes in the distributions are found when aqueous-phase chemical reactions are included. The result is loss of ozone in the aqueous phase, with pronounced reductions in ozone levels in the middle and lower troposphere. Ozone levels are reduced by 10 to 30% with the largest reductions in the remote middle troposphere, bringing the values in better agreement with observations. Changes in H₂O₂ are harder to predict. Although, in one case study, hydrogen peroxide is produced within the aqueous phase, concentrations are mostly comparable or even lower than in the other cases. Hydrogen peroxide levels are, however, shown to be very pH sensitive. pH values around 5 seem to favour high H₂O₂ levels. High H₂O₂ concentrations may be found particularly in the upper part of the clouds under favourable conditions.     

Braid perthite in nepheline syenite pegmatite, Langesundsfjorden, Oslo Region (Norway)

Three occurrences of braid perthite (lamellae parallel to (110) and ( )) and micro braid perthite (lamellae parallel to ( ) and ( )) from Permian nepheline syenite pegmatites in monzonite (larvikite) of the Oslo Graben are described. All the crystals studied show a zoned arrangement with either alternating mmacro- and microperthitic bands parallel to (010) or with microperthitic cores surrounded by macroperthite and a marginal zone of plagioclase. Both types of perthite are mesoperthitic and composed of maximum microcline and low albite. Chemical analyses suggest that the alkali feldspar is stoichiometric, while precession exposures imply unusual cell parameters in the host K-feldspar phase. The macroperthite seems to have crystallized at the expense of the microperthite. The braided texture of exsolved albite lamellae may be due to some kind of strain causing cracking along the prism and pyramidal planes.     

Cephalopods Burying in Soft Substrata: Agents of Bioturbation?

Abstract. Among the bottom-living cephalopods, those able to dig into soft substrata show special behaviour patterns involving coordinated mantle/funnel, fin, and arm movements. This activity is triggered by light, and in the euphotic zone thus occurs at least once in a 24 h cycle. Effects of burial on the sediments are considered, drawing attention to the likely chemical side effects, especially relating to the mucus released by burying cephalopods. Persistent burrows are produced only by some octopuses. Their burial activities and the sand/mud digging of many squids and cuttlefishes are likely to play a notable role in bioturbation.     

The quantifiable clinothem – types,shapes and geometric relationships in the Plio‐Pleistocene Giant Foresets Formation,Taranaki Basin,New Zealand

The understanding of how clinoforms develop is approached based on shape and dimensions, correlation between geometric parameters, and internal characteristics of clinothems bounded by clinoform surfaces in high‐resolution 2D seismic data from the Giant Foresets Formation, Taranaki Basin, offshore New Zealand. The study subdivides the observed clinothems to identify nine types: 1. Oblique 2. Tangential oblique 3. Tangential oblique chaotic 4. Sigmoidal symmetrical 5. Sigmoidal divergent 6. Sigmoidal chaotic 7. Asymmetrical top‐heavy 8. Asymmetrical bottom‐heavy 9. Complex. Accommodation is a dominant control on the type of clinothem that develops, whereby limited accommodation promotes clinothems with significant shelf‐edge advance and low trajectory angles, while increasing accommodation promotes higher trajectory angles and increased deposition on the shelf. Further variations in shape, slope and deposition are influenced by many factors of which sediment influx appears be a fundamental driver. Sigmoidal clinothems tend to show a strong relationship between their maximum thickness and average thickness, their overall slope and maximum foreset angle, along with a high correlation between average thickness and toe advance. This suggests that they distribute sediment in a manner that may be possible to predict and quantify. The increasing steepness of the foreset slope from bottom‐heavy to symmetrical to top‐heavy clinothems, respectively, is dominantly the result of decreasing sediment influx. The clinothems with the steepest slopes, along with chaotic clinothems, are associated with comparatively large toe advance suggesting a strong link between over‐steepened slopes and/or collapse, and processes promoting sediment deposition along the basin floor. Apart from toe advance, the two types of chaotic clinothems develop differently from each other, and from their assumed parent‐clinothem. Tangential oblique chaotic forms steepen, and shelf‐edge advance is limited, suggesting upper slope collapse. Sigmoidal chaotic clinothems have comparatively higher shelf‐edge advance, lower shelf‐edge trajectories and gentler slopes and profiles, suggesting different processes are responsible for their development and resulting shape.     

A generalized cubic equation of state with application to pure CO<Subscript>2</Subscript> injection in aquifers

A generalized cubic equation of state is given. The Peng-Robinson and the Soave-Redlich-Kwong equations are special cases of this equation. The generalized equation of state is precisely as simple and computationally efficient as these classical equations. Through comparison with the Span-Wagner equation for CO ₂, we obtain an improved density accuracy in predefined temperature-pressure domains. The generalized equation is then verified through two relevant examples of CO ₂ injection and migration. Comparisons are made with other standard cubic EOS in order to show the range of solutions obtained with less accurate EOS.     

Interpretation of well-cell pressures on stretched hexagonal grids in numerical reservoir simulation

Peaceman’s equivalent well-cell radius for 2D Cartesian grids has been generalized to 2D uniform Voronoi grids consisting of stretched hexagons in an isotropic medium. An analytical expression for the equivalent well-cell radius for infinitely fine grids is derived. The derivation is performed by comparison of analytical and numerical solution for boundary value problems with one or two wells. Since the well-cell radius varies slowly with the grid fineness, the found formula can be considered representative for all grid sizes.