The unsteady flow of a weakly compressible fluid in a thin porous layer. I: Two-dimensional theory

We consider the problem of determining the pressure and velocity fields for a weakly compressible fluid flowing in a two-dimensional reservoir in an inhomogeneous, anisotropic porous medium, with vertical side walls and variable upper and lower boundaries, in the presence of vertical wells injecting or extracting fluid. Numerical solution of this problem may be expensive, particularly in the case that the depth scale of the layer h is small compared to the horizontal length scale l. This is a situation which occurs frequently in the application to oil reservoir recovery. Under the assumption that epsilon=h/l<<1, we show that the pressure field varies only in the horizontal direction away from the wells (the outer region). We construct two-term asymptotic expansions in epsilon in both the inner (near the wells) and outer regions and use the asymptotic matching principle to derive analytical expressions for all significant process quantities. This approach, via the method of matched asymptotic expansions, takes advantage of the small aspect ratio of the reservoir, epsilon, at precisely the stage where full numerical computations become stiff, and also reveals the detailed structure of the dynamics of the flow, both in the neighborhood of wells and away from wells.

On the connection between dissipation enhancement in the ocean surface layer and Langmuir circulations

A mechanism for the enhancement of the viscous dissipation rate of turbulent kinetic energy (TKE) in the oceanic boundary layer (OBL) is proposed, based on insights gained from rapid-distortion theory (RDT). In this mechanism, which complements mechanisms purely based on wave breaking, preexisting TKE is amplified and subsequently dissipated by the joint action of a mean Eulerian wind-induced shear current and the Stokes drift of surface waves, the same elements thought to be responsible for the generation of Langmuir circulations. Assuming that the TKE dissipation rate epsilon saturates to its equilibrium value over a time of the order one eddy turnover time of the turbulence, a new scaling expression, dependent on the turbulent Langmuir number, is derived for epsilon. For reasonable values of the input parameters, the new expression predicts an increase of the dissipation rate near the surface by orders of magnitude compared with usual surface-layer scaling estimates, consistent with available OBL data. These results establish on firmer grounds a suspected connection between two central OBL phenomena: dissipation enhancement and Langmuir circulations.

The unsteady flow of a weakly compressible fluid in a thin porous layer II: three-dimensional theory

We consider the problem of determining the pressure and velocity fields for a weakly compressible fluid flowing in a three-dimensional layer, composed of an inhomogeneous, anisotropic porous medium, with vertical side walls and variable upper and lower boundaries, in the presence of vertical wells injecting and/or extracting fluid. Numerical solution of this three-dimensional evolution problem may be expensive, particularly in the case that the depth scale of the layer h is small compared to the horizontal length scale l, a situation which occurs frequently in the application to oil and gas reservoir recovery and which leads to significant stiffness in the numerical problem. Under the assumption that $\epsilon\propto h/l\ll 1$, we show that, to leading order in $\epsilon$, the pressure field varies only in the horizontal directions away from the wells (the outer region). We construct asymptotic expansions in $\epsilon$ in both the inner (near the wells) and outer regions and use the asymptotic matching principle to derive expressions for all significant process quantities. The only computations required are for the solution of non-stiff linear, elliptic, two-dimensional boundary-value, and eigenvalue problems. This approach, via the method of matched asymptotic expansions, takes advantage of the small aspect ratio of the layer, $\epsilon$, at precisely the stage where full numerical computations become stiff, and also reveals the detailed structure of the dynamics of the flow, both in the neighbourhood of wells and away from wells.

The unsteady flow of a weakly compressible fluid in a thin porous layer III: three-dimensional computations

We describe a novel method for determining the pressure and velocity fields for a weakly compressible fluid flowing in a thin three-dimensional layer composed of an inhomogeneous, anisotropic porous medium, with vertical side walls and variable upper and lower boundaries, in the presence of vertical wells injecting and/or extracting fluid. Our approach uses the method of matched asymptotic expansions to derive expressions for all significant process quantities, the computation of which requires only the solution of linear, elliptic, two-dimensional boundary value and eigenvalue problems. In this article, we provide full implementation details and present numerical results demonstrating the efficiency and accuracy of our scheme.

The role of an insulating surface layer on the relaxation time of the ionic redistribution in an electrolytic cell

We analyze the influence of a surface dielectric layer on the transient phenomena related to the ionic redistribution in an electrolytic cell submitted to a step-like external voltage. The adsorption-desorption phenomenon is taken into account in the famework of the Gouy-Chapman approximation, where the ions are assumed dimensionless. In the limit of small amplitude of the applied voltage, where the equations of the problem can be linearized, we obtain an analytical solution for the surface densities of ions, for the electrical potential and for the relaxation time for the transient phenomena. In the general case, when the linearized analysis is no longer valid, the solution of the problem is obtained numerically. The role of the thickness of the dielectric layer on the relaxation time is also discussed.

Co-accumulation of microbial residues and particulate organic matter in the surface layer of a no-till Oxisol under different crops

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Electrochemical kinetic study of surface layer growth on natural pyrite in acid medium

This paper presents electrochemical experiments on natural pyrite that combine potentiostatic and voltammetric techniques. X-ray microanalysis is used as an auxiliary technique. The layer growth on pyrite surface is conducted in a wide range of pH and potential range: 3.4 <= pH <= 5.9 with E = 0.80 V (versus SHE), and 0.80 V <= E <= 1.00 V with pH 4.5 (versus SHE) in acetic acid-acetate buffer. This work is unique for two reasons: (1) phenomenological model about layer growth is applied and mathematical-physic consistence is verified and (2) Meyer's hypotheses of chemical mechanism are used to explain kinetic parameters of the phenomenological model. (c) 2005 Elsevier B.V. All rights reserved.

Dynamics of the cold surface layer of polythermal Storglaciären, Sweden

Polythermal glaciers, i.e. glaciers with a combination of ice at and below the freezing point, are widespread in arctic and subarctic environments. The polythermal structure has major implications for glacier hydrology, ice flow and glacial erosion. However, the interplay of factors governing its spatial and temporal variations such as net mass balance, ice advection and water content in the ice is poorly investigated and as yet not fully understood. This study deals with a thorough investigation of the polythermal regime on Storglaciären, northern Sweden, a small valley glacier with a cold surface layer in the ablation area. Extensive field work was performed including mapping of the cold surface layer using ground-penetrating radar, ice temperature measurements, mass balance and ice velocity measurements. Analyses of these data combined with numerical modelling were used specifically to investigate the spatial and temporal variability of the cold surface layer, the spatial distribution of the water content just below the cold surface layer transition, the effect of radar frequency on the detection of the surface layer, and the sensitivity of the cold surface layer to changes in forcing. A comparison between direct temperature measurements in boreholes and ground-penetrating surveys shows that the radar-inferred cold-temperate transition depth is within ±1 m from the melting point of ice at frequencies above ~300 MHz. At frequencies below ~155 MHz, the accuracy degrades because of reduced scattering efficiency that occurs when the scatterers become much smaller compared to the wavelength. The mapped spatial pattern of the englacial cold-temperate transition boundary is complex. This pattern reflects the observed spatial variation in net loss of ice at the surface by ablation and vertical advection of ice, which is suggested to provide the predominant forcing of the cold surface layer thickness pattern. This is further supported by thermomechanical modeling of the cold surface layer, which indicates high sensitivity of the cold surface layer thickness to changes in vertical advection rates. The water content is the least investigated quantity that is relevant for the thermal regime of glaciers, but also the most difficult to assess. Spatial variability of absolute water content in the temperate ice immediately below the cold surface layer on Storglaciären was determined by combining relative estimates of water content from ground-penetrating radar data with absolute determination from temperature measurements and the thermal boundary condition at the freezing front. These measurements indicate large-scale spatial variability in the water content, which seems to arise from variations in entrapment of water at the firn-ice transition. However, this variability cannot alone explain the spatial pattern in the thermal regime on Storglaciären. Repeated surveys of the cold surface layer show a 22% average thinning of the cold surface layer on Storglaciären between 1989 and 2001. Transient thermomechanical modeling results suggest that the cold surface layer adapts to new equilibrium conditions in only a few decades after a perturbation in the forcing is introduced. An increased winter air temperature since mid-1980s seems to be the cause of the observed thinning of the cold surface layer. Over the last decades, mass balance measurements indicate that the glacier has been close to a steady state. The quasi-steady state situation is also reflected in the vertical advection, which shows no significant changes during the last decades. Increased winter temperatures at the ice surface would result in a slow-down of the formation of cold ice at the base of the cold surface layer and lead to a larger imbalance between net loss of ice at the surface and freezing of temperate ice at the cold-temperate transition.

Surface layer formation in polymer melts and in solutions

In this work the surface layer formation in polymer melts and in polymer solutions have been investigated with the atomic force microscope (AFM). In polymer melts, the formation of an immobile surface layer results in a steric repulsion, which can be measured by the AFM. From former work it is know, that polydimethyl siloxane (PDMS) forms a stable surface layer for molecular weights above 12 kDa. In the present thesis, polyisoprene (PI) was investigated apart from PDMS, by a)measuring the steric surface interactions and b)measuring the surface slip in hydrodynamic experiments. If a polymer flows over a surface, the flow velocity at the surface is larger then zero. If case of a surface layer formation the flow plane changes to the top of the adsorbed layer and the surface slip is reduced to zero. By measuring the surface slip in hydrodynamic experiments, it is therefore possible to determine the presence of a stable surface layer. The results show no stable repulsion for PI and only a small decrease of the surface slip. This indicates that PI does not form a stable surface layer, but is only adsorbed weakly to the surface. Furthermore for 8 kDa PDMS the timescale of the formation of a surface layer was investigated by changing themaximal force the tip applied to the surface. With a repulsive force present, applying a higher force than 15 nN resulted in a destruction of the surface layer, indicated by attractive forces. Reducing the applied force below 15 nN then resulted in an increase of the repulsion to the former state during one minute, thus indicating that a surface layer can be formed within one minute even under the influence of continuous measurements. As a next step, mixtures of two PDMS homopolymers with different chain lengths have been investigated. The aim was to verify theoretical predictions that shorter chains should predominate at the surface due to their smaller loss in conformational entropy. The measurements where done in dependence of the volume fractions of short and long chain PMDS. The results confirmed the short chain dominance for all mixtures with less then 90 vol.% long chain PDMS. Surface layer formation in solution was investigated for superplasticizers which are industrially used as an additive to cement. They change the surface interaction between the cement grains from attractive to repulsive and the freshlymixed cement paste therefore becomes liquid. The aimin this part of the thesis was, to investigate cement particle interactions in a close to real environment. Therefore calcium silicate hydrate phases have been precipitated onto an AFM tip and onto a calcite crystal and the interaction between these surfaces have beenmeasured with and without addition of superplasticizers. The measurements confirmed the change from attraction to repulsion upon addition of superplasticizers. The repulsive steric interaction increased with the length of the sidechain of the superplasticizer, and the dependence of the range of the steric interactions on the sidechain length indicated that the sidechains are in a coiled conformation.

(Table 1) Abundance of radiolarians in the surface layer of bottom sediments from the Peru-Chile trench and shelf

Two radiolarian assemblages are distinguished: an equatorial sub-assemblage of the tropical assemblage in the East Pacific Ocean, which differs somewhat from association of radiolarians in the western part of the ocean, and an assemblage close to transitional one between the tropical and the boreal. The latter is characterized by presence of considerable number of species typical for cold-water regions. Some criteria are presented for distinguishing radiolarian associations in nearshore regions from similar associations in regions of the open ocean.