Exponential time integrators for stochastic partial differential equations in 3D reservoir simulation

The transport of chemically reactive solutes (e.g. surfactants, CO₂ or dissolved minerals) is of fundamental importance to a wide range of applications in oil and gas reservoirs such as enhanced oil recovery and mineral scale formation. In this work, we investigate exponential time integrators, in conjunction with an upwind weighted finite volume discretisation in space, for the efficient and accurate simulation of advection–dispersion processes including non-linear chemical reactions in highly heterogeneous 3D oil reservoirs. We model sub-grid fluctuations in transport velocities and uncertainty in the reaction term by writing the advection–dispersion–reaction equation as a stochastic partial differential equation with multiplicative noise. The exponential integrators are based on the variation of constants solution and solve the linear system exactly. While this is at the expense of computing the exponential of the stiff matrix representing the finite volume discretisation, the use of real Léja point or the Krylov subspace technique to approximate the exponential makes these methods competitive compared to standard finite difference-based time integrators. For the deterministic system, we investigate two exponential time integrators, the second-order accurate exponential Euler midpoint (EEM) scheme and exponential time differencing of order one (ETD1). All our numerical examples demonstrate that our methods can compete in terms of efficiency and accuracy compared with standard first-order semi-implicit time integrators when solving (stochastic) partial differential equations that model mixing and chemical reactions in 3D heterogeneous porous media. Our results suggest that exponential time integrators such as the ETD1 and EEM schemes could be applied to typical 3D reservoir models comprising tens to hundreds of thousands unknowns.     

Estimated Green’s function extracted from superconducting gravimeters and seismometers

Estimated Green’s function (EGF) between stations has been extracted from ambient seismic noise, direct surface wave and coda waves. It is also confirmed by laboratory experiments on ultrasonics and theoretical derivations assuming diffusive wave field, equi-partition of modes or random sources on an enclosed surface. This method provides a new approach to study the crust and mantle structure at regional scale, continental scale and global scale. Following the achievements with seismometer records, the reco...     

The burial efficiency of organic carbon in the sediments of Lake Kinneret

Even though lake sediments constitute a significant long-term carbon sink, studies on the regulation of carbon burial in lakes sediments have, to date, been surprisingly few. We investigated to what degree the organic carbon (OC) being deposited onto the bottom of Lake Kinneret (Israel) is buried in the sediment at four different sites with varying degrees of oxygenation and varying supply of allochthonous particles from the River Jordan. For estimation of the OC burial efficiency (OC BE), i.e., the ratio between buried and deposited OC, we calculated OC burial from dated sediment cores, and calculated OC deposition using three different approaches. Calculation of OC deposition from sediment trap-derived mass deposition rates multiplied with the OC content of surface sediment yielded OC BE values that were at odds with published values for sediments dominated by autochthonous OC sources. Calculation via sediment trap data on organic matter flux collected within the Lake Kinneret monitoring program, as well as calculation of OC deposition as the sum of OC burial plus OC mineralization, returned fairly congruent estimates of OC BE (range 10–41%), but only if the sediment trap data were corrected for the proportion of resuspended particles in the traps. Differences in OC BE between sites were small, indicating that OC source (common to all sites) was a more important regulator of OC BE in Lake Kinneret than oxygen exposure or mineral particles characteristics.     

A seismological study of shallow weak micro-earthquakes in the urban area of Hamburg city,Germany, and its possible relation to salt dissolution

In the night from 8/9 April 2009, shortly after midnight on Maundy Thursday before Easter, several people in Gross Flottbek, Hamburg, felt unusual strong ground shocks so that some of them left their houses in fear of earthquake shaking. Police and fire brigade received phone calls of worried residents. A few days later, Internet pages were published where people reported their observations. On 21 April 2009 at about 8 p.m. local time, a second ground-shaking event was felt. Damage to buildings or infrastructure did not occur to our knowledge. The Institute of Geophysics, University of Hamburg, installed from 22 April to 17 May 2009 three temporal seismic stations in the epicentral area. Seismological data from two nearby stations at the Deutsches Elektronen-Synchrotron at 1 km and the Geophysical Institute at 7 km distance were collected and integrated to the temporal network. The events occurred above the roof of the shallow Othmarschen Langenfelde salt diapir, in an area known for active sinkhole formation and previous historic ground-shaking events. The analysis of the seismological data shows that three shallow micro-earthquakes occurred from 8 to 21 April at a depth of about 100 m, the largest one with a moment magnitude of about M _W 0.6. Depth location of such shallow events is difficult with standard methods and is here constrained by waveform modeling of surface waves. Earthquakes occurring in soft sediments within the uppermost 100 m are a rare phenomena and cannot be explained by standard models. Rupture process in soft sediments differs from those on faults in more competent rock. We discuss the rupture and source mechanism of the events in the context of previous historic shocks and existing sinkhole and deformation data. Although the event was weak, the rupture duration of 0.3 s was unusual long. Three possible models for the generation of repeated ground-shaking events in Gross Flottbek are developed and discussed, implying quit different hazards for subsidence, ground motion, and sinkhole formation. Our favored model postulates that roof failure occurs in an existing soil cavity beneath the epicenter at a depth of about 100 m. Other models bearing a smaller geo-hazard cannot be disproved with the data available, but future geophysical experiments may be planned to resolve this question.     

Nuclear and incommensurate magnetic structure of NaFeGe2O6 between 5?K and 298?K and new data on multiferroic NaFeSi2O6

The compound NaFeGe₂O₆ was grown synthetically as polycrystalline powder and as large single crystals suitable for X-ray and neutron-diffraction experiments to clarify the low temperature evolution of secondary structural parameters and to determine the low temperature magnetic spins structure. NaFeGe₂O₆ is isotypic to the clinopyroxene-type compound aegirine and adopts the typical HT-C2/c clinopyroxene structure down to 2.5?K. The Na-bearing M2 polyhedra were identified to show the largest volume expansion between 2.5?K and room temperature, while the GeO₄ tetrahedra behave as stiff units. Magnetic susceptibility measurements show a broad maximum around 33?K, which marks the onset of low-dimensional magnetic ordering. Below 12?K NaFeGe₂O₆ transforms to an incommensurately modulated magnetic spin state, with k?=?[0.323, 1.0, 0.080] and a helical order of spins within the M1-chains of FeO₆ octahedra. This is determined by neutron-diffraction experiments on a single crystal. Comparison of NaFeGe₂O₆ with NaFeSi₂O₆ is given and it is shown that the magnetic ordering in the latter compound, aegirine, also is complex and is best described by two different spin states, a commensurate one with C2??/c?? symmetry and an incommensurate one, best being described by a spin density wave, oriented within the (1 0 1) plane.     

白岩脚煤矿环境水文地质问题及防治对策

对白岩脚煤矿含水层特征、地下水赋存、转化与排泄等水文地质条件分析的基础上,对区内水土流失、石漠化、内涝、地下水污染等原生的和煤炭开采可能引发的环境水文地质问题进行梳理,并提出对策建议,为矿井设计和矿山环境保护与恢复治理提供参考。     

Mass fluxes of xenobiotics below cities: challenges in urban hydrogeology

Urban areas are the focus of major ecological, social and economical activity. They are thus also prime locations of increasing conflict with regard to water use and water protection. As a direct and/or indirect consequence of urban land use and human activity, urban water systems are frequently polluted with organic contaminants including waste water-born xenobiotics such as pharmaceuticals, personal care products (collectively known as PPCPs) and endocrine-active substances. This study reviews new integrated methodologies including flux calculations as well as chemical investigations for determining the impact of human activities on urban water systems and on processes within the urban watershed. The use of indicator substances, representing different contaminant sources and pathways, integral pumping tests and mass balance approaches are suitable alternatives within these environments. The issues are explored using contaminant mass balance examples from Halle/Saale and Leipzig, Germany.     

Influence of the atmospheric conditions on PM<Subscript>10</Subscript> concentrations in Poznań, Poland

This study investigates atmospheric conditions’ influence on the mean and extreme characteristics of PM₁₀ concentrations in Poznań during the period 2006–2013. A correlation analysis was carried out to identify the most important meteorological variables influencing the seasonal dynamics of PM₁₀ concentrations. The highest absolute correlation values were obtained for planetary boundary layer height (r = ?0.57), thermal (daily minimum air temperature: r = ?0.51), anemological (average daily wind speed: r = ?0.37), and pluvial (precipitation occurrence: r = ?0.36) conditions, however the highest correlations were observed for temporal autocorrelations (1 day lag: r = 0.70). As regulated by law, extreme events were identified on the basis of daily threshold value i.e. 50 μg m^?3. On average, annually there are approximately 71.3 days anywhere in the city when the threshold value is exceeded, 46.6 % of those occur in winter. Additionally, 83.7 % of these cases have been found to be continuous episodes of a few days, with the longest one persisting for 22 days. The analysis of the macro-scale circulation patterns led to the identification of an easy-to-perceive seasonal relations between atmospheric fields that favour the occurrence of high PM₁₀ concentration, as well as synoptic situations contributing to the rapid air quality improvement. The highest PM₁₀ concentrations are a clear reaction to a decrease in air temperature by over 3 °C, with simultaneous lowering of PBL height, mean wind speed (by around 1 m s^?1) and changing dominant wind directions from western to eastern sectors. In most cases, such a situation is related to the expansion of a high pressure system over eastern Europe and weakening of the Icelandic Low. Usually, air quality conditions improve along with an intensification of westerlies associated with the occurrence of low pressure systems over western and central Europe. Opposite relations are distinguishable in summer, when air quality deterioration is related to the inflow of tropical air masses originating over the Sahara desert.