Observing the Symmetry of Attractors

We show how the symmetry of attractors of equivariant dynamical systems can be observed by equivariant projections of the phase space. Equivariant projections have long been used, but they can give misleading results if used improperly and have been considered untrustworthy. We find conditions under which an equivariant projection generically shows the correct symmetry of the attractor.Comment: 28 page LaTeX document with 9 ps figures included. Supplementary color figures available at http://odin.math.nau.edu/~jws

About convergence of numerical approximations to homoclinic twist bifurcation points in Z2-symmetric systems in R^4

An algorithm to detect homoclinic twist bifurcation points in Z2 -\ud symmetric autonomous systems of ordinary differential equations in R4\ud along curves of symmetric homoclinic orbits to hyperbolic equilibria has\ud been developed. We show convergence of numerical approximations to homoclinic\ud twist bifurcation points in such systems. A test function is defined\ud on the homoclinic solutions, which has a regular zero in the codimensiontwo\ud bifurcation points. This codimension-two singularity can be continued\ud appending the test function to a three parameter vector field. We demonstrate\ud the use of the test function on several examples of two coupled\ud Josephson junctions

Behavior of a deep hole drilled in ice at Vostok Station

A coring hole (5G) was drilled at Vostok station down to the depth of 2500m using an electro-thermal drilling system. Relationships between ice core, hole diameters, and drill speed are presented. The hole was only partially filled with fluid (of density of 860kg m^) so that ice pressure was not counter-balanced by the fluid column. After one year, diameter us, depth was measured. The hole deformation was found to be significant for depths below 1500m. The hole closure rate is in agreement with the law proposed by PATERSON (Rev. Geophys. Space Phys., 15,47,1977) and extrapolated to Vostok conditions as well as with previous studies from BLINOV and DMITRIEV (Antarktika, 26,95,1987). This information as well as the data from the fluid density properties is used to predict the hole closure for greater depths. Due to some drawbacks in using a high density fluid for thermal drilling operations a technical strategy for drilling toward 3000m is presented

Detecting symmetry breaking bifurcations in the system describing the dynamics of coupled arrays of Joseph junctions

Symmetry breaking and symmetry increasing bifurcations in a system of globally coupled Josephson junctions which possesses Sn symmetry have been investigated by constructing a detective for the group Sn, the permutation group of n elements. In addition, with help of this detective several bifurcations are followed numerically in two parameters.\ud \ud An algorithm to obtain a detective for any finite subgroup of O(n) is given

Implementation of ISO-14000 Standards In Routine Environmental Management of Oil And Gas Fields By Means of GIS And Remote Sensing

Abstract All industrialized countries face the challenge to combine long term, low cost energy supply and continuous reduction of the environmental impact. Therefore the strategic target of the HSE standards is the sustainable and environmentally sound development of the Earth's energy resources. The main goal of our research is the development of a new environmental management methodology supported by software tools for implementation of the ISO-14000 standards in oil and gas operations. On one hand, this methodology has to be generic; on the other hand, the proposed methods of environmental impact assessment must be applicable for each specific situation. We have reinterpreted the ISO environmental monitoring model in terms of remote sensing survey and GIS models. Besides storage of the scalable earth surface and underground information, the methodology and suggested software tools allow for the modelling of the interaction between engineering objects and the environment during full life cycle of oil and gas fields starting from their exploration until their abandonment. The remote sensing methods reviewed in this article, as well as the suggested methodology, can be applied for a wide range of targets in different regions. Some examples are the monitoring of pipelines in the North Sea or Mexican Gulf, control of pipeline security or vegetation degradation in tropical countries, as well as monitoring of oil operations in remote Arctic locations. Introduction Protection of the environment, the health and safety of citizens, and sustainable and economically effective exploitation of domestic natural resources are key issues in many industrially developed countries. The international Health, Safety and Environment (HSE) regulations have been finalized in the ISO-14000 standards. The United Nations Conference on Environment and Sustainable Development (UNCED), as well as the International Expert Meeting on Environmental Practices in Offshore Oil and Gas Activities (Reference Technical Background document, 1997) have emphasized the significance of implementation of the international environmental standards and innovation of environmental monitoring systems in oil and gas operations. However, oilfield oriented database management (or monitoring) systems, currently available on the market, contain mainly (or only) exploration and production (E&amp;P) inventory databases. They do not include any environment, health or safety related parameters or functions. Moreover, in spite of the tremendous progress in information technologies (such as GIS, remote sensing, Internet), they are hardly used either in oilfield environmental management systems or in E&amp;P databases. Objectives In the last few years, there have been numerous cases of largescale environmental damage caused by oil and gas production. They involve contamination of surface water, underground water and marine seawater, agricultural soils, air pollution, etc. In many countries, extensive development of the oil industry has resulted in degradation of other natural resources, including deforestation of the surroundings of exploration and production facilities. Thus, oil and gas exploitation needs to improve on the point of environmental side effects. Unfortunately, there are no broadly available software tools for long-term comprehensive environmental monitoring. Therefore, TNO-NITG has initiated a new project aimed at the development of an Integrated Oil and Gas Environmental Monitoring and Management System (IOGEMMS). </jats:sec

The Application of Computed Tomography Scanning and Nuclear Magnetic Resonance for Rock Typing of Polymineral Clastic Reservoirs

Summary The main objective of this study was to provide rock typing of the producing formation based on high-resolution computed tomography (CT) scanning and nuclear magnetic resonance (NMR) data in combination with routine core analyses results. The target formation is composed of a shallowing up sequence of clastic rocks. Siltstones in its base are gradually replaced by sandstones toward its top. Initially, only sandstones were considered as oil-bearing, while siltstones were considered as water-bearing based on saturation calculation by means of Archie’s equation (Archie 1942) with the same values of cementation and saturation exponent for the whole formation. However, follow-up well tests detected considerable oil inflow also from the base of the reservoir composed of siltstones. Therefore, better rock typing was needed to improve the initial saturation distribution calculation. An applied approach that was based on integrated analysis of rock microstructural characteristics and derived from the NMR and CT techniques and conventional properties used for reserves calculation appeared to be an effective tool for rock typing polymineral clastic reservoirs. Measuring porous network characteristics and conventional properties in the same core plug enables a confident correlation between all measured parameters. Consequently, rock typing of samples based on flow units’ microstructural characteristics derived from NMR and CT scanning has shown a very good consistency with each other. As a result, four rock types were distinguished within a formation, which were previously interpreted as a single rock type. The detailed rock typing of the reservoir allowed more accurate reserves calculation and involvement of additional intervals into the production. Besides porous media characterization, CT scanning proved to be an effective tool for detecting minerals, such as pyrite and carbonates, characterizing depositional environments. Increasing content of pyrite in siltstones, detected by CT scanning and X-ray fluorescence spectroscopy, indicates deeper and less oxic conditions, while the presence of carbonate shell debris indicates shallower, more oxic depositional settings. The NMR test results show that the NMR signal distribution is affected by both pore size distribution and mineralogical composition. An increase of pyrite content caused shifting of the T2 distribution to the lower values, while carbonate inclusions caused shifting of the T2 distribution to higher values relative to the other samples not affected by these mineral inclusions. Because NMR distribution is affected by multiple factors, applying Т2cutoff values alone for rock typing can lead to ambiguous interpretation. Applying CT scanning next to NMR data increases the reliability of rock typing. The proposed laboratory workflow, including a combination of nonhazardous and nondestructive tests, allowed reliable differentiation of the rock samples based on multiple parameters that were interpreted in relationship with each other. Because the designed laboratory test workflow enabled both justified separation of the samples by rock type and determination of parameters used for reserves calculation, it can be recommended for further application in polymineral clastic reservoirs. Because the proposed techniques are nondestructive, the same samples can be applied for multiple tests including special core analysis (or SCAL).</jats:p