A multiobjective steepest descent method with applications to optimal well control

Multiobjective optimization deals with mathematical optimization problems where two or more objective functions (cost functions) are to be optimized (maximized or minimized) simultaneously. In most cases of interest, the objective functions are in conflict, i.e., there does not exist a decision (design) vector (vector of optimization variables) at which every objective function takes on its optimal value. The solution of a multiobjective problem is commonly defined as a Pareto front, and any decision vector which maps to a point on the Pareto front is said to be Pareto optimal. We present an original derivation of an analytical expression for the steepest descent direction for multiobjective optimization for the case of two objectives. This leads to an algorithm which can be applied to obtain Pareto optimal points or, equivalently, points on the Pareto front when the problem is the minimization of two conflicting objectives. The method is in effect a generalization of the steepest descent algorithm for minimizing a single objective function. The steepest-descent multiobjective optimization algorithm is applied to obtain optimal well controls for two example problems where the two conflicting objectives are the maximization of the life-cycle (long-term) net-present-value (NPV) and the maximization of the short-term NPV. The results strongly suggest the multiobjective steepest-descent (MOSD) algorithm is more efficient than competing multiobjective optimization algorithms.     

Geodetic observation crucial to sea level monitoring

The relative rate of rise of the sea levels measured by a tide gauge is made of a sea and a land component. The first is usually restricted to the global short-term effect of melting icecaps and expansion of water mass due to global temperature change. The second is often limited to the regional long-term effects of glacial isostatic adjustment (GIA). Sometimes, the regional subsidence, due to compaction and ground water withdrawal, is considered. Here we show as this assumption of regional subsidence fails to represent the relative sea level patterns of Sandy Hook, NJ, and The Battery, NY, as well as of Venezia Punta Della Salute, Venezia II, Trieste and Trieste II. The subsidence of the tide gauge instrument may only be addressed by the precise monitoring of the tide gauge vs. a Global Navigation Satellite System (GNSS) antenna, even if the GNSS tracking is only recent and not yet very accurate. The relative sea level records are much more complicated than what is thought.     

Evaluation of the Reduction in Uncertainty Obtained by Conditioning a 3D Stochastic Channel to Multiwell Pressure Data

A stochastic channel embedded in a background facies is conditioned to data observed at wells. The background facies is a fixed rectangular box. The model parameters consist of geometric parameters that describe the shape, size, and location of the channel, and permeability and porosity in the channel and nonchannel facies. We extend methodology previously developed to condition a stochastic channel to well-test pressure data, and well observations of the channel thickness and the depth of the top of the channel. The main objective of this work is to characterize the reduction in uncertainty in channel model parameters and predicted reservoir performance that can be achieved by conditioning to well-test pressure data at one or more wells. Multiple conditional realizations of the geometric parameters and rock properties are generated to evaluate the uncertainty in model parameters. The ensemble of predictions of reservoir performance generated from the suite of realizations provides a Monte Carlo estimate of the uncertainty in future performance predictions. In addition, we provide some insight on how prior variances, data measurement errors, and sensitivity coefficients interact to determine the reduction in model parameters obtained by conditioning to pressure data and examine the value of active and observation well data in resolving model parameters.     

A Reflection on Mg, Cd, Ca, Li and Si Isotopic Measurements and Related Reference Materials

This contribution aims to report the reflections we had with the scientific community during two international workshops on reference materials for stable isotopes in Davos (2002) and Nice (2003). After evaluating the isotopic homogeneity of some existing reference materials, based on either certificates, literature data or specific inter-laboratory rounds, we confirm these as primary reference materials or propose new ones relative to which stable isotope compositions should be reported. We propose DSM-3 for Mg, NIST SRM 915a for Ca, L-SVEC for Li and NBS28 for Si. Cadmium does not yet have a well identified delta zero material, although three commercial mono-elemental Cd solutions have yielded the same isotopic composition relative to one another. In order to scale the linearity of any mass spectrometer, some secondary reference materials are also proposed: Cambridge-1 solution for Mg, the "Münster-Cd" and JEPPIM Cd solutions for Cd and the "Big Batch" silicate for Si. The team from Nancy propose to prepare a mixed spike solution for Li isotopes. Well-characterised natural samples such as ocean or continental waters, diatoms, sponges, rocks and minerals are needed to validate the entire analytical procedure, particularly to take into account the effect of sample mineralisation and of chemical manipulations for elemental separation prior to analysis.     

Mineralisation of amethyst-bearing geodes in Ametista do Sul (Brazil) from low-temperature sedimentary brines: evidence from monophase liquid inclusions and stable isotopes

Fluid inclusion studies in combination with hydrogen, oxygen and sulphur isotope data provide novel insights into the genesis of giant amethyst-bearing geodes in Early Cretaceous Paraná continental flood basalts at Amestita do Sul, Brazil. Monophase liquid inclusions in colourless quartz, amethyst, calcite, barite and gypsum were analysed by microthermometry after stimulating bubble nucleation using single femtosecond laser pulses. The salinity of the fluid inclusions was determined from ice-melting temperatures and a combination of prograde and retrograde homogenisation temperatures via the density maximum of the aqueous solutions. Four mineralisation stages are distinguished. In stage I, celadonite, chalcedony and pyrite formed under reducing conditions in a thermally stable environment. Low δ³⁴S_V-CDT values of pyrite (?25 to ?32?‰) suggest biogenic sulphate reduction by organotrophic bacteria. During the subsequent stages II (amethyst, goethite and anhydrite), III (early subhedral calcite) and IV (barite, late subhedral calcite and gypsum), the oxidation state of the fluid changed towards more oxidising conditions and microbial sulphate reduction ceased. Three distinct modes of fluid salinities around 5.3, 3.4 and 0.3 wt% NaCl-equivalent characterise the mineralisation stages II, III and IV, respectively. The salinity of the stage I fluid is unknown due to lack of fluid inclusions. Variation in homogenisation temperatures and in δ¹⁸O values of amethyst show evidence of repeated pulses of ascending hydrothermal fluids of up to 80–90 °C infiltrating a basaltic host rock of less than 45 °C. Colourless quartz and amethyst formed at temperatures between 40 and 80 °C, while the different calcite generations and late gypsum precipitated at temperatures below 45 °C. Calculated oxygen isotope composition of the amethyst-precipitating fluid in combination with δD values of amethyst-hosted fluid inclusions (?59 to ?51?‰) show a significant ¹⁸O-shift from the meteoric water line. This ¹⁸O-shift, high salinities of the fluid inclusions with chloride-sulphate composition, and high δ³⁴S values of anhydrite and barite (7.5 to 9.9?‰) suggest that sedimentary brines from deeper parts of the Guaraní aquifer system must have been responsible for the amethyst mineralisation.     

Tektonik und zyklische Sedimentation in der helvetischen Zone der Schweizer Alpen

Zusammenfassung In der helvetischen Kreide scheint es also im ganzen so zu sein, daß die einfachen Rhythmen (Feinschichtung und Kalk-Mergel-Schichtwechsel) klimatisch, d. h. exogen, die Zyklen und Großzyklen tektonisch, d. h. endogen, begründet sind (3).     

Zeitgebundene Erzlagerstätten

Proceeding from the observation that in the Early Paleozoic there is a time-bound, world-wide distributed ore deposit type with scheelite in volcanic-sedimentary series, the question concerning a systematic development of ore deposits connected with an evolution of the earth's crust and mantle is discussed. A schematic model of this development is constructed, which, beginning with a still thin, primeval crust, by way of time-bound stages as for instance greenstone belts and mobile zones, receiving abundant material introduction from juvenile volcanism accompanied with corresponding time-bound ores, leads to the “Assynthic” revolution, giving rise to a crust which is essentially dependent on selfsupport by sedimentary reworking and palingenic magmatism. During the initial “juvenile” period as well as during the palingenic there is significant participation of sedimentary processes, in dependence upon time-bound evolution of the atmosphere and biosphere, for material transport, redeposition and renewed concentration. During the “palingenic” stage the crust is only episodically supplied with mantle material along world-wide volcanic, tectonic lineaments, whereby new ore types, for example the scheelite ores of the Early Paleozoic or the copper-molybdenum ores at the Mesozoic-Cenozoic transition, experience their time-bound formation.