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 Dominique Lecomte Mathematics , 2007, Abstract: We want to give a construction as simple as possible of a Borel subset of a product of two Polish spaces. This introduces the notion of potential Wadge class. Among other things, we study the non-potentially closed sets, by proving Hurewicz-like results. This leads to partial uniformization theorems, on big sets, in the sense of cardinality or Baire category.
 Dominique Lecomte Mathematics , 2010, Abstract: Let $\bf\Gamma$ be a Borel class, or a Wadge class of Borel sets, and $2\leq d\leq\omega$ a cardinal. We study the Borel subsets of ${\mathbb R}^d$ that can be made $\bf\Gamma$ by refining the Polish topology on the real line. These sets are called potentially $\bf\Gamma$. We give a test to recognize potentially $\bf\Gamma$ sets.
 Kent H. C. Oil & Gas Science and Technology , 2006, DOI: 10.2516/ogst:1980014 Abstract: Updated resource estimates of the natural gas potential for the United States using the results of developments through 1978 are now available. The estimated resources include 200 trillion cubic feet of proved reserves and 1,019 trillion cubic feet of potential resources from conventional reservoirs. More than 50% of the proved reserves are located in three principal areas: South Louisiana; Alaska; and the Mid-Continent region of Oklahoma, Kansas and the Texas Panhandle. Approximately 50% of the potential resources are located in four areas: the northern and central Rocky Mountain states, the Mid-Continent region, offshore Alaska, and offshore Louisiana. Projections indicate that these potential sources, including Alaska, can continue to provide through the year 2000 approximately the same amount of gas, on an annual basis, as is currently being produced in the US. Slnce 1968, proved reserves of gas in the lower 48 states have declined. Part of the decline can be attributed to the decline in drilling activity from 1956 through 1972, but location and depth of wells are also important. About 14% of oil wells drilled in the United States in 1978 were drilled as new field wildcats and only 4% of the successful gas wells completed were drilled as new field wildcats. In 1977, 80% of the wells were completed in areas and at depths where only 22% of the natural gas resource potential is believed to exist. Clearly, the emphasis on exploration and drilling must be redirected toward those areas of greater gas resource potential in order to meet future needs. On dispose maintenant d'estimation à jour des ressources potentielles en gaz naturel pour les états-Unis utilisant les résultats des développements en 1978. Les ressources estimées comprennent 200 Tcf (± 5,7 Tm3) de réserves prouvées et 1,019 Tcf (± 29 Tm3) de ressources potentielles pour les réservoirs conventionnels. Plus de 50 % des réserves prouvées se situent dans trois secteurs principaux Louisiane méridionale, Alaska et ta région du Mid-Continent qui groupe l'Oklahoma, le Kansas et l'appendice du Texas ditPanhandle . A peu près 50 % des ressources potentielles se trouvent dans quatre zones : les Etats du nord et du centre des Rocheuses, la région du Mid-Continent, le plateau continental au large de l'Alaska et celui de la Louisiane. Les prévisions indiquent que ces sources potentielles, Alaska inclus, pourraient continuer à fournir une quantité annuelle de l'ordre de celle qui est actuellement produite aux états-Unis, et cela jusque vers l'an 2000. Depuis 1968, les réserves prouvées ont diminué dans les
 Mathematics , 2013, DOI: 10.1017/S0960129513000248 Abstract: We prove some results on the Wadge order on the space of sets of natural numbers endowed with Scott topology, and more generally, on omega-continuous domains. Using alternating decreasing chains we characterize the property of Wadge hardness for the classes of the Hausdorff difference hierarchy (iterated differences of open sets). A similar characterization holds for Wadge one-to-one and finite-to-one completeness. We consider the same questions for the effectivization of the Wadge relation. We also show that for the space of sets of natural numbers endowed with the Scott topology, in each class of the Hausdorff difference hierarchy there are two strictly increasing chains of Wadge degrees of sets properly in that class. The length of these chains is the rank of the considered class, and each element in one chain is incomparable with all the elements in the other chain.
 Oil & Gas Science and Technology , 2006, DOI: 10.2516/ogst:1988017 Abstract: Les procédés rencontrés dans la valorisation des résidus et des huiles lourdes font appel à des équipements dont le dimensionnement optimal exige la connaissance précise des propriétés rhéologiques de la phase hydrocarbonée impliquée et ce, dans un large domaine de température et de pression. En conséquence, le Laboratoire de Thermodynamique du Centre Réacteurs et Processus de l'école Nationale Supérieure des Mines (ENSM) de Paris s'est attaché au développement d'un viscosimètre approprié à ces mesures. Il est basé sur la détermination du couple résistant provoqué par le fluide à étudier, cisaillé entre deux cylindres coaxiaux en rotation relative. Le domaine de viscosité balayé s'étend de 10 à 40 000 cP, les température et pression maximales d'utilisation étant respectivement de 500°C et 30 MPa. La qualité des résultats fournis par cet appareillage a été testée, à des températures et dilution variables, sur quelques coupes lourdes issues des bruts Safaniya et Boscan après désasphaltage ou hydroviscoréduction. On obtient ainsi des valeurs fiables, reproductibles et précises de la viscosité des coupes lourdes hydrocarbonées sur un large domaine de température. Au-delà de 430-440°C toutefois, la pression opératoire de la cellule, fixée par la quantité du gaz admis, augmente brusquement, révélant un craquage thermique important des échantillons et offrant ainsi un moyen d'étude et de simulation des procédés industriels de viscoréduction. Processes used for the upgrading of residues and heavy oils makes use of equipment for which the optimal sizing requires the exact understanding of the rheological properties of the hydrocarbon phase involved over a wide temperature and pressure range. Therefore, the thermodynamics laboratory of the ENSM Center for Reactors and Processes has carried out the development of a viscosimeter suited for such measurements. It is based on determining the resistant torque caused by the fluid to be analyzed, sheared between twocoaxial cylinders with relative rotation. The viscosity range covered goes from 10 to 40,000 cP, with maximum temperatures and pressures of use being respectively 500°C and 30 MPa. The quality of the results obtained with this device was tested at varying temperatures and dilutions with several heavy cuts coming from Safaniya and Boscan crudes after deasphalting or hydrovisbreaking. Reliable, reproducible and accurate values were thus obtained for the viscosity of heavy hydrocarbon cuts over a wide temperature range. Above 430-440°C, however, the operating pressure of the cell, determined by the amount of gas
 Oil & Gas Science and Technology , 2006, DOI: 10.2516/ogst:1981029 Abstract: Ce travail est le fruit d'une action concertée entre Institut Fran ais du Pétrole (IFP), Compagnie Fran aise de Raffinage (CFR) et Société Nationale Elf Aquitaine (Production) (SNEA (P)) au sein du GEC (Groupe d'Etudes Concertées) sur l'analyse des fractions lourdes du pétrole. On décrit dans cette étude une méthode de chromatographie gazeuse permettant de caractériser par une courbe de distillation simulée, des coupes lourdes 370-535 °C, obtenues par distillation sous vide des résidus atmosphériques. Un mode opératoire détaillé est fourni, contenant des indications précises sur la préparation des colonnes, leur conditionnement, leurs conditions optimales d'emploi et sur les précautions d'exploitation quantitative des chromatogrammes obtenus. Des essais de répétabilité et de reproductibilité ont été réalisés sur différentes coupes de produits lourds. La qualité des résultats obtenus a conduit à une tentative de normalisation de la méthode au sein du Bureau de Normalisation du Pétrole. This article reports on the research done by a GEC (Groupe d'Etudes Concertées) committee made up of scientists from the Institut Fran ais du Pétrole (IFP), Compagnie Fran aise de Raffinage (CFR) and Société Nationale Elf Aquitaine (Production) (SNEA(P)) who worked on joint research on heavy petroleum fractions. A gas chromatography method is described wich leads to characterize heavy cuts (370-535°C) obtained by the vacuum distillation of atmospherie residues, by the simulated distillation curve. Detailed operating instructions are given, including specific recommendations for preparing and conditioning columns, optimum operating conditions, and precautions for the quantitative use of chromatograms. Repeatability and reproducibility tests were performed on several heavy cuts by four independent laboratories. The quality of the results obtained led to an attempt to have the method standardized by the Bureau de Normalisation du Pétrole.
 Oil & Gas Science and Technology , 2006, DOI: 10.2516/ogst:1999039 Abstract: Characterization of petroleum cuts constitutes a necessary stage to perfect understanding of the reaction mechanisms and to the description of the kinetics of certain refining processes such as hydrotreating or catalytic cracking. Mass spectrometry (MS), thanks to group-type quantitative analysis methods, enables to access detailed description of complex hydrocarbon mixtures such as middle distillates or heavy cuts such as vacuum distillates. But these methods are also subject to some drawbacks and we shall expose, thereunder, two examples of improvements. In a first part, the accuracy of MS quantification of thiophenic sulphured compounds in middle distillates is studied by intertechnique comparison with the results obtained by gas phase chromatography coupled to sulphur-specific detection by chemiluminescence (GC/SCD). Improving on the MS method is suggested. In the second part, a new system for introducing the sample in the spectrometer source, dedicated to group-type analysis of heavy cuts is described. Its validation, by comparison of the MS results to those of liquid chromatography (LC) as well as its performances, is exposed. La caractérisation des coupes pétrolières est une étape indispensable à la compréhension des mécanismes réactionnels et à la description de la cinétique de certains procédés de raffinage comme l'hydrotraitement ou le craquage catalytique. La spectrométrie de masse (SM), grace aux méthodes d'analyse quantitative par famille, permet d'accéder à une description détaillée des mélanges complexes d'hydrocarbures que sont les distillats moyens ou les coupes lourdes comme les distillats sous vide. Mais ces méthodes présentent certaines limitations et nous exposons ici deux exemples d'amélioration. Dans une première partie, la justesse de la quantification par SM des composés soufrés thiophéniques dans les distillats moyens est étudiée par comparaison intertechniques avec les résultats obtenus par chromatographie gazeuse couplée à une détection spécifique du soufre par chimiluminescence (CG/SCD). Une amélioration de la méthode SM est proposée. La seconde partie présente la description d'un nouveau système d'introduction de l'échantillon dans la source du spectromètre, dédié à l'analyse par famille des coupes lourdes. Nous exposons sa validation, par comparaison des résultats de SM avec ceux de la chromatographie liquide (CL), ainsi que ses performances.
 Filip Murlak Computer Science , 2008, DOI: 10.2168/LMCS-4(4:15)2008 Abstract: We provide a complete description of the Wadge hierarchy for deterministically recognisable sets of infinite trees. In particular we give an elementary procedure to decide if one deterministic tree language is continuously reducible to another. This extends Wagner's results on the hierarchy of omega-regular languages of words to the case of trees.
 Olivier Finkel Mathematics , 2008, DOI: 10.1007/s11786-008-0045-7 Abstract: We show that, from the topological point of view, 2-tape B\"uchi automata have the same accepting power as Turing machines equipped with a B\"uchi acceptance condition. The Borel and the Wadge hierarchies of the class RAT_omega of infinitary rational relations accepted by 2-tape B\"uchi automata are equal to the Borel and the Wadge hierarchies of omega-languages accepted by real-time B\"uchi 1-counter automata or by B\"uchi Turing machines. In particular, for every non-null recursive ordinal $\alpha$, there exist some $\Sigma^0_\alpha$-complete and some $\Pi^0_\alpha$-complete infinitary rational relations. And the supremum of the set of Borel ranks of infinitary rational relations is an ordinal $\gamma^1_2$ which is strictly greater than the first non-recursive ordinal $\omega_1^{CK}$. This very surprising result gives answers to questions of Simonnet (1992) and of Lescow and Thomas (1988,1994).
 Oil & Gas Science and Technology , 2013, DOI: 10.2516/ogst/2012061 Abstract: The Grayson Streed (GS) method [Grayson H.G. and Streed C.W. (1963) 6th World Petroleum Congress , Frankfurt am Main, Germany, 19-26 June, pp. 169-181] is often used by the industry for calculating hydrogen solubility in petroleum fluids. However, its accuracy becomes very bad when very heavy fluids are considered. An improvement is proposed in this work, based on a Flory-augmented activity coefficient model. Hydrogen solubilities in n-alkanes from n C7 up to n C36 have been investigated and a decreasing Henry constant with molecular weight is evidenced. The analysis of the Henry constant behaviour with molecular weight suggests a simple improvement to the model, using a Flory entropic contribution, thus keeping its predictive character. This improvement led to the necessity of refitting a number of fundamental hydrogen parameters. The resulting model behaves better for heavy components and for aromatics. The petroleum fractions evaluated with the Augmented Grayson-Streed (AGS) model are taken from Cai et al. [Cai H.Y. et al. (2001) Fuel 80, 1055-1063] and Lin et al. [Lin H.M. et al. (1981) Ind. Eng. Chem. Process Des. Dev. 20, 2, 253-256]. The importance of the petroleum fluid characterization is stressed. A sensitivity analysis has shown that the solubility parameter has a much larger effect than the other parameters: great care must be taken at calculating that property. The predictions of hydrogen solubility in petroleum fractions and in coal liquids were improved compared with the Grayson Streed model, resulting in an Absolute Average Deviation (AAD) of 30% for AGS model compared to 55% for Grayson-Streed model, in the range of 80-380°C and 6.3-258.9 bar. La méthode de Grayson Streed (GS) [Grayson H.G. and Streed C.W. (1963) 6th World Petroleum Congress, Frankfurt am Main, Germany, 19-26 June, pp. 169-181] est souvent préconisée dans l’industrie pour calculer la solubilité de l’hydrogène dans des coupes pétrolières. Il se fait cependant que sa précision se dégrade rapidement pour les coupes lourdes. Une amélioration est proposée dans ce travail, basée sur l’ajout d’un terme de Flory dans le calcul du coefficient d’activité. L’étude de la solubilité de l’hydrogène dans les n-alcanes du n-C7 au n-C36 fait appara tre que la constante de Henry diminue avec la masse molaire. L’analyse de ce comportement suggère la présence d’une déviation entropique à l’idéalité non prise en compte dans le modèle des solutions régulières. L’utilisation d’une correction de Flory permet de garder l’aspect prédictif du modèle. Elle nécessite néanmoins un nouveau calage de c
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