Dynamic simulation of the THAI heavy oil recovery process

Toe-to-Heel Air Injection (THAI) is a variant of conventional In-Situ Combustion (ISC) that uses a horizontal production well to recover mobilised partially upgraded heavy oil. It has a number of advantages over other heavy oil recovery techniques such as high recovery potential. However, existing models are unable to predict the effect of the most important operational parameters, such as fuel availability and produced oxygen concentration, which will give rise to unsafe designs. Therefore, we have developed a new model that accurately predicts dynamic conditions in the reservoir and also is easily scalable to investigate different field scenarios. The model used a three component direct conversion cracking kinetics scheme, which does not depend on the stoichiometry of the products and, thus, reduces the extent of uncertainty in the simulation results as the number of unknowns is reduced. The oil production rate and cumulative oil produced were well predicted, with the latter deviating from the experimental value by only 4%. The improved ability of the model to emulate real process dynamics meant it also accurately predicted when the oxygen was first produced, thereby enabling a more accurate assessment to be made of when it would be safe to shut-in the process, prior to oxygen breakthrough occurring. The increasing trend in produced oxygen concentration following a step change in the injected oxygen rate by 33 % was closely replicated by the model. The new simulations have now elucidated the mechanism of oxygen production during the later stages of the experiment. The model has allowed limits to be placed on the air injection rates that ensure stability of operation. Unlike previous models, the new simulations have provided better quantitative prediction of fuel laydown, which is a key phenomenon that determines whether, or not, successful operation of the THAI process can be achieved. The new model has also shown that, for completely stable operation, the combustion zone must be restricted to the upper portion of the sand pack, which can be achieved by using higher producer back pressure

In Search of the “Géométrie de situation” in Mathematical Journals of the Second Half of the 19th century

International audienc

Un " rapprochement curieux de l'algèbre et de la théorie des nombres" : études sur l'utilisation des congruences en France de 1801 à 1850

Gauss introduced the notion of congruence in 1801 in the Disquisitiones Arithmeticae. The standard historiography connects its history to the development of algebraic number theory, a history built around a group of German mathematicians. However other authors in the first half of the nineteenth century published works related to congruences from different perspectives. We study here some of them while focusing on the French scene between 1801 and 1850. From a global reading of the texts of our corpus, we first show that congruences did not develop in France as an autonomous field, but as one tightly linked to the theory of equations. However, the different practices thus encountered were far from uniform, whether in terms of methods, tools or disciplinary configurations. We then study arithmetical works of Euler, Lagrange, Legendre and Gauss in order to understand some of the origins of the multifarious activity analyzed in our first part. Finally, we focus on the work of two authors, Louis Poinsot and Augustin Louis Cauchy, who played a key role in elaborating and circulating results and practices related to congruences, but who have virtually disappeared from twentieth-century histories of number theory.Gauss introduit la notion de congruence en 1801 dans les Disquisitiones Arithmeticae. L'historiographie classique relie le plus souvent l'histoire de cette notion au développement de la théorie des nombres algébriques, une histoire construite autour d'un groupe de mathématiciens allemands. Pourtant, d'autres auteurs ont publié des travaux en lien avec les congruences dans la première moitié du XIXe siècle, et ce dans des perspectives différentes. Dans ce travail, nous nous proposons de rendre compte de ces dernières en nous concentrant sur les travaux de la scène française publiés entre 1801 et 1850. À partir d'une première lecture globale des textes de notre corpus, nous montrons d'abord que les congruences n'y ont pas connu un développement autonome mais ont été étudiées dans un lien étroit avec les équations. Toutefois, les différentes pratiques rencontrées sont très variées, que ce soit du point de vue des méthodes, des outils en jeu ou des configurations disciplinaires en jeu. Nous étudions ensuite plusieurs travaux arithmétiques d'Euler, de Lagrange, de Legendre et de Gauss afin de comprendre certaines origines de cette activité multiforme mise en évidence dans notre première partie. Nous nous concentrons enfin sur les travaux de deux auteurs de notre corpus, Louis Poinsot et Augustin Louis Cauchy, qui ont joué un rôle important dans l'élaboration et la diffusion de résultats et de pratiques liés aux congruences, même s'ils ont pratiquement disparu des histoires de la théorie des nombres publiées au XXe siècle

Résidus et congruences de 1750 à 1850 : une diversité de pratiques entre algèbre et théorie des nombres

International audienc

Chapitre 7 : Eugène Charles Catalan et la théorie des nombres

International audienc

Introduction - Pluralité et structuration des recherches du Centre François Viète

International audienc

Number Theory in Teaching Mathematical Journals : the Case of Nouvelles Annales de Mathématiques (1842- 1927)

International audienc

Joseph-Louis Lagrange e il teorema dei quattro quadrati

International audienc

Lagrange and the four-square theorem

International audienceIn this article we will first provide an overview of Lagrange’s arithmetic work, written between 1768 and 1777. We then focus on the proof of the four-square theorem published in 1772, and shed light on the context of its implementation by relying on other memoirs by Lagrange and Leonhard Euler. By means of this analysis, our goal is to give a concrete vision of the arithmetic, algebraic and analytical methods and tools used by Lagrange in number theory and place his arithmetic practice in the context of the second half of the eighteenth century

Sophie Germain and Fermat’s Last Theorem : Number-theoretical Practices by a Marginal Ma- thematician in 19th century

International audienc