Superposition time functions offer one of the effective ways of handling variable-rate data. However, they can also be biased and misleading the engineer to the wrong diagnosis and eventually to the wrong analysis. Since the superposition time functions involve rate as essential constituent, the superposition time is affected greatly with rate issues. Production data of shale gas wells are usually subjected to operating issues that yield noise and outliers. Whenever the rate data is noisy or contains outliers, it will be hard to distinguish their effects from common regime if the superposition time functions are used as plotting time function on log-log plots. Such deceiving presence of these flow regimes will define erroneous well and reservoir parameters. Based on these results and with the upsurge of energy needs there might be some costly decisions will be taken such as refracting or re-stimulating the well especially in tight formations. In this work, a simple technique is presented in order to rapidly check whether there is data bias on the superposition-time specialized plots or not. The technique is based on evaluating the kernel of the superposition time function of each flow regime for the maximum production time. Whatever beyond the Kernel-Equivalent Maximum Production Time (KEMPT) it is considered as biased data. The hypothesis of this technique is that there is no way to see in the reservoir more than what has been seen. A workflow involving different diagnostic and filtering techniques has been proposed to verify proposed notion. Different synthetic and field examples were used in this study. Once the all problematic issues have been detected and filtered out, it was clear that whatever went beyond the KEMPT is a consequence of these issues. Thus, the proposed KEMPT technique can be relied on in order to detect and filter out the biased data points on superposition-time log-log plots. Both raw and filtered data were analyzed using type-curve matching of linear flow type-curves for calculating the original gas in-place (OGIP). It has been found that biased data yield noticeable reduced OGIP. Such reduction is attributed to the early fictitious onset of boundary dominated flow, where early false detection of the drainage boundaries defines less gas in-place occupied in these boundaries.

Cette thèse comporte deux parties, axées sur des aspects différents de la géométrie lorentzienne. La première partie porte sur les groupes d’isométries de surfaces lorentziennes globalement hyperboliques spatialement compactes, particulièrement lorsque le groupe exhibe une dynamique non triviale (action non propre). Le groupe d'isométries agit naturellement sur le cercle par difféomorphismes, et les résultats principaux portent sur la classification de ces représentations. Sous une hypothèse sur le bord conforme, on obtient une conjugaison par homéomorphisme avec l'action projective d'un sous-groupe de PSL(2,R) ou de l'un de ses revêtements finis. La différentiabilité de la conjuguante est étudiée, avec des résultats qui garantissent une conjugaison dans le groupe de difféomorphismes du cercle dans certains cas. On donne également des contre-exemples à l'existence d'une conjugaison différentiable, y compris pour des groupes ayant une dynamique riche. Ces constructions s'appuient sur l'étude de flots hyperboliques en dimension trois. Sans l'hypothèse sur le bord conforme, on obtient une semi conjugaison et un isomorphisme de groupes. On construit également des exemples pour lesquels il n'existe pas de conjugaison topologique. La seconde partie de cette thèse étudie un espace-temps vu comme un système dynamique multi-valuée : à un point on associe sont futur causal. Cette approche, déjà présente dans les travaux de Fathi et Siconolfi, permet de concrétiser le lien entre fonctions de Lyapunov en systèmes dynamiques et fonctions temps. Le résultat principal est une version lorentzienne du Théorème de Conley : on peut définir l'ensemble récurrent par chaînes d'un espace-temps, et il existe une fonction continue croissante le long de toute courbe causale orientée vers le futur, strictement croissante si le point de départ de la courbe n'est pas dans l'ensemble récurrent par chaînes. Ces techniques s'adaptent aussi dans un espace-temps stablement causal, ce qui permet de donner une nouvelle preuve d'une partie du Théorème d'Hawking. / This thesis is divided into two parts, dealing with two different aspects of Lorentzian geometry. The first part deals with isometry groups of globally hyperbolic spatially compact Lorentz surfaces, especially when it has a non trivial dynamical behavior (non proper action). The isometry group acts on circle by diffeomorphisms, and the main results of this part concern the classification of these actions. Under a hypothesis on the conformal boundary, we show that they are topologically conjugate to the projective action of a subgroup of PSL(2,R), or one of its finite covers. The differentiability of the conjugacy is studied, with some results giving a differentiable conjugacy under additional hypotheses. We also give counter examples to such a differentiable conjugacy, even for groups with rich dynamics. These constructions use hyperbolic flows on three manifolds. Without the hypothesis on the conformal boundary, we obtain a semi conjugacy and a group isomorphism. We also give examples where a topological conjugacy cannot exist. In the second part of this thesis, we see a spacetime as a multi valued dynamical system: we map a point to its causal future. This point of view was already adopted by Fathi and Siconolfi, and it gives a concrete meaning to the link between Lyapunov functions in dynamical systems and time functions. The main result is a Lorentzian version of Conley's Theorem: we define the chain recurrent set of a spacetime, and construct a continuous function that increases along future directed causal curves outside the chain recurrent set, and that is non decreasing along other future curves. These techniques also apply to the stably causal setting, and we obtain a new proof of a part of Hawking's Theorem.

Annotation: This thesis aims to reveal to the general public, what dance is in the eyes of professional dancers, and to recommend ballroom dancing as one of the very good ways to meaningfully use their free time. The aim is to find out how pupils and students under 20 years of age spend their free time and how they perceive dance as a leisure activity. This work is divided into theoretical and empirical part. In the theoretical part, I explain the concept of free time and the importance of meaningful use of it. Further, I detail the history of dance, which shows why people started to dance and what it yields to them. The theoretical part also includes information about the dance sport, institutions providing dance training, sports nutrition, and also the fact that dance can help and heal. The empirical part is devoted to questionnaires measuring how much of their free time children spend on dance activities, and guided interviews with professional dancers who let us peek into their dance world. These dancers will answer the questions: why dancing became their way of life, what positives and negatives it brings, what is so beautiful and liberating about the dance, and also why a place called Blackpool is often mentioned in the dance environment.