For effective reservoir management and production optimization, it is important to understand drained volumes, pressure depletion and reservoir well rates at all flow times. For conventional reservoirs, this behavior is based on the concepts of reservoir pressure and energy and convective flow. But, with the development of unconventional reservoirs, there is increased focus on the unsteady state transient flow behavior. For analyzing such flow behaviors, well test analysis concepts are commonly applied, based on the analytical solutions of the diffusivity equation. In this thesis, we have proposed a novel methodology for estimating the drainage volumes and utilizing it to obtain the pressure and flux at any location in the reservoir. The result is a semi-analytic calculation only, with close to the simplicity of an analytic approach, but with significantly more generality. The approach is significantly faster than a conventional finite difference solution, although with some simplifying assumptions. The proposed solution is generalized to handle heterogeneous reservoirs, complex well geometries and bounded and semi-bounded reservoirs. Therefore, this approach is particularly beneficial for unconventional reservoir development with multiple transverse fractured horizontal wells, where limited analytical solutions are available. To estimate the drainage volume, we have applied an asymptotic solution to the diffusivity equation and determined the diffusive time of flight distribution. For the pressure solution, a geometric approximation has been applied within the drainage volume to reduce the full solution of the diffusivity equation to a system of decoupled ordinary differential equations. Besides, this asymptotic expression can also be extended to obtain the well rates, producing under constant bottomhole pressure constraint. In this thesis, we have described the detailed methodology and its validation through various case studies. We have also studied the limits of validity of the approximation to better understand the general applicability. We expect that this approach will enable the inversion of field performance data for improved well and/or fracture characterization, and similarly, the optimization of well trajectories and fracture design, in an analogous manner to how rapid but approximate streamline techniques have been used for improved conventional reservoir management.

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L'objectif de cette recherche est de construire un modèle réduit de petite dimension pour prévoir les réponses dynamiques dans une bande BF sur les parties rigides d'un véhicule automobile complet. Un tel modèle réduit "léger" est une aide à la phase de conception en "Avant Projet" de ces véhicules qui ont la particularité de présenter de nombreux modes élastiques locaux en BF dues à la présence de nombreuses parties flexibles et d'équipements. Pour la construction du modèle réduit, nous avons introduit une base non usuelle de l'espace admissible des déplacements globaux. La construction de cette base requiert la décomposition en sous-domaines du domaine de la structure qui peut présenter une très grande complexité géométrique et dont les modèles EF font intervenir de très nombreux types d'éléments finis. Cette décomposition en sous-domaines a été réalisée par la Fast Marching Method que nous avons due étendre pour pouvoir traiter la complexité des modèles EF des véhicules automobiles. Puis les équations matricielles du modèle EF sont projetées sur cette base. Afin de prendre en compte les incertitudes sur les paramètres du modèle, les incertitudes de modèle induites par les erreurs de modélisation et enfin les incertitudes liées à la non prise en compte des contributions locales dans le modèle réduit des déplacements globaux, un unique modèle probabiliste non paramétrique de ces trois sources d'incertitude a été implémenté sur le modèle réduit construit avec les vecteurs propres globaux. Les paramètres de dispersion de ce modèle probabiliste ont été identifiés en utilisant le principe du maximum de vraisemblance et des réponses obtenues à l'aide d'un modèle stochastique de référence qui inclut des informations expérimentales résultant de travaux précédents. Le modèle réduit stochastique, pour la prévision des déplacements globaux sur les parties rigides dans la bande BF qui a été développé, a été validé sur un modèle de structure automobile "nue" puis a été appliqué avec succès sur un modèle complet de véhicule automobile / The objective of this research is to construct a reduced-order model to predict the dynamical response, in the LF band, of the stiff parts of a complete automotive vehicle in order to facilitate the draft design. The vehicles under consideration have many elastic modes in LF due to the presence of many flexible parts and equipments. To build such a model, we introduced a non-usual basis of the admissible space of global displacements. The construction of this basis requires the decomposition of the domain of the structure. This subdomain decomposition is performed by using the Fast Marching Method that we have extended to take into account the high complexity of the mesh of an automotive vehicle. Then the matrix equations of the FE model are projected on this basis. To take into account the system parameters uncertainties, the model uncertainties induced by the modeling errors and finally, the uncertainties related to the neglecting of local contributions in the reduced-order model, a nonparametric probabilistic model of the three sources of uncertainties has been implemented on the reduced-order model constructed with the global displacements eigenvectors. The dispersion parameters of the probabilistic model are identified using the maximum likelihood method and the responses obtained from a stochastic reference model which includes experimental data resulting from previous works. This stochastic model which has been designed for the prediction of the global displacements of the rigid parts in the LF band is validated on a simple structure of an automotive model and has been successfully applied on a complete model of automotive vehicle

Rapid economic evaluations of investment alternatives in the oil and gas industry are typically contingent on fast and credible evaluations of reservoir models to make future forecasts. It is often important to also quantify inherent risks and uncertainties in these evaluations. These ideally require several full-scale numerical simulations which is time consuming, impractical, if not impossible to do with conventional (Finite Difference) simulators in real life situations. In this research, the aim will be to improve on the efficiencies associated with these tasks. This involved exploring the applications of Fast Marching Methods (FMM) in both conventional and unconventional reservoir characterization problems. In this work, we first applied the FMM for rapidly ranking multiple equi-probable geologic models. We demonstrated the suitability of drainage volume, efficiently calculated using FMM, as a surrogate parameter for field-wide cumulative oil production (FOPT). The probability distribution function (PDF) of the surrogate parameter was point-discretized to obtain 3 representative models for full simulations. Using the results from the simulations, the PDF of the reservoir performance parameter was constructed. Also, we investigated the applicability of a higher-order-moment-preserving approach which resulted in better uncertainty quantification over the traditional model selection methods. Next we applied the FMM for a hydraulically fractured tight oil reservoir model calibration problem. We specifically applied the FMM geometric pressure approximation as a proxy for rapidly evaluating model proposals in a two-stage Markov Chain Monte Carlo (MCMC) algorithm. Here, we demonstrated the FMM-based proxy as a suitable proxy for evaluating model proposals. We obtained results showing a significant improvement in the efficiency compared to conventional single stage MCMC algorithm. Also in this work, we investigated the possibility of enhancing the computational efficiency for calculating the pressure field for both conventional and unconventional reservoirs using FMM. Good approximations of the steady state pressure distributions were obtained for homogeneous conventional waterflood systems. In unconventional system, we also recorded slight improvement in computational efficiency using FMM pressure approximations as initial guess in pressure solvers.

Unconventional reservoirs are typically characterized by very low permeabilities, and thus, the pressure depletion from a producing well may not propagate far from the well during the life of a development. Currently, two approaches are widely utilized to perform unconventional reservoir analysis: analytical techniques, including the decline curve analysis and the pressure/rate transient analysis, and numerical simulation. The numerical simulation can rigorously account for complex well geometry and reservoir heterogeneity but also is time consuming. In this thesis, we propose and apply an efficient technique, fast marching method (FMM), to analyze the shale gas reservoirs. Our proposed approach stands midway between analytic techniques and numerical simulation. In contrast to analytical techniques, it takes into account complex well geometry and reservoir heterogeneity, and it is less time consuming compared to numerical simulation. The fast marching method can efficiently provide us with the solution of the pressure front propagation equation, which can be expressed as an Eikonal equation. Our approach is based on the generalization of the concept of depth of investigation. Its application to unconventional reservoirs can provide the understanding necessary to describe and optimize the interaction between complex multi-stage fractured wells, reservoir heterogeneity, drainage volumes, pressure depletion, and well rates. The proposed method allows rapid approximation of reservoir simulation results without resorting to detailed flow simulation, and also provides the time-evolution of the well drainage volume for visualization. Calibration of reservoir models to match historical dynamic data is necessary to increase confidence in simulation models and also minimize risks in decision making. In this thesis, we propose an integrated workflow: applying the genetic algorithm (GA) to calibrate the model parameters, and utilizing the fast marching based approach for forward simulation. This workflow takes advantages of both the derivative free characteristics of GA and the speed of FMM. In addition, we also provide a novel approach to incorporate the micro-seismic events (if available) into our history matching workflow so as to further constrain and better calibrate our models.

<p>The prediction and characterisation of chemical and biochemical processes are fundamental tasks in computational chemistry. Small chemical systems can be characterised by the stationary points on potential energy surface and reaction paths linking them. For large biological systems, statistical sampling is required to characterising their average properties.</p> <p>This thesis presents my Ph.D. work on developing new methods to predict and characterise chemical and biological processes. Two path-finding methods for finding the minimum energy reaction path and alternative reaction paths for small gas-phase reactions have been elucidated with examples, and molecular dynamic simulations have been used to characterise the binding affinity of protein-ligand complex and the free energy of protonation processes in a protein.</p> <p>Specifically, the fast marching method (FMM) has been used to find the minimum energy path (MEP) on the potential energy surface (PES) for small gas-phase reactions. In this thesis, FMM is shown to be one of the most general and reliable surface-walking algorithms for finding the MEP. However, it is an expensive method. Some improvements have been illustrated in chapter 2 and chapter 3.</p> <p>I also proposed a new method (called QSM-NT) for finding all stationary points, accordingly all alternative reaction paths on the PES. Unlike other path-finding methods, QSM-NT overcomes the need of an initial guess of the path, and it can find all stationary points on the PES. QSM-NT has been proven to be efficient and reliable through applications on analytical PES and real chemical reaction. The difficulties and pitfalls associated with QSM-NT have been elucidated with examples.</p> <p>Molecular dynamic (MD) simulation and associated postprocessing procedures have been used to study the binding properties of caffeine-A_2A complex. The binding affinities of different binding modes have been calculated using MM/PBSA method. The binding pocket has been characterised with MM/GBSA energy decomposition. Our computational work provides significant insight to the targeted drug design of the adenosine A_2A receptor.</p> <p>The pH-dependent properties of a protein play important roles in the fundamental biological processes. The protonation states, namely, the pK_a values of ionisable residues, especially active-site residues are the prerequisites to understanding of the mechanisms of many biological processes. In this thesis, acetoacetate decarboxylase (AADase) is used as a test case for studying different types of pK_a prediction methods. Our computational results have shown that the site-site interactions from other ionisable residues are crucial to the pK_a prediction of the target residue.</p> <p>This thesis covers the range from small gas phase reaction prediction to large complex biological systems characterisation using quantum mechanical and molecular mechanical methods.</p> / Doctor of Philosophy (PhD)

Diffusion Tensor Magnetic Resonance Imaging (DT-MRI), also known as Diffusion Tensor Imaging (DTI), is a unique medical imaging modality that provides non-invasive estimates of White Matter (WM) connectivity based on local principal directions of anisotropic water diffusion. DTI tractography estimates are a macroscopically sampled description of underlying microscopic structure, and are therefore of limited validity. The under-sampling of underlying white matter structure in DTI data gives rise to Intra-Voxel Orientational Heterogeneity (IVOH), a condition in which white matter structures of multiple different orientations are averaged into a single DTI voxel sample, causing a loss of validity in the diffusion tensor model. Fast Marching Tractography (FMT) algorithms based on fast marching level set methods have been proposed to better handle the presence of IVOH in DTI data when compared to older Streamline Tractography (SLT) methods. However, the actual performance advantage of any tractography algorithm over another cannot be conclusively stated until a ground truth standard of comparison is developed. This work develops an optimized version of the FMT algorithm that is dubbed the Front Propagation Tractography (FPT) algorithm. The FPT algorithm includes unique approaches to the speed function, connectivity estimation, and likelihood estimation components of the FMT framework. The performance of the FPT algorithm is compared against the SLT algorithm using ground truth software phantom data and human brain data. Software phantom ground truth experiments compare the performance of each algorithm in single tract and crossing tract structures for varying levels of diffusion tensor field perturbation. Human brain estimates in the corpus callosum yield qualitative comparisons from inspection of 3D visualizations. A final area of exploration is the construction and analysis of a ground truth physical DTI phantom manifesting IVOH. / Master of Science

La simulation numérique est indissociable du calcul haute performance. Ces vingt dernières années,l'informatique a connu l'émergence d'architectures parallèles multi-niveaux. Exploiter efficacement lapuissance de calcul de ces machines peut s'avérer être une tâche délicate et requérir une expertise à la foistechnologique sur des notions avancées de parallélisme ainsi que scientifique de part la nature même desproblèmes traités.Le travail de cette thèse est pluri-disciplinaire s'appuyant sur la conception d'une librairie de calculparallèle réutilisable pour la résolution des équations Hamilton-Jacobi-Bellman. Ces équations peuventse retrouver dans des domaines diverses et variés tels qu'en biomédical, géophysique, ou encore robotiqueen l'occurence sur les applications de planification de mouvement et de reconstruction de formestri-dimensionnelles à partir d'images bi-dimensionnelles. Nous montrons que les principaux algorithmesnumériques amenant a résoudre ces équations telles que les méthodes de type fast marching, ne sont pasappropriés pour être efficaces dans un contexte parallèle. Nous proposons la méthode buffered fast iterativequi permet d'obtenir une scalabilité parallèle non obtenue jusqu'alors. Un des points sensibles relevésdans cette thèse est de parvenir à trouver une recette de compromis entre abstraction, performance etmaintenabilité afin de garantir non seulement une réutilisabilitédans le sens classique du domaine de génielogiciel mais également en terme de réutilisabilité séquentielle/parallèle / Numerical simulation is strongly bound with high performance computing. Programming scientificsoftwares requires at the same time good knowledge on the mathematical numerical models and alsoon the techniques to make them efficient on today's computers. Indeed, these last twenty years, wehave experienced the rising of multi-level parallel architectures. The work in this thesis dissertation ismultidisciplinary by designing a reusable parallel numerical library for solving Hamilton-Jacobi-Bellmanequations. Such equations are involved in various fields such as in biomedical, geophysics or robotics. Inparticular, we will show interests in path planning and shape from shading applications. We show thatthe methods to solve these equations such as the widely used fast marching method, are not designedto be used effciently in a parallel context. We propose a buffered fast iterative method which givesan interesting parallel scalability. This dissertation takes interest in the challenge to find compromisesbetween abstraction, performance and maintainability in order to combine both software reusability andalso sequential/parallel reusability. We propose code abstraction allowing algorithmic and data genericitywhile trying to keep a maintainable and performant code potentially parallelizable

Wildfire hazard and its destructive consequences have become a growing issue around the world especially in the context of global warming. An effective and efficient fire simulation model will make it possible to predict the fire spread and assist firefighters in the process of controlling the damage and containing the fire area. Simulating wildfire spread remains challenging due to the complexity of fire behaviors. The raster-based method and the vector-based method are two major approaches that allow one to perform computerized fire spread simulation. In this thesis, we present a scheme we have developed that utilizes a level set method to build a fire spread simulation model. The scheme applies the strengths and overcomes some of the shortcomings of the two major types of simulation method. We store fire data and local rules at cells. Instead of calculating which are the next ignition points cell by cell, we apply Huygens' principle and elliptical spread assumption to calculate the direction and distance of the expanding fire by the level set method. The advantage to storing data at cells is that it makes our simulation model more suitable for heterogeneous fuel and complex topographic environment. Using a level set method for our simulation model makes it possible to overcome the crossover problem. Another strength of the level set method is its continuous data processing. Applying the level set method in the simulation models, we need fewer vector points than raster cells to produce a more realistic fire shape. We demonstrate this fire simulation model through two implementations using narrow band level set method and fast marching method. The simulated results are compared to the real fire image data generated from Troy and Colina fires. The simulation data are then studied and compared. The ultimate goal is to apply this simulation model to the broader picture to better predict different types of fires such as crown fire, spotting fires, etc.

Modern reservoir management typically involves simulations of geological models to predict future recovery estimates, providing the economic assessment of different field development strategies. Integrating reservoir data is a vital step in developing reliable reservoir performance models. Currently, most effective strategies for traditional manual history matching commonly follow a structured approach with a sequence of adjustments from global to regional parameters, followed by local changes in model properties. In contrast, many of the recent automatic history matching methods utilize parameter sensitivities or gradients to directly update the fine-scale reservoir properties, often ignoring geological inconsistency. Therefore, there is need for combining elements of all of these scales in a seamless manner. We present a hierarchical streamline-assisted history matching, with a framework of global-local updates. A probabilistic approach, consisting of design of experiments, response surface methodology and the genetic algorithm, is used to understand the uncertainty in the large-scale static and dynamic parameters. This global update step is followed by a streamline-based model calibration for high resolution reservoir heterogeneity. This local update step assimilates dynamic production data. We apply the genetic global calibration to unconventional shale gas reservoir specifically we include stimulated reservoir volume as a constraint term in the data integration to improve history matching and reduce prediction uncertainty. We introduce a novel approach for efficiently computing well drainage volumes for shale gas wells with multistage fractures and fracture clusters, and we will filter stochastic shale gas reservoir models by comparing the computed drainage volume with the measured SRV within specified confidence limits. Finally, we demonstrate the value of integrating downhole temperature measurements as coarse-scale constraint during streamline-based history matching of dynamic production data. We first derive coarse-scale permeability trends in the reservoir from temperature data. The coarse information are then downscaled into fine scale permeability by sequential Gaussian simulation with block kriging, and updated by local-scale streamline-based history matching. he power and utility of our approaches have been demonstrated using both synthetic and field examples.