This thesis deals with the systems reliability. At First, there is discussed the concept of reliability itself and its indicators, which can specifically express reliability. The second chapter describes the different kinds of reliability models for simple and complex systems. It further describes the basic methods for construction of reliability models. The fourth chapter is devoted to a very important Markov models. Markov models are very powerful and complex model for calculating the reliability of advanced systems. Their suitability is explained here for recovered systems, which may contain absorption states. The next chapter describes the standby redundancy. Discusses the advantages and disadvantages of static, dynamic and hybrid standby. There is described the influence of different load levels on the service life. The sixth chapter is devoted to the implementation, description of the application and description of the input file in XML format. There are discussed the results obtaining in experimental calculations.

Une nouvelle méthodologie de modélisation cinétique des procédés de raffinage traitant les charges lourdes a été développée. Elle modélise, au niveau moléculaire, la composition de la charge et les réactions mises en œuvre dans le procédé.La composition de la charge est modélisée à travers un mélange de molécules dont les propriétés sont proches de celles de la charge. Le mélange de molécules est généré par une méthode de reconstruction moléculaire en deux étapes. Dans la première étape, les molécules sont créées par assemblage de blocs structuraux de manière stochastique. Dans la deuxième étape, les fractions molaires sont ajustées en maximisant un critère d’entropie d’information.Le procédé de raffinage est ensuite simulé en appliquant, réaction par réaction, ses principales transformations sur le mélange de molécules, à l'aide d'un algorithme de Monte Carlo.Cette méthodologie est appliquée à deux cas particuliers : l’hydrotraitement de gazoles et l’hydroconversion de résidus sous vide (RSV). Pour le premier cas, les propriétés globales de l’effluent sont bien prédites, ainsi que certaines propriétés moléculaires qui ne sont pas accessibles dans les modèles traditionnels. Pour l'hydroconversion de RSV, dont la structure moléculaire est nettement plus complexe, la conversion des coupes lourdes est correctement reproduite. Par contre, la prédiction des rendements en coupes légères et de la performance en désulfuration est moins précise. Pour les améliorer, il faut d'une part inclure de nouvelles réactions d'ouverture de cycle et d'autre part mieux représenter la charge en tenant compte des informations moléculaires issues des analyses des coupes de l'effluent. / In the present PhD thesis, a novel methodology for the kinetic modelling of heavy oil refining processes is developed. The methodology models both the feedstock composition and the process reactions at a molecular level. The composition modelling consists of generating a set of molecules whose properties are close to those obtained from the process feedstock analyses. The set of molecules is generated by a two-step molecular reconstruction algorithm. In the first step, an equimolar set of molecules is built by assembling structural blocks in a stochastic manner. In the second step, the mole fractions of the molecules are adjusted by maximizing an information entropy criterion. The refining process is then simulated by applying, step by step, its main reactions to the set of molecules, by a Monte Carlo method. This methodology has been applied to two refining processes: The hydrotreating (HDT) of Light Cycle Oil (LCO) gas oils and the hydroconversion of vacuum residues (VR). For the HDT of LCO gas oils, the overall properties of the effluent are well predicted. The methodology is also able to predict molecular properties of the effluent that are not accessible from traditional kinetic models. For the hydroconversion of VR, which have more complex molecules than LCO gas oils, the conversion of heavy fractions is correctly predicted. However, the results for the composition of lighter fractions and the desulfurization yield are less accurate. To improve them, one must on one hand include new ring opening reactions and on the other hand refine the feedstock representation by using additional molecular information from the analyses of the process effluents.

Complex spatial structures in biology arise from random interactions of molecules. These molecular interactions can be studied using spatial stochastic models, such as Reaction Diffusion Master Equation (RDME), a mesoscopic model that subdivides the spatial domain into smaller, well mixed grid cells, in which the macroscopic diffusion-controlled reactions take place. While RDME has been widely used to study how fluctuations in number of molecules affect spatial patterns, simulations are computationally expensive and it requires a lower bound for grid cell size to avoid an apparent unphysical loss of bimolecular reactions. In this thesis, we propose Gaussian Reaction Diffusion Master Equation (GRDME), a novel model in the RDME framework, based on the discretization of the Laplace operator with Particle Strength Exchange (PSE) method with a Gaussian kernel. We show that GRDME is a computationally efficient model compared to RDME. We further resolve the controversy regarding the loss of bimolecular reactions and argue that GRDME can flexibly bridge the diffusion-controlled and ballistic regimes in mesoscopic simulations involving multiple species. To efficiently simulate GRDME, we develop Gaussian Next Subvolume Method (GNSM). GRDME simulated with GNSM up to six-times lower computational cost for a three-dimensional simulation, providing a significant computational advantage for modeling three-dimensional systems. The computational cost can be further lowered by increasing the so-called smoothing length of the Gassian jumps. We develop a guideline to estimate the grid resolution below which RDME and GRDME exhibit loss of bimolecular reactions. This loss of reactions has been considered unphysical by others. Here we show that this loss of bimolecular reactions is consistent with the well-established theory on diffusion-controlled reaction rates by Collins and Kimball, provided that the rate of bimolecular propensity is interpreted as the rate of the ballistic step, rather than the macroscopic reaction rate. We show that the reaction radius is set by the grid resolution. Unlike RDME, GRDME enables us to explicitly model various sizes of the molecules. Using this insight, we explore the diffusion-limited regime of reaction dynamics and discover that diffusion-controlled systems resemble small, discrete systems. Others have shown that a reaction system can have discreteness-induced state inversion, a phenomenon where the order of the concentrations differs when the system size is small. We show that the same reaction system also has diffusion-controlled state inversion, where the order of concentrations changes, when the diffusion is slow. In summary, we show that GRDME is a computationally efficient model, which enables us to include the information of the molecular sizes into the model.:1 Modeling Mesoscopic Biology 1.1 RDME Models Mesoscopic Stochastic Spatial Phenomena 1.2 A New Diffusion Model Presents an Opportunity For A More Efficient RDME 1.3 Can A New Diffusion Model Provide Insights Into The Loss Of Reactions? 1.4 Overview 2 Preliminaries 2.1 Reaction Diffusion Master Equation 2.1.1 Chemical Master Equation 2.1.2 Diffusion-controlled Bimolecular Reaction Rate 2.1.3 RDME is an Extention of CME to Spatial Problems 2.2 Next Subvolume Method 2.2.1 First Reaction Method 2.2.2 NSM is an Efficient Spatial Stochastic Algorithm for RDME 2.3 Discretization of the Laplace Operator Using Particle Strength Exchange 2.4 Summary 3 Gaussian Reaction Diffusion Master Equation 3.1 Design Constraints for the Diffusion Model in the RDME Framework 3.2 Gaussian-jump-based Model for RDME 3.3 Summary 4 Gaussian Next Subvolume Method 4.1 Constructing the neighborhood N 4.2 Finding the Diffusion Event 4.3 Comparing GNSM to NSM 4.4 Summary 5 Limits of Validity for (G)RDME with Macroscopic Bimolecular Propensity Rate 5.1 Previous Works 5.2 hmin Based on the Kuramoto length of a Grid Cell 5.3 hmin of the Two Limiting Regimes 5.4 hmin of Bimolecular Reactions for the Three Cases of Dimensionality 5.5 hmin of GRDME in Comparison to hmin of RDME 5.6 Summary 6 Numerical Experiments To Verify Accuracy, Efficiency and Validity of GRDME 6.1 Accuracy of the Diffusion Model 6.2 Computational Cost 6.3 hmin and Reaction Loss for (G)RDME With Macroscopic Bimolecular Propensity Rate kCK 6.3.1 Homobiomlecular Reaction With kCK at the Ballistic Limit 6.3.2 Homobiomlecular Reaction With kCK at the Diffusional Limit 6.3.3 Heterobiomlecular Reaction With kCK at the Ballistic Limit 6.4 Summary 7 (G)RDME as a Spatial Model of Collins-Kimball Diffusion-controlled Reaction Dynamics 7.1 Loss of Reactions in Diffusion-controlled Reaction Systems 7.2 The Loss of Reactions in (G)RDME Can Be Explained by Collins Kimball Theory 7.3 Cell Width h Sets the Reaction Radius σ∗ 7.4 Smoothing Length ε′ Sets the Size of the Molecules in the System 7.5 Heterobimolecular Reactions Can Only Be Modeled With GRDME 7.6 Zeroth Order Reactions Impose a Lower Limit on Diffusivity Dmin 7.6.1 Consistency of (G)RDME Could Be Improved by Redesigning Zeroth Order Reactions 7.7 Summary 8 Difussion-Controlled State Inversion 8.1 Diffusion-controlled Systems Resemble Small Systems 8.2 Slow Diffusion Leads to an Inversion of Steady States 8.3 Summary 9 Conclusion and Outlook 9.1 Two Physical Interpretations of (G)RDME 9.2 Advantages of GRDME 9.3 Towards Numerically Consistent (G)RDME 9.4 Exploring Mesoscopic Biology With GRDME Bibliography