No description available.

Information about the capillary pressure has a wide range of applications in the petroleum industry, such as an estimation of irreducible water saturation, calculation of formation absolute permeability, determination of hydrocarbon-water contact and the thickness of the transition zone, evaluation of the seal capacity, and an estimation of relative permeability. All the listed parameters in the combination with petrophysical features, pressures, and fluid properties allow us to evaluate the economic viability of the well or the field overall. For this reason, capillary pressure curves are of great importance for petroleum engineers working on any stage of the field development: starting from exploration and finishing with production stages. Nowadays, capillary pressure experiments are provided either in the lab on the plugs of the rocks, either in the well on the certain stop points with the formation tester tools on the wire or tubes. Core extraction and formation testing are both laborious, expensive, and complicated processes since the newly-drilled well remain in the risky uncased condition during these operations, and for this reason, usually the listed works are provided in the exploration wells only. Afterward, the properties obtained from the exploration wells are assumed to be the same for the extraction or any other kinds of wells. Therefore, these days petroleum engineers have limited access to the capillary pressure curves: the modern tests are provided on the limited points of formation in the limited number of wells. An extension of capillary pressure measurements in the continuous mode for every well will dramatically expand the abilities of modern formation evaluation and significantly improve the field operation management by reducing the degree of uncertainty in the decision-making processes. This work is the first step toward continuous capillary pressure evaluation. Here we describe the procedure of finding the correlation between the results of the lab Nuclear Magnetic Resonance (NMR) experiment and lab Mercury Injection Capillary Pressure (MICP) measurements. Both experiments were provided on the 9 core plugs of the sandstone. Afterward, a Machine Learning (ML) algorithm was applied to generate additional samples of the porous media with different petrophysical properties representing the variations of the real cores of available sandstones. Overall, 405 additional digital rock models were generated. Thereafter, the digital simulations of MICP and NMR experiments were provided on the generated database of digital rocks. All the simulations were corrected for limited resolution of the CT scan. Based on the created database of experiments, we implemented a ML algorithm that found a correlation between the NMR echo data and MICP capillary pressure curves. Obtained correlation allows to calculate capillary pressure curve from the NMR echo data. Since NMR logging may be implemented in every well in the continuous mode, an extension of the created technique provides an opportunity for continuous estimation of capillary pressure for the whole logging interval. This extension is planned as future work.

Simulation and optimization of complex physical systems are an integral part of modern science and engineering. The systems of interest in many fields have a multiphysics nature, with complex interactions between physical, chemical and in some cases even biological processes. This dissertation seeks to advance forward and adjoint numerical time integration methodologies for the simulation and optimization of semi-discretized multiphysics partial differential equations (PDEs), and to estimate and control numerical errors via a goal-oriented a posteriori error framework. We extend exponential propagation iterative methods of Runge-Kutta type (EPIRK) by [Tokman, JCP 2011], to build EPIRK-W and EPIRK-K time integration methods that admit approximate Jacobians in the matrix-exponential like operations. EPIRK-W methods extend the W-method theory by [Steihaug and Wofbrandt, Math. Comp. 1979] to preserve their order of accuracy under arbitrary Jacobian approximations. EPIRK-K methods extend the theory of K-methods by [Tranquilli and Sandu, JCP 2014] to EPIRK and use a Krylov-subspace based approximation of Jacobians to gain computational efficiency. New families of partitioned exponential methods for multiphysics problems are developed using the classical order condition theory via particular variants of T-trees and corresponding B-series. The new partitioned methods are found to perform better than traditional unpartitioned exponential methods for some problems in mild-medium stiffness regimes. Subsequently, partitioned stiff exponential Runge-Kutta (PEXPRK) methods -- that extend stiffly accurate exponential Runge-Kutta methods from [Hochbruck and Ostermann, SINUM 2005] to a multiphysics context -- are constructed and analyzed. PEXPRK methods show full convergence under various splittings of a diffusion-reaction system. We address the problem of estimation of numerical errors in a multiphysics discretization by developing a goal-oriented a posteriori error framework. Discrete adjoints of GARK methods are derived from their forward formulation [Sandu and Guenther, SINUM 2015]. Based on these, we build a posteriori estimators for both spatial and temporal discretization errors. We validate the estimators on a number of reaction-diffusion systems and use it to simultaneously refine spatial and temporal grids. / Doctor of Philosophy / The study of modern science and engineering begins with descriptions of a system of mathematical equations (a model). Different models require different techniques to both accurately and effectively solve them on a computer. In this dissertation, we focus on developing novel mathematical solvers for models expressed as a system of equations, where only the initial state and the rate of change of state as a function are known. The solvers we develop can be used to both forecast the behavior of the system and to optimize its characteristics to achieve specific goals. We also build methodologies to estimate and control errors introduced by mathematical solvers in obtaining a solution for models involving multiple interacting physical, chemical, or biological phenomena. Our solvers build on state of the art in the research community by introducing new approximations that exploit the underlying mathematical structure of a model. Where it is necessary, we provide concrete mathematical proofs to validate theoretically the correctness of the approximations we introduce and correlate with follow-up experiments. We also present detailed descriptions of the procedure for implementing each mathematical solver that we develop throughout the dissertation while emphasizing on means to obtain maximal performance from the solver. We demonstrate significant performance improvements on a range of models that serve as running examples, describing chemical reactions among distinct species as they diffuse over a surface medium. Also provided are results and procedures that a curious researcher can use to advance the ideas presented in the dissertation to other types of solvers that we have not considered. Research on mathematical solvers for different mathematical models is rich and rewarding with numerous open-ended questions and is a critical component in the progress of modern science and engineering.

For the exponential response η_u = α + βe^γZ_u (u = 1,2,…,N) where α and β lie on the real line (-∞,∞), and γ is a positive integer; the designs are given which minimize the bias due to the inherent inability of the approximation function ŷ_u = Σ_j=0<sup>d</sub>b_je^jZ_u to fit such a model. Transformation to η_u = α + βx_u^γ and ŷ_u = Σ_j=0<sup>d</sub>b_jx_u^j facilitates the solution for minimum bias designs. The requirements for minimum bias designs follow along lines similar to those given by Box and Draper (J. Amer. Stat. Assoc., 54, 1959, p. 622). The minimum bias designs are obtained for specific values of N with a maximum protection level, γ_d*(N), for the parameter γ and an approximation function of degree d. These designs obtained possess several degrees of freedom in the choice of the design levels of the x_u or the Z_uu , which may be used to satisfy additional design requirements. It is shown that for a given N, the same designs which minimize bias for approximation functions of degree one also minimize bias for general degree d, with a decrease in γ_d*(N) as d increases. In fact γ_d*(N) = γ₁*(N) - d + 1, but with the decrease in γ_d*(N) is a compensating decrease in the actual level of the minimum bias. Furthermore, γ_d*(N) increases monotonically with N, thereby allowing the maximum protection level on 1 to be increased as desired by increasing N. In the course of obtaining solutions, some interesting techniques are developed for determining the nature of the roots of a polynomial equation which has several known coefficients and several variable coefficients. / Ph. D.

Coarse woody debris (CWD) plays an influential role in forested ecosystems by adding organic matter to soils, stabilizing the soil environment, providing wildlife habitat, preventing soil erosion, providing seedling establishment habitat, and involvement in the nutrient cycle. Most CWD research has been conducted in old-growth and unmanaged, second-growth forests. However, less is understood about CWD in intensively managed ecosystems, such as industrialized southern pine plantations. The objectives of this study were to determine the climatic and ecological factors that affect the decomposition rate of CWD, to predict the decomposition rate, specific gravity, and time since death (TSD) using multiple linear regression in industrial loblolly pine (Pinus taeda L.) plantations in the southeastern United States. The study sites for this project were part of a long-term, loblolly pine thinning study maintained by the Loblolly Pine Growth and Yield Research Cooperative at Virginia Tech. Measurements included piece size, position, and decay class. Samples of CWD were collected and analyzed to determine their mass and density. Decomposition rate of CWD was significantly different across position classes and decay classes: disk decomposition rates were significantly negatively correlated with disk diameter, large and small end piece diameter, estimated disk height, and disk dry weight. Average annual precipitation and average annual temperature were not significantly correlated with CWD disk decomposition rate. / Master of Science

Many experimental problems in the natural sciences result in data which can best be represented by linear combinations of exponentials of the form f(t) = ∑[with p above and k=1 below] α_k e^-λ_kt. Among such problems are those dealing with growth, decay, ion concentration, and survival and mortality. Also, in general, the solution to any problem which may be represented by linear differential equations with constant coefficients is a linear combination of exponentials. In most problems like those which have been mentioned, the parameters α_k and λ_k have biological or physical significance. Therefore, in fitting the. function f(t) to the data it is not only necessary that the function approximate the data closely, but it is also necessary that the parameters α_k and λ_k be accurately estimated. Furthermore, a measure of the accuracy of the estimation of the parameters is required. A new estimation procedure for linear combinations of exponentials is developed in this paper. Unlike the iterative maximum likelihood and least-squares methods for estimating the parameters for such a model, the new procedure is noniterative and can be easily applied. Also, in contrast to other non-iterative methods, error estimates are available for the parameter estimates yielded by the new procedure. In the model for the new procedure the points t_i at which observations are taken are assumed to be equally spaced and the number of such points is specified to be an integral multiple of the number of parameters to be estimated. Moreover, each observation is specified to have expectation f (t_i), where f is the function mentioned earlier. The coefficients α_k are assumed to be non-zero and the exponents λ_k are assumed to be distinct and positive. Then in the derivation of new procedure, the observations are reduced to as many sums as there are parameters to be estimated. Each of these sums is equated to its expected value and the resultant equations are solved for estimators of the parameters. The estimators from the new procedure are shown to be asymptotically normally distributed as either the number of points at which observations are taken or the number of observations made at each such point approaches infinity. The asymptotic variances obtained are used to form approximate confidence limits for the α_k and λ_k. The statistical properties of the estimators are also studied. It is found that they are consistent, but not in general unbiased or efficient. Asymptotic efficiencies are calculated tor a few sets of parameter values and a bias approximation is obtained for two special cases. The new method is also shown to be optimum relative to certain similar methods and necessary conditions for the new procedure to lead to admissible estimates are studied. In the last portion of the thesis a sampling study is reported for observations generated with a model containing only one exponential term and with errors which are normally distributed. The small sample biases and variances for the estimates computed from these observations are given and the effects of changes in the parameters in the model are investigated. Then some actual experimental data are fitted using both the new procedure and some alternative methods. The final chapter in the body of the thesis contains a critical evaluation of the new procedure relative to other estimation methods. / Ph. D.

No description available.

Cette thèse concerne quelques problèmes liés à la répartition des entiers sans facteur carré dansles progressions arithmétiques. Ces problèmes s’expriment en termes de majorations du terme d’erreurassocié à cette répartition.Les premier, deuxième et quatrième chapitres sont concentrés sur l’étude statistique des termesd’erreur quand on fait varier la progression arithmétique modulo q. En particulier on obtient une formuleasymptotique pour la variance et des majorations non triviales pour les moments d’ordre supérieur. Onfait appel à plusieurs techniques de théorie analytique des nombres comme les méthodes de crible et lessommes d’exponentielles, notamment une majoration récente pour les sommes d’exponentielles courtesdue à Bourgain dans le deuxième chapitre.Dans le troisième chapitre on s’intéresse à estimer le terme d’erreur pour une progression fixée. Onaméliore un résultat de Hooley de 1975 dans deux directions différentes. On utilise ici des majorationsrécentes de sommes d’exponentielles courtes de Bourgain-Garaev et de sommes d’exponentielles torduespar la fonction de Möbius dues à Bourgain et Fouvry-Kowalski-Michel. / This thesis concerns a few problems linked with the distribution of squarefree integers in arithmeticprogressions. Such problems are usually phrased in terms of upper bounds for the error term relatedto this distribution.The first, second and fourth chapter focus on the satistical study of the error terms as the progres-sions varies modulo q. In particular we obtain an asymptotic formula for the variance and non-trivialupper bounds for the higher moments. We make use of many technics from analytic number theorysuch as sieve methods and exponential sums. In particular, in the second chapter we make use of arecent upper bound for short exponential sums by Bourgain.In the third chapter we give estimates for the error term for a fixed arithmetic progression. Weimprove on a result of Hooley from 1975 in two different directions. Here we use recent upper boundsfor short exponential sums by Bourgain-Garaev and exponential sums twisted by the Möbius functionby Bourgain et Fouvry-Kowalski-Michel.

Neste trabalho, estudamos uma generalização dos semigrupos gradientes, os semigrupos gradiente-like, algumas de suas propriedades e a sua invariância por pequenas perturbações; isto é, pequenas perturbações de sistemas gradiente-like continuam sendo gradiente-like. Como consequência da caracterização dos atratores para este tipo de sistema, estudamos a atração exponencial de atratores. Por fim, estudamos o concetio de dimensão de Hausdorff e dimensão fractal de atratores e apresentamos alguns resultados sobre este assunto, e estudamos a construção de uma nova classe de atratores, os atratores exponenciais fractais / In this work, we study a generalization of gradient discrete semigroups, the gradientlike semigroups, some of its properties and its invariance under small perturbations; that is, small perturbations of gradient-like semigroups are still gradient-like semigroups. As a consequence of the characterization of the attractors for this sort of semigroups, we study the exponential attraction of attractors. Finally, we study some concepts of Hausdorff dimension and fractal dimension and present some results about this subject, and we studied the construction of a new class of attractors, the exponential fractal attractors

I denna rapport presenteras ett tillvägagångssätt för att hitta och datera brytpunkter i tidsserier. En brytpunkt definieras av det datum då det skett en stor nivåförändring i tidsserien. Det presenteras även en strategi för att skatta effekten av daterade brytpunkter. Genom att analysera tidsserier över AFA Försäkrings ärendeinflöde visar det sig att brytpunkter i tidsserien sammanfaller med exogena händelser som kan ha orsakat dessa brytpunkter, till exempel villkors- eller lagförändringar inom försäkringsbranschen. Rapporten visar att det genom ett metodiskt angreppssätt går att skatta effekten av en exogen händelse. Dessa skattade effekter kan användas vid framtida prognoser då en liknande förändring förväntas inträffa. Dessutom skapas prognoser över ärendeinflödet två år framåt med olika tidsseriemodeller.