Reservoir Flooding Optimization by Control Polynomial Approximations

In this dissertation, we provide novel parametrization procedures for water-flooding production optimization problems, using polynomial approximation techniques. The methods project the original infinite dimensional controls space into a polynomial subspace. Our contribution includes new parameterization formulations using natural polynomials, orthogonal Chebyshev polynomials and Cubic spline interpolation. We show that the proposed methods are well suited for black-box approach with stochastic global-search method as they tend to produce smooth control trajectories, while reducing the solution space size. We demonstrate their efficiency on synthetic two-dimensional problems and on a realistic 3-dimensional problem. By contributing with a new adjoint method formulation for polynomial approximation, we implemented the methods also with gradient-based algorithms. In addition to fine-scale simulation, we also performed reduced order modeling, where we demonstrated a synergistic effect when combining polynomial approximation with model order reduction, that leads to faster optimization with higher gains in terms of Net Present Value. Finally, we performed gradient-based optimization under uncertainty. We proposed a new multi-objective function with three components, one that maximizes the expected value of all realizations, and two that maximize the averages of distribution tails from both sides. The new objective provides decision makers with the flexibility to choose the amount of risk they are willing to take, while deciding on production strategy or performing reserves estimation (P10;P50;P90)

Optimal control problems solved via swarm intelligence

Questa tesi descrive come risolvere problemi di controllo ottimo tramite swarm in telligence. Grande enfasi viene posta circa la formulazione del problema di controllo ottimo, in particolare riguardo a punti fondamentali come l’identificazione delle incognite, la trascrizione numerica e la scelta del risolutore per la programmazione non lineare. L’algoritmo Particle Swarm Optimization viene preso in considerazione e la maggior parte dei problemi proposti sono risolti utilizzando una formulazione differential flatness. Quando viene usato l’approccio di dinamica inversa, il problema di ottimo relativo ai parametri di trascrizione è risolto assumendo che le traiettorie da identificare siano approssimate con curve B-splines. La tecnica Inverse-dynamics Particle Swarm Optimization, che viene impiegata nella maggior parte delle applicazioni numeriche di questa tesi, è una combinazione del Particle Swarm e della formulazione differential flatness. La tesi investiga anche altre opportunità di risolvere problemi di controllo ottimo tramite swarm intelligence, per esempio usando un approccio di dinamica diretta e imponendo a priori le condizioni necessarie di ottimalitá alla legge di controllo. Per tutti i problemi proposti, i risultati sono analizzati e confrontati con altri lavori in letteratura. Questa tesi mostra quindi the algoritmi metaeuristici possono essere usati per risolvere problemi di controllo ottimo, ma soluzioni ottime o quasi-ottime possono essere ottenute al variare della formulazione del problema.This thesis deals with solving optimal control problems via swarm intelligence. Great emphasis is given to the formulation of the optimal control problem regarding fundamental issues such as unknowns identification, numerical transcription and choice of the nonlinear programming solver. The Particle Swarm Optimization is taken into account, and most of the proposed problems are solved using a differential flatness formulation. When the inverse-dynamics approach is used, the transcribed parameter optimization problem is solved assuming that the unknown trajectories are approximated with B-spline curves. The Inverse-dynamics Particle Swarm Optimization technique, which is employed in the majority of the numerical applications in this work, is a combination of Particle Swarm and differential flatness formulation. This thesis also investigates other opportunities to solve optimal control problems with swarm intelligence, for instance using a direct dynamics approach and imposing a-priori the necessary optimality conditions to the control policy. For all the proposed problems, results are analyzed and compared with other works in the literature. This thesis shows that metaheuristic algorithms can be used to solve optimal control problems, but near-optimal or optimal solutions can be attained depending on the problem formulation

Optimal designs for comparing curves

We consider the optimal design problem for a comparison of two regression curves, which is used to establish the similarity between the dose response relationships of two groups. An optimal pair of designs minimizes the width of the confidence band for the difference between the two regression functions. Optimal design theory (equivalence theorems, efficiency bounds) is developed for this non standard design problem and for some commonly used dose response models optimal designs are found explicitly. The results are illustrated in several examples modeling dose response relationships. It is demonstrated that the optimal pair of designs for the comparison of the regression curves is not the pair of the optimal designs for the individual models. In particular it is shown that the use of the optimal designs proposed in this paper instead of commonly used "non-optimal" designs yields a reduction of the width of the confidence band by more than 50%.Comment: 27 pages, 3 figure

Digital Filters and Signal Processing

Digital filters, together with signal processing, are being employed in the new technologies and information systems, and are implemented in different areas and applications. Digital filters and signal processing are used with no costs and they can be adapted to different cases with great flexibility and reliability. This book presents advanced developments in digital filters and signal process methods covering different cases studies. They present the main essence of the subject, with the principal approaches to the most recent mathematical models that are being employed worldwide

Inverse Geometry Design of Radiative Enclosures Using Particle Swarm Optimization Algorithms

Three different Particle Swarm Optimization (PSO) algorithms—standard PSO, stochastic PSO (SPSO) and differential evolution PSO (DEPSO)—are applied to solve the inverse geometry design problems of radiative enclosures. The design purpose is to satisfy a uniform distribution of radiative heat flux on the designed surface. The design surface is discretized into a series of control points, the PSO algorithms are used to optimize the locations of these points and the Akima cubic interpolation is utilized to approximate the changing boundary shape. The retrieval results show that PSO algorithms can be successfully applied to solve inverse geometry design problems and SPSO achieves the best performance on computational time. The influences of the number of control points and the radiative properties of the media on the retrieval geometry design results are also investigated

Parametric Model Order Reduction For Optimization in Closed Loop Field Development Using Machine Learning Techniques

Field development workflows consist of production optimization and data assimilation procedures that require running large number of reservoir simulations for fine scale models. Recent advancements in parallel computing and accelerated solvers have reduced simulation times for such high-fidelity models, however, repeated simulations and underlying complex non-linearities involved in multiphase and multicomponent models still remain a bottleneck. This computational challenge has motivated the development of Model Order Reduction (MOR) techniques which provide low dimensional representation of high-fidelity models and thus provide significant computational savings with the efforts to preserve the accuracy of simulation outputs. The aim of my research is to develop projection based MOR workflows for optimization problems in closed loop field development procedure, which include well control optimization and well placement optimization. We pose the problem formulation as Parametric Model Order Reduction (PMOR) that allows for taking into consideration a system parameter for each optimization problem considered. For developing Reduced Order Models (ROMs) for such problems, we use projection based Proper Orthogonal Decomposition (POD) which enables representation of reservoir state variables in terms of highly reduced set of variables. First part of the research is based on developing ROMs for well control optimization problem, where we look for the optimal strategy to control the wells settings. Here we use DEIM in addition to POD for quick evaluation of non-linear functions. We introduce a novel training procedure for global ROM during control optimization, which proved to give accurate results when compared to optimization using fine scale simulations. We test the performance of POD-DEIM for different optimization parameterization methods like polynomial and piecewise polynomial approximations on a waterflooding scenario. Polynomial approximation of BHP control served as good training sets for POD-DEIM with the training strategy proposed leading to accurate and fast reduced model. The second part of my research, which is a major contribution of my work, is based on developing ROMs for changing well locations during well placement optimization problem. Here, we do not employ proposed MOR on well location optimization problem, rather develop MOR strategies as a precursor to be used for well location optimization in future. Projection based reduced order modeling methodologies for well control optimization have reached a good level of maturity, however, MOR development for changing well configurations, is unexplored. We first propose error based local PMOR for new well location using a Machine Learning (ML) framework with POD. ML algorithms like Neural Networks and Random Forests help us predict the ROM error that eventually will choose appropriate basis at a new well location from previously computed reduced models. We introduce geometry based features and physics based flow diagnostics features to train ML models. In efforts to tackle the issues with local PMOR technique proposed, we introduce a novel global non-intrusive PMOR technique based on machine learning. The idea here is to represent the entire parameter space of well location by a single global ROB and then using ML model to establish a relation between the input well location information and the POD basis coefficients of each state. We then also formulate the error correction model based on the reduced model solution, to account for solution discrepancies. The proposed method, that can make use of parallel resources efficiently, shows promising results on waterflooding case studies in predicting various quantities of interest (QoI) at new well locations such as oil production rates and water cut, and showed significant speedups of one to two orders of magnitude for the test cases

Modeling and Optimization of Dynamical Systems in Epidemiology using Sparse Grid Interpolation

Infectious diseases pose a perpetual threat across the globe, devastating communities, and straining public health resources to their limit. The ease and speed of modern communications and transportation networks means policy makers are often playing catch-up to nascent epidemics, formulating critical, yet hasty, responses with insufficient, possibly inaccurate, information. In light of these difficulties, it is crucial to first understand the causes of a disease, then to predict its course, and finally to develop ways of controlling it. Mathematical modeling provides a methodical, in silico solution to all of these challenges, as we explore in this work. We accomplish these tasks with the aid of a surrogate modeling technique known as sparse grid interpolation, which approximates dynamical systems using a compact polynomial representation. Our contributions to the disease modeling community are encapsulated in the following endeavors. We first explore transmission and recovery mechanisms for disease eradication, identifying a relationship between the reproductive potential of a disease and the maximum allowable disease burden. We then conduct a comparative computational study to improve simulation fits to existing case data by exploiting the approximation properties of sparse grid interpolants both on the global and local levels. Finally, we solve a joint optimization problem of periodically selecting field sensors and deploying public health interventions to progressively enhance the understanding of a metapopulation-based infectious disease system using a robust model predictive control scheme