A branch-and-price algorith, for a compressor scheduling problem

This work presents the study and application of a branch-and-price algorithm for solving a compressor scheduling problem. The problem is related to oil production and consists of defining a set of compressors to be activated, supplying the gas-lift demand of a set of wells and minimizing the associated costs. The problem has a non-convex objective function, to which a piecewise-linear formulation has been proposed. This dissertation proposes a column generation approach based on the Dantzig-Wolfe decomposition, which achieves tighter lower bounds than the straightforward linear relaxation of the piecewise-linear formulation. The column generation was embedded in a branch-and-price algorithm and further compared with CPLEX, obtaining optimal solutions in lesser time for a set of instances. Further, the branch-and-price algorithm can find better feasible solutions for large instances under a limited processing time.O presente trabalho realiza o estudo e aplicação de um algoritmo de branch-and-price para a resolução de um problema de escalonamento de compressores. O problema é ligado à produção petrolífera, o qual consiste em definir um conjunto de compressores a serem ativados para fornecer gas de elevação a um conjunto de poços, atendendo toda demanda e minimizando os custos envolvidos. O problema é caracterizado por uma função objetivo não-convexa que é linearizada por partes de forma a ser formulada como um problema de programação inteira mista. A abordagem de geração de colunas é baseada na decomposição de Dantzig-Wolfe e apresenta melhores limitantes inferiores em relação à relaxação linear da formulação compacta. O branch-and-price é comparado ao solver CPLEX, sendo capaz de encontrar a solução ótima em menor tempo para um conjunto de instâncias, bem como melhores soluções factíveis para instâncias maiores em um período de tempo limitado

Deterministic global optimization approach to bilinear process network synthesis

Master'sMASTER OF ENGINEERIN

O problema da otimização do gás lift com alocação de poços aos separadores de produção

The development of optimization methodologies is very important for the production phase of an oil field, since small changes in the operational point can increase the revenue without adding costs. The objective of this work is to optimize the oil production at the arrival of the production unit considering the allocation of the wells to the production separators. The constraints are related to the water, oil and gas processing capacities. The decision variables are the gas-lift rate of the wells, the separators pressure and the allocation wells - separators. Thus, the problem is a mixed integer linear programming. The performance curves of the wells were linearized by SOS2 interpolation. These curves were generated by the own multiphase flow model simulation and using the same computational language (Pyhton) than the optimization. This same computational language enables a robust formulation to communicate the simulation and the optimization. The study concluded that the operational point, a result of optimization, is highly sensitive to platform capabilities. In addition, a quality of the manifold performance curve is most significant in more restricted production scenarios.O desenvolvimento de metodologias de otimização é de extrema importância para a área de produção de um campo petrolífero, uma vez que pequenas alterações no ponto operacional podem gerar incremento na receita sem adicionar custos. Este trabalho tem como objetivo fazer a otimização da produção de petróleo na chegada da unidade de produção considerando a alocação dos poços aos separadores de produção. As restrições consideradas no modelo são relacionadas às capacidades de processamento de água, óleo e gás nos separadores. As variáveis de decisão são a vazão de gás-lift dos poços, pressão dos separadores e a alocação dos poços aos separadores. Assim, o problema é de programação linear inteira mista. As curvas de desempenho dos poços foram linearizadas por meio de interpolação do tipo SOS2. Essas curvas foram geradas em um modelo de simulação da elevação e escoamento da produção próprio e de mesma linguagem computacional (Pyhton) que a otimização, o que possibilita a formulação de uma comunicação robusta entre a simulação e a otimização. O estudo concluiu que o ponto operacional, resultado da otimização, é altamente sensível às capacidades da plataforma. Além disso, a qualidade da curva de desempenho do manifold é mais importante em cenários de produção mais restritos

Otimização da produção de poços de petróleo com injeção contínua de gás e alinhamento poço-separador: modelos lineares por partes e algoritmos

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia de Automação e SistemasThe lift-gas allocation problem with well-separator routing constraints is a mixed-integer nonlinear program of considerable complexity. To this end, a mixed-integer linear formulation (compact) is obtained by piecewise-linearizing the nonlinear curves, using binary variables to express the linearization and routing decisions. A new formulation (integrated) combining the decisions on linearization and routing is developed by using a single type of binary variable. The structures of both formulations are explored to generate lifted cover cuts. Numerical tests show that the use of cutting planes in a cut-and-branch scheme accelerates the resolution time. The solution of the integrated formulation using cutting-plane generation is faster in spite of having more variables than the compact formulatio

Modelling, Aging and Optimal Operation of Lithium-ion Batteries

Energy storage has a big role to play in power systems across the world in order to integrate increasing amounts of intermittent renewable sources of energy. Among the different storage technologies, lithium-ion batteries exhibit favourable characteristics that make them suitable for power system applications. However, commercial success of lithium-ion battery based storage is limited not only for grid applications but also for electric vehicles. This is due to three inter-related factors - safety, price-performance ratio and lifetime, which largely offset the advantages that these batteries offer and impede their adoption for potential applications. Any improvement in these factors is tied to better understanding of the functioning and of the limits of these batteries. This work is an attempt to further this understanding using modelling and experimental means, such that the behaviour of these batteries can be predicted over their lifetime, and their operation can be optimized. The contributions of this thesis are three-fold, as described in the following paragraphs. A battery model that is not only able to accurately estimate the electrochemical but also the thermal behaviour of a lithium ion battery is important in order to keep track of performance and safety indices. To this end, a physics based pseudo 2D electrochemical-thermal model of a lithium iron phosphate battery is developed. Parameters for this model are determined through primary information from manufacturer, literature studies and experimental data analysis. The developed model accurately predicts the electrochemical and thermal behaviour of the battery for both charging and discharging conditions for a wide range of current rates. Heat generation in the cell is investigated using the validated model and the important role of reversible heat and the dominant role of graphite electrode is highlighted. The model is extended to determine thermal behaviour of module, pack and study different thermal management systems. Given that battery performance degrades over time, long-term accelerated aging tests are used to quantify calendar and cycle aging in commercial lithium nickel manganese cobalt oxide batteries. Capacity and impedance measurements, electrochemical impedance spectroscopy as well as post-mortem analysis are used to study aging. Calendar aging is analysed as a function of temperature and storage state of charge. In general, low temperatures and low states of charge cause less degradation in the battery. Considerable influence of the periodic characterization process on the calendar aging results is noticed. Cycle aging is analysed as a function of temperature, current rate, depth of discharge and state of charge. In general, fast aging in batteries is observed when they are operated at low temperatures, high current rates and around high states of charge. The effects of local potentials at the two electrodes and staging behaviour of graphite in causing capacity fade and increase in the resistances of the cell are elucidated. Finally, the integration of storage in power systems is investigated. Technically, lithium-ion batteries are found to be suitable for a variety of applications in power systems both at utility scale as well as for home storage. Their economic feasibility is however debatable and dependent on local market conditions. To optimally use batteries in power system applications, an accurate degradation model that takes into account the complex, non-linear dependence of battery aging on operating parameters is developed. A mixed integer linear program is formulated, which produces an optimal charge-discharge schedule for the energy storage when trading in electricity markets. This program optimizes the operation of battery systems considering the twin objectives of maximizing revenue from market transactions and minimizing degradation. Such a multi-objective approach yields a Pareto-front of feasible operating strategies putting onus on a decision maker to choose a desirable operational strategy for implementation

Formulações inteiras mistas para modelos lineares por partes multidimensionais: aplicações na otimização da produção de petróleo sob restrições de pressão

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro Tecnológico. Programa de Pós-Graduação em Engenharia de Automação e SistemasO problema de alocação de gás de injeção com restrições de alinhamento poço-manifold e restrições de pressão no sistema de produção é um problema não linear inteiro-misto de dificuldade considerável. A complexidade deste problema reside na natureza das decisões discretas do alinhamento e nas não linearidades presentes nas curvas de produção dos poços e de queda de pressão nas tubulações. A abordagem de solução utilizada neste trabalho é a reformulação deste problema em programas lineares inteiros-mistos com o uso de ferramentas de linearização por partes para funções multidimensionais. Foram desenvolvidas sete reformulações lineares inteiras-mistas, considerando aproximações por hipercubos e por simplexes. Enquanto a aproximação por hipercubos é mais simples e possui menos variáveis, a aproximação por simplexes possui mais variáveis, mas é mais detalhada. Foi apresentada uma análise computacional destas formulações para um cenário modelado a partir de um sistema de produção sintético construído com uma ferramenta de escoamento multifásico. Para avaliar o desempenho das formulações desenvolvidas, foram considerados cenários com diferentes disponibilidades de gás no compressor e diferentes qualidades de aproximação. Os resultados da análise computacional mostraram que, para as aproximações por hipercubos, o modelo SOS2 teve melhor desempenho na maioria dos cenários. Para as aproximações por simplexes, o modelo Log teve o melhor desempenho dentre os modelos. Considerando ambas aproximações, para um cenário com qualidade de aproximação fina e com uma restrição mais apertada na disponibilidade de gás de injeção, apenas o modelo Log conseguiu obter a solução ótima para o problema.The problem of allocating lift-gas to oil wells subject to well-manifold routing, and pressure constraints in the production system is a mixed-integer non-linear problem of considerable difficulty. The complexity of this problem rests on the nature of discrete decisions of the routing and the non linearities of the well production curves and pressure drops in the pipelines. The solution approach used in this work is the reformulation of this problem into mixed-integer linear programs with piecewise-linearization tools for multidimensional functions. Seven mixed-integer linear reformulations were developed with hypercube and simplex approximations. While the hypercube approximation is simpler and more compact, the simplex approximation has more variables, but is more accurate. A computational analysis of the application of these formulations to a synthetic production system represented in a multi-flow simulator is presented. In order to evaluate the performance of these formulations, instances with different availability of lift-gas in the compressor and different qualities of approximation were considered. The results of the computational analysis showed that the SOS2 model solved the problem faster in most instances of the hypercube approximation. With simplex approximations, the Log model was faster in all scenarios. Considering both approximations, when the quality of approximation is accurate and the lift-gas availability is low, only the Log model obtained the optimal solution

Modeling and optimization of liquefied natural gas process

Ph.DDOCTOR OF PHILOSOPH

Capacity expansion modelling to aid water supply investment decisions

Increasing population, economic development, and environmental changes imply that maintaining the water supply-demand balance will remain a top priority. Water resource systems may need to be expanded in order to respond to demand growth. Capacity expansion studies can be used to answer the question of what the optimal expansion size, timing and location of new infrastructure should be. This thesis develops and applies capacity expansion optimisation modelling approaches. We begin with the 'Economics of Balancing Supply and Demand’ (EBSD) planning framework used by the water industry since 2002 in England. The base model is formulated as a mixed integer linear programming optimisation model that selects the least cost annual schedule of supply and demand management options that meet forecasted demand over the planning horizon. Custom water saving profiles are allowed for demand management options. Multiple demand scenarios are considered to ensure the supply-demand balance is preserved under different demand conditions and that operating costs of selected options are accurately assessed. The base deterministic EBSD model is applied to the water companies of South East England (the WRSE area). Various extensions to the EBSD framework are then proposed and implemented. The model formulation is first expanded to incorporate a generic cost estimate for options not yet proposed in water company resources management plans. This allows to extend the WRSE network with new inter-company transfers for which costs are represented by a concave cost curve approximated by a piece-wise linear function. Considering additional interconnections allows evaluating the financial implications of further interconnectivity in the WRSE area. Next, an extension is proposed to improve the application of the stochastic version of the EBSD approach. The proposed method allows to identify the set of future capacity expansions that withstand uncertainty of supply and demand estimates and still achieve a required reliability. The method consists of an iterative process: at each iteration the EBSD optimisation model is run and the reliability of the solution set (supply-demand schedules) is tested under Monte Carlo simulation. Ad-hoc model constraints are introduced at each iteration to enable the EBSD model to exclude unreliable solutions identified at previous iterations. Next, the English price-cap regulatory process is represented within a modified EBSD model formulation. The model identifies future capacity expansions that maximise water company profit under constraints on the maximum price that can be charged to customers and on the allowed rate of return. The incentive schemes that the regulator uses to reward (or penalise) companies for out- (or under-) performance, are also represented. The goal is to help explain how the current regulatory system of incentives motivates water company investment decisions. Two further extensions are then presented in the appendixes. The first one allows the EBSD model formulation to be extended so that costs of activated schemes are accounted over the schemes’ useful life, beyond the typical 25-30 year planning horizon. This eliminates biased comparisons of schemes with different economic lifetimes. With the second extension, a diverse set of supply-demand schedules are generated, that solve the capacity expansion problem and are sufficiently ‘close’ (in terms of costs) to the least-cost solution. Generating multiple near-optimal solutions gives an idea of what alternative plans are available in addition to the leastcost one. This allows the consideration other un-modelled factors or strategic priorities in the decision making process