With the depletion of the existing reservoirs and the decline in oil discoveries during the last few decades, enhanced oil recovery (EOR) methods have gained a lot of attention. Among the various improved recovery methods, waterflooding is by far the most widely used. However, the presence of reservoir heterogeneity such as high permeability streaks often leads to premature breakthrough and poor sweep resulting in reduced oil recovery. This underscores the need for a prudent reservoir management, in terms of optimal production and injection rates, to maximize recovery. The increasing deployment of smart well completions and i-field has inspired many researchers to develop algorithms to optimize the production/injection rates along intervals of smart wells. However, the application of rate control for other EOR methods has been relatively few. This research aims to extend previous streamline-based rate optimization workflow to polymer flooding and CO2 flooding. The objective of the approach is to maximize sweep efficiency and minimize recycling of injected fluid (polymer/CO2) by delaying its breakthrough. This is achieved by equalizing the front arrival time at the producers using streamline time-of-flight. Arrival time is rescaled to allow for optimization after breakthrough of injected fluid. Additionally, we propose an accelerated production strategy to increase NPV over sweep efficiency maximization case. The optimization is performed under operational and facility constraints using a sequential quadratic programming approach. The geological uncertainty has been accounted via a stochastic optimization framework based on the combination of the expected value and variance of a performance measure from multiple realizations. Synthetic and field examples are used extensively to demonstrate the practical feasibility and robustness of our approach for application to EOR processes.

[pt] Estudos econômicos de áreas com indícios de hidrocarbonetos estão imersos em incertezas de diferentes naturezas (geológicas, de engenharia e econômicas). No início do estudo, aspectos da geologia, dos fluidos, das rochas e do reservatório só são conhecidos por métodos indiretos que fornecem informações imprecisas. A redução dessas incertezas é limitada pelos elevados custos de perfuração de poços que permitam testes diretos. Conseqüentemente, decisões de investimentos de exploração têm que ser tomadas sob risco motivando, assim, o desenvolvimento de métodos para a avaliação econômica probabilística de propriedades. O foco desta dissertação é a avaliação econômica probabilística de recursos petrolíferos, antes da perfuração do poço pioneiro. O cálculo do valor econômico de uma propriedade depende das estimativas dos perfis temporais de receitas e custos associados ao seu desenvolvimento e produção (D e P). A obtenção de tais elementos requer um projeto de D e P para a propriedade que, em função dos dados disponíveis, é menos detalhado do que um projeto de simulação multicelular. Nesta dissertação, uma metodologia de avaliação baseada em simulação de Monte Carlo é apresentada juntamente com uma implementação- protótipo. A realização das numerosas replicações, necessárias para se obter uma avaliação probabilística, se torna viável graças a um programa capaz de gerar o projeto de D e P automaticamente. Esse programa foi desenvolvido pela Petrobras com base em regras fornecidas por um especialista. Além da justificativa para a abordagem adotada, da descrição e implementação do método, são feitas considerações sobre distribuições de probabilidade para codificar incertezas e sobre os resultados dos testes iniciais do sistema protótipo. / [en] Economics studies of areas with indications of hydrocarbons are submerged in uncertainties of assorted natures (geological, of engineering and economical). At the start of the study, aspects concerning the geology, the fluids, the rocks and the reservoir are only known through indirect methods that yield imprecise information. The reduction of these uncertainties is limited by high costs of drilling wells that allow direct tests. Consequently, decisions on exploration investments have to be made under risk. This motivates the development of methods for probabilistic economic evaluation of properties. This dissertation addresses the probabilistic economic evaluation of petroleum resources, prior wildcat well drilling. Assessing the economic value of a property depends on estimates of incomes and costs time profiles associated to its development and production (D and P). Obtaining such elements requires a D and P project for the property that, due to the limited data available, is less detailed than a multi- cellular simulation project. In this thesis, a probabilistic evaluation methodology based on Monte Carlo simulation is presented along with a prototype implementation. Performing the numerous replications necessary to obtain a probabilistic evaluation becomes feasible thanks to a procedure capable of automatically generating the D and P project. That procedure was developed by Petrobras based on heuristic rules supplied by an expert. In addition to a justification for the proposed approach, the description of the method and its implementation, comments are made on probability density functions used for encoding uncertainties, and on the results of the initial tests with the prototype system.

Waterflood optimization via rate control is receiving increased interest because of rapid developments in the smart well completions and I-field technology. The use of inflow control valves (ICV) allows us to optimize the production/injection rates of various segments along the wellbore, thereby maximizing sweep efficiency and delaying water breakthrough. It is well recognized that field scale rate optimization problems are difficult because they often involve highly complex reservoir models, production and facilities related constraints and a large number of unknowns. Some aspects of the optimization problem have been studied before using mainly optimal control theory. However, the applications to-date have been limited to rather small problems because of the computation time and the complexities associated with the formulation and solution of adjoint equations. Field-scale rate optimization for maximizing waterflood sweep efficiency under realistic field conditions has still remained largely unexplored. We propose a practical and efficient approach for computing optimal injection and production rates and thereby manage the waterflood front to maximize sweep efficiency and delay the arrival time to minimize water cycling. Our work relies on equalizing the arrival times of the waterfront at all producers within selected sub-regions of a water flood project. The arrival time optimization has favorable quasi-linear properties and the optimization proceeds smoothly even if our initial conditions are far from the solution. We account for geologic uncertainty using two optimization schemes. The first one is to formulate the objective function in a stochastic form which relies on a combination of expected value and standard deviation combined with a risk attitude coefficient. The second one is to minimize the worst case scenario using a min-max problem formulation. The optimization is performed under operational and facility constraints using a sequential quadratic programming approach. A major advantage of our approach is the analytical computation of the gradient and Hessian of the objective which makes it computationally efficient and suitable for large field cases. Multiple examples are presented to support the robustness and efficiency of the proposed optimization scheme. These include several 2D synthetic examples for validation purposes and 3D field applications.

[pt] A definição da estratégia de produção de petróleo é uma tarefa muito importante que consiste em um processo bastante complexo devido à grande quantidade de variáveis envolvidas. Estas variáveis estão relacionadas com características geológicas, fatores econômicos e decisões como alocação de poços, número de poços produtores e injetores, condições operacionais e cronograma de abertura de poços. No contexto da otimização da produção de petróleo, o objetivo é encontrar a melhor configuração de poços que contribua para maximizar, na maioria dos casos, o valor presente líquido (VPL). Esse valor é calculado, principalmente, a partir do óleo, gás e água produzidos do campo, que são encontrados através do uso do simulador de reservatórios. Porém, vários parâmetros e variáveis devem ser prefixados e inseridos no sistema de simulação para que esses valores de produção sejam previstos. Esse processo geralmente exige um alto custo computacional para modelar as transferências de fluidos dentro do reservatório simulado. Assim, o uso de simuladores pode ser substituído por aproximadores. Neste estudo, eles são desenvolvidos através da Programação Genética Linear com Inspiração Quântica, uma técnica da Computação Evolucionária. Esses aproximadores serão utilizados para substituir a simulação do reservatório no processo de otimização da localização e tipo de poços a serem perfurados em um campo petrolífero. Para a construção dos proxies de reservatório, as amostras, originadas utilizando a técnica do Hipercubo Latino, foram simuladas para a criação da base de dados. O modelo para criação de aproximadores foi testado em um reservatório sintético. Dois tipos de otimização foram realizados para a validação do modelo. A primeira foi a otimização determinística e a segunda uma otimização sob incerteza considerando três diferentes cenários geológicos, um caso onde o número de simulações é extremamente alto. Os resultados encontrados apontam que o modelo para a criação de proxies consegue bom desempenho na substituição dos simuladores devido aos baixos erros encontrados e na considerável redução do custo computacional. / [en] The purpose of oil production strategy in the context of production optimization is to find the best configuration of wells that contributes to maximizing the Net Present Value. This value is calculated mainly from the amount of oil, gas, and water recovered from the field, which can be obtained by running the reservoir simulator. However, many parameters and variables must be prefixed and inserted into the simulation system in order to generate these production values. This process involves a high computational cost for modeling the transfer of fluids within the simulated reservoir. Thus, the use of simulators may be substituted by approximators. In this thesis, we aim to develop these approximators using Quantum-Inspired Linear Genetic Programming, a technique of Evolutionary Computation. These approximators were used to replace the reservoir simulation in the process of optimizing the location and type of wells to be drilled in a field. For the reservoir proxies construction, samples obtained from the technique of Latin Hypercube were simulated to create the database. The model for creating approximators was tested on a synthetic reservoir. Two types of optimization were performed to validate the model. The first was a deterministic optimization and the second an optimization under uncertainty considering three different geological settings, a situation in which the number of simulations becomes extremely high. Our results indicated that the model for the creation of proxies achieves a satisfactory performance in the replacement of simulators due to low levels of errors and a considerable reduction of the computational cost.