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.

Esta dissertação de mestrado aborda o problema de regulação robusta recursiva para sistemas lineares discretos sujeitos a incertezas paramétricas. Um novo funcional quadrático, baseado na combinação de função penalidade e função custo do tipo jogos, é projetado para lidar com este problema. Uma característica interessante desta abordagem é que a recursividade pode ser realizada sem a necessidade do ajuste de parâmetros auxiliares. Bastante útil para aplicações online. A solução proposta é baseada numa equação recursiva de Riccati. Também, a convergência e a estabilidade do regulador para o sistema linear incerto invariante no tempo são garantidas. / This dissertation deals with robust recursive regulators for discrete-time systems subject to parametric uncertainties. A new quadratic functional based on the combination of penalty functions and game theory is proposed to solve this class of problems. An important issue of this approach is that the recursiveness can be performed without the need of adjusting auxiliary parameters. It is useful for online applications. The solution proposed is based on Riccati equation which guarantees the convergence and stability of the time-invariant system.

Esta dissertação de mestrado aborda o problema de regulação robusta recursiva para sistemas lineares discretos sujeitos a incertezas paramétricas. Um novo funcional quadrático, baseado na combinação de função penalidade e função custo do tipo jogos, é projetado para lidar com este problema. Uma característica interessante desta abordagem é que a recursividade pode ser realizada sem a necessidade do ajuste de parâmetros auxiliares. Bastante útil para aplicações online. A solução proposta é baseada numa equação recursiva de Riccati. Também, a convergência e a estabilidade do regulador para o sistema linear incerto invariante no tempo são garantidas. / This dissertation deals with robust recursive regulators for discrete-time systems subject to parametric uncertainties. A new quadratic functional based on the combination of penalty functions and game theory is proposed to solve this class of problems. An important issue of this approach is that the recursiveness can be performed without the need of adjusting auxiliary parameters. It is useful for online applications. The solution proposed is based on Riccati equation which guarantees the convergence and stability of the time-invariant system.

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