Stochastic programming approaches for the optimal development of gas fields under uncertainty

This dissertation addresses the problem of optimizing decisions in the presence of uncertainty, given that the optimization decisions determine the times when uncertainties in some of the parameters will be resolved. Chapter 1 presents a review of optimal planning for the development of oil and gas fields. A brief discussion of stochastic programming as an approach for optimal decision-making under uncertainty is also presented. Chapter 2 addresses the problem of optimal planning under uncertainty where the times when the uncertainties in some of the parameters will be resolved depend on the optimization decisions. For such problems, the scenario tree depends on the optimization decisions. We present a novel mixed-integer disjunctive programming model where the decision-dependence of the scenario tree is modeled by conditional non-anticipativity constraints. A set of theoretical properties satisfied by every feasible solution of the proposed model is presented and used to achieve significant reduction in the size of the model without altering the feasible space. Chapter 3 presents a Lagrangean duality based branch and bound algorithm for solving the model of Chapter 2 efficiently and rigorously. Lower bounds at each node of this branch and bound algorithm are generated by solving a Lagrangean dual problem where the non-anticipativity constraints have been relaxed. Infeasibilities in the solution of the Lagrangean dual are eliminated by branching on the violated non-anticipativity constraints. Chapter 4 addresses the optimal development of gas fields under uncertainty in reserves. In this problem, the uncertainty in the reserves of a field is resolved only when capital investment is carried out at the field. The model presented in Chapter 2 is specialized to this problem. A heuristic algorithm for solving the model approximately is also presented. This algorithm restricts the search to solutions where investment at a field that has some associated uncertainty takes place in the same year in all scenarios. It is shown that this algorithm will give the optimal solution of the model for problems that involve only one uncertain field. Chapter 5 specializes the theoretical properties presented in Chapter 2 and the branch and bound algorithm presented in Chapter 3 to the gas field problem. A new theoretical property specific to the gas field problem is also presented. Finally, Chapter 6 summarizes the major contributions of this dissertation and indicates promising directions for future work.