Development and application of multiobjective steepest descent method for water flooding optimization

Xin Liu

Multiobjective optimization has gained increasing attention in the reservoir simulation/optimization community. One of several important biobjective problems involved the potentially conflicting objectives of maximizing the long-term and maximizing the short term net-present value, and we focus on this this biobjective optimization problem. We also consider this problem in the presence of nonlinear (state) constraints which adds complications but is of immense practical importance for field applications.

The gradient-based steepest descent method provides an efficient method for biobjective optimization. Here, we show that an additional computational efficiency gain on the order of 50% can be made by replace a backtracking line search method that has been used in previous implementations by a procedure where the line search step size is systematically generated as the analytical solution of a min-max problem arising from the a quadratic interpolation of each objective function in the direction of its gradient.

Secondly, we provide a theorem which we recently proved that provides the multiobjective steepest descent search direction for an arbitrary number of objective functions. As a novel application of this method, we consider the set of nonlinear constraints as the third objective where the first two objectives are the maximization of the life-cycle NPV and short-term NPV of production.

The theorem that provides a means to analytically compute the multiobjective steepest descent direction enables the consideration of multiobjective optimization problems such as one where the objectives are to maximize long-term NPV, maximize short-term NPV and minimize risk such that bound, linear and nonlinear constraints are satisfied.

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