Optimization of the Water-Flooding Process in a Small 2D Horizontal Oil Reservoir by Direct Transcription

Optimization of the Water-Flooding Process in a Small 2D Horizontal Oil Reservoir by Direct Transcription

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Abstract

The water flooding optimization problem is an important challenge in reservoir engineering, and is often approached using adjoint-based techniques. Optimal control theory, using an adjoint formulation, offers an efficient way to obtain gradients of an objective function with respect to the control inputs. However, a known limitation in this approach is the difficulty of systematically incorporating constraints. In this work, the system is fully discretized in space and time into a large-scale nonlinear program, with an objective function and a set of constraints representing the model equations. This simultaneous method is commonly termed direct transcription, and allows a simultaneous approach to the optimization problem. The approach relies on effective general purpose optimization solvers for an optimal control policy and does not require repeated simulation of the system. Constraints are given either as bounds on variables or as more complex expressions, such as limits on power consumption, implemented as equalities or inequalities. The approach we suggest here is well suited to handle such path constraints. We also present a smooth approximation to upstream weighting of relative permeabilities to avoid the use of integer variables in the optimization problem.
Content

The water flooding optimization problem is an important challenge in reservoir engineering, and is often approached using adjoint-based techniques. Optimal control theory, using an adjoint formulation, offers an efficient way to obtain gradients of an objective function with respect to the control inputs. However, a known limitation in this approach is the difficulty of systematically incorporating constraints. In this work, the system is fully discretized in space and time into a large-scale nonlinear program, with an objective function and a set of constraints representing the model equations. This simultaneous method is commonly termed direct transcription, and allows a simultaneous approach to the optimization problem. The approach relies on effective general purpose optimization solvers for an optimal control policy and does not require repeated simulation of the system. Constraints are given either as bounds on variables or as more complex expressions, such as limits on power consumption, implemented as equalities or inequalities. The approach we suggest here is well suited to handle such path constraints. We also present a smooth approximation to upstream weighting of relative permeabilities to avoid the use of integer variables in the optimization problem. The method is demonstrated by solving a test problem.

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