Sensitivity Analysis of Water Flooding Optimization by Dynamic Optimization

Abstract

This study concerns the scope to improve water flooding in heterogeneous reservoirs. We used an existing, in-house developed, optimization program consisting of a reservoir simulator in combination with an adjoint-based optimal control algorithm. In particular we aimed to examine the scope for optimization in a two-dimensional horizontal reservoir containing a single high permeable streak, as a function of reservoir and fluid parameters, which we combined in the form of 10 dimensionless parameters. We defined the parameter NPVimprovement to indicate the improvement in net present value (NPV) that can be achieved through optimization. For initial screening of the effect of the dimensionless parameters, a two-level D-optimal design of experiments (DOE) technique was used to obtain a linear response surface model with the aid of 11 water-flooding simulations. As a result 8 dimensionless groups were selected for more detailed analysis, and a full quadratic NPVimprovement model was constructed using a three-level D-optimal design using 50 simulations. It should be reminded that all the D-optimal matrix designs were generated by using commands of statistics Toolbox of MATLAB software. Finally, Pareto charts were plotted to visualize the sensitivity of the model as a function of the dimensionless parameters. Based on the present model we can draw the conclusion that the parameters (relative streak length), (relative streak permeability) and the ratio of water cost and oil price have the largest effect on the scope for obtaining a high value of NPVimprovement.

Keywords

• water flooding optimization
• dynamic optimization
• design of experiments
• multiple linear regression
• response surface model
• npvimprovement