# Surrogate-Based Optimization

Activitties:

The main focus of this research is life cycle reservoir management by rate control optimization. The design variables, the controls, are total fluid rates at producer wells and water injector rates at injectors. The objective function is the net present value (NPV) for the life cycle, i.e., the whole concession period. Traditionally the total concession period is subdivided into a pre-determined number of time intervals where the rates are to be optimally computed. These rates are the design variables and each time interval constitutes a control cycle. The objective function evaluation requires a complete simulation, which is numerically expensive. The usual technique to tackle this kind of problem is to replace the numerical (high fidelity) function with a surrogate function that follows well the trends of the high fidelity function, is numerically cheap to compute and has the additional benefit of being smooth, which partially tames the possible numerical noise of the simulation. In the above context the following research topics will be further investigated. All simulation work will be performed using CMG current software.

- Tuning of SAO parameters

Sequential approximate optimization (SAO) is a local strategy where the original optimization problem is decomposed into a sequence of optimization sub-problems, confined into a small sub-region (trust region ) of the design space. An initial trust region size has to be set and in the sequence of each optimization sub-problem its size is updated according to accuracy checks between the high fidelity and surrogate models. A number of parameters have to be set which depend on the size and type of the investigated problem. Specifically we plan to study the following parameters:- Initial trust region size;
- Number of samples at each SAO iteration;
- Reuse of previously computed samples;
- Point selection strategy to minimize predictor variance;
- Tolerance setting of both simulator and SAO strategy;
- Comparative study of different solvers for the surrogate optimization problem.

- Alternate Definition of design variables

Critical changes of control rates are associated with water breakthrough at producers. We therefore intend to optimally determine the duration of the control cycles. This, in turn, results in two distinct types of design variables: fluids rates and time of switching of control cycles. This may drastically reduce the number of design variables and therefore the required optimization time without significant deterioration of the solution accuracy.

- Hybrid Optimization Strategies

SAO techniques are local, i.e., it tends to find the closest local optimum to the starting design point. However some reservoir engineering problems are known to be multimodal, i.e., they have multiple local optima. Global strategies search the design space for the global solution. Global solutions are much harder to be obtained demanding much higher computational effort. This is compounded by the dimensionality of the problem. A usual approach to overcome the above drawbacks is to couple global and local searches: the method starts out with a global search to bring the initial design to the optimal basin of attraction followed by a local algorithm to efficiently converge to the optimal solution. This is called a hybrid strategy. We plan to couple the above SAO techniques with global searches using evolutionary algorithms or algorithms based on bayesian analysis.

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