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Implementation of Trust-region Algorithm for Well Placement Optimization in FieldOpt Framework

Wang, Lingya
Master thesis
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URI
http://hdl.handle.net/11250/2453091
Date
2017
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  • Institutt for geovitenskap og petroleum [1840]
Abstract
Oil field development is a challenging engineering task that involves optimization

problems such as the types, numbers, scheduling, location, and controls of wells.

Optimization algorithm is the keyfactor for optimization model. Each algorithm

has its own strengths and weaknesses, hence we need to apply efficent and

effective methodologies to solve optimizatiom problems. This thesis concerns

the implementation of local search trust-region derivative-free algorithm for well

placement into the FieldOpt optimization framework developed at the Petroleum

Cybernetics Group, NTNU.

The C++-written FieldOpt software program serves as a framework and

enabler for algorithm development aimed at petroleum problems that require the

efficient computations of reservoir simulations for cost function evaluation. The

reservoir simulation works as a Black Box , but the FieldOpt software allows for

a straightforward one-to-one communication between the algorithm logic and the

multiple driver files and settings needed by the simulator.

We start with general introduction of well placement optimization and widely

used algorithms for optimizaton problems. Gradients with respect to well place-

ment variables are commonly not available and therefore derivative-free methods

are often proposed for well placement optimization. The trust region method

implemented in this work does not require cost function derivatives, but instead

constructs surrogate models of the objective function obtained during the optimiza-

tion process. Our approach is based on building a quadratic interpolation model,

which reasonably reflects the local behavior of the original objective function in a

subregion.

After implementation of the algorithm in FieldOpt, we apply test functions

to validate the performance of the algorithm. One of them is the plated-shaped

Matyas function and the other one is the valley-shaped Rosen-brock function.

We used Cauchy point calculation and Dogleg method to solve the optimization

problem and analyzed their convergence properties. The results show that the

convergence of the Cauchy point algorithm by taking the steepest descent direction

is inefficient in some cases. A future improvement could be achieved by using

the Dogleg method. We also notice that values of predetermined parameters

can affect algorithm performance. Therefore, it is also important to choose a

proper parameter value to improve the convergence of method. Then, we apply

the model-based trust-region method to solve some well placement optimization

cases, for exapmle single producer or five-spot model.
Publisher
NTNU

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