| dc.description.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. | |
