###
Wolfgang Bangerth, Hector
Klie, Mary F. Wheeler, Paul Stoffa, Mrinal Sen

**On optimization algorithms for the reservoir
oil well placement problem**

Computational Geosciences, vol. 10 (2006), pp. 303-319.

Determining optimal locations and operation parameters for wells in oil and gas
reservoirs has a potentially high economic impact. Finding these optima
depends on a complex combination of geological, petrophysical, flow regimen,
and economical parameters that are hard to grasp intuitively. On the other
hand, automatic approaches have in the past been hampered by the
overwhelming computational cost of running thousands of potential cases
using reservoir simulators, given that each of these runs can take on the
order of hours. Therefore, the key issue to such automatic optimization is
the development of algorithms that
find good solutions with a minimum number of function evaluations. In this work, we
compare and analyze the efficiency, effectiveness, and reliability
of several optimization algorithms for the well placement problem. In particular, we
consider the Simultaneous Perturbation Stochastic
Approximation (SPSA), Finite Difference Gradient (FDG), and Very
Fast Simulated Annealing (VFSA) algorithms. None of these algorithms
guarantees to find the optimal solution,
but we show that both SPSA and VFSA are very efficient in finding nearly
optimal solutions with a high probability. We illustrate this with a set of
numerical experiments based on real data for single and multiple well
placement problems.

*Wolfgang Bangerth*

* Thu May 4 14:55:18 MDT 2017 *