Optimal well placement

One is often faced with the problem of finding the optimal location and trajectory for an oil well. Increasingly this includes the additional complication of optimising the design of a multilateral well. We present a new approach based on the theory of expensive function optimisation. The key idea is to replace the underlying expensive function (ie. the simulator response) by a cheap approximation (ie. an emulator). This enables one to apply existing optimisation techniques to the emulator. Our approach uses a radial basis function interpolant to the simulator response as the emulator. Note that the case of a Gaussian radial basis function is equivalent to the geostatistical method of Kriging and radial basis functions can be interpreted as a single-layer neural network. We use a stochastic model of the simulator response to adaptively refine the emulator and optimise it using a branch and bound global optimisation algorithm. To illustrate our approach we apply it numerically to finding the optimal location and trajectory of a multilateral well in a reservoir simulation model using the industry standard ECLIPSE simulator. We compare our results to existing approaches and show that our technique is comparable, if not superior, in performance to these approaches