(248a) Well Placement Optimization Under Geological Uncertainty with Optimally Selected Realizations

Uncertainty in the geological properties of a reservoir has a major impact in determining well locations and well production parameters [1]. To quantify reservoir production performance, flow simulations are performed on multiple geological model realizations generated by geostatistical tools. Since reservoir flow simulation is a computationally intensive task due to complex geological heterogeneities and numerical thermal modeling, generally only few selected realizations are chosen for flow simulations. In our previous work [2], an optimization based geological realization selection method has been proposed, which minimize the probability distance between the discrete distribution represented by the superset of realizations and the reduced discrete distribution represented by the selected realizations.

In this work, the reservoir well placement optimization problem is studied with the consideration of geological uncertainty. To account for the geological uncertainty, the well placement problem is formulated as a mean-variance optimization problem by maximizing the risk averted expected cumulative oil production. The objective function evaluation is based on time-consuming reservoir flow simulation, so derivative-free optimization techniques have been adopted to solve the optimization problem. Specifically, we have implemented a Gaussian surrogate model based optimization algorithm and have also adopted a mesh adaptive direct search algorithm NOMAD [3] to generate the well placement plan. To compare the solution quality, different well placement plans are generated by using: 1) the superset of realizations; 2) the subset of realizations determined by the optimal realization selection method [2]; and 3) the subset of realizations selected through traditional ranking method [4].

Case study results demonstrate the benefits of optimal realization selection. The well placement plan obtained using optimally selected realizations has higher cumulative oil production rates than the well placement plan obtained based on realizations generated through ranking method. The optimally selected realizations lead to a distribution of cumulative oil production that is close to the cumulative oil production distribution obtained using the superset of realizations. Those results suggest that optimal realization selection algorithm is promising in selecting the geological realizations and reducing the flow simulation efforts, and can lead to good well placement plans that capture the distribution of the geological uncertainty well.

References:

[1] Bangerth, W., Klie, H., Wheeler, M. F., Stoffa, P. L., & Sen, M. K. On optimization algorithms for the reservoir oil well placement problem. Computational Geosciences, 2006, 10, 303.

[2] Rahim, Shahed, Li, Zukui, Trivedi, Japan. Reservoir Geological Uncertainty Reduction: an Optimization based Method using Multiple Static Measures. Mathematical Geosciences, 2014, under review.

[3] S. Le Digabel. Algorithm 909: NOMAD: Nonlinear optimization with the MADS algorithm. ACM Transactions on Mathematical Software, 2011, 37, 44.

[4] Fenik D.R., Nouri A., Deutsch C.V. Criteria for ranking realizations in the investigation of SAGD reservoir performance. Canadian International Petroleum Conference. 2009, 191.