Robust Well Placement Optimization Through Universal Trace Kriging with Adaptive Sampling

Optimizing well locations for a green field is critical to mitigate development risks. Performing such workflows with reservoir simulations is very challenging due to the huge computational cost. Proxy models can instead provide accurate estimates at a fraction of the computing time. This study presents an application of new generation functional proxies to optimize the well locations in a real oil field with respect to the actualized oil production on all the different geological realizations. Proxies are built with the Universal Trace Kriging and are functional in time allowing to actualize oil flows over the asset lifetime. Proxies are trained on the reservoir simulations using randomly sampled well locations. Two proxies are created for a pessimistic model (P10) and a mid-case model (P50) to capture the geological uncertainties. The optimization step uses the Non-dominated Sorting Genetic Algorithm, with discounted oil productions of the two proxies, as objective functions. An adaptive approach was employed: optimized points found from a first optimization were used to re-train the proxy models and a second run of optimization was performed. The methodology was applied on a real oil reservoir to optimize the location of four vertical production wells and compared against reference locations. 111 geological realizations were available, in which one relevant uncertainty is the presence of possible compartments. The decision space represented by the horizontal translation vectors for each well was sampled using Plackett-Burman and Latin-Hypercube designs. A first application produced a proxy with poor predictive quality. Redrawing the areas to avoid overlaps and to confine the decision space of each well in one compartment, improved the quality. This suggests that the proxy predictive ability deteriorates in presence of highly non-linear responses caused by sealing faults or by well interchanging positions. We then followed a 2-step adaptive approach: a first optimization was performed and the resulting Pareto front was validated with reservoir simulations; to further improve the proxy quality in this region of the decision space, the validated Pareto front points were added to the initial dataset to retrain the proxy and consequently rerun the optimization. The final well locations were validated on all 111 realizations with reservoir simulations and resulted in an overall increase of the discounted production of about 5% compared to the reference development strategy. The adaptive approach, combined with functional proxy, proved to be successful in improving the workflow by purposefully increasing the training set samples with data points able to enhance the optimization step effectiveness. Each optimization run performed relies on about 1 million proxy evaluations which required negligible computational time. The same workflow carried out with standard reservoir simulations would have been practically unfeasible.