Optimization of Well Placement and Assessment of Uncertainty


Baris Guyaguler







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Determining the best location for new wells is a complex problem that depends on reservoir and fluid properties, well and surface equipment specifications, and economic criteria. Various approaches have been proposed for this problem. Among those, direct optimization using the simulator as the evaluation function, although accurate, is in most cases infeasible due to the number of simulations required.

This study proposes a hybrid optimization technique (HGA) based on the genetic algorithm (GA) with helper functions based on the polytope algorithm and the kriging algorithm. Hybridization of the GA with these helper methods introduces hill-climbing into the stochastic search and also makes use of proxies created and calibrated iteratively throughout the run, following the idea of using cheap substitutes for the expensive numerical simulation. Performance of the technique was investigated by optimizing placement of injection wells in the Gulf of Mexico Pompano field. A
single realization of the reservoir was used. It was observed from controlled experiments that the number of simulations required to find optimal well configurations was reduced significantly. This reduction in the number of simulations enabled the use of full-scale simulation for optimization even for this full-scale field problem. Well configuration and injection rate were optimized with net present value maximization of the water flooding project as the objective.

The optimum development plan for another real world reservoir located in the Middle East was investigated. Optimization using the numerical simulator as the evaluation function for the field posed significant challenges since the model has half a million cells. The GA was setup in parallel on four processors to speed up the optimization process. The optimal deployment schedule of 13 predrilled wells that would meet the production target specified by the operating company was sought. The problem was formulated as a traveling salesman problem and the order of wells in the drilling queue was optimized.

Ways to assess the uncertainty in the proposed reservoir development plan were also investigated since we never possess the exhaustive information about the true reservoir but rather we may have geostatistical realizations of the truth constructed from the information available. An approach that can translate the uncertainty in the data to uncertainty in terms of monetary value was developed. In this study the uncertainties associated with well placement were addressed within the utility theory framework using numerical simulation as the evaluation tool. The HGA was used to reduce the computational burden of making numerous numerical simulations. The methodology was evaluated using the PUNQ-S3 model, which is a standard test case that was based on a real field and was used for the PUNQ project in context of the EU-Joule program. Experiments were carried on 23 history-matched realizations and a truth case was also available. The results were varied by comparison to exhaustive simulations. Utility theory not only offered the framework to quantify the influence of uncertainties in the reservoir description in terms of monetary value but also provided
the tools to quantify the otherwise arbitrary notion of the risk attitude of the decision maker.

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