Sobol and Halton Sequences: Efficient Experimental Design Techniques towards Improved Uncertainty Quantification of Petroleum Reservoirs

Abstract

Abstract Reservoir simulation models often suffer from significant uncertainties due to the lack and inaccuracies of the measured data. Hence, uncertainty analysis and quantification are considered as major concerns in building robust and predictive simulation models. The conventional approach of the uncertainty analysis is conducted by running a very large number of simulation runs in an attempt to capture all effects of the uncertain parameters. Running a large number of simulation runs is costly and very time consuming and therefore efficient approaches have been arisen. One of these efficient approaches is the Experimental Design technique. The experimental design technique is widely applied in different engineering practices for assessing and quantifying uncertainties. Experimental design is the technique used to guide the selection of the samples within the design search space of the uncertain parameters in order to obtain the maximum amount of information using low number of experiments. Several experimental design techniques are applied in petroleum industry and specially in reservoir simulation assisted history matching. Some experimental design techniques shows more effectiveness than others. The objective of this paper is to introduce two efficient experimental design techniques (Halton and Sobol sequences) to the reservoir simulation assisted history matching workflow. This work is to complete the work done by the authors and published in Shams et al. (2017). Shams et al. (2017) applied and tested the potentiality of the two proposed experimental design techniques through a comparative study between their performance in solving assisted history matching problems of different scale material balance problems and the performance of the most widely used experimental design technique, Latin hypercube. In this paper the comparative study is conducted using numerical reservoir simulation model. A performance indicator is developed to compare between the three studied techniques. The performance indicator represents the relative error between the estimated values of history matching parameters calculated using the studied experimental design methods and their exact solutions. The results of this work validate the previous obtained conclusions and indicate that the Sobol and Halton sequences experimental design techniques are more efficient and superior to Latin hypercube method.