Uncertainty quantification using a multi-objectivised randomised maximum likelihood method

Abstract

To propagate uncertainty in reservoir production forecasts, it is typically required to sample a nonlinear and multimodal posterior density function. To do so, different techniques have been proposed and used, such as Markovian algorithms, data assimilation methods and randomised maximum likelihood (RML) method. Through several studies, it has been shown that the RML method provides a reasonable approximation of the posterior distribution, despite the fact that it does not have any rigorous theoretical foundation for nonlinear problems. In order to reduce the computation and also provide an extensive search for multimodal density functions, in this study, the RML method is proposed in a context of a multi-objective genetic algorithm in which each of the equations is considered as a separate objective function. The proposed technique was compared against a Metropolis-Hastings algorithm and an RML with a Levenberg-Marquardt minimiser, using IC-Fault model. The comparison showed that an acceptable set of samples for uncertainty quantification is obtained, and given the fact that the parallelisation of the algorithm is straightforward, it makes the proposed algorithm, efficient in terms of the total processing time.