Towards Multiobjective History Matching: Faster Convergence and Uncertainty Quantification

Abstract

Today we have 50 years of research in assisted history matching that bring us many fascinating frameworks to obtain multiple history matched models. Recently the evolutionary optimization algorithms for history matching have enjoyed an increasing popularity in our community. However these methods are often criticized for their high computational demands. We are looking to improve the convergence speed of these algorithms while maintaining their ability to obtain multiple history-matched models to have realistic uncertainty quantification.In this paper, we discuss a new approach to history matching and uncertainty quantification using multiobjective stochastic population-based optimization. The current practice in industry is to sum the individual match results from wells and minimize a global misfit value in order to get a history matched model. This work proposes a methodology where we can handle different objectives of history matching separately. We extend original differential evolution (DE) algorithm to optimize multiple objectives. The new algorithm is called differential evolution for multiobjective optimization using Pareto ranking (DEMOPR). We couple this algorithm with Bayesian uncertainty quantification framework to estimate the uncertainty in future recovery.The DEMOPR algorithm is tested for history matching and uncertainty quantification of the PUNQ-S3 reservoir. We have discussed the benefits of new multiobjective approach in fulfilling the targets of PUNQ-S3 problem: obtaining good history matching results and accurate prediction of the ultimate oil recovery. Results are very promising and show better final misfit values and simultaneously, two times increase in the speed of history matching in comparison with the original DE algorithm. We also study the number of models required to reach a stable Bayesian credible interval in quantifying the production uncertainty. We show that multiobjective approach stabilizes faster than original DE which means we need fewer simulations to have a reliable uncertainty estimate in the proposed workflow.

Development of Pareto-based evolutionary model integrated with dynamic goal programming and successive linear objective reduction

“…The purpose of the multi-objective history matching was to predict the future production probabilistically by generating multiple trade-off petrophysical reservoir models [7,[115][116][117][118][119][120]. Each objective function was quantified in terms of the sum of the data mismatch between the production obtained from the reservoir and obtained from the reservoir models.…”

Impact of Model Parameterisation and Objective Choices on Assisted History Matching and Reservoir Forecasting

“…Fig. 16 shows average minimum so-far misfit value over 10 runs for MO without any grouping (18 objectives) and MO with the grouping (2 group of objectives as in Hajizadeh et al 2011b andMohamed et al 2011, next on this section this will be defined as Grouping 1). Sum of objectives from both objectives was plotted over iterations as in Fig 16.…”

“…Grouping 1 (G1) Grouping 1 (G1) is based on well grouping adopted from previous study (Hajizadeh et al 2011b;Mohamed et al 2011) Grouping 2 (G2) Grouping 2 (G2) is based on the Spearman rank correlation between each objective component. A prior history matching run was used to generate this correlation.…”

“…These algorithms minimize a misfit function and thus obtain the reservoir model that best approximates the dynamic variable data recorded during reservoir life. Powered by stochastic optimiser, AHM can be approached by Single Objective (SO) (Schulze-Riegert et al 2001;Ferraro and Verga 2009;Hajizadeh et al 2010;Mohamed et al 2010a;Mohamed et al 2010b;Hajizadeh et al 2011a;Abdollahzadeh et al 2012a; or Multi-Objective (MO) (Schulze-Riegert et al 2007;Ferraro and Verga 2009;Hajizadeh et al 2011b;Mohamed et al 2012;Sayyafzadeh et al 2012;Christie et al 2013;Park et al 2013;Min, B., et al 2014). The last block in the workflow is quantifying uncertainty of reservoir performance prediction from ensemble of matched models.…”

Pareto-based robust optimization of water-flooding using multiple realizations

“…There has been some multi-objective optimization within the petroleum engineering literature. But, most of the applications of these approaches appear to be in the area of history matching, where various measures of misfit have been used as the objective functions (Hajizadeh et al, 2011;Shelkov et al, 2013;Mohamed et al, 2011;Ferraro and Verga, 2009;Sayyafzadeh and Haghighi, 2012).…”