History Matching and Uncertainty Quantification: Multiobjective Particle Swarm Optimisation Approach
Authors: Mohamed Linah , Christie Mike , Demyanov Vasily 
Published: September 2011

Abstract
Quantifying uncertainty in hydrocarbon production forecasts is critical in the petroleum industry because of the dominant role uncertainty quantification plays in reservoir management decisions. An efficient application of global optimisation methods to history matching and uncertainty quantification of real complex reservoirs has been an extensively an active area of research. The goals of these methods are to navigate the parameter space for multiple good fitting models quickly and identify as many different optima as possible. Obtaining multiple optima can result in an ensemble of history matches that has divergent prediction profiles for more accurate and reliable predictive uncertainty estimates.
The present study extends the application of particle swarm optimisation to handle multi-objective optimisation in reservoir history matching context. Previous research studies in assisted history matching primarily focused on optimising a single objective function in which all the production data coming from the wells are aggregated into a single misfit value. The single misfit value is constructed by summing the weighted squared differences between historical and simulated production data. In the multi-objective optimisation scheme, multiple objectives can be defined representing each or some of the weighted squared difference of a production type. By constructing multiple objectives that measure the contribution of each objective in the multi-objective optimisation scheme, it can be possible to find a set of solutions which optimally balances the different objectives simultaneously while maintaining solution diversity. The advantage of this construction is that the tradeoffs between the objectives can be explored and explicitly exploited in the course of optimisation to find all possible combination of good fitting model solutions that have similar match quality. In history matching, it is desirable to have various solutions that map to relatively similar low misfit values that can represent all the possible geological scenarios. The new multi-objective particle swarm optimisation uses a crowding distance mechanism jointly with a mutation operator to preserve the diversity of solutions.
In this paper, the multi-objective particle swarm optimisation scheme has been investigated on history matching a well-known synthetic reservoir simulation model and the results were compared with a single objective methodology. Analyses of history matching quality and predictive uncertainty estimation based on the resulted models have been conducted to obtain the uncertainty predictions envelopes for both strategies. The comparative results suggest that, for the reservoir under consideration, the multi-objective particle swarm approach obtains better history matches and has achieved over twofold faster convergence speed than the single objective approach. The benefits of using multi-objective scheme by comparison with the single objective scheme to obtain a diverse set of history matches while reducing the number of simulations required for achieving a similar matching performance have led to more reliable predictions.