Data Assimilation Coupled to Evolutionary Algorithms—A Case Example in History Matching

Abstract

Abstract Data assimilation techniques are on the verge of being employed in real field history matching processes in a production environment. In a previous publication on "Stochastic Optimization using EA and EnKF - A Comparison" (cf. Pajonk 2008) similarities between data assimilation techniques (EnKF) and stochastic optimizers (Evolutionary Algorithm - EA) were analyzed. Both algorithms are population based, they have similar implementation properties but differing optimization characteristics. A hybrid optimizer which couples an EnKF approach and the advantages of an Evolutionary Algorithm was introduced and applied to a synthetic test function. In this paper the formulation of a hybrid optimization approach with application to a history matching process is presented. Techniques are applied to the Brugge field simulation model which was taken from a recent SPE benchmark study. Production data is assimilated via a continuous update of 3D porosity and permeability fields. Global parameter uncertainties are included in a parameter estimation process guided by an evolutionary optimization method. In this paper we will concentrate on an Evolution Strategy with local and global search properties. It is shown that an EnKF workflow can be effectively coupled to other stochastic optimization schemes with complimentary optimization features. The EnKF formulation reduces a non-linear optimization problem in a large parameter space to a statistical optimization problem in ensemble space. An Evolution Strategy (ES) gradually modifies individual parameters and can be applied to mixed-integer parameter types. The case example shows that an EnKF ensemble can be combined with a population of individual realizations from a generational update scheme using an Evolution Strategy. Benefits are seen in alternative performance properties and the use of mixed-integer parameter types. This paper will include the first example of a hybrid EnKF-ES approach with application to reservoir simulation. Practical implications for history matching processes with mixed-integer parameter types which have not been used in a standard EnKF approach are discussed.