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

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. Introduction In recent years more and more attention has been given to workflows for uncertainty assessment in reservoir management. It is generally accepted that any model reliably predicting future quantities should be able to reproduce known history data. This requires a model validation process (History Matching) which is traditionally cumbersome and time consuming. Most optimization methods described in the literature that have relevance for history matching in reservoir simulation use an objective function definition based on the overall simulation period. This applies to gradient techniques, evolutionary algorithms or combinations of experimental design and proxy modeling techniques, i.e., methods which are commonly used in modern history matching and uncertainty quantification workflows in the oil and gas industry. The integration of a sequential data assimilation process is not included as an integral part of such optimization methods. Frequent model updates would also incur high computational costs since existing concepts of an error function or objective function require computation of the entire simulation period. The Ensemble Kalman Filter method (EnKF) is a data assimilation technique that was developed for use in complex and highly non-linear simulation models (Evensen 1994). The EnKF technique was first applied to reservoir simulation in order to estimate lesser known rock properties as part of a history matching process (Nævdal 2003).

A Geostatistical Evolution Strategy for Subsurface Characterization: Theory and Validation Through Hypothetical Two‐Dimensional Hydraulic Conductivity Fields

“…For example, the CMA‐ES has been adopted to optimize pump‐and‐treat systems (Bayer & Finkel, ) and funnel‐and‐gate systems (Bürger et al, ) and improve pumping well layouts (Bayer et al, ). Beyond hydrogeology studies, the CMA‐ES has been used in petroleum engineering for similar purposes (Fonseca et al, ; Forouzanfar et al, ; Lu et al, ; Schulze‐Riegert et al, ). More recently, the CMA‐ES algorithm has been applied to transmissivity identification (Smaoui et al, ).…”

Estimation of Distribution Algorithms Applied to History Matching

“…For a good review of EnKF, see Evensen et al (2007). EnKF has also been coupled to evolutionary algorithms in history matching (Schulze-Riegert et al 2009). …”

Bayesian Optimization Algorithm Applied to Uncertainty Quantification

“…The ensemble Kalman filter is a well-known data-assimilation method applied to history-matching problems (Evensen et al 2007). Many combinations of the gradient methods, evolutionary algorithms, and data-assimilation methods have also been used in history matching (Schulze-Riegert et al 2009;Mantica et al 2002;Gómez et al 2001).…”