Summary
The ensemble Kalman filter (EnKF) is one of the most promising tools for assisted history matching of reservoir models, but challenges remain for applications on complex geological structures (facies fields). In this paper, we propose a method that uses distance functions to estimate such fields. The definition of a distance function is “the shortest distance between a given position in the field and the boundary separating facies types.” The idea behind this approach is that distances have smooth properties, and the distribution of the ensemble in a given gridblock is without multimodality and in better agreement with the EnKF Gaussianity assumptions. The distances are then updated by use of the EnKF and converted to petrophysical parameters when the reservoir simulator is run to the next assimilation time. The approach is flexible and simple and possesses several advantages compared with other existing methods: The input items for the method are facies realizations that can be generated with any preferred geostatistical tool; we ensure that the updated fields always are facies realizations; we ensure the conditioning of the correct facies types at the well location, both initially and during the assimilation steps; and the method does not involve complex modifications of the standard EnKF equations.
The approach presented here is based on an extension of previous work performed by the authors. The novelty of the extension is summarized by the following: Any number of specified facies types can be estimated; one distance function is used for each facies type—at each gridblock, the facies type that corresponds to the distance function with maximal value is selected; there are no restrictions on the structure of the facies field to be estimated; and the methodology is extended to update variations in the petrophysical parameters within each facies type. The first of these extensions is considered the most important because the flexibility regarding the number of facies types is necessary for every real industrial application.
We demonstrate the methodology on a field with shallow-marine-environment characteristics. The conclusions from the example are that the history match is improved, uncertainty is reduced, and the method always returns facies realizations with geological authenticity.
Iterative Ensemble Smoother as an Approximate Solution to a Regularized Minimum-Average-Cost Problem: Theory and Applications
