Estimating Facies Felds using the Ensemble Kalman Filter and Distance Functions–Applied to Shallow-Marine Environments

Abstract

Abstract The ensemble Kalman Filter (EnKF) is one of the most promising tools for assisted history matching of reservoir models, and it has in particular proven to work well on cases where petrophysical properties are modeled using Gaussian random fields with variogram models. However, many operative oil and gas reservoirs have challenging complex geological structures. These structures typically have rapid spatial variations in the petrophysical properties (e.g., permeability and porosity). The consequence of applying the EnKF directly on such reservoirs is that the characteristics of the fields are lost, i.e., sharp gradients are smeared out. In this paper we propose a method where distance functions are used to estimate an arbitrary number of facies types. A distance function is defined as 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 therefore in agreement with the EnKF Gaussianity assumptions. The distances are then updated using the EnKF, and converted to petrophysical parameters when the reservoir simulator is run to the next assimilation time. One distance function is used for each facies type. The approach is flexible and simple, and possesses several advantages compared to other existing methods: There is no restrictions on the structure of the facies field to be estimated.The methodology is able to update variations in the petrophysical parameters within each facies type.The input 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 conditioning of the correct facies types at the well location, both initially and during the assimilation steps.The method does not involve complex modifications of the standard EnKF equations. Additional improvements in the quality of the updated facies fields are obtained by proper handling of the distances close to the reservoir boundaries, and conditioning on specific statistical measures to better preserve prior information about the field properties. 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.