Estimating Facies Fields Using the Ensemble Kalman Filter and Distance Functions

Abstract

This article, written by Senior Technology Editor Dennis Denney, contains highlights of paper SPE 143031, ’Estimating Facies Fields Using the Ensemble Kalman Filter and Distance Functions - Applied to Shallow Marine Environments,’ by Rolf J. Lorentzen, SPE, Geir Nevdal, SPE, and Ali Shafieirad, SPE, International Research Institute of Stavanger, prepared for the 2011 SPE Europec/EAGE Annual Conference and Exhibition, Vienna, Austria, 23-26 May 2011. The paper has not been peer reviewed. The ensemble Kalman filter (EnKF) is a promising tool for assisted history matching of reservoir models, and it works well for cases in which petrophysical properties are modeled by use of Gaussian random fields with variogram models. Many reservoirs have complex geological structures, which can have rapid spatial variations in the petrophysical properties (e.g., permeability and porosity). Applying the EnKF directly on such reservoirs can lose characteristics of the fields (i.e., sharp gradients are smeared). A method is proposed in which distance functions are used to estimate an arbitrary number of facies types. Introduction The goal for using the EnKF on complex reservoirs is to ensure that the updated fields are facies realizations, or at least approximations, and that a good history match is obtained. Truncated pluri-Gaussian methods are used for updating facies fields. Here, two Gaussian random fields are defined on the model grid. These fields then are updated by use of the EnKF, instead of updating the petrophysical properties directly. A truncation map then is used to assign specific combinations of the two Gaussian fields to a particular facies type. A different approach is to extend the EnKF to sample from Gaussian mixture models. The Gaussian mixture models can have multimodal distributions and are, thereby, more suited for facies fields. The distributions are obtained by computing a weighted sum of standard Gaussian distributions. The extension of the EnKF involves computation of the weights, conditional mean, and conditional covariances. The method presented here introduces one level-set function for each facies type. The result is several distances at each gridblock with the same sign; therefore, the maximum of the distances in a given gridblock is used to determine the facies type. This method presents no restrictions on the structure of the facies field to be estimated, and any type of facies field may be estimated. A problem with this approach is that it is unlikely that the two functions change sign in the same gridblock, which makes it difficult to estimate fields if all types of transitions between facies types occur (i.e., it is difficult to estimate fields in which Facies 1 borders against Facies 4, or Facies 2 borders against Facies 3).