Automatic History Matching of Production and Facies Data with Non-stationary Proportions using EnKF

Abstract

Most geostatistical methods for generating plausible facies models require prior knowledge of the facies proportions distribution to account for heterogeneity within the reservoir. This parameter affects the flow behavior, predictive performance and fluid volume distribution of the model. In practice, it is hardly known with certainty and it is important to account for this uncertainty in the modeling and history matching phases.The ensemble Kalman filter (EnKF), when modified appropriately, to account for non-linearity and non-Gaussianity, is quite robust for automatic history matching problems. However, because the problem of history matching applied to facies is complex, most attempts at solving this problem typically assume constant petrophysical properties and stationary facies proportions. However, realistic representation of facies distribution requires incorporating the variation in petrophysical properties in the geologic model, in addition to any associated uncertainty. This is critical to correctly defining the flow connectivity within the model and the variations in storativity within facies.In this paper, we investigate a number of practical issues in history matching applied to facies with heterogeneous petrophysical properties and non-stationary proportions: (1) Can we account for heterogeneity in facies petrophysical properties during history matching and subsequently reduce any associated uncertainty in them by sequential calibration to data? To the best of our knowledge, this is the first time that heterogeneity in facies petrophysical properties has ever been applied to problems of this kind; (2) What is the EnKF performance when the facies proportions are stationary but implicitly uncertain? (3) Can EnKF efficiently adjust the facies boundaries and distributions when the prior proportions are assumed known but non-stationary?To answer these questions we designed three different test problems. We show that when the facies proportion is non-stationary the EnKF is a robust in estimating the facies properties and distribution.

History Matching Channelized Reservoirs Using the Ensemble Kalman Filter

“…Liu and Oliver (2005a, b) and Agbalaka and Oliver (2009) introduced use of truncated pluri-Gaussian methods for updating facies fields. The goal is to ensure that the updated fields are facies realizations, or at least approximations of such, and that a good history match is obtained.…”

Performance of the ensemble Kalman filter outside of existing wells for a channelized reservoir

“…To deal with this, several methods for estimating multimodal distributions or facies distributions are being developed. Examples of methods for estimating facies distributions rather than gridblock properties are the EnKF in combination with the truncated pluriGaussian method [3,16], EnKF in combination with the level set method ( [18,19], the gradual deformation method [11,15,20]) or the iterative approach based on the representer method by [13]. On the other hand, [26] and [4] propose extensions to the EnKF, which can retain the characteristics of multi-point statistics.…”

Facies estimation through data assimilation and structure parameterization

“…2 Vese-Chan LS representation with four facies (a) 3 Vese-Chan LS representation with four facies applied in an imaginary estimation sequence: (a) snapshot at stage i, (b) snapshot at stage i + 1 representation without any need for additional measures being taken-the hierarchical LS representation-will be described.…”

“…If this parameterization is applied to a facies property field, any reasonable prior pdf for p will be multimodal, and thereby highly non-Gaussian. Earlier work within sequential data assimilation for facies fields, seeking to overcome this challenge, include [2,12,18,19,23,24,31,33,37]. These approaches are briefly reviewed in the introduction section in [25,26].…”