Updating multipoint simulations using the ensemble Kalman filter

Abstract

In the last two decades, the multipoint simulation (MPS) method has been developed and increasingly used for building complex geological facies models that are conditioned to geological and geophysical data. In the meantime, the ensemble Kalman filter (EnKF) approach has been developed and recognized as a promising way for assimilating dynamic production data into reservoir models. So far, the EnKF approach is proven efficient for updating continuous model parameters that have a linear statistical relation with the flow responses. It remains challenging to extend the EnKF approach to updating complex geological facies models generated by MPS, while preserving their geological and statistical consistency.In this paper, we introduce a new method for parameterizing geostatistical reservoir models generated by MPS. It is mathematically proven that updating these parameters during a history matching process does not compromise the hard data conditioning and the geological and statistical consistency of the reservoir model defined by the training image and other information including global facies proportions, trend maps etc. This method is an alternative to the gradual deformation method but has an enlarged search space for covering possible solutions. Based on the above parameterization, we present two algorithms of using EnKF approach to update multipoint simulations to dynamic data. We also present encouraging results of using the above methodology to condition a sector model of a fluvial reservoir to dynamic data.

Simultaneous Estimation of Geologic and Reservoir State Variables Within an Ensemble-Based Multiple-Point Statistic Framework

“…A spurious correlation could be observed when the ensemble size is small and/or the transfer function is extremely non-linear such as multiple phase flow, which results in the inconsistency between the updated state and parameter (i.e., it does not honor the flow equation). Two approaches are commonly used to resolve this issue: (1) the most straightforward way is to increase the ensemble size, however the high computational cost of flow simulations could be a deterrent; A fast proxy of flow simulator coupling with the data assimilation algorithm could improve the results (He et al 2013); (2) only the geologic parameter is updated, and the corresponding state is obtained by running the forward simulator based on the estimated parameter so that the consistency is ensured; this approach has already been used in the EnKF-based method (Wen and Chen 2006;Jafarpour and Khodabakhshi 2011;Hu et al 2012) and in EnPAT (Li et al 2013). Here, in the synthetic example, as shown in Fig.…”

“…MultiGaussianity is not ensured by this procedure and the method may yield sub-optimal solutions. Hu et al (2012) proposed to update the uniform random field, which is used to draw outcomes from the conditional distribution in the MPS algorithm, using the EnKF.…”

A review of closed-loop reservoir management

“…Chang et al (2010) proposed a methodology to combine a level set method with EnKF for history matching of facies distribution in a 2D reservoir model. Hu et al (2013) introduced a new method to update complex facies models generated by multipoint simulation while preserving their geological and statistical consistency. Jafarpour and McLaughlin (2008) tested a discrete cosine transform method on two 2D, two-phase reservoir models.…”

Ensemble Kalman filtering for hydraulic conductivity characterization: Parallelization and non-Gaussianity

“…Unlike the idea of (Hu et al, 2013), v vi which uses the EnKF to directly update uncorrelated uniform random fields (those used to draw from the local conditional marginal distributions in sequential simulation), the new version propose working on correlated uniform random fields, more precisely the same uniform random field used in probability field simulation (Froidevaux, 1993). The comparison of both versions shows that the new proposed one is much better than the original in order to capture the main patterns of conductivity and in reducing uncertainty.…”

“…Covariance inflation is a technique used to avoid filter inbreeding by inflating the empirical covariance. The results show the importance of covariance localization and covariance inflation to reduce filter inbreeding.The third part investigates the inverse method proposed by (Hu et al, 2013) and proposes an improved version. Unlike the idea of (Hu et al, 2013), v vi which uses the EnKF to directly update uncorrelated uniform random fields (those used to draw from the local conditional marginal distributions in sequential simulation), the new version propose working on correlated uniform random fields, more precisely the same uniform random field used in probability field simulation (Froidevaux, 1993).…”