Sigurd Ivar Aanonsen

Estimation of Initial Fluid Contacts by Assimilation of Production Data With EnKF

Much recent work on automatic history matching and data assimilation has focused on the adjustment of simulator gridblockpermeabilitiesandporosities. Here, weshowthatwhen production data are assimilated into reservoir models with the ensemble Kalman filter, it is relatively easy to account for uncertainty in the depths of the initial fluid contacts and provide estimates of these depths in addition to the traditional estimates of rock properties fields. The contact depths strongly affect the initial oil in place and cumulative oil production. We demonstrate that if one uses fixed, but incorrect fluid contacts when assimilating data with EnKF, reasonable matches of production data are obtained, but future performance predictions are inaccurate and severely biased. Considering these same inaccurate contact depths as the means of probability density functions for the two depths and including both the contact depths and rock property fields in the EnKF state vector, we obtain improved performance predictions compared with the case where incorrect depths are assumed to be correct. With uncertain initial fluid contacts, the estimates of the location (depths) of the contacts obtained by matching production data are more accurate than the prior estimates, but unfortunately, do not always provide an improved estimate of the thickness of the oil column. However, this is reflected in a larger estimated uncertainty in the predictions. In the reservoir engineering community, there exists some uncertainty about whether performance prediction runs with a reservoir simulator should be made by predicting forward from the end of data assimilation or by rerunning the reservoir simulator from time zero using the final ensemble of reservoir parameters obtained at the final data assimilation step. We show that if the model error is negligible and the relation between data and the combined state vector is linear, then both procedures give the same predictions. We demonstrate, that for the nonlinear examples considered here the two procedures give reasonably consistent results, although rerunning from time zero tends to give slightly larger estimates of uncertainty in the predictions.

Reservoir description using a binary level set model

We consider the inverse problem of permeability estimation for two-phase flow in porous media. In the parameter estimation process we utilize both data from the wells (production data) and spatially distributed data (from time-lapse seismic data). The problem is solved by approximating the permeability field by a piecewise constant function, where we allow the discontinuity curves to have arbitrary shape with some forced regularity. To achieve this, we have utilized level set functions to represent the permeability field and applied an additional total variation regularization. The optimization problem is solved by a variational augmented Lagrangian approach. A binary level set formulation is used to determine both the curves of discontinuities and the constant values for each region. We do not need any initial guess for the geometries of the discontinuities, only a reasonable guess of the constant levels is required.

Structural Surface Uncertainty Modeling and Updating Using the Ensemble Kalman Filter

This paper (SPE 125352) was accepted for presentation at the SPE/EAGE Reservoir Characterization and Simulation Conference, Abu Dhabi, UAE, 19–21 October 2009, and revised for publication. Original manuscript received for review 7 September 2009. Revised manuscript received for review 18 December 2009. Paper peer approved 18 March 2010. Summary Although typically large uncertainties are associated with reservoir structure, the reservoir geometry is usually fixed to a single interpretation in history-matching workflows, and focus is on the estimation of geological properties such as facies location, porosity, and permeability fields. Structural uncertainties can have significant effects on the bulk reservoir volume, well planning, and predictions of future production. In this paper, we consider an integrated reservoir-characterization workflow for structural-uncertainty assessment and continuous updating of the structural reservoir model by assimilation of production data. We address some of the challenges linked to structural-surface updating with the ensemble Kalman filter (EnKF). An ensemble of reservoir models, expressing explicitly the uncertainty resulting from seismic interpretation and time-to-depth conversion, is created. The top and bottom reservoir-horizon uncertainties are considered as a parameter for assisted history matching and are updated by sequential assimilation of production data using the EnKF. To avoid modifications in the grid architecture and thus to ensure a fixed dimension of the state vector, an elastic-grid approach is proposed. The geometry of a base-case simulation grid is deformed to match the realizations of the top and bottom reservoir horizons. The method is applied to a synthetic example, and promising results are obtained. The result is an ensemble of history-matched structural models with reduced and quantified uncertainty. The updated ensemble of structures provides a more reliable characterization of the reservoir architecture and a better estimate of the field oil in place.