History Matching and Production Forecast Uncertainty by Means of the Ensemble Kalman Filter: A Real Field Application

Abstract

Abstract During history match reservoir models are calibrated against production data to improve forecasts reliability. Often, the calibration ends up with a handful of matched models, sometime achieved without preserving the prior geological interpretation. This makes the outcome of many history matching projects unsuitable for a probabilistic approach to production forecast, then motivating the quest of methodologies casting history match in a stochastic framework. The Ensemble Kalman Filter (EnKF) has gained popularity as Monte-Carlo based methodology for history matching and real time updates of reservoir models. With EnKF an ensemble of models is updated whenever production data are available. The initial ensemble is generated according to the prior model, while the sequential updates lead to a sampling of the posterior probability function. This work is one of the first to successfully use EnKF to history match a real field reservoir model. It is, to our knowledge, the first paper showing how the EnKF can be used to evaluate the uncertainty in the production forecast for a given development plan for a real field model. The field at hand was an on-shore saturated oil reservoir. Porosity distribution was one of the main uncertainties in the model, while permeability was considered a porosity function. According to the geological knowledge, the prior uncertainty was modeled using Sequential Gaussian Simulation and ensembles of porosity realizations were generated. Initial sensitivities indicated that conditioning porosity to available well data gives superior results in the history matching phase. Next, to achieve a compromise between accuracy and computational efficiency, the impact of the size of the ensemble on history matching, porosity distribution and uncertainty assessment was investigated. In the different ensembles the reduction of porosity uncertainty due to production data was noticed. Moreover, EnKF narrowed the production forecast confidence intervals with respect to estimate based on prior distribution. Introduction Reservoir management of modern oil and gas fields requires periodic updates of the simulation models to integrate in the geological parameterization production data collected over time. In these processes the challenges nowadays are many. First, a coherent view of the geomodel requires updating the simulation decks in ways consistent with geological assumptions. Second, the management is requiring more and more often a probabilistic assessment of the different development scenarios. This means that cumulative distribution functions, reflecting the underlying uncertainty in the knowledge of the reservoir, for key production indicators, e.g. cumulative oil production at Stock Tank condition (STC), along the entire time-life of the field, are expected outcomes of a reservoir modeling project. Moreover, production data are nowadays collected with increasing frequencies, especially for wells equipped with permanent down-hole sensors. Decision making, based on most current information, requires frequent and rapid updates of the reservoir models. The Ensemble Kalman Filter (EnKF) is a Monte-Carlo based method developed by Evensen 1 to calibrate oceanographic models by sequential data assimilation. Since the pioneering application on near-well modeling problems by Naevdal et al.2, EnKF has become in the reservoir simulation community a popular approach for history matching and uncertainty assessment 3–7. This popularity is motivated by key inherent features of the method. EnKF is a sequential data assimilation methodology, and then production data can be integrated in the simulation model as they are available. This makes EnKF well suited for real-time application, where data continuously collected have to be used to improve the reliability of predictive models. EnKF maintains a Gaussian ensemble of models aligned with the most current production data by linear updates of the model parameters. In that way the statistical properties of the Gaussian ensemble, that is to say mean, variance and two-point correlations are preserved.