QUANTIFYING PREDICTION UNCERTAINTY IN RESERVOIR MODELLING USING STREAMLINE SIMULATION

Abstract eng:
The performance of oil reservoirs is inherently uncertain: data constraining the rock and rockfluid properties is available at only a small number of spatial locations, and other measurements are integrated responses providing limited constraints on model properties. Calibrating a reservoir model to observed data is time consuming, and it is rare for multiple models to be ‘history matched’. Uncertainty quantification usually consists of identifying high-side and low-side adjustments to the base case. The Neighbourhood Algorithm is a stochastic sampling algorithm developed for earthquake seismology. It works by adaptively sampling in parameter space using geometrical properties of Voronoi cells to bias the sampling to regions of good fit to data. The algorithm evaluates the high dimensional integrals needed for quantifying the posterior probability distribution using Markov Chain Monte Carlo run on the misfit surface defined on the Voronoi cells. This paper describes the use of the Neighbourhood Algorithm for obtaining multiple history matched reservoir models and using the ensemble of models to quantify uncertainty in reservoir performance forecasting. We describe the changes needed to generate multiple history matched models, and to sample from the posterior distribution to quantify uncertainty in forward predictions. Effective quantification of uncertainty can require thousands of reservoir model runs, each of which can take several minutes for a relatively coarse grid to several hours for a fine grid. As part of this paper, we describe the use of approximate streamline simulations to rapidly explore parameter space. This allows us to switch to slower conventional simulation in regions of good fit to the data. We demonstrate the performance of the algorithm on the SPE 10th Comparative Solution Project dataset. This is a benchmark dataset for which a fine grid reservoir description is known. We take this as ”truth” and use a coarser model to match the history data for a limited period of time. We then predict both the maximum likelihood performance and the uncertainty envelope for the remaining time. The maximum likelihood solution is close to the truth case for much of the time, and the true solution always lies within the uncertainty bounds predicted by the algorithm.

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