Uncertainty Quantification in Reservoir Prediction Modelling

Tuesday, 20 December 2011 Read 4177 times
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Uncertainty is an inherent feature of our understanding of the explored reality. Mathematical models describe our vision of reality in the analytical form and are used to predict oil reservoir production. Model uncertainty is associated with the lack of our knowledge about the reservoir properties.

Uncertainty in the model definitions/parameters reflects our prior beliefs about the reservoir description. Therefore, there is a diverse ensemble of possible model realisations, which represents a spread of the model predictions. On the other hand our observations of the reality constrain the model with spatio-temporal data, which are also subject to uncertainty.

The problem of calibrating the model based to the production data ? known as history matching in the oil industry ? has an inverse nature and is ill-posed, since the target history data can be matched well by multiple realizations. Multiple history matched models describe uncertainty range as a spread of the predictions. The history matching problem can be solved by a variety of optimisation or assimilation methods, which aim to provide an ensemble of multiple history-matched solutions. This task is especially difficult with reservoir models, which are highly complex and, usually, highly parametric. Thus, the optimisation/assimilation task performed in a high dimensional model space becomes computationally expensive with multiple flow simulations to compute. Usually, we can afford to run a limited number of flow simulations corresponding to the set of spatial distributions of porous properties. Therefore, there is a need for adaptive fast converging algorithms to solve inverse optimisation problem in high dimensions. The importance of the optimisation algorithm choice and tuning becomes essential when we try to estimate tens or even hundreds of model parameters in the presence of multiple local minima. Stochastic population based algorithms are seen as good candidates to solve history matching problems.

We will demonstrate how adaptive stochastic sampling algorithms provide a solution for assisted history matching and uncertainty quantification in several of case studies, make comparison with rival approaches, and explain importance of geological realism in history matching. Advanced evolutionary algorithms are able to find effectively multiple good solutions, which correspond to local minima of the optimisation problem. Contemporary stochastic evolutionary population-based algorithms are capable of solving multi-criteria optimisation problems, which improve computational efficiency and reliability in obtaining solutions for inverse problems. Uncertainty assessment using Bayesian inference provides a way to rigorously integrate prior geological beliefs and quantify posterior probability of the model predictions and the associated model uncertainty.

Dr Vasily Demyanov is a research fellow at Heriot-Watt University since 2003. He lectures geostatistics and leads industry sponsored research in machine learning and uncertainty quantification in reservoir modelling. He is a co-author of over 50 publications, including books: “Geostatistics: Theory and Practice (Nauka, 2010, in Russian), “Advanced Mapping of Environmental Data - Geostatistics, Machine Learning and Bayesian Maximum Entropy” (Wiley, 2008). Demyanov is an Associate editor of Computer and Geosciences Elsevier journal.

V. Demyanov has obtained his first degree in physics from Moscow State University (1994) and a PhD in physics and mathematics from Russian Academy of Sciences (1998) with a thesis on radioactive pollution modelling with geostatistics and artificial neural networks. Prior to joining Heriot-Watt he worked with University of St. Andrews (2001) and Nuclear Safety Institute (1994).

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