HR: 1340h
AN: H43A-0491    [Abstracts]
TI: Uncertainty Quantification Bayesian Framework for Porous Media Flows
AU: * Demyanov, V
EM: Vasily.Demyanov@pet.hw.ac.uk
AF: Heriot Watt Institute of Petroleum Engineering, Heriot-Watt University, Edinburgh, GBR EH14 4AS
AU: Christie, M
EM: Vasily.Demyanov@pet.hw.ac.uk
AF: Heriot Watt Institute of Petroleum Engineering, Heriot-Watt University, Edinburgh, GBR EH14 4AS
AU: Erbas, D
EM: Vasily.Demyanov@pet.hw.ac.uk
AF: Heriot Watt Institute of Petroleum Engineering, Heriot-Watt University, Edinburgh, GBR EH14 4AS
AB: Uncertainty quantification is an increasingly important aspect of many areas of applied science, where the challenge is to make reliable predictions about the performance of complex physical systems in the absence of complete or reliable data. Predicting flows of fluids through undersurface reservoirs is an example of a complex system where accuracy in prediction is needed (e.g. in oil industry it is essential for financial reasons). Simulation of fluid flow in oil reservoirs is usually carried out using large commercially written finite difference simulators solving conservation equations describing the multi-phase flow through the porous reservoir rocks, which is a highly computationally expensive task. This work examines a Bayesian Framework for uncertainty quantification in porous media flows that uses a stochastic sampling algorithm to generate models that match observed time series data. The framework is flexible for a wide range of general physical/statistical parametric models, which are used to describe the underlying hydro-geological process in its temporal dynamics. The approach is based on exploration of the parameter space and update of the prior beliefs about what the most likely model definitions are. Optimization problem for a highly parametric physical model usually have multiple solutions, which impact the uncertainty of the made predictions. Stochastic search algorithm (e.g. genetic algorithm) allows to identify multiple "good enough" models in the parameter space. Furthermore, inference of the generated model ensemble via MCMC based algorithm evaluates the posterior probability of the generated models and quantifies uncertainty of the predictions. Machine learning algorithm - Artificial Neural Networks - are used to speed up the identification of regions in parameter space where good matches to observed data can be found. Adaptive nature of ANN allows to develop different ways of integrating them into the Bayesian framework: as direct time-series estimators, as interim algorithm to predict function of certain shape (using GLM), as direct estimators of models' likelihood surface in the parameter space. Application of the described above approaches are illustrated in a simple synthetic example of oil/water flow in a 1D porous system with a fault. Despite the simplicity f the system it appear to have a vast uncertainty range and multiple solutions, which are not practical to assess using e.g. gradient optimization methods. The proposed Bayesian framework in a combination with ANN is capable of assessing uncertainty in predictions with significant saving in computational costs. The predicted uncertainty was calibrated to the available exhaustive reference distribution of possible model solutions (160 thous. of MCMC generated models) to validate the algorithms.
DE: 1846 Model calibration (3333)
DE: 1869 Stochastic hydrology
DE: 1873 Uncertainty assessment (3275)
DE: 1894 Instruments and techniques: modeling
SC: Hydrology [H]
MN: Fall Meeting 2005