Sparse Randomized Maximum Likelihood (SpRML) for subsurface flow model calibration and uncertainty quantification |
| |
| Institution: | 1. Consiglio Nazionale delle Ricerche, Istituto di Ricerca Sulle Acque, Via Salaria km 29.300, 00015 Monterotondo, RM, Italy;2. Dipartimento DICATAM, Università degli Studi di Brescia, Via Branze 43, 25123 Brescia, Italy;3. Consiglio Nazionale delle Ricerche, Istituto di Ricerca Sulle Acque, UOS Brugherio, Via del Mulino, 19, 20861 Brugherio, MB, Italy;1. University of Padova, Department of Mathematics, Via Trieste, 63, I-35121 Padova, Italy;2. University of Fribourg, Department of Mathematics, Chemin du Musée, 23, CH-1700 Fribourg, Switzerland |
| |
| Abstract: | Despite their apparent high dimensionality, spatially distributed hydraulic properties of geologic formations can often be compactly (sparsely) described in a properly designed basis. Hence, the estimation of high-dimensional subsurface flow properties from dynamic performance and monitoring data can be formulated and solved as a sparse reconstruction inverse problem. Recent advances in statistical signal processing, formalized under the compressed sensing paradigm, provide important guidelines on formulating and solving sparse inverse problems, primarily for linear models and using a deterministic framework. Given the uncertainty in describing subsurface physical properties, even after integration of the dynamic data, it is important to develop a practical sparse Bayesian inversion approach to enable uncertainty quantification. In this paper, we use sparse geologic dictionaries to compactly represent uncertain subsurface flow properties and develop a practical sparse Bayesian method for effective data integration and uncertainty quantification. The multi-Gaussian assumption that is widely used in classical probabilistic inverse theory is not appropriate for representing sparse prior models. Following the results presented by the compressed sensing paradigm, the Laplace (or double exponential) probability distribution is found to be more suitable for representing sparse parameters. However, combining Laplace priors with the frequently used Gaussian likelihood functions leads to neither a Laplace nor a Gaussian posterior distribution, which complicates the analytical characterization of the posterior. Here, we first express the form of the Maximum A-Posteriori (MAP) estimate for Laplace priors and then use the Monte-Carlo-based Randomize Maximum Likelihood (RML) method to generate approximate samples from the posterior distribution. The proposed Sparse RML (SpRML) approximate sampling approach can be used to assess the uncertainty in the calibrated model with a relatively modest computational complexity. We demonstrate the suitability and effectiveness of the SpRML formulation using a series of numerical experiments of two-phase flow systems in both Gaussian and non-Gaussian property distributions in petroleum reservoirs and successfully apply the method to an adapted version of the PUNQ-S3 benchmark reservoir model. |
| |
| Keywords: | Sparsity Compressed sensing Laplace priors Bayesian inversion Randomized Maximum Likelihood Model calibration |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
