Prior model identification during subsurface flow data integration with adaptive sparse representation techniques
- 329 Downloads
Construction of predictive reservoir models invariably involves interpretation and interpolation between limited available data and adoption of imperfect modeling assumptions that introduce significant subjectivity and uncertainty into the modeling process. In particular, uncertainty in the geologic continuity model can significantly degrade the quality of fluid displacement patterns and predictive modeling outcomes. Here, we address a standing challenge in flow model calibration under uncertainty in geologic continuity by developing an adaptive sparse representation formulation for prior model identification (PMI) during model calibration. We develop a flow-data-driven sparsity-promoting inversion to discriminate against distinct prior geologic continuity models (e.g., variograms). Realizations of reservoir properties from each geologic continuity model are used to generate sparse geologic dictionaries that compactly represent models from each respective prior. For inversion initially the same number of elements from each prior dictionary is used to construct a diverse geologic dictionary that reflects a wide range of variability and uncertainty in the prior continuity. The inversion is formulated as a sparse reconstruction problem that inverts the flow data to identify and linearly combine the relevant elements from the large and diverse set of geologic dictionary elements to reconstruct the solution. We develop an adaptive sparse reconstruction algorithm in which, at every iteration, the contribution of each dictionary to the solution is monitored to replace irrelevant (insignificant) elements with more geologically relevant (significant) elements to improve the solution quality. Several numerical examples are used to illustrate the effectiveness of the proposed approach for identification of geologic continuity in practical model calibration problems where the uncertainty in the prior geologic continuity model can lead to biased inversion results and prediction.
KeywordsSparsity Compressed sensing Prior uncertainty Model calibration Flow data integration
Unable to display preview. Download preview PDF.
- 4.Britanak, P.C., Yip, P., Rao, K.: Discrete Cosine Transform: General Properties, Fast Algorithms, and Integer Approximation. Academic, New York (2006)Google Scholar
- 8.Deutsch, C.V., Journel, A.G.: GSLIB—Geostatistical Software Library and User’s Guide. Oxford University Press, New York (1998)Google Scholar
- 12.ElSheikh, A.H., Wheeler, M.F., Hoteit, I.: Sparse calibration of subsurface flow models using nonlinear orthogonal matching pursuit and an iterative stochastic ensemble method. Adv. Water Resour. (2013). doi: 10.1016/j.advwatres.2013.02.002
- 13.Gavalas, G.R., Shah, P.C., Seinfeld, J.H.: Reservoir history matching by Bayesian estimation. Soc. Petrol. Eng. J. 16(6), 337–350 (1976)Google Scholar
- 15.Jacquard, P., Jain, C.: Permeability distribution from field pressure data. Soc. Petrol. Eng. J. 281–294 (1965)Google Scholar
- 19.Jafarpour, B., McLaughlin, D.B.: Reservoir characterization with discrete cosine transform, part-1: parameterization, part-2: history matching. Soc. Petrol. Eng. J. 14(1), 182–201 (2009)Google Scholar
- 20.Jafarpour, B., Tarrahi, M.: Assessing the performance of the ensemble Kalman filter for subsurface flow data integration under variogram uncertainty. Water Resour. Res. 47, W05537 (2011). 26PPGoogle Scholar
- 21.Jahns, O.J.: A rapid method for obtaining a two-dimensional reservoir description from well pressure response data. Soc. Petrol. Eng. J. 6(12), 315–327 (1966)Google Scholar
- 25.Mallat, S.: A Wavelet Tour of Signal Processing. The Sparse Way, 3rd edn.Academic Press, New York (2008)Google Scholar
- 29.Tibshirani, R.: Regression shrinkage and selection via the lasso. J. R. Stat. Soc. Ser. B 58(1), 267–288 (1996)Google Scholar