Pilot points method for conditioning multiple-point statistical facies simulation on flow data

• Published in: Advances in water resources 2018-05, Vol.115, p.219-233
• Main Authors: Ma, Wei, Jafarpour, Behnam
• Format: Article
• Language: English
• Subjects: Algorithms; Calibration; Computer simulation; Conditioning; Data; Data processing; Ensemble Kalman filter; Ensemble smoother; Flow; Geologic facies; Kalman filters; Locations (working); Mathematical models; Methods; Model calibration; Multiple point statistics (MPS); Numerical experiments; Permeability; Pilot points; Pilot training; Simulation; Statistics; Training; Water resources
• ISSN: 0309-1708; 1872-9657
• DOI: 10.1016/j.advwatres.2018.01.021

•A novel extension of pilot points for application with complex multiple-point statistical models.•A stochastic implementation of pilot points to enable uncertainty quantification.•Strategic placement of pilot points based on sensitivity information, prior covariance model, and dynamic flow data. We propose a new pilot points method for conditioning discrete multiple-point statistical (MPS) facies simulation on dynamic flow data. While conditioning MPS simulation on static hard data is straightforward, their calibration against nonlinear flow data is nontrivial. The proposed method generates conditional models from a conceptual model of geologic connectivity, known as a training image (TI), by strategically placing and estimating pilot points. To place pilot points, a score map is generated based on three sources of information: (i) the uncertainty in facies distribution, (ii) the model response sensitivity information, and (iii) the observed flow data. Once the pilot points are placed, the facies values at these points are inferred from production data and then are used, along with available hard data at well locations, to simulate a new set of conditional facies realizations. While facies estimation at the pilot points can be performed using different inversion algorithms, in this study the ensemble smoother (ES) is adopted to update permeability maps from production data, which are then used to statistically infer facies types at the pilot point locations. The developed method combines the information in the flow data and the TI by using the former to infer facies values at selected locations away from the wells and the latter to ensure consistent facies structure and connectivity where away from measurement locations. Several numerical experiments are used to evaluate the performance of the developed method and to discuss its important properties.