Obtaining representative fracture geometries is important for unconventional well placement and production/engineering optimization. Assisted history matching (AHM) is the process of calibrating fracture geometries to the field productions. However, AHM is often obstructed by the large uncertainty of model parameters due to complex physics and is often computationally expensive. The objective of this study is to establish a novel statistical sampling procedure to accurately and efficiently sample model parameters to improve the AHM results. The new workflow provides highly accurate results and reduces the computational time by 70% compared to other AHM workflows. We developed a statistical sampling procedure in which uncertainty parameters are drawn from Multivariate Gaussian distributions (MGD). The method initially samples 50 sets of parameters from user-defined mean vector and the variance-covariance matrix with zeros on the off-diagonals. The sampled 50 sets of model parameters are fed into embedded discrete fracture model (EDFM), along with a reservoir simulator to obtain modeling results. In the subsequent iterations, the mean vector and the variance-covariance matrix are updated based on 10 best modeling results where the selection is governed by a multi-objective loss function of the mismatch between field measurements and modeling results. The process repeats until the global error converges to a user-defined threshold and the best match is chosen with the smallest global error value. We demonstrated the application of the proposed workflow through both a synthetic and a real shale-gas field case study. Results show the workflow is robust against poor initial parametrizations and reduces the computational time from 13 hours to 3.5 hours when compared to another AHM workflow. Importantly, the variance-covariance matrix captures the inter-correlations between uncertainty parameters, which, in turn, act as a sampling constraint that eliminates non-physical samples, and greatly improves sampling efficiency. Results show the workflow accurately captures the "best" values of model parameters with high precision. We further analyzed the probabilistic production forecast for all history matching solutions and showed the uncertainties of P10/P50/P90 estimated ultimate recoveries of gas production are greatly reduced. Our proposed workflow improved the matching between modeling results and the field productions at a quarter of the computational cost compared to the previous workflow. We gathered the model parameter values whose modeling results have good matches with the field measurements and analyzed the distribution of all model parameters. The results from the synthetic case show the workflow accurately captures the true model parameters with high precision as the modes of the distributions are bordering the true model parameter values and the distributions all have small variances. Similarly, for the real shale-gas field case, the modes of distributions of model parameters are neighboring the "best" model parameters that produce smallest global error with high precision. The proposed workflow allows us to provide accurate characterizations of fracture geometries/reservoir properties with high precision and would provide valuable insights for well-spacing optimization.
Robust Uncertainty Quantification of Fracture Geometries Through Automatic History Matching with Application in Real Shale Gas
Xiao, Yuchen, Liu, Chuxi, Yu, Wei, Sepehrnoori, Kamy, and Corwin Zigler. "Robust Uncertainty Quantification of Fracture Geometries Through Automatic History Matching with Application in Real Shale Gas." Paper presented at the SPE/AAPG/SEG Unconventional Resources Technology Conference, Houston, Texas, USA, June 2022. doi: https://doi.org/10.15530/urtec-2022-3720381
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