Calibrating Field-Scale Uncertainties to Local Data: Is the Learning Being Overgeneralized?
- Jincong He (Chevron Energy Technology Company) | Albert C. Reynolds (University of Tulsa) | Shusei Tanaka (Chevron Energy Technology Company) | Xian-Huan Wen (Chevron Energy Technology Company) | Jairam Kamath (Chevron Energy Technology Company)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- February 2020
- Document Type
- Journal Paper
- 139 - 161
- 2020.Society of Petroleum Engineers
- analytical formula, modeling error, history matching, data assimilation
- 4 in the last 30 days
- 198 since 2007
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A common pitfall in probabilistic history matching is omitting the local variation of spatial uncertainties and falsely generalizing the learning from local data to the entire field. This can lead to radical overestimation of uncertainty reduction and bad reservoir-management decisions. In this paper, we propose a methodology to quantify and correct for the error that arises from the omission of local variation in probabilistic history matching.
Most performance metrics in an oil field, such as the original oil in place (OOIP) and the estimated ultimate recovery (EUR), are field-scale objective functions that depend on properties (e.g., porosity) over the entire field. On the other hand, many measurement data from wells [e.g., bottomhole pressure (BHP)] are mainly sensitive to the reservoir properties near the locations where they are measured, and thus they are susceptible to local variations of reservoir properties. Calibrating field-scale objective functions to local well data without properly characterizing the local variation can overestimate the uncertainty reduction of field-scale objective functions. In this paper, we derived formulas to quantify errors in the posterior cumulative distribution functions (CDFs) of the objective functions resulting from the omission of local variation. We also provide a way to correct for the error and to recover the true posterior CDFs.
Through theoretical derivation, we show that the modeling error that arises from the omission of local variation is dependent on the magnitude of the global and local variations of the uncertain properties (e.g., porosity). The larger the local variation relative to the global variation, the larger the error in the estimated posterior distributions. The error also depends on the variogram of the local variation and the detection range of the data. The error is larger for cases with a long variogram for the local variation and a short data-detection range. In addition, the modeling errors for different measurement data points can be highly correlated even when the measurement errors for these data are independent. To correct for this modeling error, analytical and empirical formulas are proposed that have been shown to greatly improve the accuracy of the posterior distributions in a number of cases.
To the best of our knowledge, this is the first time that the modeling error from the omission of local variation in the probabilistic history-matching process has been quantified and corrected. The methodology proposed could help improve the reliability of the result from probabilistic history matching.
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