Bayesian updating with machine learning and geostatistics for posterior predictions of unconventional reservoir performance

Accurate forecasting of hydrocarbon production in unconventional reservoirs requires integrating spatial heterogeneity with well-scale geological and engineering data. Traditional machine learning regression approaches often neglect spatial context, including spatial continuity, spatial trends and data locations, resulting in potential overestimation of uncertainty. To address this limitation, we introduce a Gaussian Bayesian updating workflow that combines a secondary data collocated prior distribution of production with a geostatistical spatially informed conditional distribution using analytical Gaussian updating to estimate the posterior production distribution. The workflow is applied after normal score transformation of all features in Gaussian space to provide complete local uncertainty models from geostatistical kriging estimates and variances and to facilitate the use of closed-form analytical Bayesian updating. Our proposed workflow is demonstrated with 9 geological and 6 completion secondary features to forecast cumulative one-year oil production as the primary feature for an unconventional reservoir. A multivariate machine learning-based prior model is first calculated using local ridge regression with hyperparameter tuning to relate the secondary features to production. The geostatistical spatially informed conditional distribution is calculated by ordinary kriging based on an additive deterministic trend and residual estimation. Bayesian updating with K-fold cross-validation is then applied to tune the workflow, demonstrating a reduction of the high uncertainty of the prior model, yielding a posterior distribution that is both more accurate and precise than the machine learning or geostatistical distributions on their own.