Conclusion

In this work, machine learning and statistical regression models were evaluated for the prediction of routine and special core analysis petrophysical properties on datasets containing experimental results for rock samples from many Brazilian reservoirs.

Several feature engineering and machine learning techniques were evaluated for the estimation of absolute permeability from mercury injection capillary pressure curves. The absolute permeability regression models that achieved the lowest median absolute errors and largest correlation coefficients used the support-vector machine (SVR), random forest or gradient boosted decision trees algorithms, and several features extracted from the mercury porosimetry capillary pressure curve data. Among the linear models for prediction of absolute permeability, the models proposed by Swanson (Swanson 1981) and Winland (Kolodzie 1980) obtained the lowest root mean squared errors and highest correlation coefficients.

Using a parametric formulation, special core analysis capillary pressure and relative permeability curve regression problems were framed in a multi-task regression approach. For the estimation of capillary pressure curve parameters, an analytic formulation of the multi-task linear regression problem was considered using the multivariate gaussian conditional distribution. This model was evaluated on an experimental dataset, comparing average predictions and samples from the conditional distribution of parameters, to the observed capillary pressure curve parameters. Although significant dispersion of experimental and predicted parameters values were observed, it was possible to identify that predictions followed expected linear tendencies of capillary pressure curve parameters and absolute permeability.

Posterior distribution of partially pooled varying slopes hierarchical and completely pooled simple linear regression models, with respect to logarithmic absolute permeability, were inferred for relative permeability parameters. Hierarchical linear regression models displayed overall improved information criteria metrics, evaluated using bayesian Watanabe-Akaike and Leave-one-out information criteria. Due to the regularizing effect of the information sharing between different reservoir categories, posterior distribution of relative permeability parameters of hierarchical linear regression models displayed smaller uncertainties and greater consistency.

Posterior distribution of latent parameters of hierarchical linear regression models represent average behavior of model parameters across the different evaluated categories and may be used as quantified petrophysical parameter model analogues for petrophysical characterization of reservoirs with similar characteristics as the ones used in the assembled model, but with no sampled data.

References

Kolodzie, Stanley. 1980. “Analysis of Pore Throat Size and Use of the Waxman-Smits Equation to Determine Ooip in Spindle Field, Colorado.” In SPE Annual Technical Conference and Exhibition, 10. Dallas, Texas: Society of Petroleum Engineers. https://doi.org/10.2118/9382-MS.

Swanson, B. F. 1981. “A Simple Correlation Between Permeabilities and Mercury Capillary Pressures.” Journal of Petroleum Technology 33 (12): 2498–2504. https://doi.org/10.2118/8234-PA.