Wen Pan, Carlos Torres-Verdín, Ian J Duncan, Micheal J. Pyrcz

Well-log interpretation provides in situ estimates of formation properties such as porosity, hydrocarbon pore volume, and permeability. Reservoir models based on well-log-derived formation properties deliver reserve-volume estimates, production forecasts, and help with decision making in reservoir development. However, due to measurement errors, variability of well logs due to multiple measurement vendors, different borehole tools, and non-uniform drilling/borehole conditions, conventional well-log interpretation methods may not yield accurate estimates of formation properties, especially in the context of multi-well interpretation. To improve the robustness of multi-well petrophysical interpretation, well-log normalization techniques such as two-point scaling and mean-variance normalization are commonly used to impose stationarity constraints for well logs requiring correction. However, these techniques are mostly based on the marginal distribution of well logs and require expert knowledge to be effectively implemented. To reduce the uncertainties and time associated with multi-well petrophysical interpretation, we develop the discriminative adversarial (DA) model and the linear constraint model for well-log normalization and interpretation. We also develop a new divergence-based type well identification method for improved test-well and training-well adaptation.

The DA neural network model developed for well-log normalization and interpretation can perform both linear and nonlinear well-log normalization by considering the joint distribution of all types of well logs and formation properties. To train the DA model, classical machine-learning models or classical petrophysical models are first trained to minimize the prediction error of formation properties in the training data set; then the adversarial model is trained to normalize well logs in the test set, such that the joint distribution of normalized well logs and formation property estimates of the test data set reproduce those of the training data set. The linear constraint model uses an ensemble of predictions from linear models to constrain both well-log normalization and interpretation. To identify wells with stationary formation properties as well as well logs, the divergence-based type well identification method is developed to choose type wells for wells requiring correction based on well-log statistical similarity instead of closeness of wells.

We apply the developed methods to improve the accuracy of well-log normalization and the estimation of permeability in a carbonate reservoir. Six types of well logs and over 9000 feet of core measurements from 30 wells drilled between 1980s and 2010s in the Seminole San Andres Unit are available to validate the new multi-well interpretation workflow. Our interpretation models is flexible to integrate any types of classical machine-learning methods and petrophysical assumptions for robust petrophysical estimations. In comparison to classical machine-learning models with no normalization, with two-point scaling normalization and with linear constraints, the DA method yields better performance, e.g., the mean-squared error of permeability estimation decreases by approximately 20-50%. Our interpretation workflow can be applied to other stationary signal and image processing problems to mitigate errors introduced by biased measurements, and to better adapt models calibrated with data from one field to other neighboring fields.