A new physics-guided AI machine learning method for petrophysical interpretation model development is described. The workflow consists of the following five constituents: (1) statistical tools such as correlation heatmaps are employed to select the best candidate input variables for the target petrophysical equations; (2) genetic programming based symbolic regression approach is used to fuse multiphysics measurements data for training the petrophysical prediction equations; (3) an optional ensemble modeling procedure is applied for maximally utilizing all available training data by integrating multiple instances of prediction equations objectively, which is especially useful for a small training dataset; (4) a means of obtaining conditional branching in prediction equations is enabled in symbolic regression to handle certain formation heterogeneity; and (5) a model discrimination framework is introduced tofinalize the model selection based on mathematicalcomplexity, physics complexity, and modelperformance.

The efficacy of the five-constituents petrophysical interpretation development process is demonstrated on a dataset collected from six wells for a goal of obtaining formation resistivity factor (F) and permeability (k) equations for heterogenous carbonate reservoirs. This study demonstrates that this new petrophysical model development process has many advantages over traditional empirical methods or other commonly used AI methods.


For rock formations having complex lithology and mineralogy, especially where the underlying correlations between logging responses and the target petrophysical attributes are nonlinear, it is difficult to come up with mechanistic or even empirical correlation equations. It is more challenging if data collected from multiple logging tools are used to build a petrophysical interpretation equation. On the other hand, most commonly used data-driven methods, such as Neural Network (NN), Decision Tree (DT), K-Nearest Neighbor (KNN), Support Vector Machine (SVM), or Random Forest (RF), etc., deliver predicted results in numerical quantities, rather than analytical equations. It would be extremely difficult, if not impossible, to assess whether such a solution is consistent to measurement physics with a black-box prediction. Further, in the case where multiple physics measurement data are included in the input variables, there is no transparency on how each measurement contributes to the predicted results with these black-box machine learning methods.

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