Photoelectric factor prediction using automated learning and uncertainty quantification

The photoelectric factor (PEF) is an important well-logging tool to distinguish between different types of reservoir rocks because PEF measurement is sensitive to elements with high atomic numbers. Furthermore, the ratio of rock minerals could be determined by combining PEF log with other well logs. However, PEF logs could be missing in some cases such as in old well logs and wells drilled with barite-based mud. Therefore, developing models for estimating missing PEF logs is essential in those circumstances. In this work, we developed various machine learning models to predict PEF values using the following well logs as inputs: bulk density (RHOB), neutron porosity (NPHI), gamma ray (GR), compressional and shear velocity. The predictions of PEF values using adaptive-network-fuzzy inference system (ANFIS) and artificial neural network (ANN) models have errors of about 16% and 14% average absolute percentage error (AAPE) in the testing dataset, respectively. Thus, a different approach was proposed that is based on the concept of automated machine learning. It works by automatically searching for the optimal model type and optimizes its hyperparameters for the dataset under investigation. This approach selected a Gaussian process regression (GPR) model for the accurate estimation of PEF values. The developed GPR model decreases the AAPE of the predicted PEF values in the testing dataset to about 10% AAPE. This error could be further decreased to about 2% by modeling the potential noise in the measurements using the GPR model.