Real-Time Gamma Ray Log Generation from Drilling Parameters of Offset Wells Using Physics-Informed Machine Learning
Authors: Sheth Prasham , Sistla Sai Shravani , Roychoudhury Indranil , Gao Mengdi , Chatar Crispin , Celaya Jose , Mishra Priya 
Published: November 2023

Summary
By 2026, USD 5.05 billion will be spent per year on logging while drilling (LWD) according to the market report from Fortune Business Insights (2020). Logging tools and wireline tools are costly services for operators to pay for, and the companies providing the services also have a high cost of service delivery. They are, however, an essential service for drilling wells efficiently. The ability to computationally generate logs in real time using known relationships between the rock formations and drilling parameters, namely, rate of penetration (ROP), rotations per minute (RPM), surface weight on bit (SWOB), surface torque (TQX), standpipe pressure (SPPA), and hookload (HKLD), provides an alternative method to generate formation evaluation information (analysis of the subsurface formation characteristics such as lithology, porosity, permeability, and saturation). This paper describes an approach to creating a digital formation evaluation log generator using a novel physics-informed machine learning (PIML) approach that combines physics-based approaches with machine learning (ML) algorithms. The designed approach consists of blocks that calculate mechanical specific energy (MSE), physical estimates of gamma ray (GR) using physical and empirical models, and formation information. All this information and the drilling parameters are used to build a classification model to predict the formations, followed by formation-based regression models to get the final estimate of GR log.
The designed PIML approach learns the relationships between drilling parameters and the GR logs using the data from the offset wells. The decomposition of the model into multiple stages enables the model to learn the relationship between drilling parameters data and formation evaluation data. It makes it easier for the model to generate GR measurements consistent with the rock formations of the subject well being drilled. Because the computationally generated GR by the model is not just dependent on the relationships between drilling parameters and GR logs, this model is also generalizable and capable of being deployed into the application with only retraining on the offset wells and no change in the model structure or complexity. For this paper, the drilling of the horizontal section will not be discussed, as this was done as a separate body of work.
Historically collected data from the US Land Permian Basin wells are used as the primary data set for this work. Results from the experiments based on the data collected from five different wells have been presented. Leave-one-out validation for each of the wells was performed. In the leave-one-out validation process, four of the wells represent the set of offset wells and the remaining one becomes the subject well. The same process is repeated for each of the wells as they are in turn defined as a subject well. Results show that the framework can infer and generate logs such as GR logs in real time. The average root-mean-squared error (RMSE) observed from the experiments is 27.25 api, representing about 10% error. This error value is calculated based on the mean estimate and does not consider the predicted confidence interval. Considering the confidence interval helps further reduce the error margin.