Complex lithology petrophysical interpretation with multiphysics logging tools has been and continues to be a major challenge in formation evaluation. Many currently used data-driven approaches, such as a neural network (NN), deliver predicted results in numerical quantities rather than analytical equations. It is more challenging if multiphysics logging measurements are collectively used to estimate a petrophysical parameter. To overcome these problems, a physics-guided, artificial intelligence (AI) machine-learning (ML) 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) a 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 data set; (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 to finalize the model selection based on mathematical complexity, physics complexity, and model performance. The efficacy of the five-constituents petrophysical interpretation development process is demonstrated on a data set collected from six wells with the goal of obtaining formation resistivity factor (F) and permeability (k) equations for heterogeneous carbonate reservoirs. We show quantitatively how individual constituents of the workflow improve the model performance with two error metrics. A comparison of NN-method-predicted permeability values vs. SR-based-workflow-predicted permeability equation is included to showcase many advantages of the latter. Beyond the transparency of an analytical form of the prediction equations, the SR method intrinsically has a more relaxed requirement on the training data size, is less prone to overfitting, yet can deliver superior model performance rival to the NN approach.

Songhua Chen

Wei Shao

Huiwen Sheng

Hyung Kwak

Petrophysics – The SPWLA Journal of Formation Evaluation and Reservoir Description

PETROPHYSICS 包含对地层评价的理论和应用方面的原创性贡献，包括裸眼和套管井测井、岩心分析和地层测试。

The journal "Petrophysics" publishes original research contributions on the theory and application of formation evaluation, including open-hole and cased-hole logging, core analysis, and formation testing.

《Petrophysics》期刊发表关于地层评价的原创性研究，包括裸眼和套管井测井、岩心分析及地层测试等理论与应用方面的贡献。

Category	Quartile
工程技术	4
工程技术, 工程石油	4
工程技术, 地球化学与地球物理	4

Use of Symbolic Regression for Developing Petrophysical Interpretation Models

ivySCI AI Smartly Parses PDF, Answers Researchers' Questions, and Helps You Understand Papers in Seconds

Journal Info

Category	Quartile
GEOCHEMISTRY & GEOPHYSICS	4