Modeling the Cementation Exponent Using Pore Structure Descriptions in Heterogeneous Carbonate Formations Through Robust Intelligent Modeling

Rostami, Alireza; Helalizadeh, Abbas; Bahari Moghaddam, Mehdi; Soleymanzadeh, Aboozar

doi:10.22050/ijogst.2025.445375.1705

Modeling the Cementation Exponent Using Pore Structure Descriptions in Heterogeneous Carbonate Formations Through Robust Intelligent Modeling

Document Type : Research Paper

Authors

Alireza Rostami ¹

Abbas Helalizadeh ²

Mehdi Bahari Moghaddam ²

Aboozar Soleymanzadeh ³

¹ PhD of Petroleum Engineering, Department of Petroleum Engineering, Petroleum University of Technology (PUT), Ahwaz, Iran

² Assistant Professor of Petroleum Engineering, Department of Petroleum Engineering, Petroleum University of Technology (PUT), Ahwaz, Iran

³ Director of Research Affairs, Department of Petroleum Engineering, Petroleum University of Technology (PUT), Ahwaz, Iran

https://doi.org/10.22050/ijogst.2025.445375.1705

Abstract

In this study, several robust and computationally efficient machine learning methods are developed to estimate the cementation exponent in carbonate formations characterized by heterogeneous pore systems, thereby addressing a critical need for accurate petrophysical property prediction in complex geological settings. Unlike conventional empirical correlations, support vector regression (SVR), multilayer perceptron neural network (MLPNN), probabilistic neural network (PNN), random forest (RF), decision tree (DT), and eXtreme gradient boosting (XGBoost) are implemented as predictive algorithms to simulate the cementation exponent based on detailed pore structure descriptions and total porosity. To optimize the parameters of the MLPNN model, the Levenberg–Marquardt (LM) algorithm is integrated with MLPNN, resulting in a hybrid framework referred to as MLPNN-LM. This hybrid approach enhances parameter optimization, leading to improved predictive accuracy and faster convergence.
The database required for model development, validation, and testing is compiled from Ragland’s dataset and is systematically divided into training, validation, and testing subsets. The results indicate high predictive performance for the hybrid MLPNN-LM and RF models. Key statistical indicators include Average Absolute Percentage Relative Deviation AAPRD values of 4.3781% for MLPNN-LM and 4.8690% for RF, along with coefficients of determination R² of 0.8654 and 0.8731, respectively. These findings demonstrate that MLPNN-LM and RF provide more accurate cementation exponent estimates than widely used literature correlations and other machine learning approaches.
Sensitivity analysis reveals that interparticle, moldic, and connected vuggy pore types exert the most significant influence on model predictions. The reliability of the dataset and the robustness of the MLPNN-LM and RF models are further evaluated using Williams plots. Approximately 93.75% and 91.96% of the data points fall within the applicability domain of the MLPNN-LM and RF models, respectively, confirming their generalizability. Trend analysis further demonstrates strong agreement between predicted and measured cementation exponent values, particularly for deep formations with depths greater than 1200 m and tight carbonate reservoirs with total porosity below 10%, where traditional correlations often fail due to the complex behavior of the cementation exponent.
In conclusion, reliable and accurate computational frameworks are introduced for estimating the cementation exponent as a function of pore structure characteristics. These models are well suited for fluid flow simulation and reservoir characterization in carbonate and heterogeneous formations, especially in deep and tight carbonate reservoirs.

Highlights

· The most advanced and hybrid approaches, namely support vector regression (SVR), eXtreme gradient boosting (XGBoost), probabilistic neural networks (PNN), decision trees (DT), multilayer perceptron neural networks trained with the Levenberg–Marquardt algorithm (MLPNN-LM), and random forest (RF), are employed for model development.

· A comprehensive literature database of cementation exponent data for tight and deep carbonate reservoirs is compiled and analyzed.

· Multiple statistical performance metrics and graphical analyses are utilized to evaluate model performance.

· The MLPNN-LM and RF models demonstrate the strongest agreement with the measured cementation exponent data compared with existing literature correlations and other machine learning techniques.

· The developed MLPNN-LM and RF models represent reliable candidates for simulating tight and deep carbonate reservoirs.

Keywords

Cementation exponent

Deep and tight carbonate reservoirs

Random forest (RF)

Multilayer perceptron neural network (MLPNN)

Levenberg–Marquardt (LM)

Pore structure description

Subjects

Petroleum Engineering

Asquith, G., The importance of determining pore type from petrophysical logs in the evaluation of a Permian Wolfcamp reentry northern Midland Basin, The Log Analyst, Vol. 38, No. 03, p. 37-46, 1997.

Awad, M., and Khanna, R., Efficient learning machines: Theories, concepts, and applications for engineers and system designers, 268 p. Springer Nature, 2015.

Biau, G., Analysis of a random forests model, The Journal of Machine Learning Research, Vol. 13, No. 1, p. 1063–1095, 2012.

Blockeel, H., Devos, L., Frénay, B., Nanfack, G., and Nijssen, S., Decision trees: from efficient prediction to responsible AI, Frontiers in Artificial Intelligence, Vol. 6, Article ID 1215873, 2023.

Borai, A., A new correlation for the cementation factor in low-porosity carbonates, SPE Formation Evaluation, Vol. 2, No. 04, p. 495–499, 1987.

Breiman, L., Random forests, Machine Learning, Vol. 45, No. 1, p. 5–32, 2001.

Brownlee, J., A gentle introduction to XGBoost loss functions, Machine Learning Mastery, 2021. Available: https://machinelearningmastery.com/xgboost-loss-functions.

Chang, D. T., Probabilistic deep learning with probabilistic neural networks and deep probabilistic models, arXiv preprint, arXiv:2106.00120, 2021.

Chang, P., Multi-layer perceptron neural network for improving detection performance of malicious phishing URLs without affecting other attack types classification, arXiv preprint, arXiv:2203.00774, 2022.

Chen, H. C., and Fang, J. H., Sensitivity analysis of the parameters in Archie's water saturation equation, The Log Analyst, Vol. 27, No. 05, 1986.

Chen, T., and Guestrin, C., XGBoost: a scalable tree boosting system, Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Association for Computing Machinery, San Francisco, California, USA, p. 785–794, 2016.

Chen, T., Story and lessons behind the evolution of XG-Boost, 7 p. 2016.

Chilingarian, G. V., Chang, J., and Bagrintseva, K. J., Empirical expression of permeability in terms of porosity, specific surface area, and residual water saturation of carbonate rocks, Journal of Petroleum Science and Engineering, Vol. 4, No. 4, p. 317–322, 1990.

Chok, N. S., ms, Pearson's versus Spearman's and Kendall's correlation coefficients for continuous data, Ph.D. thesis, University of Pittsburgh, Pittsburgh, 2010.

Costa, V. G., and Pedreira, C. E., Recent advances in decision trees: an updated survey, Artificial Intelligence Review, Vol. 56, No. 5, p. 4765–4800, 2023.

Fischer, A., Izmailov, A. F., and Solodov, M. V., The Levenberg–Marquardt method: an overview of modern convergence theories and more, Computational Optimization and Applications, Vol. 89, No. 1, p. 33–67, 2024.

Focke, J., and Munn, D., Cementation exponents in Middle Eastern carbonate reservoirs, SPE Formation Evaluation, Vol. 2, No. 02, p. 155–167, 1987.

Goodall, C. R., 13 Computation using the QR decomposition, Handbook of Statistics, Elsevier, Vol. 9, p. 467–508, 1993.

Gramatica, P., Principles of QSAR models validation: internal and external, QSAR & Combinatorial Science, Vol. 26, No. 5, p. 694–701, 2007.

Hemmati-Sarapardeh, A., Ameli, F., Dabir, B., Ahmadi, M., and Mohammadi, A. H., On the evaluation of asphaltene precipitation titration data: modeling and data assessment, Fluid Phase Equilibria, Vol. 415, p. 88–100, 2016.

Herrick, D. C., and Kennedy, W. D., Electrical efficiency; a pore geometric theory for interpreting the electrical properties of reservoir rocks, Geophysics, Vol. 59, No. 6, p. 918–927, 1994.

Herrick, D., and Kennedy, W. D., Formation resistivity factor and permeability relationships in rocks characterized by secondary solution porosity, SPWLA 36th Annual Logging Symposium, OnePetro, 1995.

Huang, X., Cao, H., and Jia, B., Optimization of Levenberg Marquardt algorithm applied to nonlinear systems, Processes, Vol. 11, No. 6, p. 1794, 2023.

Iranzad, R., and Liu, X., A review of random forest-based feature selection methods for data science education and applications, International Journal of Data Science and Analytics, Vol. 20, p. 1–15, 2024.

Kolah-Kaj, P., Kord, S., and Soleymanzadeh, A., Application of electrical rock typing for quantification of pore network geometry and cementation factor assessment, Journal of Petroleum Science and Engineering, Vol. 208, Article ID 109426, 2022.

Li, F., Zhang, X., Lu, A., Xu, L., Ren, D., and You, T., Estimation of metal elements content in soil using x-ray fluorescence based on multilayer perceptron, Environmental Monitoring and Assessment, Vol. 194, No. 2, p. 95, 2022.

Loh, W. Y., Classification and regression trees, WIREs Data Mining and Knowledge Discovery, Vol. 1, No. 1, p. 14–23, 2011.

Lv, X., and Yu, Z., A modified Levenberg–Marquardt algorithm for low order-value optimization problem, Journal of Applied Mathematics and Computing, Vol. 70, No. 6, p. 5629–5644, 2024.

Mahdaviara, M., Rostami, A., and Shahbazi, K., Smart learning strategy for predicting viscoelastic surfactant (VES) viscosity in oil well matrix acidizing process using a rigorous mathematical approach, SN Applied Sciences, Vol. 3, No. 10, p. 815, 2021.

Mahdavi-Ara, M., Rostami, A., Shahbazi, K., Shokrollahi, A., and Ghazanfari, M. H., Estimating aqueous nanofluids viscosity via GEP modeling: correlation development and data assessment, Iranian Journal of Chemistry and Chemical Engineering, Vol. 41, No. 1, p. 266–283, 2022.

Najafi-Silab, R., Soleymanzadeh, A., Kolah-Kaj, P., and Kord, S., Electrical rock typing using Gaussian mixture model to determine cementation factor, Journal of Petroleum Exploration and Production Technology, Vol. 13, No. 5, p. 1329–1344, 2023.

Neustaedter, R. H., Log evaluation of deep Ellenburger gas zones, SPE Deep Drilling and Development Symposium, Monahans, Texas, SPE-2071-MS, 1968.

Pourkamali-Anaraki, F., Husseini, J. F., and Stapleton, S. E., Probabilistic neural networks (PNNs) for modeling aleatoric uncertainty in scientific machine learning, IEEE Access, Vol. 12, p. 178816–178831, 2024.

Ragland, D. A., Trends in cementation exponents (m) for carbonate pore systems, Petrophysics, Vol. 43, No. 05, 2002.

Rostami, A., Helalizadeh, A., Moghaddam, M. B., and Soleymanzadeh, A., New insights into estimating the cementation exponent of the tight and deep carbonate pore systems via rigorous numerical strategies, Journal of Petroleum Exploration and Production Technology, Vol. 14, No. 6, p. 1605–1629, 2024.

Rostami, A., Kordavani, A., Parchekhari, S., Hemmati-Sarapardeh, A., and Helalizadeh, A., New insights into permeability determination by coupling Stoneley wave propagation and conventional petrophysical logs in carbonate oil reservoirs, Scientific Reports, Vol. 12, Article ID 11618, 2022.

Rousseeuw, P. J., and Leroy, A. M., Robust regression and outlier detection, John Wiley & Sons, 2003.

Sayahi, T., Tatar, A., Rostami, A., Anbaz, M. A., and Shahbazi, K., Determining solubility of CO2 in aqueous brine systems via hybrid smart strategies, International Journal of Computer Applications in Technology, Vol. 65, No. 1, p. 1–13, 2021.

Smola, A. J., and Schölkopf, B., A tutorial on support vector regression, Statistics and Computing, Vol. 14, No. 3, p. 199–222, 2004.

Soleymanzadeh, A., Helalizadeh, A., Jamialahmadi, M., and Soulgani, B. S., Development of a new model for prediction of cementation factor in tight gas sandstones based on electrical rock typing, Journal of Natural Gas Science and Engineering, Vol. 94, Article ID 104128, 2021.

Soleymanzadeh, A., Helalizadeh, A., Jamialahmadi, M., and Soulgani, B. S., Investigation of analogy between thermal and electrical properties of some reservoir rocks, Bulletin of Engineering Geology and the Environment, Vol. 80, No. 1, p. 507–517, 2021.

Soleymanzadeh, A., Jamialahmadi, M., Helalizadeh, A., and Soulgani, B. S., A new technique for electrical rock typing and estimation of cementation factor in carbonate rocks, Journal of Petroleum Science and Engineering, Vol. 166, p. 381–388, 2018.

Soleymanzadeh, A., Kolah kaj, P., Kord, S., and Monjezi, M., A new technique for determining water saturation based on conventional logs using dynamic electrical rock typing, Journal of Petroleum Science and Engineering, Vol. 196, Article ID 107803, 2021.

Stebakov, I., Kornaev, A., Popov, S., and Savin, L., Fault diagnosis systems for rotating machines operating with fluid-film bearings, Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, Vol. 236, No. 10, p. 1917–1931, 2022.

Watfa, M., and Nurmi, R., Calculation of saturation, secondary porosity and producibility in complex Middle East carbonate reservoirs, SPWLA Annual Logging Symposium, Paper No. SPWLA-1987, 1987.

Yan, C., Shen, X., and Guo, F., An improved support vector regression using least squares method, Structural and Multidisciplinary Optimization, Vol. 57, No. 6, p. 2431–2445, 2018.