Journal of Petroleum Science and Technology

Journal of Petroleum Science and Technology

Extending Dual Porosity Models to Anisotropic Fractured Reservoirs Using Physics-Guided Neural Networks

Document Type : Research Paper

Authors
mohsen masihi 1
mohammad zaree
ali salehi
qingrong xiong 2
1 Department of Chemical and Petroleum Engineering, Sharif University of Technology, Iran
2 School of Civil Engineering, Shandong University, China
10.22078/jpst.2026.5818.1994
Abstract
The non-orthogonal fractures in conventional Warren and Root (WR) induce directional permeabilities and anisotropic flow patterns that cannot be captured using simple fracture properties. In this paper, we use the proposed equivalent fracture aperture, obtained via a correction coefficient (η), to account for this effect. Previous studies estimated this coefficient by calibrating to static field data. The main contribution is to treat this coefficient as a physics-dependent parameter rather than a calibration value to bridge fracture-scale flow with the continuum model. A data-driven approach is developed to quantify η as a function of fracture geometry and reservoir-scale properties. Moreover, a dataset of 2,478 simulation samples was generated using COMSOL Multiphysics, covering a range of fracture and reservoir properties. In addition, an artificial neural network (ANN) was trained and optimized on this dataset to learn the nonlinear relation with the correction coefficient, achieving a predictive accuracy of R² = 0.9946. By using the ANN-predicted correction coefficient in the WR approach, a multiscale bridge between fracture-scale physics and dual-porosity models can be achieved. Furthermore, the cubic relationship between permeability and fracture aperture (kθ = η3 k) highlights the importance of accurate η estimation, as any error in η propagates results into large permeability uncertainties. Ultimately, the numerical results showed that the dependency of the correction coefficient η on fracture orientation is much greater than its dependency on either fracture size and matrix shape or system size. Also, using this simple correction factor, the applicability of conventional dual-porosity models to anisotropic fractured reservoirs with non-orthogonal fractures is extended.
Keywords
Naturally Fractured Reservoirs
COMSOL
Anisotropy
Artificial Neural Network (ANN)
Fracture Aperture Correction Coefficient
Saeedi, M. (2016). Application of Multi-Stage Fracturing of Horizontal Wells in SAGD Technology (Doctoral dissertation, University of Calgary (Canada)).
Nelson, R. A. (1985). Geologic analysis of naturally fractured reservoirs (Vol. 1). Gulf Professional Publishing.
Allen, P. A., & Allen, J. R. (2013). Basin analysis: Principles and application to petroleum play assessment. John Wiley & Sons.
Narr, W., Schechter, D. S., & Thompson, L. B. (2006). Naturally fractured reservoir characterization. (No Title).
Dershowitz, W. S., & Einstein, H. H. (1988). Characterizing rock joint geometry with joint system models. Rock mechanics and rock engineering, 21(1), 21-51.
Aguilera, R. (1995). Naturally fractured reservoirs (2nd ed.). PennWell Books.
Bear, J. (1972). Dynamics of fluids in porous media. Elsevier.
Reiss, L. H. (1980). The reservoir engineering aspects of fractured formations. Editions Technip.
Lucia, F. J. (1995). Rock-fabric/petrophysical classification of carbonate pore space for reservoir characterization. AAPG bulletin, 79(9), 1275-1300.
Aguilera, R. (2002). Incorporating capillary pressure, pore throat aperture radii, height above free-water table, and Winland r 35 values on Pickett plots. AAPG bulletin, 86(4), 605-624. doi.org/10.1306/61EEDB5C-173E-11D7-8645000102C1865D.
Corey, A. T. (1977). Mechanics of heterogeneous fluids in porous media (pp. 259-pp). ISBN (Hardback): 978-0-918334-17-6.
Parsons, R. W. (1966). Permeability of idealized fractured rock. Society of Petroleum Engineers Journal, 6(02), 126-136. doi.org/10.2118/1289-PA.
Long, J. C., Remer, J. S., Wilson, C. R., & Witherspoon, P. A. (1982). Porous media equivalents for networks of discontinuous fractures. Water resources research, 18(3), 645-658. doi.org/10.1029/WR018i003p00645.
Dershowitz, W., & Miller, I. (1995). Dual porosity fracture flow and transport. Geophysical Research Letters, 22(11), 1441-1444. doi.org/10.1029/95GL01099.
Barenblatt, G. I., Zheltov, Y. P., & Kochina, I. N. (1960). Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks. Journal of Applied Mathematics and Mechanics, 24(5), 852-864.
Warren, J. E., & Root, P. J. (1963). The behavior of naturally fractured reservoirs. Society of Petroleum Engineers Journal, *3*(3), 245–255.
Kazemi, H. (1969). Pressure transient analysis of naturally fractured reservoirs with uniform fracture distribution. Society of Petroleum Engineers Journal, *9*(4), 451–462.
de Swaan, A. (1990). Analytic solutions for determining naturally fractured reservoir properties by well testing. Society of Petroleum Engineers Journal, *30*(3), 479–486.
Gerke, H. H., & van Genuchten, M. T. (1993). A dual-porosity model for simulating the preferential movement of water and solutes in structured porous media. Water Resources Research, *29*(2), 305–319.
Zimmerman, R. W., Chen, G., Hadgu, T., & Bodvarsson, G. S. (1993). A numerical dual-porosity model with semianalytical treatment of fracture/matrix flow. Water Resources Research, 29(7), 2127–2137.
Young, R. A., Randolph, P. L., & Lee, W. J. (1989). Application of the equivalent fracture aperture in the Warren-Root model. SPE Formation Evaluation, 4(2), 233–240.
Zhang, Z., Li, X., & Wang, X. (2022). Improved permeability model with equivalent fracture aperture for coal anisotropy. International Journal of Coal Geology, *261*, 104077.
Geiger, S., & Matthäi, S. K. (2012). What can we learn from high-resolution numerical simulations of single- and multi-phase fluid flow in fractured outcrop analogues? Advances in Water Resources, 51, 220–236.
Tryggvason, G., Bunner, B., Esmaeeli, A., Juric, D., Al-Rawahi, N., Tauber, W., Han, J., Nas, S., & Jan, Y. J. (2001). A front-tracking method for the computations of multiphase flow. Journal of Computational Physics, 169(2), 708–759.
Hirt, C. W., & Nichols, B. D. (1981). Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics, *39*(1), 201–225.
Osher, S., & Sethian, J. A. (1988). Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics, 79(1), 12–49. doi: 10.1016/0021-9991(88)90002-2.
Sussman, M., Smereka, P., & Osher, S. (1994). A level set approach for computing solutions to incompressible two-phase flow. Journal of Computational Physics, 114(1), 146–159. doi: 10.1006/jcph.1994.1155
Guadala, A., Dvorkin, J., & Mavko, G. (2020). Coupled hydro-geomechanical modeling of fractured reservoirs. Journal of Geophysical Research: Solid Earth, *125*(7), e2020JB019587.
Kumar, A., Ozkan, E., & Gokaraju, B. (2016). Simulation of viscous fingering in homogeneous porous media using COMSOL. In COMSOL Conference.
Patani, P., Smith, R., & Kumar, A. (2023). Probabilistic assessment of equivalent fracture aperture constrained by real-time drilling mud loss data. Journal of Petroleum Science and Engineering, 224, 111234.
Zhou, Y., Wang, X., & Li, Q. (2023). Phase-field modeling of fluid-driven dynamic crack propagation in porous media using COMSOL Multiphysics. International Journal of Rock Mechanics and Mining Sciences, 168, 105401.
El Ouahed, A. K., Tiab, D., & Mazouzi, A. (2005). Application of artificial intelligence to characterize naturally fractured zones in Hassi Messaoud oil field, Algeria. Journal of Petroleum Science and Engineering, 49(3–4), 122–141. doi: 10.1016/j.petrol.2005.05.003.
Al-Dhamen, M., Al-Mulhem, A., & Al-Yami, A. (2021). AI-based model for predicting acid fracturing performance in naturally fractured reservoirs. Journal of Petroleum Science and Engineering, 196, 107689.
Peng, C., Zhang, L., & Li, X. (2019). Integration of EDFM and AI for history matching in fractured reservoirs. Journal of Natural Gas Science and Engineering, 71, 102982.
Kumar, S., Ghassemi, A., & Pandey, V. (2023). Integration of SVM and neural networks for natural fracture characterization in shale gas reservoirs. Fuel, *332*, 126112.
Zheng, S., Li, H., & Zhang, T. (2022). Coupling reservoir simulation with AI for fracture property optimization in shale gas sweet spot prediction. Energy, 239, 122345. doi.org/10.1016/j.energy.2021.122345.
Alqahtani, A., Khan, M. A., & Al-Hajri, M. (2023). Application of random forests and neural networks for  predicting fluid loss and complex flow behavior in fractured reservoirs. Journal of Petroleum Exploration and Production Technology, 13(2), 451–463.
Al-Sulaiman, S., Rahman, M., & Al-Shammari, H. (2023). Machine learning investigation of single fracture influence on flow dynamics in dolomite formations. Energy Reports, 9, 788–799.
Hassan, A., Mohebian R. (2023). Machine learning applications in fractured reservoir characterization. Journal of Petroleum Technology. doi.org/10.1016/j.ptlrs.2025.04.006.
Bian, X., Zhou, J., Fu, L., Jin, A., Gorelick S., & Zhang, W. (2026). Artificial Intelligence for Hydraulic Fracturing Decision Support: A Workflow-Oriented Critical Review. Processes, 14(16), 2537-2546. doi.org/10.3390/pr14162537.
Nick, H. M., & Bisdom, K. (2018, February). Fracture aperture in flow models: to average, or not to average?. In Third EAGE Workshop on Naturally Fractured Reservoirs. 2018, 1, 1-4. European Association of Geoscientists & Engineers. doi.org/10.3997/2214-4609.201800028.
Hu, M., & Rutqvist, J. (2022). Multi-scale coupled processes modeling of fractures as porous, interfacial and granular systems from rock images with the numerical manifold method. Rock Mechanics and Rock Engineering, 55(5), 3041-3059. doi.org/10.1007/s00603-021-02455-6.
Luo, B., & Wong, G. K. (2024, June). Enhancing Cluster Efficiency by Modeling Swelling Diverter Particles in PKN-Type Fractures. In ARMA US Rock Mechanics/Geomechanics Symposium (p. D031S027R002). ARMA. 
Yang, Z., Li, D., Xue, S., Hu, R., Gorelick S. & Chen, Y. F. (2019). Effect of aperture field anisotropy on two-phase flow in rough fractures, Advances in Water Resources, 132, 103390-103397, doi.org.10.1016/j.advwatres.2019.103390.
Kim, S., Lee, J. (2024). Dual-porosity modeling improvements for anisotropic fractured reservoirs. SPE Journal.
Goodfellow, I., Bengio, Y., & Courville, A. (2016). Deep learning. MIT Press.
Mohaghegh, S. (2000). Virtual-intelligence applications in petroleum engineering: Part 1—Artificial neural networks. Journal of Petroleum Technology, *52*(9), 64–73.
Ouenes, A., Bhagavan, S., & Bunge, R. (1995). Application of neural networks in petroleum engineering. SPE Computer Applications, 7(2), 42–48.