Peng-Robinson (P-R) equation of state (EOS) has been widely used in the petroleum industry for hydrocarbon fluids. In this work, a three-dimensional diffuse interface model with P-R EOS for two-phase fluid system is solved by the lattice Boltzmann (LB) method. In this diffuse interface model, an Allen-Cahn (A-C) type phase equation with strong nonlinear source term is derived. Using the multiscale Chapman-Enskog analysis, the A-C type phase equation can be recovered from the proposed LB method. Besides, a Lagrange multiplier is introduced based on the mesoscopic character of the LB scheme so that total mass of the hydrocarbon system is preserved. Three-dimensional numerical simulations of realistic hydrocarbon components, such as isobutane and propane, are implemented to illustrate the effectiveness of the proposed mass conservative LB scheme. Numerical results reach a better agreement with laboratory data compared to previous results of two-dimensional numerical simulations.

The Journal of Computational Mathematics published bi-monthly. It is an international journal covering all branches of modern computational mathematics such as numerical linear algebra, numerical optimization, computational geometry, numerical PDEs and inverse problems. Papers containing new ideas, creative approaches and/or innovative applications as well as invited reviews are expected to appear regularly in the journal. JCM is a refereed international journal sponsored by the Institute of Computational Mathematics and Scientific/Engineering Computing (ICMSEC) of the Chinese Academy of Sciences.

Pore-network models are widely used to describe pore-scale flow in porous media, and their reliability depends critically on accurate extraction of pore and throat structures. A new extraction framework, termed the topological pore-network finder, is proposed in this work, which combines topological data analysis, medial access path search, and flashlight search medial axis. The topological data analysis is used to identify pore connectivity and cluster the void space, thereby providing robust initial pore centers. The medial access path search method then traces strings between connected pore centers along the medial axis, while the flashlight search medial axis method is used to refine the resulting paths and improve computational efficiency. The method is validated using toy porous media, two- and three-dimensional digital rock samples. Sensitivity analyses show that the pore-network finder is stable with respect to image resolution and string discretization. Compared with the classical maximal-ball method, the pore-network finder achieves at least an order-of-magnitude acceleration while preserving the main geometric statistics and f low-response characteristics of the extracted networks. In addition, because the method operates in continuous space and can reuse information from previous states, it is well suited to quasi-dynamic updates during deformation. The pore-network finder therefore provides an efficient and accurate tool for pore-network extraction and subsequent pore-scale characterization in geo-energy systems. Document Type: Original article Cited as: Liu, J., Zhang, T., Duan, Z., Zhang, Y., Sun, S. Topological data analysis for pore-network extraction in porous media. Advances in Geo-Energy Research, 2026, 20(2): 101-113. https://doi.org/10.46690/ager.2026.05.01