Two-phase flow simulation algorithm for numerical estimation of relative phase permeability curves of porous materials
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Tatyana S. Khachkova
, Elena A. Gondul
Abstract
The paper presents an algorithm for three-dimensional modelling of two-phase flows on the scale of pore size order for numerical evaluation of relative phase permeability curves of porous materials. Such an evaluation is performed based on the results of numerical simulation of primary drainage with subsequent waterflooding. In this case, models of porous materials based on three-dimensional tomographic images of rocks are used. The simulation of the flow considers the Stokes equation and the Cahn–Hilliard equation for modelling phase transfer, which allows us to determine phases using the concentration function. The combination of the phase field method and finite difference method makes it possible to correctly take into account the contact angle and stably calculate surface tension forces in domains with complex topology.
Funding statement: The work was supported by the FSR project FWZZ–2022–0022. The calculations were carried out on the NKS-30T cluster of the Siberian Supercomputer Center.
References
[1] N. Alyafei, Fundamentals of Reservoir Rock Properties. Hamad Bin Khalifa University Press, Doha, 2021.10.5339/Fundamentals_of_Reservoir_Rock_Properties_2ndEditionSearch in Google Scholar
[2] H. Andra, N. Combaret, J. Dvorkin, E. Glatt, J. Han, M. Kabel, Y. Keehm, F. Krzikalla, M. Lee, C. Madonna, M. Marsh, T. Mukerji, E. H. Saenger, R. Sain, N. Saxena, S. Ricker, A. Wiegmann, and Xin Zhan, Digital rock physics benchmarks. Part I: Imaging and segmentation. Computers and Geosciences 50 (2013), 25–32.10.1016/j.cageo.2012.09.005Search in Google Scholar
[3] Y. Bazaikin, B. Gurevich, S. Iglauer, T. Khachkova, D. Kolyukhin, M. Lebedev, V. Lisitsa, and G. Reshetova, Effect of CT image size and resolution on the accuracy of rock property estimates. J. Geophys. Res. Solid Earth 122 (2017), 3635–3647.10.1002/2016JB013575Search in Google Scholar
[4] R. Croce, M. Griebel, and M. A. Schweitzer, Numerical simulation of bubble and droplet deformation by a level set approach with surface tension in three dimensions. Int. J. Numer. Meth. Fluids 62 (2010), 963–993.10.1002/fld.2051Search in Google Scholar
[5] F. Gibou, R. Fedkiw, and S. Osher, A review of level-set methods and some recent applications. J. Comp. Phys. 353 (2018), 82–109.10.1016/j.jcp.2017.10.006Search in Google Scholar
[6] R. D. Groot, Second order front tracking algorithm for Stefan problem on a regular grid. J. Comp. Phys. 372 (2018), 956–971.10.1016/j.jcp.2018.04.051Search in Google Scholar
[7] D. Jacqmin, Contact-line dynamics of a diffuse fluid interface. J. Fluid Mech. 402 (2000), 57–88.10.1017/S0022112099006874Search in Google Scholar
[8] E. Jettestuen, H. A. Friis, and J. O. Helland, A locally conservative multiphase level set method for capillary-controlled displacements in porous media. J. Comp. Phys. 428 (2021), 109965.10.1016/j.jcp.2020.109965Search in Google Scholar
[9] T. Khachkova, V. Lisitsa, G. Reshetova, and V. Tcheverda, GPU-based algorithm for evaluating the electrical resistivity of digital rocks. Comp. Math. Appl. 82 (2021), 200–211.10.1016/j.camwa.2020.11.005Search in Google Scholar
[10] J. Kim, Phase-field models for multi-component fluid flows. Communs in Comp. Phys. 12 (2012), 613–661.10.4208/cicp.301110.040811aSearch in Google Scholar
[11] L. D. Landau and E. M. Lifshitz, Fluid Mechanics, Course of Theoretical Physics, Vol. 6. Pergamon Press, 1959.Search in Google Scholar
[12] X.-D. Liu, S. Osher, and T. Chan, Weighted essentially non-oscillatory schemes. J. Comp. Phys. 115 (1994), 200–212.10.1006/jcph.1994.1187Search in Google Scholar
[13] C. S. Peskin, Flow patterns around heart valves: A numerical method. J. Comp. Phys. 10 (1972), 252–271.10.1016/0021-9991(72)90065-4Search in Google Scholar
[14] V. I. Vasil’ev, M. V. Vasil’eva, Yu. M. Laevsky, and T. S. Timofeeva, Numerical simulation of the two-phase fluid filtration in heterogeneous media. J. Appl. Indust. Math. 11 (2017), 289–295.10.1134/S1990478917020156Search in Google Scholar
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Articles in the same Issue
- Frontmatter
- Numerical solution of optimal control problems for linear systems of ordinary differential equations
- Nitrogen cycle module for INM RAS climate model
- Evaluation of 2010 heatwave prediction skill by SLNE coupled model
- Two-phase flow simulation algorithm for numerical estimation of relative phase permeability curves of porous materials
Articles in the same Issue
- Frontmatter
- Numerical solution of optimal control problems for linear systems of ordinary differential equations
- Nitrogen cycle module for INM RAS climate model
- Evaluation of 2010 heatwave prediction skill by SLNE coupled model
- Two-phase flow simulation algorithm for numerical estimation of relative phase permeability curves of porous materials