Acta Geophysica

, Volume 66, Issue 3, pp 243–266 | Cite as

Stochastic porous media modeling and high-resolution schemes for numerical simulation of subsurface immiscible fluid flow transport

  • Eric Thompson Brantson
  • Binshan Ju
  • Dan Wu
  • Patricia Semwaah Gyan
Research Article - Solid Earth Sciences


This paper proposes stochastic petroleum porous media modeling for immiscible fluid flow simulation using Dykstra–Parson coefficient (VDP) and autocorrelation lengths to generate 2D stochastic permeability values which were also used to generate porosity fields through a linear interpolation technique based on Carman–Kozeny equation. The proposed method of permeability field generation in this study was compared to turning bands method (TBM) and uniform sampling randomization method (USRM). On the other hand, many studies have also reported that, upstream mobility weighting schemes, commonly used in conventional numerical reservoir simulators do not accurately capture immiscible displacement shocks and discontinuities through stochastically generated porous media. This can be attributed to high level of numerical smearing in first-order schemes, oftentimes misinterpreted as subsurface geological features. Therefore, this work employs high-resolution schemes of SUPERBEE flux limiter, weighted essentially non-oscillatory scheme (WENO), and monotone upstream-centered schemes for conservation laws (MUSCL) to accurately capture immiscible fluid flow transport in stochastic porous media. The high-order schemes results match well with Buckley Leverett (BL) analytical solution without any non-oscillatory solutions. The governing fluid flow equations were solved numerically using simultaneous solution (SS) technique, sequential solution (SEQ) technique and iterative implicit pressure and explicit saturation (IMPES) technique which produce acceptable numerical stability and convergence rate. A comparative and numerical examples study of flow transport through the proposed method, TBM and USRM permeability fields revealed detailed subsurface instabilities with their corresponding ultimate recovery factors. Also, the impact of autocorrelation lengths on immiscible fluid flow transport were analyzed and quantified. A finite number of lines used in the TBM resulted into visual artifact banding phenomenon unlike the proposed method and USRM. In all, the proposed permeability and porosity fields generation coupled with the numerical simulator developed will aid in developing efficient mobility control schemes to improve on poor volumetric sweep efficiency in porous media.


Permeability and porosity fields Turning bands method Carman–Kozeny equation SUPERBEE flux limiter Monotone upstream-centered schemes for conservation laws Weighted essentially non-oscillatory schemes 



The work was supported by the Fundamental Research Funds for National Science and Technology Major Projects (2016ZX05011-002) and the Central Universities (2652015142). The kind effort from Dr. Y.Y Ziggah, Dr. A.A Eftekhari, Dr. K. Schüller, and Dr. X. Emery for their tireless assistance in carrying out this research. We also thank Mr. Bright Junior Addo for his kind assistance with fruitful and constructive criticism of this research paper. We would also like to thank the anonymous reviewers for their comments and suggestions that were helpful in improving the manuscript.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflicts of interest with respect to the research, authorship, and/or publication of this article.


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Copyright information

© Institute of Geophysics, Polish Academy of Sciences & Polish Academy of Sciences 2018

Authors and Affiliations

  1. 1.School of Energy ResourcesChina University of Geosciences (Beijing)BeijingChina
  2. 2.Key Laboratory of Marine Reservoir Evolution and Hydrocarbon Accumulation Mechanism, Ministry of educationChina University of Geosciences (Beijing)BeijingChina
  3. 3.Patent Examination Cooperation CentreSIPOBeijingChina
  4. 4.Faculty of Earth ResourcesChina University of GeosciencesWuhanChina

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