Water Flooding Performance Evaluation Using Percolation Theory

Document Type : Research Paper

Authors

Department of Chemical and Petroleum Eng., Sharif University of Technology, Azadi Ave., Tehran, I.R. Iran

Abstract

Water flooding is a well-known secondary mechanism for improving oil recovery. Conventional approach to evaluate the performance of a water flooding process (e.g. breakthrough and post breakthrough behavior) is to establish a reliable geological reservoir model, upscale it, and then perform flow simulations. To evaluate the uncertainty in the breakthrough time or post breakthrough behavior, this procedure has to be repeated for many realizations of the geological model, which takes many hours of CPU time. Moreover, during the early stage of reservoir life, when data is scare, breakthrough and post breakthrough time behavior prediction are usually based on analogues or rules of thumb. Alternative statistical approach is to use percolation theory to predict breakthrough and post breakthrough bahavior. The main contribution is to evaluate the applicability of the existing scaling laws of the breakthrough time by the numerical flow simulation results using the Burgan formation dataset of Norouz offshore oilfield in the south of Iran. Moreover, we extend the scaling to the post breakthrough behavior. There is good agreement between the predictions from the percolation based expressions and the numerical simulation results. Moreover, the prediction from the scaling law took a fraction of a second of CPU times (as it only needs some algebraic calculations) compared with many hours required for the conventional numerical simulations.

Keywords

References

[1] Donato D., G. & Blunt M.J., Streamline based dual porosity simulation of reactive transport and flow in fractured reservoirs, Water Resour, Res. 40, W04203.1-12, 2004.
[2] Huang W., D. Donato G. & Blunt M.J., “Comparison of streamline based and grid based dual porosity simulation”, J. Pet. Sci. Eng. 43, pp. 129-137, 2004.
[3] Stauffer D. & Aharony A., Introduction to Percolation theory, second Ed., Taylor and Francis, London, 1994.
[4] Andrade J.S., Jr., Buldyrev S.V., Dokholyan N.V., Havlin S., King P.R., Lee Y., Paul G. & Stanley H.E., “Flow between two sites on a percolation cluster”, Phys. Rev. E 62 pp. 8270-8281, 2000.
[5] Dokholyan N.V., Buldyrev S.V., Havlin S., King P.R., Lee Y. & Stanley H.E., “Distribution of shortest paths in percolation”, Phys. Rev. A 266, pp. 55-61, 1999.
[6] Lee Y., J.S. Andrade Jr., Buldyrev S.V. , Dokholyan N.V. , Havlin S., King P.R. , Paul G., Stanley H E., “Traveling time and traveling length in critical percolation clusters”, Phys. Rev. E 60, pp. 3245-3248, 1999.
[7] King P.R., J.S. Andrade Jr., Buldyrev S.V., Dokholyan N., Lee Y., Havlin S., Stanley H.E., Predicting oil recovery using percolation, Phys. Rev.  A 266 107-114, 1999.
[8] Andrade J.S. Jr., Araujo A.D., Buldyrev S.V. , Havlin S., Stanley H.E., Dynamics of viscous penetration in percolation porous media, Phys. Rev. E  63, 051403, 2001.
[9] Araujo D., Moreira A.A., Makse H.A., Stanley H.E., & Andrade J.S. Jr., Traveling length and minimal traveling time for flow through percolation networks with long-range spatial correlations, Phys. Rev. E 66, 046304, 2002.
[10] Paul G., Havlin S. & Stanley H.E., Fractal behavior of the shortest path between two lines in percolation systems, Phys. Rev. E 65, 066105, 2002.
[11] King P.R., Buldyrev S.V., Dokholyan N.V., Havlin S., Lopez E., Paul G. , Stanley H.E., “Uncertainty in oil production predicted by percolation theory”, Phys. Rev. A 306, pp. 376-380, 2002.
[12] Lopez E., Buldyrev S.V., Dokholyan N.V., Goldmakher L., Havlin S., King P.R. & Stanley H.E., Postbreakthrough behavior in flow through porous media, Phys. Rev. E 67, 056314, 2003.
[13] Soares R.F., Corso G., Lucen L.S., Freitas J.E., da Silva L.R., Paul G. & Stanley H.E., “Distributionof shortest paths at percolation threshold: application to oil recovery with multiple wells”, Phys. A 343, pp. 739-747, 2004.
[14] López E., Buldyrev S.V., Braunstein L.A., Havlin S. & Stanley H.E., Possible connection between the optimal path and flow in percolation clusters, Phys. Rev. E 72, 056131, 2005.
[15] Li W., Jensen J.L., Ayers W.B., Hubbard S.M. & Heidari M.R., “Comparison of interwell connectivity predictions using percolation, geometrical, and Monte Carlo models”, J. Pet. Sci. Eng. 25, pp.125-129, 2009.
[16] Huerlimann A., MDP technical report of Shell Company, Appendix seven of Soroosh & Nowrooz Burgan rock properties, NISOC, Iran, 2004.
Journal of Petroleum Science and Technology
Volume 1, Issue 2 - Serial Number 2
September 2011
Pages 19-23

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