Mathematical modeling and numerical simulation of porous media single-phase fluid flow problem: a scientific review

  • Yahya Jirjees Tawfeeq Kirkuk University, Kirkuk, Iraq
Keywords: 1D flow, numerical modeling, porous media, reservoir simulation, single-phase flow

Abstract

The complexity of porous media makes the classical methods used to study hydrocarbon reservoirs inaccurate and insufficient to predict the performance and behavior of the reservoir. Recently, fluid flow simulation and modeling used to decrease the risks in the decision of the evaluation of the reservoir and achieve the best possible economic feasibility. This study deals with a brief review of the fundamental equations required to simulate fluid flow through porous media. In this study, we review the derivative of partial differential equations governing the fluid flow through pores media. The physical interpretation of partial differential equations (especially the pressures diffusive nature) and discretization with finite differences are studied.  We restricted theoretic research to slightly compressible fluids, single-phase flow through porous media, and these are sufficient to show various typical aspects of subsurface flow numerical simulation. Moreover, only spatial and time discretization with finite differences will be considered. In this study, a mathematical model is formulated to express single-phase fluid flow in a one-dimensional porous medium. The formulated mathematical model is a partial differential equation of pressure change concerning distance and time.  Then this mathematical model converted into a numerical model using the finite differences method.

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References

Aarnes, J. E., Gimse, T., & Lie, K. A. (2007). An introduction to the numerics of flow in porous media using Matlab. In Geometric modelling, numerical simulation, and optimization (pp. 265-306). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68783-2_9

Ahmed, Tarek, H. (2010). Reservoir Eng. Handbook. 4th edition. Gulf Professional Publishing is an imprint of Elsevier, 30 Corporate Drive, Suite 400, Burlington, MA 01803, USA. The Boulevard, Langford Lane, Kidlington, Oxford, OX5 1GB, U.K.

Aziz, K. (1979). Petroleum reservoir simulation. Applied Science Publishers, 476.

Bear, J. (1988). Dynamics of fluids in porous media Dover Publications. INC, New York.

Chen, Z., Huan, G., & Ma, Y. (2006). Computational methods for multiphase flows in porous media. Society for Industrial and Applied Mathematics.

Ertekin T., Jamal H. Abou-Kassem & Gregory R. King. (2001). Basic Applied Reservoir Simulation. Henry L. Doherty Memorial Fund of AIME. Society of Petroleum Engineers. Richardson, Texas

Ewing, R. E. (1983). Problems arising in the modeling of processes for hydrocarbon recovery. In The mathematics of reservoir simulation (pp. 3-34). Society for Industrial and Applied Mathematics. https://doi.org/10.1137/1.9781611971071.ch1

Fanchi, J. R. (2001). Principles of Applied Reservoir Simulation. 2nd Edition. Vol. I. United States of America: Gulf Professional Publishing.

Fanchi, J.R. (2006). Principles of applied reservoir simulation, 3rd ed., Gulf Professional. Publishing, Burlington.

Gerritsen, M. G., & Durlofsky, L. J. (2005). Modeling fluid flow in oil reservoirs. Annu. Rev. Fluid Mech., 37, 211-238. https://doi.org/10.1146/annurev.fluid.37.061903.175748

Baker, H. A., & Awad, A. S. (2017). Reservoir Characterizations and Reservoir Performance of Mishrif Formation in Amara Oil Field. Journal of Engineering, 23(12), 33-50.

Jansen, J. D. (2013). A systems description of flow through porous media (Vol. 570). New York: Springer.

Cosentino, L. (2001). Integrated reservoir studies. Editions Technip.

Mattax, C. C., & Dalton, R. L. (1990). Reservoir Simulation (includes associated papers 21606 and 21620). Journal of Petroleum Technology, 42(06), 692-695. https://doi.org/10.2118/20399-PA

Mohammed, M. A., Hamd-Allah, S., & Hameed, R. (2020). Diagnosing Water Problem for Asmari Reservoir in Abu Ghirab Oilfield Using Analytical and Numerical Approaches. Journal of Engineering, 26(4), 94-110. https://doi.org/10.31026/j.eng.2020.04.07

Odeh, A. S. (1982). An overview of mathematical modeling of the behavior of hydrocarbon reservoirs. Siam Review, 24(3), 263-273. https://doi.org/10.1137/1024062

Peaceman, D. W. (2000). Fundamentals of numerical reservoir simulation. Elsevier.

Published
2020-07-09
How to Cite
Tawfeeq, Y. J. (2020). Mathematical modeling and numerical simulation of porous media single-phase fluid flow problem: a scientific review. International Research Journal of Engineering, IT & Scientific Research, 6(4), 15-28. https://doi.org/10.21744/irjeis.v6n4.955
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Articles