Fluid Flow Modeling in Single Fracture Using Cellular Automata Method

Document Type : Research Article



Fluid flow simulation through a natural fracture is one of the most important and complex problem in Geomechanics. In general, various analytical and numerical methods are used to model fluid flow in fractures. Cellular automata method has been known as a powerful tool for simulation of complex phenomena such as fluid flow, fault movement and fracture production and propagation in a media. As a result, it can have predominant role on simulation of fluid flow in rock fractures.
In this study, the modeling of fluid flow in ideal fracture has been carried out employing cellular automata method. For this purpose, a computer program has been developed and used in Fortran Power Station Domain. In this paper, the cellular automata method has been introduced and its application in fluid flow modeling described. The method of fluid flow simulation has also been presented and the results compared with available analytical solution. 


[1]Snow, D. T.; “Anisotropic Permeability of Fractured Media”, Water Resources Res., Vol.5,No. 6, p.p. 1273-1289, 1965.
[2]Louis, C. A; “A study of groundwater flow in jointed rock and its influence on the stability of rock masses”, Rock Mech. Res. Rep. 10, Imperial College, London, 90 pp, 1969.
[3]Golf-Racht, Van, T. D.; Fundamentals of Fractured Reservoir Engineering, Elsevier Publishing Company, 710 pp, 1982.
[4]Withersphoon, P. A.; Wang, J. S. Y.; Iwai K; Gale, J. E.; “Validity of the cubic law for fluid flow in a deformable rock fracture”, Water Resources Res. Vol. 16, No. 6, p.p. 1016-1024, 1980.
[5]Gutfraind, R.; Hansen, A.; “Study of fracture permeability using lattice-gas automata”, Transport Porous Media, Vol. 18, No. 2, p.p. 131-149, 1995.
[6]Zhang, X.; Knackstedt, M. A.; Sahimi, M.; “Fluid flow across mass fractals and self-affine surfaces”, Physica A, Vol. 233, p.p. 835, 1996.
[7]Chen, S.; Doolen, G. D.; “Lattice Boltzmann Method for Fluid Flows”, Fluid Mech., Vol. 30,p.p. 329-364, 1998.
[8]Von Neumann, J.; “The Theory of Self- Reproducing Automata”, Urbana, University of Illinois Press 1966.
[9]Wolfram, S.; “Universality and complexity in cellular automata”, Physica D Vol. 10, p.p. 1–35,1984.
[10]Frisch, U.; Hasslacher, B.; Pomeau, Y.; “Lattice- Gas Automata for the Navier-Stokes Equation”,Phys. Rev. Lett., Vol. 56, p.p. 1505-1508, 1986.
[11]McNamara, G.; Zanetti, G.; “Use of the Boltzmann equation to simulate lattice-gas automata”, Phys.Rev. Lett. Vol. 61, p.p. 2332–2335, 1988.
[12]D’Humi`eres, D.; Lallemand, P.; Frisch, U.; “Lattice-gas models for 3D hydrodynamics”,Europhys. Lett. 2, 291–297, 1986.
[13]Sukop, M. C.; Trone, T. D.; Lattice Boltzmann Modeling (An Introduction for Geoscientists and Engineers), Springer-Verlag publication, Berlin,Heidelberg, 2006.
[14]Rothman, D.H.,; Zaleski, S.; Lattice-Gas Cellular Automata (Simple Models of Complex Hydrodynamics), Cambridge University press,Cambridge, 1997.
[15]Chen, S.; Wang Z.; Shan X.W.; Doolen G.D.; “Lattice Boltzmann computational fluid dynamics in three dimensions”, J. Stat. Phys., Vol. 68, p.p.379–400, 1992.
[16]Qian, Y.H.; d’Humi`eres, D.; Lallemand, P.; “Lattice BGK models for Navier-Stokes equation”,Europhys. Lett., Vol. 17, p.p. 479–84, 1992.
[17]Feng, Y. T.; Han, K; Owen, D. R. J.; Coupled lattice Boltzmann method and discrete element modeling of article transport in turbulent fluid flow: Computational issue”, Int. J. Numer. Meth. Engng., Vol. 72, p.p. 1111–1134, 2007.
[18]Aaltosalmi, U.; Fluid Flow in Porous Media with the Lattice-Boltzmann Method, Ph.D. Thesis, University of Jyvaskyla, Finland, 2005.
[19]Succi, S.; The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Oxford University Press, 2001.