Open Access Open Access  Restricted Access Subscription or Fee Access

Langevin Dynamics Study of the Mean Flow Rate-Energy Stochastic Fluid Intrusion Process in Porous Media


(*) Corresponding author


Authors' affiliations


DOI: https://doi.org/10.15866/iremos.v12i6.17037

Abstract


Fluid transport phenomena in porous media exhibit different properties with scaling law behavior according to different universal components, which describe the corresponding universal classes exactly. A numerical study of the fluid intrusion process in a porous medium under the effect of a static pressing force is introduced. Investigations are developed by using Langevin dynamic based on the competition between the stochastic and the dissipation processes. The mean flow rate is studied with an energetic study, then the temporal profiles are shown. The results show that the time evolution of these two magnitudes exhibits exponential profiles with two different regimes; transient and permanent, characterized by their cross-over time. They also exhibit a decreasing behavior versus the friction coefficient, but an increasing behavior versus both the static pressure and the medium porosity. Scaling laws with universal exponents of the mean flow rate are checked for different parameters, namely the static pressure and the friction coefficient. The system mean energy follows a scaling law with universal exponents, independently of the parameters (static pressure, friction coefficient, medium porosity, and system size), which proves their universal character.
Copyright © 2019 Praise Worthy Prize - All rights reserved.

Keywords


Porous Media; Langevin Dynamics; Mean Flow Rate; Scaling Law; Average Kinetic Energy; Average Potential Energy

Full Text:

PDF


References


G. Pia, U. Sanna, An intermingled fractal units model and method to predict permeability in porous rock. Int. J. Eng. Sci, 75: 31–39, February 2014.
https://doi.org/10.1016/j.ijengsci.2013.11.002

G. Pia, E. Sassoni, E. Franzoni, and U. Sanna, Predicting capillary absorption of porous stones by a procedure based on an intermingled fractal units model. Int. J. Eng. Sci, 82: 196–204, September 2014.
https://doi.org/10.1016/j.ijengsci.2014.05.013

J. Cai, X.Hu, Standnes, D.C.You and L.You, An analytical model for spontaneous imbibition in fractal porous media including gravity. Colloids Surf, 414: 228–233, November 2012.
https://doi.org/10.1016/j.colsurfa.2012.08.047

M. Dong, F.A.L. Dullien, L. Dai, and D. Li, Immiscible displacement in the interacting capillary bundle model Part I. Development of interacting capillary bundle model. Transp. Porous Media, 59(1): 1-18, April 2005.
https://doi.org/10.1007/s11242-004-0763-5

J. Xiong, X. Liu, L. Liang. and Q. Zeng, Adsorption of methane in organic-rich shale nanopores: an experimental and molecular simulation study. Fuel, 200: 299–315, July 2017.
https://doi.org/10.1016/j.fuel.2017.03.083

Bourouis, A., Omara, A., Numerical Simulation on Mixed Convection in a Square Lid-Driven Cavity Provided with a Vertical Porous Layer of Finite Thickness, (2013) International Review on Modelling and Simulations (IREMOS), 6 (2), pp. 588-599.

S. Yang, H. Fu and B. Yu, Fractal analysis of flow resistance in tree-like branching networks with roughened microchannels. Fractals, 25(1):1750008, February 2017.
https://doi.org/10.1142/s0218348x17500086

L.Guarracino, T.Rötting, and J.Carrera, A fractal model to describe the evolution of multiphase flow properties during mineral dissolution. Adv. Water Resour, 67: 78–86, May 2014.
https://doi.org/10.1016/j.advwatres.2014.02.011

R.Liu, B.Li and Y.Jiang, A fractal model based on a new governing equation of fluid flow in fractures for characterizing hydraulic properties of rock fracture networks. Comput. Geotech, 75: 57–68, May 2016.
https://doi.org/10.1016/j.compgeo.2016.01.025

P. Xu, A.P. Sasmito, Yu, B. and Mujumdar, A.S, Transport phenomena and properties in treelike networks. Appl. Mech. Rev, 68(4): 040802, July 2016.
https://doi.org/10.1115/1.4033966

X. Huai, W. Wang and Z. Li, Analysis of the effective thermal conductivity of fractal porous media. Appl. Therm. Eng, 27(17-18):2815–2821, December 2007.
https://doi.org/10.1016/j.applthermaleng.2007.01.031

G. Pia and U. Sanna, An intermingled fractal units model to evaluate pore size distribution influence on thermal conductivity values in porous materials. Appl.Therm. Eng, 65(1-2):330–336, April 2014.
https://doi.org/10.1016/j.applthermaleng.2014.01.037

X. Gou and J. Schwartz, Fractal analysis of the role of the rough interface between Bi2Sr2CaCu2Ox filaments and the Ag matrix in the mechanical behavior of composite round wires. Supercond. Sci. Technol. 26(5): 055016, May 2013.
https://doi.org/10.1088/0953-2048/26/5/055016

L. Cao, X. Li, C. Luo, L. Yuan, J. Zhang, and X. Tan, Horizontal well transient rate decline analysis in low permeability gas reservoirs employing an orthogonal transformation method. J. Nat. Gas Sci. Eng, 33: 703-716, June 2016.
https://doi.org/10.1016/j.jngse.2016.06.001

S. Yang, M. Liang, B. Yu, and M. Zou, Permeability model for fractal porous media with rough surfaces, Microfluid Nanofluid, 18(5-6):1085-1093, October 2014.
https://doi.org/10.1007/s10404-014-1500-1

M. Tuller, D. Or, and L.M. Dudley, Adsorption and capillary condensation in porous media: liquid retention and interfacial configurations in angular pores. Water Resour. Res. 35(7): 1949–1964, July 1999.
https://doi.org/10.1029/1999wr900098

M. Tuller, and D. Or, Unsaturated hydraulic conductivity of structured porous media: A Review of Liquid Configuration–Based Models. Vadose Zone J, 1(1): 14–37, August 2002.
https://doi.org/10.2136/vzj2002.1400

A. Peters, and W. Durner, A simple model for describing hydraulic conductivity in unsaturated porous media accounting for film and capillary flow. Water Resour. Res. 44(11): W11417, November 2008.
https://doi.org/10.1029/2008wr007136

M. Lebeau, and J.M. Konrad, A new capillary and thin film flow model for predicting the hydraulic conductivity of unsaturated porous media. Water Resour. Res. 46(12): W12554, December 2010.
https://doi.org/10.1029/2010wr009092

Yu, B. and Cheng, P, A fractal permeability model for bi-dispersed porous media. Int. J. Heat Mass Transf. 45(14):2983–2993, July 2002.
https://doi.org/10.1016/s0017-9310(02)00014-5

T. Miao, B. Yu, Y. Duan, and Q. Fang, A fractal analysis of permeability for fractured rocks. Int. J. Heat Mass Trans, 81:75–80, February 2015.
https://doi.org/10.1016/j.ijheatmasstransfer.2014.10.010

X.H. Tan, J.Y. Liu, X.P. Li, L.H. Zhang, and J. Cai, A simulation method for permeability of porous media based on multiple fractal model. Int. J. Eng. Sci, 95: 76–84, October 2015.

P. Xu, B. Yu, X. Qiao, S. Qiu, and Z. Jiang, Radial permeability of fractured porous media by Monte Carlo simulations. Int. J. Heat Mass Transf. 57(1):369–374, January 2013.
https://doi.org/10.1016/j.ijheatmasstransfer.2012.10.040

S. Yang, B. Yu, M. Zou, and M. Liang, A fractal analysis of laminar flow resistance in roughened microchannels. Int. J. Heat Mass Transf. 77:208–217, October 2014.
https://doi.org/10.1016/j.ijheatmasstransfer.2014.05.016

A. Czirok, A. B. Barabasi, and T. Vicsek, Collective Motion of Self-Propelled Particles: Kinetic Phase Transition in One Dimension. Phys. Rev. Lett, 82(1-4):209, January 1999.
https://doi.org/10.1103/physrevlett.82.209

R. Bakir, I. Tarras, A. Hader, H. Sbiaai, M. Mazroui, and Y. Boughaleb, Scaling behavior of non-equilibrium phase transitions in spontaneously ordered motion of self-propelled particles. Mod. Phys. Lett. B. 30(24): 1650304, September 2016.
https://doi.org/10.1142/s0217984916503048

F. Family, and T. Vicsek, Scaling of the active zone in the Eden process on percolation networks and the ballistic deposition model. J. Phys. A, 18(2): L75, October 1985.
https://doi.org/10.1088/0305-4470/18/2/005

V. K. Horváth, F. Family, and T. Vicsek, Dynamic scaling of the interface in two-phase fluid flows. J. Phys. A, 24(1):L25, October 1991.

I. Achik, A. Hader, Y. Boughaleb, A. Hajjaji, and M. Bakasse, The kinetics of ordered domains in monolayer deposition, J. Optoelectron. Adv. Mater. 13(3):319-323, March 2011.


Refbacks

  • There are currently no refbacks.


Please send any question about this web site to info@praiseworthyprize.com
Copyright © 2005-2024 Praise Worthy Prize