Skip to main content
Log in

Numerical Simulation of Ferrofluid Flow for Subsurface Environmental Engineering Applications

  • Published:
Transport in Porous Media Aims and scope Submit manuscript

Abstract

Ferrofluids are suspensions of magnetic particles of diameter approximately 10 nm stabilized by surfactants in carrier liquids. The large magnetic susceptibility of ferrofluids allows the mobilization of ferrofluid through permeable rock and soil by the application of strong external magnetic fields. We have developed simulation capabilities for both miscible and immiscible conceptualizations of ferrofluid flow through porous media in response to magnetic forces arising from the magnetic field of a rectangular permanent magnet. The flow of ferrofluid is caused by the magnetization of the particles and their attraction toward a magnet, regardless of the orientation of the magnet. The steps involved in calculating the flow of ferrofluid are (1) calculation of the external magnetic field, (2) calculation of the gradient of the external magnetic field, (3) calculation of the magnetization of the ferrofluid, and (4) assembly of the magnetic body force term and addition of this term to the standard pressure gradient and gravity force terms. We compare numerical simulations to laboratory measurements of the magnetic field, fluid pressures, and the two‐dimensional flow of ferrofluid to demonstrate the applicability of the methods coded in the numerical simulators. We present an example of the use of the simulator for a field‐scale application of ferrofluids for barrier verification.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Berkovski, B. M., Medvedev, V. F. and Krakov, M. S.: 1993, Magnetic Fluids Engineering Applications, Oxford University Press, New York.

    Google Scholar 

  • Borglin, S. E., Moridis, G. J. and Oldenburg, C. M.: 1998, Experimental studies of magnetically driven flow of ferrofluids through porous media, Lawrence Berkeley National Laboratory Report LBL-40126, Berkeley, California.

  • Borglin, S. E., Moridis, G. J. and Becker, A.: 1998, Magnetic detection of ferrofluid injection zones, Lawrence Berkeley National Laboratory Report LBL-40127, Berkeley, California.

  • Duff, I. S.: 1977, MA28 - A set of FORTRAN subroutines for sparse unsymmetric linear equations, AERE Harwell Report R 8730.

  • Falta, R. W., Pruess, K., Javandel, I. and Witherspoon, P. A.: 1992a, Numerical modeling of steam injection for the removal of nonaqueous phase liquids from the subsurface 1. Numerical formulation, Water Resour. Res. 28, 433-449.

    Google Scholar 

  • Falta, R. W., Pruess, K., Javandel, I. and Witherspoon P A.: 1992b, Numerical modeling of steam injection for the removal of nonaqueous phase liquids from the subsurface 2. Code validation and application, Water Resour. Res. 28, 451-465.

    Google Scholar 

  • Falta, R. W., Pruess, K., Finsterle, S. and Battistelli A.: 1995, T2VOC User's Guide, Lawrence Berkeley Laboratory Report LBL-36400, Berkeley, California.

  • Herbert, A.W., Jackson, C. P. and Lever, D. A.: 1988, Coupled groundwater flow and solute transport with fluid density strongly dependent on concentration, Water Resour. Res. 24(10), 1781-1795.

    Google Scholar 

  • Ida, N.: 1995, Numerical Modeling for Electromagnetic Non-Destructive Evaluation, 1st edn, Chapman & Hall, New York.

    Google Scholar 

  • International Formulation Committee: 1967, A Formulation of the Thermodynamic Properties of Ordinary Water Substance, IFC Secretariat, Düsseldorf, Germany.

    Google Scholar 

  • Jackson, J. D.: 1967, Classical Electrodynamics, Wiley, New York, pp. 153-154.

    Google Scholar 

  • deMarsily, G.: 1986, Quantitative Hydrogeology, Academic Press.

  • McCaig, M.: 1977, Permanent Magnets in Theory and Practice, Wiley, New York, pp. 187-188.

    Google Scholar 

  • McCaig, M. and Clegg, A. G.: 1987, Permanent Magnets in Theory and Practice, 2nd edn, Halsted Press, Wiley, New York.

    Google Scholar 

  • Moridis, G. J., Borglin, S. E., Oldenburg, C. M. and Becker, A.: 1998, Theoretical and experimental investigations of ferrofluids for guiding and detecting liquids in the subsurface, Lawrence Berkeley National Laboratory Report LBL-41069, Berkeley, California.

  • Moridis, G. and Pruess, K.: 1995, Flow and transport simulations using T2CG1, a package of conjugate gradient solvers for the TOUGH2 family of codes, Lawrence Berkeley Laboratory Report LBL-36235, Berkeley, California.

  • Moridis, G. J., Myer, L., Persoff, P., Finsterle, S., Apps, J. A., Vasco, D., Muller, S., Yen, P., Williams, P., Freifeld, B. and Pruess, K.: 1995, First-level field demonstration of subsurface barrier technology using viscous liquids, Lawrence Berkeley National Laboratory Report LBL-37520, Berkeley, California.

  • Oldenburg, C. M. and Pruess, K.: 1995, Dispersive transport dynamics in a strongly coupled groundwater-brine flow system, Water Resour. Res. 31(2), 289-302.

    Google Scholar 

  • Oldenburg, C. M., Moridis, G. J. and Pruess, K.: 1998, Ferrofluid flow and transport for the TOUGH2 simulator, Lawrence Berkeley Laboratory Report LBL-40776, Berkeley, California.

  • Pruess, K.: 1987, TOUGH User's guide, nuclear regulatory commission, Report NUREG/CR-4645, (also Lawrence Berkeley Laboratory Report LBL-20700, Berkeley, California, June 1987).

  • Pruess, K.: 1991a, TOUGH2 - A general purpose numerical simulator for multiphase fluid and heat flow, Lawrence Berkeley Laboratory Report LBL-29400, Berkeley, California.

  • Pruess, K.: 1991b, EOS7, An equation-of-state module for the TOUGH2 simulator for two-phase flow of saline water and air, Lawrence Berkeley Laboratory Report LBL-31114, Berkeley, California.

  • Raj, K. and Moskowitz, R.: 1990, Commercial applications of ferrofluids, J. Magnetism and Magnetic Materials 85, 233-245.

    Google Scholar 

  • Reeves, M., Ward, D. S., Johns, N. D. and Cranwell, R. M.: 1986, Theory and implementation of SWIFT II, the Sandia waste-isolation flow and transport model for fractured media, Report No. SAND83-1159, Sandia National Laboratories, Albuquerque, NM.

    Google Scholar 

  • Rosensweig, R. E.: 1985, Ferrohydrodynamics, Cambridge University Press.

  • Saffman, P. G. and Taylor, Sir Geoffrey: 1958, The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid, Proc. R. Soc. London A 246, 312-331.

    Google Scholar 

  • Stone, H. L: 1970, Probability model for estimating three-phase relative permeability, Trans. SPE AIME 249, 214-218.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Oldenburg, C.M., Borglin, S.E. & Moridis, G.J. Numerical Simulation of Ferrofluid Flow for Subsurface Environmental Engineering Applications. Transport in Porous Media 38, 319–344 (2000). https://doi.org/10.1023/A:1006611702281

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1006611702281

Navigation