Hostname: page-component-745bb68f8f-kw2vx Total loading time: 0 Render date: 2025-01-26T04:57:31.497Z Has data issue: false hasContentIssue false
  • English
  • Français

Random Walks for Magnetic Decay in Porous Media

Published online by Cambridge University Press:  10 February 2011

Weicheng Cai ,
Thomas C. Halsey ,
John H. Hardenbergs  and
Michael Leibig
Weicheng Cai
Affiliation:
Exxon Research and Engineering Co., Annandale, NJ 08801
Thomas C. Halsey
Affiliation:
Exxon Research and Engineering Co., Annandale, NJ 08801
John H. Hardenbergs
Affiliation:
Exxon Research and Engineering Co., Annandale, NJ 08801
Michael Leibig
Affiliation:
Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106
Get access

Abstract

We propose a Monte Carlo method to simulate the magnetization decay for NMR in porous media. In this method, the diffusive spins in the fluid phase are modeled by 3-d random walkers, whose absorption at the solid surface simulates surface-mediated decay. Our method is 20 times faster than direct relaxation of the diffusion equation when a variable-step size implementation is used. We demonstrate our method by computing the surface relaxivity ρ for a Fontainebleau sandstone, whose structure was determined by X-ray tomography.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 463: Symposia EE – Statistical Mechanics in Physics and Biology , 1996 , 251
Copyright
Copyright © Materials Research Society 1997

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. For a recent review of applications in the petroleum industry, see Kleinberg, R., Industr. Phys. 2 (2), 18 (1996).Google Scholar
2. Abragam, A., Principles of Nuclear Magnetism, (Oxford U.P., New York, 1994) Chapter III.Google Scholar
3. Brownstein, K.R. and Tarr, C.E., Phys. Rev. A 19, 2446 (1979).Google Scholar
4. Torrey, H.C., Phys. Rev. 104, 563 (1956);Google Scholar
Cohen, M.H. & Mendelson, K.S., J. Appl. Phys. 53, 1127(1982).Google Scholar
5. Hürlimann, M.D., Helmer, K.G., Latour, L.L., and Sotak, C.H., J. Mag. Res. A 111, 169 (1994).Google Scholar
6. Leibig, M., J. Phys. A: Math. Gen. 26, 3349 (1993).Google Scholar
7. Meakin, P., J. Phys. A 18, L661 (1985).Google Scholar
8. Flannery, B.P., Deckman, H.W., Roberge, W.G., and D'Amico, K.L., Science 237, 1439 (1987).Google Scholar
9. The X-ray tomography data for the sample was provided by J. Dunsmuir at Exxon Research and Engineering Co.Google Scholar
10. “NMR Short Course,” SPWLA 36th Annual Symposium (in Paris) 1995.Google Scholar