Magnetic resonance as a probe of permeability in porous media

Jayanth R. Banavar; Lawrence M. Schwartz

doi:10.1103/PhysRevLett.58.1411

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Magnetic resonance as a probe of permeability in porous media

Jayanth R. Banavar and Lawrence M. Schwartz

Schlumberger-Doll Research, Ridgefield, Connecticut 06877-4108

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Phys. Rev. Lett. 58, 1411 – Published 6 April, 1987

DOI: https://doi.org/10.1103/PhysRevLett.58.1411

Abstract

Results of a theoretical study of the permeability k and proton relaxation rate $T_{1}^{- 1}$ in fully and partially saturated porous media are presented. Numerical calculations on two distinct geometrical models of granular materials predict a strong correlation between k and $φ^{4}$ $T_{1}^{2}$ for fully saturated systems (with porosity φ) in agreement with a recent experimental study.

References (14)

A. Timur, J. Pet. Technol. 21, 775 (1969), and Log. Anal. 10, 3 (1969); J. D. Loren and J. D. Robinson, Soc. Pet. Eng. J. 10, 268 (1970).
W. E. Kenyon, P. Day, C. Straley, and J. Willemsen, in Proceedings of the 61st Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, New Orleans, LA, 1986, to be published.
J. B. Roberts and L. M. Schwartz, Phys. Rev. B 31, 5990 (1985).
P.-z. Wong, J. Koplik and J. P. Tomanic, Phys. Rev. B 30, 6606 (1984).
A. J. Katz and A. H. Thompson, J. Geophys. Res. (to be published), and Phys. Rev. B 34, 8179 (1986).
D. L. Johnson, J. Koplik and L. M. Schwartz, Phys. Rev. Lett. 57, 2564 (1986).
K. R. Brownstein and C. E. Tarr, Phys. Rev. A 19, 2446 (1979).
M. H. Cohen and K. S. Mendelson, J. Appl. Phys. 53, 1127 (1982).
M. Lipsicas, J. R. Banavar and J. Willemsen, Appl. Phys. Lett. 48, 1554 (1986).
J. Willemsen, private communication.
All the lifetimes reported in this paper were obtained by fitting the decay by a stretched exponential (see Ref. 2). Thus $T_{1}$ is the time at which the magnetization reaches $e^{- 1}$ of its initial value and the exponent alpha is a measure of the distribution of relaxation times governing the overall decay.
J. R. Banavar and D. L. Johnson, Phys. Rev. B (to be published).
Indeed, we find that the slope of the k vs $φ^{4}$ $T_{1}^{2}$ cross plot is controlled by the conductivity exponent m. To verify this we have carried out calculations on the ST model with x = 0.25 ( 2.55 < m < 2.96 ) and x = 0.75 ( m approx 1.32 ). The slopes of the corresponding k vs $φ^{4}$ $T_{1}^{2}$ cross plots are 0.92 ( x = 0.25 ) and 0.48 ( x = 0.75 ).
R. Chandler, J. Koplik, J. Lerman and J. Willemsen, J. Fluid Mech. 119, 249 (1982); D. Wilkinson and J. F. Willemsen, J. Phys. A 16, 3365 (1983).

[c1] A. Timur, J. Pet. Technol. 21, 775 (1969), and Log. Anal. 10, 3 (1969); J. D. Loren and J. D. Robinson, Soc. Pet. Eng. J. 10, 268 (1970).

[c2] W. E. Kenyon, P. Day, C. Straley, and J. Willemsen, in Proceedings of the 61st Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, New Orleans, LA, 1986, to be published.

[c3] J. B. Roberts and L. M. Schwartz, Phys. Rev. B 31, 5990 (1985).

[c4] P.-z. Wong, J. Koplik and J. P. Tomanic, Phys. Rev. B 30, 6606 (1984).

[c5] A. J. Katz and A. H. Thompson, J. Geophys. Res. (to be published), and Phys. Rev. B 34, 8179 (1986).

[c6] D. L. Johnson, J. Koplik and L. M. Schwartz, Phys. Rev. Lett. 57, 2564 (1986).

[c7] K. R. Brownstein and C. E. Tarr, Phys. Rev. A 19, 2446 (1979).

[c8] M. H. Cohen and K. S. Mendelson, J. Appl. Phys. 53, 1127 (1982).

[c9] M. Lipsicas, J. R. Banavar and J. Willemsen, Appl. Phys. Lett. 48, 1554 (1986).

[c10] J. Willemsen, private communication.

[c11] All the lifetimes reported in this paper were obtained by fitting the decay by a stretched exponential (see Ref. 2). Thus $T_{1}$ is the time at which the magnetization reaches $e^{- 1}$ of its initial value and the exponent alpha is a measure of the distribution of relaxation times governing the overall decay.

[c12] J. R. Banavar and D. L. Johnson, Phys. Rev. B (to be published).

[c13] Indeed, we find that the slope of the k vs $φ^{4}$ $T_{1}^{2}$ cross plot is controlled by the conductivity exponent m. To verify this we have carried out calculations on the ST model with x = 0.25 ( 2.55 < m < 2.96 ) and x = 0.75 ( m approx 1.32 ). The slopes of the corresponding k vs $φ^{4}$ $T_{1}^{2}$ cross plots are 0.92 ( x = 0.25 ) and 0.48 ( x = 0.75 ).

[c14] R. Chandler, J. Koplik, J. Lerman and J. Willemsen, J. Fluid Mech. 119, 249 (1982); D. Wilkinson and J. F. Willemsen, J. Phys. A 16, 3365 (1983).

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Magnetic resonance as a probe of permeability in porous media

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