Estimates of frequency-dependent compressibility from a quasistatic double-porosity model

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Gassmann's relationship between the drained and undrained bulk modulus of a porous medium is often used to relate the dry bulk modulus to the saturated bulk modulus for elastic waves, because the compressibility of air is considered so high that the dry rock behaves in a drained fashion and the frequency of elastic waves is considered so high that the saturated rock behaves in an undrained fashion. The bulk modulus calculated from ultrasonic velocities, however, often does not match the Gassmann prediction. Mavko and Jizba examined how local flow effects and unequilibrated pore pressures can lead to greater stiffnesses. Their ... continued below

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Berryman, J. G. & Wang, H. F. September 16, 1998.

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Gassmann's relationship between the drained and undrained bulk modulus of a porous medium is often used to relate the dry bulk modulus to the saturated bulk modulus for elastic waves, because the compressibility of air is considered so high that the dry rock behaves in a drained fashion and the frequency of elastic waves is considered so high that the saturated rock behaves in an undrained fashion. The bulk modulus calculated from ultrasonic velocities, however, often does not match the Gassmann prediction. Mavko and Jizba examined how local flow effects and unequilibrated pore pressures can lead to greater stiffnesses. Their conceptual model consists of a distribution of porosities obtained from the strain-versus-confining-pressure behavior. Stiff pores that close at higher confining pressures are considered to remain undrained (unrelaxed) while soft pores drain even for high-frequency stress changes. If the pore shape distribution is bimodal, then the rock approximately satisfies the assumptions of a double-porosity, poroelastic material. Berryman and Wang [1995] established linear constitutive equations and identified four different time scales of ow behavior: (1) totally drained, (2) soft pores are drained but stiff pores are undrained, (3) soft and stiff pores are locally equilibrated, but undrained beyond the grain scale, and (4) both soft and stiff pores are undrained. The relative magnitudes of the four associated bulk moduli will be examined for all four moduli and illustrated for several sandstones.

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142 Kilobytes

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  • Dynamics of Fluids in Fractured Rocks Symposium (In honor of Paul A. Witherspoon), Berkeley, CA, February 10-12, 1999

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  • Other: DE00003417
  • Report No.: UCRL-JC-132013
  • Grant Number: W-7405-Eng-48
  • Office of Scientific & Technical Information Report Number: 3417
  • Archival Resource Key: ark:/67531/metadc688705

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  • September 16, 1998

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  • July 25, 2015, 2:20 a.m.

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  • Feb. 24, 2016, 3:49 p.m.

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Berryman, J. G. & Wang, H. F. Estimates of frequency-dependent compressibility from a quasistatic double-porosity model, article, September 16, 1998; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc688705/: accessed August 22, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.