RIGOROUS CONNECTION BETWEEN PHYSICAL-PROPERTIES OF POROUS ROCKS

Rigorous cross-property bounds that connect the effective thermal cond uctivity k (or the electrical conductivity sigma*) and the effective bulk modulus K of any isotropic, two-phase composite were recently de rived by the authors. Here we reformulate these bounds and apply them to porous rocks with dry or fluid-filled pores. It is shown that knowl edge of the effective conductivity can yield sharp estimates of the ef fective bulk modulus (and vice versa), ever, in cases where there is a wide disparity in the phase properties. The bounds yield, in particul ar, relations between the formation factor and the bulk modulus of the porous medium. By using the same approach we obtain new relations bet ween the bulk moduli of a dry porous material and the bulk modulus of the same material with fluid-filled pores that are more general than t he traditional Gassmann equation. The Gassmann formula for the bulk mo dulus of the fluid-saturated porous medium is shown to correspond to a lower bound on this quantity. Limiting cases that we consider include cracked materials with dry and fluid-saturated pores. Theoretical res ults are tested against experimental measurements of the effective bul k modulus of dry and water-saturated Westerly granite and sandstone sa mples. We found good agreement between our cross-property bounds and t he experimental data, even when the experimental data depart from the Gassmann formula. Our results add new insight to understanding of the properties of the porous media. They show that the Gassmann approximat ion works well for rocks with high porosity but needs to be corrected for rocks with high crack-type porosity.