Fluid Substitution In Rocks Research Articles

Rock-physics models for heavy-oil and organic-solid substitution

Rock-physics models are often needed to interpret fluid signatures from subsurface seismic data. Over the last decade or so, generalized fluid- and solid-substitution equations have been derived for estimating the exact change in seismic velocity or rock moduli upon changes in properties of quasisolids (e.g., heavy oil, bitumen, kerogen, ice, and salt) for the specified model conditions. However, these exact and mathematically elegant substitution equations fundamentally require details of rock microstructure, which are seldom known. Still, for problems involving solid or fluid substitution in rocks with heterogeneous pores, a rigorous solution range can be predicted using recently derived substitution bounds. These bounds only require total rock porosity, which can be inferred easily from geophysical data. In fact, Gassmann's equations are one of the lower bounds on the change in rock moduli upon fluid substitution, but, for solid substitution, Gassmann's predictions can be outside the bounds. Thus, for solid substitution, the lower bound itself is a better model than Gassmann. If additional microstructural parameters are known, it is possible to further constrain solid substitution or fluid substitution for heterogeneous rocks using the solid-squirt models. The solution range can be further constrained using additional effective moduli measurements of the same rock but filled with materials of varied elastic properties.

Estimating Brown-Korringa constants for fluid substitution in multimineralic rocks

Brown and Korringa extended Gassmann’s equations for fluid substitution in rocks to allow for arbitrarily mixed mineralogy. This extension was accomplished by adding just one additional constant—replacing the mineral bulk modulus with two less intuitive constants. Even though virtually all rocks have mixed mineralogy, the Brown and Korringa equations are seldom used because values for the constants are unknown. We estimate plausible values for the Brown-Korringa constants, based on effective medium models. The self-consistent formulation is used to describe a rock whose mineral and pore phases are randomly distributed ellipsoids—a plausible representation of randomly mixed mineral grains, as with dispersed clay in sandstone. Using the self-consistent model, the two constants are predicted to be nearly identical, justifying the use of an average mineral modulus in Gassmann’s equations. For small contrasts in mineral stiffness, the Brown-Korringa constants are approximately equal to the Voigt-Reuss-Hill average of the individual mineral bulk moduli. In a second approach, a multilayered spherical shell model is used to describe a rock where a particular solid phase preferentially coats grains or lines pores. In this case, the constants can differ substantially from each other, demonstrating the need for the Brown-Korringa equation. A third model represents weak pore-lining or pore-filling clay within an arbitrary pore geometry. The clay-fluid mix can be replaced exactly with an average fluid or “mud.” When the nonclay minerals have similar moduli, then the replacement of the clay-fluid mix causes the Brown-Korringa equation to revert to Gassmann’s equation.

Fluid substitution in rocks saturated with viscoelastic fluids

Heavy oils have high densities and extremely high viscosities, and they exhibit viscoelastic behavior. Traditional rock physics based on Gassmann theory does not apply to materials saturated with viscoelastic fluids. We use an effective-medium approach known as coherent potential approximation (CPA) as an alternative fluid-substitution scheme for rocks saturated with viscoelastic fluids. Such rocks are modeled as solids with elliptical fluid inclusions when fluid concentration is small and as suspensions of solid particles in the fluid when the solid concentration is small. This approach is consistent with concepts of percolation and critical porosity, and it allows one to model sandstones and unconsolidated sands.We model the viscoelastic properties of a heavy-oil-saturated rock sample using CPA and a measured frequency-dependent complex shear modulus of the heavy oil. Comparison of modeled results with measured properties of the heavy-oil rock reveals a large discrepancy over a range of frequencies and temperatures. We modify the CPA scheme to account for the effect of binary pore structure by introducing a compliant porosity term. This dramatically improves the predictions. The predicted values of the effective shear modulus of the rock are in good agreement with laboratory data for the range of frequencies and temperatures. This confirms that our scheme realistically estimates the frequency- and temperature-dependent properties of heavy-oil rocks and can be used as an approximate fluid-substitution approach for rocks saturated with viscoelastic fluids.