Frequency dependent bulk and shear moduli of heavy oil saturated rocks were modeled using a combination of Self Consistent Approximation (SCA) and Differential Effective Medium (DEM) theory. Such an approach honors the rock microstructure, i.e., a continuity of both the solid and fluid phases in the rock; and also makes realistic estimates that fall within the Hashin-Shtrikman (HS) bounds for elastic moduli. We have modeled two heavy oil saturated rocks that have widely different lithology. One is a carbonate rock from Uvalde County, Texas and the other is tar sand from Canada. Calculated modulus values using the combined effective medium scheme are in good agreement with measured data. This approach could be used as a fluid substitution scheme for heavy oil reservoirs especially tar sands underdoing thermal depletion, where even the generalized Gassmann’s equation doesn’t work.


Rocks filled with heavy oil do not comply with established theories of porous media. Understanding the viscoelastic behavior of heavy oil and heavy oil bearing rocks is crucial to identify heavy oil bearing formations from well logs and inferring changes in the seismic properties from time lapse seismic studiesthat can aid in recovery monitoring of heavy-oil reservoirs. One of the challenges has been the estimation of saturated shear modulus of the rocks. Due to the non-negligible shear modulus of heavy oil the saturated shear modulus is quite different from the dry shear modulus and hence Gassmann’s equation is inapplicable. Estimation of the viscoelastic properties of heavy oil bearing rocks using rock physics theories have been attempted by a number of earlier researchers (Ciz and Shapiro, 2007; Leurer and Dvorkin, 2006; Gurevich et al., 2008; Das and Batzle, 2008), but the work is far from being conclusive. Gurevich et al. (2008) used Coherent Potential Approximation (CPA) to compute the viscoelastic properties of a system of grains and heavy oil. Ciz and Shapiro (2007) used generalized Gassmann’s equations for calculating both saturated bulk and shear moduli of a heavy oil saturated rock (Figure 1). The generalized Gassmann’s equations are applicable for rocks that have a rigid matrix, example Uvalde Rock (Das and Batzle, 2008), but not for rocks that lack a rigid matrix, example tar sands.

It is important to realise that the choice of a suitable model is crucial due to the following reasons :

• The rock microstructure implied by the model should be realistic.

• The model should be easy to use and should not involve too many parameters that are not readily available or not easy to measure.

• The modeled results should match the measured data reasonably well.

No single effective medium theory honors the bicontinous microstructure of rocks. We have used a combined effective medium approach to model the bulk and shear modulus of the Uvalde carbonate rock and tar sands. Our approach involves a combination of the Self Consistent Approximation (SCA) and the Differential Effective Medium (DEM) theory to construct the rock microstructure. A similar approach had been used to model the elastic modulus of shales (Hornby et al., 1994) and sandstones (Sheng, 1990, 1991).

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