204 Stanford Rock Physics Laboratory - Gary Mavko
Tremendous Variety of Microstructures
Granular Inclusions
Diversity of pore shapes
Microstructural diversity leads to: • Non-unique velocity-porosity relations • Non-unique Vp/Vs relations • Uncertainty in fluid substitution practices • Non-unique porosity-permeability relations • Important variations in mineral moduli
Round Grains Round Pores
205 Stanford Rock Physics Laboratory - Gary Mavko
Again, carbonate data fall along modified upper Hashin-Shtrikman line, now in the Vp-Porosity plane. Shalier data fall below it, similar to clastics.
Comparison of ellipsoidal crack models with carbonate data, classified by pore shape. The rocks with stiffer pore shapes fit best the spherical pore models, while the rocks with thinner, more crack-like pores fit best the lower aspect ratio models.
Velocity-Porosity: Interpretation Ambiguity
206 Stanford Rock Physics Laboratory - Gary Mavko
Differential Effective Medium (DEM) model is superimposed for aspect ratios [.01,.03,.1,.3,1]. Chalk data (low vclay) generally follow the DEM trend. Shales (high vclay) follow two shale trends consisting of clay with small amounts of calcite cement.
DEM model
Shale trend
Carbonate
Velocity-Porosity Distinct trends for carbonates and shales
207 Stanford Rock Physics Laboratory - Gary Mavko
C. Scotellaro
dolomitic
micrite
Velocity-Porosity: Textural, Mineralogic Variations
209 Stanford Rock Physics Laboratory - Gary Mavko
We have observed that model-based interpretation depends quite a bit on mineralogy. Here, we examine log data to infer mineral properties. The assumption is that minerals represent upper bounds for data clouds, in the limit of zero porosity. At least some of the data are too dense and too stiff to be calcite.
Inferring Mineralogy
210 Stanford Rock Physics Laboratory - Gary Mavko
The density-porosity trend should be a simple linear combination of fluid and mineral. These plots show that low-gamma rocks are consistent with calcite. Errors in porosity estimation (especially with shale) will lead to incorrect intercept, and misinterpreted mineral density.
Inferring Mineralogy
211 Stanford Rock Physics Laboratory - Gary Mavko
The density-porosity trend should be a simple linear combination of fluid and mineral.
Bootstrap Analysis for Mineralogy
212 Stanford Rock Physics Laboratory - Gary Mavko
Water-saturated Greenberg-Castagna lines
GR
Comparison of carbonate log data with Greenberg-Castagna lines.
Carbonate Vp-Vs Relations
213 Stanford Rock Physics Laboratory - Gary Mavko
Water-saturated Greenberg-Castagna lines
Looking more closely at the data in the previous slide, we can find intervals that are more calcite-rich.
Carbonate Vp-Vs Relations
214 Stanford Rock Physics Laboratory - Gary Mavko
Water-saturated Greenberg-Castagna lines
In this interval, the data appear to be more dolomite-rich.
Carbonate Vp-Vs Relations
215 Stanford Rock Physics Laboratory - Gary Mavko
The Hashin-Shtrikman bounds can help detect the presence of dolomite in the Vp-Vs plane.
Interpreting Pore Shape from Vp-Vs Data
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For these chalks, there is an ambiguity between mineral and pore stiffness.
Well A Well B
Carbonate Inclusion Models
217 Stanford Rock Physics Laboratory - Gary Mavko
Example of substituting brine for oil
There is no fundamental reason why Gassmann theory should not apply to carbonates. Yet, there are assumptions in the model:
• Homogeneous mineralogy • Isotropic • Well-connected pore space The dominant consideration, as with Gassmann applied to any rock,
is the stiffness of the pore space.
Fluid Substitution
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