Effective bulk modulus of the pore fluid at patchy saturation |
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| Authors: | Uri Wollner Jack Dvorkin |
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| Affiliation: | Stanford University, CA, USA |
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| Abstract: | We explore a package of parallel porous layers, each filled with a different fluid. Assume that this package is sampled by an elastic wave with the wavelength much larger than the thickness of an individual layer. Also assume that the layers are hydraulically isolated from each other, meaning that the diffusion length is smaller than that of the individual layer. This assumption is relevant to a patchy saturation scenario. Suppose that we wish to conduct the fluid substitution operation on this package treated as a single porous elastic body. What is the effective bulk modulus of the pore fluid to be used in this operation that will result in the same elastic modulus as computed by Backus averaging the individual moduli of the layers? We address this question analytically by assuming that the porosity, dry frame, and the mineral matrix properties of the individual layers are the same for all layers. The only difference between the layers is the pore fluid. We find that the resulting effective bulk modulus of the fluid thus derived falls between the arithmetic and harmonic averages of the fluid bulk moduli in the layers. It can be approximated by a linear combination of these two bounds where the weights are 0.50 and 0.50 or 0.75 for the arithmetic average and 0.25 for the harmonic average, depending on the elastic moduli of the dry frame, the mineral, and the pore fluids. This solution also provides a relation between the effective bulk modulus of the pore fluid in the system under examination and water saturation to be used in the fluid substitution operation at a coarse spatial scale. |
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| Keywords: | Fluid substitution layered media Backus averaging |
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