We extended the embedded bound method to the calculation of the exact change in effective shear modulus of a two-phase material under fluid or solid substitution. Except for points lying on the upper or lower Hashin-Shtrikman bounds, the change in effective modulus upon replacing the pore-fill and/or the mineral with another is not unique unless detailed information is available about the microstructure. The reason is that points falling between the bounds can be realized by an infinite number of different microgeometries. Each one transforms to a slightly different modulus upon substitution. We have also developed equations for the calculation of fluid and solid substitution of the mineral and the pore-fill material for bulk and shear moduli. Using laboratory measurements and numerical simulation data, we determined that the predictions of the embedded bound method describe the possible range of change in rock moduli upon substitution.

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