Already established models unable to handle low porosity for velocity estimation. To study sensitivity of velocities to low porosity!
If you cannot find anything else, I suggest you try the BGK model as described in a recent publication, the HANDBOOK OF BOREHOLE ACOUSTICS AND ROCK PHYSICS FOR RESERVOIR CHARACTERIZATION, Vimal Saxena, Michel Krief, Ludmila Adam, 2018 Elsevier.
The model makes use of the Biot coefficient and the Gassmann coefficient (similar to the Biot coefficient, but applied to the shear modulus). Both Biot- and Gassmann-coefficients are parameterized with distinct exponent values (Biot-Krief and Gassmann-Krief exponents) that allow to model closely the rock properties in any porosity range.
Biot- and Gassmann-coefficients behave differently as a function of porosity (I use total porosity when modelling). If you have enough experimental data, you can derive Biot- and Gassmann-coefficients regressions with porosity (second order polynomes should be enough).
Abdel Moktader El Sayed;
Although I am satisfied with BGK model for clay rich shale, interested to look into your recommendation. Please share the detail of Tiab A. Fourth Eddition
maybe you can use my model here Article A Systematic Dependence of Acoustic Velocity on Internal Por...
It is not tested yet in organic -rich shale, but it was built from many kind of sandstones with heterogeneous pore system. Maybe it will work in your case study.
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