Carbonate formations are highly heterogeneous, and the velocity-porosity relationships are controlled by various microstructural parameters, such as the types of pores and their distribution. Because diagenesis is responsible for important changes in the microstructure of carbonate rocks, we have extended the standard effective medium approach to model the impact of diagenesis on the carbonate elastic properties through a step-by-step effective medium modeling. Two different carbonate rocks deposited, respectively, in lacustrine and marine environments are considered in this study. The first key step is the characterization of the diagenesis, which affected the two studied carbonate sample sets. Effective medium models integrating all of the geologic information accessible from petrographic analysis are then built. The evolution of the microstructural parameters during diagenesis is thoroughly constrained based on an extensive experimental data set, including X-ray diffraction analysis, different porosimetry methods, and ultrasonic velocity measurements. A new theoretical approach including two sources of compliance is developed to model the specific behavior of carbonates. A compliant interface is introduced around the main carbonate grains to represent grain contacts and the different pore scales are taken into account through multiscale modeling. Finally, direct calculations with the model provide elastic wave velocities representative of the different diagenetic stages. An extrapolation to permeability evolution is also introduced. This approach allows the identification of the acoustic signature of specific diagenetic events, such as dolomitization, dissolution, or cementation, and the assessment of their impact on the elastic properties of carbonates.

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