Bounds for Pore Space Parameters of Petroelastic Models of Carbonate Rocks

This work is devoted to constructing parametric mathematical models of effective elastic properties of carbonate rocks based on the effective medium theory (petroelastic models). These models have recently been particularly in demand for exploration geophysics because they link the elastic properties of hydrocarbon reservoir rocks with the parameters of the void space-the shape and volume concentration of pores, cracks, and voids, and the degree of their connectivity. These parameters are determined from the measured velocities of elastic waves. However, the number of the unknown model parameters is, as a rule, larger than the number of the measured quantities so that such problems are underdetermined. In this case, the inverse problem of finding the model parameters may have an infinite number of solutions. Constraining the sought parameters with taking into account their physical meaning and existing experimental data can significantly increase the reliability of the obtained results and reduce the region of possible solutions of the inverse problem. In this work, we propose new approaches for constraining variations in the unknown model parameters which cannot be established from direct measurements, namely, for the connectivity of voids, crack porosity, and crack aspect ratio. Based on the correlation between the parameter of connectivity of voids and permeability, we developed an approach for constraining the range of variations in the parameter of connectivity of voids which relies on the Kozeny-Carman equation. The results of triaxial testing of rock samples on a servo hydraulic testing machine (press) are used for estimating the upper limit of crack porosity and assessing the crack shape. The characteristics of microstructure of the studied rocks obtained with the use of the established constraints increase the reliability of the constructed petroelastic models for carbonate rocks. These models can be subsequently used in various geophysical studies implying a relationship between the analyzed processes or properties and the microstructure of the rocks.