Rock physics modeling of carbonates: a review of effective medium theory methods and aspects of their applicability

10.24411/2076-6785-2019-10015

The article reports an overview of effective media methods in the context of computation elastic properties of rocks (Rock Physics) with constraints of applicability. For comparison purposes, several methods were applied to estimate effective elastic properties of modeled space consisting of the calcite matrix and the pore space divided according to double porosity model. For the three types of carbonate rocks parameter-oriented elastic models on the core scale were constructed based on generalized singular approximation method, using data of rocks microstructure analysis at various scales, as well as measurements of the elastic waves velocities on the standard samples. The parameters of petroelastic models were obtained during solving the inverse problem. 

Materials and methods
Methods of eff e medium theory, Fortran programming language, IMSL Fortran library. 

Results
Author provided a review of the most common methods of rock physics: Kuster- Toksoz, self-consistency, differential scheme, Mori-Tanaka, generalized singular approximation, in case of the matrix consisting of calcite, and the pore space, considering as the dual porosity model. Parametric-oriented mathematical models of the isotropic elastic properties for three types of carbonate rocks are constructed. 

Conclusions
The paper presented a comparative analysis of the rock physics methods and highlighted their important features for petro-elastic modeling of hydrocarbon reservoirs. All examined methods are approximation schemes since effective properties evaluation is reduced to the problem of many bodies interaction, which does not have an exact solution. In general, the results obtained by different methods will vary due to the difference in theoretical approaches to the modeling of stress and strain fields. For isotropic rock and small porosity values, the considered methods give close estimates of the effective properties. The sensitivity analysis of petro-elastic models of carbonate rocks showed that the main influence on the effective elastic properties caused by total porosity, mineral composition, and microporosity. The information about the microstructure of rocks at different scales, pore space morphology, and connectivity of pores maximize the success of petro-elastic modeling. Also, this information allows calibrating the porosity parameters in the model to types of porosity actually presented in the rock. From the analysis of the simulation results, it follows that the micritic elastic moduli are almost equal to the moduli of the monomineral polycrystal of calcite.