Petroelastic modeling of carbonate rocks using a dual porosity model

Mohammad F. Ghasemi Schmidt Institute of Physics of the Earth of the Russian Academy of Sciences Moscow
Irina O. Bayuk Schmidt Institute of Physics of the Earth of the Russian Academy of Sciences Moscow

In this work, parametric petroelastic models for four different carbonate rocks containing pores and cracks in the sample scale (double porosity models) are presented. To construct models are applied approaches of the Effective Medium Theory, in particular, the generalized singular approximation method are used. This method takes into account the hydraulic connectivity of the void space. The parameters of the petroelastic models can be estimated through solution of the inverse problem using measured acoustic waves velocities. Analysis of SEM images and primary petrophysical properties along with triaxial test data were used to narrow the search domain of the applied optimization algorithm. The obtained petroelastic models can be used to study the behavior of the physical properties of rocks as a function of their structural characteristics (such as, fracture and matrix porosity, the shape of voids and the degree of their connectivity).
Materials and methods
General singular approximation method, fortran programming language, IMSL Fortran library.
Parametric mathematical models of isotropic elastic properties of four carbonate rocks have been constructed. The models refl the presence of two types of voids in pore space - pores and cracks. Estimated numerical values for the parameters of the models characterize the shape of the pores and cracks, the fracture porosity, and the degree of connectivity of the voids.
A dual porosity petroelastic model was suggested for four carbonate rocks, with different internal structure and petrophysical properties, based on the laboratory investigation. The implemented double porosity model suggests the presence of two types of interconnected voids - pores and cracks with spatially chaotic orientation in studied rocks volume. A comparison of the obtained parameters of the microstructure of the rocks with its SEM images manifests satisfactory agreement. This, in turn, indicates the applicability of the proposed model of double porosity and the method of searching for model parameters (nonlinear optimization with constraints on parameters). Further, the estimated structural parameters in various scales, can be used to analyze for determination of eff e physical the influence of these parameters on the elastic properties of these rocks, and for the theoretical evaluation of other physical properties, such as the coefficient of thermal conductivity, electrical conductivity, etc...
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carbonate rocks mathematical modeling GSA method inverse problem