A fractal model for physical properties of porous rock: Theoretical formulations and application to elastic properties

Abstract

Besides the mineralogical composition and porosity the elastic properties of porous rock are strongly influenced by the rock microstructure (pore shapes, pore size distribution, grain-to-grain contacts, etc.). Quantitative microstructural models can provide an important contribution to achieve a fundamental understanding of the relationship between microscopic rock structures and macroscopic rock properties which is crucial for the interpretation of seismic velocity data. The conceptual model presented here provides the possibility of considering different geometries of the pore canals as well as the influences of different grain-to-grain contacts. The main difference to other structural rock models is the use of a fractal approach for the modeling of the grain-to-grain contacts. This approach results in a discrete pore size distribution and an enlarged internal surface. The contact conditions in the model are characterized by a contact parameter which varies between 1 for a pore free rock and 0 for a suspension. The application of this model to the elastic properties allows the calculation of velocities as a function of porosity and degree of contact. The model may be either isotropic concerning the velocities or anisotropic, up to an orthorhombic anisotropy. Model calculations concerning the influence of contact cementation on the elastic velocities are in good agreement with other experimental and theoretical investigations. When combining the model with Gassmann's [1951] theory, it is possible to derive and compare the predictions for high- and low-frequency velocities in the case of fluid saturation for rocks with different microstructures.