A FRACTAL MODEL FOR PHYSICAL-PROPERTIES OF POROUS ROCK - THEORETICAL FORMULATIONS AND APPLICATION TO ELASTIC PROPERTIES

Besides the mineralogical composition and porosity the elastic propert ies of porous rock are strongly influenced by the rock microstructure (pore shapes, pore size distribution, grain-to-grain contacts, etc.).q uantitative microstructural models can provide an important contributi on to achieve a fundamental understanding of the relationship between microscopic rock structures and macroscopic rock properties which is c rucial for the interpretation of seismic velocity data. The conceptual model presented here provides the possibility of considering differen t 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 dist ribution and an enlarged internal surface. The contact conditions in t he model are characterized by a contact parameter which varies between 1 for a pore free rock and 0 for a suspension. The application of thi s model to the elastic properties allows the calculation of velocities as a function of porosity and degree of contact. The model may be eit her isotropic concerning the velocities or anisotropic, up to an ortho rhombic anisotropy. Model calculations concerning the influence of con tact 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 comp are the predictions for high- and low-frequency velocities in the case of fluid saturation for rocks with different microstructures.