DIFFERENTIAL EFFECTIVE-MEDIUM MODELING OF ROCK ELASTIC-MODULI WITH CRITICAL POROSITY CONSTRAINTS

Rocks generally have a percolation porosity at which they lose rigidit y and fall apart. Percolation behavior is a purely geometrical propert y, independent of any physical properties, and is a powerful constrain t on any valid velocity-porosity relation. We show how the conventiona l Differential Effective Medium (DEM) theory can be modified to incorp orate percolation of elastic moduli in rocks by taking the material at the critical porosity as one of the constituents of a two-phase compo site. Any desired percolation porosity can be specified as an input. I n contrast, the conventional DEM model always predicts percolation at a porosity of either 0 or 100 percent. Most sedimentary rocks however have intermediate percolation porosities and are therefore not well re presented by the conventional theory. The modified DEM model incorpora tes percolation behavior, and at the same time is always consistent wi th the Hashin-Shtrikman bounds. The predictions compare favorably with laboratory sandstone data.