ULTRASONIC VELOCITY POROSITY RELATIONSHIPS FOR SANDSTONE ANALOGS MADE FROM FUSED GLASS-BEADS

Using fused glass beads, we have constructed a suite of clean sandstone analogs, with porosities ranging from about 1 to 43 percent, to test the applicability of various composite medium theories that model elastic properties. We measured P- and S-wave velocities in dry and saturated cases for our synthetic sandstones and compared the observations to theoretical predictions of the Hashin-Shtrikman bounds, a differential effective medium approach, and a self-consistent theory known as the coherent potential approximation. The self-consistent theory fits the observed velocities in these sandstone analogs because it allows both grains and pores to remain connected over a wide range of porosities. This behavior occurs because this theory treats grains and pores symmetrically without requiring a single background (host) material, and it also allows the composite medium to become disconnected at a finite porosity. In contrast, the differential effective medium theory and the Hashin-Shtrikman upper bound overestimate the observed velocities of the sandstone analogs because these theories assume the microgeometry is represented by isolated pores embedded in a host material that remains continuous even for high porosities. We also demonstrate that the differential effective medium theory and the Hashin-Shtrikman upper bound correctly estimate bulk moduli of porous glass foams, again because the microstructure of the samples is consistent with the implicit assumptions of these two theoretical approaches.