William F. Murphy, Lawrence M. Schwartz, and Brian Hornby
Schlumberger-Doll Research
ABSTRACT
The recent development of new downhole sonic measurement techniques provides the opportunity for significant progress in formation evaluation and in the mapping of subsurface geological structures. In particular, the advent of dipole shear slowness measurements in slow formations necessitates a fresh look at the physics underlying primary (P) and secondary (S) sonic arrivals. Both theory and experiment suggest that the ratio of squared acoustic speeds, VP2/Vs2 should play a central role in new sonic interpretation schemes. We propose that the interpretation of both laboratory and borehole measurements is best performed by decomposing this ratio into a sum of modulus ratios, consistent with the Biot-Gassmann equations:
Vp2 / Vs = Kp / N + Kb /N + 4/3
Here Kb and N are the frame moduli, and Kp describes the pore space effects of fluid saturation, Sw, and porosity, f. In general, the frame moduli depend on mineralogy, cementation, and grain contacts. For uniformly consolidated sandstones, we advance three theoretical predictions: (1) the ratio Kb/N is independent of f, (2) Kb and N are nearly linear functions of f, and (3) Kb and N are roughly linear in Pc 1/3 where Pc is the confining pressure. These predictions are in good agreement with laboratory data on clean quartz sands. Once the frame parameters are understood, fluid saturation effects can easily be included through the additional modulus, Kp. In high porosity sands the fluid’s influence is so dramatic that not only gas, but also oil can be distinguished from water. The new sonic interpretation algorithms are tested in a Gulf Coast case study, where the results are encouraging. In addition to petrophysical analysis, we envision the application of these algorithms to the mapping of borehole information on hydrocarbon content and lithology onto seismic inversions.