Sandstone and limestone porosity determination from shear and compressional wave velocity

Recent and ongoing development of seismic petroleum exploration methods for generating and recording shear waves requires companion efforts to extract useful information from these data. Data examined in this study are previously published laboratory measurements of shear (S) and compressional (P) wave velocity measurements on water-saturated sandstone, calcareous sandstone, dolomite, and limestone cores, as well as laboratory measurements of porosity on the sandstone and limestone cores. Sandstone and limestone porosities range from 0.092 to 0.299 and from 0.006 to 0.229, respectively. Differential pressure was varied from 500 to 6000 psi, corresponding to approximate burial depths from 290 to 3450 m, respectively.

The above lithologies appear effectively separated by Poisson’s ratio σ or, equivalently, by the ratio of P to S-wave velocity. Rock types are bounded by the 90 percentile values of Poisson’s ratio of 0.17 and 0.26 for sandstone, 0.27 and 0.29 for dolomite, and 0.29 and 0.33 for limestone. The values for calcareous sandstones correspond to the upper sandstone range of values. Separation of sandstone and limestone appears to result from the difference in Poisson’s ratio of the matrix material, namely, quartz (0.056) and calcite (0.316), respectively.

An empirical function, 1/V = A + Bϕ, was fitted by regression analysis to sandstone and limestone velocity (Vs and Vp) versus porosity (ϕ) values at each differential pressure. In this equation, A and B are constants at each pressure, A being approximately equal to the reciprocal of matrix velocity. Decreasing standard deviation indicates that the equation becomes an appreciably more accurate representation of the measured data as pressure increases. Correlation coefficients for sandstone are significantly larger than those for limestone, and approach unity at high pressure. The constant A generally decreases slightly with increasing pressure; average values are near the reciprocal-velocities of quartz (sandstone averages) and calcite (limestoneaverages). The constant B (the rate of change of reciprocal-velocity with porosity) is a critical measure of the sensitivity of velocity to porosity and, therefore, the usefulness of velocity in estimation of porosity. As pressure increases, B decreases non-linearly for a given porosity, the largest decrease occurring between 500 and about 2000 psi. Sandstone S-wave B values are from two to five times greater than all other values, indicating that sandstone S-wave velocity is by far the most sensitive to porosity variation. Least sensitive is the limestone P-wave velocity. Unfortunately, limestone S-wave velocity is less sensitive than sandstone P-wave velocity to porosity variation, except at very low pressures.