Elastic properties of unconsolidated porous sand reservoirs (1977)

Abstract The effect of (1) compressive stress and (2) pore fluid properties on elastic properties of unconsolidated sand reservoirs was determined by laboratory velocity and pore volume measurements on two specimens. The latter consisted of a naturally occurring very fine-grained sand and glass beads, each with a porosity of approximately 38 percent. Constituent compressibilities and densities of the two reservoir specimens are similar; thus, differences in measured elastic properties likely are attributable to differences in grain shape and pore size.Compressional- and shear-wave velocities and pore compressibility were measured in the brine- and gas-saturated specimens over a differential pressure range of 400 to 5000 psi. Measured velocities increase with increasing pressure very closely as a power of pressure. Shear-wave velocity for both brine- and gas-saturated specimens and compressional-wave velocity for the gas-saturated specimen all increase approximately as the 1/4th power of differential pressure. The replacement of gas with brine increases the compressional-wave velocity substantially and reduces the rate of increase with pressure, the velocity increasing as approximately the 1/18th power of differential pressure. Pore compressibility of the glass bead specimen exceeds that of the Ottawa sand specimen by a factor of approximately 1.3 and, accordingly, static frame (bulk) compressibility of the glass bead specimen also is substantially greater. Shear modulus increases nonlinearly with differential pressure, the shear modulus of the Ottawa sand specimen becoming increasingly greater than that of the glass bead specimen with increasing pressure. Poisson's ratio is moderately greater for the Ottawa sand specimen, decreasing from slightly less than 0.5 to slightly less than 0.4 for the brine-saturated specimens as differential pressure increases from 400 to 5000 psi. Poisson's ratios of the gas-saturated specimens are nearly invariant with differential pressure and are in the range of 0.10 to 0.15. The frame-fluid coupling factor appears to vary with differential pressure, being bear 1.0 (no coupling) at 400 psi and increasing to values between 2.0 and 3.0 as differential pressure approaches 5000 psi, with the exception of the glass bead shear-wave coupling factor which appears to remain between a value of 2.0 and 3.0 with increasing differential pressure.Compressional- and shear-wave velocities also were measured with a brine-gas mixture in the reservoir pore space at various brine saturations and at differential pressures of 1500 and 4500 psi. A modified fluid injection technique resulted in a more uniform distribution of the brine-gas mixture in the pore space and in measured compressional-wave velocities more nearly in conformity with theoretical velocities at high brine saturations. Theoretically, compressional-wave velocity decreases with increasing brine saturation, becoming minimum in the vicinity of 90 percent brine saturation and then increasing to the highest value at full brine saturation. Measured shear-wave velocities generally decrease moderately with increasing brine saturation, substantially in conformance with theoretical curves. Scatter of measured velocities precluded accurate estimations of variation in frame-fluid coupling with brine-saturation. Effective fluid compressibilities, derived from compressional-wave velocity measurements, in general are between theoretical values given by the weighted-by-volume average of the compressibilities (direct weighting) and of the incompressibilities (inverse weighting) of the gas and brine. Direct weighting implies a uniform distribution of the brine-gas mixture and, consequently, effective fluid compressibilities derived from velocities measured after fluid injection by the modified technique were more nearly in agreement with theoretical values given by direct weighting. Theoretically, the pore fluid and frame affect compressional-wave velocity nearly equally at full brine saturation. The effect of pore fluid on velocity diminishes rapidly as brine-saturation decreases, having only approximately one-thousandth the effect of the frame at full gas saturation for a coupling factor of infinity (perfect coupling). As frame-fluid coupling decreases, the effect of pore fluid on velocity increases, having approximately one-third the effect of the frame for a coupling factor of 1.0 (no coupling) at full gas saturation. The compressional-wave reflection coefficient of the interface between the portion of a reservoir containing a brine-gas mixture and the underlying fully brine-saturated portion varies nonlinearly with brine-saturation, the largest change occurring between 90 percent and full brine-saturation at which the coefficient is zero. The shear-wave reflection coefficient is substantially lower than the compressional-wave reflection coefficient and decreases essentially linearly with increasing brine saturation.