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.
Gas in an unconsolidated sand reservoir encased in shale often results in a dramatic increase in amplitude of the seismic reflection from the shale/gas‐sand interface. Unfortunately, reflection amplitude appears not to vary linearly with water (brine) saturation, and thus cannot be used to estimate gas quantity. Previously presented theoretical velocity computations, for a Tertiary sedimentary section, which demonstrate that compressional‐wave velocity in an unconsolidated gas sand varies nonlinearly with brine saturation, qualitatively agree with laboratory velocity measurements on a sand specimen composed of pure quartz grains. However, significant departure of measured and theoretical velocities at high brine saturation indicates that the technique for partially saturating the sand specimen by flowing a gas‐brine mixture through the specimen does not provide a sufficiently uniform distribution. The gas preferentially seeks larger pores. In a subsequent experiment on a specimen composed of spherical glass beads of nearly uniform size, the previous, as well as a modified, fluid injection technique was used. For the latter, brine only was injected into the pore space previously filled with a mixture of gas and brine in nearly equal proportions. This resulted in a more uniform distribution of the gas‐brine mixture. For approximately equal brine saturations, this modified technique resulted in a measured compressional‐wave velocity approximately one‐half of the velocity measured for the previously used fluid injection technique. This result implies that if the gas‐brine mixture is uniformly distributed in a reservoir, the fluid compressibility is the weighted‐by‐volume average of the constituent compressibilities.
Data examined in this study are previously published laboratory shear (S) and compressional (P) wave velocity measurements on water‐saturated sandstone, calcareous sandstone, dolomite, and limestone cores, as well as laboratory porosity measurements on the sandstone and limestone cores. Sandstone and limestone porosities range from .092 to .299 and from .006 to .229, respectively. Differential pressure was varied from 500 to 6000 psi, corresponding to approximate burial depths from 290 to 3460 m, respectively. Sandstone, limestone, and dolomite are effectively separated by Poisson’s ratio σ or, equivalently, by the ratio of P- to S-wave velocity. Separation of sandstone and limestone appears to result from the difference in σ of the matrix material, namely, quartz (.056) and calcite (.316), respectively. An empirical function, [Formula: see text], was fit by regression analysis to sandstone and limestone velocity ([Formula: see text] and [Formula: see text]) 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 matrix velocity. Decreasing standard deviation indicates that the equation becomes an appreciably more accurate representation of the measured data as pressure increases. Average values of A are near reciprocal velocities of quartz (sandstone averages) and calcite (limestone averages). The constant B, rate of change of reciprocal velocity with porosity, is a critical measure of the sensitivity of velocity to porosity, hence the usefulness of velocity in estimation of porosity. Sandstone S-wave B values are from 2 to 5 times greater than all other values, indicating that sandstone S-wave velocity is by far the most sensitive to porosity variation. Least sensitive is limestone P-wave velocity.
Recent discoveries of the correspondence between seismic reflectivity and the presence of hydrocarbons in reservoirs have had a profound effect on petroleum exploration. This correspondence appears most pronounced in poorly consolidated sand reservoirs encased in shale. Reflectivity, defined as the absolute value of the reflection coefficient at the shale/sand‐reservoir interface, is determined by the product of the longitudinal velocity and bulk density of the shale and, separately, of the sand reservoir. The formula for velocity taken from Geertsma shows that the square of the velocity in a sand reservoir varies inversely with bulk density and also inversely with fluid compressibility. As water saturation (fractional value of pore space occupied by water) increases in an oil sand, decrease in velocity caused by increasing bulk density is more than compensated by increase in velocity due to decreasing fluid compressibility. On the contrary, in a gas sand, the decrease in velocity due to increasing bulk density with increasing water saturation is not completely compensated by the increase in velocity due to decreasing fluid compressibility. Appropriate values for shale density and velocity, for reservoir porosity, and for reservoir constituent densities and compressibilities are used to determine the reflectivity of a shale/oil‐sand and, separately, a shale/gas‐sand interface as a function of water saturation at depths of 2000, 6000, and 10,000 ft. At each depth, the reflectivity of a shale/oil‐sand interface decreases moderately with increasing water saturation; whereas, the reflectivity of a shale/gas‐sand interface decreases moderately from a completely gas‐saturated reservoir to a water saturation of approximately 0.95, after which the reflectivity decreases abruptly and appreciably to the reflectivity of a completely water‐saturated sand reservoir. Thus, a small quantity of gas (5 percent or less) increases reflection amplitude significantly, and reflection amplitude is not a simple linear measure of the amount of gas in the reservoir.
Possibly the first practical application of the pronounced at-I Air bubbles in water increase the compressibility several tenuating-property of-air bubbl& in water was one proposed and orders of magnitude above that in bubble-free water, thereby greatly reducing the velocity and increasing attenuation of acoustic waves. The effect of air bubbles in water on acoustic wave propagation was studied extensively during World War II as part of an overall effort to apply underwater sound in submarine warfare. Currently, air bubble curtains are used to prevent damage of submerged structures (e.g., dams) by shock waves from submarine explosives. Also, air-bubble curtains are used to reduce damage to waterfilled tanks in which metals are formed by explosives. Since World War II, research has progressed less feverishly in government and university laboratories. Published results of laboratory experiments generally confirm theoretical velocity and attenuation functions and demonstrate that these quantities are dependent principally upon frequency, bubble size, and fractional volume of air. Below the bubble resonant frequency and in the frequency range of marine energy sources, acoustic wave velocity is essentially independent of frequency and bubble radius, being well below the velocity in bubble-free water. In this frequency range, attenuation increases with increasing frequency, decreasing bubble radius, and increasing fractional air volume. Domenico Canal Blast Holes Loaded With Explosive Perforaied Air Pipes FIG. 2. Cross-section view of the rock barrier ("plug"), forebay, and dam showing air-bubble curtains used to reduce pressure of the explosive shock wave created by blasting of the barrier. (From La Prairie, 1955.) destroyer from explosive shock waves. As shown in Figure 1, air would issue from the pipe within the oil tank on the port side when it is desired to block sound waves arriving from that direction. Air-bubble streams would be generated outside the destroyer hull as indicated to attenuate explosive shock waves or to block sound waves arriving from that direction. The air streams also would be used to block sound waves from the oscillator in the desired direction. The effect of air bubbles in water on acoustic wave propagation was studied extensively during World War II. The studies were a small part of an overall effort to utilize underwater sound in antisubmarine and prosubmarine warfare. Most of the information on underwater sound obtained during World War II resulted from a research program organized by the National Defense Research Committee (NDRC) and performed by various U. S. Navy laboratories, Since then, the NDRC technical reports describing this research have been compiled and published in a four-part volume, entitled Physics of Sound in the Sea, by the Research Analysis Group of the National Research Council' s Committee on Undersea Warfare. results pertinent to this study are~in Part I~V of that volume, which is entitled Acoustic Properties of Wakes. Since World War II, research has progressed les...
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