De-hua Han

Effects of porosity and clay content on wave velocities in sandstones

The ultrasonic compressional (Vp) and shear (Vs) velocities and first‐arrival peak amplitude (Ap) were measured as functions of differential pressure to 50 MPa and to a state of saturation on 75 different sandstone samples, with porosities ϕ ranging from 2 to 30 percent and volume clay content C ranging from 0 to 50 percent, respectively. Both Vp and Vs were found to correlate linearly with porosity and clay content in shaly sandstones. At confining pressure of 40 MPa and pore pressure of 1.0 MPa, the best least‐squares fits to the velocity data are Vp(km/s)=5.59-6.93ϕ-2.18C and Vs(km/s)=3.52-4.91ϕ-1.89C. Deviations from these equations are less than 3 percent and 5 percent for Vp and Vs, respectively. The velocities of clean sandstones are significantly higher than those predicted by the above linear fits (about 7 percent for Vp and 11 percent for Vs), which indicates that a very small amount of clay (1 or a few percent of volume fraction) significantly reduces the elastic moduli of sandstones. For shaly...

Empirical relationships among seismic velocity, effective pressure, porosity, and clay content in sandstone

We use a multivariate analysis to investigate the influence of effective pressure Pe, porosity ϕ, and clay content C on the compressional velocity Vp and shear velocity Vs of sandstones. Laboratory measurements on water‐saturated samples of 64 different sandstones provide a large data set that was analyzed statistically. For each sample, relationships between effective pressure and Vp and Vs have been determined. All samples were well fit by relationships that have an exponential increase in velocity at low Pe, tapering to a linear increase with Pe for Pe greater than 0.2 kbar. There are differences in the pressure dependences of velocity for different rocks, particularly at very low pressures; however, the differences cannot be attributed to ϕ or C. For the combined set of measurements from all samples, the best fitting formulations are Vp=5.77-6.94ϕ-1.73C+0.446(Pe-e-16.7Pe) and Vs=3.70-4.94ϕ-1.57C+0.361(Pe-e-16.7Pe). While this is admittedly a very simplified parameterization, it is remarkable how well ...

Fluid mobility and frequency-dependent seismic velocity — Direct measurements

The influence of fluid mobility on seismic velocity dispersion is directly observed in laboratory measurements from seismic to ultrasonic frequencies. A forceddeformation system is used in conjunction with pulse transmission to obtain elastic properties at seismic strain amplitude (10 −7 ) from 5 Hz to 800 kHz. Varying fluid types and saturations document the influence of pore-fluids. The ratio of rock permeability to fluid viscosity defines mobility, which largely controls pore-fluid motion and pore pressure in a porous medium. High fluid mobility permits pore-pressure equilibrium either between pores or between heterogeneous regions, resulting in a low-frequency domain where Gassmann’s equations are valid. In contrast, low fluid mobility can produce strong dispersion, even within the seismic band. Here, the low-frequency assumption fails. Since most rocks in the general sedimentary section have very low permeability and fluid mobility (shales, siltstones, tight limestones, etc.), most rocks are not in the lowfrequency domain, even at seismic frequencies. Only those rocks with high permeability (porous sands and carbonates) will remain in the low-frequency domain in the seismic or sonic band.

Gassmann's equation and fluid-saturation effects on seismic velocities

Gassmann’s (1951) equations commonly are used to predict velocity changes resulting from different porefluid saturations. However, the input parameters are often crudely estimated, and the resulting estimates of fluid effects can be unrealistic. In rocks, parameters such as porosity, density, and velocity are not independent, and values must be kept consistent and constrained. Otherwise, estimating fluid substitution can result in substantial errors. We recast the Gassmann’s relations in terms of a porosity-dependent normalized modulus Kn and the fluid sensitivity in terms of a simplified gain function G. General Voigt-Reuss bounds and critical porosity limits constrain the equations and provide upper and lower bounds of the fluid-saturation effect on bulk modulus. The “D” functions are simplified modulus-porosity relations that are based on empirical porosity-velocity trends. These functions are applicable to fluid-substitution calculations and add important constraints on the results. More importantly, the simplified Gassmann’s relations provide better physical insight into the significance of each parameter. The estimated moduli remain physical, the calculations are more stable, and the results are more realistic.

Heavy oils—seismic properties

Heavy-oil seismic properties are strongly dependent on composition and temperature. In biodegraded oils, straight chain alkanes are destroyed and complex heavy compounds dominate. As a result, the simple empirical trends developed for light oils for fluid properties such as viscosities, densities, gas-oil ratios, and bubble points may not apply well to heavy oils.

Fluids and frequency dependent seismic velocity of rocks

Summary Compressional and shear velocities of rocks are dependent on frequency and this dispersion may be significant even within the seismic band. The amount and position of dispersion will be largely a function of fluid properties, distribution, and motion in the pores. Velocities are thus directly coupled to rock permeability and pore compliance. Propagation often will be in the high frequency regime, even at a few tens of Hertz. Static, or low frequency models such as Gasmann will fail under such conditions. In addition, Biot theory will not correctly model wave propagation in many cases.

Pore Shape Effect On Elastic Properties of Carbonate Rocks

The presence of non-interactive porosities of spherical or near-spherical type along with microporosity changes the effective elastic properties of the rock frame making pore geometries an important parameter, that must be taken in to account for estimating elastic moduli by any theoretical effective medium models. Differential effective medium (DEM) model is one such theoretical model which accounts for changes in elastic moduli due to changing pore geometries and facilitates inclusion of two or more than two pore shapes. If bulk porosity and water-saturated P-wave velocities are available, one can estimate the average aspect ratio of the different pore shapes and their relative volume fraction in the rock. These two parameters when used in DEM will predict dry rock moduli and shear velocities. An example on 52 measured carbonate rock samples is shown, in the end.

Seismic properties of heavy oils—measured data

Seismic techniques hold great potential for characterization and recovery monitoring of heavy oil reservoirs. However, to be more effective, we must understand the seismic properties of the heavy oils and the heavy oil sands because this knowledge of in-situ properties is key to linking the seismic response to reservoir properties and changes. In this article, we examine the seismic properties of heavy oils in detail.

Seismic characterization of naturally fractured reservoirs using amplitude versus offset and azimuth analysis

P-wave seismic reflection data, with variable offset and azimuth, acquired over a fractured reservoir can theoretically be inverted for the effective compliance of the fractures. The total effective compliance of a fractured rock, which is described using second- and fourth-rank fracture tensors, can be represented as background compliance plus additional compliance due to fractures. Assuming monoclinic or orthotropic symmetry (which take into account layering and multiple fracture sets), the components of the effective second- and fourth-rank fracture compliance tensors can be used as attributes related to the characteristics of the fractured medium. Synthetic tests indicate that using a priori knowledge of the properties of the unfractured medium, the inversion can be effective on noisy data, with S/N on the order of 2. Monte Carlo simulation was used to test the effect of uncertainties in the a priori information about elastic properties of unfractured rock. Two cases were considered with Wide Azimuth (WAZ) and Narrow Azimuth (NAZ) reflection data and assuming that the fractures have rotationally invariant shear compliance. The relative errors in determination of the components of the fourth-rank tensor are substantially larger compared to the second-rank tensor, under the same assumptions. Elastic properties of background media, consisting in horizontal layers without fractures, do not cause azimuthal changes in the reflection coefficient variation with offset. Thus, due to the different nature of these properties compared to fracture tensor components (which cause azimuthal anomalies), simultaneous inversion for background isotropic properties and fracture tensor components requires additional constraints. Singular value decomposition (SVD) and resolution matrix analysis can be used to predict fracture inversion efficacy before acquiring data. Therefore, they can be used to determine the optimal seismic survey design for inversion of fracture parameters. However, results of synthetic inversion in some cases are not consistent with resolution matrix results and resolution matrix results are reliable only after one can see a consistent and robust behaviour in inversion of synthetics with different noise levels.

The effect of pore fluid on the stress-dependent elastic wave velocities in sandstones

Summary Elastic wave velocities in sandstones vary with stress due to the presence of discontinuities such as grain boundaries and microcracks within the rock. The effect of any discontinuities on the elastic wave velocities can be written in terms of a second-rank and fourth-rank tensor that quantify the dependence of the elastic wave velocities on the orientation distribution and normal and shear compliances of the discontinuities. This allows the normal and shear compliance of these discontinuities to be obtained as a function of stress by inverting measurements of P- and S-wave velocities. Inversion of ultrasonic velocity measurements on dry and fluid saturated sandstones shows that the ratio of the normal to shear compliance of the discontinuities is reduced in the presence of fluid in the grain boundaries and microcracks. This is consistent with the expected reduction in the normal compliance of the discontinuities in the presence of a fluid with non-zero bulk modulus.