We develop a modified grain contact theory to better describe the pressure-dependent elastic properties of uncemented sediments. The Hertz-Mindlin (HM) theory typically predicts shear moduli that are much higher than observed laboratory measurements, resulting in inaccurate estimates of the dry bulk to shear modulus ratio [Formula: see text]. The HM theory further predicts that the [Formula: see text] ratio is constant with pressure, whereas ultrasonic core measurements typically show an increasing [Formula: see text] ratio as effective pressure decreases. Laboratory data also suggest that the dry bulk and shear moduli variation with effective pressure is greater than the cube-root power law predicted by the HM theory. We introduce two new pressure-dependent calibration parameters to account for the shortcomings in effective medium theory, and we develop a new method to predict pressure-dependent elastic properties. Our calibration parameters agree with the results of published granular dynamics simulations, and they incorporate grain relaxation and porosity effects not included in existing effective medium theories. Our new model provides improved fits to laboratory data when compared with existing models, and it can be used for improved prediction of elastic properties as a function of effective pressure. Our new theory can also be used to model uncemented sediments with values of Poisson’s ratio [Formula: see text], where many existing grain contact and effective medium theories currently fail.
Knowledge of the pressure dependence of elastic rock properties is useful for time-lapse monitoring of hydrocarbon, groundwater, and CO2 sequestration reservoirs. A longstanding problem is that theoretical models of velocity-pressure relationships (e.g., Hertz-Mindlin) often do not match lab measurements, and alternately, empirical regressions fit to lab measurements do not extrapolate well to wider pressure ranges because they have little-to-no physical basis. We present a new velocity-pressure-compaction model to describe the pressure sensitivity of bulk (K) and shear (G) moduli for uncemented sediments. The physical basis for this model incorporates compaction theory and the concept of critical porosity. A porosity-pressure relationship is included in our model to account for porosity loss with increasing effective pressure, which leads to an additional relationship to predict density changes with pressure. The model also includes a zero effective pressure constraint that can be calculated using grain-size distribution data and the Reuss bound. This constraint allows accurate predictions to be made of pressure sensitivity at low effective pressures, even when ultrasonic velocity measurements in this pressure range are not available. Our new model is verified with laboratory measurements of unsaturated sand samples and fits well over a wide range of pressures.
SummaryKnowledge of the pressure dependencies of rock properties in unconsolidated sands is important for accurate time-lapse feasibility studies, pore pressure prediction, and reservoir characterization. A key problem that arises in determining such pressure dependencies is an accurate model at low effective stress. We propose a double exponential model to describe the pressure sensitivity of the bulk modulus (K) or shear modulus (G) for unconsolidated sands. The physical basis for our model relies on observed porosity-depth trends in unconsolidated sands, and the concept of critical porosity. Our new model matches laboratory measurements on unsaturated sand samples that have a range of grain size distributions and compositions. Grain size distribution data is first used to estimate critical porosity, which is then used as a zero effective pressure constraint in the data fitting process. We show that our new model more accurately predicts pressure sensitivity near zero-effective pressure compared to current methods, and is thus more accurate for situations in which core measurements at low effective stresses are not available.
The analysis of well data from the Enfield field of the Exmouth Sub-basin, WA, indicates that both cementation and pore-filling clay appear to have a stiffening effect on the reservoir sands. The elastic contrast between brine sand and the overlying shale is often small and the large amplitudes observed from seismic data are associated with hydrocarbon content. More detailed rock physics and depth trend analysis of elastic and petrophysical properties, however, indicate significant spatial variability in the cap rock shales across the field with different sand shale mixtures, causing changes in the elastic response of the rock. Areas where shales are softer produce weak seismic amplitude contrasts even with high hydrocarbon saturation; the amplitude response being similar to areas with stiffer shales and brine-filled sands. The variations in reservoir quality are, therefore, masked by the distribution of the brine, oil and gas, as well as the variations in the cap rock. The Enfield rock physics analysis provides an example of reducing amplitude ambiguity over lithology-fluid variation and improves the chance of successful interpretation of the results of seismic inversion.
Time-lapse seismology has proven to be a useful method for monitoring reservoir fluid flow, identifying unproduced hydrocarbons and injected fluids, and improving overall reservoir management decisions. The large magnitudes of observed time-lapse seismic anomalies associated with strong pore pressure increases are sometimes not explainable by velocity-pressure relationships determined by fitting elastic theory to core data. This can lead to difficulties in interpreting time-lapse seismic data in terms of physically realizable changes in reservoir properties during injection. It is commonly assumed that certain geologic properties remain constant during fluid production/injection, including rock porosity and grain cementation. We have developed a new nonelastic method based on rock physics diagnostics to describe the pressure sensitivity of rock properties that includes changes in the grain contact cement, and we applied the method to a 4D seismic data example from offshore Australia. We found that water injection at high pore pressure may mechanically weaken the poorly consolidated reservoir sands in a nonelastic manner, allowing us to explain observed 4D seismic signals that are larger than can be predicted by elastic theory fits to the core data. A comparison of our new model with the observed 4D seismic response around a large water injector suggested a significant mechanical weakening of the reservoir rock, consistent with a decrease in the effective grain contact cement from 2.5% at the time/pressure of the preinjection baseline survey, to 0.75% at the time/pressure of the monitor survey. This approach may enable more accurate interpretations and future predictions of the 4D signal for subsequent monitor surveys and improve 4D feasibility and interpretation studies in other reservoirs with geomechanically similar rocks.
SUMMARY Knowledge of the pressure dependence of rock properties is useful for a wide range of earth science problems, especially related to pore pressure changes caused by fluid injection or withdrawal, as often occurs in groundwater, hydrocarbon and CO2 sequestration reservoirs. A long-standing problem is that theoretical models of velocity-pressure response often do not match laboratory measurements, and alternately, empirical regressions fit to such data do not extrapolate accurately to wider pressure ranges since they have little or no physical basis. Accurate determination of the dry rock frame properties at low effective pressure is a key aspect of the problem, particularly when ultrasonic laboratory measurements are not available in this pressure range. We present a new model to describe the pressure sensitivity of the bulk and shear moduli for uncemented sedimentary rocks. Our model incorporates effects of sedimentary compaction and critical porosity, including a relationship to account for porosityanddensitychangewithpressure.Themodelistestedonlaboratorymeasurementsfor various rock samples and fits well over a wide range of pressures. The new velocity‐pressure model should be useful for improved prediction and interpretation of pressure-dependent rock properties and seismic data.
We present a modified effective medium theory to better describe the pressure-dependent elastic properties of uncemented sediments. Hertz-Mindlin theory typically predicts shear moduli that are higher than observed laboratory measurements, resulting in inaccurate estimates of the dry bulk to shear modulus ratio (Kdry/Gdry). Hertz-Mindlin theory further predicts that the Kdry/Gdry ratio is constant with pressure, whereas ultrasonic core measurements show increasing Kdry/Gdry ratio as effective pressure decreases. Laboratory data also suggest that dry bulk and shear moduli vary with effective pressure stronger than the cube-root power law predicted by Hertz-Mindlin theory. We introduce two new pressure-dependent calibration parameters to account for the shortcomings in effective medium theory, and present a new method to predict pressure-dependent elastic properties. Our calibration parameters agree with results of published granular dynamics simulations, and incorporate grain relaxation and porosity effects not included in existing effective medium theories. Our new model provides improved fits to laboratory data when compared to existing models, and can be used for improved prediction of elastic properties as a function of effective pressure. Our theory can also be used to model uncemented sediments with values of Poisson's ratio > 0.25, where a number of existing effective medium theories currently fail.
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