Marina Pervukhina

A simple model for squirt-flow dispersion and attenuation in fluid-saturated granular rocks

A major cause of seismic attenuation in fluid-saturated rocks is the flow of the pore fluid induced by the passing wave. At sonic and ultrasonic frequencies, attenuation appears to be dominated by the local (pore-scale) flow between pores of different shapes and orientations. A simple squirt flow model is developed in which all of the parameters can be independently measured or estimated from measurements. The pore space of the rock is assumed to consist of stiff porosity and compliant (or soft) pores present at grain contacts. The effect of isotropically distributed compliant pores is modeled by considering pressure relaxation in a disk-shaped gap between adjacent grains. This derivation gives the complex and frequency-dependent effective bulk and shear moduli of a rock, in which the compliant pores are liquid saturated and stiff pores are dry. The resulting squirt model is consistent with Gassmann’s and Mavko–Jizba equations at low and high frequencies, respectively. The magnitude of attenuation and dis...

Direct laboratory observation of patchy saturation and its effects on ultrasonic velocities

Maximizing the recovery of known hydrocarbon reserves is one of the biggest challenges facing the petroleum industry today. Optimal production strategies require accurate monitoring of production-induced changes of reservoir saturation and pressure over the life of the field. Time-lapse seismic technology is increasingly used to map these changes in space and time. However, until now, interpretation of time-lapse seismic data has been mostly qualitative. In order to allow accurate estimation of the saturation, it is necessary to know the quantitative relationship between fluid saturation and seismic characteristics (elastic moduli, velocity dispersion, and attenuation). The problem of calculating acoustic properties of rocks saturated with a mixture of two fluids has attracted considerable interest (Gist, 1994; Mavko and Nolen-Hoeksema, 1994; Knight et al., 1998. For a comprehensive review of theoretical and experimental studies of the patchy saturation problem see Toms et al., 2006).

An analytic model for the stress-induced anisotropy of dry rocks

One of the main causes of azimuthal anisotropy in sedimentary rocks is anisotropy of tectonic stresses in the earth’s crust. We have developed an analytic model for seismic anisotropy caused by the application of a small anisotropic stress. We first considered an isotropic linearly elastic medium (porous or nonporous) permeated by a distribution of discontinuities with random (isotropic) orientation (such as randomly oriented compliant grain contacts or cracks). The geometry of individual discontinuities is not specified. Instead, their behavior is defined by a ratio B of the normal to tangential excess compliances. When this isotropic rock is subjected to a small compressive stress (isotropic or anisotropic), the number of cracks along a particular plane is reduced in proportion to the normal stress traction acting on that plane. This effect is modeled using the Sayers-Kachanov noninteractive approximation. The model predicts that such anisotropic crack closure yields elliptical anisotropy, regardless of...

Ultrasonic moduli for fluid-saturated rocks: Mavko-Jizba relations rederived and generalized

Mavko and Jizba propose a quantitative model for squirt dispersion of elastic-wave velocities between seismic and ultrasonic frequencies in granular rocks. Their central results are the expressions for the so-called unrelaxed frame bulk and shear moduli computed under an assumption that the stiff pores are drained (or dry) but the soft pores are filled with fluid. Mavko-Jizba expressions are limited to liquid-saturated rocks but become inaccurate when the fluid-bulk modulus is small (e.g., for gas-saturated rocks). We have derived new expressions for unrelaxed moduli of fluid-saturated porous rocks using Sayers-Kachanov discontinuity formalism. The derived expressions generalize the established Mavko-Jizba relations to gas-saturated rocks, reduce to Mavko-Jizba results when the pore fluid is liquid, and yield dry moduli when fluid-bulk modulus tends to zero. We tested this by comparing our model and the model of Mavko and Jizba against laboratory measurements on a sample of Westerly granite.

Feasibility of a data-constrained prediction of hydrocarbon reservoir sandstone microstructures

Microstructures are critical for defining material characteristics such as permeability, mechanical, electrical and other physical properties. However, the available techniques for determining compositional microstructures through segmentation of x-ray computed tomography (CT) images are inadequate when there are finer structures than the CT spatial resolution, i.e. when there is more than one material in each voxel. This is the case for CT imaging of geomaterials characterized with submicron porosity and clay coating that control petrophysical properties of rock. This note outlines our data-constrained modelling (DCM) approach for prediction of compositional microstructures, and our investigation of the feasibility of determining sandstone microstructures using multiple CT data sets with different x-ray beam energies. In the DCM approach, each voxel is assumed to contain a mixture of multiple materials, optionally including voids. Our preliminary comparisons using model samples indicate that the DCM-predicted compositional microstructure is consistent with the known original microstructure under low noise conditions. The approach is quite generic and is applicable to predictions of microstructure of various materials.

Parameterization of elastic stress sensitivity in shales

Stress dependency and anisotropy of dynamic elastic properties of shales is important for a number of geophysical applications, including seismic interpretation, fluid identification, and 4D seismic monitoring. Using SayersKachanov formalism, we developed a new model for transversely isotropic (TI) media that describes stress sensitivity behavior of all five elastic coefficients using four physically meaningful parameters. The model is used to parameterize elastic properties of about 20 shales obtained from laboratory measurements and the literature. The four fitting parameters, namely, specific tangential compliance of a single crack, ratio of normal to tangential compliances, characteristic pressure, and crack orientation anisotropy parameter, show moderate to good correlations with the depth from which the shale was extracted. With increasing depth, the tangential compliance exponentially decreases. The crack orientation anisotropy parameter broadly increases with depth for most of the shales, indicating that cracks are getting more aligned in the bedding plane. The ratio of normal to shear compliance and characteristic pressure decreases with depth to 2500 m and then increases below this to 3600 m. The suggested model allows us to evaluate the stress dependency of all five elastic compliances of a TI medium, even if only some of them are known. This may allow the reconstruction of the stress dependency of all five elastic compliances of a shale from log data, for example.

Stress-dependent elastic properties of shales: measurement and modeling

Despite decades of research, current understanding of elastic properties of shales is insufficient as it is based on a limited number of observations caused by the time-consuming nature of testing resulting from their low permeability. Though it is well known that shales are highly anisotropic and assumed to be transversely isotropic (TI) media, few laboratory experiments have been carried out for measuring the five elastic constants that define TI media on well-preserved shales. Many previous measurements were made without control of pore pressure, which is crucial for the determination of shale elastic properties.

Are penny-shaped cracks a good model for compliant porosity?

Summary Variation of elastic properties of rocks with pressure is often modeled using penny-shaped or spheroidal cracks as idealization of real crack/pore geometry. We analyze the validity of this approach by extracting the ratios of shear to bulk stress sensitivity coefficients, and normal to tangential compliances from ultrasonic measurements on 76 dry sandstone samples. Comparison of these ratios against the predictions of the spheroidal crack theory shows that for roughly half of the samples, the ratio of normal to tangential compliance is significantly lower than predicted by spherodical crack theory. This inconsistency results in significantly different estimates of crack density from bulk and shear moduli, and in deviation of predicted pressure variation of Poisson’s ratio from the measured data.

Experimental verification of the physical nature of velocity-stress relationship for isotropic porous rocks

The exponential increase of seismic velocities with effective stress has usually been explained by the presence of pores with a broad distribution of aspect ratios. More recently, a stress-related closure of soft pores with a narrow distribution of compliances (e.g. grain contacts) has been suggested to be sufficient to explain such exponential stress dependency. This theoretical interpretation has been verified here using laboratory measurements on dry sandstones. On the basis of these experimental data, linear dependency of elastic compressibility on soft porosity and exponential decay of soft porosity and elastic compressibility with effective stress up to 60 MPa is confirmed. Soft porosity, estimated from the fitting coefficients of elastic compressibilities, is on the same order of magnitude but slightly lower than obtained from strain measurements. The results confirm applicability ofpreviously proposed stress sensitivity models and provide justification for using this approach to model stress dependency of elastic properties for isotropic and anisotropic rocks.

Research of CO 2 and N 2 Adsorption Behavior in K-Illite Slit Pores by GCMC Method

Understanding the adsorption mechanisms of CO2 and N2 in illite, one of the main components of clay in shale, is important to improve the precision of the shale gas exploration and development. We investigated the adsorption mechanisms of CO2 and N2 in K-illite with varying pore sizes at the temperature of 333, 363 and 393 K over a broad range of pressures up to 30 MPa using the grand canonical Monte Carlo (GCMC) simulation method. The simulation system is proved to be reasonable and suitable through the discussion of the impact of cation dynamics and pore wall thickness. The simulation results of the excess adsorption amount, expressed per unit surface area of illite, is in general consistency with published experimental results. It is found that the sorption potential overlaps in micropores, leading to a decreasing excess adsorption amount with the increase of pore size at low pressure, and a reverse trend at high pressure. The excess adsorption amount increases with increasing pressure to a maximum and then decreases with further increase in the pressure, and the decreasing amount is found to increase with the increasing pore size. For pores with size greater larger than 2 nm, the overlap effect disappears.