Irina O. Bayuk

Correlation between elastic and transport properties of porous cracked anisotropic media

Abstract The general singular approximation (GSA) method is shown to be the most applicable among other mathematical methods for the explanation of laboratory data on artificial rock samples. This method is used for the simultaneous calculation of the effective physical (elastic and transport) properties of porous cracked anisotropic media. The revealed correlation between elastic and electric properties makes it possible to discriminate the sort of fluid in inclusions. It is shown that the use of experimental data on elasticity and conductivity of a porous-cracked anisotropic medium allows the estimation of its permeability by the GAS method.

Comparison of seismic upscaling methods: From sonic to seismic

The term “upscaling” used here means a prediction of elastic-wave velocities at lower frequencies from the velocities at higher frequencies. Three different methods of upscaling are considered, including the simple averaging, Backus averaging, and pair correlation function methods. These methods are applied to upscale the elastic-wave velocities measured at sonic frequencies ( 2 kHz , logging data) available for a well penetrating layers of gas-bearing shales and carbonates. As a result, a velocity distribution over depth for VP and VS is found in the frequency range of 50–500 Hz . The difference in the results obtained for a particular depth by the three theoretical methods in the surface seismic frequency bandwidth (50–100 Hz) is ∼600 m∕s for P-wave and ∼260 m∕s for S-wave velocity. This difference is attributed to different theoretical backgrounds underlying these methods.

Elastic Properties of Four Shales Reconstructed From Laboratory Measurements At Unloaded Conditions

Summary The elastic properties of four shales (Barnett, Woodford, Muscogee, and Caney) are studied on 11 samples at the room conditions with the help of specially developed and constructed apparatus, allowing us to measure the elastic wave velocities (VP, VSH, and VSV) in different directions relative to the axis of cylindrical sample. The difference in the angular behavior of the velocities is attributed to the different mineral composition and microfabric of the shales. The stiffness tensors of shales are reconstructed from the measurements taking into account the experimental errors in velocities and rotation angle and possible disorientation of the sample axis relative to the elastic symmetry axis. The closest VTI stiffness tensors are inverted for all shale samples, and the accuracy of such an approximation is given in terms of relative average errors between experimental and theoretical velocities. These errors are shown to vary from 0.5% to 8%. These errors can be decreased if the tensor is approximated by the monoclinic symmetry in the laboratory coordinate system.

Comparison of Seismic Upscaling Methods

Random presence of various minerals, cracks and voids in different proportion make a rock inhomogeneous. These heterogeneities may be characterized by their different elastic constants. The size of heterogeneities can vary from micro-scale to macro-scale, and therefore the elastic properties of a rock become scale dependent. There has been great deal of efforts to estimate the effective properties of the heterogeneous materials, such as upper and lower bounds, self-consistent theory, differential effective medium theory; are based on the assumption that the inclusions occur in a particular shape. The mathematical formulations, based upon the solution of singularly perturbed linear equations approximation, partial differential equations, stochastic differential equations, ordinary differential equations and Markov chains, are used to estimate effective media properties . But these approximation methods, generally, do not take into account the interaction between heterogeneities. Our upscaling method is based upon pairand multispatial correlation function. Comparison of these two methods has been done with Backus averaging and simple running window averaging. Results indicate that the upscaling based pairand multicorrelation function are in good agreement to the original data.

Prediction of Frequency Dependent Velocity in Porous Reservoirs

Summary This paper presents a mathematical technique to predict sonic logs at the seismic frequency from well logs. A correlation approximation technique has been developed that takes into account the effect of 1-D scattering from random layered media with inhomogeneous inclusions. The results demonstrate that the dynamic characteristics of porous media are substantially dependent on the inclusion sizes. The dependencies of velocities and inverse quality factor on frequency have maxima whose locations are governed by the inclusion size. Predicted velocities at seismic frequencies derived using the correlation approximation indicate major differences from the Backus averaging technique near heterogeneous inclusions.

Dispersive properties of porous cracked media

The method of averaging has been very effective in modeling the elastic constants of inhomogeneous anisotropic multiphase media. There are however, many, cases of interest where difficulties arise applying this approach.

MODELING OF A MEDIUM WITH HIERARCHIC MICROCRACK STRUCTURE BY THE GENERAL SINGULAR APPROXIMATION METHOD

Abstract In thermodynamic equilibrium, a fluid forms isolated inclusions in the grain corners, because of a low wettability of rocks. The influence of the isolated fluid inclusions on the physical properties of rocks at small fluid concentrations typical of the deep horizons of the crust must be small. However, there is a clear evidence of the considerable effect of the fluid component on the physical properties of rocks. Such an inconsistency may be explained assuming that, in some zones of the crust, the fluid phase is in a nonequilibrium state (at least occasionally) with a hierarchic interconnected microcrack structure. In order to model the macroscopic elastic properties and the electric conductivity of rocks with the various pore structures, we use the general singular approximation method (GSA), combined with a procedure of the sequential addition of cracks. This paper is concerned with the method and results of modeling, which confirm the aforesaid suggestion on the medium structure in equilibrium and nonequilibrium state. The observed anomalies in elastic properties and electric conductivity of lower crust are explained on the basis on the numerical results.

3D Velocity Reconstruction In Shale Derived From Limited Number of Measurements

A technique allowing the determination of 3D distribution of both compressional and shear wave velocities in shales from limited number of experimental data has been developed. The technique involves an EMT (effective medium theory)-based inversion of shale’s microstructure (clay platelet orientation, crack shape and their connectivity). The knowledge of the microstructure and shale’s mineral composition makes it possible to find the shale’s stiffness tensor with the help of EMT methods. The stiffness tensor and density are necessary data to obtain the 3D distribution of velocities in shale. We demonstrate that this technique is applicable if only Vp is measured in some directions in the normal-to-bedding plane of shale, or Vp and Vs measurements are available only in the directions parallel and normal to bedding.

Fluid Substitution Problem for Thermal Conductivity of Hydrocarbon Reservoirs Based on Rock Physics Methods

Thermal conductivity of rocks is used in different specialized area of prospecting geophysics. This is a key parameter of basin modelling, it is used while developing of enhanced oil recovery (EOR) methods. Several experimental methods exist to measure thermal conductivity: optical scanning technique, TPS etc. However it is a bit technical challenge to make measurements of rock saturated with high viscous fluid. Sometimes in case of weak consolidated rock it is impossible to keep a sample while saturation. This forces us to solve the fluid substitution problem for this thermal property. In this study we develop EMT-based models of carbonate and terrigenuos rocks and apply them to solve the fluid substitution problem. Specifically, we predict the thermal conductivity of oil-saturated rocks using data on thermal conductivity obtained for dry and water-saturated rocks. The predicted values are tested on experimental data obtained with the optical scanning method. We compare our results with other well known theoretical approaches (Lichtenecker and Roy-Adler formulae).

A New Approach for Relating Dynamic Elastic Properties and Geomechanical Parameters Based on Rock Physics Modeling

Geomechanical modeling is of great importance for different tasks of prospecting geophysics. This modeling requires knowledge on geomechanical characteristics including the static moduli (Young modulus and Poisson coefficient), the uniaxial compression strength and internal friction angle. The only way to get reliable geomechanical parameters is laboratory tests providing “stress-strain” curves. However, this way is time consuming and should be performed for many representative samples of all stratigraphic units penetrated by a well. Many empirical relations exist that allow one to relate the dynamic moduli provided by logging with the geomechanical parameters. However these relations work only locally. In this work we propose an approach based on classification of rocks with respect to their macrostructure controlling the both dynamic moduli and geomechanical characteristics. The microstructure is described by the rock’s model parameters inverted from the experimental data with the help of the Rock Physics modeling. This makes it possible to group different rocks into classes with respect to the model parameters. As a result this allows one to find relations between the dynamic elastic parameters measured in field and geomechanical and other physical parameters (not measured) for different rock groups via the rock microstructure parameters specific of each rock group.