Evgeni M. Chesnokov

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

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.

Automated detection and location of hydrofracking‐induced microseismic event from 3C observations in an offsetting monitor well

The idea of construction of algorithm and results of developed software on the determination of microearthquake locations due to frac job is given. Influence of anisotropy on the accuracy of frac event locations is briefly discussed. Methodology of determination of horizontal component of geophones is developed based on perfshots and earlier located frac events data. Produced software works in real time and in automated regime.

Analysis of Frequency-dependent Seismic Anisotropy From a Multicomponent VSP

In this study, we present results from the analysis of a multicomponent VSP for frequency-dependent anisotropy. The recorded four-component shear-wave data were first band-pass filtered into different frequency bands and then rotated to the natural coordinates to separate the fast and slow shear-waves. The polarizations of the fast shear-waves are found to be constant over the whole depth interval, and show no apparent variation with frequency. However, the time delays between split shear-waves decrease systematically as the frequency increases. We apply a timefrequency analysis method based on the wavelet transform with a Morlet wavelet to the data. A strong and consistent variation of shear-wave time delays with frequency is highlighted in the time-delay and frequency spectra. Two mechanisms are likely to explain the observation, i.e. scattering of seismic waves by preferentially aligned open fractures, and fluid flow in porous rocks with micro-cracks and macro-fractures.

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.

Diagram technique method for calculation of effective physical parameters of microinhomogeneous media

For microhomogeneous media with inclusions the problem of construction of macroscopic equations is solved using diagram technique. Distribution of inclusions in a medium is considered as an arbitrary stochastic tensor field of macroscopic elastic modules, which are defined by correlation functions of an arbitrary order. The exact expression of an effective tensor of elastic modules is deduced using mass operator. The calculation of Green functions, mass operator and effective elastic tensor for media with inclusions is carried out in a frame of correlation approximation. The existence of elastic anisotropy due to an order in location of pores in a space is shown. Numerical estimations of influence of space distribution of inclusions on a coefficient of effective elastic anisotropy are obtained.

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.

P-wave And Converted-waves Anisotropy Due to Multiple Fracture Sets

P and S waves velocity characteristics of hydrocarbon reservoirs are altered by hydraulically induced fractures. In the case where a reservoir is fractured at various stages, a complex fracture network is formed within the reservoir. In this abstract, the reflectivity method is used to compute reflection coefficients for PP, PS1 and PS2 waves at an interface of two initially VTI (vertically transverse isotropic) half-spaces (shales) and four vertical fracture sets are introduced in the lower half space at 0, 30, 60 and 90 degrees successively. Schoenberg and Sayers’ method is utilized to calculate the effective elastic constants of the fractured medium. Two shear waves in general anisotropic media are tracked based on the continuity of their polarization vectors instead of their velocities. This technique is important while tracing the continuity of reflection coefficients in the critical and supercritical zones. Fracture modeling suggests that velocity anisotropy in conjunction with AVAZ (Amplitude variation with Angle and Azimuth) response should be utilized to understand fractured media. It is observed that as the number of fracture sets increases, critical angle moves towards higher angle.

Behavior of Shear waves in water- and gas- filled cracks in anisotropic matrix

Summary Shales are complex porous rock materials, and can be considered as an aggregate of matrix and inclusions of various properties. The inclusions are primarily characterized by the contrast in elastic constants from the matrix. We have considered two types of shale samples: Huron shale (clay content = 62%), and Red bed member shale (clay content = 11.5%); for the modeling in which the clay minerals are mostly illite (87 %). The modeling has been carried out in mainly three steps: (a) define the clay matrix properties, K and μ for isotropic matrix, and five independent elastic constants for the anisotropic matrix with transversely isotropic symmetry (VTI), (b) introduce quartz and other minerals as inclusions, and (c) introduce fractures, either aligned, or randomly distributed. The general singular approximation (GSA) method, which takes in to account the connectedness of, has been used to calculate the effective elastic constants of the shale. Water and gas filled cracks have been considered in the modeling, and phase velocities for the two cases have been calculated. Modeling results show that the shale having water filled cracks shows singularity point in fast and slow shear waves, which is absent in shale with gas filled cracks.