M. Markov

Model of sand formations for joint simulation of elastic moduli and electrical conductivity

This paper presents an approach for the joint simulation of elastic-wave velocities (compressional and shear waves) and electrical conductivity for clastic rocks using a unified microstructural model. We treat clastic formations as porous composite materials containing two components: solid grains and pores completely saturated with fluids (gas–water–oil mixture). The effective shapes of both components correspond to triaxial ellipsoids. For calculating the effective properties of such a composite, we apply the self-consistent effective media approximation (EMA) method. This method treats all components equally without introducing any host and requires having knowledge of their shapes. To determine the pore and grain effective aspect ratios, we have used a set of experimental data that included the empirical regression equations published for the elastic-wave velocities in clean sandstone formations and Archie’s law for the electrical conductivity. By applying the inversion procedure that consists of minimizing the difference between the experimental and EMA-predicted data, the aspect ratios of grains and pores as a porosity function have been obtained. Based on this relation and knowing individual property components (elastic and electrical conductivity) for grains and conductivity for pore saturating fluids, we can calculate effective properties of the clean sandstone formations. We demonstrate that to simplify the simulation of effective properties, grains and pores can be approximated by spheroids. However, in this case, the relative errors that the inversion process yields are higher in comparison with those of the three-axis ellipsoids. Additionally, we have determined the aspect ratios of components for several velocity equations (including different confinement pressures) and various cementation factors ‘m’ in Archie’s law. We have modelled electrical conductivity for clastic formations with different water mineralization and oil saturation. The effective conductivity obtained by using our approach reflects a good fit with the published experimental data.

Acoustic reverberation in a logging tool-borehole-saturated porous medium system

The influence of the elastic and hydrodynamic properties of a rock on the time attenuation coefficient of an acoustic wave, which is reflected from the borehole wall, is considered using the methods of the mechanics of saturated porous media. The calculations were performed for a system consisting of an acoustic logging tool of a finite with a finite diameter, a fluid-filled borehole, and a porous permeable rock. The performed simulation showed that in rocks with a low hydrodynamic permeability, the acoustic-reverberation time is determined by the acoustic impedance of the borehole wall (product of the rock density and the longitudinal-wave velocity in it). In the case of rocks with a permeability of about several hundred millidarcy, the time signal’s attenuation coefficient substantially depends on the rock’s permeability.

Prediction of the s-wave velocity in carbonate formation using joint inversion of conventional well logs

In this paper, we propose a technique for the prediction of s-wave velocity in carbonate formations with different types of secondary porosity using conventional logs (p-wave slowness, micro-resistivity, total porosity and density). The technique consists of the determination of the pore microstructure parameters (matrix and secondary porosities, shapes of the secondary pores) using the joint petrophysical inversion of well logs and simulation of the s-wave log for the medium with obtained characteristics. In the inversion procedure, the calculation of the theoretical logs is based on the model of a double-porosity medium that consists of a homogeneous isotropic matrix with a primary pore system and secondary pores approximated by spheroidal inclusions placed in the matrix. Selecting the aspect ratio of inclusions we have simulated different types of secondary porosity such as vugs (close to spherical inclusions), vugs connected by channels (prolate spheroids) and cracks (flattened spheroids). We have applied the self-consistent method (the effective medium approximation) to simulate physical properties including the s-wave slowness from the double-porosity model. The technique has been verified using a theoretical model and experimental data from the South Zone of Mexico. The results of this technique application have demonstrated a good agreement between measured and reconstructed s-wave logs in carbonate formations.

Numerical simulations of acoustic signals in a borehole containing a viscoelastic tool

A theoretical analysis of the effect of a logging tool on kinematic and dynamic parameters of elastic waves generated in a fluid-filled borehole by an impulse acoustic source is presented. To calculate synthetic microseismograms we use the semianalytical real axis integration method. The calculations performed have shown that the logging tool parameters have a significant influence on the amplitudes of all wave packets. The comparison of synthetic microseismograms with borehole waveforms shows good agreement.

Computation of continuum percolation threshold for pore systems composed of vugs and fractures

Abstract In this research, we study the connectivity of a network composed of pores with different shapes including combinations of vugs and fractures. For this purpose, we have developed a numerical simulation technique to determine the dependence of continuum percolation threshold on the pore-shape distribution for isotropic porous 2D and 3D networks composed by elliptical and spheroidal elements respectively. This technique is based on the following new algorithms: (1) analytical estimation of overlapping between inclusions; (2) partial discretization schemes (elements of a discrete pixel base with one continuous dimension) for numerical calculation of connected-cluster porosity; and (3) determining the percolation-threshold porosity by using Monte Carlo simulations for different relative pore sizes. By approximating the pore shapes by ellipses (2D) and spheroids (3D) and varying their aspect ratios, we can model different types of pores from vugs (spheres) to fractures (oblate spheroids) and channels (prolate spheroids). We have calculated the critical percolation porosity for the following models: (1) a network consisting of elements with constant shapes; (2) a network composed of elements with the uniform logarithmic distribution of aspect ratios; and (3) a network containing elements of two different shapes. To validate the simulation technique, we have compared the modeling results for the first model with a threshold-aspect ratio relationship published previously. Based on the modeling results we have found simple and explicit equations for 2D and 3D models to determine the percolation threshold for pore networks with the bimodal distribution of shapes. The equations use only the element concentrations and percolation-threshold values for each elements shape.

Acoustic reflection logging for open and cased holes

In the present work, the waveforms of reflected wave sonic log for open and cased boreholes are calculated. Calculations are performed for a borehole containing an acoustic multipole source (monopole, dipole, or quadrupole). A reflected wave is more efficiently excited at resonant frequencies. These frequencies for all source types are close to the frequencies of oscillations of a fluid column located in an absolutely rigid hollow cylinder. It is shown that the acoustic reverberation is controlled by the acoustic impedance of the rock Z = Vp ρs for fixed parameters of the borehole fluid, where Vp is the compressional wave velocity in the rock, and ρs is the rock density. This result is correct for all types of acoustic sources (monopole, dipole, or quadrupole). Methods of the waveform processing for determining parameters characterizing the reflected wave are discussed.

Propagation of Elastic Waves in a Gas-Filled Poroelastic Medium: The Influence of the Boundary Conditions

We consider the propagation of elastic waves in gas-filled porous media at small but non-zero values of Knudsen numbers

Generalized Differential Effective Medium Method for Simulating Effective Physical Properties of 2D Percolating Composites

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