Miroslav Brajanovski

Attenuation and dispersion of P-waves in porous rocks with planar fractures: Comparison of theory and numerical simulations

To explore the validity and limitations of the theoretical model of wave propagation in porous rocks with periodic distribution of planar fractures, we perform numerical simulation using a poroelastic reflectivity algorithm. The numerical results are found to be in good agreement with the analytical model, not only for periodic fractures, but also for random distribution of constant thickness fractures.

Fluid substitution, dispersion, and attenuation in fractured and porous reservoirs - Insights from new rock physics models

The importance of natural fractures for development and production of hydrocarbon reservoirs requires little justification. While in clastic reservoirs fractures can cause permeability anisotropy and thus affect field development, in carbonates and tight sands they are often critical for reservoir production. If open fractures have a preferential direction (which is almost always the case), they cause azimuthal seismic anisotropy, making seismic a powerful tool for the characterization of fractured reservoirs.

Estimation of stress-dependent anisotropy from P-wave measurements on a spherical sample

Our aim is to understand the stress-dependent seismic anisotropy of the overburden shale in an oil field in the North West Shelf of Western Australia. We analyze data from measurements of ultrasonic P-wave velocities in 132 directions for confining pressures of 0.1‐400 MPa on a spherical shale sample. First, we find the orientation of the symmetry axis, assuming that the sample is transversely isotropic, and then transform the ray velocities to the symmetry axis coordinates. We use two parameterizations of the phase velocity; one, in terms of the Thomsen anisotropy parameters a, b, e, d as the main approach, and the other in terms of a, b, g, d. We invert the ray velocities to estimate the anisotropy parameters a, e, d, and g using a very fast simulated reannealing algorithm. Both approaches result in the same estimation for the anisotropy parameters but with different uncertainties. The main approach is robust but produces higher uncertainties, in particular for g, whereas the alternative approach is unstable but gives lower uncertainties. These approaches are used to find the anisotropy parameters for the different confining pressures. The dependency of P-wave velocity, a, on pressure has exponential and linear components, which can be contributed to the compliant and stiff porosities. The exponential dependence at lower pressures up to 100 MPa corresponds to the closure of compliant pores and microcracks, whereas the linear dependence at higher pressures corresponds to contraction of the stiff pores. The anisotropy parameters e and d are quite large at lower pressures but decrease exponentially with pressure. For lower pressures up to 10 MPa, d always is larger than e; this trend is reversed for higher pressures. Despite the hydrostatic pressure, the symmetry axis orientation changes noticeably, in particular at lower pressures.

Attenuation And Dispersion of Compressional Waves In Porous Rocks With Aligned Fractures

Fractures in a porous rock can be modeled as very thin and highly porous layers in a porous background. Elastic moduli of such fractured medium can be obtained using the result of Norris (1993) for wave propagation in periodically layered poroelastic media. When this porous fractured system is dry, it is equivalent to a transversely isotropic dry elastic porous material with linear-slip interfaces. When saturated with a liquid this system exhibits significant attenuation and velocity dispersion due to wave-induced fluid flow between pores and fractures. The characteristic frequency of such attenuation and dispersion depends on the background permeability, fluid viscosity, as well as fracture density and spacing. The theoretical results are in a good agreement with numerical simulations using the reflectivity algorithm generalized to poroelasticity.

Elasticity tensor inversion from spherical sample measurements

From the P-wave traveltime measurements over a spherical shale sample at 40 MPa we find the symmetry axis. We transform the ray velocities from the measurement coordinate system to the symmetry axis coordinate system. Assuming transverse isotropy symmetry

1-D Random Patchy Saturation Model For Velocity And Attenuation In Porous Rocks

Existing models for seismic wave velocity dispersion and attenuation in porous rocks containing a mixture of two pore fluids are based on the assumption of a regular distribution of the fluid phases. However, in reality fluids are distributed in a random fashion forming fluid patches of varying shape and size. We develop a model to predict velocity dispersion and attenuation of such random structures based on the theory of statistical wave propagation. We demonstrate that the assumption of random fluid distribution results in a significantly different behavior of velocity and attenuation as functions of frequency and saturation. Specifically, the randomly layered patchy model predicts a much more gradual increase of -wave velocity with frequency. This means that the effects of patchy saturation can be observed in a broader frequency range than previously assumed.

Strong dispersion and attenuation of P‐waves in a partially saturated fractured reservoir

In this work we interpret data showing strong velocity dispersion of P-waves (up to 30%) and attenuation in a relatively narrow frequency range. The cross-hole and VSP data were measured in a reservoir, which is in the porous zone of the Silurian Kankakee Limestone Formation formed by vertical fractures within a porous matrix saturated by oil, and gas patches. Such a medium exhibits significant attenuation due to wave-induced fluid flow across the interfaces between different type of inclusions (fractures, fluid patches) and background. Other models of intrinsic attenuation (in particular squirt flow models) cannot explain amount of observed dispersion when using realistic rock properties. In order to interpret data in satisfactory way we develop a superposition model for fractured porous rocks accounting also for the patchy saturation effect.

Estimation of elasticity tensor from the inversion of traveltimes in spherical shale samples

Due to sedimentation pattern of clay minerals, shal e formations generally show transverse isotropy (TI) with vertical axis of symmetry. The main motivation of t his study is to understand the seismic anisotropy of th e overburden shale. Geological formations in the regi on under study are generally experiencing a horizontal stress field. This stress field may cause azimuthal anisot ropy by either tilting the symmetry axis of shale formation s and/or causing the directional planes of weakness. To char a terize the seismic anisotropy, we have used P-wave travelt imes from a spherical shale core sample from the top of a sand reservoir. Unlike others, e.g Delinger (2005) and Vestrum and Brown (1994), we find the symmetry axis first a nd then invert for elasticity parameters to reduce the comp lexity of the inversion. Assuming TI symmetry, we have estima ted the elasticity tensor using the Simulating Annealin g followed by quasi Newton algorithm .

Estimation of Stress Induced Azimuthal Anisotropy – AVO Modeling

The analysis of rock anisotropy in terms of seismic velocities and within the context of rock-physics (Biot-Gassmann theory of poroelasticity) provides important information for the evaluation of the stress state (tensors) of rocks, detection of the directions of formation weaknesses, helps in the estimation of overall permeability and failure prediction. Understanding the influence of stress and pore pressure on seismic velocities is important for 4-D reflection seismic interpretation, AVO analysis and reservoir modeling. Laboratory measurements were carried out on spherical shale samples from the overburden under confining stress up to 400 MPa, by means of ultrasonic soundings in 132 independent directions. Such an approach enables the estimation of 3-D elastic anisotropy. Assuming VTI symmetry approximation, from the measured velocities the stiffness tensor was inverted. Since the sandstones were partly unconsolidated, it was not possible to take ultrasonic measurements . To overcome this, we developed a method for stress induced azimuthal anisotropy estimation using only cross-dipole logging data. These results give the possibility for anisotropic correction in AVO analysis.

Two Models for Seismic Attenuation and Dispersion in Fractured Porous Reservoirs

Natural fractures in hydrocarbon reservoirs can cause significant seismic attenuation and dispersion due to wave induced fluid flow between pores and fractures. We present two theoretical models explicitly based on the solution of Biot’s equations of poroelasticity. The first model considers fractures as planes of weakness (or highly compliant and very thin layers) of infinite extent. In the second model fractures are modeled as thin penny-shaped voids of finite radius. In both models attenuation exhibits a typical relaxation peak around a normalized frequency of about 1. This corresponds to a frequency where the fluid diffusion length is of the order of crack spacing for the first model, and the crack diameter for the second. This is consistent with an intuitive understanding of the nature of attenuation: when fractures are closely space, the waves reflected/scattered by cracks interfere with each other, with the interference pattern controlled by the fracture spacing. Conversely, if fracture length is smaller than spacing, then fractures act as independent scatterers and the attenuation resembles the pattern of scattering isolated cracks.