Dina Makarynska

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...

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...

Fluid substitution in rocks saturated with viscoelastic fluids

Heavyoilshavehighdensitiesandextremelyhighviscosities, and they exhibit viscoelastic behavior. Traditional rock physics based on Gassmann theory does not apply to materials saturated with viscoelastic fluids. We use an effective-medium approach known as coherent potential approximation CPA as an alternativefluid-substitutionschemeforrockssaturatedwithviscoelasticfluids.Suchrocksaremodeledassolidswithellipticalfluidinclusions when fluid concentration is small and as suspensions of solid particles in the fluid when the solid concentration is small. Thisapproachisconsistentwithconceptsofpercolationandcritical porosity, and it allows one to model sandstones and unconsolidated sands.We model the viscoelastic properties of a heavyoil-saturated rock sample using CPAand a measured frequencydependent complex shear modulus of the heavy oil. Comparison of modeled results with measured properties of the heavy-oil rock reveals a large discrepancy over a range of frequencies and temperatures. We modify the CPAscheme to account for the effect of binary pore structure by introducing a compliant porosity term. This dramatically improves the predictions. The predicted values of the effective shear modulus of the rock are in good agreement with laboratory data for the range of frequencies and temperatures. This confirms that our scheme realistically estimates the frequency- and temperature-dependent properties of heavy-oil rocks and can be used as an approximate fluid-substitutionapproachforrockssaturatedwithviscoelasticfluids.

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.

Modeling elastic wave velocities and attenuation in rocks saturated with heavy oil

Although properties of bulk heavy oil can be approximated by an appropriate viscoelastic model, only a few attempts to model properties of rocks saturated with heavy oil have been reported. Rock-physics models used for rocks saturated with conventional fluids are inapplicable to those saturated with heavy oil because its viscoelastic rheology invalidates the main assumptions of the Gassmann and Biot theories. We estimate viscoelastic properties of mixtures of rock and heavy oil by considering (1) a system of layers of a solid and a viscoelastic medium and (2) by computing Hashin-Shtrikman (HS) bounds for this system. These two methods give approximate bounds for the frequency- and temperature-dependent velocities and attenuation coefficients in rocks saturated with heavy oil. We also propose a method to compute a realistic estimate of these properties that lie between those bounds. This estimate is based on a self-consistent equivalent-medium approach known as coherent-potential approximation. In a more general form, this approximation can be used for approximate fluid substitution for heavy oil. This approach gives frequency-dependent velocities and attenuation values that are qualitatively consistent with experimental observations.

Finite element modelling of the effective elastic properties of partially saturated rocks

Simulation of effective physical properties from microtomographic 3D images of porous structures allows one to relate properties of rocks directly to their microstructure. A static FEM code has been previously used to estimate effective elastic properties of fully saturated monomineralic (quartz) rock under wet and dry conditions. We use the code to calculate elastic properties under partially saturated conditions. The numerical predictions are compared to the Gassmann theory combined with Woods formula (GW) for a mixture of pore fluids, which is exact for a monomineralic macroscopically homogeneous porous medium.Results of the numerical simulations performed for two Boolean sphere pack distributions show significant deviation from the GW limit and depend on the spatial distribution of fluids. This is shown to be a numerical artefact caused by incomplete equilibration of fluid pressure, which is primarily due to insufficient spatial resolution.To investigate the effect of pore-size and pore geometry, we perform FEM simulations for a model with regular pore geometry, where all pore channels have the same size and shape. Accuracy of these simulations increases with the total cross-section area of the channels and the size of individual channels. For the case where the total cross-section of the channels is large enough (on the same order as total porosity), there is a minimum of 4 voxels per channel diameter required for adequate fluid pressure equilibration throughout the pore space. Increasing the spatial resolution of the digital models reduces the discrepancy between the simulations and theory, but unfortunately increases the memory and CPU requirements of the simulations.

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.

Combining deterministic modelling with artificial neural networks for suspended sediment estimates

The presented manuscript presents a novel approach to the applied ocean and coastal engineering problem of sediment concentration estimates.The approach has been developed on the basis of numerical modelling and with application of artificial neural networks.It has been demonstrated that the proposed methodology can be generalised onto near-by locations.Further generalisation must be tested before applying. Estimates of suspended sediment concentrations and transport are an important part of any marine environment assessment study because these factors have a direct impact on the life cycle and survival of marine ecosystems. This paper proposes to implement a combined methodology to tackle these estimates. The first component of the methodology comprised two numerical current and wave models, while the second component was based on the artificial intelligence technique of neural networks (ANNs) used to reproduce values of sediment concentrations observed at two sites. The ANNs were fed with modelled currents and waves and trained to produce area-specific concentration estimates. The trained ANNs were then applied to predict sediment concentrations over an independent period of observations. The use of a data set that merged together observations from both the mentioned sites provided the best ANN testing results in terms of both the normalised root mean square error (0.13) and the mean relative error (0.02).

Genetic Programming for Sea Level Predictions in an Island Environment

Accurate predictions of sea-level are important for geodetic applications, navigation, coastal, industrial and tourist activities. In the current work, the Genetic Programming (GP) and artificial neural networks (ANNs) were applied to forecast half-daily and daily sea-level variations from 12 hours to 5 days ahead. The measurements at the Cocos (Keeling) Islands in the Indian Ocean were used for training and testing of the employed artificial intelligence techniques. A comparison was performed of the predictions from the GP model and the ANN simulations. Based on the comparison outcomes, it was found that the Genetic Programming approach can be successfully employed in forecasting of sea level variations.

Bounds For Seismic Dispersion And Attenuation In Poroelastic Rocks

Recently, Hashin-Shtrikman bounds for bulk and shear moduli of elastic composites have been extended to the moduli of composite viscoelastic media. Since viscoelastic moduli are complex, the viscoelastic bounds form a closed curve on a complex plane. We apply these general viscoelastic bounds to a particular case of a porous solid saturated with a Newtonian fluid. Our analysis shows that for poroelastic media, the viscoelastic bounds for the bulk modulus are represented by a semi-circle and a segment of the real axis, connecting formal HS bounds (computed for an inviscid fluid). Furthermore, these bounds are independent of frequency and realizable. We also show that these viscoelastic bounds account for viscous shear relaxation and squirt-flow dispersion, but do not account for Biot’s global flow dispersion.