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Low-frequency forced-oscillation methods applied to a reservoir sandstone allowed determination of the Young’s modulus and Poisson’s ratio (from axial loading), bulk modulus (by oscillation of the confining pressure) and shear modulus (from torsionalforced oscillations) for comparison with conventional ultrasonic data. All tests were performed on a common sandstone core sample from an oil reservoir offshore West Africa. The results show a steady increase in ultrasonic velocities and shear modulus of the dry specimen as functions of pressure, which suggests a progressive closure of the inter-granular contacts. An increase of bulk and Young’s moduli and Poisson’s ratio is observed on decane saturation of the sample when tested with a sufficiently small dead volume. This observation, consistent with Gassmann’s theory, suggests that such measurements probe undrained (saturated isobaric) conditions. Diminution or absence of such fluid-related stiffening for low-frequency measurements with dead volumes comparable with the pore volume of the specimen indicates partially drained conditions and highlights the critical role of experimental boundary conditions. Directly measured bulk and shear moduli are consistent with those derived from Young’s modulus and Poisson’s ratio. These results of the inter-laboratory testing using different measurement devices are consistent in terms of the effect of frequency and fluid saturation for the reservoir sandstone specimen. Such broad consistency illustrates the validity of forced-oscillation techniques and constitutes an important benchmarking of laboratory testing of the elastic properties of a porous medium.

Estimating the effects of pore filling material on the elastic moduli or velocities of porous and fractured rocks attracts widespread attention. This effect can be modelled by a recently proposed triple-porosity scheme, which quantifies this effect from parameters of the pressure dependency of the elastic properties of the dry rock. This scheme divides total porosity into three parts: compliant, intermediate and stiff. Each type of pores is assumed to be spheroidal and characterized by a single aspect ratio. However, the implementation of this model requires the asymptotic values of the elastic moduli at much higher pressures where only non-closable pores remain open. Those pressures are beyond the capacity of most rock physics laboratories and can even crush typical sandstone samples. Experimental data at such pressures are usually unavailable. To address this issue, we introduce pore-scale numerical simulations in conjunction with effective medium theories (EMT) to compute the asymptotic values directly from the microtomographic images. This workflow reduces the uncertainty of model predictions on the geometric information of stiff pores and strengthens the predictive power and usefulness of the model without any adjustable parameters. Applying this to a Bentheim sandstone fully filled with liquid and solid octadecane gives a reasonable match between model predictions and laboratory measurements. This success verifies the accuracy and applicability of the model and indicates its potential in further exploitation and characterization of heavy oil reservoirs and other similar reservoirs.

Copyright © (2008) by the Society of Exploration Geophysicists All rights reserved. Ultrasonic velocities and fluid saturations are measured simultaneously during water injection into sandstone core samples. The experimental results obtained on low-permeability samples show that at low saturation values the velocity-saturation dependence can be described by the Gassmann-Wood relationship. However, with increasing saturation a sharp increase of P-wave velocity is observed, eventually approaching the Gassmann-Hill relationship. We relate this transition behavior to the change of the fluid distribution characteristics inferred from CT scans. In particular, we show that for relatively large fluid injection rate this transition occurs at smaller degrees of saturation as compared with high injection rate.

Copyright © (2008) by the Society of Exploration Geophysicists All rights reserved. Heavy oils are defined as having high densities and extremely high viscosities. Due to their viscoelastic behavior the traditional rock physics based on Gassmann theory becomes inapplicable. In this paper, we use effective-medium approach known as coherent potential approximation or CPA as an alternative fluid substitution scheme for rocks saturated with viscoelastic fluids. Such rocks are modelled as solids with elliptical fluid inclusions when fluid concentration is small and as suspensions of solid particles in the fluid when the solid concentration is small. This approach is consistent with concepts of percolation and critical porosity, and allows one to model both sandstones and unconsolidated sands. We test the approach against known solutions. First, we apply CPA to fluid-solid mixtures and compare the obtained estimates with Gassmann results. Second, we compare CPA predictions for solid-solid mixtures with numerical simulations. Good match between the results confirms the applicability of the CPA scheme. We extend the scheme to predict the effective frequency- and temperature-dependent properties of heavy oil rocks. CPA scheme reproduces frequency-dependent attenuation and dispersion which are qualitatively consistent with laboratory measurements and numerical simulations. This confirms that the proposed scheme provides realistic estimates of the properties of rocks saturated with heavy oil.

The elastic properties of crystalline rocks can be estimated from ultrasonic measurements on the powders of crushed rocks produced by the drilling process. To determine the elastic properties of grains from properties of powder packs, we study the dependence of their ultrasonic wave velocities on pressure. From this dependency, using the Hertz–Mindlin theory, we can calculate the effective ratio of the grain shear modulus to one minus the Poisson ratio. The Hertz–Mindlin theory requires the knowledge of grain coordination number as a function of pressure, which can be obtained using an empirical relation based on published numerical simulations. Previous work has shown that this approach gives an accurate prediction of the effective bulk modulus of glass beads but produces a significant discrepancy for sand. This discrepancy may be attributed to the angularity of sand grains. To overcome this problem, we introduce a shape factor into the empirical relation for the coordination number. This new shape factor allows us to reconcile the rock physics model with laboratory measurements. We show that the shape factor varies from 1 to 2.5 for different grain shape angularity and sorting (grain size distributions). The modified theory allows us to estimate a combination of elasticity parameters of the grains from the measured dependence of P-wave velocity in the pack on the pressure.

Quantifying the effects of pore-filling materials on elastic properties of porous rocks is of considerable interest in geophysical practice. For rocks saturated with fluids, the Gassmann equation is proved effective in estimating the exact change in seismic velocity or rock moduli upon the changes in properties of pore infill. For solid substance or viscoelastic materials, however, the Gassmann theory is not applicable as the rigidity of the pore fill (either elastic or viscoelastic) prevents pressure communication in the pore space, which is a key assumption of the Gassmann equation. In this paper, we explored the elastic properties of a sandstone sample saturated with fluid and solid substance under different confining pressures. This sandstone sample is saturated with octadecane, which is a hydrocarbon with a melting point of 28°C, making it convenient to use in the lab in both solid and fluid forms. Ultrasonically measured velocities of the dry rock exhibit strong pressure dependency, which is largely reduced for the filling of solid octadecane. Predictions by the Gassmann theory for the elastic moduli of the sandstone saturated with liquid octadecane are consistent with ultrasonic measurements, but underestimate the elastic moduli of the sandstone saturated with solid octadecane. Our analysis shows that the difference between the elastic moduli of the dry and solid-octadecane-saturated sandstone is controlled by the squirt flow between stiff, compliant, and the so-called intermediate pores (with an aspect ratio larger than that of compliant pore but much less than that of stiff pores). Therefore, we developed a triple porosity model to quantify the combined squirt flow effects of compliant and intermediate pores saturated with solid or viscoelastic infill. Full saturation of remaining stiff pores with solid or viscoelastic materials is then considered by the lower embedded bound theory. The proposed model gave a reasonable fit to the ultrasonic measurements of

© 2018 European Association of Geoscientists & Engineers Shales play an important role in many engineering applications such as nuclear waste, CO2 storage and oil or gas production. Shales are often utilized as an impermeable seal or an unconventional reservoir. For both situations, shales are often studied using seismic waves. Elastic properties of shales strongly depend on their hydration, which can lead to substantial structural changes. Thus, in order to explore shaly formations with seismic methods, it is necessary to understand the dependency of shale elastic properties on variations in hydration. In this work, we investigate structural changes in Opalinus shale at different hydration states using laboratory measurements and X-ray micro-computed tomography. We show that the shale swells with hydration and shrinks with drying with no visible damage. The pore space of the shale deforms, exhibiting a reduction in the total porosity with drying and an increase in the total porosity with hydration. We study the elastic properties of the shale at different hydration states using ultrasonic velocities measurements. The elastic moduli of the shale show substantial changes with variations in hydration, which cannot be explained with a single driving mechanism. We suggest that changes of the elastic moduli with variations in hydration are driven by multiple competing factors: (1) variations in total porosity, (2) substitution of pore-filling fluid, (3) change in stiffness of contacts between clay particles and (4) chemical hardening/softening of clay particles. We qualitatively and quantitatively analyse and discuss the influence of each of these factors on the elastic moduli. We conclude that depending on the microstructure and composition of a particular shale, some of the factors dominate over the others, resulting in different dependencies of the elastic moduli on hydration.

Fractures often play an important role in controlling the fluid flow in hydrocarbon reservoirs. When the seismic wave propagates through media containing fracture corridors, significant scattering dispersion and attenuation can occur. In this work, we study the P-wave dispersion and attenuation due to the scattering caused by 2-D fluid-saturated aligned fractures with finite thickness, which are embedded in an isotropic elastic background medium. Using the Foldy approximation and the representation theorem, the P-wave dispersion and attenuation are related to the displacement discontinuities across the fractures. These fracture displacement discontinuities are obtained from the boundary conditions and the P-wave dispersion and attenuation can thus be calculated. A numerical example shows that the fracture thickness has significant influence on the dispersion and attenuation, especially in the low-frequency regime when the fracture size is smaller than the seismic wavelength. The effects of the fluid bulk modulus are also significant,which are opposite to those of the fracture thickness. However, the effect of the fluid viscosity is found to be negligible for the studied configurations. To validate the proposed model, the theoretical predictions are compared with ultrasonic measurements on fractured samples. The comparison shows overall good agreement between theory and experiment. This work reveals the important influence of fracture thickness and saturating fluid properties on the P-wave scattering dispersion and attenuation. Hence, it shows a potential to extract these parameters from seismic data.

©2018. American Geophysical Union. All Rights Reserved. A number of studies show that adsorption of small amount of water causes significant reduction of elastic moduli and increase of elastic wave attenuation in sandstones. This effect is of practical importance for near-surface seismic studies and for applications of conventional rock physics theories, which require measurements of elastic properties of dry rock. Additionally, adsorption of water causes deformation of porous materials and rocks, which can be explained by the concept of varying surface stress, or change in the pressure of fluid adsorbed in pores. In this work we suggest that the adsorption-induced elastic weakening of sandstones is caused by changing fluid pressure in compliant pores on grain contacts. In order to validate this concept, we conduct simultaneous measurements of the elastic moduli and deformation of the Bentheim sandstone with adsorption and desorption of water and observe ~20% change in the bulk and shear moduli accompanied with the strain of the order of 10-4. Then, we estimate that the fluid pressure change should be of the order of several megapascals to cause such deformation. Comparison of the measured variations in the elastic moduli related to the estimated change in the fluid pressure with the stress dependency of the bulk and shear moduli in Bentheim sandstone shows a broad agreement of the two sets of measurements. A reasonable magnitude of the estimated fluid pressure change is consistent with the suggested hypothesis.

©2018. American Geophysical Union. All Rights Reserved. We estimate the seismic attenuation and velocity dispersion induced by fluid pressure diffusion in a saturated porous medium containing a sparse distribution of aligned slit fractures. This is done by solving the scattering problem for a single crack and using Waterman-Truell scattering approximation for a distribution of cracks. This approach gives a numerical solution for the entire frequency range and analytical solutions for the low- and high-frequency limits. Analysis of the results shows that the characteristics of the seismic dispersion and attenuation for the slit cracks are similar to known results for penny-shaped crack. At high frequencies, the attenuation and dispersion are controlled by the crack density regardless of the crack geometry. At low frequencies, due to the different geometries of the slit and penny-shaped cracks, the characteristics of seismic dispersion and attenuation are different. For both the slit and penny-shaped crack case, the slope of the frequency dependence attenuation of factor (inverse quality factor) Q-1 tends to be 1. Yet the low-frequency asymptotic solutions for these two cases are somewhat different. For penny-shaped cracks, the Q-1(?) on the bilogarithmic scale has a straight line asymptote with slope 1, so that the attenuation factor at low frequencies is proportional to the frequency ?. However, for slit cracks, the asymptotic low-frequency solution contains a logarithmic function of ?, and no such asymptote exists. At the same time, similarly to the penny-shaped crack case, the solution for compressional velocity in the low-frequency limit is consistent with the anisotropic Gassmann theory.

© 2018 EAGE. Estimations of the elastic properties of a core sample are extremely sensitive to the quality of the CT-scan image. A coarse image resolution does not allow separating the grains and estimating their roughness. The size of images with fine resolution is either below representative volume or so representatively large that require huge computational resources for the numerical simulation of static loading tests. We present a new multi-scale numerical methodology that combines the geostatistics, computational topology and numerical upscaling. The essence of the approach is to estimate the distribution of the grain surface roughness, the distance between them and cement material by microscopic images (SEM), then to calculate the effective parameters of cement distribution for an equivalent model with flat contacts between grains. Finally, to use this effective cement to fill the interfaces between grains in a digital model built on CT images of medium resolution by computational topology.

© 2017 American Geophysical Union. All Rights Reserved. Recent progress in extraction of unconventional hydrocarbon resources has ignited the interest in the studies of nanoporous media. Since many thermodynamic and mechanical properties of nanoscale solids and fluids differ from the analogous bulk materials, it is not obvious whether wave propagation in nanoporous media can be described using the same framework as in macroporous media. Here we test the validity of Gassmann equation using two published sets of ultrasonic measurements for a model nanoporous medium, Vycor glass, saturated with two different fluids, argon, and n-hexane. Predictions of the Gassmann theory depend on the bulk and shear moduli of the dry samples, which are known from ultrasonic measurements and the bulk moduli of the solid and fluid constituents. The solid bulk modulus can be estimated from adsorption-induced deformation or from elastic effective medium theory. The fluid modulus can be calculated according to the Tait-Murnaghan equation at the solvation pressure in the pore. Substitution of these parameters into the Gassmann equation provides predictions consistent with measured data. Our findings set up a theoretical framework for investigation of fluid-saturated nanoporous media using ultrasonic elastic wave propagation.

When a seismic wave travels through a fluid-saturated porous reservoir containing aligned fractures, it induces oscillatory fluid flow between the fractures and the embedding background medium. Although there are numerous theoretical models for quantifying the associated seismic attenuation and velocity dispersion, they rely on certain assumptions, such as infinitesimal fracture thickness and dilute fracture concentration, which rarely hold in real reservoirs. The objective of this work is to overcome some of these limitations and, therefore, improve the applicability of the available theoretical models. To do so, we extend existing models to the finite fracture thickness case for P-waves propagating perpendicular to the fracture plane using the so-called branching function approach. We consider three types of fractures, namely, periodically and randomly spaced planar fractures, as well as penny-shaped cracks. The extended unified model is then tested by comparing with corresponding numerical simulations based on Biot's theory of poroelasticity. We consider two cases of 2D rock samples with aligned elliptical fractures, one with low fracture density and the other with high fracture density. The results indicate that the influence of the finite fracture thickness on seismic dispersion and attenuation is small at low frequencies when the fluid pressure has enough time to equilibrate between the fractures and background medium. However, this effect is significant at high frequencies w hen there is not sufficient time for the fluid pressure equilibration. In addition, the theoretical predictions of the pennyshaped crack model are found to match the numerical simulation results very well, even under relatively high fracture density. Analyses of stress distributions suggest that the small discrepancies found between theoretical predictions and numerical simulations are probably due to fracture interactions. In a companion paper, we will extend the analysis for considering