Frequency-dependent attenuation and elasticity in unconsolidated earth materials: effect of damping

We use the Discrete Element Method (DEM) to understand the underlying attenuation mechanism in granular media, with special applicability to the measurements of the so-called effective mass developed earlier. We consider that the particles interact via Hertz-Mindlin elastic contact forces and that the damping is describable as a force proportional to the velocity difference of contacting grains. We determine the behavior of the complex-valued normal mode frequencies using 1) DEM, 2) direct diagonalization of the relevant matrix, and 3) a numerical search for the zeros of the relevant determinant. All three methods are in strong agreement with each other. The real and the imaginary parts of each normal mode frequency characterize the elastic and the dissipative properties, respectively, of the granular medium. We demonstrate that, as the interparticle damping, $\xi$, increases, the normal modes exhibit nearly circular trajectories in the complex frequency plane and that for a given value of $\xi$ they all lie on or near a circle of radius $R$ centered on the point $-iR$ in the complex plane, where $R\propto 1/\xi$. We show that each normal mode becomes critically damped at a value of the damping parameter $\xi \approx 1/\omega_n^0$, where $\omega_n^0$ is the (real-valued) frequency when there is no damping. The strong indication is that these conclusions carry over to the properties of real granular media whose dissipation is dominated by the relative motion of contacting grains. For example, compressional or shear waves in unconsolidated dry sediments can be expected to become overdamped beyond a critical frequency, depending upon the strength of the intergranular damping constant.Comment: 28 pages, 7 figure

Dynamic effective mass of granular media

We develop the concept of frequency dependent effective mass, M(omega), of jammed granular materials which occupy a rigid cavity to a filling fraction of 48%, the remaining volume being air of normal room condition or controlled humidity. The dominant features of M(omega) provide signatures of the dissipation of acoustic modes, elasticity and aging effects in the granular medium. We perform humidity controlled experiments and interpret the data in terms of a continuum model and a "trap" model of thermally activated capillary bridges at the contact points. The results suggest that attenuation in the granular materials is influenced significantly by the kinetics of capillary condensation between the asperities at the contacts.Comment: 4 pages, 3 figure

Ultrasonic Study of Water Adsorbed in Nanoporous Glasses

Thermodynamic properties of fluids confined in nanopores differ from those observed in the bulk. To investigate the effect of nanoconfinement on water compressibility, we performed water sorption experiments on two nanoporous glass samples while concomitantly measuring the speed of longitudinal and shear ultrasonic waves in these samples. These measurements yield the longitudinal and shear moduli of the water laden nanoporous glass as a function of relative humidity that we utilized in the Gassmann theory to infer the bulk modulus of the confined water. This analysis shows that the bulk modulus (inverse of compressibility) of confined water is noticeably higher than that of the bulk water at the same temperature. Moreover, the modulus exhibits a linear dependence on the Laplace pressure. The results for water, which is a polar fluid, agree with previous experimental and numerical data reported for non-polar fluids. This similarity suggests that irrespective of intermolecular forces, confined fluids are stiffer than bulk fluids. Accounting for fluid stiffening in nanopores may be important for accurate interpretation of wave propagation measurements in fluid-filled nanoporous media, including in petrophysics, catalysis, and other applications, such as in porous materials characterization

Origins of pressure dependent permeability in unconventional hydrocarbon reservoirs

Abstract Unconventional hydrocarbon assets represent a rapidly expanding proportion of North American oil and gas production. Similar to the incipient phase of conventional oil production at the turn of the twentieth century, there are ample opportunities to improve production efficiency. In this work we demonstrate that pressure dependent permeability degradation exhibited by unconventional reservoir materials is due to the mechanical response of a few commonly encountered microstructural constituents. In particular, the mechanical response of unconventional reservoir materials may be conceptualized as the superposed deformation of matrix (or ~ cylindrical/spherical), and compliant (or slit) pores. The former are representative of pores in a granular medium or a cemented sandstone, while the latter represent pores in an aligned clay compact or a microcrack. As a result of this simplicity, we demonstrate that permeability degradation is accounted for through a weighted superposition of conventional permeability models for these pore architectures. This approach permits us to conclude that the most severe pressure dependence is due to imperceptible bedding parallel delamination cracks in the oil bearing argillaceous (clay-rich) mudstones. Finally, we demonstrate that these delaminations tend to populate layers that are enriched with organic carbon. These findings are a basis for improving recovery factors through the development of new completion techniques to exploit, then mitigate pressure dependent permeability in practice

Small-amplitude acoustics in bulk granular media

We propose and validate a three-dimensional continuum modeling approach that predicts small-amplitude acoustic behavior of dense-packed granular media. The model is obtained through a joint experimental and finite-element study focused on the benchmark example of a vibrated container of grains. Using a three-parameter linear viscoelastic constitutive relation, our continuum model is shown to quantitatively predict the effective mass spectra in this geometry, even as geometric parameters for the environment are varied. Further, the model's predictions for the surface displacement field are validated mode-by-mode against experiment. A primary observation is the importance of the boundary condition between grains and the quasirigid walls.Schlumberger-Doll Research Cente

An NMR study of porous rock and biochar containing organic material

With traditional sandstone oil reservoirs coming to the end of their useful lives, there is interest in extracting oil and gas from shale and carbonate rocks. Recovered samples often contain hydrocarbon material, sometimes in a fairly mobile form, sometimes in a tarry form. There is also an interest in studying forms of porous carbon, such as biochar, both for their soil-remedial properties, and for carbon sequestration. Biochars, depending on heat-treatment temperature and duration, also frequently contain residual hydrocarbon matter. There are two techniques that will be discussed: Proton NMR Relaxation (NMRR) and NMR Cryoporometry (NMRC) [10.1016/j.physrep.2008.02.001]. This study applies proton NMR Relaxation to characterise the quantity and mobility of hydrocarbon matter in dried shale and carbonate rock and biochar pores. Curve-fitting is applied to the Free Induction Decays (FIDs) and Carr-Purcell-Meiboom-Gill (CPMG) echo trains to quantify the measurements. This study also applies NMR Cryoporometry, to measure structure: pore-size distribution and pore volumes of the rock, and of the stable carbon skeleton. It has the significant advantage of being usable even when there are liquids and volatile components already in the pores. In porous rocks, combining mobility and structural information will provide a measure of the difficulty of removing the tar/oil from the rock. In biochar, combining the mobility of the labile components with the structural information for the stable biochar skeleton will inform calculations of lifetime of the labile components within the biochar. The NMRC data will also inform estimates of the lifetime of the biochar carbon skeleton