Zhu & Granick [Phys. Rev. Lett. 87, 096105 (2001)] have recently experimentally established existence of a boundary slip in a Newtonian liquid. They reported typical values of the slip length of the order of few micro-meters. In this light, the effect of introduction of the boundary slip into the theory of propagation of elastic waves in a fluid-saturated porous medium formulated by Biot is investigated. The new model should allow to fit the experimental seismic data in circumstances when Biot's theory fails, as the introduction of phenomenological dependence of the slip velocity upon frequency, which is based on robust physical arguments, adds an additional degree of freedom to the model. If fact, it predicts higher than the Biot's theory values of attenuation coefficients of the both rotational and dilatational waves in the intermediate frequency domain, which is in qualitative agreement with the experimental data. Therefore, the introduction of the boundary slip yields three-fold benefits: (A) Better agreement of theory with an experimental data since the parametric space of the model is larger (includes effects of boundary slip); (B) Possibility to identify types of porous medium and physical situations where boundary slip is important; (C) Constrain model parameters that are related to the boundary slip.
This paper has been withdrawn by the author due to the physically inconsistent assumption of constant slip velocity, instead, see a new improved model - physics/0201045.
We derive and study a new hyperbolic two-phase model of a porous deformable medium saturated by a viscous fluid. The governing equations of the model are derived in the framework of Symmetric Hyperbolic Thermodynamically Compatible (SHTC) systems and by generalizing the unified hyperbolic model of continuum fluid and solid mechanics. Similarly to the unified model, the presented model takes into account the viscosity of the saturating fluid through a hyperbolic reformulation. The model accounts for such dissipative mechanisms as interfacial friction and viscous dissipation of the saturated flu…
Soil salinization is a major cause of soil degradation and hampers plant growth. For soils saturated with saline water, the evaporation of water induces accumulation of salt near the top of the soil. The remaining liquid gets an increasingly larger density due to the accumulation of salt, giving a gravitationally unstable situation, where instabilities in the form of fingers can form. These fingers can hence lead to a net downwards transport of salt. We here investigate the appearance of these fingers through a linear stability analysis and through numerical simulations. The linear stability a…
Predicting the permeability of porous media in saturated and partially saturated conditions is of crucial importance in many geo-engineering areas, from water resources to vadose zone hydrology or contaminant transport predictions. Many models have been proposed in the literature to estimate the permeability from properties of the porous media such as porosity, grain size or pore size. In this study, we develop a model of the permeability for porous media saturated by one or two fluid phases with all physically-based parameters using a fractal upscaling technique. The model is related to micro…
We study non-isothermal diffusive transport of a weakly-soluble two-component substance in a liquid-saturated porous medium being in contact with the reservoir of this substance. Particular attention is given to the example case of infiltration of nitrogen and oxygen from the atmosphere under the annual temperature oscillation. The surface temperature of the porous medium half-space oscillates in time, which results in a decaying solubility wave propagating deep into the porous medium. In such a system, the zones of saturated solution and nondissolved phase coexist with the zones of undersatur…
We study the effect of surface temperature oscillations on diffusive transport of solutes of weaklysoluble substances through liquid-saturated porous media. Temperature wave induced by these oscillations and decaying deep in the porous massif creates the solubility wave along with the corresponding solute diffusion flux wave. When the non-dissolved fraction is immobilized in pores---for gases the bubbles can be immobilized by the surface tension force, for solids (e.g., limestone, gas-hydrates) the immobilization of non-dissolved phase is obvious---the only remaining mechanisms of mass transpo…
We study non-isothermal diffusion transport of a weakly-soluble substance in a liquid-saturated porous medium being in contact with the reservoir of this substance. The surface temperature of the porous medium half-space oscillates in time, which results in a decaying solubility wave propagating deep into the porous medium. In such a system, the zones of saturated solution and non-dissolved phase coexist with the zones of undersaturated solution. The effect is firstly considered for the case of annual oscillation of the surface temperature of water-saturated ground being in contact with atmosp…
Precipitation and dissolution are prime processes in carbonate rocks and being able to monitor them is of major importance for aquifer and reservoir exploitation or environmental studies. Electrical conductivity is a physical property sensitive both to transport phenomena of porous media and to dissolution and precipitation processes. However, its quantitative use depends on the effectiveness of the petrophysical relationship to relate the electrical conductivity to hydrological properties of interest. In this work, we develop a new physically-based model to estimate the electrical conductivit…
This work is concerned with the Biot/squirt (BISQ) models for wave propagation in saturated porous media. We show that the models allow exponentially exploding solutions, as time goes to infinity, when the characteristic squirt-flow coefficient is negative or has a non-zero imaginary part. We also show that the squirt-flow coefficient does have non-zero imaginary parts for some experimental parameters. Because the models are linear, the existence of such exploding solutions indicates instability of the BISQ models. This result calls on a reconsideration of the widely used BISQ theory. Furtherm…
In this paper, the reservoir is modeled by homogeneous two-phase media based on BISQ model. We focus on the effects of the squirt flow on the fundamental guided waves propagation in borehole embedded in saturated porous media excited by monopole, dipole and quadrupole point sources. The full waveforms acoustic logging in a fluid-filled borehole are simulated. The curves of velocity dispersion, attenuation coefficients and excitation of the fundamental guided waves have shown that velocity dispersions are almost independent of the characteristic squirt flow length, attenuations of guided waves …
Electrical conductivity is one of the most commonly used geophysical method for reservoir and environmental studies. Its main interest lies in its sensitivity to key properties of storage and transport in porous media. Its quantitative use therefore depends on the efficiency of the petrophysical relationship to link them. In this work, we develop a new physically based model for estimating electrical conductivity of saturated porous media. The model is derived assuming that the porous media is represented by a bundle of tortuous capillary tubes with a fractal pore-size distribution. The model …
The present study investigates novelties brought about into the classic Biot's theory of propagation of elastic waves in a fluid-saturated porous solid by inclusion of non-Newtonian effects that are important, for example, for hydrocarbons. Based on our previous results (Tsiklauri and Beresnev: 2001, Phys. Rev. E, 63, 046304), we have investigated the propagation of rotational and dilatational elastic waves, through calculating their phase velocities and attenuation coefficients as a function of frequency. We found that the replacement of an ordinary Newtonian fluid by a Maxwell fluid in the f…
The paper provides a macro-microscopic coupled constitutive model for fluid-saturated porous media with respect to the compressibility of the solid skeleton, the real solid material and the fluid phase. The derivation of the model is carried out based on the porous media theory and is consistent with the second law of thermodynamics. In the present paper, two different sets of independent variables are introduced to implement the coupled behavior between the compressibility of the solid skeleton and the real solid material. Altogether the proposed model exploits five independent variables, i.e…
In order to reveal the coupling effect among the chemical activity and the hydraulic seepage as well as the mechanical properties, a constitutive theoretical framework considering the chemical activity for saturated porous media is derived from the mixture theory incorporated with the chemical thermodynamics. First, to highlight the important role of porosity in the hydro-mechanical-chemical multi-field coupling mechanism, the solid strain is divided into the porosity-dependent skeleton strain, the matrix strain and the mass-exchange strain. The stress and strain state variables are determined…
Among the different contributions generating self-potential, the streaming potential is of particular interest in hydrogeology for its sensitivity to water flow. Estimating water flux in porous media using streaming potential data relies on our capacity to understand, model, and upscale the electrokinetic coupling at the mineral-solution interface. Different approaches have been proposed to predict streaming potential generation in porous media. One of these approaches is the flux averaging which is based on determining the excess charge which is effectively dragged in the medium by water flow…
Reactive transport in saturated/unsaturated porous media is numerically upscaled to the space-time scale of a hypothetical measurement through coarse-grained space-time (CGST) averages. The reactive transport is modeled at the fine-grained Darcy scale by the actual number of molecules involved in reactions which undergo advective and diffusive movements described by global random walk (GRW) simulations. The CGST averages verify identities similar to a local balance equation which allow us to derive expressions for the flow velocity and the intrinsic diffusion coefficient in terms of averaged m…
In subduction zones, seismic slip at shallow crustal depths can lead to the generation of tsunamis. Large slip displacements during tsunamogenic earthquakes are attributed to the low coseismic shear strength of the fluid-saturated and non-lithified clay-rich fault rocks. However, because of experimental challenges in confining these materials, the physical processes responsible of the coseismic reduction in fault shear strength are poorly understood. Using a novel experimental setup, we measured pore fluid pressure during simulated seismic slip in clay-rich materials sampled from the deep ocea…
The theoretical basis of the thermal response of the fluid-saturated porous materials in undrained condition is presented. It has been demonstrated that the thermal pressurization phenomenon is controlled by the discrepancy between the thermal expansion of the pore fluid and of the solid phase, the stress-dependency of the compressibility and the non-elastic volume changes of the porous material. For evaluation of the undrained thermo-poro-elastic properties of saturated porous materials in conventional triaxial cells, it is important to take into account the effect of the dead volume of the d…
Gas slippage occurs when the mean free path of the gas molecules is in the order of the characteristic pore size of a porous medium. This phenomenon leads to the Klinkenberg's effect where the measured permeability of a gas (apparent permeability) is higher than that of the liquid (intrinsic permeability). A generalized lattice Boltzmann model is proposed for flow through porous media that includes Klinkenberg's effect, which is based on the model of Guo et al. (Z.L. Guo et al., Phys.Rev.E 65, 046308 (2002)). The second-order Beskok and Karniadakis-Civan's correlation (A. Beskok and G. Karniad…
This study investigates the effect of a Maxwellian fluid on the propagation of waves in poroelastic media. Based on a fractional derivative stress-strain relation, a viscous dissipation function is obtained to measure the viscoelastic fluid-solid coupling effect. With the viscous dissipation function, elastic waves propagation is formulated in poroelastic media saturated by a fractional derivative Maxwellian fluid, and the analytical expression of the P- and S-wave dispersion/attenuation is presented. Numerical examples show that the fractional derivative Maxwell strain-stress relation has a s…
We propose a theory for erosional channelization induced by fluid flow in a saturated granular porous medium. When the local fluid flow-induced stress is larger than a critical threshold, grains are dislodged and carried away so that the porosity of the medium is altered by erosion. This in turn affects the local hydraulic conductivity and pressure in the medium and results in the growth and development of channels that preferentially conduct the flow. Our multiphase model involves a dynamical porosity field that evolves along with the volume fraction of the mobile and immobile grains in respo…
Fluids confined in nanopores are ubiquitous in nature and technology. In recent years, the interest in confined fluids has grown, driven by research on unconventional hydrocarbon resources -- shale gas and shale oil, much of which are confined in nanopores. When fluids are confined in nanopores, many of their properties differ from those of the same fluid in the bulk. These properties include density, freezing point, transport coefficients, thermal expansion coefficient, and elastic properties. The elastic moduli of a fluid confined in the pores contribute to the overall elasticity of the flui…
Reservoir rocks are usually composed of a coherent heterogeneous porous matrix saturated by multiple fluids. At long wavelength limit, the composite material of solid skeleton is usually regarded as homogeneous media. However, at grain scale or high loading rate, non-uniform fluid flow at internal interface of heterogeneity plays essential role in wave dispersion and attenuation. Formulating wave propagation in partially saturated and fractured rocks is challenging and of great interests in geoscience. Here we raise a Biot-patchy-squirt (BIPS) model to characterize wave dispersion/attenuation …
Temperature increase in saturated porous materials under undrained conditions leads to thermal pressurization of the pore fluid due to the discrepancy between the thermal expansion coefficients of the pore fluid and of the solid matrix. This increase in the pore fluid pressure induces a reduction of the effective mean stress and can lead to shear failure or hydraulic fracturing. The equations governing the phenomenon of thermal pressurization are presented and this phenomenon is studied experimentally for a saturated granular rock in an undrained heating test under constant isotropic stress. C…
Biot's theory provides a framework for computing seismic wavefields in fluid saturated porous media. Here we implement a velocity-stress staggered grid 2D finite difference algorithm to model the wave-propagation in poroelastic media. The Biot's equation of motion are formulated using a finite difference algorithm with fourth order accuracy in space and second order accuracy in time. Seismic wave propagation in reservoir rocks is also strongly affected by fractures and faults. We next derive the equivalent media model for fractured porous rocks using the linear slip model and perform numerical…
A model is presented for the gravity-driven flow of rainwater descending through the soil layer of a green roof, treated as a porous medium on a flat permeable surface representing an efficient drainage layer. A fully saturated zone is shown to occur. It is typically a thin layer, relative to the total soil thickness, and lies at the bottom of the soil layer. This provides a bottom boundary condition for the partially saturated upper zone. It is shown that after the onset of rainfall, well-defined fronts of water can descend through the soil layer. Also the rainwater flow is relatively quick c…
Fluid-saturated granular and porous layers can undergo liquefaction and lose their shear resistance when subjected to shear forcing. In geosystems, such a process can lead to severe natural hazards of soil liquefaction, accelerating slope failure, and large earthquakes. Terzaghi's principle of effective stress predicts that liquefaction occurs when the pore pressure within the layer becomes equal to the applied normal stress on the layer. However, under dynamic loading and when the internal permeability is relatively small the pore pressure is spatially heterogeneous and it is not clear what m…
