Dynamic Stress and Pore Pressure Around Circular Cavity in Saturated Porous Elastic Half-space Under Harmonic Plane Dilatational Waves

Dynamic stress concentration and pore pressure concentration around an infinitely long cylindrical cavity of circular cross-section subjected to harmonic plane dilatational waves in fluid-saturated porous elastic half-space were obtained by a complex function method based on potential function and multi-polar coordinate. The steady state Biot’s dynamic field equations of porous elastic solid with a viscous liquid were uncoupled into Helmholtz equations via given potential functions. A circular cavity with large radius is used to replace the straight boundary of the saturated porous elastic half-space. The stresses and pore pressures were obtained by using complex functions in multi-polar coordinates with certain boundary conditions of the solid matrix and the fluid matrix. The approximate solutions were compared to existing numerical solutions. Then the variations of the coefficients of dynamic stress concentration and the pore pressures concentration on boundaries of the cavity were discussed with different parameter conditions. The results of the given numerical example indicate that the method used is useful and efficient to the scattering and dynamic stress concentration of plane dilatational waves in saturated porous elastic half-space.

Solution of a Green's function for a saturated porous medium in a half-space subjected to a torsional force

Based on the solutions of the Green＇s function for a saturated porous medium obtained by the authors, and using transformation of axisymmetric coordinates, Sommerfeld integrals and superposition of the influence field on a free surface, the authors have obtained displacement solutions of a saturated porous medium subjected to a torsional force in a half-space. The relationship curves of the displacement solutions and various parameters （permeability, frequency, etc.） under action of a unit of torque are also given in this paper. The results are consistent with previous Reissner＇s solutions, where a two-phase medium decays to a single-phase medium. The solution is useful in solving relevant dynamic problems of a two- phase saturated medium in engineering.

GURTIN VARIATIONAL PRINCIPLE AND FINITE ELEMENT SIMULATION FOR DYNAMICAL PROBLEMS OF FLUID-SATURATED POROUS MEDIA

Based on the theory of porous media, a general Gurtin variational principle for the initial boundary value problem of dynamical response of fluid-saturated elastic porous media is developed by assuming infinitesimal deformation and incompressible constituents of the solid and fluid phase. The finite element formulation based on this variational principle is also derived. As the functional of the variational principle is a spatial integral of the convolution formulation, the general finite element discretization in space results in symmetrical differential-integral equations in the time domain. In some situations, the differential-integral equations can be reduced to symmetrical differential equations and, as a numerical example, it is employed to analyze the reflection of one-dimensional longitudinal wave in a fluid-saturated porous solid. The numerical results can provide further understanding of the wave propagation in porous media.

Response of saturated porous media subjected to local thermal loading on the surface of semi-infinite space

Heat source function method is adopted in the present paper to derive elementary solutions of coupled thermo-hydro-mechanical consolidation for saturated porous media under conjunct actions of instantaneous point heat source, instantaneous point fluid source and constant volume force. By using the so-called fictitious heat source method and images method, the solutions of a semi-infinite saturated porous medium subjected to a local heat source with time-varied intensity on its free surface are developed from elementary solutions. The numerical integral methods for calculating the unsteady temperature, pore pressure and displacement fields are given. The thermomechanical response are analyzed for the case of a circular planar heat source. Besides, the thermal consolidation characteristics of a saturated porous medium subjected to a harmonic thermal loading are also given, and the fluctuation processes of the field variables located below the center of heat source are analyzed.

Digital image processing of saturation for two-phase flow in planar porous media model

In this paper, the accuracy of estimating stained non-wetting phase saturation using digital image processing is examined, and a novel post-processing approach for calculating threshold is presented. In order to remove the effect of the background noise of images and to enhance the high-frequency component of the original image, image smoothing and image sharpening methods are introduced. Depending on the correct threshold, the image binarization processing is particularly useful for estimating stained non-wetting phase saturation. Calculated saturation data are compared with the measured saturation data during the two-phase flow experiment in an artificial steel planar porous media model. The results show that the calculated saturation data agree with the measured ones. With the help of an artificial steel planar porous media model, digital image processing is an accurate and simple method for obtaining the stained non-wetting phase saturation.

Visualization of CO_2 and oil immiscible and miscible flow processes in porous media using NMR micro-imaging

CO2 flooding is considered not only one of the most effective enhanced oil recovery （EOR） methods, but also an important alternative for geological CO2 storage. In this paper, the visualization of CO2 flooding was studied using a 400 MHz NMR micro-imaging system. For gaseous CO2 immiscible displacement, it was found that CO2 channeling or fingering occurred due to the difference of fluid viscosity and density. Thus, the sweep efficiency was small and the final residual oil saturation was 53.1%. For supercritical CO2 miscible displacement, the results showed that piston-like displacement occurred, viscous fingering and the gravity override caused by the low viscosity and density of the gas was effectively restrained, and the velocity of CO2 front was uniform. The sweep efficiency was so high that the final residual oil saturation was 33.9%, which indicated CO2 miscible displacement could enhance oil recovery more than CO2 immiscible displacement. In addition, the average velocity of CO2 front was evaluated through analyzing the oil saturation profile. A special core analysis method has been applied to in-situ oil saturation data to directly evaluate the local Darcy phase velocities and capillary dispersion rate.

Study of the permeability characteristics of porous media with methane hydrate by pore network model

The permeability in the methane hydrate reservoir is one of the key parameters in estimating the gas production performance and the flow behavior of gas and water during dissociation.In this paper,a three-dimensional cubic pore-network model based on invasion percolation is developed to study the effect of hydrate particle formation and growth habit on the permeability.The variation of permeability in porous media with different hydrate saturation is studied by solving the network problem.The simulation results are well consistent with the experimental data.The proposed model predicts that the permeability will reduce exponentially with the increase of hydrate saturation,which is crucial in developing a deeper understanding of the mechanism of hydrate formation and dissociation in porous media.

Numerical simulation of two-phase flow in fractured porous media using streamline simulation and IMPES methods and comparing results with a commercial software

Streamline simulation is developed to simulate waterflooding in fractured reservoirs. Conventional reservoir simulation methods for fluid flow simulation in large and complex reservoirs are very costly and time consuming. In streamline method, transport equations are solved on one-dimensional streamlines to reduce the computation time with less memory for simulation. First, pressure equation is solved on an Eulerian grid and streamlines are traced. Defining the "time of flight", saturation equations are mapped and solved on streamlines. Finally, the results are mapped back on Eulerian grid and the process is repeated until the simulation end time. The waterflooding process is considered in a fractured reservoir using the dual porosity model. Afterwards, a computational code is developed to solve the same problem by the IMPES method and the results of streamline simulation are compared to those of the IMPES and a commercial software. Finally, the accuracy and efficiency of streamline simulator for simulation of two-phase flow in fractured reservoirs has been proved.

Water transfer characteristics during methane hydrate formation and dissociation processes inside saturated sand

Gas hydrates formation and dissociation processes inside porous media are always accompanied by water transfer behavior, which is similar to the water behavior of ice freezing and thawing processes. These processes have been studied by many researchers, but all the studies are so far on the water transfer characteristics outside porous media and the water transfer characteristics inside porous media have been little known. In this study, in order to study the water transfer characteristics inside porous media during methane hydrate formation and dissociation processes, a novel apparatus with three pF-meter sensors which can detect water content changes inside porous media was applied. It was experimentally observed that methane hydrate formation processes were accompanied by water transfer from bottom to top inside porous media, however, the water behavior during hydrate dissociation processes was abnormal, for which more studies are needed to find out the real reason in our future work.

Experimental Study on Mechanism of Depressurizing Dissociation of Methane Hydrate under Saturated Pore Fluid

Sediment-hosted hydrate reservoir often contains saturated pore fluid, which changes the heat transfer and mass transfer characteristics of the hydrate reservoir. The exploitation of hydrate under saturated pore fluid using depressurization is simulated experimentally to investigate the influence of particle size of porous media, dissociation temperature, pressure drop and injected fluid type on gas production behavior. Homogeneous methane hydrate was firstly formed in frozen quartz sand. With the formed hydrate sample, hydrate dissociation experiments by depressurization were conducted. The test results showed that the gas production rate of hydrate under saturated pore fluid was substantially influenced by the particle size, the pressure drop and the injected fluid type, while it was influenced little by the dissociation temperature. The hydrate dissociates faster under larger pressure drop and in the presence of smaller porous media within the experimental region. The dissociation rate increases with an increasing fluid salinity in the initial stage, while it decreases in the later stage. The increase of gas diffusion resistance resulted from ionic hydration atmosphere in saturated chloride solution impeded the dissociation of hydrate. It can be solved by increasing the pressure drop and decreasing the fluid salinity in the process of gas recovery from hydrate reservoir.

Dynamic and quasi-static bending of saturated poroelastic Timoshenko cantilever beam

Based on the three-dimensional Gurtin-type variational principle of the incompressible saturated porous media, a one-dimensional mathematical model for dynamics of the saturated poroelastic Timoshenko cantilever beam is established with two assumptions, i.e., the deformation satisfies the classical single phase Timoshenko beam and the movement of the pore fluid is only in the axial direction of the saturated poroelastic beam. Under some special cases, this mathematical model can be degenerated into the Euler-Bernoulli model, the Rayleigh model, and the shear model of the saturated poroelastic beam, respectively. The dynamic and quasi-static behaviors of a saturated poroelastic Timoshenko cantilever beam with an impermeable fixed end and a permeable free end subjected to a step load at its free end are analyzed by the Laplace transform. The variations of the deflections at the beam free end against time are shown in figures. The influences of the interaction coefficient between the pore fluid and the solid skeleton as well as the slenderness ratio of the beam on the dynamic/quasi-static performances of the beam are examined. It is shown that the quasi-static deflections of the saturated poroelastic beam possess a creep behavior similar to that of viscoelastic beams. In dynamic responses, with the increase of the slenderness ratio, the vibration periods and amplitudes of the deflections at the free end increase, and the time needed for deflections approaching to their stationary values also increases. Moreover, with the increase of the interaction coefficient, the vibrations of the beam deflections decay more strongly, and, eventually, the deflections of the saturated poroelastic beam converge to the static deflections of the classic single phase Timoshenko beam.

Bending of simply supported incompressible saturated poroelastic beams with axial diffusion

Based on the mathematical model of the bending of the incompressible saturated poroelastic beam with axial diffusion, the qUasi-static bendings of the simply supported poroelastic beam subjected to a suddenly applied constant load were investigated, and the analytical solutions were obtained for different diffusion conditions of the pore fluid at the beam ends. The deflections, the bending moments of the solid skeleton and the equivalent couples of the pore pressures were presented in figures. It is also shown that the behavior of the saturated poroelastic beams depends closely on the diffusion conditions at the beam ends, especially for the equivalent couples of the pore pressures. It is found that the Mandel-Cryer effect also exists in the bending of the saturated poroelastic beams under specific diffusion conditions at the beam ends.

Analytical solutions for dynamic pressures of coupling fluid-solid-porous medium due to P wave incidence

Wave reflection and refraction in layered media is a topic closely related to seismology,acoustics,geophysics and earthquake engineering.Analytical solutions for wave reflection and refraction coefficients in multi-layered media subjected to P wave incidence from the elastic half-space are derived in terms of displacement potentials.The system is composed of ideal fluid,porous medium,and underlying elastic solid.By numerical examples,the effects of porous medium and the incident wave angle on the dynamic pressures of ideal fluid are analyzed.The results show that the existence of the porous medium,especially in the partially saturated case,may significantly affect the dynamic pressures of the overlying fluid.

Dynamic response of bilayered saturated porous media based on fractional thermoelastic theory

Considering the thermal contact resistance and elastic wave impedance at the interface,in this paper we theoretically investigate the thermo-hydro-mechanical(THM)coupling dynamic response of bilayered saturated porous media.Fractional thermoelastic theory is applied to porous media with imperfect thermal and mechanical contact.The analytical solutions of the dynamic response of the bilayered saturated porous media are obtained in frequency domain.Furthermore,the effects of fractional derivative parameters and thermal contact resistance on the dynamic response of such media are systematically discussed.Results show that the effects of fractional derivative parameters on the dynamic response of bilayered saturated porous media are related to the thermal contact resistance at the interface.With increasing thermal contact resistance,the displacement,pore water pressure,and stress decrease gradually.

AN ELLIPTIC-PARABOLIC SYSTEM ARISING FROM THE FLUID-SOLITE-HEAT FLOW THROUGH SATURATED POROUS MEDIA

In this paper an elliptic-parabolic coupled system arising from the fluid-solute-heat flowthrough a saturated porous medium is considerd.The uniqueness and the existence of classicalsolutions are proved.The asymptotic behavior of solutions for large time is shown,too.

In-situ observation for formation and dissociation of carbon dioxide hydrate in porous media by magnetic resonance imaging

The study of formation and dissociation of CO 2 hydrate in porous media was characterized by magnetic resonance imaging (MRI) system in in situ conditions. This work simulated porous media by using glass beads of uniform size. The growth and dissociation habit of CO2 hydrate was observed under different temperature and pressure conditions. The induction time and the hydrate saturation during the growth and dissociation process in different sizes of porous media were obtained by using the MRI signal intensity. The results indicate that hydrate growth rate and the induction time are affected by the size of porous media, pressure, and degree of supercooling. There are three hydrate growth stages, i.e., initial growth stage, rapid growth stage and steady stage. In this study,the CO2 hydrate forms preferentially at the surface of vessel and then gradually grows inward. The hydrate tends to cement the glass beads together and occupies the pore gradually. As the hydrate decomposes gradually, the dissociation rate increases to the maximum and then decreases to zero.

Numerical experiments for the conductive properties of saturated rock

The reservoir evaluation as a key technology in oil exploration and production is based on the electrical transport property (ETP) of saturated rock that is described in a mathematical form with Arhcie’s equa-tion. But there have been increasing cases observed in many researches indicating that the ETP is non-Archie especially for the complex reservoir with low porosity and permeability. In this paper,the numerical experiments based on the Lattice Boltzmann method (LBM) have been employed to study the effect of porous structure and fluids on the ETP for revealing the nature of non-Archie phenomenon in micro-scale. The results of numerical experiments have proved that the saturation exponent n is a function of water saturation and porosity instead of being a constant in Archie’s equation. And then,a new formula has been developed for the EPT through combining the result of numerical simulation with that of laboratory measurements. The calculations from the new formula show very good agreement with laboratory measurements to demonstrate the efficiency of the new formula over the conventional methods in non-Archie rock.

Seismic responses of a hemispherical alluvial valley to SV waves: a three-dimensional analytical approximation

Abstract An analytical solution to the three-dimen-sional scattering and diffraction of plane SV-waves by a saturated hemispherical alluvial valley in elastic half-space is obtained by using Fourier-Bessel series expan-sion technique. The hemispherical alluvial valley with saturated soil deposits is simulated with Biot＇s dynamic theory for saturated porous media. The following conclusions based on numerical results can be drawn： （1） there are a significant differences in the seismic response simulation between the previous single-phase models and the present two-phase model; （2） the nor-malized displacements on the free surface of the alluvial valley depend mainly on the incident wave angles, the dimensionless frequency of the incident SV waves and the porosity of sediments; （3） with the increase of the incident angle, the displacement distributions become more complicated; and the displacements on the free surface of the alluvial valley increase as the porosity of sediments increases.

Prediction of elastic and acoustic behaviors of calcarenite used for construction of historical monuments of Rabat, Morocco

Natural materials(e.g. rocks and soils) are porous media, whose microstructures present a wide diversity.They generally consist of a heterogeneous solid phase and a porous phase which may be fully or partially saturated with one or more fluids. The prediction of elastic and acoustic properties of porous materials is very important in many fields, such as physics of rocks, reservoir geophysics, civil engineering, construction field and study of the behavior of historical monuments. The aim of this work is to predict the elastic and acoustic behaviors of isotropic porous materials of a solid matrix containing dry, saturated and partially saturated spherical pores. For this, a homogenization technique based on the Morie Tanaka model is presented to connect the elastic and acoustic properties to porosity and degree of water saturation. Non-destructive ultrasonic technique is used to determine the elastic properties from measurements of P-wave velocities. The results obtained show the influence of porosity and degree of water saturation on the effective properties. The various predictions of Morie Tanaka model are then compared with experimental results for the elastic and acoustic properties of calcarenite.

Multi-transmitting formula for attenuating waves

The MTF is extended to case of attenuating incident wave by introducing an attenuation coefficient. The reflection coefficients of this modified MTF and MTF are evaluated and compared when an attenuating wave impinges on the boundary, and the results demonstrate that MTF can be used to absorb slightly attenuating waves and the modified MTF is more capable of absorbing heavily attenuating waves than MTF. The accuracy of modified MTF is also tested by numerical examples of fluid saturated porous media.