Effects of confining pressure and pore pressure on multipole borehole acoustic field in fluid-saturated porous media

In-situ stress is a common stress in the exploration and development of oil reservoirs. Therefore, it is of great significance to study the propagation characteristics of borehole acoustic waves in fluid-saturated porous media under stress.Based on the acoustoelastic theory of fluid-saturated porous media, the field equation of fluid-saturated porous media under the conditions of confining pressure and pore pressure and the acoustic field formula of multipole source excitation in open hole are given. The influences of pore pressure and confining pressure on guided waves of multipole borehole acoustic field in fluid-saturated porous media are investigated. The numerical results show that the phase velocity and excitation intensity of guided wave increase significantly under the confining pressure. For a given confining pressure, the phase velocity of the guided wave decreases with pore pressure increasing. The excitation intensity of guided wave increases at low frequency and then decreases at high frequency with pore pressure increasing, except for that of Stoneley wave which decreases in the whole frequency range. These results will help us get an insight into the influences of confining pressure and pore pressure on the acoustic field of multipole source in borehole around fluid-saturated porous media.

A wavelet finite-difference method for numerical simulation of wave propagation in fluid-saturated porous media

In this paper, we consider numerical simulation of wave propagation in fluidsaturated porous media. A wavelet finite-difference method is proposed to solve the 2-D elastic wave equation. The algorithm combines flexibility and computational efficiency of wavelet multi-resolution method with easy implementation of the finite-difference method. The orthogonal wavelet basis provides a natural framework, which adapt spatial grids to local wavefield properties. Numerical results show usefulness of the approach as an accurate and stable tool for simulation of wave propagation in fluid-saturated porous media.

Vibration Reduction Performance of Damping-Enhanced Water-Lubricated Bearing Using Fluid-Saturated Perforated Slabs

As the first link element for the transmission of shaft vibration to the pedestal and even to the hull,water-lubricated bearing plays a key role in suppressing vibration.Although the porous structure is considered as one of the main methods for improving the wideband vibration and noise reduction performance of materials in many industrial fields,the studies in the field of water-lubricated bearing remain insufficient.To enhance vibration reduction performance,a fluid-saturated perforated slab is designed in this study,and via the establishment of a fluid-solid coupled vibration model,the influence law and impact levels were analyzed and verified by simulation and experiments.The results obtained verified that the total vibration amplitude of damping-enhanced stern bearing in the vertical direction was smaller than that of the normal stern bearing,and the reduction amplitude of the characteristic frequency agreed with the optimal value at approximately 0.1 of the volume fraction of the liquid phase when the solid-fluid phase was rubber–water.Additionally,the increase in fluid fraction did not enhance the damping effect,instead,it unexpectedly reduced the natural frequency of the raw material significantly.This research indicates that the design of the fluid-saturated perforated slab is effective in reducing the transmission of the vibration amplitude from the shaft,and presents the best volume fraction of the liquid phase.

WAVE PROPAGATION WITH MASS-COUPLING EFFECT IN FLUID-SATURATED POROUS MEDIA

This article utilizes the theory of mixtures to formulate a general theory of wave propagation with mass-coupling effect in fluid-saturated porous media. An attempt is made to discuss the physical interpretation and the thermodynamic restriction of the coefficients appearing in the equations obtained, by the comparison it is shown that Biot's classical theory and the present one are essentially consistent. Also wave velocities in some special cases are calculated, from which it is concluded that mass-coupling and permeability of media greatly affect wave propagation behavior.

CHARACTERISTIC ANALYSIS FOR STRESS WAVE PROPAGATION IN TRANSVERSELY ISOTROPIC FLUID-SATURATED POROUS MEDIA

According to generalized characteristic theory, a characteristic analysis for stress wave propagation in transversely isotropic fluid-saturated porous media was performed. The characteristic differential equations and compatibility relations along bicharacteristics were deduced and the analytical expressions for wave surfaces were obtained. The characteristic and shapes of the velocity surfaces and wave surfaces in the transversely isotropic fluid-saturated porous media were discussed in detail. The results also show that the characteristic equations for stress waves in pure solids are particular cases of the characteristic equations for fluid-saturated porous media.

PARAMETERS INVERSION OF FLUID-SATURATED POROUS MEDIA BASED ON NEURAL NETWORKS

The multi- layers feedforward neural network is used for inversion ofmaterial constants of fluid-saturated porous media. The direct analysis of fluid-saturated porousmedia is carried out with the boundary element method. The dynamic displacement responses obtainedfrom direct analysis for prescribed material parameters constitute the sample sets training neuralnetwork. By virtue of the effective L-M training algorithm and the Tikhonov regularization method aswell as the GCV method for an appropriate selection of regu-larization parameter, the inversemapping from dynamic displacement responses to material constants is performed. Numerical examplesdemonstrate the validity of the neural network method.

The scattering of plane P1 wave by a 3-D sedimentary basin in a fluid-saturated poroelastic half-space using IBEM

The indirect boundary element method(IBEM)is applied to investigate the scattering of elastic waves around a 3-D sedimentary basin filled with fluid-saturated poroelastic medium.Based on this method,the free field and scattered field can be solved according to the boundary conditions.And the numerical accuracy has been verified.The effects of parameters on elastic wave scattering are studied,such as boundary condition,incident frequency,incident angle and porosity of medium.Numerical results illustrate that the amplification effect of surface displacement near poroelastic sedimentary basin is notable.In addition,for the case of large porosity the drainage condition has a significant impact on the response amplitude.Due to the fluid exchange at the interface under the drained condition,the displacement amplitude can be much larger than that under the undrained condition in present study.The study can provide a theoretical basis for the anti-seismic design of engineering structures located in sedimentary basin.

Stress dependence of elastic wave dispersion and attenuation in fluid-saturated porous layered media

The fluid-saturated porous layered(FSPL)media widely exist in the Earth's subsurface and their overall mechanical properties,microscopic pore structure and wave propagation characteristics are highly relevant to the in-situ stress.However,the effect of in-situ stress on wave propagation in FSPL media cannot be well explained with the existing theories.To fill this gap,we propose the dynamic equations for FSPL media under the effect of in-situ stress based on the theories of poroacoustoelasticity and anisotropic elasticity.Biot loss mechanism is considered to account for the stress-dependent wave dispersion and attenuation induced by global wave-induced fluid flow.Thomsen's elastic anisotropy parameters are used to represent the anisotropy of the skeleton.A plane-wave analysis is implemented on dynamic equations yields the analytic solutions for fast and slow P waves and two S waves.Modelling results show that the elastic anisotropy parameters significantly determine the stress dependence of wave velocities.Vertical tortuosity and permeability have remarkable effects on fast and slow P-wave velocity curves and the corresponding attenuation peaks but have little effect on S-wave velocity.The difference in velocities of two S waves occurs when the FSPL medium is subjected to horizontal uniaxial stress,and the S wave along the stress direction has a larger velocity,which implies that the additional anisotropy other than that induced by the beddings appears due to horizontal stress.Besides,the predicted velocity results have the reasonable agreement with laboratory measurements.Our equations and results are relevant to a better understanding of wave propagation in deep strata,which provide some new theoretical insights in the rock physics,hydrocarbon exploration and stress detection in deep-strata shale reservoirs.

ACOUSTOELASTIC THEORY FOR FLUID-SATURATED POROUS MEDIA

Based on the finite deformation theory of the continuum and poroelastic theory, the aeoustoelastic theory for fluid-saturated porous media （FSPM） in natural and initial coordi- nates is developed to investigate the influence of effective stresses and fluid pore pressure on wave velocities. Firstly, the assumption of a small dynamic motion superimposed on a largely static pre- deformation of the FSPM yields natural, initial, and final configurations, whose displacements, strains, and stresses of the solid-skeleton and the fluid in an FSPM particle could be described in natural and initial coordinates, respectively. Secondly, the subtraction of initial-state equations of equilibrium from the final-state equations of motion and the introduction of non-linear constitu- rive relations of the FSPM lead to equations of motion for the small dynamic motion. Thirdly, the consideration of homogeneous pre-deformation and the plane harmonic form of the small dynamic motion gives an acoustoelastic equation, which provides analytical formulations for the relation of the fast longitudinal wave, the fast shear wave, the slow shear wave, and the slow longitudinal wave with solid-skeleton stresses and fluid pore-pressure. Lastly, an isotropic FSPM under the close-pore jacketed condition, open-pore jacketed condition, traditional unjacketed condition, and triaxial condition is taken as an example to discuss the velocities of the fast and slow shear waves propagating along the direction of one of the initial principal solid-skeleton strains. The detailed discussion shows that the wave velocities of the FSPM are usually influenced by the effective stresses and the fluid pore pressure. The fluid pore-pressure has little effect on the wave velocities of the FSPM only when the components of the applied initial principal solid-skeleton stresses or strains are equal, which is consistent with the previous experimental results.

PML Absorbing Boundary Condition for Seismic Numerical Modeling by Convolutional Differentiator in Fluid-Saturated Porous Media

The perfectly matched layer（PML） was first introduced by Berenger as an absorbing boundary condition for electromagnetic wave propagation.In this article,a method is developed to ex-tend the PML to simulating seismic wave propagation in fluid-saturated porous medium.This non-physical boundary is used at the computational edge of a Forsyte polynomial convolutional differenti-ator（FPCD） algorithm as an absorbing boundary condition to truncate unbounded media.The incor-poration of PML in Biot＇s equations is given.Numerical results show that the PML absorbing bound-ary condition attenuates the outgoing waves effectively and eliminates the reflections adequately.

Two different mathematical schemes for solving chemical dissolution-front instability problems in fluid-saturated rocks

Chemical dissolution-front instability(CDFI)problems usually involve multiple temporal and spatial scales,as well as multiple processes.A key issue associated with solving a CDFI problem in a fluid-saturated rock is to mathematically establish a theoretical criterion,which can be used to judge the instability of a chemical dissolution-front(CDF)propagating in the fluidsaturated rock.This theoretical paper deals with how two different mathematical schemes can be used to precisely establish such a theoretical criterion in a purely mathematical manner,rather than in a numerical simulation manner.The main distinguishment between these two different mathematical schemes is that in the first mathematical scheme,a curved surface coordinate system is used,while in the second mathematical scheme,a planar surface coordinate system is employed.In particular,all the key mathematical deduction steps associated with using these two different mathematical schemes are described and discussed in great detail.The main theoretical outcomes of this study have demonstrated that(1)two different mathematical schemes under consideration can produce exactly the same theoretical criterion;(2)the main advantage of using the first mathematical scheme is that the interface conditions at the curved interface between the downstream and upstream regions can be easily described mathematically;(3)the main advantage of using the second mathematical scheme is that the first-order perturbation equations of the CDFI problem can be easily described in a purely mathematical manner.

A Level Set Method for the Inverse Problem of Wave Equation in the Fluid-Saturated Porous Media

In this paper,a level set method is applied to the inverse problem of 2-D wave equation in the fluid-saturated media.We only consider the situation that the parameter to be recovered takes two different values,which leads to a shape reconstruction problem.A level set function is used to present the discontinuous parameter,and a regularization functional is applied to the level set function for the ill-posed problem.Then the resulting inverse problem with respect to the level set function is solved by using the damped Gauss-Newton method.Numerical experiments show that the method can recover parameter with complicated geometry and the noise in the observation data.

A dynamic model for computing elastic wave velocities in fluid-saturated sandstones

Based on the Wyllie time-average relation and sonic velocity-log conditions, by introducing three basic assumptions and applying conventional elastic wave dynamic method , both P-wave and S-wave velocities for fluid-saturated sandstones are derived theoretically in this paper . And Wyllie 's kinematic model for computing P-wave velocity is developed into a dynamic model for computing P-wave and S-wave velocities . The results are consistent with the data on P-wave and S-wave velocities for air-saturated sandstones measured by Wyllie et al.

Two species of microcracks

We identify two interrelated but independent species of microcracks with different origins and different distributions. One species is the classic high-stress microcracks identified in laboratory stress-cells associated with acoustic emissions as microcracks open with increasing stress. The other species is the low-stress distributions of closely-spaced stress-aligned fluid-saturated microcracks that observations of shear-wave splitting(SWS) demonstrate pervade almost all in situ rocks in the upper crust, the lower crust, and the uppermost 400 km of the mantle. On some occasions these two sets of microcracks may be interrelated and similar(hence ‘species') but they typically have fundamentally-different properties, different distributions, and different implications. The importance for hydrocarbon exploration and recovery is that SWS in hydrocarbon reservoirs monitors crack alignments and preferred directions of fluid-flow. The importance for earthquake seismology is that SWS above small earthquakes monitors the effects of increasing stress on the pervasive low-stress microcrack distributions so that stress-accumulation before, possibly distant, earthquakes can be recognised and impending earthquakes stress-forecast.