Borehole guided waves in a non-Newtonian(Maxwell) fluid-saturated porous medium

The property of acoustic guided waves generated in a fluid-filled borehole surrounded by a non-Newtonian （Maxwell） fluid-saturated porous formation with a permeable wall is investigated. The influence of non-Newtonian effects on acoustic guided waves such as Stoneley waves, pseudo-Rayleigh waves, flexural waves, and screw waves propagations in a fluid-filled borehole is demonstrated based on the generalized Biot-Tsiklauri model by calculating their velocity dispersion and attenuation coefficients. The corresponding acoustic waveforms illustrate their properties in time domain. The results are also compared with those based on generalized Biot＇s theory. The results show that the influence of non-Newtonian effect on acoustic guided wave, especially on the attenuation coefficient of guided wave propagation in borehole is noticeable.

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.

Flow and Heat Transfer of a Dusty Williamson MHD Nanofluid Flow over a Permeable Cylinder in a Porous Medium

This study investigates the flow and heat transfer of dusty Williamson (MHD) Nanofluid flow over a stretching permeable cylinder in a porous medium. Dusty Williamson Nanofluid was considered due to its thermal properties and potential benefits of increasing the heat transfer rate. Firstly, partial differential equations are transformed into coupled non-linear ordinary differential equations through a similarity variables transformation. The resulting set of dimensionless equations is solved analytically by using the Homogony Perturbation Method (HPM). The effects of the emerging parameters on the velocity and temperature profiles as well as skin-friction coefficient and Nusselt number are publicized through tables and graphs with appropriate discussions. The present result has been compared with published papers and found to be in agreement. To the best of author’s knowledge, there has been sparse research work in the literature that considers the effect of dust with Williamson Nanofluid and also solving the problem analytically. Therefore to the best of author’s knowledge, this is the first time analytical solution has been established for the problem. The results revealed that the fluid velocity of both the fluid and dust phases decreases as the Williamson parameter increases. Motivated by the above limitations and the gaps in past works, therefore, it is hoped that the present work will assist in providing accurate solutions to many practical problems in science, industry and engineering.

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.

Flow and heat transfer of a nanofluid through a porous medium due to stretching/shrinking sheet with suction,magnetic field and thermal radiation

This study investigates the suction and magnetic field effects on the two-dimensional nanofluid flow through a stretching/shrinking sheet at the stagnation point in the porous medium with thermal radiation.The governing partial differential equations(PDEs)are converted into ordinary differential equations(ODEs)using the similarity transformation.The resulting ODEs are then solved numerically by using the bvp4c solver in MATLAB software.It was found that dual solutions exist for the shrinking parameter values up to a certain range.The numerical results obtained are compared,and the comparison showed a good agreement with the existing results in the literature.The governing parameters’effect on the velocity,temperature and nanoparticle fraction fields as well as the skin friction coefficient,the local Nusselt number and the Sherwood number are represented graphically and analyzed.The variation of the velocity,temperature and concentration increase with the increase in the suction and magnetic field parameters.It seems that the thermal radiation effect has increased the local Sherwood number while the local Nusselt number is reduced with it.

Analysis of a Stagnation Point Flow with Hybrid Nanoparticles over a Porous Medium

The unsteady stagnation-point flow of a hybrid nanofluid over a stretching/shrinking sheet embedded in a porous medium with mass transpiration and chemical reactions is considered.The momentum and mass transfer problems are combined to form a system of partial differential equations,which is converted into a set of ordinary differential equations via similarity transformation.These ordinary differential equations are solved analytically to obtain the solution for velocity and concentration profiles in exponential and hypergeometric forms,respectively.The concentration profile is obtained for four different cases namely constant wall concentration,uniform mass flux,general power law wall con-centration and general power law mass flux.The effect of different physical parameters such as Darcy number Da^(1-1),mass transpiration parameter V_(C),stretching/shrinking parameter (d),chemical reaction parameter(β)and Schmidt number (Sc)on velocity and concentration profile is examined.Results show that,the axial velocity will decreases as the shrinking sheet parameter increases,regardless of whether the suction or injection case is examined.The concentration decreases with an increase in the shrinking sheet parameter and the chemical reaction rate parameter.

Exact solutions to one-dimensional transient response of incompressible fluid-saturated single-layer porous media

Based on the Biot theory of porous media, the exact solutions to one- dimensional transient response of incompressible saturated single-layer porous media un- der four types of boundary conditions are developed. In the procedure, a relation between the solid displacement u and the relative displacement ＇w is derived, and the well-posed initial conditions and boundary conditions are proposed. The derivation of the solution for one type of boundary condition is then illustrated in detail. The exact solutions for the other three types of boundary conditions are given directly. The propagation of the compressional wave is investigated through numerical examples. It is verified that only one type of compressional wave exists in the incompressible 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.

Slip Condition Effects on Unsteady MHD Fluid Flow with Radiative Heatflux over a Porous Medium

The objective of this paper is to study unsteady magneto hydrodynamic (MHD) free flow of viscoelastic fluid (Walter’s B) past an infinite vertical plate through porous medium. The temperature is assumed to be oscillating with time. The solution obtained shows different profiles of effects of slip conditions on primary and secondary velocity. Also, the effects of various parameters on temperature, concentration, primary and secondary velocity profiles were presented graphically. The result indicated the secondary velocity is enhanced with increase in slip parameter. Primary velocity demonstrated opposite trend.

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.

Influence of variable viscosity and double diffusion on the convective stability of a nanofluid flow in an inclined porous channel

The influence of variable viscosity and double diffusion on the convective stability of a nanofluid flow in an inclined porous channel is investigated.The DarcyBrinkman model is used to characterize the fluid flow dynamics in porous materials.The analytical solutions are obtained for the unidirectional and completely developed flow.Based on a normal mode analysis,the generalized eigenvalue problem under a perturbed state is solved.The eigenvalue problem is then solved by the spectral method.Finally,the critical Rayleigh number with the corresponding wavenumber is evaluated at the assigned values of the other flow-governing parameters.The results show that increasing the Darcy number,the Lewis number,the Dufour parameter,or the Soret parameter increases the stability of the system,whereas increasing the inclination angle of the channel destabilizes the flow.Besides,the flow is the most unstable when the channel is vertically oriented.

Formation Characteristics of CO_(2) Hydrates in the Presence of Porous Media and NaCl

Hydrate-based CO_(2) sequestration is an effective method for reducing the greenhouse effect,and the presence of porous media and NaCl can impact the formation characteristics of hydrates.This study uses the constant volume temperature search method to investigate the effects of quartz sand particle size(0.006‒0.03 mm),water saturation(30%–90%),and NaCl concentration(1%‒9%)on the phase equilibrium and kinetics of CO_(2) hydrates within a temperature range of 273‒285 K and pressure range of 1.0‒3.5 MPa.The results indicate that a decrease in quartz sand particle size or an increase in NaCl concentration shifts the hydrate phase equilibrium curve towards lower temperatures and higher pressures,making hydrate generation conditions more demanding.In different particle size systems,there are no significant changes in the rate of CO_(2) hydrate formation or conversion rate.The highest hydrate conversion rate of 71.1%is observed in a 0.015 mm particle size system.With increasing water saturation,both the generation rate and conversion rate of CO_(2) hydrates show a trend of first increasing and then decreasing.Meanwhile,low concentrations of NaCl(1%–3%)are found to enhance the formation and conversion rates of CO_(2) hydrates.However,as NaCl concentration increases,the rate of CO_(2) hydrate formation and conversion rate decrease.

Stability of buoyancy-driven convection in an Oldroyd-B fluid-saturated anisotropic porous layer

The nonlinear stability of thermal convection in a layer of an Oldroyd-B fluid-saturated Darcy porous medium with anisotropic permeability and thermal diffu- sivity is investigated with the perturbation method. A modified Darcy-Oldroyd model is used to describe the flow in a layer of an anisotropic porous medium. The results of the linear instability theory are delineated. The thresholds for the stationary and oscillatory convection boundaries are established, and the crossover boundary between them is de- marcated by identifying a codimension-two point in the viscoelastic parameter plane. The stability of the stationary and oscillatory bifurcating solutions is analyzed by deriving the cubic Landau equations. It shows that these solutions always bifurcate supercritically. The heat transfer is estimated in terms of the Nusselt number for the stationary and oscillatory modes. The result shows that, when the ratio of the thermal to mechanical anisotropy parameters increases, the heat transfer decreases.

Natural convection of non-Newtonian power-law fluid over axisymmetric and two-dimensional bodies of arbitrary shape in fluid-saturated porous media

Numerical analysis of the free convection coupled heat and mass transfer is presented for non-Newtonian power-law fluids with the yield stress flowing over a two-dimensional or axisymmetric body of an arbitrary shape in a fluid-saturated porous medium. The governing boundary layer equations and boundary conditions are cast into a dimensionless form by the similarity transformation. The resulting system of equations is solved by a finite difference method. The parameters studied are the rheological constants, the buoyancy ratio, and the Lewis number. Representative velocity, temperature, and concentration profiles are presented and discussed. It is found that the results depend strongly on the values of the yield stress parameter and the power-law index of the non-Newtonian fluid.

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.

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.

Slip flow of Maxwell viscoelasticity-based micropolar nanoparticles with porous medium: a numerical study

This article presents the mass and heat transport aspects in viscoelastic nanofluid flows under the presence of velocity slip conditions. To explore the nonNewtonian behavior, a Maxwell viscoelasticity-based micropolar is considered. Moreover, a porous medium saturates the stretching sheet. A set of similarity variables is introduced to derive the dimensionless ordinary differential equations of velocity, concentration, and temperature profiles. The numerical solution is computed by using the MATLAB bvp4c package. The salient flow features of velocity, concentration, and temperature profiles are described and discussed through various graphs. It is observed that with an increase in the slip parameter, the micro-rotation velocity also increases. The temperature of nanoparticles gets maximum values by varying the viscoelastic parameter and the porosity parameter while an opposite trend is noted for the micro-rotation parameter. The local Nusselt number and the local Sherwood number increase by increasing the viscoelastic parameter, the porosity parameter, and the slip velocity parameter. The graphical computation is performed for a specified range of parameters, such as 0 ≤ M ≤ 2.5, 0 ≤σm ≤ 2.5, 0 ≤ K1 ≤ 1.5, 0.5 ≤ Pr ≤ 3.0, 0 ≤σ≤ 1.5, 0.5 ≤ Sc ≤ 2.0, 0.2 ≤ Nb ≤ 0.8, and 0.2 ≤ Nt ≤ 0.8.

ON THE INTERACTION OF WATER WAVES AND SEABED BY THE POROUS MEDIUM MODEL

The interaction of water waves and seabed is studied by using Yamamoto's model, which takes into account the deformation of soil skeletal frame, compressibility of pore fluid flow as well as the Coulumb friction. When analyzing the propagation of three kinds of stress waves in seabed, a simplified dispersion relation and a specific damping formula are derived. The problem of seabed stability is further treated analytically based on the Mohr-Coulomb theory. The theory is finally applied to the coastal problems in the Lian-Yun Harbour and compared with observations and measurements in soil-wave tank with satisfactory results.

Utilization of Maxwell-Cattaneo law for MHD swirling flow through oscillatory disk subject to porous medium

The present study aims to investigate the salient features of incompressible, hydromagnetic, three-dimensional flow of viscous fluid subject to the oscillatory motion of a disk. The rotating disk is contained in a porous medium. Furthermore, a time-invariant version of the Maxwell-Cattaneo law is implemented in the energy equation. The flow problem is normalized by obtaining similarity variables. The resulting nonlinear system is solved numerically using the successive over-relaxation method. The main results are discussed through graphical representations and tables. It is perceived that the thermal relaxation time parameter decreases the temperature curves and increases the heat trans- fer rate. The oscillatory curves for the velocity field demonstrate a decreasing tendency with the increasing porosity parameter values. Two- and three-dimensional flow phenom- ena are also shown through graphical results.

Heat and Mass Transfer in MHD Visco-Elastic Fluid Flow through a Porous Medium over a Stretching Sheet with Chemical Reaction

This paper presents the study of convective heat and mass transfer characteristics of an incompressible MHD visco-elastic fluid flow immersed in a porous medium over a stretching sheet with chemical reaction and thermal stratification effects. The resultant governing boundary layer equations are highly non-linear and coupled form of partial differential equations, and they have been solved by using fourth order Runge-Kutta integration scheme with Newton Raphson shooting method. Numerical computations are carried out for the non-dimensional physical parameters. Here a numerical has been carried out to study the effect of different physical parameters such as visco-elasticity, permeability of the porous medium, magnetic field, Grashof number, Schmidt number, heat source parameter and chemical reaction parameter on the flow, heat and mass transfer characteristics.