scholarly journals Effect of fluid viscosity on elastic wave attenuation in porous rocks

Geophysics ◽  
2002 ◽  
Vol 67 (1) ◽  
pp. 264-270 ◽  
Author(s):  
Boris Gurevich
Keyword(s):  
Viscous Fluid ◽  
Dispersion Equation ◽  
Shear Wave ◽  
Low Frequency ◽  
Frequency Dispersion ◽  
Fluid Viscosity ◽  
Fast Wave ◽  
Compressional Waves ◽  
Dispersion Equations ◽  
Fluid Layers

Attenuation and dispersion of elastic waves in fluid‐saturated rocks due to pore fluid viscosity is investigated using an idealized exactly solvable example of a system of alternating solid and viscous fluid layers. Waves in periodic layered systems at low frequencies can be studied using an asymptotic analysis of Rytov's exact dispersion equations. Since the wavelength of the shear wave in the fluid (viscous skin depth) is much smaller than the wavelength of the shear or compressional waves in the solid, the presence of viscous fluid layers requires a consideration of higher‐order terms in the low‐frequency asymptotic expansions. This expansion leads to asymptotic low‐frequency dispersion equations. For a shear wave with the directions of propagation and of particle motion in the bedding plane, the dispersion equation yields the low‐frequency attenuation (inverse quality factor) as a sum of two terms which are both proportional to frequency ω but have different dependencies on viscosity η: one term is proportional to ω/η, the other to ωη. The low‐frequency dispersion equation for compressional waves allows for the propagation of two waves corresponding to Biot's fast and slow waves. Attenuation of the fast wave has the same two‐term structure as that of the shear wave. The slow wave is a rapidly attenuating diffusion‐type wave, whose squared complex velocity again consists of two terms which scale with iω/η and iωη. For all three waves, the terms proportional to η are responsible for the viscoelastc phenomena (viscous shear relaxation), whereas the terms proportional to η−1 account for the visco‐inertial (poroelastic) mechanism of Biot's type. Furthermore, the characteristic frequencies of visco‐elastic ωV and poroelastic ωB attenuation mechanisms obey the relation ωVωB = AωR2, where ωR is the resonant frequency of the layered system, and A is a dimensionless constant of order 1. This result explains why the visco‐elastic and poroelastic mechanisms are usually treated separately in the context of macroscopic theories that imply ω << ωR. The poroelastic mechanism dominates over the visco‐elastic one when the frequency‐indepenent parameter B = ωB/ωV = 12η2/μsρfhf2 << 1, and vice versa, where hf is the fluid layer thickness, ρf the fluid density, and μs represents the shear modulus of the solid.

Dispersion equation for ballooning modes in two-component plasma

2013 ◽  
Vol 80 (3) ◽  
pp. 379-393 ◽  
Author(s):  
D. A. Kozlov ◽  
N. G. Mazur ◽  
V. A. Pilipenko ◽  
E. N. Fedorov
Keyword(s):  
Dispersion Equation ◽  
Low Frequency ◽  
Mhd Equations ◽  
Small Scale ◽  
Inner Magnetosphere ◽  
Compressional Waves ◽  
Local Dispersion ◽  
Coupled Equations ◽  
Two Component ◽  
Component Plasma

The ballooning magnetohydrodynamic (MHD) modes have been often suggested as a possible instability trigger of the substorm onset, and a mechanism of compressional waves in the outer magnetosphere and magnetotail. Commonly, these disturbances are characterized by the local dispersion equation that is widely applied for the description of ultra-low-frequency oscillatory disturbances and instabilities in the nightside magnetosphere. In realistic situations, especially in the inner magnetosphere, the magnetospheric plasma is composed of two components: background ‘cold’ plasma and ‘hot’ particles. The ballooning disturbances in a two-component plasma immersed into a curved magnetic field are described with the system of coupled equations for the Alfvén and slow magnetosonic (SMS) modes. We have reduced the basic system of MHD equations to the dispersion equation for the small-scale in transverse direction disturbances, and applied WKB approximation along a field line. As a result, we have derived a dispersion equation that can be used for geophysical applications. In particular, from this relationship the dispersion, instability threshold, and stop-bands of the Alfvén and SMS modes in two-component plasma have been examined.

Experiments and mechanistic modeling of viscosity effect on a multistage ESP performance under viscous fluid flow

2021 ◽  
pp. 095765092110149
Author(s):  
Yi Shi ◽  
Jianjun Zhu ◽  
Haoyu Wang ◽  
Haiwen Zhu ◽  
Jiecheng Zhang ◽  
...  
Keyword(s):  
Fluid Flow ◽  
Viscous Fluid ◽  
Prediction Error ◽  
Flow Direction ◽  
Fluid Viscosity ◽  
Oil Viscosity ◽  
Viscous Fluid Flow ◽  
Viscosity Effect ◽  
High Production Rate ◽  
Pump Head

Assembled in series with multistage, Electrical Submersible Pumps (ESP) are widely used in offshore petroleum production due to the high production rate and efficiency. The hydraulic performance of ESPs is subjected to the fluid viscosity. High oil viscosity leads to the degradation of ESP boosting pressure compared to the catalog curves under water flow. In this paper, the influence of fluid viscosity on the performance of a 14-stage radial-type ESP under varying operational conditions, e.g. rotational speeds 1800–3500 r/min, viscosities 25–520 cP, was investigated. Numerical simulations were conducted on the same ESP model using a commercial Computational Fluid Dynamics (CFD) software. The simulated average pump head is comparable to the corresponding experimental data under different viscosities and rotational speeds with less than ±20% prediction error. A mechanistic model accounting for the viscosity effect on ESP boosting pressure is proposed based on the Euler head in a centrifugal pump. A conceptual best-match flowrate QBM is introduced, at which the impeller outlet flow direction matches the designed flow direction. The recirculation losses caused by the mismatch of velocity triangles and other head losses resulted from the flow direction change, friction loss and leakage flow etc., are included in the model. The comparison of model predicted pump head versus experimental measurements under viscous fluid flow conditions demonstrates good agreement. The overall prediction error is less than ±10%.

Magnetic Permeability and Relaxation Frequency in High Frequency Magnetic Materials.

2001 ◽  
Vol 674 ◽  
Author(s):  
M.I. Rosales ◽  
H. Montiel ◽  
R. Valenzuela
Keyword(s):  
High Frequency ◽  
Domain Walls ◽  
Magnetocrystalline Anisotropy ◽  
Low Frequency ◽  
Frequency Dispersion ◽  
Anisotropy Constant ◽  
Relaxation Frequency ◽  
Resonance Relaxation ◽  
Frequency Behavior

ABSTRACTAn investigation of the frequency behavior of polycrystalline ferrites is presented. It is shown that the low frequency dispersion (f < 10 MHz) of permeability is associated with the bulging of pinned domain walls, and has a mixed resonance-relaxation character, closer to the latter. It is also shown that there is a linear relationship between the magnetocrystalline anisotropy constant, K1, and the relaxation frequency. The slope of this correlation depends on the grain size. Such a relationship could allow the determination of this basic parameter from polycrystalline samples.

Delineating a cased borehole in unconsolidated formations using dipole acoustic data from a nearby well

Geophysics ◽  
2021 ◽  
pp. 1-39
Author(s):  
Gu Xihao ◽  
Xiao-Ming Tang ◽  
Yuan-Da Su
Keyword(s):  
Shear Waves ◽  
Low Frequency ◽  
Well Being ◽  
Compressional Wave ◽  
Acoustic Imaging ◽  
Wave Radiation ◽  
Dipole Source ◽  
Compressional Waves ◽  
Single Well ◽  
Cased Borehole

A potential application for single-well acoustic imaging is the detection of an existing cased borehole in the vicinity of the well being drilled, which is important for drilling toward (when drilling a relief well), or away from (collision prevention), the existing borehole. To fulfill this application in the unconsolidated formation of shallow sediments, we propose a detection method using the low-frequency compressional waves from dipole acoustic logging. For this application, we perform theoretical analyses on elastic wave scattering from the cased borehole and derive the analytical expressions for the scattered wavefield for the incidence of compressional and shear waves from a borehole dipole source. The analytical solution, in conjunction with the elastic reciprocity theorem, provides a fast algorithm for modeling the whole process of wave radiation, scattering, and reception for the borehole acoustic detection problem. The analytical results agree well with those from 3D finite-difference simulations. The results show that compressional waves, instead of shear waves as commonly used for dipole acoustic imaging, are particularly advantageous for the borehole detection in the unconsolidated formation. Field data examples are used to demonstrate the application in a shallow marine environment, where dipole-compressional wave data in the measurement well successfully delineate a nearby cased borehole, validating our analysis results and application.

scholarly journals Steady MHD Flow of Viscous Fluid between Two Parallel Porous Plates with Heat Transfer in an Inclined Magnetic Field

2015 ◽  
Vol 7 (3) ◽  
pp. 21-31 ◽  
Author(s):  
D. R. Kuiry ◽  
S. Bahadur
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Viscous Fluid ◽  
Pressure Gradient ◽  
Reverse Flow ◽  
Flow Behavior ◽  
Fluid Pressure ◽  
Mhd Flow ◽  
Fluid Viscosity ◽  
Temperature Dependent Viscosity

The steady flow behavior of a viscous, incompressible and electrically conducting fluid between two parallel infinite insulated horizontal porous plates with heat transfer is investigated along with the effect of an external uniform transverse magnetic field, the action of inflow normal to the plates, the pressure gradient on the flow and temperature. The fluid viscosity is supposed to vary exponentially with the temperature. A numerical solution for the governing equations for both the momentum transfer and energy transfer has been developed using the finite difference method. The velocity and temperature distribution graphs have been presented under the influence of different values of magnetic inclination, fluid pressure gradient, inflow acting perpendicularly on the plates, temperature dependent viscosity and the Hartmann number. In our study viscosity is shown to affect the velocity graph. The flow parameters such as viscosity, pressure and injection of fluid normal to the plate can cause reverse flow. For highly viscous fluid, reverse flow is observed. The effect of magnetic force helps to restrain this reverse flow.

Volume low-frequency dispersion in a semi-insulating system

1988 ◽  
Vol 23 (2) ◽  
pp. 209-213 ◽  
Author(s):  
A.K. Jonscher ◽  
L. Levesque
Keyword(s):  
Low Frequency ◽  
Frequency Dispersion

The Effects of Vibrations on Particle Motion in a Viscous Fluid Cell

2008 ◽  
Vol 75 (3) ◽  
Author(s):  
Samer Hassan ◽  
Masahiro Kawaji
Keyword(s):  
Viscous Fluid ◽  
Drag Force ◽  
Particle Motion ◽  
Fluid Model ◽  
Resonance Phenomenon ◽  
Fluid Viscosity ◽  
Mass Force ◽  
Amplitude Data ◽  
Viscous Fluid Model ◽  
Fluid Cell

The effects of small vibrations on particle motion in a viscous fluid cell have been investigated experimentally and theoretically. A steel particle was suspended by a thin wire at the center of a fluid cell, and the cell was vibrated horizontally using an electromagnetic actuator and an air bearing stage. The vibration-induced particle amplitude measurements were performed for different fluid viscosities (58.0cP and 945cP), and cell vibration amplitudes and frequencies. A viscous fluid model was also developed to predict the vibration-induced particle motion. This model shows the effect of fluid viscosity compared to the inviscid model, which was presented earlier by Hassan et al. (2004, “The Effects of Vibrations on Particle Motion in an Infinite Fluid Cell,” ASME J. Appl. Mech., 73(1), pp. 72–78) and validated using data obtained for water. The viscous model with modified drag coefficients is shown to predict well the particle amplitude data for the fluid viscosities of 58.5cP and 945cP. While there is a resonance frequency corresponding to the particle peak amplitude for oil (58.0cP), this phenomenon disappeared for glycerol (945cP). This disappearance of resonance phenomenon is explained by referring to the theory of mechanical vibrations of a mass-spring-damper system. For the sinusoidal particle motion in a viscous fluid, the effective drag force has been obtained, which includes the virtual mass force, drag force proportional to the velocity, and the Basset or history force terms.

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