Laboratory study of fluid viscosity induced ultrasonic velocity dispersion in reservoir sandstones

Ultrasonic velocities of a set of saturated sandstone samples were measured at simulated in-situ pressures in the laboratory.The samples were obtained from the W formation of the WXS Depression and covered low to nearly high porosity and permeability ranges.The brine and four different density oils were used as pore fluids,which provided a good chance to investigate fluid viscosity-induced velocity dispersion.The analysis of experimental observations of velocity dispersion indicates that（1）the Biot model can explain most of the small discrepancy（about 2–3%）between ultrasonic measurements and zero frequency Gassmann predictions for high porosity and permeability samples saturated by all the fluids used in this experiment and is also valid for medium porosity and permeability samples saturated with low viscosity fluids（less than approximately 3 mP·S）and（2）the squirt flow mechanism dominates the low to medium porosity and permeability samples when fluid viscosity increases and produces large velocity dispersions as high as about 8%. The microfracture aspect ratios were also estimated for the reservoir sandstones and applied to calculate the characteristic frequency of the squirt flow model,above which the Gassmann’ s assumptions are violated and the measured high frequency velocities cannot be directly used for Gassmann’s fluid replacement at the exploration seismic frequency band for W formation sandstones.

Seismic Attenuation and Velocity Dispersion to Discriminate Gas Hydrates and Free Gas Zone, Makran Offshore, Pakistan

Gas hydrates gained a remarkable attention as an unconventional energy resource recently. In order to interpret gas hydrates (part of fluid) and free gas saturated zone accurately, it is essential to implement new technique related to seismic attenuation and velocity dispersion. P wave attenuation and velocity dispersion in porous media made promising imprints for exploration of gas hydrates. The most prominent phenomenon for attenuation and velocity dispersion in porous media is wave induced fluid flow in which wave inhomogeneities are larger than pore size but smaller than wavelength. Numerical simulation technique is applied to analyze frequency dependent velocity dispersion and attenuation in gas hydrates and free gas layer in Makran offshore of Pakistan. Homogeneous and patchy distribution patterns of gas hydrates and free gas within pore spaces of host sediments at lower and higher frequency regime are considered. It is noted that the attenuation and velocity dispersion increase with the increase in gas hydrates saturation. The maximum attenuation is observed at 66% saturation of gas hydrates in the area under investigation. However, in case of water and gas mixture the maximum attenuation and velocity dispersion occur at low gas saturation (~15%). Therefore, based on our numerical simulation, velocity dispersion and attenuation can be used as seismic attributes to differentiate various gas saturations and gas hydrates saturation for Makran offshore area of Pakistan.

Group velocity dispersion effect on the collapse of femtosecond laser pulses in air: a revised form for Marburger's law

The influence of group velocity dispersion（GVD） on the self-focusing of femtosecond laser pulses is investigated by numerically solving the extended nonlinear Schr？dinger equation. By introducing the GVD length LGVDinto the semi-empirical, self-focusing formula proposed by Marburger, a revised one is proposed, which can not only well explain the influence of GVD on the collapse distance, but also is in good agreement with the numerical results, making the self-focusing formula applicable for more cases.

A WEAKLY NONLINEAR WATER WAVE MODEL TAKING INTO ACCOUNT DISPERSION OF WAVE PHASE VELOCITY

This paper presents a weakly nonlinear water wave model using a mild slope equation and a new explicit formulation which takes into account dispersion of wave phase velocity, approximates Hedges’ (1987) nonlinear dispersion relationship, and accords well with the original empirical formula. Comparison of the calculating results with those obtained from the experimental data and those obtained from linear wave theory showed that the present water wave model considering the dispersion of phase velocity is rational and in good agreement with experiment data.

Experimental study on the multiscale scattering of high-velocity heterogeneous bodies

There are complex heterogeneous entities in the underground medium,and the heterogeneous scale has a substantial impact on wave propagation.In this study,we used a set of 11 samples of glass beads as high-velocity heterogeneous bodies to evaluate the impact of such heterogeneous bodies on the propagation of P-wave.We vary the heterogeneous scale by changing the diameter of the glass beads from 0.18 to 11 mm while keeping the same volume proportion(10%)of the beads for the set of 11 samples.The pulse transmission method was used to record measurements at the ultrasonic frequencies of 0.34,0.61,and 0.84 MHz in the homogeneous matrix.The relationship between P-wave fi eld features and heterogeneity scale,P-wave velocity,and the multiple of the wave number and heterogeneous scale(ka)was observed in the laboratory,which has sparked widespread interest and research.Heterogeneous scale affects P-wave propagation,and its wave field changes are complex.The waveform,amplitude,and velocity of the recorded P-waves correlate with the heterogeneous scale.For the forward scattering while large-scale heterogeneities,noticeable direct and diff racted waves are observed in the laboratory,which indicates that the infl uence of direct and diff racted waves cannot be ignored for large-scale heterogeneities.The relationship between velocity and ka shows frequency dependence;the reason is that the magnitude of change in velocity caused by wave number is diff erent from that caused by heterogeneous scale.According to the change in the recorded waveform,amplitude variation,or the relationship between the velocity measured at diff erent frequencies and the heterogeneous scale,the identifi ed turning points of the ray approximation are all around ka=10.When ka is less than 1,the velocity changes slowly and gradually approaches the eff ective medium velocity.The ray velocity measured for heterogeneous media with large velocity perturbations in the laboratory is signifi cantly smaller than the velocity predicted by the perturbation theory.

Effects of the Reynolds number on a scale-similarity model of Lagrangian velocity correlations in isotropic turbulent flows

A scale-similarity model of a two-point two-time Lagrangian velocity correlation(LVC) was originally developed for the relative dispersion of tracer particles in isotropic turbulent flows(HE, G. W., JIN, G. D., and ZHAO, X. Scale-similarity model for Lagrangian velocity correlations in isotropic and stationary turbulence. Physical Review E, 80, 066313(2009)). The model can be expressed as a two-point Eulerian space correlation and the dispersion velocity V. The dispersion velocity denotes the rate at which one moving particle departs from another fixed particle. This paper numerically validates the robustness of the scale-similarity model at high Taylor micro-scale Reynolds numbers up to 373, which are much higher than the original values(R_λ = 66, 102). The effect of the Reynolds number on the dispersion velocity in the scale-similarity model is carefully investigated. The results show that the scale-similarity model is more accurate at higher Reynolds numbers because the two-point Lagrangian velocity correlations with different initial spatial separations collapse into a universal form compared with a combination of the initial separation and the temporal separation via the dispersion velocity.Moreover, the dispersion velocity V normalized by the Kolmogorov velocity V_η ≡ η/τ_η in which η and τ_η are the Kolmogorov space and time scales, respectively, scales with the Reynolds number R_λ as V/V_η ∝ R_λ^(1.39) obtained from the numerical data.

Petrophysical parameters inversion for heavy oil reservoir based on a laboratory-calibrated frequency-variant rock-physics model

Heavy oil has high density and viscosity, and exhibits viscoelasticity. Gassmann's theory is not suitable for materials saturated with viscoelastic fluids. Directly applying such model leads to unreliable results for seismic inversion of heavy oil reservoir. To describe the viscoelastic behavior of heavy oil, we modeled the elastic properties of heavy oil with varying viscosity and frequency using the Cole-Cole-Maxwell (CCM) model. Then, we used a CCoherent Potential Approximation (CPA) instead of the Gassmann equations to account for the fluid effect, by extending the single-phase fluid condition to two-phase fluid (heavy oil and water) condition, so that partial saturation of heavy oil can be considered. This rock physics model establishes the relationship between the elastic modulus of reservoir rock and viscosity, frequency and saturation. The viscosity of the heavy oil and the elastic moduli and porosity of typical reservoir rock samples were measured in laboratory, which were used for calibration of the rock physics model. The well-calibrated frequency-variant CPA model was applied to the prediction of the P- and S-wave velocities in the seismic frequency range (1–100 Hz) and the inversion of petrophysical parameters for a heavy oil reservoir. The pre-stack inversion results of elastic parameters are improved compared with those results using the CPA model in the sonic logging frequency (∼10 kHz), or conventional rock physics model such as the Xu-Payne model. In addition, the inversion of the porosity of the reservoir was conducted with the simulated annealing method, and the result fits reasonably well with the logging curve and depicts the location of the heavy oil reservoir on the time slice. The application of the laboratory-calibrated CPA model provides better results with the velocity dispersion correction, suggesting the important role of accurate frequency dependent rock physics models in the seismic prediction of heavy oil reservoirs.

Petrophysical properties and their influencing factors of carbonates in the fourth member of Sinian Dengying Formation, Sichuan Basin, SW China

Based on the measurements of petrological, petrophysical and elastic properties of the samples of different sedimentary facies in the fourth member of Sinian Dengying Formation (Deng 4 Member) in the Sichuan Basin, the diagenetic processes of reservoirs of different sedimentary facies and their controls on the petrophysical properties were discussed. The results show that cracks and mineral composition jointly control the petrophysical properties, and both are significantly influenced by sedimentary environment and diagenesis. The microbial dolomite of mound-shoal facies mainly experienced multi-stage dolomitization, penecontemporaneous dissolution, tectonic rupture and hydrothermal/organic acid dissolution processes, giving rise to cracks and dissolved pores. The grannular dolomite of inter-mound-shoal bottomland or dolomitic lagoon facies mainly underwent mechanical compaction, burial dolomitization and tectonic-hydrothermal action, creating cracks and intercrystalline pores. The diagenesis related to crack development increases the pressure- and saturation-dependent effects of samples, leading to significant decrease in the compressional wave impedance and Poisson's ratio. Dolomitization changes the properties of mineral particles, resulting in a Poisson's ratio close to dolomite. The muddy, siliceous and calcareous sediments in the low-energy environment lead to the decrease of impedance and the differential change of Poisson's ratio (significantly increased or decreased). The samples with both cracks and dissolved pores show high P-wave velocity dispersion characteristics, and the P-wave velocity dispersion of samples with only fractures or pores is the lowest.

Numerical simulation of seismic low-frequency shadows and its application

Strong low-frequency energy beneath a hydrocarbon reservoir is called a seismic low-frequency shadow and can be used as a hydrocarbon indicator （Tarter et al., 1979） bu the physical mechanism of the observed low-frequency shadow is still unclear. To stud） the mechanism, we performed seismic numerical simulation of geological models with a hydrocarbon-bearing zone using the 2-D diffusive-viscous wave equation which car effectively model the characteristics of velocity dispersion and transform the seismic dat~ centered in a target layer slice within a time window to the time-frequency domain by usinl time-frequency signal analysis and sort the frequency gathers to common frequency cubes. Then, we observe the characteristics of the seismic low-frequency shadow in the common frequency cubes. The numerical simulations reveal that the main mechanism of seismic lowfrequency shadows is attributed to high attenuation of the medium to high seismic frequency components caused by absorption in the hydrocarbon-filled reservoir. Results from a practical example of seismic low-frequency shadows show that it is possible to identify the reservoir by the low-frequency shadow with high S/N seismic data.

Viscoelastic characteristics of low-frequency seismic wave attenuation in porous media

Mesoscopic fluid flow is the major cause of wave attenuation and velocity dispersion at seismic frequencies in porous rocks. The Johnson model provides solutions for the frequency-dependent quality factor and phase velocity in partially saturated porous media with pore patches of arbitrary shapes. We use the Johnson model to derive approximations for the quality factor Q at the high and low frequency limit, and obtain the approximate equation for Qmin based on geophysical and geometric parameters. A more accurate equation for Qmin is obtained after correcting for the linear errors between the exact and approximate Q values. The complexity of the pore patch shape affects the maximum attenuation of Qmin and the transition frequency ftr; furthermore, the effect on ftr is stronger than that on Qmin. Numerical solutions to Biot’s equation are computationally intensive; thus, we build an equivalent viscoelastic model on the basis of the Zener model, which well approximates the wave attenuation and dispersion in porous rocks in the seismic band.

On the M-σ Relationship and SMBH Mass Estimates of Selected Nearby Galaxies

Super massive black holes are believed to influence galactic evolution and dynamics. A histogram of SMBH masses for different redshift regimes may reveal clues on how the SMBH evolve in time. A prominent method for SMBH mass estimation is based on the linear correlation between the bulge velocity dispersion and the SMBH mass. Known as M-σ relationship, this method is known to provide reasonable but not very accurate mass estimates due to considerable scatter in data. In order to increase the precision, we surveyed the literature and gathered SMBH and velocity dispersion data for low redshift (z 0.02) spiral galaxies. We report the M-σ relationship for low redshift spiral galaxies as, By using this refined M-σ relationship we measured 32 SMBH masses and determined upper and lower mass boundaries and the mass histogram for spiral galaxies in a narrow redshift regime (0.016 z < 0.017). The spectroscopic data are obtained from The SLOAN Digital Survey and The National Observatory of Turkey (TUG). The targets are selected within a low redshift range for discernible [OIII] lines. TUG observations are carried out on the RTT150 1.5 m telescope using TUG Faint Object Spectrographic Camera and the SLOAN data are obtained from the 7th data release of the survey. We measured the bandwidths of narrow [OIII] lines, which are shown to be indicative in estimating stellar bulge velocity dispersion and estimated the central black hole masses from the refined version of the empirical M-σ relationship. The estimated masses vary between 9.51 × 106 - 2.36 × 108 solar masses.

A patchy-saturated rock physics model for tight sandstone based on microscopic pore structures

The wave-induced local fluid flow mechanism is relevant to the complex heterogeneity of pore structures in rocks.The analysis of the local fluid flow mechanism is useful for accurately describing the wave propagation characteristics in reservoir rocks.In the exploration and production of hydrocarbon reservoirs,the real stratum may be partially saturated with a multi-phase fluid mixture in general.Therefore,it is of great significance to investigate the wave velocity dispersion and attenuation features in relation to pore structures and fluids.In this work,the characteristics of fabric microstructures are obtained on the basis of pressure dependency of dry rock moduli using the effective medium theory.A novel anelasticity theoretical model for the wave propagation in a partially-saturated medium is presented by combining the extended Gurevich squirt-flow model and White patchysaturation theory.Numerical simulations are used to analyze wave propagation characteristics that depend on water saturation,external patchy diameter,and viscosity.We consider a tight sandstone from the Qingyang area of the Ordos Basin in west China and perform ultrasonic measurements under partial saturation states and different confining pressures,where the basic properties of the rock are obtained at the full gas saturation.The comparison of experimental data and theoretical modeling results shows a fairly good agreement,indicating that the new theory is effective.

Nonlinear Propagation of Coupling Optical Pulse under Compton Scattering in Laser Medium

After considering Kerr nonlinear effect, group velocity dispersion of host and gain distribution of active particle in laser amplifying medium, a basic equation describing propagation of the coupling optical pulse under the multi-photon nonlinear Compton scattering in the laser amplifying medium has been deduced. Besides, the profile and power spectrum of a picosecond-level super-Gaussian coupling pulse in the laser amplifying medium have been discussed when its central frequency coincides with the gain peak frequency of the laser amplifying medium.

Dynamic fluid transport property of hydraulic fractures and its evaluation using acoustic logging

The existing acoustic logging methods for evaluating the hydraulic fracturing effectiveness usually use the fracture density to evaluate the fracture volume, and the results often cannot accurately reflect the actual productivity. This paper studies the dynamic fluid flow through hydraulic fractures and its effect on borehole acoustic waves. Firstly, based on the fractal characteristics of fractures observed in hydraulic fracturing experiments, a permeability model of complex fracture network is established. Combining the dynamic fluid flow response of the model with the Biot-Rosenbaum theory that describes the acoustic wave propagation in permeable formations, the influence of hydraulic fractures on the velocity dispersion of borehole Stoneley-wave is then calculated and analyzed, whereby a novel hydraulic fracture fluid transport property evaluation method is proposed. The results show that the Stoneley-wave velocity dispersion characteristics caused by complex fractures can be equivalent to those of the plane fracture model, provided that the average permeability of the complex fracture model is equal to the permeability of the plane fracture. In addition, for fractures under high-permeability(fracture width 10~100 μm, permeability ~100 μm^(2)) and reduced permeability(1~10 μm, ~10 μm^(2), as in fracture closure) conditions, the Stoneley-wave velocity dispersion characteristics are significantly different. The field application shows that this fluid transport property evaluation method is practical to assess the permeability and the connectivity of hydraulic fractures.

Formation and Evolution of Galaxies: Starlight Synthesis Algorithm

This study will see the resurgence of interest in precise velocity dispersion measurements, both for the study of galactic and active nuclei kinematics. As several works suggest, an excellent tactic to measure σ is to use the absorption lines of the calcium triplet, as it is a spectral region relatively free from complications. The discovery of an empirical relationship between the mass of the central black hole (M&bull;) and σ was the leading guide of my detailed study of the calcium triplet region. This search for more accurate methods to calculate the dispersion of velocities, in addition to the careful study of uncertainties. After investing so much time in the development and improvement of the method and its application to so many galaxies, it is time to reap the rewards of this effort, using my results to address a series of questions concerning the physics of galaxies.

The Transmission Performance of Non-zero Dispersion Shifted Fiber Communication Systems Using In-line Phase-sensitive Amplifiers

This paper focuses on the non zero dispersion shifted fiber optical transmission system which employs cascaded in line Phase sensitive Amplifiers ( PSAs ). By computer simulation, we have revealed that the eye penalty of high speed signal pulses increases with the accretion of dispersion and the transmission distance limited by Intersymbol Interference ( ISI ) of signals varies with the spacing and average output power of amplifiers for positive and negative fiber dispersion. The analysis shows that although PSA can compensate for both positive and negative dispersion, it is only valid for small dispersion coefficient fiber. Owing to the effect of Self phase modulation ( SPM ), the ISI limited transmission distance of positive dispersion fiber is much longer than that of negative dispersion fiber. In addition, for positive fiber dispersion, there is an optimum value of average output signal power from PSA leading to the longest ISI limited transmission distance.

Velocity field of wave-induced local fluid flow in double-porosity media

Under the excitation of elastic waves,local fluid flow in a complex porous medium is a major cause for wave dispersion and attenuation.When the local fluid flow process is simulated with wave propagation equations in the double-porosity medium,two porous skeletons are usually assumed,namely,host and inclusions.Of them,the volume ratio of inclusion skeletons is low.All previous studies have ignored the consideration of local fluid flow velocity field in inclusions,and therefore they can not completely describe the physical process of local flow oscillation and should not be applied to the situation where the fluid kinetic energy in inclusions cannot be neglected.In this paper,we analyze the local fluid flow velocity fields inside and outside the inclusion,rewrite the kinetic energy function and dissipation function based on the double-porosity medium model containing spherical inclusions,and derive the reformulated Biot-Rayleigh(BR)equations of elastic wave propagation based on Hamilton’s principle.We present simulation examples with different rock and fluid types.Comparisons between BR equations and reformulated BR equations show that there are significant differences in wave response characteristics.Finally,we compare the reformulated BR equations with the previous theories and experimental data,and the results show that the theoretical results of this paper are correct and effective.

The Effect of Polarization Mode Dispersion on the Transmission System Using Dispersion Compensation Fiber

In this paper, we simulate the effect of Polarization Mode Dispersion( PMD ) on 40 Gb/s dispersion compensation transmission system by resolving the coupled nonlinear Schrodinger equation, and calculate the performance of system with different duty cycle order and chirp of the super Gaussian pulse. The results show that the performance of the system changes with these parameters, and there is a group of optimum parameters for the optimum performance of the system.

Dispersion characteristics of nanometer-scaled silicon nitride suspended membrane waveguides

We investigate the dispersion properties ofnanometer-scaled silicon nitride suspended membrane wave- guides around the communication wavelength and systematically study their relationship with the key structural parameters of the waveguide. The simulation results show that a suspended membrane waveguide can realize anomalous dispersion with a relatively thinner silicon nitride thickness in the range of 400 to 600 nm, whereas, for the same membrane thickness, a conventional rib or strip silicon nitride waveguide cannot support anomalous dispersion. In particular, a waveguide with 400 nm silicon nitride thickness and deep etch depth （r = 0.05） exhibits anomalous dispersion around the communication wavelength when the waveguide width ranges from 990 to 1255 nm, and the maximum dispersion is 22.56 ps/（nm.km）. This specially designed anomalous dispersion silicon nitride waveguide is highly desirable for micro-resonator based optical frequency combs due to its potential to meet the phase-matching condition required for cascaded four-wave-mixing.

Enhanced slow light propagation in photonic crystal waveguides using angular properties of scatter elements

Applicability of the angular properties of scatter elements as a tool to achieve improved slow light per- formance with small group velocity dispersion and large bandwidth in photonic crystal waveguides is investigated. A polyatomic photonic crystal waveguide, including two scatter elements with different geo- metrical shapes in each primitive cell, is proposed to investigate the feasibility of our method. Numerical results show that a versatile control of the dispersion relation of slow light modes, with large normalized delay-bandwidth products ranging from 0.2085 to 0.3394, can be obtained using a unique geometrical pa- rameter.