Seismic Wave Reflection From a Permeable Layer: Low-Frequency Asymptotic Analysis

Prospective assessment of corneal biomechanical properties and intraocular pressure after scleral lens wear: A 12-month follow-up study

To evaluate the short-term influence of scleral lenses (SL) with different diameters on intraocular pressure (IOP) and corneal biomechanics. A secondary objective was to investigate the relationship between fluid reservoir (FR) thickness and IOP and biomechanical parameters. Thirty healthy subjects were randomly fitted with L1 (diameter of 15.80 mm) and L2 (diameter of 16.80 mm) on the right eye and worn for 2 hr. On IOP and corneal biomechanical parameters were measured with the CORVIS ST before and after SL removal. Fluid reservoir thickness at 0 and 2 hr of wear was measured using anterior segment optical coherence tomography. Biomechanical parameters decreased after removal of L1 (-1.04±1.47 mm Hg) ( P <0.01) and L2 (-0.80±1.74 mm Hg) ( P =0.02). The biomechanical parameters A1T (-0.11±0.18 ms) ( P =0.01) and SP-A1 (-4.29±9.97 mm Hg/mm) ( P =0.02) decreased after L1 removal, whereas a decrease in highest concavity time (-0.21±0.50 m/s) ( P =0.03) and an increase in highest concavity radius (+0.17±0.43 mm) ( P =0.04) were observed after L2 removal. A significant, negative, and moderate correlation was found between highest concavity deformation amplitude and FR thickness with L1 (r=-0.42, P =0.02). The small changes in corneal biomechanical parameters and IOP values induced by short-term SL wear have no significant clinical impact and were not influenced by the diameter of the SL.

Purpose:To investigate the impact of different-thickness scleral lenses (SLs) on corneal thickness, curvature, and fluid reservoir thickness in keratoconic eyes.Methods:Schiempflug imaging and AS-OCT was captured before and immediately following 6 h of SL wear. Different-thickness lenses were used while keeping the other parameters the same. The timing of the measurement for day 1 and day 2 was matched to allow for the control of the confounding influence of diurnal variation.Results:Immediately after 6 h of lens wear, no statistically significant difference (P > 0.05) was noted in corneal edema in any region and quadrants between thin- and thick-lens wearers. The calculated percentage of corneal edema was also within the range of overnight closed eye physiological swelling. Pentacam measured higher central corneal thickness compared to AS-OCT in both baselines and after 6 h of lens wear. The current investigation reported minimal but not statistically significant (P > 0.05) flattening in anterior and steepening in posterior curvature parameters in both thin and thick SLs. The mean reduction in the fluid reservoir thickness was 80.00 ± 3.99 and 79.36 ± 3.84 microns after 6 h of thin- and thick-lens wear, respectively, which was not statistically significant (P > 0.05). A statistically significant positive correlation (r = 0.67, P = 0.02) was found between lens thickness and change in anterior steep k with thick-lens wear.Conclusion:Central lens thickness of 200–400 mm did not cause any significant change in corneal curvature and fluid reservoir thickness and did not induce clinically significant corneal edema after short-term SL wear.

Subtraction of baseline and monitoring seismic data is a common step in highlighting reservoir changes in time-lapse seismic interpretation. However, ambiguity exists in the interpretation of the amplitude difference, which is controlled by fluid change and reservoir thickness. To estimate the residual oil saturation quantitatively, we have developed a time-lapse seismic interpretation method that uses the ratio of amplitude attributes extracted from the baseline and monitoring seismic data. The relationship between impedance change and the ratio of the baseline and monitoring amplitude attributes is determined to avoid the influence of reservoir thickness. Subsequently, the fluid saturation is calculated from the impedance change by using a proper petrophysical relationship. We have tested our new method on a real time-lapse seismic data set from a water-flooded reservoir in the deepwater area of West Africa. The water-flooded area determined from the amplitude difference does not completely match the production logs because of the influence of variations in the reservoir thickness. However, the residual oil distribution calculated with the proposed method matches the production logs well. The connectivity of sandstone bodies is also evaluated based on an integrated interpretation of estimated oil saturation. With its simple principles and easy accessibility, our method improves the accuracy of time-lapse seismic data interpretation in water-flooded oil reservoirs. Furthermore, the quantitative interpretation of fluid change enables the time-lapse seismic technology to guide reservoir development directly.

Stability analysis of mixed convection in a porous horizontal channel filled with a Newtonian Al2O3/Water nanofluid in presence of magnetic field and thermal radiation

A partial differential equation was developed and programed to compute the cumulation and flow of the liquid phase of a gas-condensate fluid. It was found that such cumulation near the wellbore may attain saturations permitting liquid flow within periods of the order of 1 day. The radius at which this saturation obtains advances toward the external reservoir boundary with continued recovery, although it may move only 2 to 5 percent of that distance during the productive life of the well. This relatively high saturation can cause a serious diminution in delivery capacity. The pressure differential required for flow of gas through a formation with such saturation may be as much as three times greater than the corresponding differential in a formation where saturation is less than 2 percent. Because of the radial geometry, total reservoir pressure differential required for flow with a zone of relatively high liquid saturation about the well was indicated to be two to three times greater than without the saturation. Introduction A computing program developed by the authors to integrate the partial differential equation for transient radial flow of gas-condensate fluids required a prevalued function, (1) related to cumulation of condensate in pores of the reservoir as pressure declines. Methods were available for relating mobility to saturation, saturation to liquid-vapor volume ratio, liquid-vapor volume ratio to pressure and, hence, mobility to pressure to obtain W(PD). However, certain assumptions had to be made in advance of program execution concerning movement of the liquid phase and change in radial distribution of liquid saturation as recovery progressed. Because reservoir fluid mobility and related pressure gradients are markedly dependent on liquid saturation, it was desirable to eliminate the necessity for these assumptions and in this respect improve the reliability of a result obtained by integration. Experimental research was begun to determine the relationship of variables that control the reservoir flow of low liquid-vapor ratio fluids. With the porous medium partly saturated, permeability to a two-phase flowing fluid could not be measured because the viscosity was unknown. Viscosity could not be measured without knowing permeability of the liquid-containing medium; but mobility, the ratio of permeability to viscosity, was measurable. This property, and liquid-vapor volume ratio of the flowing phases, have values determined by nature of the fluid and porous medium and, in addition, were found to be pressure, velocity and saturation dependent. A program developed by Kniazeff and Naville for computing multicomponent, two-phase flow used polynomials to represent saturation dependence of permeabilities for gas and for liquid phases, and an effluent viscosity constant under reservoir conditions. The authors developed a program based on a partial differential equation of similar mass balance origin but designed to represent distribution of an unlimited number of components between gas and liquid phases utilizing the experimental information available as to variable dependence. Attention was given to liquid-vapor volume ratio of the flowing phases, a property which is essential as a liquid saturation boundary condition. A program for computing implicitly saturation increase at uniform intervals along the drainage radius was combined with an existing program for calculating pressures, and the two were used alternately in an iterative solution for both saturations and pressures. The function W(PD) needed for calculating pressures was replaced by the ratio of mobility to compressibility factor. SPEJ P. 125ˆ

Instability of a laminar flow in a parallel-plate channel filled with a fluid saturated porous medium is investigated on the basis of a modified Orr-Sommerfeld equation. This equation takes into account three drag terms: the Darcy term that describes friction between the fluid and the porous matrix, the Forchheimer quadratic drag term that describes a form drag due to the solid obstacles, and the Brinkman term, which is a viscous term similar to the Laplacian term in the Navier-Stokes equations. Numerical analysis is carried out using the collocation method. The dependence of the critical Reynolds number on porosity and permeability of the porous medium is analyzed numerically.

The Frenkel-Biot theory is used to study the reflection of elastic waves from the boundary of a non-Newtonian (Maxwell) fluid-saturated porous medium. The velocity and attenuation of a Rayleigh surface wave propagating along the boundary of the medium are determined. Two models of a fluid-saturated porous medium are used for calculation: with pore channels of a fixed diameter and with a lognormal distribution of pore channels in size. The results of calculations show that, when the fluid in the porous medium is characterized by a small Deborah number (i.e., exhibits non-Newtonian properties), the velocity of Rayleigh waves exhibits a considerable frequency dispersion. The results also suggest that, in principle, it is possible to estimate the Deborah number from the measured frequency dispersion of the Rayleigh wave velocity.

Unsteady MHD combined convection over a moving vertical sheet in a fluid saturated porous medium with uniform surface heat flux

The propagation of the Biot slow wave in a fluid-saturated porous medium at low frequencies is investigated by asymptotic methods. It is proven that the Biot wave has a bifurcation behavior depending on its wave number. The bifurcation occurs in a neighborhood of the critical value k(cr), which depends on the permeability of a medium and the viscosity of a fluid. The P2 wave is fully attenuated if its wave number is smaller than k(cr) and it becomes propagatory with wave numbers bigger than k(cr). Asymptotic formulas for the phase velocity and attenuation of the Biot wave are derived.

Stealthy hyperuniform (SHU) many-particle systems in d-dimensional Euclidean space are distinguished by a structure factor that vanishes not only at zero wave number (as in "standard" hyperuniform systems) but also across an extended range of wave numbers near the origin. We generate disordered SHU packings of identical and "nonoverlapping" spheres in two and three dimensions using a modified collective-coordinate optimization algorithm that incorporates a soft-core repulsive potential between particles in addition to the standard stealthy pair potential. Compared to SHU packings without soft-core repulsions, these SHU packings are ultradense with packing fractions ranging from 0.67 to 0.86 for d=2 and 0.47to 0.63 for d=3, spanning a broad spectrum of structures depending on the stealthiness parameter χ. We consider two-phase media composed of hard particles derived from ultradense SHU packings (phase 2) embedded in a matrix phase (phase 1) with varying stealthiness parameter χ and packing fractions ϕ. Our main objective is the estimation of the dynamical physical properties of such two-phase media, namely the effective dynamic dielectric constant and the time-dependent diffusion spreadability, which is directly related to nuclear magnetic relaxation in fluid-saturated porous media. We show through spreadability that two-phase media derived from ultradense SHU packings exhibit faster interphase diffusion due to the higher packing fractions achievable compared to SHU media obtained without soft-core repulsion. The imaginary part of the effective dynamic dielectric constant of SHU packings vanishes for a range of small wave numbers, implying perfect transparency for the corresponding wave vectors. While a larger packing fraction yields a smaller transparency interval, we show that it also displays a reduced height of the attenuation peak. We also obtain cross-property relations between transparency characteristics and long-time behavior of the spreadability for such two-phase media, showing that one leads to information about the other and vice versa. Our results demonstrate that disordered two-phase media derived from ultradense SHU packings exhibit advantageous transport and optical behaviors of both theoretical and experimental significance.

Seismic low-frequency amplitude anomalies can be correlated with the existence of hydrocarbon reservoirs, but the generation mechanism of these low-frequency amplitude anomalies is very complicated. We investigated the effect of the Biot slow P-waves on the seismic reflection amplitude at low frequencies from fluid-saturated porous media using techniques of both theoretical calculation and physical modelling. First, we used theoretical calculation to study the effects of the frequency, the fluid content and the heterogeneity of layered media on the conversion of the Biot slow waves, and the reflection coefficients. Then, we used physical modelling data to show a low-frequency shadow of the air-saturated layered model. The phenomenon was similar to that in the theoretical calculation. A combination of the theoretical calculation and physical modelling results provided a reasonable explanation of the low-frequency shadow. The conclusion is that whether the actual hydrocarbon reservoirs exhibit low-frequency shadow phenomena depends on the frequency, the consolidation, the thickness of the hydrocarbon reservoirs, the homogeneity of the porosity and the fluid distributions of the reservoirs. The proposed method can be used to analyse the low-frequency anomalies and to identify the fluid properties using seismic data.

Reflection of plane waves from the stress-free isothermal and insulated boundaries of a nonlocal thermoelastic solid

The relation between arterial function indices, such as pulse wave velocity and augmentation index with parameters derived from input impedance analysis, is still incompletely understood. Carotid pressure, central flow waveforms, and pulse wave velocity were noninvasively acquired in 2026 apparently healthy, middle-aged subjects (1052 women and 974 men) 35 to 55 years old at inclusion. Input and characteristic impedance, reflection coefficient, the ratio of backward-to-forward pressure amplitude (reflection magnitude), and augmentation index were derived. Pulse wave velocity increased by 15% (from 6.1 to 7.0 m/s) both in men and women. In qualitative terms, input impedance evolved from a pattern indicative of wave transmission and reflection to a pattern more compatible with a windkessel-like system. In women, a decrease in total arterial compliance led to an increased input impedance in the low frequency range, whereas few changes were observed in men. Characteristic impedance did not change with age in women and even decreased in men (P<0.001) and could not be identified as the primary determinant of central pulse pressure. Augmentation index increased with age, as was expected, and was systematically higher in women (P<0.001). Reflection coefficient and reflection magnitude increased with age (P<0.001) without gender differences. We conclude that, in healthy middle-aged subjects, the age-related increase in arterial stiffness (pulse wave velocity) is not fully paralleled by an increase in arterial impedance, suggesting a role for age-dependent modulation of aortic cross-sectional area. Wave reflection increases with age and is not higher in women than in men.

By using the factorial design method, statistically significant correlations have been developed which enable one to predict steamflood performance in terms of project life, oil recovery and cumulative steam-oil ratio. The effects of various reservoir rock and fluid properties and steamflood design and operating variables on steamflood performance were discusssed.