Aperture Length Research Articles

An XFEM Model for Hydraulic Fracturing in Partially Saturated Rocks

Hydraulic fracturing is a complex multi-physics phenomenon. Numerous analytical and numerical models of hydraulic fracturing processes have been proposed. Analytical solutions commonly are able to model the growth of a single hydraulic fracture into an initially intact, homogeneous rock mass. Numerical models are able to analyse complex problems such as multiple hydraulic fractures and fracturing in heterogeneous media. However, majority of available models are restricted to single-phase flow through fracture and permeable porous rock. This is not compatible with actual field conditions where the injected fluid does not have similar properties as the host fluid. In this study we present a fully coupled hydro-poroelastic model which incorporates two fluids i.e. fracturing fluid and host fluid. Flow through fracture is defined based on lubrication assumption, while flow through matrix is defined as Darcy flow. The fracture discontinuity in the mechanical model is captured using eXtended Finite Element Method (XFEM) while the fracture propagation criterion is defined through cohesive fracture model. The discontinuous matrix fluid velocity across fracture is modelled using leak-off loading which couples fracture flow and matrix flow. The proposed model has been discretised using standard Galerkin method, implemented in Matlab and verified against several published solutions. Multiple hydraulic fracturing simulations are performed to show the model robustness and to illustrate how problem parameters such as injection rate and rock permeability affect the hydraulic fracturing variables i.e. injection pressure, fracture aperture and fracture length. The results show the impact of partial saturation on leak-off and the fact that single-phase models may underestimate the leak-off.

Effects of shading and blocking in compact linear fresnel reflector field

In a compact linear fresnel reflector field, ‘s’ number of reflector-rows lying between two receivers can be configured in 2s ways. Each possible configuration will lead to different energy loss, electricity generation and cost of electricity. The variations in energy losses, energy collection by fluid, electricity generation and cost of electricity with length (L) and width (w) of aperture of a reflector-row, spacing between adjacent reflector-rows (p), number of reflector-rows (2n), receiver-height (H), collector-configuration and location have been studied. It is found that the collector configuration has no significant effect on annual shading. However, it affects annual energy losses due to cosine effect, blocking and the factors τ and α significantly. As a result, the cost of electricity can be improved significantly by varying collector configuration. The cost of electricity decreases with increment in p/w and later on, it starts increasing. The best p/w ratio corresponding to minimum cost of electricity is 1.44 for H/nw = 0.3 and 1.85 for H/nw = 0.7. The energy collection by fluid increases rapidly with increment in H/nw initially. However, beyond H/nw about 0.7, further increase in H/nw does not lead to significant increase in energy collection.

Sub-10 nm near-field localization by plasmonic metal nanoaperture arrays with ultrashort light pulses.

Near-field localization by ultrashort femtosecond light pulses has been investigated using simple geometrical nanoapertures. The apertures employ circular, rhombic, and triangular shapes to localize the distribution of surface plasmon. To understand the geometrical effect on the localization, aperture length and period of the nanoapertures were varied. Aperture length was shown to affect the performance more than aperture period due mainly to intra-aperture coupling of near-fields. Triangular apertures provided the strongest spatial localization below 10 nm in size as well as the highest enhancement of field intensity by more than 7000 times compared to the incident light pulse. Use of ultrashort pulses was found to allow much stronger light localization than with continuous-wave light. The results can be used for super-localization sensing and imaging applications where spatially localized fields can break through the limits in achieving improved sensitivity and resolution.

Compression tests on aluminum honeycomb and epoxy resin sandwich panels

In order to realize the functional integration and improve the bearing and energy absorption capability of aluminum honeycomb sandwich panel under compression, aluminum honeycomb and epoxy resin sandwich panels were made. By carrying out quasi-static compression experiments, we investigated their absorption function with different resin thickness, diameter of aperture, and thickness. The experiments indicated that the energy absorption function of the aluminum honeycomb sandwich panel declined with increase of resin thickness and length of aperture but improved with increase of specimen thickness.

Pitfalls of using entrenched fracture relationships: Fractures in bedded carbonates of the Hidden Valley Fault Zone, Canyon Lake Gorge, Comal County, Texas

Characterizing natural fracture systems involves understanding fracture types (faults, joints, and veins), patterns (orientations, sets, and spacing within sets), size distributions (penetration across layering, aperture, and trace length), and timing relationships. Traditionally, observation-based relationships to lithology, mechanical stratigraphy, bed thickness, structural position, failure mode, and stress history have been proposed for predicting fracture spacing along with the relative abundance of opening-mode fracture versus faults in fractured rocks. Developing a conceptual fracture model from these relationships can be a useful process to help predict deformation in a fractured reservoir or other fractured rock systems. A major pitfall when developing these models is using assumptions based on general relationships that are often site specific rather than universal. In this paper, we examine a mixed carbonate-shale sequence that is cut by a seismic-scale normal fault where fracture attributes do not follow commonly reported fracture relationships. Specifically, we find (1) no clear relationship between frequency (or spacing) of opening-mode fractures (joints and veins) and proximity to the main fault trace and (2) no detectable relationship between fracture spacing and bed thickness. However, we did find that (1) the frequency of small-displacement faults is strongly and positively correlated with proximity to the main fault trace, (2) fracture networks change pattern and failure mode (extension versus shear fracture) from pavement to pavement through the mechanically layered stratigraphic section, and (3) faults are more abundant than opening-mode fractures in many areas within the fracture network. We interpret that the major fracturing initiated near maximum burial under relatively high-differential stress conditions where shear failure dominated and that mode-1 extension fracturing occurred later under lower differential stress conditions, filling in between earlier formed shear fractures. We conclude that whenever possible, site-specific observations need to be carefully analyzed prior to developing fracture models and perhaps a different set of fracture network rules apply in rocks where shear failure dominates and mechanical stratigraphy influences deformation.

Matrix-Completion-Based Airborne Tomographic SAR Inversion Under Missing Data

Tomographic synthetic aperture radar imaging (TomoSAR) is a new SAR imaging modality that extends the synthetic aperture principle into the elevation direction. In TomoSAR, the elevation resolution depends on the length of elevation aperture and the baseline distribution. When the length of elevation aperture is fixed, the number of baselines is important for the elevation reconstruction. Therefore, improving the elevation imaging quality with the finite amount of baselines is worth researching. This letter proposes a novel missing data compensation approach in TomoSAR via matrix completion (MC), which is a technique of the low-rank matrix recovery from a subset of the matrix elements. In the proposed method, we first exploit MC to estimate the 2-D focused image data of unknown baselines, which are located on the uniform data grid without changing the length of elevation aperture. Based on the recovered data, we then recover the elevation reflectivity function by the spectral analysis (SA) method. Compared with the conventional SA technique, the proposed approach can achieve much higher elevation image quality, due to more available data offered by MC. The effectiveness of the proposed method is validated with the experimental results based on simulated and real airborne data.

Morphometric relationships and relative growth ofHexaplex trunculusandBolinus brandaris(Gastropoda: Muricidae) from the Ria Formosa lagoon (southern Portugal)

The present study reports morphometric relationships and discusses the relative growth in the banded murex (Hexaplex trunculus) and the purple dye murex (Bolinus brandaris) from the Ria Formosa lagoon (southern Portugal). A total of 11 morphometric parameters (eight linear variables: shell length, shell width, total aperture length, aperture length, aperture width, spire length, spire width and siphonal canal length; three ponderal variables: total weight, soft parts weight and shell weight) were analysed in both species. The analyses comprised numerous individuals of both sexes and with broad size ranges (H. trunculus: 10.7–82.8 mm shell length;B. brandaris: 14.6–107.7 mm shell length), fairly representative of the populations from the Ria Formosa lagoon. In general,B. brandarisexhibited greater morphological plasticity and higher variability in shell shape compared withH. trunculus. In both species, the vast majority of morphometric relationships displayed positive allometries, distantly followed by negative allometries and by isometries. AlthoughH. trunculusandB. brandarisare known to lack external sexual dimorphism, several morphometric relationships revealed significant differences in the type of growth between sexes, which should be further confirmed using more powerful techniques, such as geometric morphometric analyses of shell shape.

Optimal design of the multiple-apertures-GaN-based vertical HEMTs with $$\hbox {SiO}_{2}$$ SiO 2 current blocking layer

Gallium nitride (GaN) based vertical high electron mobility transistor (HEMT) is very crucial for high power applications. Combination of advantageous material properties of GaN for high speed applications and novel vertical structure makes this device very beneficial for high power application. To improve the device performance especially in high drain bias condition, a novel GaN based vertical HEMT with silicon dioxide $$(\hbox {SiO}_{2})$$(SiO2) current blocking layer (CBL) was reported recently. In this paper, effects of the thickness of CBL layer and the aperture length on the electrical and breakdown characteristics of GaN vertical HEMTs with $$\hbox {SiO}_{2}$$SiO2 CBL are simulated by using two-dimensional quantum-mechanically corrected device simulation. Intensive numerical study on the device enables us to optimize and conclude that devices with $$0.5\hbox {-}\upmu \hbox {m}$$0.5-μm-thick $$\hbox {SiO}_{2}$$SiO2 layer and $$1\hbox {-}\upmu \hbox {m}$$1-μm-long aperture will be beneficial considerations to improve the device performance. Notably, using the multiple apertures can effectively reduce the on-state conducting resistance of the device. On increasing the number of apertures, the drain current is increased but the breakdown voltage is decreased. Therefore, device with four apertures is taken as an optimized result. The maximum drain current of 84 mA at $$\hbox {V}_\mathrm{G}= 1\,\hbox {V}$$VG=1V and $$\hbox {V}_\mathrm{D}= 30\,\hbox {V}$$VD=30V, and the breakdown voltage of 480 V have been achieved for the optimized device.

Method of Measuring the Distance to an Object Based on One Shot Obtained from a Motionless Camera with a Fixed-Focus Lens

(Received May 12, 2014) The paper presents the method of measuring the distance to the object based on digital image processing. The solution is characterized in that the distance measurement to the object is performed by a motionless camera with established and unchanged parameters during measurement. The camera is equipped with a one non-stereoscopic lens. The measured distance is determined on the basis of one view of an object presented on one image. The image is made at a constant and invariant setting of the optical path such as: focus, aperture and focal length.

Precise Focusing of Airborne SAR Data With Wide Apertures Large Trajectory Deviations: A Chirp Modulated Back-Projection Approach

In the area of airborne synthetic aperture radar (SAR), motion compensation (MOCO) is a crucial technique employed to correct the SAR data affected by nonlinear platform trajectory during data acquisition. Due to range-azimuth coupling and computational burden consideration, some approximations, which are valid for SAR systems of moderate aperture length, are usually adopted in commonly used MOCO approaches. However, a much more accurate SAR data processing approach is appealing to process the low-frequency SAR systems with large aperture length, such as P-band. In this paper, a new MOCO approach with high precision and high efficiency is proposed. After the ω - κ processing and the range-dependent MOCO, the analytical expression of a 2-D spectrum of a partially focused SAR image is given. Afterward, aperture reduction is achieved by a chirp modulation technique. Finally, with high precision and less computation cost, back projection along the new built short apertures (affected by the residual motion errors) is employed to yield a fairly well-focused SAR image. Experimental results on simulated and actual P-band SAR data are presented to verify the performance of the proposed approach.

Fabrication of micro-lens array using surface acoustic wave

A technique to form an optical micro-lens array using surface acoustic wave (SAW) was investigated. The lens has no mechanical moving parts, such as gearing systems, and is composed of a simple structure. A viscoelastic transparent silicone gel film with the thickness of 20 μm was formed on a 128°-rotated Y-cut X-propagation LiNbO3 (LN) substrate between two interdigitated transducers (IDTs). The IDT electrodes consisted of 30 finger pairs with the aperture length of 9.1 mm and the periodic pitch of 200 μm were fabricated on the LN substrate. The IDTs was excited with a continuous sine wave with the amplitude of 0 to 15 Vpp at the resonance frequency (20 MHz) to generate the SAW. The leaky SAW propagated into the gel, and the acoustic radiation force acted to the surface of the gel film so that the surface profile of the gel could change and a micro-lens array could be fabricated on the gel. The lens height could be controlled by varying the voltage applied to the IDTs.

Physiological Responses of Oil Palm Seedlings to the Drought Stress Using Boron and Silicon Applications

A B S T R A C T The objectives of the study were to determine (1) The level of physiological resistance of oil palm seedlings to drought stress by boron (B) and silicon (Si) application and (2) The mechanism of B and Si actions to induce physiological resistance of oil palm seedlings to drought stress. The B and Si were the elements capably inducing the internal resistance of plant tissues to drought stress, especially through physiological resistance mechanisms. Field trial was arranged in the factorial Randomized Complete Block Design (RCBD) using three blocks as replications. The first factor was six dose of B: 0.00, 0.17, 0.44, 0.87 and 1.31 g plantG 1 . The second factor was five dose of Si: 0.00, 1.15, 2.31, 3.46 and 4.69 g plantG 1 . Observations were done on the Nitrate Reductase Activity (NRA), the content of chlorophyll a, b and total, density, length and width of stomatal aperture, stomatal conductance and transpiration rate, photosynthetic rate and photosynthetic activity per plant, dry weight of plant parts and trunk height and diameter of the oil palm seedlings. The data were analyzed using ANOVA and the means were separated using Duncan's multiple range test at 5% level. Meanwhile, the optimum dose of B and Si were determined using regression analysis. The results showed that B and Si application could induce physiological resistance of oil palm seedlings to drought stress. Mechanism of action of B in inducing physiological resistance of oil palm seedlings to drought stress were by increasing of greenish leaves, width of stomatal aperture and photosynthetic activity per plant while Si application capable to increase of greenish leaves and to decrease the density of lower leaf surface stomatal. The optimal dose of B was 0.33-0.57 g/seedlings and the optimal dose of Si was 2.22 g/seedling in inducing physiological resistance of oil palm seedlings to drought stress.

Effects of shading and blocking in linear Fresnel reflector field

In a linear Fresnel reflector field, parallel rows of reflectors in a collector direct the incident sun rays towards a common linear receiver. Some portion of reflector aperture remains unused due to end effect, inter-row shading and blocking. In addition to these factors, cosine effect, cleanliness factor, reflectivity of reflectors, intercept factor, transmissivity of receiver cover, reflectivity of secondary reflector, absorptivity of absorber tube and thermal losses are other factors that contribute to energy losses and thus affect net energy collection by the heat transfer fluid in the absorber, electricity generation and cost of electricity. Conventionally, the collectors are oriented either along North–South or East–West directions in most cases. However the energy collection, electricity generation and cost of electricity need to be found out for all possible collector-orientations lying between North–South and East–West. This can be used in designing collectors for places where the available land strip does not align with any of these two directions. In this work, explicit analytical expressions for energy losses due to cosine effect, end effect, shading and blocking are derived for any desired time interval as functions of length (L) and width (w) of aperture of reflector-row, spacing between adjacent reflector-rows (p), number of reflector-rows in a collector (n), height of receiver (H), collector-orientation angle (Ω) and location. The expressions for the net energy collected by the working fluid, electricity generated by a collector and the cost of electricity are presented. The effects of L, w, p, n, H, Ω and location on energy losses, net energy collection by fluid, electricity generation and cost of electricity are studied. The minimum cost of electricity is found out for different collector-orientations at various locations and relative comparisons have been made. The corresponding collector parameters, annual energy collection by fluid and the annual electricity generation are also found out.

Assessment of Growth Rate of Juvenile African Giant Land Snail, <i>Archachatina marginate</i>, Under Three Feeding Treatments

This study assessed the growth rate of snailets of A. marginata under three feed treatment. Ninety snailets divided into thirty snailets per treatment were used for the study. Data collected include Shell Length, Shell Width, Aperture Length and Weight gained. The results indicate that Treatment C (T C ) had the highest value for all the growth parameters assessed, while Treatment A (T A ) had the least values. The mean Weight gained varied between 16.01±1.92g (T C ) and 12.55±0.90g (T A ) and was significantly different between the treatments (p<0.01), mean length and shell width varied between T A (4.24±0.40, 6.50±0.40) and T C (4.48±0.13, 6.92±0.30) and were not significantly different (p<0.05). The mean mouth aperture of A. marginata fed with T C (4.90±0.19) was greater than and significantly different form T A (4.35±0.30) and T B (4.58±0.28) at p<0.05. These findings indicate that local farmers who feed their snailets with only vegetable leaves and fruits obtained locally could obtain mature snails with good weight and shell growth even without combination with any other feed material.

Recovering a Function from Circular Means or Wave Data on the Boundary of Parabolic Domains

Determining a function from its circular means with restricted centers is crucial for many modern medical imaging and remote sensing applications. Examples include photo- and thermoacoustic tomography, ultrasound imaging, and synthetic aperture radar. In this paper we derive an explicit inversion formula for the case where the centers of the circles of integration are restricted to the boundary of parabolic domains. A similar result is obtained for recovering the initial data of the wave equation from data on the boundary of a parabolic domain. These results show that the universal back-projection formulas, previously known to be exact for half-spaces, discs, and ellipsoids, are also exact for parabolic domains. We further present numerical simulations supporting our theoretical results. There, we also include two previously proposed strategies (dynamic aperture length correction and weight factor correction) accounting for the truncation of the parabola in practical applications.

Pore pressure cohesive zone modeling of hydraulic fracture in quasi-brittle rocks

Hydraulic fracturing technology has been widely applied in the petroleum industry for both waste injection and unconventional gas production wells. The prevailing analytical solutions for hydraulic fracture mainly depend on linear elastic fracture mechanics. These methods can give reasonable prediction for hard rock, but are ineffective in predicting hydraulic fractures in quasi-brittle materials, such as ductile shale and sandstone. One of the reasons is that the fracture process zone ahead of the crack tip and the softening effect should not be neglected for quasi-brittle materials. In the current work, a set of chevron-notch three point bending tests were performed on sandstone samples from an oil field in Ordos Basin, Shaanxi province, China, and the results were compared with the cohesive zone method based on finite element analysis. The numerical results fit the experimental data well and it shows that the cohesive zone model and the Traction-Separation law used in the model are effective in modeling fracture nucleation and propagation in sandstone without considering the porous effect. A 3D pore pressure cohesive zone model was developed to predict nucleation and propagation of a penny-shaped fluid-driven fracture. The predictions were compared with the analytical asymptotic solutions and a field minifrac test from the literature; it shows that the proposed method can not only predict the length and aperture of hydraulic fracture well, but also predict the bottomhole pressure with reasonable accuracy. Based on analytical asymptotic and computational solutions, parametric studies were conducted to investigate the effects of different parameters on the fracture aperture and fracture length, fracture process zone and bottomhole pressure.

Generalized pseudopolar format algorithm for radar imaging with highly suboptimal aperture length

Different from conventional spaceborne or airborne synthetic aperture radar (SAR) with optimal aperture length, an imaging radar with highly suboptimal aperture length acquires the data in short bursts by a geometry spreading over a large range. A polarlike or pseudopolar format grid is introduced to sample data close to the resolution, which presents the design of a separable kernel for efficient FFT implementation. The proposed imaging algorithm formulates the reflectivity image of the target scene as an interpolation-free double image series expansion with two usual approximation-induced phase error terms being taken into account, whereby more generalized application scenarios with high frequency, large bandwidth or larger aperture length for imaging a target scene located within either the far-field or the near-field of the radar aperture are processable with high accuracy. In addition, convergence acceleration methods in computational mathematics are introduced to accelerate the convergence of the image series expansion, so as to make the algorithm more efficient. The proposed algorithm has been validated both qualitatively and quantitatively with an extensive collection of numerical simulations and field measurements of ground-based SAR (GB-SAR) data set.

Natural Convection of a Nanofluid in Inclined, Partially Open Cavities: Thermal Effects

This paper discusses the phenomenon of natural convection flow in an inclined, partially open enclosure filled with –water nanofluid. In the cavity, the horizontal walls and the closed portions of the right wall are thermally insulated. Three thermal cases were considered for the left wall; in the first case, the left wall was considered to be uniformly heated; in the second case, a heat source was attached to the left wall; and in the third, the left wall had a heat sink. For case 2, there is a heat source attached to the left wall. For case 3, the left wall contains a heat sink. The partial differential equations governing the problem were solved numerically using the finite difference method. The obtained results were presented by the local Nusselt number, the average Nusselt number, streamlines, and isotherms with various pertinent parameters, namely, the Rayleigh number (), the solid volume fraction (), different lengths of the heat source/sink (), different locations of the heat source/sink (), different lengths of the aperture (), different locations of the aperture (), and an inclination angle (). It is found that, for all cases, the fluid features were strongly affected by changing the aperture length or the aperture location. Also, a clear increase in the mean Nusselt number could be obtained by increasing the Rayleigh number.Moreover, an enhancement in the average Nusselt number was found by increasing the nanoparticle volume fraction. A good natural convection could be obtained by increasing the heat source/sink length. Title the cavity by 60 deg leads to increase the absolute values of the stream function and a decrease in the maximum values of the maximum temperature. The best location of the heat source was found to be at the top of the left wall, whereas the best position of the aperture was found to be at the top of the right wall.

Fracture Capillary Pressure Based on the Liquid Bridge Dynamic Stability Study

Performance study of gas oil gravity drainage in stacks of overwhelmed blocks in a gas-invaded zone of naturally fractured reservoirs presents difficult challenges to petroleum engineers. It is believed that there exists some degree of block-to-block interaction that may lead to capillary continuity in fractured reservoirs. Effect of such continuity in gravity drainage is much more pronounced as it increases the height of the continuous fluid column in a reservoir and thereby the recovery of oil as height is a key parameter in gravity drainage mechanisms. It has been experimentally proven that liquid or solid bridges in horizontal fracture can contribute to wetting phase transfer across the horizontal fracture, but there is no mathematical model that predicts the probability of such continuity. In this article, a mathematical model developed by using 1-D Navier-Stock for the free surface flow equation and Young-Laplace of capillary for breakage of the stable liquid bridge held between two pairs of support while stretching. The model gives critical length of fracture aperture, which surely provides capillary continuity. Moreover, the developed model shows flow dependency of fracture capillary pressure and predicts a nonzero value for this parameter, while in the past many researchers used zero fracture capillary pressure for history matching of fractured reservoirs.

Morphological analysis of the Chinese Cipangopaludina species (Gastropoda; Caenogastropoda: Viviparidae).

Viviparidae are widely distributed around the globe, but there are considerable gaps in the taxonomic record. To date, 18 species of the viviparid genus Cipangopaludina have been recorded in China, but there is substantial disagreement on the validity of this taxonomy. In this study, we described the shell and internal traits of these species to better discuss the validity of related species. We found that C. ampulliformis is synonym of C. lecythis, and C. wingatei is synonym of C. chinensis,while C. ampullacea and C. fluminalis are subspecies of C. lecythis and C. chinensis, respectively. C. dianchiensis should be paled in the genus Margarya, while C. menglaensis and C. yunnanensisbelong to genus Mekongia. Totally, this leaves 11 species and 2 subspecies recorded in China. Based on whether these specimens' spiral whorl depth was longer than aperture depth, these species or subspecies can be further divided into two groups, viz. chinensis group and cathayensis group, which can be determined from one another via the ratio of spiral depth and aperture depth, vas deferens and number of secondary branches of vas deferens. Additionally, Principal Component Analysis indicated that body whorl depth, shell width, aperture width and aperture length were main variables during species of Cipangopaludina. A key to all valid Chinese Cipangopaludina specieswere given.