Random Aperture Research Articles

Influence of extreme fracture flow channels on the thermal performance of open-loop geothermal systems at commercial scale

Adequate stewardship of geothermal resources requires accurate forecasting of long-term thermal performance. In enhanced geothermal systems and other fracture-dominated reservoirs, predictive models commonly assume constant-aperture fractures, although spatial variations in aperture can greatly affect reservoir permeability, fluid flow distribution, and heat transport. Whereas previous authors have investigated the effects of theoretical random aperture distributions on thermal performance, here we further explore the influence of permeability heterogeneity considering field-constrained aperture distributions from a meso-scale field site in northern New York, USA. Using numerical models of coupled fluid flow and heat transport, we conduct thermal–hydraulic simulations for a hypothetical reservoir consisting of a relatively impervious porous matrix and a single, horizontal fracture. Our results indicate that in highly channelized fields, most well design configurations and operating conditions result in extreme rates of thermal drawdown (e.g., 50% drop in production well temperatures in under 2 years). However, some other scenarios that account for the risks of short-circuiting can potentially enhance heat extraction when mass flow rate is not excessively high, and the direction of geothermal extraction is not aligned with the most permeable features in the reservoir. Through a parametric approach, we illustrate that well separation distance and relative positioning play a major role in the long-term performance of highly channelized fields, and both can be used to help mitigate premature thermal breakthrough.

3-D H-scan ultrasound imaging of relative scatterer size using a matrix array transducer and sparse random aperture compounding

H-scan ultrasound (US) is a high-resolution imaging technique for soft tissue characterization. By acquiring data in volume space, H-scan US can provide insight into subtle tissue changes or heterogenous patterns that might be missed using traditional cross-sectional US imaging approaches. In this study, we introduce a 3-dimensional (3-D) H-scan US imaging technology for voxel-level tissue characterization in simulation and experimentation. Using a matrix array transducer, H-scan US imaging was developed to evaluate the relative size of US scattering aggregates in volume space. Experimental data was acquired using a programmable US system (Vantage 256, Verasonics Inc, Kirkland, WA) equipped with a 1024-element (32 × 32) matrix array transducer (Vermon Inc, Tours, France). Imaging was performed using the full array in transmission. Radiofrequency (RF) data sequences were collected using a sparse random aperture compounding technique with 6 different data compounding approaches. Plane wave imaging at five angles was performed at a center frequency of 8 MHz. Scan conversion and attenuation correction were applied. To generate the 3-D H-scan US images, a convolution filter bank (N = 256) was then used to process the RF data sequences and measure the spectral content of the backscattered US signals before volume reconstruction. Preliminary experimental studies were conducted using homogeneous phantom materials embedded with spherical US scatterers of varying diameter, i.e., 27 to 45, 63 to 75, or 106–126 μm. Both simulated and experimental results revealed that 3-D H-scan US images have a low spatial variance when tested with homogeneous phantom materials. Furthermore, H-scan US is considerably more sensitive than traditional B-mode US imaging for differentiating US scatterers of varying size (p = 0.001 and p = 0.93, respectively). Overall, this study demonstrates the feasibility of 3-D H-scan US imaging using a matrix array transducer for tissue characterization in volume space.

Quantitation of the uncertainty in the prediction of flow fields induced by the spatial variation of the fracture aperture

The problem of fluid flow in a single fracture with variable aperture is analyzed from a stochastic point of view. The spatially distributed fracture aperture is treated as a random variable and the random aperture process can be characterized as a zero-order intrinsic random process (nonstationary random process with homogeneous increments), resulting in nonstationary flow fields. To characterize the stochastic behavior of the flow process, the general solutions for the mean values of and variances of the pressure head and the integrated flux in the mean flow direction are derived. These derivations are performed using the Fourier-Stieltjes representation approach. The mean is an unbiased estimator and the variance can be used to characterize the uncertainty of the mean model. The theory is applied to the case where the process of random aperture can be described as fractal Brownian motion. The analysis shows that the larger the parameter H, the greater the variance of pressure head and integrated flux. The transfer function helps smooth out much of the small-scale variation caused by the random aperture field. The variance (uncertainty) of the integrated flux in x-direction around the mean flux (or the classical deterministic model solution) increases with distance. Estimation of total flux through a natural fractured system is often evaluated for the purpose of rational management of groundwater resources. The proposed stochastic theory for flow prediction under uncertainty under the natural field conditions as input to the flow model for a fractured system should provide useful information for regional groundwater resource management. To our knowledge, the subject of fluid flow in nonstationary random flow fields has not yet been addressed in fracture. Our findings will be useful for the interpretation of real field data and as a stimulus for further research in this area.

Close packed random rectangular microlens array used for laser beam homogenization

When the high coherence laser beam is homogenized by microlens array (MLA), interference fringes will be generated reducing the uniformity of homogenized spot. A novel close packed random rectangular microlens array (rRMLA) is proposed to solve this problem. By designing the MLA with random apertures and random focal lengths of sub-lenses, the phase regulation can be realized, so as to disturb the coherent superposition fringes for improving the uniformity. To realize the dense arrangement of a MLA with random rectangular aperture, an iterative segmentation method is proposed to design the structure of rRMLA with controllable divergence angle and high filling factor. Theoretical simulations and experimental results both demonstrate the improvement of uniformity of the homogenized spot based on the proposed rRMLA.

Integrated Double-Sided Random Microlens Array Used for Laser Beam Homogenization.

Double microlens arrays (MLAs) in series can be used to divide and superpose laser beam so as to achieve a homogenized spot. However, for laser beam homogenization with high coherence, the periodic lattice distribution in the homogenized spot will be generated due to the periodicity of the traditional MLA, which greatly reduces the uniformity of the homogenized spot. To solve this problem, a monolithic and highly integrated double-sided random microlens array (D-rMLA) is proposed for the purpose of achieving laser beam homogenization. The periodicity of the MLA is disturbed by the closely arranged microlens structures with random apertures. And the random speckle field is achieved to improve the uniformity of the homogenized spot by the superposition of the divided sub-beams. In addition, the double-sided exposure technique is proposed to prepare the rMLA on both sides of the same substrate with high precision alignment to form an integrated D-rMLA structure, which avoids the strict alignment problem in the installation process of traditional discrete MLAs. Then the laser beam homogenization experiments have been carried out by using the prepared D-rMLA structure. The laser beam homogenized spots of different wavelengths have been tested, including the wavelengths of 650 nm (R), 532 nm (G), and 405 nm (B). The experimental results show that the uniformity of the RGB homogenized spots is about 91%, 89%, and 90%. And the energy utilization rate is about 89%, 87%, 86%, respectively. Hence, the prepared structure has high laser beam homogenization ability and energy utilization rate, which is suitable for wide wavelength regime.

Impact of rock fracture geometry on geotechnical barrier integrity – A numerical study

The effect of fracture geometry on bentonite erosion for a generic repository site in crystalline host rock environment was investigated by means of 2-d numerical simulations. Fracture geometry was varied systematically using random aperture normal distributions with a mean aperture of 1 mm and standard deviations between 0 and 0.7 mm, respectively. Moreover, two aperture correlation lengths (0.2 m and 2 m) were applied. Based on the synthetic fracture aperture fields generated the cubic law in conjunction with the Darcy equation is used to simulate fracture flow fields for mean flow velocities in the fracture between 1 × 10−5 m/s and 1 × 10−7 m/s. These flow fields are used in a two-way coupling approach to bentonite erosion simulations.The results of the study clearly show the influence of variable fracture aperture on bentonite erosion behaviour and erosion rates (kg/a). Increasing fracture aperture standard deviation leads to increasing heterogeneous flow velocity distributions governing the erosion behaviour and erosion rates. Calculated steady state erosion rates are in the range of ~0.25 kg/a down to ~0.014 kg/a. The highest erosion rate is calculated for the highest mean flow velocity in conjunction with the highest standard deviation. The effect of aperture heterogeneity diminishes for the lowest flow velocities.In summary, the results show the effect of fracture heterogeneity on bentonite erosion, especially for high to medium mean flow velocities combined with high to medium fracture heterogeneity under the model boundary conditions and model capabilities and limitations considered. An increase of up to ~83% in erosion rate compared to the constant aperture case highlights the need to consider fracture aperture heterogeneity and its effect on the bentonite erosion in the assessment of the safety and evolution of a high-level nuclear waste repository.

Method of Green’s Potentials for Elliptic PDEs in Domains with Random Apertures

Problems with topological uncertainties appear in many fields ranging from nano-device engineering to the design of bridges. In many of such problems, a part of the domains boundaries is subjected to random perturbations making inefficient conventional schemes that rely on discretization of the whole domain. In this paper, we study elliptic PDEs in domains with boundaries comprised of a deterministic part and random apertures, and apply the method of modified potentials with Green's kernels defined on the deterministic part of the domain. This approach allows to reduce the dimension of the original differential problem by reformulating it as a boundary integral equation posed on the random apertures only. The multilevel Monte Carlo method is then applied to this modified integral equation and its optimal $\epsilon^{-2}$ asymptotical complexity is shown. Finally, we provide the qualitative analysis of the proposed technique and support it with numerical results.

Back-projection imaging algorithm of random noise frequency modulation continuous wave SAR

The combination of random noise frequency-modulation continuous wave technology and synthetic aperture radar (SAR) promises a cost-effective, low probability of intercept and high electromagnetic compatibility. This paper analyses the time-domain restricting algorithms for random noise frequency modulation continuous wave (RNFMCW) SAR. Two versions of the back-projection algorithm are proposed. At first, the radar antenna continuous motion in a pulse repetition period of RNFMCW SAR is analysed. Then the phase term which is caused by the continuous motion is described by a approximate expression with Taylor expansion. Meanwhile, both the start-stop approximate back-projection algorithm and the modified back-projection algorithm are proposed. In the end, with the help of numerical simulation, the limitations of the start-stop approximation back-projection algorithm and the validity of the modified back-projection algorithms are illustrated.

Coherent amplitude modulation imaging based on partially saturated diffraction pattern.

A single-shot phase retrieval algorithm based on a random aperture and partially saturated diffraction pattern is proposed. The diffraction pattern in the saturated area could be retrieved during the iterative process, which circumvents the problem of limited dynamic range of the detector. Besides, the random aperture is easier to be manufactured and if the accuracy of the random aperture is high enough, the design value could be used directly for iterations. It has the potential to be adapted for different wavelengths without additional transmission measurement of the wave modulator. The validity has been demonstrated by simulations and experiment.

AUTOCORRELATIONS OF RANDOM FRACTAL APERTURES AND PHASE SCREENS

We introduce a new product representation for general random binary fractal apertures defined by removing voids from Euclidean space, and use it to derive a simple closed-form expression for ensemble-averaged correlations. Power-law scaling at short distance follows almost immediately. Similar techniques provide easy constructions of objects with fractional Brownian short-distance behavior for phase screens and other applications.

Effect of random fracture aperture on the transport of colloids in a coupled fracture-matrix system

A variable aperture model, including the random variation of fracture aperture as against the conventional parallel plate model, has been developed to adequately examine the transport of colloids/suspended particles in a single coupled fracturematrix system. Rather than relying on a complex geostatistical method for an accurate representation of fracture aperture, which requires an enormous field data and resource for its validation, a simple statistical method (linear congruential generator) is implemented in the present article. The random variation of fracture aperture is an honest representation of the unpredictable geometry/ morphology of fracture aperture in comparison with widely applied the conventional parallel plate model or the simple mathematical functions based on fractal theory (self-affine structures). A considerable number of parameters are involved in investigating the extent of penetration of colloids into the rock matrix, which creates complexity and ambiguity in the analysis. To overcome this problem, a single parameter “Maximum Penetration Factor” has been introduced for simple and reliable assessment of diffusion of colloids within the rock matrix. Additionally, a non-dimensional parameter ‘Matrix Mitigation Factor’ has been introduced in the present study, which can provide a means of evaluating the diffusion of suspended particles within the rock matrix when it comes to real time applications like microbial enhanced recovery (MEOR) and chemical enhanced recovery (CEOR) in the petroleum industry (nanoparticles and nanofluids). A semi-implicit finite difference model has been adopted for solving the coupled partial differential equations in the present numerical study. Finally, Neumann and Robinson boundary conditions as a function of time have been applied at the fracture inlet to better represent the field scenario as against the conventional constant source condition (Dirichlet). The model results indicate that there is a difference in concentration between the parallel plate model and random fracture model when it comes to colloidal concentration in the fracture and rock matrix. The variance in concentration is due to the inclusion of variation of the aperture in the variable aperture model, which is absent in the parallel plate model. Additionally, the results suggest that the variable source boundary condition has a significant influence on the transport of colloids in fracture-matrix system. Finally, from the evaluation of the extent of diffusion of colloids into rock matrix, it was concluded that that variable aperture model is associated with more mitigation of colloids compared to the parallel plate model, especially in the case of random fracture.

Near-field surface plasmons on quasicrystal metasurfaces.

Excitation and manipulation of surface plasmons (SPs) are essential in developing cutting-edge plasmonic devices for medical diagnostics, biochemical spectroscopy and communications. The most common approach involves designing an array of periodic slits or grating apertures that enables coupling of the incident light to the SP modes. In recent years, plasmonic resonances, including extraordinary optical transmission through periodic arrays, quasicrystals and random aperture arrays, have been investigated in the free space. However, most of the studies have been limited to the far field detection of the transmission resonance. Here, we perform near-field measurements of the SPs on quasicrystal metasurfaces. We discover that the reciprocal vector determines the propagation modes of the SPs in the quasicrystal lattice which can be well explained by the quasi-momentum conservation rule. Our findings demonstrate vast potential in developing plasmonic metasurfaces with unique device functionalities that are controlled by the propagation modes of the SPs in quasicrystals.

Improved resolution integral imaging using random aperture coding based on compressive sensing

The low-resolution of the three-dimensional (3D) image is the main limitation for the development of integral imaging. We proposed a resolution enhanced integral imaging method by using a randomly coded aperture based on compressive sensing (CS). The compressive integral imaging model is derived based on wave optics theory. Instead of sensing raw pixel data, the recording device measures the compressive samples of the observed 3D scene through a random phase mask attached to each lenslet. The coded elemental images are captured with a single exposure and the super-resolution elemental images can be reconstructed by an optimization algorithm. In this paper, we use CS in the acquisition of the elemental images, and ultimately on improving the image quality of reproduced 3D scene either by optical experiment or computational method. Both the theoretical model and experimental results show the feasibility of the proposed method.

Compressive Sensing and Recovery for Binary Images

We propose a method for compressive sensing and recovery of binary images. To achieve this, we combine two ideas: in the sensing step, ordered aperture patterns are employed instead of random aperture patterns, and in the recovery step, a dense reconstruction scheme replaces sparse reconstruction. We demonstrate that this approach is more effective for binary images than the state-of-the-art algorithms relying on random sensing and sparse reconstruction.

An Imaging Algorithm for Random Noise Synthetic Aperture Radar Based on Double Spectral Signal Processing

An Imaging Algorithm for Random Noise Synthetic Aperture Radar Based on Double Spectral Signal Processing

Fluid trapping during capillary displacement in fractures

The spatial distribution of fluid phases and the geometry of fluid–fluid interfaces resulting from immiscible displacement in fractures cast decisive influence on a range of macroscopic flow parameters. Most importantly, these are the relative permeabilities of the fluids as well as the macroscopic irreducible saturations. They also influence parameters for component (solute) transport, as it usually occurs through one of the fluid phase only. Here, we present a numerical investigation on the critical role of aperture variation and spatial correlation on fluid trapping and the morphology of fluid phase distributions in a geological fracture. We consider drainage in the capillary dominated regime. The correlation scale, that is, the scale over which the two facing fracture walls are matched, varies among the investigated geometries between L/256 and L (self-affine fields), L being the domain/fracture length. The aperture variability is quantified by the coefficient of variation (δ), ranging among the various geometries from 0.05 to 0.25. We use an invasion percolation based model which has been shown to properly reproduce displacement patterns observed in previous experiments. We present a quantitative analysis of the size distribution of trapped fluid clusters. We show that when the in-plane curvature is considered, the amount of trapped fluid mass first increases with increasing correlation scale Lc and then decreases as Lc further increases from some intermediate scale towards the domain length scale L. The in-plane curvature contributes to smoothening the invasion front and to dampening the entrapment of fluid clusters of a certain size range that depends on the combination of random aperture standard deviation and spatial correlation.

Fresnel diffraction by a square aperture with rough edge

In this paper, we study Fresnel diffraction of a square aperture with rough edge with Gaussian random process. The diffraction intensity formula depending on the random parameters is deduced by use of the scalar diffraction theory. The simulation calculations of the diffraction of the square aperture with different statistic parameters are performed. The diffraction intensity distributions exhibit elaborately the influence of the random parameters of rough edge on the diffraction of a square aperture. The results show that the larger the lateral correlation length and the larger roughness of the rough edge are, the more severe the modulation of the random spots is and the more unsymmetrical the diffraction distribution is. For the same random parameters, the modulation degree of the random spots changes with the propagation distance. Moreover, we also manufacture practically the random apertures with the help of the laser direct writing technology, and measure the diffraction distribution of the square aperture with random edge. The experimental results are consistent with the theoretic ones. These results will be instructively meaningful for the applications of the diffraction of the practical aperture.

Statistical models of the wave field of a random aperture antenna

The method of statistical imitation simulation (SIS) is applied to analyze the characteristics of the electromagnetic field produced by a random aperture antenna (RAA) excited by a harmonic signal with a preassigned distribution of amplitude and phase errors. In the study, SIS models of the orthogonal and quadrature components of the RAA field intensity vector and its scalar E are considered. As the conditions for the applicability of the central limit theorem of the probability theory are fulfilled, these models approach standard models (the normal law, the Rayleigh and Rice laws, the distribution of the scalar of a multidimensional vector with normal components).

Statistical characteristics of the field of an array of random aperture antennas

The subject area and the initial data for statistical simulation of the field generated by an antenna array consisting of three rectangular apertures excited by a random signal and representing a three-element aperture random antenna (RA) are considered. Results of the analysis of statistical characteristics of the amplitude and phase of the RA field are presented in the form of histograms of their random deviations from deterministic values, which are caused by the influence of amplitude and phase errors.

Research on Compressive Sensing‐Based 3D Imaging Method Applied to GPR

ABSTRACTResults in theory of compressive sensing enable the reconstruction of sparse signals from a small set of nonadaptive linear measurements by solving a convex optimization problem. Considering the sparse structure of actual target space in ground penetrating radar (GPR) application, three‐dimensional imaging method based on random aperture compressive sensing (RACS) is brought up, which requires the GPR transceiver to record only a minimum amount of samples through incoherent measurement at each aperture point, and only to measure a small number of random apertures in x‐y plane of interested target space. Simulation and experimental results verified that the proposed RACS method allow much fewer measurement aperture points, and has much sparse imaging results with much higher resolution. © 2013 Wiley Periodicals, Inc. Microwave Opt Technol Lett 55:2896–2901, 2013