Late Time Response Research Articles

Novel analytical solution for solvent-solute flow: Application to pressure transmission testing of reactive shales

Coupled solvent-solute flow is a common phenomenon observed while drilling shale formations using water-based fluids, leading to unfavorable outcomes. Designing optimal fluid formulation requires laboratory tests, such as pressure transmission tests, to evaluate shale-fluid interactions. In this study, an analytical solution was derived for the coupled flow of solvent-solute under pressure transmission testing conditions. It was derived based on the semi-infinite domain solution employing the method of images. The solution was then verified against the semi-analytical solution from the literature. The analysis of the solution revealed that early time pressure response at the outer boundary is primarily governed by hydraulic diffusivity while late time response is by ion diffusion. It also showed that the coefficient of lambda, introduced during derivations, quantifies the chemical effects. In addition, sensitivity analysis was conducted to better understand how variations in key parameters impact the overall transport processes within reactive shales. Finally, a good agreement was obtained by comparing the analytical solution with experimental data from various published sources. The solution will help researchers in gaining new insights into the shale fluid interactions and designing optimal fluid formulations.

Extracting Pole Characteristics of Complex Radar Targets for the Aircraft in Resonance Region Using RMSPSO_ARMA

The extraction algorithm of target characteristics resonance set at the high-frequency band plays a significant role in defense applications like early warning. The paper proposes a new method to extract the characteristic resonance set of radar targets in the resonance frequency region using an autoregressive moving average model optimized by root mean square propagation particle swarm optimization. Considering that the total scattering response in the resonant region consists of early-time and late-time responses, the autoregressive moving average model approximate the total scattering responses to avoid errors caused by intercepting the late-time response. Further, the paper investigated the impact of the swarm optimization algorithm on the accuracy of moving average model parameters when obtaining the resonance set at different target aspects. The extracted characteristic resonance results within a range of azimuth directions through an aircraft target paradigm indicate that the new method is more convenient and precise than the matrix beam prediction method.

A pulse-decay method for low (matrix) permeability analyses of granular rock media

Abstract. Nanodarcy level permeability measurements of porous media, such as nano-porous mudrocks, are frequently conducted with gas invasion methods into granular-sized samples with short diffusion lengths and thereby reduced experimental duration; however, these methods lack rigorous solutions and standardized experimental procedures. For the first time, we resolve this by providing an integrated technique (termed gas permeability technique, GPT) with coupled theoretical development, experimental procedures, and data interpretation workflow. Three exact mathematical solutions for transient and slightly compressible spherical flow, along with their asymptotic solutions, are developed for early- and late-time responses. Critically, one late-time solution is for an ultra-small gas-invadable volume, important for a wide range of practical usages. Developed to be applicable to different sample characteristics (permeability, porosity, and mass) in relation to the storage capacity of experimental systems, these three solutions are evaluated from essential considerations of error difference between exact and approximate solutions, optimal experimental conditions, and experimental demonstration of mudrocks and molecular-sieve samples. Moreover, a practical workflow of solution selection and data reduction to determine permeability is presented by considering samples with different permeability and porosity under various granular sizes. Overall, this work establishes a rigorous, theory-based, rapid, and versatile gas permeability measurement technique for tight media at sub-nanodarcy levels.

Osteoporosis detection with microwave signals: An investigation into natural resonance frequencies

This study analyses the dispersion behavior of microwave signals passing through biological tissues by considering various electromagnetic relaxation phenomena. The investigation concentrates on the impact of this dispersion behaviour on human bone tissues causing the health conditions of osteoporosis. Based on the attenuation profile through biological tissues, an optimum frequency range of operation is identified to capture the comprehensive target tissue profiles without minimal loss of signal strength in surrounding tissues. The dispersion through a human wrist model is analysed by extracting the late-time response. A pioneering aspect of this study lies in its utilization of the natural resonant frequency plane as a tool to gauge the dielectric properties of bone tissue, offering insights into its mineral content. To improve the ease of use and diagnostic accuracy, an automated multi-class classification using standard machine learning algorithms is developed during the final response analysis. The proposed approach effectively and accurately classifies the progression of osteoporosis.

Clutter Effect on a Combination of Microwave Imaging and Target Identification Using Ground-Penetrating Radar

This paper presents an experimental investigation of the effect of clutter on the performance of microwave imaging and target identification using ground-penetrating radar (GPR) for buried objects. Signals collected by the GPR were formed to be B-scan and 3D images to carry out the microwave imaging of buried objects. Poles extracted using the short-time matrix pencil method from a late-time response of the received signal collected at a specific position were exploited to identify buried objects. The experiment was set up by constructing a large box filled with sand where an L-shaped metallic sheet was buried. The GPR was installed along with a 2-dimensional scanner above the box to image and identify the buried metallic sheet. In order to investigate the effect of the clutter on the performance of the GPR-based microwave imaging and target identification, small rocks were arranged on the sand surface, and their density was then varied. The experimental results have shown that clutter density significantly affects the sharpness of the B-scan and 3D images. The rocks result in an additional surface layer in the images. Moreover, the results have also shown that the clutter does not affect the performance of the identification of the buried object. From the results, the poles obtained from the GPR scanning inside and outside the buried object region differed. This confirms that the poles of the buried object should be different from those without the object. The poles of the buried object remain constant, although rocks on the sand surface exist since the clutter affects only the early-time response (not the late-time response). With varying clutter densities, the underlying poles were significantly changed, but this does not affect the identification of the buried object.

Approximate extraction of late-time returns via morphological component analysis

A fundamental challenge in acoustic data processing is to separate a measured time series into relevant phenomenological components. A given measurement is typically assumed to be an additive mixture of myriad signals plus noise whose separation forms an ill-posed inverse problem. In the setting of sensing elastic objects using active sonar, we wish to separate the early-time return from the object's geometry from late-time returns caused by elastic or compressional wave coupling. Under the framework of morphological component analysis (MCA), we compare two separation models using the short-duration and long-duration responses as a proxy for early-time and late-time returns. Results are computed for a broadside response using Stanton's elastic cylinder model as well as on experimental data taken from an in-air circular synthetic aperture sonar system, whose separated time series are formed into imagery. We find that MCA can be used to separate early and late-time responses in both the analytic and experimental cases without the use of time-gating. The separation process is demonstrated to be compatible with image reconstruction. The best separation results are obtained with a flexible, but computationally intensive, frame based signal model, while a faster Fourier transform based method is shown to have competitive performance.

Approximate extraction of late-time returns via morphological component analysis

A fundamental challenge in acoustic data processing is to separate a measured time series into relevant phenomenological components. In the setting of sensing elastic objects using active sonar, we wish to separate the early-time returns (e.g., returns from the object's exterior geometry) from late-time returns caused by elastic or compressional wave coupling. Under the framework of morphological component analysis (MCA), we compare two separation models using the short-duration and long-duration responses as a proxy for early-time and late-time returns. Results are computed for broadside geometries using Stanton's elastic cylinder model as well as experimental data taken from an in-air circular synthetic aperture sonar (AirSAS) system, whose separated time series are formed into imagery. We find that MCA can be used to separate early and late-time responses in both the analytic and experimental cases without the use of time-gating. The separation process is demonstrated to be robust to noise and compatible with AirSAS image reconstruction. The best separation results are obtained with a flexible, but computationally intensive, frame based signal model, while a faster Fourier Transform based method is shown to have competitive performance.

Pressure transient analysis for stress-sensitive fractured wells with fracture face damage

Fracture networks improve wells’ deliverability of fluids from underground reservoirs. However, conductive fractures may lose efficiency because of fracture closure or formation damage that needs to be monitored and detected for proper reservoir management and intervention. Fracture hydraulic conductivity is a function of fracture geometry and its hydraulic aperture, which tends to degrade during operations because of fracture compaction and closure. Furthermore, pore-clogging of fracture walls (faces) results in a damaging skin zone that may reduce fracture-matrix transmissibility. Current Pressure Transient Analysis (PTA) models in the literature do not consider the interconnected combined effect of stress-dependent conductivity of fractures and fracture face skin. Modeling fracture closure without accounting for the skin effect may mislead the PTA interpretations of well performance. This work proposes a rigorous PTA model to account for fracture closure combined with fracture face skin for single and multistage hydraulic fractures with uniform and complex geometries. The solution approach is based on subdividing the domain into three flow regions, matrix, damage zone, and hydraulic fracture (HF). The proposed model is verified extensively using a commercial simulator and other less comprehensive models from the literature. The pressure response in fractured wells with stress-sensitive fractures is analyzed at early, middle, and late times. In each flow regime, we identify pressure signals to detect fracture closure by incorporating fracture closure and skin effects. Results show that the fracture face skin has a significant effect on fracture performance as it introduces an additional pressure drop that triggers an earlier and more pronounced occurrence of fracture closure. We proposed a semi-log approach to identify fracture closure for low compressible fractures and a pseudo-radial simplification to generate late-time response curves. The proposed method serves as a PTA diagnostic tool to detect fracture conductivity degradation due to fracture closure and formation damage.

Pole Feature Extraction of HF Radar Targets for the Large Complex Ship Based on SPSO and ARMA Model Algorithm

Radar target characteristics need to be accurately extracted to enhance the role of high-frequency (HF) radar target recognition technology in modern radar, sea and air monitoring, and other applications. The pole characteristics of radar targets have become a mainstream research focus because of their inherent advantages for target recognition. However, existing pole extraction methods for complex targets generally have problems in early- and late-time responses aliasing and target information loss. To avoid this problem, this study proposes a new method to extract radar target poles based on the special particle swarm optimization algorithm (SPSO) and an autoregressive moving average (ARMA) model. This method, which does not involve the distinction between early-and late-time responses, is used to estimate an approximation of the entire scattering echo of the target. Then the parameters of the model are precisely optimized with the help of a particle swarm optimization algorithm combined with opposition-based learning and inertia weight decreasing. Strategy. Owing to the characteristics of the azimuth consistency of the target poles, a sliding window is used to calibrate the positions of multi-azimuth poles in the complex plane. The method was demonstrated to be feasible with good performance when it was applied to extract the pole features of ships at different azimuths in the high-frequency band.

Underground Target Localization Based on Improved Magnetic Gradient Tensor With Towed Transient Electromagnetic Sensor Array

Errors of target localization with the traditional magnetic gradient tensor mainly comes from three aspects, namely, the large error of the magnetic gradient tensor for shallow targets, the low signal-to-noise ratio (SNR) of the response for deep targets, and the overlapping responses of multi-targets. In this study, a towed transient electromagnetic sensor with a <inline-formula> <tex-math notation="LaTeX">$3\times3$ </tex-math></inline-formula> receiving coils array is constructed. On the basis of the sensor array, an improved magnetic gradient tensor is proposed to accurately locate targets. For shallow targets, the magnetic gradient tensor is constructed using the responses of four adjacent receiving coils to reduce the error of the magnetic gradient tensor. For deep targets, all the responses of nine receiving coils are used to improve the SNR. Both the early and late time responses are used to roughly estimate the positions of multi-targets to improve the localization accuracy. Experimental results show that for underground targets within 2 m, the depth errors of the targets do not exceed 10 cm, and the horizontal errors of the targets are mostly within 10 cm, even if the responses of two adjacent targets overlap each other, indicating that the proposed method can effectively improve the localization accuracy of underground targets.

Dynamic adaptive mesh optimisation for immiscible viscous fingering

Immiscible fingering is challenging to model since it requires a very fine mesh for the numerical method to capture the interaction of the shock front with the capillary pressure. This can result in computationally intensive simulations if a fixed mesh is used. We apply a higher order conservative dynamic adaptive mesh optimisation (DAMO) technique, to model immiscible viscous fingering in porous media. We show that the approach accurately captures the development and growth of the interfacial instability. Convergence is demonstrated under grid refinement with capillary pressure for both a fixed unstructured mesh and with DAMO. Using DAMO leads to significantly reduced computational cost compared to the equivalent fixed mesh simulations. We also present the late-time response of viscous fingers through numerical examples in a 2D rectangular domain and in a 3D cylindrical geometry. Both problems are computationally challenging in the absence of DAMO. The dynamic adaptive problem requires up to 36 times fewer elements than the prohibitively expensive fixed mesh solution, with the computational cost reduced accordingly.

Extrapolation of the High Frequency and Late Time Response With Local Linear Basis Functions and Its Application in Evaluating Lightning Electric Field

To avoid numerical inaccuracy of the transient solution by the time-domain solvers or frequency-domain solvers, a simultaneous extrapolation approach reconstructing of the wide-band frequency spectrum using low-frequency and early-time data by the local linear basis functions is presented. The basic idea is transforming the transient integral equations into the analytical-form matrix equation, which can be solved using basis functions with a local support. By means of the early-time and low-frequency data, the matrix equation is solved by the method of singular value decomposition to obtain the wide-band spectrum. The proposed approach is validated by several numerical examples and applied in calculating the transient horizontal electric field of a lightning channel. The major advantage of the presented approach is an efficient and stable algorithm that can be generalized to apply to other transient scenarios when frequency- and time-domain-based transient analysis are involved.

On the influence of the soil stratification and frequency-dependent parameters on lightning electromagnetic fields

We present an analysis of lightning electromagnetic fields taking into account the soil stratification and frequency dependence of its electrical parameters. Two current waveforms corresponding to typical first and subsequent return strokes are considered for the analysis. Different cases for the soil (homogeneous, 2-layer, frequency-dependent/constant electrical parameters) are considered. The analysis is carried out considering different distance ranges: close (50m), intermediate (5km) and distant (100km). The obtained results confirm that the vertical electric field and the azimuthal magnetic field at close range can be evaluated assuming the ground as a perfectly conducting plane. The impact of the soil stratification and frequency-dependent parameters on the vertical electric field and azimuthal magnetic field appear at intermediate and distant ranges. On the other hand, the horizontal electric field is found to be very sensitive to the ground stratification for all the considered distance ranges. However, at close range, the impact of the soil becomes less significant for observation points that are located at above-ground heights of 10m or higher. It is shown that the three field components are affected more markedly by the soil stratification than by the frequency dependence of its electrical parameters, especially for intermediate and distant ranges (i.e., 5km and 100km). Furthermore, subsequent return stroke fields are more significantly affected by the soil stratification and frequency-dependence compared to first return stroke fields. The impact of the frequency-dependent soil parameters on the considered field components is more noticeable in a poorly conducting soil compared to a good conducting soil. We present also a comparison between simulation results with simultaneous measurements of current and distant vertical electric fields associated with rocket-triggered lightning flashes. It is shown that the computed vertical electric field waveforms for the case of a two-layer soil follow to a much better extent the corresponding experimental waveforms compared a non-stratified ground model. The frequency-dependence of the soil affects slightly the early-time response of the field. However, the late-time response of the field is essentially determined by the soil stratification.

Estimation of target circumferential size by backscattered wave

Most of target identification methods compare information of the backscattered field with an existing lookup table. Therefore, the identification of targets outside the table is impossible. However, by applying proper signal processing algorithms, some information about the target can be deduced. In this study, a new approach to estimate the circumferential size of radar targets, without their identification, is proposed on the base of a transient scattered field. Scattered transient response from the target consists of two parts: early time and late time. The early-time response corresponds to direct reflection and the late time is related to oscillation phenomena corresponding to surface-creeping waves and cavity waves. The time difference between the the start of early time and late time responses corresponds to a time interval in which creeping wave travels the geodesics surface path of the target. Therefore, by calculating the time difference between these two successive parts of response, the circumferential size of the target can be estimated. The start time of these two parts is determined by the matrix pencil method. In this study, the circumferential sizes of various simple targets such as cylinder, disc, cube, and a complex object, with an estimation error of <10% are calculated.

Importance of Taking Into Account the Soil Stratification in Reproducing the Late-Time Features of Distant Fields Radiated by Lightning

In this paper, we present an analysis of the propagation effect along a lossy ground on the characteristics of lightning-generated electric fields, using simultaneous observations of lightning currents and radiated fields measured at nine different distances associated with rocket-triggered lightning. The triggered-lightning site is located in Conghua (Guangdong, China). The electric field waveforms were measured using the sensors belonging to the Foshan three-dimensional lightning location system that are located at distances from the triggered-lightning site ranging from 69 to 126 km. The propagation path was over land and mainly over flat ground. The field sensors used had an overall bandwidth from 160 Hz to 1 MHz. It is shown that even though the early response of the field can be reproduced reasonably well by adjusting the ground electrical conductivity, the subsidiary peaks, and the late-time response of the fields cannot be satisfactorily reproduced assuming a homogeneous ground model. However, a two-layer soil model allows obtaining very good agreement between computed and measured waveforms for all the considered distances and events. Compared to the homogeneous ground case, the computed early-, intermediate-, and late-time response follows to a much better extent the experimental waveforms. We also provide a discussion on the influence of the computational model and parameters on the simulated results.

The Spatial Singularity Expansion Method for Electromagnetics

We develop a general singularity expansion method (SEM) focused on the spatial structure of electromagnetic fields and currents. In contrast to the traditional temporal SEM, where complex analytical continuation is performed on the forward Green’s function of free space, we propose applying the SEM to the reverse Green’s function of the electromagnetic device, the recently introduced antenna current Green’s function, leading to the discovery of new current and radiation modes. The new spatial SEM turns out to depend only on single-frequency field/current measurement besides completely avoiding the problem of separating early- and late-time responses that have been hindering the traditional approach. The theory is first developed at a very general level and then applied in detail to 1-D wire antennas. We manage to express the far field in terms of the spatial-SEM modes in a closed analytical form. The theory is confirmed by directly comparing with the full-wave method of moment solutions, and excellent agreement between theory and numerical analysis was obtained for generic wire array configurations. The resulting spatial-SEM is expected to stimulate researches into a new generation of frequency-domain RCS target identification technologies and electromagnetic sensing by developing special algorithms relying mainly on the spatial structure of the fields and currents fed by measurements at single frequency instead of the time-domain data usually required in traditional SEM.

Perturbation theory-based performance analysis of TLS-Prony method for natural frequency extraction

The total least squares Prony method is used for estimating s-plane natural frequencies from noisy late time response. It consists of three steps: In the first step, the minimum eigenvector of a matrix, whose entries are defined from the noisy late time response, should be computed. In the second step, the roots of a polynomial, whose coefficients are the entries of the minimum eigenvector defined in the first step, are estimated. The roots in the second step are defined as z-plane natural frequencies. In the third step, s-plane natural frequencies are obtained from z-plane natural frequencies. In this paper, a rigorous derivation of the mean square error of the estimator in each step due to an additive noise in the late time response is presented: In the first step, it is shown how the minimum eigenvector of a matrix is perturbed due to an additive noise in the late time response. In the second step, it is derived how the roots of a polynomial are perturbed due to perturbation in the coefficients of the polynomial. In the third step, it is derived how the s-plane natural frequencies are perturbed due to perturbation in z-plane natural frequencies. The mean square error for the first step, the second step and the third step are presented in (26), (36), and (44), respectively, and the validity of these expressions is illustrated in the results using simulated response and experimentally measured data. In conclusion, the mean square errors of the minimum eigenvector, the z plane natural frequencies, and the s plane natural frequencies for the total least squares Prony method can be obtained analytically from (26), (36) and (44) without a computationally intensive Monte-Carlo simulation.

Evidence of Hierarchy in the Complex Fractured System of Geropotamos (Crete, Greece), as Extracted from Transient Electromagnetic Responses

The essential goals of this paper are to test the transient electromagnetic (TEM) response in a fractured geological complex medium and to better understand the physics introduced by associating a roughness parameter β to the geological formation. An anomalous fractional diffusion approach is incorporated to describe the electromagnetic induction in rough multi-scaled geological structures. The multi-scaling characteristics of Geropotamos basin in Crete are revealed through the analysis of transient step-off response of an EM loop antenna. The semi-empirical parameters derived from late-time TEM measurements are correlated with the multi-scale heterogeneities of the medium. Certain interesting properties of the late-time slope γ(β) and the power law of near surface resistivity distribution, as extracted from TEM inversion for different depth, are presented. The analysis of the parameter γ(β) which scales the induced voltage in the loop in the late stage of the electromagnetic response leads to a different view of the EM geophysical data interpretation. We show that it is strongly correlated with areas of high fracture density within the geological formations of the Geropotamos area. For that reason, it is proposed as a local multi-scaling empirical index. The results of this paper suggest that anomalous diffusion could be a viable physical mechanism for the fractal transport of charge carriers, explaining observed late-time TEM responses across a variety of natural geological settings.

Mutual friction in superfluid He−B3 in the low-temperature regime

We measure the response of a rotating sample of superfluid $^3$He-B to spin-down to rest in the zero-temperature limit. Deviations from perfect cylindrical symmetry in the flow environment cause the initial response to become turbulent. The remaining high polarization of vortices along the rotation axis suppresses the turbulent behavior and leads to laminar late-time response. We determine the dissipation during laminar decay at $(0.13-0.22) T_{\mathrm{c}}$ from the precession frequency of the remnant vortex cluster. We extract the mutual friction parameter $\alpha$ and confirm that its dependence on temperature and pressure agrees with theoretical predictions. We find that the zero-temperature extrapolation of $\alpha$ has pressure-independent value $\alpha(T=0) \sim 5 \cdot 10^{-4}$, which we attribute to a process where Kelvin waves, excited at surfaces of the container, propagate into the bulk and enhance energy dissipation via overheating vortex core-bound fermions.

Fractured–Injection–Well Performance Under Non–Newtonian, Power–Law Fluids

Summary A new source function developed in this work is used to predict well responses to evaluate long-term injectivity and late-time responses of fractured wells after the injection of a non-Newtonian, pseudoplastic fluid. The source function yields integrals of modified Bessel functions of fractional order that are evaluated numerically by techniques developed by the authors. Consideration of well responses after the injection of pseudoplastic fluids into reservoirs through fractured wells requires the solution of a nonlinear differential equation and examination of flow fields in two dimensions. Consequently, numerical methods have been the only recourse. This work explores the applicability of new tools developed in recent times by analytical means. Calculating well injectivity accurately and rapidly for this complex situation by the methods outlined here is particularly convenient. The expressions we derive may be readily applied to concepts such as the Peaceman (1978) probe radius and transient well injectivity. Predictions by use of the new solution are compared with numerical solutions in the literature.