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Efficient and Flexible Sensitivity Matrix Computation for Adaptive Electrical Capacitance Volume Tomography

Electrical capacitance tomography is a widely used sensor modality for flow imaging in many industrial settings. Adaptive Electrical Capacitance Volume Tomography (AECVT) extends the capabilities of traditional ECT by enabling direct volumetric imaging and an improved resolution. Construction of the sensitivity matrix is a necessary step to obtain flow images. This step requires computation of the electric field inside the sensing domain, which is done via a typical field solver such as the finite element method. In this work, we present an efficient and flexible method to construct the sensitivity matrix for Adaptive Electrical Capacitance Volume Tomography (AECVT) based on individual electrode segment excitations and their judicious combination to form desired matrix elements. We illustrate how the proposed method yields the same sensitivity matrix as the traditional method but at a much lower computational cost. Once all segment contributions are obtained, we also indicate how the proposed method, unlike the traditional approach, can generate the sensitivity matrix on demand for an arbitrary combination of synthetic electrodes and obviating the need for any additional field computations. Finally, we present image reconstruction results for two different experimental scenarios where the mutual capacitance data and the corresponding sensitivity vectors are obtained through the proposed measurement combination scheme.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Cross-Plane Acquisitions in Electrical Capacitance Volume Tomography

Electrical capacitance tomography (ECT) is a widely used imaging modality to image two-dimensional cross sections of multiphase flows. Recent developments in electrical capacitance volume tomography (ECVT) have made it possible to directly obtain volumetric images from measured data. An ECVT is instrumental for obtaining accurate phase hold up information and velocity information that are needed for the optimization of certain flow processes. However, compared to ECT, the high correlation between the measurements in ECVT exacerbates the ill-conditioning of the associated image reconstruction problem. Previous studies have suggested that neglecting mutual capacitance data between the ECVT electrodes located at cross-planes that are well separated along the sensor axis can be done without significantly affecting the reconstructed image. In addition, this may help constrain the ill-conditioning of the reconstruction problem. Here, we examine in detail and quantify the effect of reduced cross-plane acquisition strategies for optimizing the image reconstruction and constraining the ill-conditioning of typical ECVT settings.

20 FOSSIL-FUELED POWER PLANTS↗

Toward Water Volume Fraction Calculation in Multiphase Flows Using Electrical Capacitance Tomography Sensors

Real-time monitoring of water volume fraction in multiphase flows is an important problem for a number of industrial applications. The water phase in the multiphase flows may correspond to either the dispersed phase or the continuous phase. In the past, several lowcost and nonintrusive techniques based on the electrical capacitance tomography (ECT) has been developed to image and monitor in real-time multiphase flows containing water. Furthermore, such monitoring becomes increasingly challenging for high salinity levels, and no reliable ECTbased method is presently available which could work for obtaining water volume fraction in multiphase flows for all water salinity levels. In this paper, we propose a new approach based on the Hanai’s formula for complex dielectric constant and taking advantage of the Maxwell- Wagner-Sillars effect to obtain, to a good approximation, water volume fractions in multiphase flows containing water as either dispersed or continuous phase.

02 PETROLEUM↗

Measurement strategy for rectangular electrical capacitance tomography sensor

To investigate the influence of the measurement strategy for the rectangular electrical capacitance tomography (ECT) sensor, a Finite Element Method (FEM) is utilized to create the model for simulation. The simulation was carried out using COMSOL Multiphysics(trade mark, serif) and Matlab(trade mark, serif). The length-width ratio of the rectangular sensing area is 5. Twelve electrodes are evenly arranged surrounding the pipe. The covering ratio of the electrodes is 90%. The capacitances between different electrode pairs are calculated for a bar distribution. The air of the relative permittivity 1.0 and the material of the permittivity 3.0 are used for the calibration. The relative permittivity of the second phase is 3.0. The noise free and noise data are used for the image reconstruction using the Linear Back Projection (LBP). The measurement strategies with 1-, 2- and 4- electrode excitation are compared using the correlation coefficient. Preliminary results show that the measurement strategy with 2-electrode excitation outperforms other measurement strategies with 1- or 4-electrode excitation.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Online monitoring of oil film using electrical capacitance tomography and level set method

In the application of oil-air lubrication system, electrical capacitance tomography (ECT) provides a promising way for monitoring oil film in the pipelines by reconstructing cross sectional oil distributions in real time. While in the case of small diameter pipe and thin oil film, the thickness of the oil film is hard to be observed visually since the interface of oil and air is not obvious in the reconstructed images. And the existence of artifacts in the reconstructions has seriously influenced the effectiveness of image segmentation techniques such as level set method. Besides, level set method is also unavailable for online monitoring due to its low computation speed. To address these problems, a modified level set method is developed: a distance regularized level set evolution formulation is extended to image two-phase flow online using an ECT system, a narrowband image filter is defined to eliminate the influence of artifacts, and considering the continuity of the oil distribution variation, the detected oil-air interface of a former image can be used as the initial contour for the detection of the subsequent frame; thus, the propagation from the initial contour to the boundary can be greatly accelerated, making it possible for real time tracking. To testify the feasibility of the proposed method, an oil-air lubrication facility with 4 mm inner diameter pipe is measured in normal operation using an 8-electrode ECT system. Both simulation and experiment results indicate that the modified level set method is capable of visualizing the oil-air interface accurately online.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Relevance Vector Machine Image Reconstruction Algorithm for Electrical Capacitance Tomography With Explicit Uncertainty Estimates

We present a Relevance Vector Machine (RVM) based algorithm for electrical capacitance tomography (ECT) applications that can concurrently provide image reconstruction results and uncertainty estimates about the reconstruction. To illustrate the RVM operation in ECT, we simulate typical ECT scenarios, making explicit the connection between the reconstructed pixel values and the corresponding uncertainty estimates in each case. We compare the RVM reconstruction performance with that of the Iterative Landweber Method (ILM) and the least absolute shrinkage and selection operator (LASSO) in all the considered scenarios. The results show that, in addition to the key advantage of providing uncertainty measures, RVM can achieve similar reconstruction results with either lower or similar computational complexity.

42 ENGINEERING↗

Inverse Normalization Method for Cross-Sectional Imaging and Velocimetry of Two-Phase Flows Based on Electrical Capacitance Tomography

Proper normalization of the measured capacitance data is a prerequisite in electrical capacitance tomography (ECT). Conventional methods, such as parallel and series normalization, assume a higher permittivity perturbation in a homogeneous (lower) permittivity background. Although this is applicable to a number of cases, some two-phase flows are better modeled instead as a lower permittivity perturbation in a homogeneous (higher) permittivity background. A different normalization method is proposed for such cases, which provides similar image quality as conventional, but is particularly beneficial for velocimetry applications based on sensitivity gradient of ECT sensor. Furthermore, simulation and experimental results are provided to illustrate the advantages for the proposed normalization technique.

47 OTHER INSTRUMENTATION↗

Electrical capacitance tomography to monitor unsaturated moisture ingress in cement-based materials

This paper reports the investigation of the feasibility of electrical capacitance tomography (ECT) for monitoring unsaturated moisture flow in cement-based materials. ECT is an imaging modality in which the electrical permittivity distribution within an object is reconstructed based on measured capacitances between electrodes attached on the object's surface. In a series of experiments, mortar specimens with different water-cement mass ratios (w/c) (0.25, 0.45 & 0.60) were monitored with ECT during the moisture ingress. The results demonstrate that ECT is able to image the moisture ingress within the specimens, and further, to distinguish between different moisture flow rates in mortars with different porosities resulting from differing w/c ratios. These findings suggest that ECT could provide a tool for monitoring, visualizing and quantifying the rate of moisture ingress in cement-based materials non-destructively.

36 MATERIALS SCIENCE↗

Preliminary Results From Propellant Mass Gauging in Microgravity with Electrical Capacitance Tomography

This presentation is a shortened and simplified version of the original from Jed Storey intended for usage with an a.i. Solutions' "Lunch-and-learn" audience. It reviews the setup, execution, and some preliminary results from the Electrical Capacitive Tomography experiment conducted by NASA KSC Launch Services Program flown aboard a Zero-G aircraft earlier this year. The original is STRIVES submission 20220010165. Some extra images and videos have been added and some detailed content removed since the purpose of this presentation is less technical than that of it's parent.

mass gauging↗

Microgravity Electrical Capacitance Tomography Data Set

Propellants mass gauging technologies designed to work in an accelerated environment, where the propellant remains settled at one end of the propellant tank, do not work well in a microgravity environment because the propellant is not necessarily settled. While some microgravity mass gauging technologies exist at various TRLs, most of them have major disadvantages. Improvements in microgravity propellant mass gauging will result in improvements to many areas of propellant management, which influences performance and mission assurance. Electrical Capacitance Tomography (ECT) is a sensing technology that has been used in the oil/gas industry for decades to measure multi-phase flow rate in pipes. ECT, when installed in a tank, is able to reconstruct the liquid distribution inside of the tank, which can then be integrated to obtain mass. ECT mass gauging recently achieved high accuracy in laboratory testing on the ground, and while ECT mass gauging will theoretically work during all phases of flight, it had not yet been tested in microgravity. The NASA KSC Launch Services Program, with support from the Flight Opportunities Program, successfully flew an ECT tank liquid mass gauging system experiment on a Zero-G parabolic flight aircraft. The experiment hardware was rented from a company; NASA LSP did no technology development work for this project. This STRIVES entry is for the entire raw data set, which consists of approximately 25GB of csv files of capacitance and motion data from the ground and flight tests of the experiment. The data set will be available on the NASA LSP Electronic Slosh Data Catalog (ESDC), and the public may request the data set from the authors (POC: Jed Storey, jedediah.m.nasa.gov).

mass gauging↗

Preliminary Results from Propellant Mass Gauging with Electrical Capacitance Tomography

Propellants mass gauging technologies designed to work in an accelerated environment, where the propellant remains settled at one end of the propellant tank, do not work well in a microgravity environment because the propellant is not necessarily settled. While some microgravity mass gauging technologies exist at various TRLs, most of them have major disadvantages. Improvements in microgravity propellant mass gauging will result in improvements to many areas of propellant management, which influences performance and mission assurance. Electrical Capacitance Tomography (ECT) is a sensing technology that is able to reconstruct the liquid distribution inside of a tank, which can then be integrated to obtain mass. ECT mass gauging recently achieved high accuracy in laboratory testing, <0.1% liquid volume measurement error, even during sloshing. While ECT mass gauging will theoretically work during all phases of flight, it had not yet been tested in microgravity. The NASA KSC Launch Services Program, with support from the Flight Opportunities Program, successfully flew an ECT liquid mass gauging system experiment on a Zero-G parabolic flight aircraft. Basics of ECT measurement theory, details of the experiment setup and flights, and preliminary results will be discussed. The preliminary results suggest that, even in the current prototype generation, ECT sensor systems will be useful as a propellant mass gauging technology in both an accelerated and microgravity environment.

mass gauging↗

Propellant Mass Gauging in Microgravity with Electrical Capacitance Tomography

Advancements in microgravity propellant mass gauging will result in improvements to many areas of propellant management, which influences space vehicle performance and mission assurance. Propellant mass gauging technologies designed to work in an accelerated environment, where the propellant remains settled at one end of the propellant tank, do not always work well in a microgravity environment because the propellant is not necessarily settled. While some microgravity mass gauging technologies exist at various stages of development, most of them have major disadvantages. Electrical Capacitance Tomography (ECT) is a sensing technology that is able to reconstruct the liquid distribution inside of a tank, which can then be integrated to obtain mass. While ECT mass gauging will theoretically work during all phases of flight, it had not yet been tested in microgravity. The NASA Kennedy Space Center Launch Services Program, with support from the Flight Opportunities Program, successfully tested an ECT liquid mass gauging system experiment on a parabolic flight aircraft in May 2022. Basics of ECT measurement theory, details of the experiment setup, data processing, ground test results, and the flight test result will be discussed. The results suggest that ECT sensor systems will be useful as a propellant mass gauging technology in both accelerated and microgravity environments.

electrical capacitance tomography↗

Comparison of electrical capacitance tomography and gamma densitometer measurement in viscous oil-gas flows

Multiphase flow is a common occurrence in industries such as nuclear, process, oil and gas, food and chemical. A prior knowledge of its features and characteristics is essential in the design, control and management of such processes due to its complex nature. Electrical Capacitance Tomography (ECT) and Gamma Densitometer (Gamma) are two promising approaches for multiphase visualization and characterization in process industries. In two phase oil and gas flow, ECT and Gamma are used in multiphase flow monitoring techniques due to their inherent simplicity, robustness, and an ability to withstand wide range of operational temperatures and pressures. High viscous oil (viscosity > 100 cP) is of interest because of its huge reserves, technological advances in its production and unlike conventional oil (oil viscosity < 100 cP) and gas flows where ECT and Gamma have been previously used, high viscous oil and gas flows comes with certain associated concerns which include; increased entrainment of gas bubbles dispersed in oil, shorter and more frequent slugs as well as oil film coatings on the walls of flowing conduits. This study aims to determine the suitability of both devices in the visualization and characterization of high-viscous oil and gas flow. Static tests are performed with both devices and liquid holdup measurements are obtained. Dynamic experiments were also conducted in a 1 and 3 inch facility at Cranfield University with a range of nominal viscosities (1000, 3000 and 7500 cP). Plug, slug and wavy annular flow patterns were identified by means of Probability Mass Function and time series analysis of the data acquired from Gamma and ECT devices with high speed camera used to validate the results. Measured Liquid holdups for both devices were also compared.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Electronic Scanning Strategies in Adaptive Electrical Capacitance Volume Tomography: Tradeoffs and Prospects

Electrical Capacitance Volume Tomography (ECVT) has been applied for imaging of multiphase flows found in industrial applications. The ill-posed nature of the image reconstruction problem in ECVT and the consequent low resolution can be alleviated by employing electronic scanning enabled by electrode segmentation and reconfiguration during data acquisition. Here we study electronic scanning strategies that mimic physical rotation and shifting of the sensor along its symmetry axis. First, we study the feasibility of electronic scanning by analyzing the capacitance transducer circuit in SPICE. Then, we simulate electronic scanning using the finite element method for different electrode shapes, for which we compare the image reconstruction results and acquisition time. We find a noticeable improvement in image resolution for the scanning cases over conventional ECVT. Lastly, among the scanning cases, we emphasize a particular electrode shape that provides the best image resolution along with the minimal amount of acquisition time.

47 OTHER INSTRUMENTATION↗

Sensitivity map computation in adaptive electrical capacitance volume tomography with multielectrode excitations

Electrical capacitance tomography (ECT) is a low‐cost, high‐speed imaging technique useful in many industrial settings. ECT is predicated on the knowledge of sensitivity maps between capacitance electrodes that blanket the imaging domain. The simultaneous activation of multiple electrodes can be advantageous to manipulate the resulting field distributions and capture additional spatial information for imaging purposes. However, conventional methods for sensitivity map computation in ECT are not adequate in the presence of multielectrode activation because the mutual coupling between electrodes is not properly accounted for. This coupling becomes especially critical in adaptive electrical capacitance volume tomography (AECVT) sensors, where signals from many small electrode segments are combined into synthetic electrodes. A more general approach is presented for sensitivity map computation in AECVT based on the actual posteriori (induced) charge distributions rather than the conventional approach based on boundary conditions with no account for electrode interactions.

Zeeshan, Z.↗