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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↗

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↗

Velocity Profiling of a Gas–Solid Fluidized Bed Using Electrical Capacitance Volume Tomography

In this study, a method of producing velocity profile maps from electrical capacitance volume tomography (ECVT) measurements by reconstructing displacement from measured changes in capacitance is developed and applied to fluidized bed systems. The mapping of the reconstruction leverages the gradient of the sensitivity distribution of the ECVT sensor to circumvent the need for image cross correlation techniques. Experimental data of both bubbling and slugging fluidized beds are collected in a cold flow model. Adaptation of the technique is discussed in detail, and velocity profiles are obtained for a range of gas flow rates. The produced velocity maps are compared against the established methods of cross correlation and against empirical correlations from the literature and are found to agree well in tracking slug and bubble velocity. The exception is when the tracked object is large relative to the ECVT sensor dimensions, a scenario that can be avoided through proper sensor design. The quantities of average velocity, momentum, and solid and gas volume fraction are derived from the image and velocity profiles. The results demonstrate and extend the power of ECVT as a measurement tool for the study and monitoring of gas–solid fluidized beds by providing a computationally cheaper alternative to 3-D cross correlation for deriving velocity profiles.

47 OTHER INSTRUMENTATION↗

Review of Selected Advances in Electrical Capacitance Volume Tomography for Multiphase Flow Monitoring

Electrical Capacitance Volume Tomography (ECVT) has emerged as an attractive technology for addressing instrumentation requirements in various energy-related multiphase flow systems. ECVT can monitor multiple flow conditions and reconstruct real-time 3D images from capacitance measurements using a large set of electrode plates placed around the processes column enclosing the sensed flow system. ECVT is non-intrusive and allows the measurement of changes in mutual capacitance between all possible plate pair combinations. The objective of this paper is to provide a comprehensive review of recent advances in ECVT, enabling robust monitoring of multiphase flows, especially water-containing multiphase flows.

02 PETROLEUM↗

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.↗

Electrical Capacitance Volume Tomography with High-Contrast Dielectrics

The Electrical Capacitance Volume Tomography (ECVT) system has been designed to complement the tools created to sense the presence of water in nonconductive spacecraft materials, by helping to not only find the approximate location of moisture but also its quantity and depth. The ECVT system has been created for use with a new image reconstruction algorithm capable of imaging high-contrast dielectric distributions. Rather than relying solely on mutual capacitance readings as is done in traditional electrical capacitance tomography applications, this method reconstructs high-resolution images using only the self-capacitance measurements. The image reconstruction method assumes that the material under inspection consists of a binary dielectric distribution, with either a high relative dielectric value representing the water or a low dielectric value for the background material. By constraining the unknown dielectric material to one of two values, the inverse math problem that must be solved to generate the image is no longer ill-determined. The image resolution becomes limited only by the accuracy and resolution of the measurement circuitry. Images were reconstructed using this method with both synthetic and real data acquired using an aluminum structure inserted at different positions within the sensing region. The cuboid geometry of the system has two parallel planes of 16 conductors arranged in a 4 4 pattern. The electrode geometry consists of parallel planes of copper conductors, connected through custom-built switch electronics, to a commercially available capacitance to digital converter. The figure shows two 4 4 arrays of electrodes milled from square sections of copper-clad circuit-board material and mounted on two pieces of glass-filled plastic backing, which were cut to approximately square shapes, 10 cm on a side. Each electrode is placed on 2.0-cm centers. The parallel arrays were mounted with the electrode arrays approximately 3 cm apart. The open ends were surrounded by a metal guard to reduce the sensitivity of the electrodes to outside interference and to help maintain the spacing between the arrays. Other uses for this innovation potentially include quantifying the amount of commodity remaining in the fuel and oxidizer tanks while on-orbit without having to fire spacecraft engines. Another orbit application is moisture sensing in plant-growth experiments because microgravity causes moisture in soil to distribute itself in unusual ways. At the moment, the hardware and image reconstruction technique may only be of interest to people involved in nondestructive evaluation. The reconstructed image takes almost a full week to reproduce with existing computer power. However, because computer power and speeds follows Moore s Law, execution times are likely to become acceptable within the next five to eight years. The code was written in Mathematica for dedicated use with the ECVT system. In its present form, it is not suitable to be used directly as a consumer product. However, the code could be likely improved by rewriting it in a compiled language such as C or Fortran.

Nurge, Mark↗

Electrical Capacitance Volume Tomography: A Comparison between 12- and 24-Channels Sensor Systems

Spatial resolution represents akey performance aspect in electrical capacitance volume tomography (ECVT). Factors affecting the resolution include the ``soft-field'' nature of ECVT, the number of capacitance channels used, the ill-conditioned nature of the imaging reconstruction problem, and the signal-to-noise ratio of the measurement apparatus. In this study, the effect of choosing different numbers of capacitance plates on the performance of ECVT is investigated. Specifically, two ECVT sensors with 12 and 24 capacitance channels but covering equal volumes of a cylinder are used to examine the resulting impact on the image resolution.

20 FOSSIL-FUELED POWER PLANTS↗

Investigation of core-annular flow in an industrial scale circulating fluidized bed riser with electrical capacitance volume tomography (ECVT)

There is a paucity of riser data for industrial scale units, particularly with regard to the solids fraction. This is especially true for detailed spatially distributed values. To alleviate this problem, NETL installed a 0.445 m tall electrical capacitance volume tomography (ECVT) sensor 9.66 m from the gas distributor of its industrial size (15.45 m high and 0.3 m diameter) circulating fluidized bed (CFB) cold model. A series of tests were conducted to investigate the gas-solid flow behavior using high density polyethylene (PPE) solids. Static electricity was successfully minimized using Larostat and humidification. Time averaged radial solid fractions profiles are presented and discussed. The time and spatially averaged solid fractions measured by the ECVT agree well with estimates from the pressure drop. The annular thickness was measured and found to increase with increases in the solids flow rate and decrease with increases in the gas velocity. Comparisons of the annular thickness and solids fraction as determined from the ECVT unit were compared to existing correlations. In conclusion, the average error ranged from 13% to 275% which is not surprising since the literature correlations were developed from data on much smaller units and for significantly different particles.

42 ENGINEERING↗

The Development of a Generalized Riser Flow Regime Map Based Upon Higher Moment and Chaotic Statistics Using Electrical Capacitance Volume Tomography (ECVT)

Dynamic analyses have been applied to the temporal signals from an Electro Capacitance Volume Tomography instrument located near mid-height on the riser of an industrial-scale cold-flow circulating fluidized bed to characterize gas-solids flow behavior in the riser. Twelve capacitance electrodes surround the cylindrical riser over a height of 1.3 m. The instrument used a neural network deconvolution algorithm to determine the spatially resolved solids fraction recorded at 52 Hz. Experiments were carried out over a range of gas and solids flows in the transport regime using a Geldart Group B bed material, high density polyethylene with mean particle size of 880 μm. The radial solids distribution was found to vary from one-time step to the next between profiles typical of laminar and turbulent flow. The duration of time spent in each of these flow profiles depended upon the operating regime – dilute, core-annular, or fast fluidized bed. The chaotic structure of the temporal data was characterized using the three conventional approaches: the first 4 moments from the distribution of signal in time, system memory parameters from the autocorrelation function and the Hurst exponent, and analysis of the correlationentropy and correlation dimension of the attractor. These signal analysis techniques were used to clearly distinguish differences between different transport operating regimes. Specifically, it was experimentally observed that a riser transitions from core annular flow profile to dilute and dense regimes via increasing the frequency of short term transients to either dilute or dense flow profiles, respectively. A regime map was generated based upon these dynamics using solids flux and gas velocity axes. Fast fluidized, core annular, and dilute each exhibited different degree of dynamic characteristics typical of fluid dominated or particle compromising behavior. It should be noted that the magnitude for the different statistics was in the same range regardless of the regime, it was the radial profile for the statistic that changed and subsequently identified that there was a change in the regime. Finally, a reduced regime map was developed consisting of plotting the gas velocity normalized by the upper transport velocity versus the solids flux normalized by the saturation carrying capacity. The use of this reduced plot allowed the data from widely different conditions to be plotted and compared on the same<p>graph. Note that in many instances, some of the statistics identified the operating point as being in one regime while others indicated that it was in another indicating a transition region between dilute or core annular regimes and between the core annular and fast fluidization regimes. This now provides a tool that can be used to optimize process performance, identify changes in operating states, or replicate process dynamics during process scaling or changing operating parameters. </p>

Breault, Ronald↗