Electrical Capacitance Tomography â A Perspective - ACS Publications

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Electrical Capacitance Tomography - A Perspective Q. Marashdeh, L.-S. Fan,* B. Du, and W. Warsito Department of Chemical and Biomolecular Engineering, The Ohio State UniVersity, Columbus, Ohio 43210

This article describes the recent progress in research and development on electrical capacitance tomography (ECT). Specifically, the article highlights several aspects of ECT including the electrical capacitance volume tomography (ECVT), 3D sensor design, 3D neural network multicriterion image reconstruction technique (3D-NN-MOIRT), multimodal imaging based on ECT and ECVT sensors, static-charge effects and the scheme of their elimination in the ECT image reconstruction, and multiphase flow imaging applications. The multimodal capability that enables permittivity and conductivity imaging to be simultaneously conducted is illustrated. The simulation and experimental results are presented to provide quantitative and/or qualitative assessment of the significance of various ECT techniques. The employment of ECVT in conjunction with using electrical capacitance based imaging sensors is shown to represent a favorable tool for industrial multiphase flow imaging. 1. Introduction Multiphase flows and multiphase reactors are commonly encountered in industrial operations for process applications. Such applications include riser flows, particle coating and blending, drying, polymerization, and Fischer-Tropsch synthesis.1,2 Nonintrusive techniques are used for tracking particle movement, and/or mapping instantaneous or time-averaged, local or cross-sectional averaged, phase hold-ups, and phase velocities. These techniques include particle image velocimetry,3-5 laser Doppler anemometry,6-9 phase Doppler anemometry,10-11 positron emission tomography12-15, and radioactive particle tracking,16-23 ultrasonic tomography,24-26 nuclear magnetic resonance imaging (NMR or MRI),27-32 and electrical impedance (resistive or capacitive) tomography.33-38 The inherently complex nature of multiphase flows requires a multidimensional measurement technique capable of providing real time monitoring of the process dynamics and physical properties. Examples of different physical properties used in tomography imaging are density, electrical capacitance and resistance, reflection and refraction index, and electric charge.39 The applicability of different imaging modalities to regimes depends on many factors related to the nature of the regime and the sensor itself. Among various factors of importance to the selection of tomography sensors are cost, safety, applicability to different sizes of vessels, and the imaging speed. In this regard, the electrical tomography sensors are attractive when compared to sensors used in other tomography techniques.40 Electrical tomography is based on the measurement of electrical properties through the utilization of the capacitive, resistive, or inductive nature of the flow media under investigation. Among different electrical tomography systems, electrical capacitance tomography (ECT) has attracted increased attention in recent years as an imaging tool for multiphase flow systems. The development of ECT started in the early 1980s when a group of researchers at the Morgantown Energy Technology Center41developed a 2D capacitance tomography system with its subsequent applications for cross-sectional imaging of fluidized bed systems. Applications of ECT to oil pipelines and pneumatic conveyors were explored by researchers at the University of Manchester Institute of Science and Technology in the early 1990s.42 These earlier works ascertain ECT as a * To whom correspondence should be addressed.Tel.: (614) 6883262. Fax: (614) 292-3769. E-mail: [email protected].

viable noninvasive measurement tool of the dynamics of twophase flows based on the variations of the dielectric constants in the phase media. ECT was subsequently applied to imaging of flow systems such as oil-gas and oil-water flows in oil wells,43 gas-solid flows in pneumatic conveyors,44 gas-solid fluidized beds,45 and trickle bed reactors.49 However, expanding the application of ECT to more complex multiphase flows is challenged by its low spatial resolution compared to other tomography systems and its limitation to nonconductive media such as organic liquids. In recent developments, the accuracy of ECT image reconstruction has been significantly improved through the employment of optimization reconstruction techniques. Such techniques can be represented by the neural network multicriterion optimization image reconstruction technique (NN-MOIRT).35 NNMOIRT is based on optimizing a set of objective functions related to both the measured capacitance vector and the reconstructed image. The improvements provided by this reconstruction technique has enabled three-phase imaging to be conducted on the basis of ECT as well as quasi-3D ECT imaging. Another development that has supported the ECT technique and its applications is 3D direct ECT imaging, noted as electrical capacitance volume tomography (ECVT).36,50,51 Unlike traditional 3D imaging, based on stacking 2D images to obtain an interpolated 3D image, the volume tomography acquires the 3D image directly from the measured capacitance data. Such imaging was made possible through the 3D ECT (ECVT) sensor design as well as the additional objective functions used in the optimization scheme for 3D reconstruction. The first published work on 3D ECT (ECVT) with the layering concept in sensor design of Warsito and Fan36 shed new light on the capability and feasibility of the 3D imaging using ECT. Subsequent work that contributes to the research and development of 3D ECT imaging was presented by others.52,53 ECVT has also been used to develop images of high-contrast dielectrics using cuboid sensors.54 Additional applications of ECVT technology are yet to be explored. For example, ECVT technology developed51 was recently recommended for demonstration by the National Aeronautics and Space Administration for a space mission for imaging high-contrast dielectrics on extraterrestrial surfaces.55 The traditional use of the ECT sensor for permittivity imaging has been extended to include conductivity imaging as well. In other recent progress, the ECT sensor has been used for dual

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Figure 1. Diagram of the ECT system including sensor, data acquisition, and computer for reconstruction.

permittivity-conductivity imaging based on the quasistatic analysis of the sensor for a time varying excitation signal.56 This progress provides a design for a global ECT sensor capable of 3D volume multimodal imaging. Ongoing activities in the area of ECT research include developments of all aspects of the ECT systems. The exploration of innovative applications of ECT systems has also gained considerable momentum in the areas including detection of flammable liquids,57 imaging of flames in porous media,58 estimation of average particle size,59 and comparative studies of other imaging modalities.60 In this article, a perspective on the development of the ECT techniques and their applications is presented. In section 2, the ECT system and reconstruction techniques are briefly reviewed. Recent advances in the ECVT sensor design are illustrated along with the ECT sensor usage for multimodal imaging. Simulation results are provided in section 3 to allow the capability of the ECVT technique to be assessed. The applications of ECVT are highlighted in section 4 for the imaging of multiphase flow systems including bubble columns, gas-liquid-solid threephase fluidized beds, gas-solid fluidized beds, and risers. 2. Review of ECT Techniques Similar to any other tomography system, an ECT system is composed of three components: (1) sensor, (2) data acquisition system, and (3) computer for reconstruction and viewing as depicted in Figure 1. The ECT sensor is composed of N capacitance plates distributed on the wall of the process vessel providing N(N - 1)/2 independent capacitance measurements. Recent developments are geared toward an ECT sensor design with 3D features for detecting the capacitance variations due to permittivity perturbations in the imaging volume. The challenge in achieving it arises from the low level of capacitance change compared to noise and stray capacitance in the system. The current ECT systems are capable of providing up to 100 frames per second for a 12-electrode system. Increasing the number of electrodes plays an important role in enhancing the reconstructed image quality. The ECT reconstruction technique is, however, an integral part of the tomography system. In the following, ECT reconstruction techniques, sensors, and applications are discussed.

2.1. Image Reconstruction. Tomography reconstruction characterizes a process in obtaining a map of physical property distribution from a set of boundary measurements. Tomography systems can generally be classified into hard field and soft field. In hard-field tomography, the field lines of the interrogating signal are independent of the physical property distribution in the imaging domain. An example of the hard-field scenario is X-ray tomography. In soft-field tomography, the field distribution is dependent on the physical property distribution, and the reconstruction process takes a higher form of complexity.61 ECT is of a soft-field category where the electric field lines are dependent on the permittivity distribution. The electric potential and permittivity distributions are related according to the Poisson equation

(x,y,z)∇2φ(x,y,z) + ∇(x,y,z)∇φ(x,y,z) ) 0

(1)

where (x,y,z) is the permittivity distribution and φ(x,y,z) is the potential distribution. The capacitance of the field is obtained by finding the accumulated charge on the capacitance plate per unit voltage according to

Qi ) I (x,y,z)∇φˆndl Γi

(2)

where Qi is the accumulated charge on plate i and Γi is a surface enclosing the plate. Equation 1 is a linear partial differential equation; however, the nonlinear coefficients pose an additional complexity to the ECT reconstruction problem. Solving eq 2 to obtain the capacitance from a known permittivity distribution is referred to as the forward problem, whereas the problem of finding the permittivity map from the capacitance measurements is referred to as the inverse problem. In hard-field tomography, the inverse problem is solved by back projecting the boundary measurement vector on a perturbation matrix known as the sensitivity matrix; this process of solving the inverse problem is known as linear back projection (LBP).62 LBP has been applied to ECT, and the sensitivity matrix in this case is constructed through finding the capacitance response of an ECT sensor for permittivity perturbations in different

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locations of the imaging domain. The permittivity distribution can be calculated by

G ) STC

(3)

where G is a 1 × M image vector, S is an N × M sensitivity matrix, and C is an N × 1 capacitance vector. LBP has been applied successfully for solving the inverse problem in hard field tomography. The use of LBP for image reconstruction has attracted attention due to its simplicity and speed in implementing the algorithm. However, the severely ill-posed ECT problem and the limited number of capacitance measurements prompted research in image reconstruction for improved image resolution. In this regard, regularization techniques have been used to enhance image quality by decreasing the level of ill-posedness. The most commonly used regularization method is the Tikhonov regularization. Tikhonov regularization is based on adding an invertible diagonal matrix to the ill-posed matrix to make it invertible. This method has been applied to ECT image reconstruction.63 However, single-step image reconstruction techniques did not provide the required image reconstruction quality, and iterative image reconstruction techniques have been developed and applied for solving the ECT problem.62 Iterative reconstruction techniques are generally classified into: (1) algebraic and (2) optimization techniques. In algebraic reconstruction techniques, the reconstructed image is obtained through minimization of the mean square error (MSE) objective function. One of the most used algebraic techniques is the iterative linear back projection (ILBP).64 The reconstruction results from the ILBP are obtained through back projecting the error vector on the sensitivity matrix iteratively according to the following equation

Gk + 1 ) Gk + RST(C - SGk)

(4)

where k is the number of iterations, and R is the relaxation factor. Minimization of MSE refers to minimization of the residual error between the capacitance vector and the forward solution of the reconstructed image. However, because of the severely ill-posed ECT problem and noise contamination in the capacitance measurements, the reconstructed image with the least MSE is not necessarily the best solution. In optimization reconstruction, the most likely image is obtained through optimization of several objective functions related to both the capacitance vector and the image itself. The NN-MOIRT35 possesses such properties and has been demonstrated to be an accurate reconstruction technique. The objective functions used by NN-MOIRT are the MSE, entropy, and smoothness functions. The MSE function used in NN-MOIRT is similar to the MSE function in algebraic techniques and is aimed at obtaining an image solution that matches the measured capacitance vector in the forward solution. The MSE function is defined as

fmse(g) ) γ1|SG - C|2

(5)

The entropy function is used to obtain the image with maximum information and is defined as N

fi(g) ) γ2

∑ Gj ln(Gj)

(6)

j)1

The smoothness function is used to minimize the noise in the reconstructed image and is defined as

fs(g) ) γ3(GTXG + GTG)

(7)

where X is an M × M smoothness matrix and plays the role of a low-pass filter to remove the noise of the high-frequency component, and γ1,γ2, and γ3 are normalization constants between 0 and 1. The NN-MOIRT uses a Hopfield neural network to optimize the weights of the three objective functions. Hopfield networks possess the advantage of guaranteed convergence to local minima and can be realized onto hardware components. As a local minimum does not necessarily correspond to the most optimal solution, a penalty factor has been added to the set of objective functions to assist in the energy function escape from entrapment in a local minimum, thereby converging to a global minimum of energy.35 In a new development, the NN-MOIRT has been extended to include volume tomography reconstruction through modification of the ECT sensor to include axial variation along with the addition of a new objective function.51 The new objective function, noted as the matching function, is used to ensure consistency between 2D and 3D volume images.51 This is achieved by comparing projections of the volume image to the 2D reconstruction results. The matching objective function takes the form

1 fm(G) ) γ4|H2DG3D - G2D|2 2

(8)

where H2D is the 2D projection matrix, G2D is the 2D image reconstruction result, and γ4 is the normalization constant between 0 and 1. The four objective functions are optimized simultaneously to obtain the most likely volume image. The use of Hopfield networks is also motivated by its fast calculation speed, convergence of monotonic decrease, and inherent parallelism of the network. Following eq 1, the potential distribution is a function of charge distribution in addition to boundary conditions and physical property (permittivity) distribution. However, image reconstruction in ECT is based on the electrostatic free charge conditions, characterized by the right side of eq 1 for being zero. Thus, in imaging fields where a high level of static-charge generation is present, the charge would distort the reconstructed ECT image. A remedy for this distortion can be made by correcting the distorted measured capacitance values by those induced by the electrostatic effect.65 The approach for correction can be implemented using the ECT capacitance sensor in its passive mode that measures the voltage difference between plates resulting from free charge distribution in the imaging domain. This measured voltage is then used to correct the applied voltage for each plate in the capacitance measurement process. Simulation results for static-charge effect are shown in section 3. 2.2. 3D ECT Sensor. In 2D ECT, the sensor has only a 2D field variation in radial directions. The sensor in this case is assumed to be infinite in length. However, the limited sensor length in reality provided distortion to electric field lines in a phenomenon known as fringing. The fringing effect in 2D ECT has been always viewed as an undesired component, which adds inaccuracy to the 2D reconstructed images. The volume tomography concept, or ECVT, is based on utilizing the fringing effect to produce a field variation in the axial direction for 3D imaging.66 Sensor design for volume tomography is an important part of the image reconstruction. A desired sensor is to be able to provide an equal distribution of the electric field in all three dimensions. Thus, the sensitivity variance and strength along the 3D imaging domain can be used as criteria for determining the suitability of a sensor for volume imaging. In an ideal scenario, a uniform field variation along all dimensions and a proper extent of difference between the maximum and minimum


Figure 2. Elements of an ECT sensor that can be used for designing a 3D capacitance volume sensor.

field values are required for volume image reconstruction. However, the ill-posedness of the ECT sensor as well as the dependence of the field variation on the permittivity distribution represented by nonlinear coefficients in the Poisson equation presents a challenge in 3D ECT sensor design. In reality, the electric field variation changes significantly in the imaging domain depending on the location of the observation point and the difference between the maximum and minimum field values, which may be of several orders of magnitude. As for the former, a nonlinear image reconstruction technique is required to solve the problem concerning nonuniformity. As for the latter, an ECT acquisition hardware of high signal-to-noise ration (SNR) is required to detect capacitance signals of low amplitude (on the order of femto Farad) and high variation in its absolute value (2 orders of magnitude). The reconstruction techniques and acquisition hardware are topics of active ongoing research. The 3D ECT sensor is an evolving topic, and two components of an ECT sensor are commonly considered in establishing the 3D field variation: (1) number of planes, and (2) shape of plates, as depicted in Figure 2. Examples of the two different design methods are depicted in Figures 3 and 4. A combination of both strategies can be used by integrating irregular shaped plates in multiple planes.66 In Figure 3, a triple plane of a square plate shape is used, whereas in Figure 4 a trapezoidal plate is used in a single plane. Single-plane capacitance sensors for volume imaging, similar to the one depicted in Figure 4, are most suited for applications with limited sensor height. Single-plane arrangements can also be used for focused volume imaging covering a relatively lesser height of the imaging domain. However, it is noted that the three-plane shifted sensor design depicted in Figure 3 was among several most viable sensor designs experimentally tested over hundreds of designs conducted in the authors’ lab. Many of the ECVT applications to multiphase flow systems reported by the authors67-68 were based on such a sensor design. The merit behind this particular design is that it increases the axial resolution while reducing its impact on the radial resolution. This design has also been used by other researchers53 in 3D imaging. In 2D ECT reconstruction, the sensor is completely utilized for providing the maximum 2D resolution. However, extending

the application of ECT sensors to include volume imaging leads to an increased number of unknowns for the same number of capacitance measurements. Thus, the ECVT reconstruction problem is of a higher level of complexity compared to the 2D case due to the increased number of unknowns, severity of the 3D ill-posed problem, and decreased absolute value of measured capacitance due to a lower value of SNR. All of the abovementioned factors contribute to a decrease in the resolution of the output volume image. Clearly, a 3D sensor is needed to provide a better image resolution. Thus, using such sensor designs as shifted layered rectangular plate sensors and multiple or single layered non-rectangular plate sensors as noted above could yield a reasonable axial resolution in imaging.51,66 2.3. Multimodal Tomography Based on ECT System. Among different process tomography techniques, the most conspicuous are those based on the measurement of electrical properties through the utilization of the capacitive, conductive, or inductive nature of the flow components under investigation. In most cases, electrical tomography is applied based on measurements of a single constitutive property; that is, permittivity for ECT or conductivity for impedance (resistivity) tomography. However, the need for real-time imaging of complex processes involving multiphase components has in recent years motivated the development of imaging systems exploiting multiple electrical properties, that is, multimodal tomography. The implementation of multimodal tomography is generally achieved through the integration of more than single tomography hardware into one system, using a reconstruction algorithm capable of differentiating between different components and phases based on a single sensor and signal, or implementing an inherently multimodal tomography sensor capable of capturing a signal related to different physical properties. An example of the first approach is demonstrated in a published work69 where an ECT system is combined with an ERT system for dual imaging of permittivity and conductivity. Considering the cost, complexity, and speed of different multimodal strategies, the multimodal system could be the most versatile. However, not all tomography sensors possess the capability of multimodal

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Figure 3. Sensitivity distributions of selective pairs for a three-layer sensor. Volume enclosed by blue isosurface represents volume covered by indicated pair of sensors for reconstruction.

Figure 4. Sensitivity distributions of selective pairs of a trapezoidal single-layer sensor. Volume enclosed by blue isosurface represents volume covered by indicated pair of sensors for reconstruction.

imaging. For the ECT sensor, it has been traditionally viewed as a single modal tomography sensor based on electrostatic analysis. In a typical ECT system, the frequency of the excitation signal is about 1-10 MHz,70 and the sensor size is less than a few meters in either dimension. As a result, the wavelength is much larger than the size of the sensor, and a static or quasistatic

approximation can be employed to describe the field behavior. The ECT analysis reported in the literature is carried out by assuming a static approximation for the electric field distribution (modulated by the time variation). In situations related to time varying fields, the electric and magnetic fields at the observation point change values some time after a change at the source. The time (propagation) delay depends on the distance between


Figure 5. Permittivity and conductivity reconstruction based on quasistatic analysis.

the source and the observation points and on the intervening media. In the cases where the physical dimensions of the problem are significantly smaller than the wavelength of the excitation, this propagation delay can be neglected and the static laws can be applied to time varying fields. Applying a quasistatic approximation in Maxwell’s equations, the electric field distribution obeys the following equation

∇(σ + jω)∇φ ) 0

(9)

where φ(r b) is the electric potential, B E(r b) ) -∇φ is the electric field intensity, ω is the angular frequency, σ(r b) is the conductivity, (r b) is the permittivity, and b r is the position vector. The mutual capacitance Cij between any two pair of electrodes i and j (source and detector) is given by

Cij )

1 I ∇φijnˆ dl ∆Vij j

(10)

where ∆Vij is the potential difference, Γj is a closed surface (or path in 2D) enclosing the detecting electrode, and nˆ is the unit normal vector to Γj. Taking under consideration the quasistatic analysis, the interrogating signal of the alternating field dissipates electric power in the presence of materials with nonzero conductivity. Measuring the power dissipated through excitation of different ECT pairs of plates provides additional boundary measurements that can be used for the reconstruction of conductivity maps. The rms power dissipated by a conductive object in the domain of interest given the potential distribution φij due to the source electrode i at voltage Vi and detector electrode j at ground voltage is given by

Pij )

1 2

∫∫Ω σ|∇φij|2 dS

(11)

Equations 10 and 11 relate the permittivity and conductivity distributions to (global) measurements of capacitance and power, respectively. The solution for Cij and Pij given (r b) and σ(r b) constitutes the forward problem. The process of obtaining (r b) and σ(r b) from capacitance and power measurements constitutes

the inverse problem for this multimodal imaging system. In Figure 5, a reconstruction result obtained using the known ILBP reconstruction technique is used to demonstrate the capability of an ECT sensor for dual permittivity and conductivity imaging. The capacitance and power measurements were given using computer simulations. 3. Reconstruction and Validation The effectiveness of NN-MOIRT reconstruction technique relative to other widely known techniques, such as LBP, ILBP, and simultaneous iterative reconstruction technique (SIRT) can be shown in figures published in earlier work.35 The first and second columns in the figures indicate the model images (permittivity distributions in the two-phase system). The following columns show, respectively, the reconstructed images using LBP, ILBP, SIRT, and NN-MOIRT where dark red refers to a normalized pixel value of 1 and dark blue refers to that of 0. The reconstructed images are of 32 × 32 pixel resolution. The reconstruction process is set to stop when all of the neuron update values are less than 10-4. The results yield an effective and noise-immune NN-MOIRT technique as compared to other reconstruction techniques (LBP, ILBP, and SIRT). Similar results have been obtained in the case of volume reconstruction. As depicted in an earlier work,51 the 3D-NN-MOIRT provides better reconstruction results when compared to LBP and Landweber reconstruction techniques. The Landweber technique is a form of ILBP.64 A sensor similar to the one in Figure 3 was used in this case. In Figure 5, a reconstruction result obtained using the known ILBP reconstruction technique is used to show an ECT sensor that is capable of performing dual permittivity and conductivity imaging. The capacitance and power measurements were obtained using computer simulations. Figure 6 depicts the reconstructed images of spheres in a bent conduit.51 Utilizing the 3D change in sensitivity variations has enabled imaging complex conduits and objects (unlike the limited traditional ECT). Although the reconstructed results in Figure 6 are elongated at the edges, the results are still reasonably accurate. Part A of Figure 7 shows the simulation of the effect of 10-8 C

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Figure 6. Volume imaging of flow in a bent pipe. (a) Sensing domain, (b) 12-electrode sensor system, (c) reconstructed result of a sphere in the center of the pipe, a cross-section of the volume image is depicted above, (d) reconstructed result of one and a half spheres located near the sensing edge, a crosssection of the volume image depicted above. The color bars represent relative permittivity for the cross-section images.

Figure 7. Reconstruction results for the capacitance data in the left image, results of charge elimination are depicted in the lower right of the right image.

charge placed at the center of the domain on capacitance measurement of a centered dielectric cylinder. As shown in the figure, the capacitance values, which reflect the permittivity distribution, are contaminated by free charge placement. Part B of Figure 7 presents the reconstruction results for the capacitance vector depicted in part A of Figure 7. The upperleft image refers to the original permittivity distribution, and the upper-right image is for the reconstruction without staticcharge contamination. The effect of free charges in the imaging

domain on reconstruction results is depicted in the lower-left image. It is clear from this image that the static charge distorts the reconstruction result. The static-charge elimination method discussed earlier is shown to remove the charge contamination in the capacitance vector, yielding desirable reconstruction results as given in the lower right part of the figure. The results indicate the effectiveness of the charge-elimination method in providing accurate reconstructed images in situations when static charges are involved.


Figure 8. Snapshots of 3D volume images of gas-liquid flow in the bubble column at Ug ) 2 cm/s obtained by ECVT.

4. Experiments and Imaging Results In this section, sample results obtained by the ECVT for the multiphase flow systems are presented. The systems considered include the bubble column and gas-liquid-solid three-phase fluidized bed,35,71-72 gas-solid fluidized bed,73-77 and circulating fluidized bed riser.78-81 The ECVT that used the sensor design given in Figure 3 comprises a 12-electrode rectangular sensor arranged in triple planes. Its performances for 3D volume imaging are examined. The choice of the electrode number is based on the data acquisition system available for experiments, which are 12 channels. The electrode number significantly greater than 12, depending on the availability of the data acquisition system, can be used, which would appreciably increase the spatial resolution of the images obtained. The electrical field intensity with the electrode arrangement given in Figure 3 can be distributed reasonably uniformly in axial and radial directions. Such sensor design is equivalent to the rectangular sensor arrangement of eight-electrode sensors per plane. The length of the sensing domain is 10 cm. The volume images are reconstructed at 20 × 20 × 20 resolution based on the algorithm described above. There are 66 combinations of independent capacitance measurements between electrode pairs from 12 electrodes. The results are obtained from a 12-channel data acquisition system (DAM200-TP-G, PTL Company, U.K.), and the image capture speed is of 80 frames per second. The reconstruction process and data postprocessing are obtained from a 3 GHz Pentium 4 machine, with a memory of 2 GB. 4.1. Bubble Column. The imaging results for a bubble column are obtained from a column size of 0.1 m ID by 1.0 m height. The top of the column is the enlargement section with a diameter of 0.2 m. The gas distributor is a single nozzle with a diameter of 0.5 cm. The experiments are conducted in semibatch mode without inlet liquid flow. Air (dielectric constant ) 1), Norpar 15 (paraffin, density ) 773 kg/m3, viscosity ) 0.253 m Pa/s, dielectric constant ) 2.2) and glass beads (density ) 2500 kg/m3, average diameter ) 200 µm,

dielectric constant ) 3.8) are used as the gas, liquid, and solids phases, respectively. The gas velocity ranges are from 2.5 to 15 cm/s. The ECVT sensor is located 18 cm above the distributor, and the total height of the measuring plane is 10 cm. The initial bed height for the bubble-column experiment is set at 35.5 cm above the distributor. The images and data presented by the ECVT represent those in a real 3D space confined by the height of the sensor plane and the diameter of the column. The image reconstruction algorithm generates the permittivity map determined on or voxels (ECVT) corresponding to the apparent permittivity of the mixed two or three phases of the system imaged. To convert the permittivity map to the phase distribution, a combined series and parallel capacitance models can be used.82 The model relates the permittivity map into the phase concentration in the mixed media through series and parallel capacitance connectivity with the same probability. Figure 8 shows a snapshot of the ECVT image (3D gas concentration distribution) of the gas-liquid system at a gas velocity of 2 cm/s. The tomography volume image is constructed from permittivity voxel values in 4D matrix components, that is, three space components with a spatial resolution of 5 × 5 × 5 mm3 and a one-time component with a temporal resolution of 12.5 ms. The first two figures in the top row are slice cut images of the planes defined by the coordinate system in the bottom-right of the figure. The first and second figures in the bottom row are, respectively, a 3D volume image that is partly cutoff to display the inside of the 3D representation and a 3D isosurface image that displays the 3D boundary (surface) of the bubble swarm image. The cutoff boundary value was set at 10% of the gas holdup value. There is no specific criterion in setting this cutoff boundary; it is arbitrary and is used to provide some sense of distinction of the boundary of high-concentration bubble swarm from the surrounding low gas concentration region. For comparisons with the tomography images, a photograph of the two-phase flow taken using a high-speed digital video camera system under the same condition is displayed in the right-hand side of the figure.

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Figure 9. Snapshot of volume image of bubble in gas-solid fluidized bed using 200 µm glass beads. (a) 3D volumetric (partly chopped) distribution of solids concentration obtained by ECVT, (b) isosurface image of bubble (Ug ) 0.1 m/s), (c) (d) X-ray photograph taken by Rowe (1971).

4.2. Gas-Solid Flows. 4.2.1. Gas-Solid Fluidized Bed. Three fluidized beds with diameters of 0.05, 0.1, and 0.3 m ID are examined for the scale effect on ECVT measurements. A two-stage cyclone separates gas and particles for each fluidized bed and is installed in the freeboard of the bed. A porous plate with a pore size of 20 µm and a fractional free area of 60% is employed as a distributor for all fluidized beds. The fluidized particles are FCC catalyst with a mean diameter of 60 µm and a particle density of 1400 kg/m3. The measuring sensor for the ECVT is located 18 cm above the distributor, and the total height of the measuring plane is 10 cm. The static bed height is 0.5 m for all fluidized beds. Figure 9 shows the snapshot of the tomography volume image of a 0.1 m ID gas-solid fluidized bed with 200 µm glass beads at a gas velocity of 0.2 m/s. The 3D solids concentration distribution in the bed is obtained by the ECVT, as shown in part a of Figure 9. The color image from blue to red represents the solids’ concentration spanning from low (empty bed) to high (packed bed). A bubble with a spherical cap shape is clearly observed in part b of Figure 9, in which the 3D isosurface image is obtained by setting the cutoff boundary of 25% (solids concentration) in the solids concentration distribution profile shown in part a of Figure 9. The 3D bubble shape obtained by the ECVT is consistent with the quasi-3D bubble obtained by the ECT technique.74 Parts c and d of Figure 9 show the X-ray photography of the bubble in the gas-solid fluidized bed with crushed coal particles (dp ) 530 µm, Fp ) 1250 kg/m3) and magnetite particles (dp ) 2800 µm, Fp ) 2930 kg/m3) ,respectively.82-83 The similarity of the images affirms the ECVT technique. 4.2.2. Circulating Fluidized Bed. The circulating fluidized bed consists of a 0.1 m ID riser with a height of 6.32 m, a separator and secondary cyclone system, a large-volume particle storage hopper and an L-valve. Particles are carried upward in

the riser and exit at the top through a right-angled bend into a horizontal tube connected to the separator and secondary cyclone where the particles are separated from the gas. Subsequently, the particles are fed back to the bottom of the riser through the nonmechanical L-valve. The solids’ circulation rate, which is controlled by adjusting the air aeration rate at the injection points of the L-valve, is measured by timing the falling distance of tracer particles in the standpipe. The compressed air is introduced into the riser through an oil filter, humidifier, pressure manometer, and flow meter. The air humidity is controlled by the water level and water temperature in the humidifier. The relative humidity and temperature are measured by means of a humidity probe inserted into the air stream. The superficial gas velocity is measured by the flow meter adjusted by the temperature and pressure of the airflow. The fluidized particles employed in this study are FCC catalysts with a mean diameter of 60 µm and particle density of 1400 kg/m3 and sand particles with a mean diameter of 240 µm and particle density of 2200 kg/m3. The measuring sensor for the ECVT is located at 0.48 m above the distributor of the riser. Figure 10 compares the quasi-3D flow structure obtained by combining a sequence of ECT images to form a quasi-3D image, and the real 3D flow structure obtained by the ECVT in a 0.1 m ID circulating fluidized bed with 200 µm sand particles (group B particles). The quasi-3D imaging provides quasi-3D images from combining 2D cross-sectional ECT images obtained from averaging over an axial distance of 5 cm, representing the thickness of the electrodes. In this kind of imaging, time serves as the third dimension. A color bar from blue to red represents the variation of the solids’ concentration from 0 to 0.3. The 3D flow structure or the volume image is constructed from permittivity voxel values in 3D matrix components, that is, three space components with spatial resolution of 5 × 5 × 5 mm3 obtained by ECVT. Under the operating conditions of Ug )


Figure 10. 2D and 3D flow structure variation during the choking transition in a 0.1 m ID circulating fluidized bed with 200 µm glass beads at Ug ) 2.4 m/s.

2.4 m/s and Gs ) 14.86 kg/m2s for group B particles, the bed undergoes the choking transition from the three-region structure with solids blobs at the central region to the formation of wall slugs as shown in the quasi-3D diagram in Figure 10. The similar bed density variation during the choking transition is observed on the basis of the real 3D flow structure with the existence of solid blobs at the center of the column before the choking transition and the formation of wall slugs after the choking transition. The similarity between the quasi-3D by ECT and the real 3D flow structure by ECVT further substantiates the inherent characteristics of the bed behavior and the choking phenomena in the gas-solid circulating fluidized bed. 5. Concluding Remarks This study presents a perspective of the development of the electrical capacitance tomography imaging techniques, particularly with respect to their recent evolution of the techniques from 2D to 3D imaging. It describes the early ECT imaging efforts that were restricted to 2D, averaged along sensor length. The technique was extended to the 3D domain through the stacking of 2D images obtained in different times or planes in what is known as quasi-3D imaging. Most recently, direct 3D imaging was realized through the introduction of the volume tomography concept in what is noted as ECVT. The ECVT development was made possible through advances in sensor design and 3D image reconstruction. In principle, the spatial resolution in volume imaging can be significantly improved with increased number of sensors augmented with innovative sensor design and image reconstruction techniques. The use of volume imaging concept allows the ECVT to be applied to qualify and quantify the 3D dynamics of multiphase flow systems, which are of considerable interest to the multiphase flow and other fields. The multiphase flow systems of which the ECVT has been applied include bubble columns, gas-solid fluidized beds, and risers. These are systems that are widely practiced in industry. The potential for ECVT usage in industry can be enhanced by the further improved accuracy and image reconstruction speed and the added capability of realizing

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ReceiVed for reView October 9, 2007 ReVised manuscript receiVed December 3, 2007 Accepted December 4, 2007 IE0713590

Electrical Capacitance Tomography â A Perspective - ACS Publications

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Electrical Capacitance Tomography â A Perspective - ACS Publications