ECT in a large scale industrial pneumatic conveying system

The application of electrical capacitance tomography (ECT) for monitoring of industrial processes has been studied and proposed by many researchers. Examples can be found in monitoring of multiphase flows or mixing processes in reactors. Demonstrations of the functionality based on lab and test rig measurements have proven the potential of the proposed principles. This paper discusses the application of an ECT system in a heavy industries application. The harsh operating conditions in the industrial environment pose several challenges for the application of sophisticated measurement technology. This work addresses key aspects for the application of an ECT measurement system in such an environment. Specifically the electrical system design and the influence of the temperature are addressed. Relevant parameters and possible solutions are discussed. Furthermore the application of ECT as instrument for mass flow metering in pneumatic conveying processes is addressed. Supportive measurement studies from test rig experiments and comparative simulation studies are presented. Therefore, the paper provides a concise discussion on the application of ECT under harsh operating conditions, as well as the use of ECT as a measurement device for process measurement. The work concludes with a presentation of a measurement system in an industrial plant in which the proposed concepts were succesfully implemented.


Introduction
The capabilities of process tomographic measurements are considered by many industries and researchers as key enabler for process optimization and control [1,2].Consequently, its different sensing modalities, e.g.electrical impedance tomography (EIT) [3] or electrical capacitance tomography (ECT) [4,5] have seen vast research spanning more than three decades.All systems aim on the visualization of the spatial material distribution within a process by means of its conductivity (EIT), or dielectric permittivity (ECT) based on electrical measurements [1].Target applications for the use of tomographic measurements systems are multiphase flows [6], mixing processes in vessels [7], monitoring of fluidized beds [8] or monitoring of particulate flows [9].Other applications which have been presented are for example the monitoring of drying processes [10] or crack detection in concrete [11], highlighting the potential of these tomographic measurement systems.The selection between ECT or EIT as sensing modality depends on the specific measurement problem.A benefit of electrical tomography systems with respect to other imaging modalities, e.g.medical systems, is the moderate instrumentation effort.The capacitive sensing used in ECT also allows non-invasive sensor designs, which is a relevant aspect for sensing in harsh environments [12].This is for example the case in pneumatic conveying, where the particulate matter causes abrasion on the sensor.Publications on electrical tomography systems cover all aspects of these measurement systems such as the sensor design [13][14][15], and the measurement electronics [16,17].The bulk of publications can yet be found in the field of signal processing and image reconstruction methods [18].Also demonstrations on test rigs for the aforementioned applications are presented, e.g.[19][20][21][22].
However, with respect to the addressed technical topics there are comparatively fewer reports that address the application of electrical tomography systems within actual industrial production plants.An representative overview is provided in [2].The review articles [23,24] address the application of ECT in particulate process measurement and circulating fluidised beds.The articles [25,26] describes the use of ECT in pharmaceutical manufacturing processes.In the conference publication [27], the authors have presented an ECT system, which is installed in a pneumatic conveyor used to transport coal powder to a pulverized coal injection (PCI) system for a blast furnace within a steel plant.The system is used to monitor the conveying process.
It is common understanding among engineering practitioners and researchers that the transition of sophisticated measurement technology from lab systems to industrial applications requires additional development steps and raises further research questions.For the present application the following main questions arise • How has a signal acquisition system, i.e. the measurement electronics, to be designed for industrial applications?• How can drift effects due to cross sensitivities, e.g.temperature, within the sensor front-end be handled?
Moreover, the question arises which capabilities are offered by ECT beyond the image reconstruction of the spatial permittivity distribution.Mass flow measurement is an obvious application here [28], yet this is again a challenging measurement problem, as the spatial mass density within the pneumatic conveying process is not known due to the aeration of the particulate matter by the transport gas.Also the humidity of the transported material is relevant here.To summarize these aspects, figure 1 shows an overview of the ECT measurement system by means of a signal flow graph.The figure also includes a photography of the sensor within the plant.We refer to this sensor as field sensor and the whole system is referred to as field system.The field sensor assembly contains two ECT sensors with 8 electrodes each.The sensors are mounted on a fibre glass pipe and the whole assembly is encapsulated in a steel housing.The assembly technique is due to the harsh operating conditions, e.g. the sensor has to withstand pressures of up to 20 bar.The temperature can rise up to 100 • C. The block 'ECT based image reconstruction' in figure 1 provides the reconstructed spatial permittivity distribution ε r (x, y) from the capacitance measurements d.This is the defacto standard output of an ECT system.The additional blocks mark adoptions for the measurement hardware and signal processing steps as necessary extensions to enable the operation of ECT within this environment.It includes a suitable design of the electrical signal path for the measurement of the coupling capacitances in the sensor, a temperature compensation method as well as dedicated modifications to the signal processing techniques.Also prior models for the incorporation of knowledge about the flow process are included.The evaluation of the mass flow rate ṁ from ECT image reconstruction results ε r (x, y) then requires the determination of the spatial mass density β s (x, y) and the velocity field v(x, y).This step requires material models to determine the spatial mass density of the aerated powder materials in the conveying system from the reconstructed permittivity images from the ECT system.The addressed elements provide a significant extension to the 'classical' image reconstruction of ECT, as the measurement methodology gives access to spatial flow parameters.Within this scheme ECT can be seen as an underlying instrument flow parameter measurement and for mass flow metering.
This work provides a concise discussion of the relevant challenges and possible solutions for the application of ECT system in industrial plants as depicted in figure 1. Specifically the following aspects are addressed • Electrical system design (section 2).
• Temperature drifts and model based temperature compensation method (section 3).• Formulation of prior information for flow processes (section 4).• Determination of the spatial density of aerated powders from ECT images (section 5).
which also form the sections of this work.Hence the first two sections specifically address the two research questions initially raised in the introduction of the work.The later two sections are related to the signal processing methods in order to use ECT as an instrument for flow parameter and mass flow measurement as depicted in figure 1.Previous work on the specific individual subjects by the authors is referenced in all sections.
The novelty of the work lies in two aspects.First a holistic representation of all necessary methods to be able to use an ECT system in an industrial setting is presented.Here the discussion is centred around the necessary steps to use an ECT system under harsh operating conditions.Secondly, the actual field system is presented, where all of the addressed aspects are implemented.This is presented in section 6.A challenge with the first-time application of a new measurement technology in a production process is the lack of a reference.Therefore, the discussions of the sections 3-5 also include reference measurements on test rigs, as well as comparative simulation studies to verify the effectiveness and functionality of the proposed approaches.The work therefore contributes to the understanding about the application of ECT in industrial applications.In addition, the proposed use of ECT as an underlying instrument, e.g. for measuring the mass flow rate, highlights new research opportunities for process tomography and process measurement.

Electrical system design
In this section the electrical system design to measure the inter-electrode capacitances within the sensor, i.e. the coupling capacitances between the electrodes, is addressed.Hereby the used circuit concept for the measurement and the realization of the electrical connection between the sensor and the electronics have to be discussed.
For the acquisition of the coupling capacitances between electrode pairs, capacitive displacement current measurements have become the established measurement technique.Hereby an excitation signal is applied to an electrode and the capacitive displacement currents at the other electrodes are measured using dedicated current measurement circuits.The electrode where the excitation signal is applied is referred to as active electrode and the technique is referred to as low-Z measurement technique.The process is repeated for all electrodes.Also potentiometric measurements (high-Z) have been proposed [29], yet low-Z measurement approaches offer better immunity with respect to parasitic capacitances.
With respect to the selection of the excitation signal two main distinctions can be made: • Charge transfer based systems [30,31].Hereby a single pulse signal is used as excitation signal for the active electrode.An advantage of this technique is in the fast measurement, as the signal acquisition takes place within the flank of the excitation signal.• Continuous displacement current measurement systems [32][33][34].Hereby a continuous AC signal is applied to the active electrode.An advantage of this technique is the signal acquisition with a defined measurement frequency.This will be exploited in section 5.
The second relevant aspect for a system is the connection between electronics and the sensor system.For capacitive sensor systems a direct connection between the electronics and the sensing electrodes is preferable due to the minimization of parasitic capacitances [12].An integration of the electronics into the steel housing of the field sensor is yet not suitable due to the heat exposure.There are also other aspects, such as the housing design and the installation location, which make a direct connection unpreferable.For the field system of this work, a connection by means of coaxial cables has to be used.Figure 2 shows an overview of the electrical system, showing the connection scheme with the coaxial cables.The inner conductors of each coaxial cable connects the individual electrodes with their individual measurement circuits, which can be used as transmitter (TX), i.e. the circuit provides the excitation signal, or as receiver (RX), i.e. the circuit measures the displacement current, respectively.The screens of the cables are used for the ground connection.An essential aspect in the design of an electrical measurement system is the existence of a defined signal propagation path.For the depicted ECT system, wave propagation effects along the coaxial cables due to the frequencies of the measurement signals have to be addressed [35].Hereby the length of the coaxial cables and the wave length λ are relevant.
For the ECT system in the process plant a continuous displacement current measurement system with an AC excitation frequency of 40 MHz was selected.The frequency was selected because of the moderate realisation effort of the circuitry [29].The wave length λ is given by λ = c/f, where f is the frequency and c denotes the speed of propagation.For coaxial cables the wave length λ at 40 MHz is about 5 m, leading to a length for a λ/4-line of about 1.2 m.This length is critical, as a λ/4-line forms a gyrator [36] for the specific frequency.The gyrator causes an inversion of the termination impedances by the coaxial cable.With respect to measurement circuits which are used as receivers, the gyrator effect transforms the low input impedance of the displacement current measurement circuits into a high impedance between the electrode and the ground at the sensor.This forms a significant deviation from the low-Z measurement scheme.For the transmitter circuit, the high input impedance of the sensor is transformed into a low impedance at the output of the transmitter electronics.Hence the signal propagation is not well defined and standing waves are formed due to the reflections, which can also harm the measurement circuits.The λ/4-line presents a worse case scenario, yet even small lines lengths can lead to significant impedance transformation effects by the coaxial cables [37], which also increases the sensitivity with respect to parasitic capacitances.
The length of the field sensor is about 500 mm and the coaxial cables are routed at the backside of the sensor, i.e. between the electrodes and the screen, to an outlet opening in the steel housing.Due to this length the coaxial lines have a significant influence on the behaviour of the measurement system.In order to overcome this issue, the cable length of the system was set to be λ/2 [37].For the λ/2-line, the aforementioned effects disappear, leading to a well defined signal propagation.From an electrical point of view the low-Z measurement circuitry appears to be directly connected to the sensor, while they are actually separated.Attenuation effects due to the lines can be reduced by calibration [37].

Summary on the electrical system design
For the presented sensor setup and the situation at the installation site, the λ/2-length provides a comfortable margin for the installation of the system, i.e. the connection of the sensor with the measurement circuitry, which is housed in the cabinet next to the sensor.See figure 18 for an illustration of the system.The solution of using a λ/2-line is feasible due to the continuous displacement current measurements, as the presented effects apply under steady state conditions.It is not applicable with charge transfer based systems, due to the spectra of the pulse.The applied technique with the λ/2line can also be useful for future measurement systems in high temperature applications [38][39][40].It must be noted that the use of transmission lines also requires a careful wiring scheme to avoid crosstalk effects between the lines.In the presented sensor setup this effect was minimized by a suitable routing and separation of the transmission lines.For arbitrary line lengths or varying frequencies also impedance matched designs [41] have been studied, which can be relevant for the application of impedance spectroscopic measurement techniques [17,42].Yet the low-Z measurement circuitry remains favourable due to the shunting of parasitic capacitances.

Temperature drift effects and model based temperature compensation method
Among the different electrical tomography approaches, ECT allows non-invasive measurements as the electrodes are not in contact with the materials inside the sensor, i.e. the transport process for this application.However, this makes ECT also sensitive with respect to variations within the sensor, e.g.variations of the dielectric properties of the sensor pipe and the backside material due to heat or heat expansion effects.This is a relevant aspect for the field system in the industrial plant.
To demonstrate the impact of temperature on the sensing behavior, figure 3 shows a reconstruction experiment, in which a sensor identical to the field sensor was heated in a climatic chamber.The left figure shows the correct reconstruction result for an empty sensor.The measurement was performed at 20 • C. Also the calibration measurements for an offset/gain calibration [43] of the sensor have been performed at this temperature.The reconstruction result for a temperature of 80 • C are depicted on the right hand side of figure 3.This temperature is comparable to the temperature in the field system.The reconstruction result shows significant artifacts with respect to the experiment at 20 • C. The artifacts are due to drift effects caused by the temperature in the sensor front end.As the artifacts cause a significant influence on the reconstruction results, a technique to reduce the influence of temperature drifts is required.In this section the drift effects of the sensor due to the temperature are addressed and a temperature compensation strategy is presented.A common practice to overcome temperature induced drift effects in sensors is to calibrate the sensor at the intended temperature, or to characterize the system behaviour for a certain temperature range and to apply a compensation strategy based on a temperature measurement within the application.However, both approaches have only limited usability for the field ECT system in the process plant.The heating of the sensor is due to the transported material and thus also depends on the conveying process.Hence a single calibration at a specific temperature is not sufficient.Likewise, it is difficult to emulate the heating process of the plant in the laboratory in order to establish a compensation strategy.Because of the aforementioned properties a model based temperature compensation strategy is meaningful.Hereby the influence of temperature drifts is compensated by means of signal processing techniques.

Temperature effects and compensation strategy
In this section a model based temperature compensation approach is presented.Such a technique was originally presented in [44].In order to develop a model based temperature compensation technique the influence of the temperature on the sensor behaviour has to be understood.Figure 4 shows a sketch of the ECT sensor and a cross-sectional image for two neighbouring electrodes.The cross-sectional image also includes several capacitances, which summarize the capacitive coupling paths between the electrodes.The capacitance C x denotes the capacitance, which is formed by the material distribution inside the sensor pipe.Note however that a lumped circuit element representation can not be used for a full description of the sensor effects.Following the illustrated lumped parameters, the capacitance between the electrodes is given by The expression for C and the equivalent circuit scheme demonstrate the noninvasive nature of ECT by the capacitive coupling through the sensor pipe.However, all of the parasitic capacitances are influenced by the temperature due to variations of the dielectric material properties and due to thermal expansion effects.
In [44] the influences of temperature variations on the coupling capacitances between the electrodes are studied.Hereby a multiphysical simulation approach is used to consider thermal expansion effects and variations of the dielectric material properties due to the temperature.Based on a sensitivity study it can be shown that temperature effects can be modeled by the two parameters κ and λ, which influence the relative permittivity of the sensor pipe and the backside, i.e. the material between the pipe and the shield, by The variables denoted with the subindex 'nominal' denote the permittivity values at the reference temperature.Based on this modelling approach, a joint estimation approach is formed [44].The parameters κ and λ are treated as nuisance parameters [45] and form the vector These parameters are then simultaneously estimated within the image reconstruction algorithm.With this approach the compensation is therefore achieved by an adoption of the sensor model.Details on the formulation of the estimator are presented in section 4. Prior knowledge for κ and λ is determined from heating experiments in a climate chamber with an empty sensor.Hereby κ and λ are determined and a Gaussian summary statistic is formulated, covering the range of the nuisance parameters from the measurements [44].prior has been used [43].The reconstruction of the rod is therefore blurred, yet the benefit of the temperature compensation is clearly visible by the significant reduction of the artifacts.Also, the estimated values for the dielectric materials correspond to the actual values and the position of the rod is correctly visualized.
Figure 7 shows a Monte Carlo simulation of the mean square error (MSE) for the ECT image reconstruction.The simulation was carried out over randomly generated material distributions for particulate flows.Details about the analysis approach are presented in [44].The generation of the used patterns for the material distribution is also addressed in section 4. The results show the severe impact of temperature effects on the MSE when no compensation approach is used.The proposed compensation scheme shows a significantly lower and almost constant MSE, demonstrating the effectiveness and performance of the approach.

Summary for temperature compensation
The analysis of cross sensitivities with respect to environmental parameters such as the temperature plays a vital role in the design of measurement systems.Due to the sensor design, the measuring capacitances in an ECT sensor are sensitive to temperature effects, which lead to significant artifacts in the reconstruction results.Countermeasures are therefore relevant for industrial applications.The modelling of temperature drift effects by means of nuisance parameters and the joint estimation of these parameters with the material distribution within the sensor provides a possible solution by means of a compensation strategy.A relevant detail about the approach is the fact that the treatment of temperature induced effects by means of nuisance parameters requires no additional temperature sensor.Hence the technique, while already efficient, has the potential for further improvements.

Formulation of prior information for flow processes
The reconstruction of the spatial distribution of the relative permittivity from the capacitive measurements forms the inverse problem of ECT.Research on image reconstruction algorithms has lead to various reconstruction methods, which differ by the parameterizations of the material distribution, the used model for the measurement process, the numerical solution methods, the incorporation of temporal information, etc.A review about reconstruction methods is provided in [18].In this section the image reconstruction is addressed.The focus will be on the incorporation of knowledge about the particulate flow processes.
For the ECT system presented in this work, linear backprojection type algorithms based on a finite element (FE) simulation model for the sensor are used.For the field system a 3D FE model of the sensor is used.However, the reconstruction is then performed by means of a 2D image representations.The computations carried out by the image reconstruction algorithm are of the form x = x 0 + P reco d, where d is an M × 1 vector holding the noisy measurements.The N × 1 vectors x and x 0 hold the image reconstruction result and a linearization point, respectively.The image reconstruction is then formulated by the matrix P reco .
The choice for such an algorithm is considered due to the following aspects: • The relative permittivity of the transported coal is small, i.e. close to the relative permittivity of air, so that a linearized approximation of the FE model can be used.• The low level representation of the material distribution based on the finite element discretization is suitable for the application.• The reconstruction methods are fast, which is crucial for online flow measurements.Overview of flow regimes in pneumatic conveying [48].
An important requirement is the reconstruction of the actual permittivity values.This will be addressed in section 5.A possible algorithm for the image reconstruction is the linear maximum a posteriori estimator, which is given by [45] x Hereby J is the Jacobian matrix, which holds the derivatives of the simulated measurements with respect to the elements of x.Efficient techniques for the computation of J are presented in [46].Σ meas is a covariance matrix incorporating knowledge about the measurement noise.However, also model errors, e.g.due to the linearization can be incorporated by means of enhanced error models [47].For the incorporation of the temperature compensation which was addressed in section 3, the estimator (1) is reformulated for the augmented state vector , where x n holds the nuisance parameters κ and λ.Prior knowledge about the material distribution is incorporated by means of a Gaussian summary statistics for x, i.e. x ∼ N (µ x , Σ x ), where µ x is a mean vector and Σ x is a covariance matrix.
While the addressed reconstruction technique is well established, an essential contribution for the quality of the reconstruction result is given by the incorporation of suitable prior information.Hereby the formulation of prior knowledge based on the flow regimes of particulate flows proofed to be essential [49].Figure 8 depicts an overview about flow profiles in pneumatic conveying [48,53].The flow regime describes the distribution and movement of the particulate material within the transport pipe.The flow regime depends on the velocity and the pressure drop along the transport pipe.For dispersed flows the particulate matter is uniformly distributed over the cross section of the transport pipe.Also the velocity profile is almost uniform and the material density is low.For the other flow regimes a distinct bottom layer with higher density is formed, which is transported with a lower velocity than the dispersed phase above.In slug flow the material is transported in a wave like motion.To formulate a Gaussian summary statistics x ∼ N (µ x , Σ x ) for the flow profiles, a sample based approach is used [49].For this approach samples of the material distribution are generated.Then µ x and Σ x are evaluated from these samples [47].
The left plot in figure 9 exemplarily depicts a possible parameterized scheme for the generation of samples for flow regimes with a dense phase on the bottom of the pipe.The transition between the dense phase at the bottom and the aerated phase is modeled by a quadratic function, which is parameterized by the height parameters h 1 to h 3 .The dielectric material properties of the phases are given by ε r,1 for the dense phase and ε r,2 for the dilute phase.The parameterized phase transition allows an incorporation of uneven surface distributions of the dense phase.Furthermore a smooth transition between the solid phase and the gas phase is incorporated.The sample generation is then performed by drawing the parameters of the model.E.g. the right plot in figure 7 exemplary depicts different height profiles of the dense phase.By this approach µ x and Σ x can be evaluated from an ensemble of samples.

Validation of the prior modelling approach
For the validation of the proposed prior schemes, measurements on flow test rigs and simulation based studies are used.Figure 10 shows three images of a pneumatic conveying stream of a flow experiment in a test rig for different time instances.The image sequence shows the transition from a stratified flow towards a moving cluster flow.Also the time instants for each image are stated.Figures 11 and 12 show the result of two ECT image reconstructions.For the result depicted in figure 11 a sample based prior for circular objects was used [43].This prior is referred to as rod-type-prior.For the results depicted in figure 12 the proposed prior for flow processes is used.Both reconstruction results represent the flow experiments depicted in figure 10.However, although the flow experiment provides no ground truth, the presence of artifacts can be seen in the images in figure 11.The results using the addressed prior for flow profiles in figure 12 do not include these artifacts and appear more realistic with respect to the expected behaviour of the flow process.Hence the impact of the prior can be directly observed.A more rigorous analysis can be performed by means of Monte Carlo simulation studies.Hereby, samples of the material distribution are generated and the reconstruction error is analyzed.Figure 13 presents an exemplary result of such a study.Details about the approach are presented in [49].The variable ϕ expresses the normalized integral over the permittivity distribution.The normalization is performed by the maximum value of the relative permittivity and the cross sectional area of the pipe.Hence ϕ = 1 represents a state where the sensor is completely filled.The two diagrams in figure 13 show the mean error and the standard deviation of the estimation error.The results show the positive impact of the correct prior information by the smaller mean error µ e and the reduced standard deviation σ e .

Summary for prior modelling
The presented technique to incorporate prior knowledge about the flow regimes, i.e. specific knowledge about the transport process and hence about the measurand, is a relevant part to obtain suitable image reconstruction results.Further details about the approach can be found in [49,50].The use of application specific priors has also been demonstrated in other research.E.g. in [54,55] the generation of reconstruction algorithms based on sampled data is presented.The study in [56] shows an approach to find optimal electrode configurations for ECT sensors for flow imaging.As flow profiles are highly symmetric, non-symmetric electrode configurations have been found to lead to reconstruction results with lower image reconstruction errors [56].In [51] an ECT sensor for flow imaging with 5 electrodes only is presented.The meaningful reconstruction results are again possible due to the symmetry and the typical patterns of the flow profiles.Hence the construction of application specific priors has also the potential for optimized sensor designs.

Determination of spatial mass density and mass flow rate measurement using ECT
The visualization of the spatial permittivity distribution is de facto the standard output of an ECT measurement system.However, flow imaging is only one aspect for the application of an ECT system in a pneumatic conveying system.The desire to determine flow parameters such as the mass flow rate ṁ is apparent and has been addressed e.g. in [28,57].
The mass flow rate ṁ is defined by where v(x, y) is the spatial velocity profile in ms −1 and β s (x, y) is the spatial mass density in kg m −3 .The cross sectional area of the sensor is denoted by Γ.The determination of v(x, y) and β s (x, y) for the evaluation of equation ( 2) is generally a challenging task in horizontally aligned conveying systems due to the different flow regimes.Flow measurements are therefore usually carried out in vertical pipe segments, as the material is more evenly distributed in such pipe sections.ECT on the other hand has the potential to determine both quantities.The velocity profile can be estimated from time of flight measurements [45] using two ECT sensors.However, the determination of the density β s (x, y) from the image reconstruction result ε r (x, y) of the relative permittivity forms a challenging problem, as the particulate matter is aerated by the gas stream of the conveyor.Hence the density is lower than the bulk density of the material.The evaluation of β s (x, y) therefore requires a material model to determine the density from the reconstructed relative permittivity.In this section a measurement strategy and a modelling approach for the determination of the spatial density of aerated powder from permittivity measurements is presented.The generation of the addressed material model requires a measurement technique for the characterization of the dielectric material properties of aerated powders.For these measurements a coaxial probe design for dielectric material characterization is used, which allows the creation of aerated particle mixtures within the probe [58].Therefore, the probe features a gas inlet for the aeration of the particulate material.Figure 14 shows a photography of the measurement setup.It consists of the probe, a scale and a network analyzer for impedance measurements at the probe.
For the measurements, the probe is filled with a defined amount of the powder material, which is transported in the conveying system.Then the material is aerated using the gas inlet of the probe.The impedance of the probe is measured and the relative permittivity of the aerated powder material is determined.As the dielectric properties of material can depend on the frequency, the use of a measurement technique with a continuous AC excitation is relevant, as it was addressed in section 2. Details about this procedure including an uncertainty assessment are presented in [59].This also includes reference measurements using particle image velocimetry (PIV) to verify the correct aeration state of the powder.
With the measurement setup and the measurement procedure, data points for the relation between the density β s and the relative permittivity ε r can be determined.Yet not all fluidization states [60] can be generated within the probe.Hence the measurement data is used for the parameterizations of a dielectric mixture model [61].A suitable approach is given by the Landau-Lifshitz-Looyenga (LLL) model [62,63] 3 The parameter η can be determined from the probe measurements.
Figure 15 depicts an exemplary result for poly-propylene (PP) particles, which are used in measurements on a test rig for flow experiments.The red dots mark the measurement points obtained with the probe.The solid line shows the behaviour of the parameterized model.The small range of achievable measuring points is due to the size of the particles, which only allow a small range of homogeneous aeration states within the probe.Yet despite the small range of data points the LLL-model correctly predicts the density of solid PP ρ s , which is plotted by the rectangular marking in figure 15.This indicates the feasibility of the model in combination with the measurements.The result in figure 15 also shows that a linear interpolation between the relative permittivity and the density is not correct and would lead to measurement errors.

ECT based mass flow metering on a test rig
With the proposed scheme model the relation between the relative permittivity ε r and the density β s , the image reconstruction results from the ECT system can be used to evaluate β s (x, y) and hence evaluate the mass flow rate ṁ using equation (2).For the validation of these methods a test rig for flow experiments is used.Figure 16 shows a photography of the setup.For flow experiments the feeding vessel is filled with the particulate material.The experiments are carried out with PP particles and pressurized air is used for the transport gas stream.Hereby different particle flows can then be generated by means of the valve settings for the feeding vessel and the compressed air [64].The test rig includes an ECT system, as well as reference sensors such as a balance.A pipe section made from perspex allows a visual inspection of the experiments and enables further reference measurements, e.g.PIV imaging.For the calibration of the ECT sensor an offset/gain calibration [43] is performed.
A crucial aspect for particulate flows are electrostatic phenomena due to the collision of particles against each other and against the wall of the test rig.Hereby the strength of the charge formation due to the triboelectric effect depends on the distance between the transport material and the wall material in the triboelectric series [65].To minimize the effect, most of the pipes in the test rig are made of the same material as the transport material, i.e.PP.In experiments with fast flow velocities also the perspex tube in front of the sensor was replaced by a PP tube.With this approach, electrostatic phenomena can be substantially diminished.PIV based reference measurements are still possible within the perspex pipe section after the sensor.
Figure 17 shows an exemplary test rig measurement for the mass flow rate ṁ and the accumulated mass m, where the ECT approach is compared against measurements with the reference balance.As the balance is placed at the end of the test rig the results depicted in figure 17 exhibit a delay.Note that the determination of ṁ from the balance data requires a differentiation step, which leads to oscillations in the balance signal for ṁ.Furthermore the balance data is acquired with a lower measurement rate.However the results for ṁ show the same behaviour.A more meaningful comparison can be made be the accumulated mass m, which is depicted in the lower diagram of figure 17.The trends show the same temporal slope and achieve almost the same end point.It is relevant to note, that these results were achieved without any additional calibration of the overall system.Only the addressed offset/gain calibration of the ECT system was used.The good agreement between the results demonstrate the potential capabilities of the approach.

Summary on mass flow rate measurement
The approaches and results presented in this section exemplify the capability of ECT to be used as an instrument for mass flow measurements.The demonstrated measurement and modelling techniques to determine the mass density from permittivity measurements provides a reasonable approach.An important aspect in the application of capacitive sensor technology is the presence of moisture [12] due to its influence on the capacitive measurement signals.The experiments presented in this section have been carried out using PP particles.In the controlled laboratory environment the humidity is low and has no relevant influence on the measurements.However, for industrial applications the influence of moisture has to be considered.Hereby an extension of the capacitive sensing technology is required.Impedance spectroscopic measurements offers a potential approach for the determination of moisture content and to further provide compensation techniques against the influence of moisture.E.g. in [66] an extension of the addressed LLL-material model is presented, which can be used to simultaneously infer information about the mass density and the moisture content of the powder material [66] from complex dielectric material properties.

Field system
In the previous four sections, the relevant aspects for the industrial application of ECT were discussed.Specifically the electrical system design (section 2) and the influence of the temperature 3) have been addressed.Technical solution approaches for these two points have been pointed out.Sections 4 and 5 then address specific signal processing techniques for the use of ECT as a mass flow meter.Hence all relevant parts regarding the system as depicted in figure 1 are addressed.Measurement studies from test rigs and simulation studies support the findings and proposed solutions within these sections.In this section details about the actual field system in the pneumatic conveyor are presented, where all the addressed elements from the previous sections are implemented.
Figure 18 depicts photographies of the ECT measurement system and the sensor, which was installed in the first half of 2019 and is in operation since then.On the left hand side of figure 18 two photographs of the system are shown.The photography on the right side of figure 18 shows the sensor during the assembly phase.It is a dual plane ECT sensor with 8 electrodes per plane.The inner sensor tube is a fibre glass tube on which the electrodes and a screen were mounted.Its inner diameter is D i = 110 mm.The whole sensor is encapsulated in a steel body, the back space is filled with a potting compound.A cabinet houses the measurement electronics, a PC-system and a modem for remote control.The connection between the sensor and the electronics is realized by means of coaxial cables, which are housed in a metallic hose for protection.For the measurement of the coupling capacitances a continuous displacement current measurement with a frequency of 40 MHz is used.The coaxial cables are cut to length λ/2 for this frequency.The ECT sensor is installed in a pneumatic conveyor used to transport coal powder to a PCI system for a blast furnace within a steel plant.A special feature of the conveyor system is its length of almost 2000 m, which makes it one of the largest systems at present.The dielectric material properties of coal are in the range of ε r ≈ 2.5 and σ ≈ 1 × 10 −4 Sm −1 , which is suitable for the application of ECT.For the used coal an LLL-based material model was determined based on the procedure discussed in section 5.The transported coal dust has a relative humidity between u = 0.5% to 1.5%.Due to the low humidity content, the influence of moisture is neglected for the following results.
In the following sections measurement results for and with the field system are presented.This includes an SNR (signal to noise ratio) characterization of the measurement circuitry, as well as reconstruction results for the spatial relative permittivity distribution ε r (x, y) and the spatial mass density β s (x, y).

Electronic system and SNR
In this section some aspects of the electronic system design are addressed and the SNR of the system is evaluated.Figure 19 depicts the assembly of the measurement electronics.For each electrode an individual circuit board is used, which hold the transmitter circuitry, as well as the displacement current measurement.The 40 MHz excitation signal is generated using digital logic gates.The use of a rectangular signal wave form instead of a sinusoidal signal is possible with the used coaxial cables, as the addressed signal propagation with the λ/2-line also applies for the harmonics of the signal.For the current to voltage converters AD8000 operational amplifiers are used [37,67].The output signals are bandpass filtered.For the demodulation an AD8307 [68] is used.Afterwards the signal is digitized.
Eight individual circuit boards are combined on a master board as depicted in figure 19.Hereby all relevant signal paths are kept short.The measuring process is controlled by a central microprocessor on the master board.The frame signal acquisition rate, i.e. the measurement rate to perform all measurements for an individual ECT sensor with 8 electrodes, is set to be 100 Hz.For the two ECT sensors a time interleaved measurement mode is used, leading to a frame measurement rate of 50 Hz for each ECT sensor.This is necessary to avoid cross talk effects between the two ECT sensors, yet it is sufficient for the flows in the plant.
Figure 20 shows the result of a SNR analysis of the measurement systems.The measurements are numbered according to their entries in the capacitance matrix of the inter-electrode capacitances, e.g. the index of measurement 1 means the measurement between the first electrode, which is used as transmitter, and the second electrode.The diagram shows the SNR for an empty sensor and the SNR with respect to the span of the measurement signal are depicted.The span of the measuring signal results from the difference between the coupling capacitances for an empty sensor and a sensor, which is filled with pulverized coal.This SNR is relevant to form the covariance matrix Σ meas of the measurement noise for the image reconstruction algorithm [47].The achieved SNR of the system for the field application is comparable to published circuit systems [31,69].
With respect to electrostatic charges, we have not observed any relevant phenomena in the field system.This is due to the small low conductivity of the coal.Furthermore the steel pipes of the conveying system and the sensor housing lead to a dissipation of possible triboelectric charges.

Reconstruction of flow profiles
In section 3 the model based temperature compensation was addressed and demonstrated for laboratory experiments.In this section reconstruction images for the relative permittivity ε r (x, y) from the industrial plant are presented.were computed without the temperature compensation.For the results depicted in figure 22 the temperature compensation is applied.While no ground truth for the measurements in the plant can be provided, typical artifacts in the reconstruction results depicted in figure 21 can be identified.In contrast, the reconstruction results with the temperature distribution show no deviations.The results are consistent with the knowledge of flow profiles and show the occurrence of slug flow, i.e. a wave like material flow.

Flow measurement in the industrial plant
In section 5 a material model for the determination of the spatial density β s (x, y) from the reconstructed permittivity images ε r (x, y) was presented.This extends the potential of ECT, e.g. for mass flow metering where ECT is used as an underlying instrument.Yet the possibility to measure the spatial density β s (x, y) is also relevant for research in particulate flows [70].
To demonstrate this, figures 23 and 24 depict two exemplary reconstruction results for the spatial density β s .Due to the symmetry of the flow profiles, the height profile is displayed and the density is normalized by the bulk density ρ b .Figure 23 shows a sequence of slug flows.Between the slugs a gravitational settling of the material height can be observed, which is due to the particle size of the pulverized material.Using the presented techniques the system can be used to determine different parameters of the flow, e.g. the velocity of the slug, or the particle velocities and densities within the slugs, which are relevant parameters for research on these flow regimes [64].Figure 24 depicts a sequence with an unstable flow condition.For short phases, a slug flow begins to form, yet this flow state cannot be maintained in a stable manner.Such processes are part of ongoing research in pneumatic conveying.Hence the presented ECT system and its capability to measure physical parameters of the flow provide a powerful extension for research [71,72] in the field of particulate flows.

Conclusion
In this work the application of ECT within industrial applications was addressed.The operation of sophisticated measurement systems under harsh operating conditions requires dedicated solutions along all parts of the measurement system.The topics presented in this work first cover the design of the electrical measurement system, the influence of temperature drifts and a compensation strategy to enable ECT imaging under harsh operating conditions.Furthermore an approach to determine mass densities from ECT image reconstruction results is presented, which enables ECT based mass flow metering.The implementation of all techniques on a field system in an actual application is demonstrated.The paper provides a coherent presentation of all subjects, which are relevant for the use of ECT in industrial environments.Discussions with respect to established techniques as well as references to relevant key publications that address all necessary details are provided.The work offers researchers an overview of relevant influencing factors and solution approaches as well as concepts for the use of ECT beyond the classical image reconstruction.

Figure 1 .
Figure 1.Overview of the relevant elements for an ECT system in an industrial application, as well as for the signal processing steps to use ECT for mass flow metering.

Figure 2 .
Figure 2. Electrical connection scheme of the ECT system.The length of the coaxial cables is matched to the excitation frequency.With a λ/2-line-length the coaxial cables have no influence on the signal propagation under steady state conditions.

Figure 3 .
Figure 3. Impact of temperature effects on the reconstruction result of the permittivity distribution.The sensor was placed in a climate chamber.The figure on the left hand side shows the result at room temperature.The figure on the right hand side shows the result at 80 • C.

Figure 4 .
Figure 4. Sketch and cross-sectional view of the ECT sensor for the discussion of temperature effects.The capacitances in the cross sectional view represent the different capacitive coupling paths, which are influenced by temperature effects.The influence is due to variations of the permittivity and heat expansion effects.

Figures 5 and 6
Figures 5 and 6 depict several reconstruction experiments to demonstrate the temperature compensation in the lab using experiments in a climate chamber.The temperature for these experiments is again 80 • C. The first figure in the series (left hand side) shows again the behaviour for an empty sensor.In the remaining experiments a plastic rod has been placed within the sensor using a template for positioning.The position of the rod is indicated by a circle within the figures.Figure5depicts the reconstruction result without the temperature compensation, figure6shows the result with the compensation.The calibration of the sensor has been performed at 20 • C. For the image reconstruction of these experiments a smoothness

Figure 5 .
Figure 5. Reconstruction results for a series of climate chamber experiments without temperature compensation.The temperature for the experiment is 80 • C. A plastic rod has been placed inside the sensor.The position is marked by a circle.

Figure 6 .
Figure 6.Reconstruction experiments for the experiments depicted in figure 5 using the proposed temperature compensation.The temperature for the experiment is 80 • C. For the experiments a smoothness prior was used.

Figure 7 .
Figure 7. Monte Carlo analysis for the image reconstruction error for the flow profiles for different temperatures.

Figure 9 .
Figure 9. Parameterized model for the generation of samples of flow regimes with a dense lower phase and a dispersed upper phase (left).Exemplary samples of the phase boundary between the two phases (right).

Figure 10 .
Figure 10.Photographies of a flow experiment.

Figure 11 .
Figure 11.Reconstructed ECT images for the flow experiment depicted in figure 10.For the reconstruction a sample based prior for circular objects was used.

Figure 12 .
Figure 12.Reconstructed ECT images for the flow experiment depicted in figure 10.For the reconstruction the proposed flow prior was used.

Figure 13 .
Figure 13.Result of a Monte Carlo simulation study.Hereby flow patterns are generated and an ECT image reconstruction is performed using different priors.The prior for the flow regimes leads to a reduced mean error and a reduced standard deviation for the estimation error.

Figure 14 .
Figure 14.Measurement setup for the dielectric characterization of aerated powder materials.

Figure 15 .
Figure 15.Exemplary measurements for fluidized PP pellets with the setup presented in figure 14 and parameterized LLL model.While the achievable measurement range is small, the LLL model approaches the density of solid PP.

Figure 16 .
Figure 16.Photo of the laboratory flow test rig.In experiments with fast flow velocities, the perspex tube in front of the sensor was replaced by a PP tube to minimize triboelectric charge phenomena.

Figure 17 .
Figure 17.Exemplary mass flow measurement with the ECT system and comparison with the reference balance.
Figures 21  and 22  show two sequences of reconstruction images from the ECT sensor in the plant.The results depicted in figure21

Figure 18 .
Figure 18.Photography of the ECT measurement system in the industrial pneumatic conveying plant (left) and of the sensor during the assembly (right).

Figure 19 .
Figure 19.Photography of the electronics for the ECT system.8 sub-boards holding the circuitry for each electrode are mounted on a master board.

Figure 20 .
Figure 20.SNR measurement of the system for all measurements of the inter electrode capacitances.The index of the measurement denotes the number of the measurement.

Figure 21 .
Figure 21.Sequence of reconstruction results from the ECT sensor in the industrial plant without the temperature compensation.

Figure 22 .
Figure 22. of reconstruction results from the ECT sensor in the industrial plant with the temperature compensation.

Figure 23 .
Figure 23.Reconstructed normalized mass density during a slug flow phase in the industrial plant.

Figure 24 .
Figure 24.Reconstructed normalized mass density from the industrial plant.The measurement shows a unstable flow.For short phases, a slug flow begins to form, yet this flow state cannot be maintained in a stable manner.