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The reconstruction of the spatial complex conductivity σ + j ω ε 0 ε r from complex valued impedance measurements forms the inverse problem of complex electrical impedance tomography or complex electrical capacitance tomography. Regularized Gauß-Newton schemes have been proposed for their solution. However, the necessary computation of the Jacobian is known to be computationally expensive, as standard techniques such as adjoint field methods require additional simulations. In this work, we show a more efficient way to computationally access the Jacobian matrix. In particular, the presented techniques do not require additional simulations, making the use of the Jacobian, free of additional computational costs. [ABSTRACT FROM AUTHOR]

Pneumatic conveying systems have become a standard technique for the transport of bulk materials such as powdery or granulates. The spatial dependence of the material density and the stream velocity in such transport systems require a volumetric measurement principle for flow measurement. In this paper we analyse the capability to estimate the volume fraction from capacitive sensing data using electrical capacitance tomography (ECT). In particular, we investigate the capability of back-projection type imaging algorithms. The ill-posed nature of the imaging problem of ECT require the incorporation of prior knowledge in the design of the estimator. We analyse the different flow profiles in pneumatic conveying in order to generate specific sample-based prior information to improve the estimation performance and robustness. We discuss the construction of different linear image reconstruction algorithms and present a framework, which allows a detailed statistical analysis of the estimator performance. Simulation studies show the estimation behaviour of different algorithms with respect to the incorporated prior information. We demonstrate, that the incorporation of specific prior knowledge leads to an improved estimator behaviour; for example, reduced variance and unbiased estimates. We implemented laboratory experiments in order to analyse the presented approach for the application in real pneumatic conveying processes. We demonstrate the improved robust estimation behaviour by means of comparative reconstruction results obtained with different algorithms and priors. Furthermore, the uncertainty of the estimated volume fraction is analysed in steady state conveying processes. Hereby, it is demonstrated, that appropriate prior information improves the estimation performance also for measurements coming from real pneumatic conveying processes, making ECT a suitable tool for the volume fraction estimation in such transport systems. [ABSTRACT FROM AUTHOR]

Pneumatic conveying is a widely applied technique for the transportation of powders. Dense phase conveying such as slug flow is the preferable operating condition of such transport systems. Advantages are the reduced energy and conveying gas consumption and reduced material wear. The design and the operation of dense phase conveyors is a challenging task due to complex flow dynamics and the lack of reliable flow meters, which are crucial for process control. In this work the capabilities of electrical capacitance tomography (ECT) for slug flow parameter estimation are analysed. The estimation of flow parameters is addressed and demonstrated by means of laboratory experiments. Amongst other parameters it is shown that mass concentration distributions as well as particle velocity fields can be obtained from tomographic image reconstruction results, which are substantial parameters for potential mass flow metering. Additionally, the proposed estimation techniques are applied to signals provided by an ECT system, which is installed within a large-scale pneumatic conveyor of an industrial process plant. It is observed that also Geldart group A powders with Archimedes numbers in the scale of A r ≈ 1 e 0 are conveyable in slug-like structures which can be separated by stationary or non-stationary layers. Furthermore, various slug flow properties of powders with A r > 1 e 2 reported in literature are confirmed but also deviating properties are observed, leading to novel insights into horizontal dense phase flow processes of powders with A r ≈ 1 e 0. The results demonstrated in this work are pointing out the capabilities of ECT for flow analyses, which are enabling further insights into flow mechanisms and future developments of flow meters for dense phase flow processes. [Display omitted] • Electrical capacitance tomography-based slug flow parameter estimation. • Tomographic imaging of mass concentration distributions. • Differentiation between slug velocity and particle velocity. • Application within an industrial-scale pneumatic conveyor with a length of 2 km. • Novel insights into dense phase conveying of Geldart group A powders with A r ≈ 1 e 0. [ABSTRACT FROM AUTHOR]

Pneumatic conveying is a standard transportation technique for bulk materials in various industrial fields. Flow metering is crucial for the efficient and reliable operation of such systems and for process control. Capacitive measurement systems are often proposed for this application. In this method, electrodes are placed on the conveyor systems transport line and capacitive signals are sensed. The design of the sensor with regard to the arrangement and the number of electrodes as well as the evaluation of the capacitive sensor signals can be divided into two categories. Calibration-based flow meters use regression methods for signal processing, which are parametrized from calibration measurements on test rigs. Their performance is limited by the extend of the calibration measurements. Electrical capacitance tomography based flow meters use model-based signal processing techniques to obtain estimates about the spatial material distribution within the sensor. In contrast to their calibration-based counterparts, this approach requires more effort with respect to modeling and instrumentation, as typically a larger number of measurement signals has to be acquired. In this work we present a comparative analysis of the two approaches, which is based on measurement experiments and a holistic system model for flow metering. For the model-based analysis Monte Carlo simulations are conducted, where randomly generated pneumatic conveying flow patterns are simulated to analyze the sensor and algorithm behavior. The results demonstrate the potential benefit of electrical capacitance tomography based flow meters over a calibration-based instrument design. [ABSTRACT FROM AUTHOR]