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.

Capacitive sensing has become a favourable measurement technology for flow metering in pneumatic conveying systems. Multi electrode sensing structures and tomographic signal evaluations enable spatially resolved flow parameter estimation, which is of particular interest for pneumatically conveyed solids due to inhomogeneous particle distributions within the pipeline. The non-invasive working principle of capacitive sensors is an important feature for the application in industrial processes with harsh environments. However, cross-sensitivities of the capacitive probe cause effects such as temperature drifts of the measurements. For a reliable operation of capacitive flow meters in harsh environments, induced drifts have to be compensated. In this paper we present detailed analyses of thermal effects within capacitive sensors. Based on the findings, a model based temperature compensation approach is developed within the Bayesian framework. The performance of the proposed compensation approach is analysed by a measurement based validation within a climate chamber and by a simulation based uncertainty quantification. The capability to obtain temperature independent estimates with calibration measurements acquired at room temperature is demonstrated.

In powder processing industries, information about the mass concentration and the moisture content of the material is often required for process monitoring and control. Capacitive sensors are widely applied for measurements of powder materials, as they are sensitive to variations in mass concentration and changes in moisture content. However, for processes where the mass concentration and the moisture content of the material can vary, it is not possible to distinguish between the two effects based on capacitive measurements alone. This paper shows how permittivity and conductivity measurements can be used to independently determine the mass concentration and the moisture content of a powder. The proposed method is demonstrated for an exemplary coal powder. A dielectric characterization based on impedance measurements of a coaxial probe is carried out. Based on these measurement experiments, a modelling approach is presented that allows the independent determination of the mass concentration and the moisture content of powders, which is of great interest for the development of measurement systems for powder processing industries.

The reconstruction of the spatial complex conductivity $\sigma +j\omega {\epsilon }_0{\epsilon }_{\mathrm{r}}$ 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.

Electrical capacitance tomography (ECT) refers to an imaging technique, which provides information about the spatial material distribution within an object. Since the image reconstruction forms a non-linear ill-posed inverse problem, prior information about the occurring material distributions is required in order to obtain stable reconstruction results. For the monitoring of dynamic industrial processes by means of ECT, recursive Bayesian estimation such as the extended Kalman filter (EKF) were shown to be suitable reconstruction algorithms. Though due to the usually high dimension of the inverse problem, computational costs are an immanent issue for the tracking of fast changes in the material distribution. In this paper we present a sample based state reduction approach for the extended Kalman filter. This approach not only allows stable reconstruction results but also involves significantly decreased reconstruction times due to the reduced state space.