Online Monitoring of Particle Distribution in Dense Phase Conveying Systems Via Electrical Capacitance Tomography and Reduced Order Reconstruction Method

Steady state conveying of solid particles is a crucial factor for many applications in industry. Although there has been research on this topic for decades there are still areas with little progress up to the present. Especially for dense conveying there were no possibilities to identify the state of a particle flow inside a conveying pipe with high temporal and spatial resolution. Methods based on laser diffraction are limited to very dilute particle flows but, if applicable, can deliver highly accurate measurements on particle size distribution and mass flow rates. For dense phase conveying the standard instrumentation are pure flow detectors which give a simple yes/no information if there is a particle flow above a certain threshold or not. However, most of these devices do not have sufficient time resolution to identify unstable plug flow conditions. Another family of flow measurement devices can be classified as capacitive sensing systems. Hereby the mass fraction is estimated from capacitive measurements based on the dielectric permittivity distribution. The quality of this estimate strongly depends on the state of the particle flow. This is due to the low number of measurements typically used and the nature of the estimation problem. By constantly recalibrating the measurement signals with balance data of the conveyed material they can give a good estimate on the mass flow rates.

A capacitive measurement system which overcomes this issue is Electrical Capacitance Tomography (ECT). ECT allows to fully reconstruct the spatial material distribution inside a pipe, as it maintains more measurements and dedicated signal processing methods. However, the process of reconstruction is not trivial as the soft field nature of the electric field inside the pipe leads to an ill-posed mathematical problem. Thus, post processing of ECT data is time consuming and was not possible in an online manner. Another shortcoming of ECT is the need for balance data to map the permittivity distribution to particle mass flow rates. In this study we designed a universal ECT signal processing hardware with 16 channels and tested new reconstruction strategies for one and two-plane pipe sensors. Test data was acquired in a vertical hopper discharge test rig and a horizontal pneumatic conveying facility.

By having a complete finite element model (FEM) of the ECT sensor, many data structures necessary for the reconstruction can be calculated a priori to the actual measurements. Using reduced order modelling via principal component analysis (PCA), can save additional computation time and finally lead to a real-time capable system which is able to record and process data with up to 100 Hz. Hence, the system presented is able to provide sufficient time resolution to detect plug flow in dense phase pneumatic conveying and deliver a good estimate of the spatial distribution of particles inside the pipe (e.g. strand formation).

The processing of ECT data can be further improved by using a priori knowledge on the conveying system. In a horizontal pipe, for example, a strand will form in the lower half of the pipe inherently when increasing the mass loading from dilute to dense flow conveying. Such physics based assumptions on the flow topology can improve the PCA approach, further reduce computing times and provide an overall good quality of flow reconstruction.