## 4 Electrical Tomography Applications
### Pulp Suspensions Characterisation Using ET: The Authors' Approach
#### 4.3.3 Fibre Flow Velocity Estimation  
By using two EIT planes and cross-correlation, EIT can also be used to determine the velocity profile in a pipe. For example, [PERSON] et al. [132] used a best-correlated pixel method to measure both axial and radial velocities simultaneously. Independently of the procedure used, a marker is needed. As a first approach, the introduction of a small fraction of conductive or non-conductive solid spheres in the flow was used. After several attempts without success to distinguish these markers in the EIT images, the authors instead decided to use a trace of a highly concentrated NaCl solution as a marker. For the purpose of introducing this NaCl solution in the flowing fibre suspension, an injection system was developed and added to the existing pilot rig: it was located around 3 m before the first EIT electrode ring. This injector was built in such a way that the flow suffered almost no disturbance. For all the tests reported in this section, two 16 electrode titanium rings A and B were used, 30 cm apart, with ring A closer to the injector inlet, as shown in Figure 10. The procedure here reported for estimating velocity was different from those reported in the literature, but, nevertheless, with some similarities with the one described by [PERSON] et al. [133]. Instead of using the complete set of EIT projections, the authors only made use of the first projection; first, the potential differences of each pair of the first projection with no marker injection in the flow were acquired, afterwards, they were subtracted to the measured voltage differences obtained during the runs with NaCl injection.  
Finally, the sum of the module of those differences was computed. For each suspension velocity and fibre concentration tested, several injection trials were performed to assess the reproducibility of this approach. The conditions used for the velocity estimation are summarised in Table 2. Some examples of data obtained with this approach are shown in Figure 11: three sets of NaCl injections for suspensions containing 1% and 2% of _Eucalyptus_ fibres with a velocity of 0.25 m/s (Figure 11a,b).  
Figure 9: EIT images obtained with a concentration of \(\pm\)1% (w/w) of _Pine_ fibres (**a–d**) for 0.5 m/s, 1 m/s, 1.5 m/s and 2.5 m/s, respectively.  
In that same figure, a graph showing the estimated velocity versus the measured suspension velocity is represented (Figure 11c). A quite reasonable estimation is obtained, and so the authors' approach was validated. Moreover, as fibre concentration increases, the advance of the NaCl front is slowed due to the presence of more fibres and to the structures that build up among fibres. This can be explained by the fact that the velocity of the fibres is increased by a factor of 1000.  
\begin{table}
\begin{tabular}{c c} \hline
**Concentration (wt/wt)** & **Flow Velocities (m/s)** \\ \hline
3 & 0.25, 0.5 \\
2 & 0.25, 0.5, 0.75, 1 \\
1 & 0.25, 0.5, 0.75, 1 \\ \hline \end{tabular}
\end{table}
Table 2: Table of fibre concentrations and flow velocities used for the velocity estimation tests.  
Figure 11: EIT injection test trials for fibre suspension concentrations of 1% and 2%, at the velocity of 0.25 m/s (**a**,**b**), and estimated velocity versus measured velocity for all fibre concentrations (**c**).  
Figure 10: Schematic of the relative position of the EIT electrodes sections and NaCl injection inlet.  
be observed between Figure 11a,b, where for the higher fibre concentration, there is a delay in the detection of the NaCl in the second ring (ring B). Therefore, in the future, it can be used to evaluate those structures as a function of fibre concentration and flow velocity.