**5. Image reconstruction for slurry applications**

### **5.1 Background**

Image reconstruction is one of the major challenges in ERT applications as it is an ill-posed problem, as noted in [15], and is still an active research area. An in-depth analysis of research work in the area of image reconstruction will not be discussed here; however, relevant points for slurry applications will be illustrated.

An overall principle of ERT is that image reconstruction is an inverse problem; it is required to calculate the conductivity distribution in a defined space based on boundary measurements. The calculation of the measurements based on a known conductivity distribution within the space and electrode injection current is relatively straightforward and is referred to as the "forward problem."

Early reconstruction methods were based around a backprojection algorithm as described in [16]. Algorithms based on this concept are still in use at the time of writing as the usual reconstruction technique supplied with commercial ERT systems. Typically, this is a linear backprojection (LBP) algorithm. It has the advantage of speed, allowing for near real-time imaging and relative simplicity. The backprojection has the disadvantage of being qualitative and also suffers from blurring in instances where high-conductivity gradients are present as noted by [17]. However, in many circumstances, it is sufficient for investigating slurry flows and is widely used. Usually, the ERT process begins with collecting a homogenous reference data set in the vessel of interest. A data set is then obtained with the solids or gas added to the vessel and the reconstruction performed using a differential approach relative to the reference.

Alternative algorithms are available to overcome some of the shortcomings of the LBP in situations where there would be a benefit such as sharp concentration gradients and rapid images are not required. These algorithms have grown in popularity, especially as computational power has increased, thus allowing more complex computational processing in a reasonable time.

Ref. [18] presented a sensitivity conjugate gradient (SCG) method for ERT which was also an early commercial offering. This technique was shown to decrease the blurring or smearing inherent in the LBP for sharp discontinuities and thereby provide improved contrast recognition than the backprojection algorithm tested on synthesized data. Examples using real data were also presented including imaging a human hand. The real data results showed that the SCG was able to provide much more detail than other contemporary alternatives.

Ref. [19] describes a MATLAB toolkit, EIDORS, which provides a framework for developing and testing tomography reconstruction algorithms. Simulations of ERT measurements can be made in the toolkit and various reconstruction approaches tested. Experimental data can also be processed in EIDORS using a wider variety of algorithms. Further details of EIDORS are given in [20].

The commercial ERT suppliers are also continuing to develop their offerings for postprocessing of ERT data. An example of this is described in [21]. A variety of algorithms were presented which were stated to be suitable for various scenarios in ERT. A recent state of the art is described in [12].

Most ERT data acquisition and reconstruction are performed assuming twodimensional behavior of the electric fields. This is a simplification as noted by [22] as the actual electric fields are three-dimensional. The effects can be mitigated in some circumstances by using a 2.5D approach as described in [23]. While the 2.5D approach was successfully used for slurry pipe imaging by [24], it is more difficult to apply the concept to a mixing tank as the invariance of the slurry condition along the axis of the vessel is not necessarily present, unlike for the case for pipe flow. Judicious choice of the injection current for the ERT test and the spacing between electrode rings may reduce the 3D effects. A full 3D data acquisition and reconstruction is also possible in principle to avoid these issues but is not available in the presently available commercial hardware, since the planes are usually measured separately in sequence. However, if the flow timescales are long relative to the data acquisition time, the data from the separate planes can be combined to provide three-dimensional information. This approach can be useful for tanks or gas/liquid systems and for the cross-correlation velocity measurements. High-speed versions (500 frames per second or more) of the commercial ERT systems are available for these applications.

#### **5.2 Comparison with other imaging techniques**

Other imaging techniques have been applied for slurry flows. An example is gamma-ray tomography which is an extension of the industrially used gamma-ray

#### *Electrical Resistance Tomography Applied to Slurry Flows DOI: http://dx.doi.org/10.5772/intechopen.107889*

density instrument. This technique relies on the attenuation of the gamma-ray varying as varying density slurry flows through the measurement section as described in [25]. Tomography applications require multiple sources and detectors or a single source and detector that can be rotated or translated across the measurement section. More details of the technique are given in [26]. Disadvantages of the method were the time taken to acquire the data (tens of minutes using a single source/detector) and an increase in errors near the pipe wall. The acquisition time can be a concern given that laboratory slurry tests are usually carried out in recirculating rigs, thus leading to potential change of the properties of the slurry due to particle attrition and temperature rise. A multiple source/detector system was described in [27] based on a system described in [28] and the errors of the system evaluated for water/clay/sand slurries in a 100-mm pipe up to 20% v/v of sand. Further work by the SRC group is given in [29], where they use the gamma-ray technique to assist with correcting ERT for conductivity changes in the carrier fluid. The device used was capable of rapid imaging (up to 100 Hz) unlike single source/detector systems.

The present author and his colleagues have used MRI imaging to investigate slurry flows, prior to using ERT. Ref. [30] describes the basic principles of NMR/MRI together with its application to flows. A useful property of NMR is that there is a velocity sensitivity inherent in the physics, which is manifested in the phase image. While it was possible to obtain velocity and concentration data from MRI for synthetic polymer solution-based slurries, the rapid decay of the NMR signal due to the short T2 relaxation time prevented application to industrial slurries in larger pipes where rapid gradient switching is difficult, although smaller systems such as the rheological application discussed in [31] are possible. A further update of MRI possibilities for rheology and fluid dynamic applications is given in [32]. Another consideration is that the MRI equipment is often larger and more expensive than ERT, although permanent magnet systems are available which are more economical than cryogenic systems, whereas ERT is more usable industrially as described in [13]. It is possible to obtain velocity information from ERT data via a cross-correlation technique using two electrode planes. This technique was used by [9] with a high-speed ERT data acquisition system to obtain velocity data in slurry pipe flow.

**Figure 5** from [33] shows a comparison between a photograph, MRI and ERT from the CSIRO pipe rig where a bed of solids was present in the pipe flow. The ERT data includes LBP as well as a more advanced SCG processing [18] of the same data. This algorithm was one of the early postprocessing options available commercially, and the results are in better qualitative agreement with the MRI and photograph than the LBP. Slurry velocity images obtained by MRI over a range of velocities are shown in **Figure 6**. These flows were all in the laminar regime. Unfortunately, the MRI system was not usable with industrial slurries or the later development of the pipe rig which had a steel structure.

#### **5.3 ERT image reconstruction for pipe flow**

The commercial ERT systems (ITS P2000 and p2+) used at CSIRO for slurry flow research were supplied with the LBP reconstruction as the default option. In practice, when operating the pipe rig and mixing tanks, the real-time LBP images are very useful in monitoring the state of suspension in the flow and adequate for determining the effect of pipe velocity or impeller speed on particle suspension.

An early comparison between LBP and a more advanced algorithm (SCG) for a settled bed of solids was given previously in **Figure 5**.

#### **Figure 5.**

*Comparison between (a) photograph, (b) MRI and ERT algorithms, (c) LBP, and (d) SCG ([18]). As originally published and presented at the BHR 15th International conference on Hydrotransport, Banff, Canada, 3rd-5th, June 2002, [33].*

#### **Figure 6.**

*MRI velocity images (5% v/v solids in Ultrez 10 (Carbopol polymer solution)) at superficial velocities from 0.3 to 1.1 m s−1. The distortion in the velocity images is due to the bed of solids.*

The author and his colleagues also use a 2.5D approach as described in more detail in [24] which describes the application of an absolute image reconstruction approach which does not require a reference image other than for data acquisition. The essential

**Figure 7.**

*ERT voltages from experiment and simulation of a homogenous fluid in a pipe asssuming 2D and 3D behavior. As originally published and presented at the BHR 20th International conference on Hydrotransport, Melbourne, Australia, 3rd–5th may 2017, [24].*

feature of this approach is to conduct the forward problem in 3D (assuming that the pipe flow is invariant along the pipe axis) and the inverse problem as a 2D slice through the center of the electrodes. The significance of the 3D forward problem is shown in **Figure 7** where measured ERT from a pipe with a homogenous fluid is shown compared with 2D and 3D forward solutions. It is clear the 3D forward problem is the most appropriate.

The results from conventional LBP differential processing and 2.5D absolute processing are shown in **Figures 8** and **9**, respectively, for a high-conductivity tailings sample in a 100-mm pipe. In this case, the reference data were taken from a homogenized sample of the slurry. It should be noted that both approaches adequately detect the stratification of the flow, but the absolute processing allows for the case where obtaining a suitable carrier fluid reference image is difficult. The author's colleagues are continuing research into image reconstruction approaches for pipe flow at the time of writing.
