<figure><img src="image_1.png" /></figure>

HAL
open science

Metrology of Tomography for Engineering

Mi Wang

► To cite this version:

Mi Wang. Metrology of Tomography for Engineering. International Symposium on Image based Metrology (ISIMet 2), Dec 2017, Maui, United States. hal-02419859

HAL Id: hal-02419859

https://hal.science/hal-02419859

Submitted on 19 Dec 2019

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_2.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Metrology of Tomography for Engineering

Mi Wang<fnref n="1" />*

<figure><img src="image_3.png" /></figure>

ISIMet 2
International
Symposium on
Image based
Metrology

Hawaii, Maui
December 16-21
2017

**Abstract**

Tomographic imaging has unique features at “seeing” through the optical opaque medium and “building” up a volumetric view of multiphase dynamics in process pipelines or reactors in a nonintrusive manner. At other aspects, raw tomograms are reconstructed with a specific algorithm, which usually present distributions of a specific physical property of the process medium, e.g. the electrical conductivity of mixture in the use of electrical resistance tomography. However, these volumetric measurements are not conventionally understood, which may create a level of challenges in industrial application. Normally, specific theories or methods have to be employed to convert raw tomograms to meaningful engineering data. This paper reviews typical methods in tomographic data fusion and their implementations for process applications via a number of case studies carried out by the author and his team, providing a glance of view of the imaging metrology. The electrical resistance tomography is particularly expressed for measurement of various multiphase flows, including mixing processes, slurry, oil-in-water and gas-in-water two-phase flows, as well as 3-dimensional rendered flow regimes. It emphasises the important role of engineering data fusion in the metrology of tomography for engineering application.

**Keywords**

Tomography — Metrology — Engineering

## INTRODUCTION

Tomography has become one of common methods for visualizing and characterizing process dynamics of multiphase flows in chemical, petroleum, nuclear engineering and many other areas over the past decades. Electrical tomographic imaging, comparing the conventional direct imaging methods such as Optical reflection, PIV and X-ray transmission, can “see” the multiphase flow dynamics through the optical opaque medium without the use of radioactive source. However, the physical properties of mediums sensed by tomography are normally not as engineering parameters as expected. An interpretation from tomographic data to engineering parameters is always required. However, the method of the interpretation might be different from one case to other, involving multiple sciences at physics, statistics, computing as well as process engineering knowledge, which raises the specific features of the tomographic metrology for solving engineering problems.

The aim of the paper is to emphasise the important role of data fusion in bridging between tomography and process engineering for advanced process measurement and control. Typical methods for interpretation of disperse phase or miscible mixing dynamics from tomography data are summarily expressed and a number of case studies carried out by the author and his team are reviewed in following sections, which address both aspects of science and engineering, typically based on electrical resistance tomography (ERT), in engineering measurement

challenges.

## 1. Metrology of tomography

Tomography is recognized as an indirect imaging method comparing the conventional reflection, absorption and transmission imaging, which is based on measurement of electrical properties of materials by applying a low frequency (from DC up to few MHz) electric field or a magnetic field. A low frequency electromagnetic field can penetrate most process materials which are opaque to the light. The electrical techniques also avoid the hazards of ionising radiation generated from nuclear emission techniques, e.g. x-ray or γ-ray based techniques. They are inexpensive and relatively straightforward to implement with sub-millisecond temporal resolution. Tomographic images (tomograms) needs to be reconstructed from boundary measurements with a specific algorithm. The reconstructed images generally do not report the engineering parameters of the process and are suffered from a level of artificial errors from the inverse solution process. Due to the limited number of measurements and the propagation nature of low frequency electromagnetic waves, they provide images with a spatial resolution around 5% (the diameter of the object to the diameter of the vessel) and a homogeneity resolution better than 1% (e.g. the mean concentration of gas in water).

Further data process are normally required in order to derive meaningful engineering data from conductivity tomograms. Typically, it can be employed to derive the disperse phase concentration distribution or mixing homogeneity in multiphase flows or mixing processes

<footnote n="1">¹School of Chemical and Process Engineering, University of Leeds, Leeds, LS2 9JT, United Kingdom</footnote>

<footnote>*Corresponding author: m.wang@leeds.ac.uk</footnote>
respectively. It is also used to investigate the permeability of materials, foam structure, velocity distribution and further, the flowrate of disperse phase in multiphase flows. There are many industrials applications reported, demonstrating its extensive applicability but also the important role of engineering interpretation as a key in the metrology of tomography for engineering.

## 1.1 Principle of process tomography

Electrical tomography, including electrical capacitance tomography (ECT), electrical impedance tomography (EIT) and electromagnetic tomography (EMT), is based on the specific properties of materials principally sensed by each technique [1]. Electrical resistance tomography (ERT) is a particular case of electrical impedance tomography when the real component of electrical impedance is the dominant property of materials in an EIT process application. ECT senses the permittivity distribution of dispersed materials in a fluid process with a non-conductive continuous phase. ERT is specified for a process that has a conductive continuous phase. EMT is mainly applied for high conductive fluids, which can induce measurable current under a magnetic field. In the case of EIT, the sensor is made from multiple electrodes arranged around the periphery of the internal wall of the process vessel or pipeline, in contact with the process medium but not intrusive to the medium. An alternating current is applied to some electrodes and voltages are measured from the remaining electrodes, according to a predefined sensing strategy. Then these voltage measurements are used to reconstruct the impedance distribution inside the vessel with a specific inverse algorithm. Based on the reciprocity and sensitivity theorem proved by Geselowiz [2] and Lehr [3] and the assumption cited for sensitivity coefficient back-projection (SBP) approximation [4], the relative change of boundary voltage measurement can be presented as Eq.1 with an assumption of ($\Delta\sigma \ll \sigma$),

$$ \frac{\Delta V_j}{V_j} \approx - \frac{\sum_{k=1}^{w} \Delta\sigma_k s_{j,k}(\sigma_k)}{\sum_{k=1}^{w} \sigma_k s_{j,k}(\sigma_k)} \quad (1) $$

where j is the measurement-projection location and k is the pixel number, $s_{j,k}$ denotes the sensitivity coefficient at pixel k under the measurement-projection j, P denotes the maximum number of measurements, w denotes the maximum number of pixels, $\sigma_k$ and $\Delta\sigma_k$ are the conductivity and conductivity change at pixel k, respectively, and $V_j$ and $\Delta V_j$ refer to the reference voltage and the voltage change at measurement-projection j.

It is known that inverse solution of Eq.1 is not directly derivable due to the ill-condition of sensitivity matrix. Many indirect methods were developed to solve the linear equation in the past. Typically, they were reported as single step method, e.g. the back-project method [5] and the Newton one-step reconstruction (NOSER) [6].

However, it should be pointed out the solution for Eq. 1 if any exists, only satisfies the change of conductivity $\Delta\sigma \ll \sigma$. The closest solution for large conductivity changes may be obtained from multi-step approach [7].

In the process, errors may also be introduced from a number of stages, e.g. (a) at the measurement stage due to limits on signal-to-noise ratio, (b) at the inverse solution stage due to the linear approximation (for a nonlinear electric field problem) and ill-condition of the inverse problem (therefore the sharp boundary of an object image not possible) and (c) at the visualisation stage due to limits of human visual capability (only about 30 shades of grey). These errors are certainly transferred to the engineering interpretation. Therefore, understanding of the tomography principles and error sources are necessary for development of the metrology for engineering. Due to the focuses of the paper, the error and uncertainty of given case studies are not extensively discussed, which may find from specific articles elsewhere.

## 1.2 Metrology for engineering

Since ERT can detect local changes in electrical conductivity, the technique is used to study unsteady mixing or fluid dynamics of flow mixtures, such as gas-liquid or solid-liquid mixtures, where the disperse phase of fluids or solids have different conductivities from the aqueous continuous phase. ERT may, therefore, be suitable for numerous aqueous-based processes. However, ERT only produces electrical conductivity distribution or maps. For most process applications, relevant engineering data have to be interpreted from conductivity-based information. Few of typical converting relationships are introduced here.

### 1.2.1 Volumetric fraction

A number of correlations were proposed in history to convert electrical conductivity of a system to volumetric fraction of a disperse phase [8]. Among them, the Maxwell relationship [9] is most widely used in ERT application for process engineering [10], which is given in Eq2.

$$ C_v = \frac{2\sigma_f + \sigma_s - 2\sigma_m - \frac{\sigma_m \sigma_s}{\sigma_f}}{2\sigma_f + \sigma_m - 2\sigma_s - \frac{\sigma_m \sigma_s}{\sigma_f}} \quad (2) $$

where $C_v$ is the local volumetric fraction of disperse phase, $\sigma_f$, $\sigma_s$ and $\sigma_m$ denote the conductivities of aqueous continuous phase, disperse phase and mixture respectively.

If the disperse phase is nonconductive, e.g. gas, oil or sands, Eq.2 can be simplified as,

$$ C_v = \frac{2\sigma_f - 2\sigma_m}{2\sigma_f + \sigma_m} \quad (3) $$

### 1.2.2 Salt concentration

In research on miscible liquid mixing, the liquids under investigation can be labelled with sufficient conductivity contrast to enhance the imaging performance [11]. High concentration saline solution can also be used as a tracer to track the dynamic trajectory of the mixing process. In an
instance of single phase miscible liquid mixing, the conductivity of mixture, $\sigma_m$, provides a linear relation to the concentration $C_w$ of salt [12,13]:

$$ \sigma_m = 1.728636 \times C_w + \sigma_f \quad (4) $$

$$ C_w = 0.5785 \times (\sigma_{mc} - \sigma_f) \quad (5) $$

where the $\sigma_m$ and $\sigma_f$ are in unit of mS cm⁻¹; the weight concentration $C_w$ is in gL⁻¹, the range of $C_w$: 0≤Cw≤10.

### 1.2.3 Porosity

Based on Archie's law, the local porosity of materials may also be derived from conductivity value [14]. The conversion is given by Archie's law [15]:

$$ \phi = \left( \frac{\sigma_m}{\sigma_f} \right)^k \quad (6) $$

where $\phi$ is the porosity (%) and k the cementation index dependent on the shape and packing of the particles (k=1.5 for spherical glass beads).

### 1.2.4 Velocity distribution

The principle of cross correlation method has been widely used to derive the velocity component of moving objects from two sets of measurements or images taken with a known time interval, e.g. the velocity distribution derived in Particle image velocimetry (PIV). Unlike PIV to statistically derive velocity component from two photo images of many seeds' over an interrogation region with a known time interval, ERT derives disperse phase velocity (or called the structural velocity) is based on many tomograms obtained from a dual-plane ERT sensor with a known distance between the two sensing planes and frame rate [16,17]. However, the concept of cross correlation method applied in PIV and tomography is the same.

The fundamental principle underpinning cross-correlation flow measurement is the 'tagging' of signal's similarity. These concepts are best illustrated in the figure below.

<figure><img src="image_4.png" /><figcaption>Figure 1. Cross-correlated two functions.</figcaption></figure>

The basic method is to find $\tau$ that can make the difference, $\epsilon$, minimum. This can be achieved using the least squares criterion,

$$ \epsilon^2(\tau) = \int_{-\infty}^{\infty} \left( (f_1(t) - f_2(t - \tau))^2 \right) dt \quad (7) $$

A revised error function is given by Eq.8, which only remains the product of two function since other terms to be constant from the integration over a sufficient time. Hence, the error function is minimum, when the last term is maximum. This expression is commonly known as the cross correlation function denoted by $R_{12}(\tau)$.

$$ R_{12}(\tau) = \int_{-\infty}^{\infty} f_1(t) f_2(t - \tau) dt \quad (8) $$

$$ R_{12}(n) = \sum_{m=1}^{l} f_{1}(m) f_{2}(m + n) \quad (9) $$

where l is the sample length, n is the offset number, $f_1$ and $f_2$ are the values at pixels positioned at the same location in two sequences of the up-flow and down-flow images respectively.

The disperse phase velocity can be simply derived as,

$$ v = \frac{d_s}{\tau} = \frac{d_s}{N_p \cdot T_{sampling}} = \frac{d_s \times f_s}{N_p} \quad (10) $$

where v is the velocity, $d_s$ is the distance between two sensors, $N_p$ is the number of offset frames to get the peak value of $R_{12}(N_p)$ and $f_s$ is the sampling frequency of ERT.

The fractional velocity discrimination, $\kappa$, can be estimated with Eq.11 and also the necessary data collection speed (sec./dual-frame), $\delta$, for a certain $\kappa$ can be expressed as Eq.12.

$$ \kappa = \frac{\delta}{2\tau} \quad (11) \qquad \delta = 2\tau\kappa \quad (12) $$

Above point-by-point cross correlation technique for flow velocity measurement is based on the assumption that flow trajectories are parallel to each other and perpendicular to the sensor plane. However in most cases this ignores the fact that the trajectories of particles of the dispersed phase exhibit a complex three-dimensional behaviour. The 'best-correlated pixels' method overcomes this problem by proposing that a signal from one pixel on plane X is somehow better correlated with a signal from a non-axially corresponding pixel on the plane Y [18]. The pixels from the second plane are chosen from the axially corresponding pixel and its neighbours, as described by Eq.13.

$$ R_{x[n,m]y[n+i,m+j]}[p] = \sum_{k=0}^{T-1} x_{[n,m]}[k] y_{[n+i,m+j]}[k+p] \quad (13) $$

where T is the number of the images, for which the cross-correlation is calculated; $p$=-(T-1), ...0, 1, 2, 3... T-1; $k$=0,1,2,3... T-1; n, m are the coordinates of the pixel; x, y are the values of the pixels on plane X and plane Y and B is the group of neighbouring pixels on plane Y.

### 1.2.5 Visualization

Multiphase flow is of practical significance in oil and gas industries, which is extremely challenging to be visualised and characterised in industrial multiphase flows due to the opaque nature of most industrial multiphase flows and pipelines. At the other aspect, the low resolution of electrical tomography with the colour mapping in commonly use is not sufficient to visualise the distinctive interface between fluid phases. As a result, the visualisation by the systems conveys limited information regarding multiphase flow dynamics, e.g. bubble size and distribution. A novel approach, namely bubble mapping, was proposed to overcome the problem. In the approach, a new lookup table is built up by means of
transferring mean concentration of an interrogation pixel into a number bubbles in a base size located randomly inside the pixel. Further, an enhanced isosurface algorithm was applied to isolate big bubbles based on the merging of neighbouring bubbles in the cell which have their mean concentration beyond a certain threshold value. With a proposed bubble mapping approach, a stack of cross-sectional tomograms by electrical tomography is transformed and displayed as individual air bubbles with different size in respecting to the air concentration in a visualization pixel. With further increment of air concentration, large bubbles will be merged from a number of pixels with full air cavity and then all bubbles are computed to 3-dimensional bubbles with an enhanced isosurface algorithm [19].

## 2. ENGINERING CASE STUDY

Phase volumetric or concentration distribution might be the first engineering characteristic data interpreted from electrical tomography. The electrical impedance in either conductivity or permittivity is converted to materials' concentration distribution, using relevant methods as stated in Section 1.2. Typical examples are expressed in the section.

### 2.1 Mixing process

The non-intrusive three-dimensional measurement of mixing inside a stirred vessel in three-dimension, using electrical resistance tomography, provided powerful opportunities for characterising and quantifying the process complexities [20]. One of the early works reported an application of ERT for three-dimensional (3D) imaging of the concentration of solids in a slurry mixer as a function of key process variables (particle size, impeller type, agitation speed) [21,22]. It was demonstrated how ERT can provide a wealth of detailed data to allow model development. On-line two-dimensional (2D) imaging of miscible liquid/liquid mixing and gas-liquid mixing in a large scale baffled mixing vessel (2.3 m³) fitted with eight planes of ERT sensor shown in Figure 1 was reported in 1996 [12, 23]. Figure 1 also shows a typical set of resistivity contours interpolated from a stack of 8-plane 2D images reconstructed with the back-projection algorithm, rendered as a solid body isometric image [24]. Results were presented from times of 1, 2, 3 and 4 s following the surface addition of 10 dm³ of concentrated brine (conductivity of 13.5 mS cm⁻¹) into a background conductivity of 0.1 mS cm⁻¹ at t = 0. The stirrer speed was 100 rpm generating an estimated internal flow of 0.686 m³ s⁻¹. The mixing time was estimated using a colorimeter probe and was approximately 14 s. In Figure 1, high conductivity is presented by red regions and low conductivity as blue regions (cut off by the isosurface). The salt concentration at the isosurface, as a mixing index derived from Eq.5, is 0.035 gl⁻¹ (0.16 mS cm⁻¹), which was adopted from the final conductivity of the liquids after mixing was completed. Further studies of a gas-liquid system (air-water) in the same mixing tank allowed tomographic gas distribution to be compared with established characteristic flow patterns. A multi-isosurface 3D gas concentration distribution was

produced from a stack of 8-plane 2D images using the Maxwell relationship (Eq.3) at a pseudo-stationary mixing, which presents two gas equal-concentration contours (Figure 2) with the values as indicated in the volume histogram shown at the bottom-right of the figure. In the experiment, gas was sparged from a pipe beneath a six-blade Rushton turbine at 3.5 litre sec⁻¹ with agitation at 73 rpm. Figure 2 reveals the high gas concentration (in red) is located beneath the turbine as well as the region close to the wall, which are reasonably reported the effect of high gas injection and agitation, respectively. In addition, a high gas concentration at the top of the figure is due to the air vertex produced by the agitation (the red colure region is hidden by the yellow isosurface).

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /><figcaption>**Figure 1.** Monitoring a dynamic miscible liquid mixing in a baffled 2.3 m³ mixing tank using ERT (mixing index: 0.035 gl⁻¹ (0.16 mS cm⁻¹) at the isosurfaces of above images; conductivity of pulse brine: 13.5 mS cm⁻¹ in volume 10 dm³, speed of Rushton stirrer: 100 rpm) [24].</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**Figure 2.** Pseudo-stationary gas-liquid mixing [24] (the images of two blades and a shaft are for purpose of illustration, which are not from the tomographic imaging).</figcaption></figure>
## 2.2 Slurry pipeline flow

Efficient slurry transportation is vital to many industries. It was proposed that helically formed pipes, which can be used to keep particulate solids in suspension, should be applied to enhance the distribution of solids in piped slurries. The use of an in-situ measurement method based on electrical impedance tomography was proposed to assist in understanding the effect of particle suspension and as well as the effect on the wear of pipes by solid particle impingement due to the application of such a swirl-inducing pipe [25]. The experiments were carried out on a 50 mm diameter hydraulic conveying pipe loop composed of transparent 1 m flanged sections in a vertical plane. The pumped medium was a mixture of water and spherical non-conductive beads (diameter 2 mm and specific gravity 1.45). ERT sensors were fitted at distances of 150 mm, 370 mm, 885 mm and 1150 mm downstream of the outlet of the swirling pipe (a meter-long with 900° of spiral). This

corresponds to downstream distances in the length to the pipe diameter ratios (L/D) of 3, 7.4, 17.7 and 23. A series of experiments were carried out at mean in situ particle burden concentrations of 2.1%, 4.0%, 6.4% and 8.6% by volume (or 3%, 6%, 9% and 12% by weight) at flow velocities of 0.5, 1.0, 1.5, 2.0 and 2.5 m/s, which are interpreted from Eq.3.Through the application of an advanced impedance image reconstruction algorithm [4] and other analysis software, the asymmetric solids concentration distribution in horizontal swirling flows can be quantified. Particle trajectories and concentration regimes are reported as a function of the water axial flow velocity and the downstream distance from the swirl-inducing pipe section. Figure 3 demonstrates the measurements obtained at the solid burden concentrations of 8.6%. In the absence of accurate predictive models for such complex flows, it is demonstrated that this method enables direct visualisation of the solids suspension as function of flow velocity in the pipes.

<figure><img src="image_8.png" /><figcaption>**Figure 3.** Solids suspension in horizontal pipeline at a fixed particle volumetric concentration of 8.6% [25]. The white triangles on the top of tomograms indicate the top direction (at 12'clock) of the pipe line. The vertical axis denotes the flow velocity in unit of ms⁻¹ and the horizontal axis denotes the downstream distance ration. The contours in topographic map indicate the equal-concentration values.</figcaption></figure>
## 2.3 Two phase flow

This study presents the use of a high performance dual-plane electrical impedance tomography system [26] to measure the vertical upward co-current oil-in-water pipe flows [27]. Experiments were carried on a flow loop with a transparent 2.5 m long, 80 mm inner diameter test section detailed in Figure 4, using kerosene and tap water. Measurement was carried out at imaging rate of 1000 dual frame per second. The oil phase concentration and velocity distribution were interpreted with Eq.3 and the cross-correlation method introduced in previous section respectively. The flow conditions were predominantly of the dispersed type with the non-slip oil concentrations of 9.1%, 16.7% and 23.1% respectively. Typical oil concentration and velocity distributions were presented in Figure 5, which were compared with measurements obtained with a mechanical orientated local intrusive conductance probe, showing a good agreement [27].

<figure><img src="image_9.png" /><figcaption>Figure 4. Schematic of the test section [27].</figcaption></figure>

## 2.4 Swirling flow

A series of air-in-water flow tests were carried out in a 0.08 m internal diameter vertical flow loop at the University of Huddersfield [28]. The working section was 2.5 m long. A dual-plane ERT sensor was installed in the upstream section of the flow loop 2 m from the base of the vertical working section. The distance between the two ERT sensing planes was 0.05 m. A 6-vane swirler with a 20° swirl angle was mounted 4D upstream of the ERT sensor (Figure 6). The volume fraction distribution for each flow condition was reconstructed from 5000 frames of data to give the 'steady state' local gas volume fraction distribution, averaged over a period of about 52.6 seconds. About 8000

dual-frames of data per flow condition were recorded and then used to obtain one velocity vector distribution. Results are shown in Figure 7 in regard the gas volume fraction and velocity distributions under three flow conditions. The results demonstrate the potential capability of electrical resistance tomography for measurement of 3-D flow vector distribution. It implies that with the assistance of a fast data collection rate, the flow vector distributions, not only in pipelines but also in other applications, can be extracted with good accuracy [28].

<figure><img src="image_10.png" /><figcaption>Figure 5. Oil concentration (the top image) and velocity (the bottom image) distributions from ERT ($Q_w=7.5 \text{ m}^3\text{/h}, Q_o=0.75 \text{ m}^3\text{/h}$) [27].</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Figure 6. Dual-plane ERT Sensor and flow swirler [28].</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>**Figure 7.** Gas volume fractions (Top) and velocity distributions in a gas-water swirling flow (Bottom) [28].</figcaption></figure>

## 2.5 Periodical flow in OBR

Oscillatory baffled reactor (OBR) has been proven to be very efficient due to its enhanced mixing mechanism, good particle suspension and excellent mass and heat transfer comparing to conventional chemical reactors. OBR is also capable of operating certain batch processes as a continuous process and is mostly employed in the polymer industry. In this study, the focus was on how to derive the periodical velocity of an OBR, where the conventional cross-correlation method based on the assumption of steady state flow condition was not applicable. By applying a period sample extraction from tomograms obtained with a sampling speed of 1000 dual-frames per second, a significantly improved temporal resolution allowing detailed analysis of the process and measurement of characteristic parameters was achieved [29]. It allowed to observe the effect of individual strokes of the OBR piston in the flow of the mixture, which established the foundation for getting instant velocity profiles. The test rig in 50cm diameter glassware pipe shown in Figure 8 was installed at the Online Instrumentation Laboratory, University of Leeds [30]. A stagnant water-oil emulsion was introduced by the piston and pulsed forward and reversely in the rig at 1.5 Hz oscillatory frequency, 20 mm amplitude. A dual-plane ERT sensor was installed in the test rig. Tomograms were reconstructed with the back-projection algorithm. The axial isosurface image of oil fraction distribution (Figure 9) and axial velocity profiles (Figure 10) provide essential information regarding the flow

conditions in the OBR that can be used to improve the OBR's performance. It provides a promising method to acquire the periodical process characteristics such as velocity profiles in the oscillatory process.

<figure><img src="image_13.png" /><figcaption>**Figure 8.** Basic diagram of the experimental setup [30].</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>**Figure 9.** 3D isosurface representation of the periodical oil concentration distribution in an OBR section [29].</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>**Figure 10.** The accuracy of forward (the top figure) and reversed (the bottom figure) axial velocity profiles is enhanced with the increment of the sampling periods [29]. (Sampled at $T=(2n+1/2)\pi$ and $(2n+3/2)\pi$, n: the sampling periods 1, 3, 9; Frames in a period: 666 frames; Frame length for cross-correlation: 80 frames (0.08s))</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>**Figure 11.** Flow regimes for gas-water flow in horizontal pipeline (from the left to the right are taken by photo, conventional colour mapping, and bubble mapping); (a) stratified flow; (b) bubbly flow; (c) plug flow; (d) slug flow; and (e) annular flow [19].</figcaption></figure>

## 2.6 Visualisation

This study deals with a fully developed turbulent two phase flow with no phase changing, and presents the outcomes of tomographic imaging techniques to visualise gas-water flows in a horizontal pipeline.

Experiments were conducted in a 50 meter long test section consisting of 4 inch nominal diameter piping within the industrial-scale three phase flow facility at

National Engineering Laboratory (TUV NEL), UK. Refined oil (HT9) of 830 kg m⁻³ density and 16.18 cP viscosity was used alongside Magnesium Sulphate saltwater substitute (MgSO4) of 1049.1 kg m⁻³ density and 1.35 cP viscosity. Nitrogen gas was supplied externally from a storage tank with density of 12 kg m⁻³ and absolute viscosity of 0.0174 cP. The total liquid flowrates were varied between 0 and 140 m³ hr⁻¹ and the gas flowrates were varied between 0 and 530 m³ hr⁻¹.
¹. A total of 270 measurements were conducted, which produced a variety of flow regimes in the horizontal pipeline, including stratified flow, slug flow, plug flow, bubble flow, and annular flow [19].

Figure 11 demonstrates the results of the approach applied to gas-liquid horizontal flow, with the flow regimes of stratified flow (Figure 11.a.), bubbly flow (Figure 11.b.), plug flow (Figure 11.c.), slug flow (Figure 11.d.), and annular flow (Figure 11.e.). The left shows the photo from camera, the middle is the axial cross section of stacked raw tomograms with colour mapping scheme, and the right shows the image produced by the bubble mapping scheme. Compared to its counterpart by conventional colour mapping, the new approach is not only able to visualise the expected flow regimes but also reveal additional flow dynamic characteristics with high temporal resolution. It is clearly demonstrated that the bubble mapping can greatly enhance the reality of flow regime visualization comparing the raw tomograms.

### 3. DISCUSSION

Electrical tomography as one of process tomography technologies appears for about three decades. Many scientists and engineers have devoted great efforts to progress the science and engineering of the technology for industrial practice. However, the unconventional features of the technology made a long standing of consideration on whether it could deliver a new practical imaging metrology for engineering. With the advantages of the unique ultrahigh temporal resolution, good penetrating and safe in operation, it was somehow over expected on its spatial resolution and neglect the importance of data fusion, which may result in improperly bridged with industrial challenges. This paper reviews and emphasises the importance of engineering interpretation in bridging between tomography and process engineering for advanced process measurement and control, provided with typical data fusion methods and a number of case studies carried out by the author and his research team, which express the specific features of the metrology, hopefully, promote the process tomography for engineering applications.

### ACKNOWLEDGMENT

This work is founded by the Engineering and Physical Sciences Research Council (EP/H023054/1, IAA (ID101204) and the European Metrology Research Programme (EMRP) project "Multiphase flow metrology in the Oil and Gas production" which is jointly funded by the European Commission and participating countries within Euramet.

### REFERENCES

[1] M. Wang. Industrial tomography: systems and application, 1st Edition, Woodhead Publishing, 2015.

[2] D. B. Geselowitz. An application of electrocardiographic lead theory to impedance plethysmography, IEEE Trans. Biomed. Eng., Vol. BME-18: 38-41, 1997.

[3] J. Lehr. A vector derivation useful in impedance plethysmographic field calculations, IEEE Trans. Biomed.

Eng., Vol. BME-19: 156-157, 1972.

[4] M. Wang. Inverse solutions for electrical impedance tomography based on conjugate gradients methods, Meas. Sci. & Technol., 13: 101-117, 2002.

[5] C. J. Kotre. EIT image reconstruction using sensitivity weighted filtered back-projection, Physiol. Meas. 15:A125-36, 1994.

[6] M. Cheney, D. Isaacson, J. G. Newell, S. Simake and J. Goble. NOSER: An algorithm for solving the inverse conductivity problem', International Journal of Imaging System Technology, 2: 66-75, 1990.

[7] T. J. Yorkey, J. G. Webster and W. J. Tompkins. Comparing reconstruction algorithm for electrical impedance tomography, IEEE Trans. Biomed. Eng. 34: 843-51, 1987.

[8] M. Wang. Chapter 2 Electrical Impedance Tomography, Industrial tomography: systems and application, Wang M (edit), 1st Edition, Woodhead Publishing, 2015.

[9] J.C. Maxwell, A Treatise on Electricity and Magnetism, 3rd ed, Clarendon Press, Oxford, 440, 1891.

[10] M. Sharifi and B Young, Electrical Resistance Tomography (ERT) applications to Chemical Engineering, Chemical Engineering Research and Design, 2013.

[11] M. Wang, R. Mann and F. J. Dickin. Electrical resistance tomographic sensing systems for industrial applications, Chemical Engineering Communications, OPA (Overseas Publishers Association), 175: 49-70, 1999.

[12] R. Mann, M. Wang, F.J. Dickin, T. Dyakowski and P.J. Holden, Resistance tomography imaging of stirred vessel mixing at plant scale, IChemE Symposium Series, IChemE, 140: 155-167,1996.

[13] P. Holden, M. Wang, R. Mann, F.J. Dickin, Macromixing using electrical resistance tomography, AIChE Journal, 44(4): 780-790, 1998.

[14] C Qiu, F. J. Dickin, A. E. James and M. Wang. Electrical resistance tomography for imaging sub-seabed sediment porosity: initial findings from laboratory-scale experiments using spherical glass beads, in Process Tomography - A Strategy for Industrial Exploitation, Oporto, UMIST, ISBN095231651X, 33-41. 1994.

[15] G. E. Archie. The electrical resistivity log as an aid in determining some reservoir characteristics', Trans. AIME, 146: 54-62, 1942.

[16] G. P. Lucas, J. Cory, R. Waterfall, W. W. Loh, and F. J. Dickin, Measurement of the Solids Volume Fraction and Velocity Distributions in Solid-liquid Flows Using Dual-plane Electrical Resistance Tomography, Flow Meas. Instrum.10: 249-258, 1999.

[17] Y. Wu, H. Li, M. Wang and R. A. Williams. Characterization of air-water two-phase vertical flow by using electrical resistance imaging, Canadian Journal of Chemical Engineering, 83(1): 37-41, 2005.

[18] V. Mosorov, D. Sankowski, L. Mazurkiewicz, T. Dyakowski. The 'Best-Correlated Pixels' Method for Solid Mass Flow Measurements Using Electrical Capacitance Tomography, Meas. Sci. & Tech., 13: 1810-1814, 2002.

[19] Q. Wang, J. Polansky, B. Karki, M. Wang, K. Wei, C.
Qiu. A. Kenbar, and D. Millington. Experimental tomographic methods for analysing flow dynamics of gas-oil-water flows in horizontal pipeline. *Journal of Hydrodynamics*, 28(6): 1018-1021, 2016

[20] R. Mann, F.J. Dickin, M. Wang, T. Dyakowski, R.A. Williams, R.B. Edwards, A.E. Forrest, P.J. Holden. Application of electrical resistance tomography to interrogate mixing processes at plant scale, *Chem. Eng. Sci.*, 52: 2087-2097, 1997.

[21] S.L. McKee, Tomographic measurements of solid-liquid mixing, PhD Thesis, UMIST, (1994).

[22] R. A. Williams, X. Jia, S. L. McKee, Development of slurry mixing models using resistance tomography. *Powder Technology*, 87: 21-27, 1996.

[23] F.J. Dickin, and M. Wang. Electrical resistance tomography for process applications, *Meas. Sci. and Technol.*, IOP, 7: 247-260, 1996.

[24] M. Wang, R. Mann, A.E. Forrest, P.J. Holden, F.J. Dickin, T. Dyakowski, R.B. Edwards. Stirred vessel mixing in 3-D using electrical resistance tomography, *Electronic Measurement and Instrument Society, CIE*, Beijing, 11(A): 650-653, 1997.

[25] M. Wang, T. F. Jones and R. A. Williams. Visualisation of asymmetric solids distribution in horizontal swirling flows using electrical resistance tomography, *Trans IChemE*, Volume 81(A): 854-861, 2003.

[26] M. Wang, Y. Ma, N. Holliday, Y. Dai, R.A. Williams and G. Lucas, A high performance EIT system, accepted for publication, *IEEE Sensors Journal*, 5(2): 289-299, 2004.

[27] H. Li, M. Wang, Y. Wu, G. Lucas, Volume flow rate measurement in vertical oil-in-water pipe flow using electrical impedance tomography and a local probe, *MultScienTechn.* 21(i1-2.70): 81-93, 2009.

[28] M. Wang, G. Lucas, Y. Dai, N. Panayotopoulos and A. Williams. Visualisation of bubbly velocity distribution in a swirling flow using electrical resistance tomography, *Part. Part. Syst. Charact.* 23: 321-329, 2006.

[29] M. Issa, H. Li, H. I. Schlaberg, M. Wang, R. Williams. Velocity measurements of multi-phase unsteady flow in oscillatory baffled reactor using electrical resistance tomography, *Proceedings of 3rd International Workshop on Process Tomography (IWPT-3)*, Tokyo, Japan, 2009.

[30] G. Vilar, R. A. Williams, M. Wang and, R. J. Tweedie. On line analysis of structure of dispersions in an oscillatory baffled reactor using electrical impedance tomography, *Chemical Engineering J.* 141: 58-66. 2008