# Electrical Resistance Tomography for Control Applications: Quantitative Study of the Gas-Liquid Distribution inside A Cyclone

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

**G**, which relates the injected voltages and measured currents, and is the opposite value of the estimated conductance for the CV case, i.e.,:

**B**,

**C**, and

**D**are discretized solutions of the FEM complete forward model, which depends on the geometry of the problem domain (e.g., electrodes size, dimensions of the area of investigation, number of mesh elements) and conductivity distribution.

## 2. Materials and Methods

#### 2.1. Flow Test Facility and Phantoms

^{3}/h in the flow rates of each phase, starting at 10 m

^{3}/h. The air values were selected at standard conditions, as provided by the MFC, and thus must be corrected based on pressure values measured right after the mass flow controller. The approach results in the experimental points presented in Table A1 Appendix A, where the superficial velocity of the fluid “j” corresponds to the bulk velocity of the phase if it was the only fluid in the pipeline:

^{3}/s, and $A$ to the pipe area (${D}_{in}=84\mathrm{mm},A=5.54\times {10}^{-3}$ m

^{2}).

#### 2.2. ERT Sensor snd Measurement Protocol

#### 2.3. Image Reconstruction Algorithms

^{®}Core™i7 1.80 GHz, 16 GB installed memory (RAM), and 64-bit Windows 10 operating system was used.

#### 2.4. Image Processing

^{®}R2019b Image Processing Toolbox™ was used for the postprocessing of images obtained by both modalities.

#### 2.4.1. ERT Image Handling

- Averaging the grayscale images.
- Image segmentation of the images

#### 2.4.2. Fast Camera Image Processing

#### Pre-Processing Routine

#### Gas Core Calculations

#### Refraction Correction

## 3. Results

#### 3.1. Static Measurements

#### 3.1.1. Camera Results

#### 3.1.2. ERT results

#### 3.2. Dynamic Measurements

^{2}is equal to 0.9914, which indicates a very good fit.

_{sl}is greater than 1 m/s, and V

_{sg}is lower than 0.4 m/s. This is visible in Figure 19 (experimental points 11–13, 16–18 and 21–23), and data are shown in Table A2, Appendix A.

## 4. Conclusions

^{2}values). PDFs of the camera and corrected ERT values for each experimental point were compared, and a good agreement between the curves was noted, although the proposed method shows limitations in measuring the instantaneous gas core size when breakages are frequent.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

Experiment Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

${\mathit{V}}_{\mathit{s}\mathit{l}}\left[\mathbf{m}/\mathbf{s}\right]$ | 0.51 | 0.55 | 0.51 | 0.52 | 0.51 | 0.75 | 0.75 | 0.75 | 0.76 | 0.76 |

${\mathit{V}}_{\mathit{s}\mathit{g}}\left[\mathbf{m}/\mathbf{s}\right]$ | 0.26 | 0.35 | 0.42 | 0.47 | 0.50 | 0.25 | 0.34 | 0.41 | 0.45 | 0.49 |

Experiment Number | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |

${\mathit{V}}_{\mathit{s}\mathit{l}}\left[\mathbf{m}/\mathbf{s}\right]$ | 1.02 | 1.01 | 1.01 | 1.01 | 1.01 | 1.25 | 1.25 | 1.26 | 1.25 | 1.25 |

${\mathit{V}}_{\mathit{s}\mathit{g}}\left[\mathbf{m}/\mathbf{s}\right]$ | 0.25 | 0.33 | 0.40 | 0.44 | 0.48 | 0.24 | 0.32 | 0.38 | 0.43 | 0.47 |

Experiment Number | 21 | 22 | 23 | 24 | 25 | |||||

${\mathit{V}}_{\mathit{s}\mathit{l}}\left[\mathbf{m}/\mathbf{s}\right]$ | 1.51 | 1.50 | 1.50 | 1.50 | 1.50 | |||||

${\mathit{V}}_{\mathit{s}\mathit{g}}\left[\mathbf{m}/\mathbf{s}\right]$ | 0.23 | 0.31 | 0.37 | 0.42 | 0.46 |

**Table A2.**Statistical Data of Figure 19. Values in mm.

Experimental Point | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |

CAMERA | Mean | 31.7 | 41.5 | 50.2 | 53.9 | 56.9 | 21.8 | 30.0 | 36.1 | 42.5 | 48.1 |

Standard Deviation | 8.47 | 7.80 | 7.38 | 7.08 | 6.15 | 7.33 | 7.43 | 7.11 | 7.51 | 7.59 | |

CORRECTED GN | Mean | 25.79 | 33.86 | 50.71 | 49.77 | 54.67 | 22.43 | 25.23 | 32.03 | 39.29 | 45.24 |

Standard Deviation | 10.05 | 11.45 | 14.58 | 16.70 | 12.70 | 8.83 | 9.58 | 10.33 | 12.74 | 13.53 | |

Experimental Point | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |

CAMERA | Mean | 17.8 | 23.5 | 27.9 | 34.6 | 38.7 | 16.2 | 20.2 | 24.0 | 29.7 | 35.0 |

Standard Deviation | 5.36 | 6.00 | 6.25 | 6.71 | 7.83 | 4.83 | 5.09 | 5.42 | 6.71 | 7.40 | |

CORRECTED GN | Mean | 18.90 | 20.93 | 23.83 | 30.81 | 36.78 | 18.60 | 20.27 | 25.91 | 30.47 | 18.45 |

Standard Deviation | 7.96 | 8.17 | 8.15 | 10.16 | 11.96 | 9.10 | 7.22 | 8.52 | 9.58 | 9.68 | |

Experimental Point | 21 | 22 | 23 | 24 | 25 | ||||||

CAMERA | Mean | 15.7 | 17.8 | 21.7 | 25.8 | 31.2 | |||||

Standard Deviation | 4.05 | 4.30 | 4.58 | 5.66 | 6.98 | ||||||

CORRECTED GN | Mean | 17.14 | 17.14 | 18.96 | 21.64 | 26.56 | |||||

Standard Deviation | 6.70 | 6.70 | 7.04 | 7.46 | 9.64 |

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**Figure 1.**Swirl Separator Schematics. An air-water separation is represented, where the air is rendered in white and water in blue. Changes in the gas core observed at the ERT location propagate to the inner and outer tubes. The separator is installed vertical, and $g$ represents the direction of the gravity vector in relation to the equipment.

**Figure 2.**Structure of typical ERT system showing: (

**a**) ERT Based sensor (

**b**) Data acquisition electronics (

**c**) Image reconstruction and visualization software.

**Figure 3.**(

**a**) Tom Dyakowski Process Tomography Laboratory horizontal and vertical liquid/gas Flow loop (

**b**) Vertical flow installation with swirl element and ERT sensor mounted on the 90 mm pipe and surrounded by a light source cage. The Figure also shows in the back the live ERT image reconstruction module from TomoKisStudio and the Rocsole Ltd. FlowWatch device.

**Figure 4.**Experimental points and inlet patterns expected upstream of the swirl element, according to [36].

**Figure 5.**(

**a**) Physical 16 electrode single layer ERT sensor placed above the swirl element (

**b**) Schematics of VC-based ERT data acquisition system.

**Figure 6.**Schematic of ABS phantom placement middle of the sensor: (

**a**) 10 mm (

**b**) 20 mm (

**c**) 30 mm (

**d**) 40 mm.

**Figure 8.**Image Processing Scheme: (

**a**) Original image (

**b**) Grayscale image (

**c**) Background (

**d**) Foreground (

**e**) Segmented image.

**Figure 9.**Original Image (2040 × 500 px) and box considered during the image processing and core size calculation. The obtained image after the cropping has a size of 200 × 400 px. The image corresponds to the 26th frame of the experimental set 11.

**Figure 10.**Pre-processing of the flow images. (

**a**) Cropped box from the original picture. (

**b**) 8-bit contrast-enhanced result.

**Figure 11.**MATLAB image processing steps. (

**a**) Binarized flow picture after color inversion. In the image, the interface between the fluids is represented in white and has value 1, and the locations inside the gas core and the water annulus are represented in black, with value 0. (

**b**) Image obtained after the removal of small (smaller than 100 px) white regions required for proper tracking of the interface between the fluids. (

**c**) interface tracked and plotted in red on top of the original image.

**Figure 12.**The refraction model is based on light rays reaching the camera. Their red line corresponds to the light ray, and the green lines correspond to extensions of the light rays that are useful for the analysis. The x-axis is placed on top of the focal plane of the camera, and the light ray path is for illustration porpoise only, without taking into account the real scales of the setup or the actual path of the reflected light ray.

**Figure 13.**Comparison between phantom sizes and values recovered from camera images. The measured points are plotted in red, the continuous line represents a perfect match between the camera and the phantom size, and the dashed lines represent $\pm 10\%$ deviation lines around the average.

**Figure 14.**Image Reconstruction based on static tests: Row 2 (Column 2-Column 4) Case 10 mm: Simulated image, LBP reconstruction, and GN reconstruction. Row 3 (Column 2–Column 4) Case 20 mm: Simulated image, LBP reconstruction, and GN reconstruction. Row 4 (Column 2–Column 4) Case 30 mm: Simulated image, LBP reconstruction, and GN reconstruction. Row 5 (Column 2–Column 4) Case 10 mm: Simulated image, LBP reconstruction, and GN reconstruction. Column 5: Colormap.

**Figure 15.**ERT reconstructed diameters plotted against the phantoms’ diameters obtained from the fast camera. The Linear Back Projection algorithm is represented in blue, with the average method presenting circle marks and the binary method presenting square marks. The results for the Gauss-Newton Reconstructed images are presented analogously but in red. The black line in the image provides a reference for a sensor mimicking the camera (parity of values).

**Figure 16.**Average equivalent diameters obtained using the camera plotted against the Gauss-Newton reconstruction scheme for the static and dynamic experimental points. (

**a**) Averaged Gauss-Newton scheme. The blue dashed line of the graph is obtained by fitting the 4 static points but plotted for the entire range of dynamic data for comparison. (

**b**) Binarized Gauss-Newton scheme. As the dynamic data does not follow a clear trend in the Figure, no fit based on the static measurements is presented.

**Figure 17.**Calibrated gas core average equivalent diameter provided by the Averaged GN scheme plotted against the camera values.

**Figure 18.**Histograms and Beta distribution PDFs for the ERT (

**a**) and Camera (

**b**) values for experimental point 11. Only the 120 frames of the last 10 s of ERT measurement are considered during the plot. Both histograms are plotted in 20 intervals uniformly spaced between 0 and 1.

**Figure 19.**Probability Density Functions for the equivalent core diameter of each experimental point studied. Camera Beta distributions are plotted in blue, while the corrected ERT distributions are plotted in red.

**Figure 20.**2.5D images for: (

**a**) Experimental point 3 (

**b**) Experimental point 4 (

**c**) Experimental point 5 (

**d**) Experimental point 6. (

**e**) Manually calibrated ERT and camera image showing the failure of ERT due to gas core breakage.

**Figure 21.**Average projection of the GN reconstructed images obtained for all experimental points. Each row shows images obtained, keeping liquid superficial velocities constant and varying the superficial gas velocities, as it can be guessed from Table A1 in Appendix A.

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Sattar, M.A.; Garcia, M.M.; Banasiak, R.; Portela, L.M.; Babout, L.
Electrical Resistance Tomography for Control Applications: Quantitative Study of the Gas-Liquid Distribution inside A Cyclone. *Sensors* **2020**, *20*, 6069.
https://doi.org/10.3390/s20216069

**AMA Style**

Sattar MA, Garcia MM, Banasiak R, Portela LM, Babout L.
Electrical Resistance Tomography for Control Applications: Quantitative Study of the Gas-Liquid Distribution inside A Cyclone. *Sensors*. 2020; 20(21):6069.
https://doi.org/10.3390/s20216069

**Chicago/Turabian Style**

Sattar, Muhammad Awais, Matheus Martinez Garcia, Robert Banasiak, Luis M. Portela, and Laurent Babout.
2020. "Electrical Resistance Tomography for Control Applications: Quantitative Study of the Gas-Liquid Distribution inside A Cyclone" *Sensors* 20, no. 21: 6069.
https://doi.org/10.3390/s20216069