# Towards Tomography-Based Real-Time Control of Multiphase Flows: A Proof of Concept in Inline Fluid Separation

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## Abstract

**:**

## 1. Introduction

## 2. A Tomography-Controlled Inline Swirl Separator

## 3. Experimental Setup

#### 3.1. Flow Loop Facility

#### 3.2. The Double-Layer Wire-Mesh Sensor

#### 3.3. High-Speed Camera

#### 3.4. The Real-Time Electrical Resistance Tomography Sensor

#### 3.5. Actuators and Control

## 4. Multiphase Flow Dynamics

#### 4.1. Vertical Non-Swirling Gas–Liquid Flow Patterns

#### 4.2. Swirling Gas–Liquid Flow Patterns

#### 4.3. Experimental Investigation of the Swirl Effects in the Upstream Flow

#### 4.4. Numerical Simulations of the Separation

## 5. The Real-Time Control of Multiphase Flows

#### 5.1. Control in the Absence of External Process Disturbances

#### 5.2. Control in the Presence of Process Disturbances

## 6. Perspective

#### 6.1. Upstream Flow and Predictive Controllers

#### 6.2. The Time Scales of Multiphase Flow Processes and the Design of Real-Time Controllers

- Safety: Fast actions in the flow, matching the time scales of the intrinsic dynamics, can result in dangerous situations, especially when dealing with liquids. As liquids are incompressible and have large densities, sudden changes in valves can cause water hammer effects and pressure spikes in the system, which can damage the equipment and result in cracks and leakages.
- The high inertia of industrial equipment: Industrial equipment typically stores large masses of liquid, which must be accelerated whenever a change is made in the boundary conditions of the system (e.g., a change in the opening of a valve). Therefore, even if an actuator fast enough to match the time scales of the intrinsic dynamics can be used in the application, the high inertia of the system often leads to a flow response too slow in relation to the intrinsic dynamics.
- Nonlinearities and robustness: Multiphase flows are nonlinear by nature, and nonlinearities in industrial equipment are also common. For instance, the control valves of the ISS used in this study have a strong hysteresis and a nonlinear impact on the flow. Therefore, it is hard to design a controller that is stable in practice and operates in the time scales of the intrinsic dynamics, especially without a careful analysis of the physics behind the process.

#### 6.3. The Effects of the Intrinsic Dynamics in the Operating Point of the System and Controller Performance

#### 6.4. Application-Specific Tomography and the Monitoring of Intrinsic Dynamics

## 7. Conclusions

- The distribution of phases in multiphase flows has two unsteady components: (i) the intrinsic dynamics, connected to the multiphase flow patterns, and (ii) the extrinsic dynamics, associated with external process disturbances.
- The intrinsic dynamics of the distribution of phases inside industrial equipment is connected to the intrinsic dynamics of the flow upstream of the equipment, due to the conservation of mass. Therefore, feedforward actions or model predictive controllers can be designed based on the measurement of the inlet of the equipment, either using tomographic or non-tomographic (as wire-mesh sensor) techniques.
- The choice between controlling the intrinsic dynamics of the flow, or limiting the control to external process disturbances, must be performed based on the knowledge of the time scales of the intrinsic dynamics, the temporal resolution of the sensor, and the time scales of the system in relation to control actions.
- If not controlled, the intrinsic dynamics strongly influences the choice of the operating point of the system and the controller setpoint, weakens the link between the filtered distribution of phases and performance (e.g., efficiency), and limits the improvements in performance that can be achieved by controlling the process.
- Classical tomographic reconstruction techniques are too slow to monitor the intrinsic dynamics of multiphase flows in real-time, and application-specific algorithms must be developed to improve the temporal resolution of the technique in control applications.
- Tomography can be applied in the real-time control of the distribution of phases of quasi-1D multiphase flows, illustrated in this paper by the successful rejection of external disturbances in the gas core by the ERT-based PI controller implemented in the inline swirl separator.
- The control multiphase flow systems using tomography has the potential of substantially increasing the performance of the process; when rejecting external process disturbances, the ERT-based PI controller implemented in the inline swirl separator increased the capture of air by the pickup tube from 76% to 93% of the total flow rate injected in the system (an increase of 17%) and the mean efficiency of the process from 75% to 78%.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

mv | Measured value |

CFD | Computational fluid dynamics |

ERT | Electrical resistance tomography |

ISS | Inline swirl separator |

PI | Proportional–integral |

UDP | User datagram protocol |

WMS | Wire-mesh sensor |

## Appendix A. Experimental Points of the Upstream–Core Connection

**Table A1.**Gas and liquid flow rates used in the study of the connection between the gas core and the upstream flow. In the table, Ln/min stands for normal liters per minute, defined as the volumetric flow rate of gas calculated from measurements of mass flow rate considering the density of air at 0 °C and 1 atm (Section 3.1).

Flow Rate of Water (L/min) | Flow Rate of Air (Ln/min) |
---|---|

80 | 20, 30, 40, 50, 70 |

100 | 30, 40, 50, 70, 90 |

120 | 40, 50, 70, 90, 110 |

140 | 50, 70, 90, 110, 130 |

150 | 20, 30, 40, 50, 60 |

150 | 70, 90, 110, 130, 150 |

160 | 90, 110, 130, 150, 170 |

## Appendix B. Estimation of the Wire-Mesh Sensor–Camera Delay

- i.
- The gas moves at the speed detected by the wire-mesh sensor (${V}_{wms}$) between the wire-mesh sensor and the swirl element, leading to ${\tau}_{1}=4.4D/{V}_{wms}$.
- ii.
- The body of the swirl element (se) causes a contraction of the flow, which leads to a mixture velocity inside the vanes of the swirl element larger than in the pipe below it. The mixture velocity is defined as the total flow rate divided by the cross-sectional area of the flow. Since the total flow rate is the same both upstream and inside the vanes, the mixture velocity of the two locations are connected by:$${V}_{m,se}=\frac{A}{{A}_{se}}{V}_{m},$$Considering a drift-flux model, the velocity of the gas in the flow is given by a term proportional to the mixture velocity plus a slip velocity:$${u}_{g}=C{V}_{m}+{V}_{slip},$$Figure A1 shows the relation obtained between gas velocity, detected by the double-layer wire-mesh sensor, and the mixture velocity, calculated based on the flow rates of liquid and gas at the location of the wire-mesh, for the points of Appendix A, in which slug flow is observed in the experiments. A least-squares fit of the graph based on the drift-flux model (${V}_{wms}=C{V}_{m}+{V}_{slip}$) leads to $C=1.34$ and ${V}_{slip}=0.43$ m/s.The flow patterns inside the vanes of the swirl element are unknown, and it is assumed that the upstream flow patterns (typically slug) are maintained during the passage of the flow through the swirl element, which allows computing the gas velocity based on the same drift-flux coefficients of the upstream flow:$${u}_{g,se}=C{V}_{m,se}+{V}_{slip},$$Instead of using ${V}_{slip}$, which is flow pattern dependent, the expression can be manipulated to include the wire-mesh sensor velocity explicitly, making it independent of the flow pattern (as long as the hypothesis of the maintenance of the upstream flow pattern along the vanes of the swirl element is still valid):$${u}_{g,se}=C\left(\right)open="("\; close=")">\frac{A}{{A}_{se}}-1$$
- iii.
- The gas moves at speed ${u}_{g}={q}_{g}/{A}_{g}$ between the swirl element outlet and the camera, where ${A}_{g}$ is the area of the gas core measured by the camera (${A}_{g}=\alpha A$). Therefore, ${\tau}_{3}=5.71DA\alpha /{q}_{g}$.

**Figure A1.**Comparison between the gas velocity and the mixture velocity in the WMS location for slug flows. The flow rate of air used in the calculation of the mixture velocity is obtained from the mass flow rate injected in the system and pressure measurements near the WMS.

**Figure A2.**Components of the delay in the void fraction signal detected by the wire-mesh sensor and by the camera, predicted according to the model described in Appendix B for all the experimental points of Appendix A. The results are presented as a function of the gas velocity measured by the double-layer WMS, since it summarizes the gas and liquid flow rates into a single variable. ${\tau}_{1}$ corresponds to the time required for the gas to move between the WMS and the swirl element; ${\tau}_{2}$ corresponds to the time required for the gas to cross the swirl element; ${\tau}_{3}$ corresponds to the time required for the gas to travel between the outlet of the swirl element and the camera.

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**Figure 1.**Distribution of gas (white) and liquid (blue) in vertical gas–liquid flows of the bubbly (

**left**) and slug (

**right**) flow regimes.

**Figure 2.**Gas–liquid inline swirl separator. The gas–liquid mixture of the upcoming flow is split into a continuous core of gas and a surrounding annulus of liquid due to the swirl. The separation is performed by the pickup tube, which collects the flow in the center of the separator.

**Figure 3.**(

**Left**) Picture of the wires of one wire-mesh sensor. The two planes of parallel wires are installed perpendicular to each other, creating a virtual grid of points; (

**Right**) Volume fraction of gas measured by the sensor, with the gas fraction proportional to the grayscale of the pixel (pure liquid is black, and pure gas is white).

**Figure 4.**Electrical resistance tomography with 16 electrodes (${E}_{1}$ to ${E}_{16}$) installed in the inline swirl separator. In this image, electrode 1 is used as the source (${V}_{1}$), and the remaining electrodes act as the sink. The sink electrodes are kept grounded at ${V}_{0}$ and have their electric currents measured (I). Image adapted from [40].

**Figure 5.**Gas core inside the inline swirl separator measured and reconstructed using classical ERT. A 2D sensor is used in the measurements, and the 3rd axis of the image (axial direction) corresponds to time.

**Figure 6.**Inline swirl separator with wire-mesh and electrical resistance tomography sensors. The feedback controller of the image connects the gas core size, measured by ERT, to inputs in the pickup tube valve.

**Figure 7.**Main section of the Inline Swirl Separator of the Delft University of Technology. The separator has an inner diameter $D=81.4$ mm.

**Figure 8.**Double-layer wire-mesh sensor installed in the Flow Facility of the Delft University of Technology.

**Figure 9.**Image processing steps performed by the MATLAB code. From left to right: raw image obtained by the high-speed camera, binary image, image after the moving average filter, and final image with holes filled.

**Figure 10.**Electrical resistance tomography sensor installed in the pipe of the inline swirl separator. The electrodes and signal conditioning units can be seen inside the shield, used to isolate the measurement region from external electromagnetic effects.

**Figure 12.**Gas–liquid distribution (

**top**) and volume fraction of air (

**bottom**) of a bubbly flow measured by the wire-mesh sensor installed upstream of the ISS for a water flow rate of 150 L/min and an air flow rate of 20 Ln/min. The two images correspond to the same data and share the same time axis. In the top image, white corresponds to gas and black to liquid, with the light intensity of gray pixels proportional to the local gas fraction measured by the WMS, such that bubbles smaller than the sensing area of the wire-mesh sensor are represented in gray.

**Figure 13.**Gas–liquid distribution (

**top**) and volumetric fraction of air (

**bottom**) of a slug flow measured by the wire-mesh sensor installed upstream of the ISS for a water flow rate of 80 L/min and an air flow rate of 70 Ln/min. The two images correspond to the same data and share the same time axis. Gas is represented in white and liquid in black in the images, with the light intensity of gray pixels proportional to the local gas fraction measured by the WMS.

**Figure 14.**Gas–liquid distribution (

**top**) and volumetric fraction of air (

**bottom**) of a stable column reconstructed based on camera recordings for a water flow rate of 150 L/min and an air flow rate of 20 Ln/min. The two images correspond to the same data and share the same time axis. Gas is represented in white and liquid in black in the images.

**Figure 15.**Gas–liquid distribution (

**top**) and volumetric fraction of air (

**bottom**) of an intermittent column reconstructed based on camera recordings for a water flow rate of 80 L/min and an air flow rate of 70 Ln/min. The two images correspond to the same data and share the same time axis. Gas is represented in white and liquid in black in the images.

**Figure 16.**Average volume fraction of the gas core downstream of the swirl element (camera gas fraction) as a function of the average gas volume fraction upstream of the swirl element (WMS gas fraction) and the liquid flow rate (${q}_{l}$).

**Figure 17.**Cross-correlation coefficient between the camera and wire-mesh sensor volumetric fractions of air for a liquid flow rate of 160 L/min and an air flow rate of 170 Ln/min.

**Figure 18.**Delay that maximizes the cross-correlation between the camera gas fraction and the wire-mesh sensor gas fraction as a function of the velocity measured by the wire-mesh sensor. The symbols are used to illustrate the dependency of the relation on the flow pattern upstream of the swirl element.

**Figure 19.**Flow reconstruction of wire-mesh sensor (

**top**) and camera (

**bottom**) synchronized by the delay of Figure 18 for a liquid flow rate of 80 L/min and a gas flow rate of 70 L/min. The top image shows the passage of large gas pockets (in white) with several small bubbles in between (gray pixels), and the bottom image shows sections of wide and thin core sections. The images together show the transformation of small bubbles upstream of the swirl element into regions of a thin gas core and the transformation of large gas pockets into regions of a wide gas core.

**Figure 20.**Simulation performed using the hybrid Lagrangian tracking–volume of fluid solver. The blue dots correspond to bubbles, and the red region corresponds to the coalesced core. (

**Top**) $t=0$ s (initial condition); (

**Middle**) $t=0.011$ s; (

**Bottom**) $t=0.040$ s.

**Figure 21.**Closed loop block diagram with the ERT sensor and the PI controller. $d\left(t\right)$ is the gas core size inside the installation (continuous-time signal), which is sampled by the ERT system as $y\left[k\right]$ (discrete-time signal). The ERT signal is filtered into $\widehat{y}$, which is compared to a core-size reference (r), and the difference between the two quantities is used by the PI controller to compute the controller output, u. The variable w summarizes the unsteady effects of the core, due to the propagation of intrinsic dynamics from the upstream flow and to external process disturbances.

**Figure 22.**Core size obtained for an air flow rate of 110 Ln/min and a water flow rate of 113 L/min at fixed valve positions, which maximize ${\eta}_{m}$. In blue: original ERT signal. In orange: output of the low-pass filter (${\omega}_{f}=1$ rad/s). Signals with standard deviation $\sigma \left(y\right)=0.0724$ and $\sigma \left(\widehat{y}\right)=0.0146$.

**Figure 23.**Controlled core size in the absence of external disturbances. In blue: original ERT signal. In orange: output of the low-pass filter (${\omega}_{f}=1$ rad/s). Signals with standard deviation $\sigma \left(y\right)=0.0719$ and $\sigma \left(\widehat{y}\right)=0.0154$.

**Figure 24.**Uncontrolled core size obtained for a square wave disturbance in the air flow rate of the experimental facility. In blue: original ERT signal. In orange: output of the low-pass filter (${\omega}_{f}=1$ rad/s). Signals with standard deviation $\sigma \left(y\right)=0.0902$ and $\sigma \left(\widehat{y}\right)=0.0323$.

**Figure 25.**Controlled core size in the presence of a square wave disturbance in the air flow rate of the experimental facility. In blue: original ERT signal. In orange: output of the low-pass filter (${\omega}_{f}=1$ rad/s). Signals with standard deviation $\sigma \left(y\right)=0.0801$ and $\sigma \left(\widehat{y}\right)=0.0227$.

**Figure 26.**Comparison between the delay obtained cross-correlating the signal of the camera and WMS (measured delay), previously shown in Figure 18, and the delay estimated based on the conservation of mass (model described in Appendix B). The perfect match between the model and experiments is represented by the dashed line.

**Table 1.**Standard deviation of core size and efficiencies measured in the experiments of Section 5.

Experiment | $\mathit{\sigma}\left(\mathit{y}\right)$ | $\mathit{\sigma}\left(\widehat{\mathit{y}}\right)$ | ${\mathit{\eta}}_{\mathit{a}}$ | ${\mathit{\eta}}_{\mathit{w}}$ | ${\mathit{\eta}}_{\mathit{m}}$ |
---|---|---|---|---|---|

Operating Point (Figure 22) | 0.0724 | 0.0146 | 88% | 74% | 81% |

Control of Intrinsic Dynamics (Figure 23) | 0.0719 | 0.0154 | 92% | 70% | 81% |

Uncontrolled Disturbance (Figure 24) | 0.0902 | 0.0323 | 76% | 75% | 75% |

Control of Disturbance (Figure 25) | 0.0801 | 0.0227 | 93% | 63% | 78% |

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Garcia, M.M.; Sattar, M.A.; Atmani, H.; Legendre, D.; Babout, L.; Schleicher, E.; Hampel, U.; Portela, L.M.
Towards Tomography-Based Real-Time Control of Multiphase Flows: A Proof of Concept in Inline Fluid Separation. *Sensors* **2022**, *22*, 4443.
https://doi.org/10.3390/s22124443

**AMA Style**

Garcia MM, Sattar MA, Atmani H, Legendre D, Babout L, Schleicher E, Hampel U, Portela LM.
Towards Tomography-Based Real-Time Control of Multiphase Flows: A Proof of Concept in Inline Fluid Separation. *Sensors*. 2022; 22(12):4443.
https://doi.org/10.3390/s22124443

**Chicago/Turabian Style**

Garcia, Matheus M., Muhammad A. Sattar, Hanane Atmani, Dominique Legendre, Laurent Babout, Eckhard Schleicher, Uwe Hampel, and Luis M. Portela.
2022. "Towards Tomography-Based Real-Time Control of Multiphase Flows: A Proof of Concept in Inline Fluid Separation" *Sensors* 22, no. 12: 4443.
https://doi.org/10.3390/s22124443