# Numerical Simulation and Experimental Study of a Multistage Multiphase Separation System

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{3}/h, the average particle size of oil drops in the blank pipe, semicircular baffle, four-hole plate, spiral track and seven-hole plate increases in turn. A continuous oil layer appears at the outlet of the vertical separator in the fully open state. The water content at the oil outlet of the semicircular baffle coalescing component is always at a high level under different flow rates. When the inlet volumetric flow rate is less than 1.6 m

^{3}/h, the performance of the spiral track coalescing component is better. With the increase of the inlet volumetric flow rate, the separation efficiency of the spiral track is lower than that of the orifice. The results show that the semicircular coalescing component has the worst performance, the spiral track coalescing component is superior at small volumetric flow rates, and the orifice coalescing component is superior at large volumetric flow rates.

## 1. Introduction

## 2. Methods and Theories

#### 2.1. Coagulation and Separation Mechanism

_{w}is the density of water; ρ

_{o}is the density of oil; g is local gravitational acceleration; ν

_{up}is the rising rate of oil droplets; μ is the viscosity of water; and d

_{o}is the oil droplet size.

_{1}, d

_{2}… d

_{n}, the velocity is:

_{ln}is the rising rate of coalescent oil droplets; d is the oil droplet size; subscript 1 refers to the first oil droplet; and d

_{i}represents the ith oil droplet.

_{c}is the coalescence time of the droplet and the oil film, s; r

_{f}is the radius of the droplet and membrane deformation zone, m; u

_{r}and u

_{cδ}are velocities of the interlayer drainage and membrane surface, respectively, m/s; h

_{0}is the interlayer thickness of the initial liquid, m; h

_{c}is the critical liquid interlayer thickness, m; σ is the surface tension of the dispersed phase, N/m; μ

_{c}is the viscosity of continuous phase, Pa s; and R is the deformation curvature radius of the droplet, m.

#### 2.2. Isoflow Theory

_{p}is the cross-section of pipes; Q is the inlet flow; and n is the number of pipes. When the flow rate is fixed, increasing the value of n can reduce ν

_{down}. Furthermore, the oil–water separation capacity of the separator is improved.

#### 2.3. Shallow Pool Theory

_{0}, the motion of droplets in the separator satisfies the formula L/H = ν/μ

_{0}. In the process of gravity separation, the separation effect of dispersed phase droplets is a function related to the droplet rate and the shallow pool area. Specifically, the efficiency of the separator can be improved by expanding the sedimentation area or increasing the settling speed.

## 3. Multistage Multiphase Oil–Water Separation System

## 4. Numerical Simulation

#### 4.1. Numerical Simulation Setup

^{3}/h, and it is considered that there is no slip between the fluid and the pipe surface. The Euler–Euler multiphase mixed model has high computational efficiency and is widely used to solve multiphase flows with different flow velocities. It is suitable for situations where the dispersed phases are widely distributed, and it is the most consistent with the experimental conditions.

^{3}, the water density is 998.2 kg/m

^{3}, the kinematical viscosity is 1.007 × 10

^{−6}m

^{2}/s, and the surface tension is 7.36 × 10

^{−2}N/m. The physical properties of white oil meet the following formula:

#### 4.2. Geometric Modeling and Meshing

#### 4.3. Numerical Simulation Results and Analysis

## 5. Laboratory Experiment

#### 5.1. Experimental Procedures

#### 5.2. Experimental Results and Analysis

#### 5.2.1. Separation Effect of the Separation System

^{3}/h. Timing was started while turning on loop II. Figure 11 and Figure 12 show the changes in water and oil contents at the oil outlet with settlement time.

#### 5.2.2. Separation Efficiency of Different Coalescing Components

^{3}/h. The working state of the five pipes is controlled by adjusting the switch, including six working states: connecting blank pipe, semicircle baffle, spiral track, four-hole plate, seven-hole plate and fully open.

#### 5.2.3. Influence of Coalescing Components on System Separation Efficiency at Different Volumetric Flow Rates

^{3}/h, 1.2 m

^{3}/h, 1.5 m

^{3}/h, 1.8 m

^{3}/h, 2.0 m

^{3}/h. The water content line diagram at the oil outlet of the five discrete risers under different volumetric flow rates is drawn and analyzed.

^{3}/h, the performance of the coalescing component is as follows: spiral track > seven-hole plate > four-hole plate > semicircle baffle. However, when the inlet flow is greater than 1.6 m

^{3}/h, the coalescence performance of the spiral track deteriorates rapidly, and the coalescence performance is as follows: seven-hole plate > four-hole plate > spiral orbit > semicircle baffle. It can be seen that the coalescence performance of the spiral track is significantly affected by the flow rate; it is superior under the condition of a small flow rate. The coalescence performance of the orifice element is not obviously affected by flow rate, which is suitable for large flow rate separation. The semicircular baffle shows the smallest improvement in system separation efficiency.

## 6. Conclusions

- (1)
- Numerical simulation of the vertical separator was carried out by Fluent software. In order to clarify the separation mechanism of parallel risers and the separation ability of a single pipe, the flow fields of pipes with different coalescing components were studied. The results show that the oil phase volume fraction distribution of the semicircle flapper is the most uneven, while the flow field of the orifice coalescing component is the most stable. Affected by contact with coalescence, the oil phase volume fraction in the vicinity of the spiral orbit coalescing component is at a high level.
- (2)
- Laboratory experiments were carried out to study the separation effect of the multiphase oil–water separation system. The results show that the water content at the oil outlet of the new separation system is 3% less than the horizontal separator, and the new separation system has a better separation effect than the horizontal separator.
- (3)
- The numerical simulation results of the parallel vertical separator are in good agreement with the experimental results. The semicircular coalescing component has the worst separation effect. Under the condition that the inlet flow is less than 1.6 m
^{3}/h, the water content at the oil outlet of the spiral track is the lowest. It can be seen that the spiral track is suitable for small volumetric flow rate separation. In contrast, the orifice coalescing component can still maintain a lower water content at the oil outlet under the condition of large flow, which performs well at a large volumetric flow rate. - (4)
- There are still some deviations in this experiment. There is a certain error of time in the sampling and measurement at the outlet, which affects the droplet morphology in the emulsion. In addition, different temperatures in the laboratory will also have an impact on the oil viscosity.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 4.**Model diagram of coalescing components. (

**a**) Spiral track model diagram; (

**b**) semicircular baffle model diagram; (

**c**) four-hole plate model diagram; and (

**d**) seven-hole plate model diagram.

**Figure 5.**Meshing diagram of discrete pipes. (

**a**) Mesh division of the spiral orbit, with an encrypted mesh of 89,900; (

**b**) mesh division of the semicircular baffle, with an encrypted mesh of 72,000; (

**c**) mesh division of the four-hole plate, with an encrypted mesh of 62,700; and (

**d**) mesh division of the seven-hole plate, with an encrypted mesh of 66,300.

**Figure 10.**Flow chart of the laboratory experiment. (a) Small mixing barrel; (b) booster pump; (c) liquid flowmeter; (d) gas pump; (e) gas flowmeter; (f) check valve; (g) tee; (h) bypass valve; (i) vertical separator; and (j) horizontal separator.

**Figure 13.**Microscopy images of oil droplet size at the outlet of the vertical separator under six working states. (

**a**) Blank tube; (

**b**) semicircular baffle; (

**c**) spiral track; (

**d**) four-hole plate; (

**e**) seven-hole plate; (

**f**) all five risers are open.

Blank Tube /(μm) | Semicircular Baffle/(μm) | Spiral Orbit /(μm) | Four-Hole Plate/(μm) | Seven-Hole Plate/(μm) | All Risers Are Open |
---|---|---|---|---|---|

69.03 | 71.49 | 75.80 | 72.99 | 78.24 | ∞ |

Blank Tube | Semicircular Baffle | Spiral Orbit | Four-Hole Plate | Seven-Hole Plate | |
---|---|---|---|---|---|

Oil content reduction/% | 6.25 | 13.3 | 10.2 | 14.8 | 20 |

Water content reduction/% | 6.9 | 15 | 13.7 | 15.5 | 17.6 |

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**MDPI and ACS Style**

Chen, X.; Zheng, J.; Jiang, J.; Peng, H.; Luo, Y.; Zhang, L.
Numerical Simulation and Experimental Study of a Multistage Multiphase Separation System. *Separations* **2022**, *9*, 405.
https://doi.org/10.3390/separations9120405

**AMA Style**

Chen X, Zheng J, Jiang J, Peng H, Luo Y, Zhang L.
Numerical Simulation and Experimental Study of a Multistage Multiphase Separation System. *Separations*. 2022; 9(12):405.
https://doi.org/10.3390/separations9120405

**Chicago/Turabian Style**

Chen, Xuezhong, Jian Zheng, Jiayu Jiang, Hao Peng, Yanli Luo, and Liming Zhang.
2022. "Numerical Simulation and Experimental Study of a Multistage Multiphase Separation System" *Separations* 9, no. 12: 405.
https://doi.org/10.3390/separations9120405