# Optimization of an Oil–Gas Separator of Gas Storage Compressor with Consideration of Velocity Uniformity in Filter Inlets

^{1}

^{2}

^{*}

## Abstract

**:**

_{b}= 0.4, l

_{b}= 3, h

_{b}= 1.5, and k

_{b}= 0.5 and l

_{e}= 0.9 and h

_{e}= 4.11, as well as l

_{c}= 0.5 and d

_{c}= 0.52, are suitable for the case of placing baffles, adjusting the separator height and inlet position, as well as adding an inner cylinder, respectively. Subsequently, the analytic hierarchy process was employed to compare different optimized cases. It is observed that the overall rating for adding an inner cylinder reaches 88.46, which is the more suitable optimized method for the oil–gas separator. This work is relevant for oil–gas systems to improve their separation efficiency and enhance the gas storage performance.

## 1. Introduction

## 2. Models and Methods

#### 2.1. Physical Model

#### 2.2. Numerical Model

_{t}, exhibits isotropy, and notable correspondences emerge between impacts of Reynolds stress and the time-averaged flow and viscous stress. This circumstance facilitates the application of a dedicated numerical computation approach for ascertaining the Reynolds stress:

_{t}can be obtained as follows:

_{μ}is the model coefficient and is typically taken as 0.09. k and ε are solved by their respective transport equations:

_{k}, C

_{ε}, C

_{ε}

_{1}, and C

_{ε}

_{2}are 0.09–0.11, 0.07–0.09, 1.41–1.45, and 1.91–1.92, respectively.

_{1}and C

_{2}are 1.5–2.2 and 0.4–0.5, respectively.

_{I}is the inertial resistance factor.

_{D}is the drag coefficient, ${C}_{D}={a}_{1}+\frac{{a}_{2}}{Re}+\frac{{a}_{3}}{Re}$; F

_{a}is the additional force, such as Saffman lift and virtual mass force.

#### 2.3. Computational Methods

## 3. Validation

#### 3.1. Grid Independence Validation

#### 3.2. Model Validation

## 4. Results and Discussion

#### 4.1. Analysis of Existing Oil–Gas Separator

_{ij}is the velocity at (i, j) of the cross-section, $\overline{u}$ is the average velocity, and N is the number of samples. Note that the lower the σ, the better the uniformity of the velocity distribution. The result corresponding to velocity in the filter inlet for the existing separator is shown in Figure 7. The velocity non-uniformity is 0.48 m/s. Obviously, the non-uniformity is attributed to the relatively high speed near the wall far from the inlet.

#### 4.2. Optimization Solutions for the Separator

#### 4.2.1. Case A

_{b}), and height (H

_{b}) are normalized by inlet diameter, and the curvature of the baffle (K

_{b}) is normalized by that of the separator ($K=1/{r}_{\mathrm{sep}}$) to make results generally applicable: ${b}_{b}=B/{d}_{\mathrm{i}}$, ${l}_{b}={L}_{b}/{d}_{\mathrm{i}}$, ${h}_{b}={H}_{b}/{d}_{\mathrm{i}}$, and ${k}_{b}={K}_{b}/{d}_{\mathrm{i}}$. When investigating how b

_{b}, l

_{b}, h

_{b}, and k

_{b}values affect the performance of the primary separation chamber, employing the controlled variables method would generate a significant number of combinations. Consequently, an orthogonal experimental design is utilized to select a representative subset of combinations for research, thereby mitigating the workload. The factors and their corresponding levels for this study are presented in Table 4. For this simulation, it is a 4-factor, 4-level study. Hence, an L16 (4

^{4}) orthogonal array is selected for the experiments. The specific experimental parameters are provided in Table 5.

#### 4.2.2. Case B

_{e}) and the distance between the inlet of the separator and that of the filter (L

_{e}) are normalized by separator diameter and cylinder height, respectively. That is, ${h}_{e}={H}_{e}/{d}_{\mathrm{sep}}$ and ${l}_{e}={L}_{e}/{H}_{e}$. The effects of h

_{e}equals 2.81, 3.46, 4.11, and 4.76, and l

_{e}equals 0.3, 0.5, 0.7, and 0.9, on the separation performance are studied.

#### 4.2.3. Case C

_{c}) and diameter (D

_{c}) of the inner cylinder on the separation efficiency needs to be investigated. The length is normalized by the separator height: ${l}_{c}={{L}_{c}/h}_{\mathrm{sep}}$. The diameter is normalized by the separator diameter: ${d}_{c}={D}_{c}/{d}_{\mathrm{sep}}$. The effects of l

_{c}equals 0.5, 0.6, 0.7, and 0.8, and d

_{c}equals 0.35, 0.43, 0.52, and 0.61, on the separation performance are discussed.

#### 4.3. Analysis of Optimized Oil–Gas Separators

#### 4.3.1. Effect of the Baffle Parameters

_{b}1, l

_{b}4, h

_{b}1, and k

_{b}1. Based on R values in Figure 13b, the order of the factors’ influence on separation efficiency is as follows: b

_{b}> l

_{b}> h

_{b}> k

_{b}. The effect of baffle parameters on pressure drop and velocity non-uniformity is exhibited in Figure 14 and Figure 15, respectively. The situation has undergone a complete transformation. For pressure loss, the best combination is b

_{b}3, l

_{b}1, h

_{b}1, and k

_{b}1, and the order of impact for each factor is b

_{b}> k

_{b}> l

_{b}> h

_{b}. For velocity non-uniformity, the best combination is b

_{b}3, l

_{b}4, h

_{b}3, and k

_{b}2, and the order of impact for each factor is b

_{b}= h

_{b}> l

_{b}> k

_{b}.

_{b}= 0.4, l

_{b}= 3, h

_{b}= 1.5, and k

_{b}= 0.5, excluded from the 16 results in the orthogonal experimental design. Thus, further discussion is necessary.

#### 4.3.2. Effect of the Cylinder Height and Entrance Position

_{e}= 0.9 and h

_{e}= 4.11. Furthermore, the optimal h

_{e}varies for different l

_{e}. It is found that the pressure drop (Figure 20b) exhibits minimal fluctuation, i.e., the difference between the maximum and minimum values is 2386.1 Pa. Accordingly, the influence of pressure drop is almost disregarded in Case B. For velocity non-uniformity in Case B (Figure 20c), it is displayed that the uniformity (maximum value reaches 2.8 m/s) is significantly larger than in Case A, which is caused by the high-speed rotation near the wall. Moreover, velocity non-uniformity is lower and decreases with the enhancement of l

_{e}when h

_{e}is 4.11 and 4.76. The optimal parameters for case B should be l

_{e}= 0.9 and h

_{e}= 4.11 because the separation efficiency is highest, and velocity non-uniformity is relatively less in this case.

#### 4.3.3. Effect of the Inner Cylinder Parameters

_{c}= 0.5 and d

_{c}= 0.52 are appropriate for case C, as both pressure drop and velocity non-uniformity are sufficiently low.

#### 4.4. Comparative Analysis of Optimized Oil–Gas Separators

_{max}) obtained is 4.066. The consistency index ($CI=\frac{{\lambda}_{\mathrm{max}}-n}{n-1}$, n is the matrix dimensions) equals 0.022. The consistency ratio ($CR=\frac{CI}{RI}$, RI equals 0.9 when n is 4) equals 0.024 and is less than 0.1. The consistency check has passed. The evaluation criteria for each factor are summarized in Table 8, and the final evaluation results are presented in Table 9. It can be observed that, although case C has a relatively high velocity non-uniformity, it has the highest overall score, reaching 88.46, making it the more optimal choice according to the analytic hierarchy process. Note that the corresponding optimized dimensionless physical parameters for case C are l

_{c}= 0.5 and d

_{c}= 0.52.

## 5. Conclusions

- (1)
- The separation efficiency of the existing separator is lower, owing to the sharp decrease in gas velocity within the separation chamber. However, the low velocity causes excellent velocity non-uniformity, i.e., 0.48 m/s.
- (2)
- For optimized collision separation (case A), the selection of the main parameters of the baffle is difficult based on the orthogonal experimental design due to the totally different sets of parameters for optimal separation efficiency, pressure drop, and velocity uniformity. Considering that separation efficiency is the most crucial factor, b
_{b}= 0.4, l_{b}= 3, h_{b}= 1.5, and k_{b}= 0.5 have been considered. The separation efficiency is 98.64%, and the velocity non-uniformity is 0.7 m/s. - (3)
- For optimized centrifugal separation (cases B and C), the separation efficiency has been effectively improved. Nevertheless, the velocity uniformity in the filter inlet has been significantly reduced because of the turbulent disturbances caused by the cyclone effect. The maximal velocity non-uniformity reaches 2.8 m/s for the case varying the cylinder height and inlet position. Considering the combined effects of parameter changes on separation efficiency, pressure drop, and velocity uniformity, l
_{e}= 0.9 and h_{e}= 4.11, as well as l_{c}= 0.5 and d_{c}= 0.52, have been taken into account for cases B and C, respectively. - (4)
- It is observed that the case of adding an inner cylinder is the more suitable optimized method for the oil–gas separator, according to the analytic hierarchy process. The overall rating for this situation reaches 88.46.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 4.**Model validation for oil–gas separator [34].

**Figure 13.**Effect of baffle parameters on separation efficiency: (

**a**) separation efficiency and (

**b**) range for separation efficiency.

**Figure 14.**Effect of baffle parameters on pressure drop: (

**a**) pressure drop and (

**b**) range for pressure drop.

**Figure 15.**Effect of baffle parameters on velocity non-uniformity: (

**a**) velocity non-uniformity and (

**b**) range for velocity non-uniformity.

**Figure 17.**Velocity distribution: (

**a**) existing separator, (

**b**) optimal case A, and (

**c**) filter inlet for optimal case A.

**Figure 19.**Flow field for case B: (

**a**) velocity, (

**b**) pressure, (

**c**) oil mass concentration, and (

**d**) filter inlet velocity.

**Figure 20.**Effect of the cylinder height and entrance position on (

**a**) separation efficiency, (

**b**) pressure drop, and (

**c**) velocity non-uniformity.

**Figure 23.**Effect of inner cylinder parameters on (

**a**) separation efficiency, (

**b**) pressure drop, and (

**c**) velocity non-uniformity.

Geometrical Properties | Dimension |
---|---|

Inlet diameter, d_{i}/mm | 100 |

Outlet diameter, d_{o}/mm | 100 |

Separator radius, r_{sep}/mm | 462 |

Mechanical separation chamber height, h_{msc}/mm | 1300 |

Filtration chamber height, h_{fc}/mm | 1600 |

Filter height, h_{f}/mm | 910 |

Filter radius, r_{f}/mm | 80 |

Parameter | Discrete Format |
---|---|

Pressure | PRESTO |

Momentum | QUICK |

Turbulence energy | Second Order Upwind |

Turbulent dissipation rate | Second Order Upwind |

Parameter | Typical Value |
---|---|

Boiling point (°C) | >315 |

Flash point (°C) | 250 |

Density (kg/m^{3}) | 877–928 |

Viscosity at 40 °C (mm^{2}/s) | 198 |

Level | Factors | |||
---|---|---|---|---|

b_{b} | l_{b} | h_{b} | k_{b} | |

1 | 0.4 | 1.5 | 1.5 | 0.5 |

2 | 0.6 | 2 | 2 | 0.75 |

3 | 0.8 | 2.5 | 2.5 | 1 |

4 | 1 | 3 | 3 | 1.25 |

No. | b_{b} | l_{b} | h_{b} | k_{b} |
---|---|---|---|---|

1 | 0.4 | 1.5 | 1.5 | 0.5 |

2 | 0.4 | 2 | 2 | 0.75 |

3 | 0.4 | 2.5 | 2.5 | 1 |

4 | 0.4 | 3 | 3 | 1.25 |

5 | 0.6 | 1.5 | 2 | 1 |

6 | 0.6 | 2 | 1.5 | 1.25 |

7 | 0.6 | 2.5 | 3 | 0.5 |

8 | 0.6 | 3 | 2.5 | 0.75 |

9 | 0.8 | 1.5 | 2.5 | 1.25 |

10 | 0.8 | 2 | 3 | 1 |

11 | 0.8 | 2.5 | 1.5 | 0.75 |

12 | 0.8 | 3 | 2 | 0.5 |

13 | 1 | 1.5 | 3 | 0.75 |

14 | 1 | 2 | 2.5 | 0.5 |

15 | 1 | 2.5 | 2 | 1.25 |

16 | 1 | 3 | 1.5 | 1 |

Factor | Separation Efficiency | Velocity Uniformity | Pressure Drop | Cost |
---|---|---|---|---|

Separation efficiency | 1 | 3 | 6 | 9 |

Velocity uniformity | 1/3 | 1 | 4 | 5 |

Pressure drop | 1/6 | 1/4 | 1 | 2 |

Cost | 1/9 | 1/5 | 1/2 | 1 |

Factor | Separation Efficiency | Velocity Uniformity | Pressure Drop | Cost | Weight |
---|---|---|---|---|---|

Separation efficiency | 0.62 | 0.62 | 0.52 | 0.53 | 0.59 |

Velocity uniformity | 0.21 | 0.22 | 0.35 | 0.29 | 0.27 |

Pressure drop | 0.1 | 0.06 | 0.09 | 0.12 | 0.09 |

Cost | 0.07 | 0.04 | 0.04 | 0.06 | 0.05 |

Factor | Criteria |
---|---|

Separation efficiency | $\frac{\eta -{\eta}_{i}}{1-{\eta}_{i}}\times 100$ |

Velocity uniformity | $\frac{{\displaystyle \sum \sigma}-{\sigma}_{i}}{{\sigma}_{i}}\times 100$ |

Pressure drop | $\frac{{\displaystyle \sum \Delta p}-\Delta {p}_{i}}{{\displaystyle \sum \Delta p}}\times 100$ |

Cost | $\frac{{\displaystyle \sum V}-{V}_{i}}{{\displaystyle \sum V}}\times 100$ |

Factor | Weight | Case A | Case B | Case C |
---|---|---|---|---|

Separation efficiency | 0.58650 | 82.61 | 94.25 | 100.00 |

Velocity uniformity | 0.26839 | 83.72 | 51.13 | 65.16 |

Pressure drop | 0.09106 | 30.60 | 90.98 | 78.42 |

Cost | 0.05405 | 98.54 | 5.55 | 95.91 |

Final score | 1 | 79.03 | 77.58 | 88.46 |

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## Share and Cite

**MDPI and ACS Style**

Hu, X.; Peng, Z.; Chen, D.; Ma, Z.; Liu, W.; Zhao, B.
Optimization of an Oil–Gas Separator of Gas Storage Compressor with Consideration of Velocity Uniformity in Filter Inlets. *Energies* **2023**, *16*, 8015.
https://doi.org/10.3390/en16248015

**AMA Style**

Hu X, Peng Z, Chen D, Ma Z, Liu W, Zhao B.
Optimization of an Oil–Gas Separator of Gas Storage Compressor with Consideration of Velocity Uniformity in Filter Inlets. *Energies*. 2023; 16(24):8015.
https://doi.org/10.3390/en16248015

**Chicago/Turabian Style**

Hu, Xiaobo, Zeyu Peng, Da Chen, Zenghui Ma, Wei Liu, and Bin Zhao.
2023. "Optimization of an Oil–Gas Separator of Gas Storage Compressor with Consideration of Velocity Uniformity in Filter Inlets" *Energies* 16, no. 24: 8015.
https://doi.org/10.3390/en16248015