# Multiphase Flow Production Enhancement Using Drag Reducing Polymers

^{*}

## Abstract

**:**

## 1. Introduction and Literature Review

## 2. Description of Experimental Setup and Procedure

#### 2.1. Preparation of the Polymer Solution

#### 2.2. System Operation

## 3. Results and Discussions

#### 3.1. Effect of DRP on Frictional Pressure Drop

#### 3.2. Effect of DRP in Two-Phase Flow Pattern Transition

#### 3.2.1. Stratified and Stratified Wavy Flow Regimes

#### 3.2.2. Annular and Wavy Annular Flow Patterns

#### 3.2.3. Dispersed Bubbly Flow Regime

#### 3.2.4. Slug and Pseudo Slug Flow Regimes

#### 3.3. Correlations for Gas –Liquid Flow with Addition of DRP

#### 3.3.1. Correlation Development

#### 3.3.2. Dimensionless Parameters

_{sl}) and the pressure drop with the addition of the drag reducing polymer (${P}_{DRP}$).

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

$\mathit{r}\mathit{u}\mathit{n}$ | ${\mathit{V}}_{\mathit{s}\mathit{l}}\left(\frac{\mathit{m}}{\mathit{s}}\right)$ | ${\mathit{V}}_{\mathit{s}\mathit{g}}\left(\frac{\mathit{m}}{\mathit{s}}\right)$ | $\frac{\mathit{d}\mathit{P}}{\mathit{d}\mathit{L}}\left(\frac{\mathit{P}\mathit{a}}{\mathit{m}}\right)$ | $\mathit{F}\mathit{l}\mathit{o}\mathit{w}\mathit{p}\mathit{a}\mathit{t}\mathit{t}\mathit{e}\mathit{r}\mathit{n}$ | $\frac{\mathit{d}\mathit{P}}{\mathit{d}\mathit{L}}\left(\frac{\mathit{P}\mathit{a}}{\mathit{m}}\right)$ | $\mathit{F}\mathit{l}\mathit{o}\mathit{w}\mathit{p}\mathit{a}\mathit{t}\mathit{t}\mathit{e}\mathit{r}\mathit{n}$ | $\mathit{D}\mathit{R}\mathit{\%}$ |
---|---|---|---|---|---|---|---|

$\mathit{w}\mathit{i}\mathit{t}\mathit{h}\mathit{o}\mathit{u}\mathit{t}\mathit{D}\mathit{R}\mathit{P}$ | $40\mathrm{ppm}\mathit{D}\mathit{R}\mathit{P}$ | ||||||

1 | 0.1 | 0.41 | 613 | St | 400 | St | 35 |

2 | 0.1 | 0.51 | 667 | St | 467 | St | 30 |

3 | 0.1 | 0.62 | 760 | St | 600 | St | 21 |

4 | 0.1 | 0.72 | 800 | St | 687 | St | 14 |

5 | 0.1 | 0.82 | 880 | St | 733 | St | 17 |

6 | 0.1 | 0.93 | 1160 | St—Slug | 800 | St Wavy | 31 |

7 | 0.1 | 1.03 | 1200 | St—Slug | 933 | St Wavy | 22 |

8 | 0.1 | 1.64 | 1800 | Slug | 667 | St Wavy | 63 |

9 | 0.1 | 2.06 | 1933 | Slug | 800 | St Wavy | 59 |

10 | 0.1 | 2.47 | 2467 | Slug | 1000 | St Wavy | 59 |

11 | 0.1 | 2.88 | 3000 | St Wavy | 1067 | St Wavy | 64 |

12 | 0.1 | 3.70 | 1467 | St Wavy | 667 | St Wavy | 55 |

13 | 0.1 | 4.11 | 1667 | St Wavy | 733 | St Wavy | 56 |

14 | 0.1 | 4.52 | 1800 | An | 867 | St Wavy | 52 |

15 | 0.1 | 4.93 | 1867 | An | 867 | St Wavy | 54 |

16 | 0.1 | 5.34 | 2000 | An | 1000 | St Wavy | 50 |

17 | 0.1 | 7.20 | 1467 | An | 773 | St Wavy | 47 |

18 | 0.1 | 7.81 | 1533 | An | 800 | St Wavy | 48 |

19 | 0.1 | 8.43 | 1600 | An | 867 | St Wavy | 46 |

20 | 0.1 | 9.05 | 1800 | An | 1000 | St Wavy | 44 |

21 | 0.1 | 9.66 | 1867 | W An | 1133 | St Wavy | 39 |

22 | 0.1 | 10.28 | 2000 | W An | 1267 | St Wavy | 37 |

23 | 0.1 | 10.90 | 2067 | W An | 1400 | St Wavy | 32 |

24 | 0.1 | 11.51 | 2133 | W An | 1467 | St Wavy | 31 |

25 | 0.1 | 12.13 | 2400 | W An | 1640 | W An | 32 |

26 | 0.1 | 12.75 | 2667 | W An | 1713 | W An | 36 |

27 | 3.08 | 1.03 | 15,480 | DB | 6905 | Pseudo Slug | 55 |

28 | 3.08 | 2.06 | 18,713 | DB | 8659 | Pseudo Slug | 54 |

29 | 3.08 | 3.08 | 21,100 | DB | 10,456 | Pseudo Slug | 50 |

30 | 3.08 | 4.11 | 23,553 | DB | 12,171 | Pseudo Slug | 48 |

31 | 3.08 | 5.14 | 25,847 | DB | 13,500 | Pseudo Slug | 48 |

32 | 3.08 | 6.17 | 27,920 | DB | 15,050 | DB | 46 |

33 | 3.08 | 7.20 | 29,287 | DB | 15,823 | DB | 46 |

34 | 3.08 | 8.22 | 31,280 | DB | 17,172 | DB | 45 |

35 | 3.08 | 9.25 | 32,067 | DB | 18,359 | DB | 43 |

36 | 3.08 | 10.28 | 33,680 | DB | 19,323 | DB | 43 |

## Appendix B

**Table A2.**Frictional Pressure Drop Associated with the Slug Flow Regime and Drag Reduction Effectiveness Using 40 ppm DRP.

$\mathit{r}\mathit{u}\mathit{n}$ | ${\mathit{V}}_{\mathit{s}\mathit{l}}\left(\frac{\mathit{m}}{\mathit{s}}\right)$ | ${\mathit{V}}_{\mathit{s}\mathit{g}}\left(\frac{\mathit{m}}{\mathit{s}}\right)$ | $\frac{\mathit{d}\mathit{P}}{\mathit{d}\mathit{L}}\left(\frac{\mathit{P}\mathit{a}}{\mathit{m}}\right)$ | $\mathit{F}\mathit{l}\mathit{o}\mathit{w}\mathit{p}\mathit{a}\mathit{t}\mathit{t}\mathit{e}\mathit{r}\mathit{n}$ | $\mathit{D}\mathit{R}\mathit{\%}$ | ||
---|---|---|---|---|---|---|---|

$\mathit{w}\mathit{i}\mathit{t}\mathit{h}\mathit{o}\mathit{u}\mathit{t}\mathit{D}\mathit{R}\mathit{P}$ | $40\mathrm{ppm}\mathit{D}\mathit{R}\mathit{P}$ | ||||||

1 | 0.72 | 0.41 | 2133 | Slug | 1000 | Slug | 53 |

2 | 0.72 | 0.51 | 2267 | Slug | 1533 | Slug | 32 |

3 | 0.72 | 0.62 | 2400 | Slug | 1733 | Slug | 28 |

4 | 0.72 | 0.72 | 2467 | Slug | 1933 | Slug | 22 |

5 | 0.72 | 0.82 | 2667 | Slug | 2133 | Slug | 20 |

6 | 0.72 | 0.93 | 3000 | Slug | 2200 | Slug | 27 |

7 | 0.72 | 1.03 | 3133 | Slug | 2333 | Slug | 26 |

8 | 0.72 | 1.13 | 3333 | Slug | 2467 | Slug | 26 |

## Appendix C

$\mathit{r}\mathit{u}\mathit{n}$ | ${\mathit{V}}_{\mathit{s}\mathit{l}}\left(\frac{\mathit{m}}{\mathit{s}}\right)$ | ${\mathit{V}}_{\mathit{s}\mathit{g}}\left(\frac{\mathit{m}}{\mathit{s}}\right)$ | $\mathit{D}\mathit{R}\mathit{\%}$ | ||||
---|---|---|---|---|---|---|---|

$\mathit{w}\mathit{i}\mathit{t}\mathit{h}\mathit{o}\mathit{u}\mathit{t}\mathit{D}\mathit{R}\mathit{P}$ | $100\mathrm{ppm}\mathit{D}\mathit{R}\mathit{P}$ | ||||||

1 | 0.72 | 0.41 | 2133 | Slug | 733 | St Wavy | 66 |

2 | 0.72 | 0.51 | 2267 | Slug | 933 | St Wavy | 59 |

3 | 0.72 | 0.62 | 2400 | Slug | 1067 | St Wavy | 56 |

4 | 0.72 | 0.72 | 2467 | Slug | 1067 | St Wavy | 57 |

5 | 0.72 | 0.82 | 2667 | Slug | 1067 | St Wavy | 60 |

6 | 0.72 | 0.93 | 3000 | Slug | 1267 | St Wavy | 58 |

7 | 0.72 | 1.03 | 3133 | Slug | 1400 | St Wavy | 55 |

8 | 0.72 | 1.13 | 3333 | Slug | 1667 | St Wavy | 50 |

## Appendix D

$\mathit{r}\mathit{u}\mathit{n}$ | ${\mathit{V}}_{\mathit{s}\mathit{l}}\left(\frac{\mathit{m}}{\mathit{s}}\right)$ | ${\mathit{V}}_{\mathit{s}\mathit{g}}\left(\frac{\mathit{m}}{\mathit{s}}\right)$ | $\mathit{D}\mathit{R}\mathit{\%}$ | ||||
---|---|---|---|---|---|---|---|

$40\mathrm{ppm}\mathit{D}\mathit{R}\mathit{P}$ | |||||||

1 | 1.03 | 1.03 | 4000 | Pseudo Slug | 2667 | W An | 33 |

2 | 1.03 | 2.06 | 5667 | Pseudo Slug | 3333 | W An | 41 |

3 | 1.03 | 3.08 | 7333 | Pseudo Slug | 4333 | W An | 41 |

4 | 1.03 | 4.11 | 8467 | Pseudo Slug | 6400 | Pseudo Slug | 24 |

5 | 1.03 | 5.14 | 9800 | Pseudo Slug | 7067 | Pseudo Slug | 28 |

6 | 1.03 | 6.17 | 10800 | Pseudo Slug | 8000 | Pseudo Slug | 26 |

## Appendix E

$\mathit{r}\mathit{u}\mathit{n}$ | ${\mathit{V}}_{\mathit{s}\mathit{l}}\left(\frac{\mathit{m}}{\mathit{s}}\right)$ | ${\mathit{V}}_{\mathit{s}\mathit{g}}\left(\frac{\mathit{m}}{\mathit{s}}\right)$ | $\mathit{D}\mathit{R}\mathit{\%}$ | ||||
---|---|---|---|---|---|---|---|

$100\mathrm{ppm}\mathit{D}\mathit{R}\mathit{P}$ | |||||||

1 | 1.03 | 1.03 | 4000 | Pseudo Slug | 1600 | W An | 60 |

2 | 1.03 | 2.06 | 5667 | Pseudo Slug | 2333 | W An | 59 |

3 | 1.03 | 3.08 | 7333 | Pseudo Slug | 2667 | W An | 64 |

4 | 1.03 | 4.11 | 8467 | Pseudo Slug | 3600 | W An | 57 |

5 | 1.03 | 5.14 | 9800 | Pseudo Slug | 4467 | W An | 54 |

6 | 1.03 | 6.17 | 10800 | Pseudo Slug | 5800 | W An | 46 |

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**Figure 2.**Comparison of the frictional pressure drop variation with respect to liquid superficial velocity at different gas superficial velocities of 2.06, 3.08 and 4.11 m/s.

**Figure 4.**(

**a**) Stratified Wavy flow without DRP (V

_{sl}= 0.1 m/s, V

_{sg}= 0.41 m/s); (

**b**) Stratified Wavy flow with 40 ppm DRP.

**Figure 5.**(

**a**) Stratified Wavy flow without DRP (V

_{sl}= 0.1 m/s, V

_{sg}= 2.88 m/s); (

**b**) Stratified Wavy flow with 40 ppm DRP.

**Figure 7.**(

**a**) Annular flow regime without DRP (V

_{sl}= 0.1 m/s, V

_{sg}= 9.05 m/s); (

**b**) Annular flow regime with 40 ppm of DRP.

**Figure 9.**(

**a**) Typical feature of a Dispersed Bubbly flow regime (V

_{sl}= 3.08 m/s, V

_{sg}= 1.03 m/s) (

**b**) Transition from Dispersed Bubbly to Pseudo slug flow regime with 40 ppm DRP.

**Figure 11.**Effect of drag reducing polymer on slug flow regime using a concentration of 40 and 100 ppm.

**Figure 12.**Effect of drag reducing polymer on pseudo slug flow regime using a concentration of 40 and 100 ppm.

**Figure 13.**(

**a**) Slug flow regime without DRP (V

_{sl}= 0.72 m/s, V

_{sg}= 0.41 m/s); (

**b**) Transition from Slug to Stratified Wavy flow regime using 100 ppm DRP.

**Figure 14.**(

**a**) Pseudo Slug flow without DRP (V

_{sl}= 1.03 m/s, V

_{sg}= 3.08 m/s); (

**b**) Transition from Pseudo Slug to Wavy Annular flow regime using 100 ppm.

**Figure 15.**Air-water (without DRP) flow pattern map using Unified [17] Model in a 1.01-cm pipe. (Dashed box is the present work flow conditions) Where:

**DB:**dispersed bubble,

**SL:**Slug,

**IN:**Intermittent,

**SS:**Smooth Stratified,

**SW:**Stratified Wavy,

**AN:**Annular.

**Figure 16.**Friction factor variation with the mixture Reynolds number times the square root of the superficial velocities ratio for different liquid superficial velocities (1.85, 2.45, 3.08, 3.7 and 4.32 m/s).

**Figure 18.**Dimensionless pressure drop ratio versus square root of the normalized superficial velocities (correlation is Equation (11)).

**Figure 19.**Comparison between measured dimensionless pressure drop ratio and the predicted by Equation (11).

Water Density | $1000\frac{\mathbf{kg}}{{{m}}^{3}}$ |
---|---|

Water viscosity | 0.000891 Pa s |

Ph | 7–8 |

Gas Density | $1.28\frac{\mathrm{kg}}{{\mathrm{m}}^{3}}$ |

Gas viscosity | 0.0000185 Pa·s |

Product Name | Coopolymer of Acrylamide and Quaternized Cationic Monomer | ||
---|---|---|---|

Product Type | Powder | ||

physical form | off-white granular solid | ||

cationic charge | Medium-high | ||

Molecular weight | very high | ||

specific gravity | 0.75 | ||

Bulk density | 749.66 kg/m^{3} | ||

Ph 1% solution | 4–6 | ||

Apparent Viscosity/(cP) 25 °C | |||

Concentration | 0.0025 | 0.005 | 0.01 |

Viscosity | 650 | 1200 | 3000 |

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**MDPI and ACS Style**

Alsarkhi, A.; Salah, M.
Multiphase Flow Production Enhancement Using Drag Reducing Polymers. *Polymers* **2023**, *15*, 1108.
https://doi.org/10.3390/polym15051108

**AMA Style**

Alsarkhi A, Salah M.
Multiphase Flow Production Enhancement Using Drag Reducing Polymers. *Polymers*. 2023; 15(5):1108.
https://doi.org/10.3390/polym15051108

**Chicago/Turabian Style**

Alsarkhi, Abdelsalam, and Mustafa Salah.
2023. "Multiphase Flow Production Enhancement Using Drag Reducing Polymers" *Polymers* 15, no. 5: 1108.
https://doi.org/10.3390/polym15051108