### Prediction of Optimum Length to Diameter Ratio for Two-Phase Fluid Flow Development in Vertical Pipes

#### Abstract

We investigate, via numerical simulation technique, the effect of length-to-diameter ratio on transient air-water two-phase flow in vertically upward cylindrical pipe geometry for parameterisation of the pilot scale laboratory multiphase flow rig. Variables such as axial velocity along the leading Taylor bubble, Taylor bubble length and Taylor bubble velocity are considered. A hydrodynamic entrance length required to establish a fully developed two phase flow was critically evaluated. Aperiodic behaviour on time and space dictates the complexity of continuous and unstable gas liquid flow. The porous injection configuration produced small bubble sizes compared to a single gas injection configuration even at higher gas injection rates.

Average axial velocity of the leading Taylor bubble of 0.411, 0.424 and 0.451 m/s were obtained for *L*/*D* ratios of 16.6, 83.3 and 166.7 respectively. The eccentricity of the axial velocity on the leading Taylor bubble stream and on its nose is perceived from *L*/*D* ratio of 166.7. We obtained a power law function for the radial component of the axial velocity profile in the liquid film ahead of the leading Taylor bubble as , with exponent *n*=16 for *L*/*D* =16.7, *n*=8 for *L*/*D*=83.3 and *n*=6 for *L*/*D* =166.7. Despite the decrease in the exponent as *L*/*D* ratio increases, a fully parabolic profile of the axial velocity on the liquid phase ahead of the Taylor bubble is not achieved. This, suggests that further studies on higher *L*/*D* ratios should be conducted.

#### Full Text:

PDF#### References

Abdulkadir, M., Hernandez-Perez, V., Lo, S., Lowndes, I. S., & Azzopardi, B. J. (2015). Comparison of experimental and Computational Fluid Dynamics (CFD) studies of slug flow in a vertical riser. *Experimental Thermal and Fluid Science, 68, *468-483.

Abdulkadir, M., Hernandez-Perez, V., Abdulkareem, L., Lowndes, I. S., & Azzopardi, B. J. (2010). Characteristics of slug flow in a vertical riser*. **Society of Petroleum Engineers*. doi:10.2118/140681-MS

Akanji, L., & Matthai, S. (2010). Finite element-based characterization of pore-scale geometry and its impact on fluid flow. *Transport in Porous Media, 81*(2), 241-259.

Ansari, M. R., & Azadi, R. (2016). Effect of diameter and axial location on upward gas–liquid two-phase flow patterns in intermediate-scale vertical tubes. *Annals of Nuclear Energy, 94, *530-540.

Araújo, J. D. P., Miranda, J. M., & Campos, J. B. L. M. (2013). Simulation of slug flow systems under laminar regime: Hydrodynamics with individual and a pair of consecutive Taylor bubbles. *Journal of Petroleum Science and Engineering, 111,* 1-14.

Brackbill, J. U., Kothe, D. B., & Zemach, C. (1992). A continuum method for modellling surface tension. *Journal of Computational Physics, 100, *335-354.

Brennen, C. E. (2005). *Fundamentals of multiphase flow*. Cambridge University Press.

Brill, J. P. (2010). Modeling multiphase flow in pipes. *Society of Petroleum Engineers.* doi:10.2118/0210-016-TWA. 2: SPE-0210-016-TWA.

Brown, R. (1965). The mechanics of large gas bubbles in tubes: I. Bubble velocities in stagnant liquids. *The Canadian Journal of Chemical Engineering, 43*(5), 217-223.

Collins, R., De Moraes, F., Davidson, J., & Harrison, D. (1978). The motion of a large gas bubble rising through liquid flowing in a tube. *Journal of Fluid Mechanics, 89*(03), 497-514.

Da Riva, E., & Del Col, D. (2009). Numerical simulation of churn flow in a vertical pipe. *Chemical Engineering Science, 64*(17), 3753-3765.

Davidson, J., Nicklin, D., & Wilkes, J. (1962). Two Phase Flow in Vertical Tubes. *Trans.Inst. Chem. Engr, *40-61.

Davies, R., & Taylor, G. (1950). The mechanics of large bubbles rising through extended liquids and through liquids in tubes. *Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, *375-390.

Fluent, A. (2006). *Fluent 6.3 documentation*. Lebanon, NH: Fluent Inc.

Frooqnia, A. (2014). *Numerical simulation and interpretation of borehole fluid-production measurement *(PhD thesis). The University of Texas at Austin.

Griffith, P., & Wallis, G. B. (1961). Two-phase slug flow. *Journal of Heat Transfer, 83*(3), 307-318.

Hirt, C. W., & Nichols, B. D. (1981). Volume of fluid (vof) mehtod for dynamics of free surfaces. *Journal of Computational Physics, 39, *201-225.

Icardi, M., Ronco, G., Marchisio, D. L., & Labois, M. (2014). Efficient simulation of gas–liquid pipe flows using a generalized population balance equation coupled with the algebraic slip model. *Applied Mathematical Modelling, 38*(17-18), 4277-4290.

Imada, F. H., Saltara, F., & Balino, J. F. (2013). Numerical study of the churn-slug transition dynamics in vertical upward air-water flows. In C. A. Brebbia & P. Vorobieff (Eds.), *Computational methods in multiphase flow VII* (VII ed., pp.101-114). Ashurst Lodge, UK: WIT Press.

Johansen, S. T., Mo, S., Meese, E., Oliveira, J. E. S., Reyes, J. F. R., & Carneiro, J. N. E. (2015). *CFD simulations of multiphase flows containing large scale interfaces and dispersed phases with selected production technology applications.* Offshore Technology Conference. doi:10.4043/26303-MS

Kaji, R., & Azzopardi, B. J. (2010). The effect of pipe diameter on the structure of gas/liquid flow in vertical pipes. *International Journal of Multiphase Flow, 36*(4), 303-313.

Kaji, R., Azzopardi, B. J., & Lucas, D. (2009). Investigation of flow development of co-current gas–liquid vertical slug flow. *International Journal of Multiphase Flow*, 35(4), 335-348.

Launder, B. E., & Spalding, D. B. (1974). The numerical computation of turbulent flows. *Computer Methods in Applied Mechanics and Engineering, 3*(2).

Levy, S. (1999).* Two-phase flow in complex systems.* John Wiley & Sons.

Liu, H., Vandu, C. O., & Krishna, R. (2005). Hydrodynamics of Taylor flow in vertical capillaries: Flow regimes, bubble rise velocity, liquid slug length, and pressure drop. *Industrial & Engineering Chemistry Research, 44*(14), 4884-4897.

Mayor, T. S., Ferreira, V., Pinto, A. M. F. R., & Campos, J. B. L. M. (2008). Hydrodynamics of gas–liquid slug flow along vertical pipes in turbulent regime–An experimental study. *International Journal of Heat and Fluid Flow, 29*(4), 1039-1053.

Mayor, T. S., Pinto, A. M. F. R., & Campos, J. B. L. M. (2007). Hydrodynamics of gas–liquid slug flow along vertical pipes in turbulent regime: A simulation study. *Chemical Engineering Research and Design, 85*(11), 1497-1513.

Mayor, T. S., Pinto, A. M. F. R., & Campos, J. B. L. M. (2008). On the gas expansion and gas hold-up in vertical slugging columns—A simulation study. *Chemical Engineering and Processing: Process Intensification, 47*(5), 799-815.

Morgado, A. O., Miranda, J. M., Araújo, J. D. P., & Campos, J. B. L. M. (2016). Review on vertical gas–liquid slug flow. *International Journal of Multiphase Flow, 85, *348-368.

Morgado, A. O., Miranda, J. M., Araújo, J. D. P., & Campos, J. B. L. M. (2016). Review on vertical gas–liquid slug flow. *International Journal of Multiphase Flow, *85348-368.

Patankar, S. V., & Spalding, D. B. (1972). A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. *International Journal of Heat and Mass Transfer, 15*(10), 1787-1806.

Polonsky, S., Shemer, L., & Barnea, D. (1999). The relation between the Taylor bubble motion and the velocity field ahead of it. *International Journal of Multiphase Flow, 25*(6-7), 957-975.

Rosa, E. S., & Souza, M. A. S. F. (2015). Spatial void fraction measurement in an upward gas–liquid flow on the slug regime. *Flow Measurement and Instrumentation, 46, *139-154.

Saffari, H., Moosavi, R., Nouri, N. M., & Lin, C. (2014). Prediction of hydrodynamic entrance length for single and two-phase flow in helical coils. *Chemical Engineering and Processing: Process Intensification, *869-21.

Santos, L. M. T., & Coelho Pinheiro, M. N. (2014). Flow around individual Taylor bubbles rising in a vertical column with water: Effect of gas expansion. *International Journal of Multiphase Flow, *6339-6351.

Sasaki, S., Hayashi, K., & Tomiyama, A. (2016). Effects of liquid height on gas holdup in air–water bubble column. *Experimental Thermal and Fluid Science, 72, *67-74.

Shao, N., Salman, W., Gavriilidis, A., & Angeli, P. (2008). CFD simulations of the effect of inlet conditions on Taylor flow formation. *International Journal of Heat and Fluid Flow, 29* (6), 1603-1611.

Sharaf, S., van der Meulen, G.P., Agunlejika, E. O., & Azzopardi, B. J. (2016). Structures in gas–liquid churn flow in a large diameter vertical pipe. *International Journal of Multiphase Flow, 78, *88-103.

Shen, X., Matsui, R., Mishima, K., & Nakamura, H. (2010). Distribution parameter and drift velocity for two-phase flow in a large diameter pipe. *Nuclear Engineering and Design, 240*(12), 3991-4000.

Szalinski, L., Abdulkareem, L. A., Da Silva, M. J., Thiele, S., Beyer, M., Lucas, D.,…Azzopardi, B. J. (2010). Comparative study of gas–oil and gas–water two-phase flow in a vertical pipe. *Chemical Engineering Science, 65*(12), 3836-3848.

Taitel, Y., Bornea, D., & Dukler, A. (1980). Modelling flow pattern transitions for steady upward gas–liquid flow in vertical tubes. *AIChE Journal, 26*(3), 345-354.

Versteeg, H. K., & Malalasekera, W. (2007). *An introduction to computational fluid dynamics: The finite volume method. *Pearson Education.

Wan, R. G., Liu, Y., & Wang, J. (2007). A multiphase flow approach to modeling sand production using finite elements. *Petroleum Society of Canada*. doi:10.2118/07-04-04.

Wang, Y., Yan, C., Cao, X., Sun, L., Yan, C., & Tian, Q. (2014). Hydrodynamics of slug flow in a vertical narrow rectangular channel under laminar flow condition. *Annals of Nuclear Energy, *73465-477.

Wang, Y., Yan, C., Sun, L., & Yan, C. (2014). Characteristics of slug flow in a vertical narrow rectangular channel. *Experimental Thermal and Fluid Science, 53,* 1-16.

Xia, G., Cui, Z., Liu, Q., Zhou, F., & Hu, M. (2009). A model for liquid slug length distribution in vertical gas-liquid slug flow. *Journal of Hydrodynamics, Ser. B, 21*(4), 491-498.

Yakhot, V., & Orszag, S. A. (1986). Renormalization group analysis of turbulence.i. basici theory. *Journal of Scientific Computer, 1*(1), 1-35

Zabaras, G. J. (2000). Prediction of slug frequency for gas/liquid flows. *Society of Petroleum Engineers,* J2: SPE-65093-PA.

Zheng, D., He, X., & Che, D. (2007). CFD simulations of hydrodynamic characteristics in a gas–liquid vertical upward slug flow.* International Journal of Heat and Mass Transfer, 50*(21), 4151-4165.

DOI: http://dx.doi.org/10.3968/9886

### Refbacks

- There are currently no refbacks.

Copyright (c) 2018 Joao Fernando Chidamoio

This work is licensed under a Creative Commons Attribution 4.0 International License.

**Reminder**

- How to do online submission to another Journal?
- If you have already registered in Journal A, then how can you submit another article to Journal B? It takes two steps to make it happen:

**1. Register yourself in Journal B as an Author**

- Find the journal you want to submit to in CATEGORIES, click on “VIEW JOURNAL”, “Online Submissions”, “GO TO LOGIN” and “Edit My Profile”. Check “Author” on the “Edit Profile” page, then “Save”.

**2. Submission**

- Go to “User Home”, and click on “Author” under the name of Journal B. You may start a New Submission by clicking on “CLICK HERE”.

We only use three mailboxes as follows to deal with issues about paper acceptance, payment and submission of electronic versions of our journals to databases:

caooc@hotmail.com; aped@cscanada.net; aped@cscanada.org

Articles published in **Advances in Petroleum Exploration and Development*** *are licensed under Creative Commons Attribution 4.0 (CC-BY).

* ADVANCES IN PETROLEUM EXPLORATION AND DEVELOPMENT* Editorial Office

**Address**:1055 Rue Lucien-L'Allier, Unit #772, Montreal, QC H3G 3C4, Canada.

**Telephone**: 1-514-558 6138**Website**: Http://www.cscanada.net

Http://www.cscanada.org**E-mail**:office@cscanada.net; office@cscanada.org

Copyright © 2010 **Canadian Research & Development Centre of Sciences and Cultures**