Abstract
In multiphase flow engineering operations, the pipelines that convey viscous fluids are subjected to interior friction where the pipe wall meets the fluid. The friction on the inner surface of the pipe causes energy losses. The losses are exhibited as a progressive pressure drop over the length of the pipe that varies with the fluid flow rate. This study develops a computational method to estimate the pressure change at any flow condition of multiphase flow (oil, gas, and water) inside a vertical pipe by developing fluid mechanics equations and using empirical correlations. Darcy and Colebrook friction factor correlations were used to ratify the predicted frictional pressure drop by computational method outcomes. OLGA dynamic simulation software was used to validate the accuracy of the computational method results. A sensitivity analysis was performed to evaluate the performance of the developed computational method, by using different well flow rate, pipe size diameter, and fluid properties. The frictional pressure drop estimation by computational method has acceptable accuracy and it is located within the accepted average relative error band (±20%). The overall performance of the method is satisfactory when compared with other observations.
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Abbreviations
- API:
-
Oil specific gravity
- A:
-
Pipe cross-sectional area, sq ft
- Bg :
-
Gas formation vol. Factor, res. CF/SCF
- Bo :
-
Oil formation vol. Factor, res. BBL/STB
- Bob:
-
Oil formation volume at bubble point pressure, BBL/STB
- Cnt:
-
Count
- d:
-
Inside pipe diameter, ft
- dp/dz:
-
Total pressure gradient (friction pressure loss is considered).
- f :
-
Friction losses factor
- FVF:
-
Formation volume factor
- g:
-
Gravity
- HG :
-
Gas holdup
- HL :
-
Liquid holdup
- H1:
-
Bubble point pressure location depth before closing the wellhead valve, ft
- H2:
-
Bubble point pressure location depth after closing the wellhead valve, ft
- m t :
-
Mass flow rate, lb/day
- NLv:
-
Liquid velocity number
- Ngv:
-
Gas velocity number
- NL:
-
Liquid viscosity number
- Nd:
-
Pipe diameter number
- NCL:
-
Correction for viscosity number coefficient
- qo :
-
Oil flow rate STB/day
- qw :
-
Water flow rate STB/day
- qg :
-
Gas flow rate STB/day
- qL:
-
Liquid flow rate STB/day
- qm:
-
Measured flow rate STB/day
- QC:
-
Quality check
- P:
-
Average pressure, psia
- Pb:
-
Bubble point pressure, psia
- Pr:
-
Pseudo-critical pressure of gas mixture, psia
- Psc :
-
Pressure at standard conditions, psia
- PSD:
-
Pump setting depth
- SGG:
-
Specific gravity of gas
- STB:
-
Stock tank barrel
- rw:
-
Wellbore radius, ft
- R:
-
Solution gas-oil ratio, SCF/STB
- Rsb:
-
Solution gas at bubble point pressure, (CF/SCF)
- Re:
-
Reynolds number
- T:
-
Average temperature, °F
- t:
-
Shut-in time, min
- Tr:
-
Pseudo-critical temperature of gas mixture, psia
- Tsc :
-
Temperature at standard condition, °R
- Tr:
-
Reservoir temperature, °F
- VR :
-
Gas volume at down-hole conditions, ft3
- Vsc :
-
Gas volume at standard condition, ft3
- VSL :
-
Superficial liquid velocity, ft/sec
- VSg :
-
Superficial gas velocity, ft/sec
- Vm:
-
Mixture velocity, ft/sec
- WHPa :
-
Wellhead pressure after closing the well, psia
- WHPb :
-
Wellhead pressure before closing the well, psia
- WC:
-
Water cut (non-dimensional)
- WHT:
-
Wellhead temperature, °F
- W:
-
Water vapour density
- Z:
-
Gas compressibility factor
- ∆P:
-
Drawdown pressure, psia
- HL/ψ:
-
Holdup factor correlation
- γo :
-
Oil gravity
- γw :
-
Water gravity
- γg :
-
Gas gravity
- σ:
-
Surface Tension
- ∆H:
-
The differences between bubble point pressure location depth before and after closing the wellhead valve, ft
- ρo :
-
Oil density lbm/ cu ft
- ρg :
-
Gas density lbm/ cu ft
- ρw :
-
Water density lbm/ cu ft
- ρL :
-
Liquid density, Ib/cu ft
- ρm :
-
Mixture density, Ibm/ cu ft
- μo :
-
Oil viscosity, cp
- μg :
-
Gas viscosity, cp
- μL :
-
Liquid viscosity, cp
- gs:
-
Gas at standard condition
- h:
-
Hydrostatic
- L:
-
Liquid
- m:
-
Mixture of liquid and gas
- o:
-
Oil
- sc:
-
Standard condition
- w:
-
Water
- SG:
-
141.5/(131.5+°API) E –00
- bbl × 1.589873 E –0:
-
m3
- cp. × 1.0 E – 03:
-
Pa.s
- ft × 3.048 E – 01:
-
m
- °F (°F-32)/1.8 E – 00:
-
°C
- psia × 6.894757 E + 00:
-
KPa
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Acknowledgments
The authors would like to thank the production technology and reservoir engineering staff of Waha oil Company in Libya, for their generous assistance and for providing technical support, collaboration and words of encouragement on the success of this paper.
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Ganat, T.A., Hrairi, M., Maulianda, B. et al. Analytical model for predicting frictional pressure drop in upward vertical two-phase flowing wells. Heat Mass Transfer 55, 2137–2151 (2019). https://doi.org/10.1007/s00231-019-02565-6
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DOI: https://doi.org/10.1007/s00231-019-02565-6