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Analytical model for predicting frictional pressure drop in upward vertical two-phase flowing wells

  • Tarek A. GanatEmail author
  • Meftah Hrairi
  • Belladonna Maulianda
  • Eghbal Motaei
Original
  • 17 Downloads

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.

Nomenclature

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

mt

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

Greek symbols

∆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

Subscripts

gs

Gas at standard condition

h

Hydrostatic

L

Liquid

m

Mixture of liquid and gas

o

Oil

sc

Standard condition

w

Water

SI Metric conversion factors

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

Notes

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.

Compliance with ethical standards

I certify that no funding has been received for the conduct of this study and/or preparation of this manuscript.

Conflict of interest statement

On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Petroleum EngineeringUniversiti Teknologi PetronasKuala LumpurMalaysia
  2. 2.Department of Mechanical EngineeringInternational Islamic UniversityKuala LumpurMalaysia
  3. 3.Department of Reservoir EngineeringPetronas Carigali SDN BHDKuala LumpurMalaysia

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