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

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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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Authors and Affiliations

  1. Department of Petroleum Engineering, Universiti Teknologi Petronas, P.O. Box 32610, Seri Iskandar, Kuala Lumpur, Perak Darul Ridzuan, Malaysia

    Tarek A. Ganat & Belladonna Maulianda

  2. Department of Mechanical Engineering, International Islamic University, P.O. Box 10, 50728, Kuala Lumpur, Malaysia

    Meftah Hrairi

  3. Department of Reservoir Engineering, Petronas Carigali SDN BHD, P.O. Box 10, 500088, Kuala Lumpur, Malaysia

    Eghbal Motaei

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  1. Tarek A. Ganat
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Correspondence to Tarek A. Ganat.

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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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