Simplified modeling of laminar helical flow in eccentric annulus with YPL fluid

ABSTRACT

Accurately predicting pressure gradient with inner pipe rotation in concentric or eccentric annuli can provide a theoretical foundation to evaluate equivalent mud weight for avoiding downhole problems caused by overlarge downhole pressure, such as: gas kick, lost circulation, even blowout. Nowadays, many studies were carried out on the basis of theoretical and experimental researches to investigate the laminar helical flow in concentric/eccentric annuli, however, to the best of our knowledge, no simplified model has been reported to predicting pressure gradient (PG) in eccentric annuli with inner pipe rotation for yield-power-law (YPL) fluids. In this paper, a simplified modeling for predicting PG of laminar helical flow in an eccentric annulus with YPL fluids has been established. In addition, the validation of simplified model has been investigated by comparing results with computational fluid dynamic (CFD) simulations, existing experimental measurements and numerical model. Predictions of the simplified model shown good agreement with CFD and experimental results within ±10% error bars for power-law and YPL fluids both in concentric and eccentric annuli.

KEYWORDS:

• Yield-power-law fluid
• helical laminar flow
• pressure gradient
• simplified model
• eccentric annulus

Nomenclature

af, bf	=	Annular parameters, dimensionless.
dp, rp,	=	Outer diameter/radius of inner pipe, m.
dh, rh,	=	Inner diameter/radius of outer pipe, m.
Dhy	=	Hydraulic diameter, Dh=dh-dp, m.
e	=	Offset distance for inner and outer pipe, m.
f	=	Fanning friction factor, dimensionless.
K,$K^{\prime }$	=	Fluid consistency index and equivalent consistency index, Pa∙sn.
Kd	=	Diameter/radius ratio, Kd=dh/dp=rh/rp, dimensionless.
n	=	Fluid behavior index, dimensionless.
m	=	Modified behavior index, dimensionless.
R	=	Pressure gradient ratio, R=(ΔP/ΔL)ecc/(ΔP/ΔL)con, dimensionless.
Re	=	Generalized Reynolds number, dimensionless.
v	=	Mean axial velocity, m/s.
Ta	=	Taylor number.

Greek Letters

ε	=	Dimensionless eccentricity, ε=2e/Dhy, dimensionless.
π	=	Plug zone thickness, m.
ρ	=	Fluid density, kg/m3.
γ	=	Shear rate, 1/s.
η	=	Apparent viscosity, Pa‧s.
τ0,${\tau }_0^{\prime }$	=	Fluid yield stress and equivalent yield stress, Pa.
ΔP/ΔL	=	Pressure gradient, Pa/m.
ω	=	Angular velocity for inner pipe rotation, rad/s.

Acronyms

CFD	=	Computational Fluid Dynamics
DRS	=	Dimensionless Radial Distance
NM	=	Numerical model
PAC	=	Polyanionic Cellulose
PG	=	Pressure Gradient
PL	=	Power-Law
RPM	=	Revolutions Per Minute
SM	=	Simplified Model
YPL	=	Yield-Power-Law
XG	=	Xanthan Gum

Additional information

Funding

This study is supported by the Open Fund (PLN201734) of the State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation (Southwest Petroleum University) and the Scientific Research Starting Project of SWPU [No. 2017QHZ001]and the National Natural Science Foundation of China[NO. 51474186, 51574202 and 51774247].