Numerical simulation on the erosion characteristics of dense particles in the annular channel of downhole fracture pipe

ABSTRACT

An extra-dense volume concentration (more than 30% vol.) of two-phase flow between liquid and solid is always encountered in the narrow annular channel in the hydraulic sand fracturing technology of the oil-gas exploitation industry. Here we investigated the characteristics of erosion in the annular channel during fracturing based on the DDPM (Dense Discrete Phase Model) and a predictive model for the erosion rate of the annular channel is developed by considering flow velocity, mass flow rate, and particle size. Its indicate that as flow velocity increases, the maximum rate of erosion rises exponentially. A larger mass flow rate may lead to a decrease in the erosion rate, with a critical mass flow rate of 5.23 kg/s identified. Additionally, the erosion rate initially decreases and then increases with an increase in particle size, with a critical particle size of 0.7 mm also observed. Finally, a predicting model for the maximum erosion is proposed, the results of agrees well with available numerical simulation values. It is expected that all findings in this study can provide some guidance for predicting the erosion and operating parameters of the pipeline in the process of fracturing technology.

KEYWORDS:

• Erosion and wear
• DDPM model
• two-phase flow of liquid and solid
• numerical simulation
• regression analysis

Nomenclature

DDPM	=	Dense Discrete Phase Model
DEM	=	Discrete Element Method
ODEM	=	one-dimensional erosion model
${\rho }_f$	=	density of the continuous phase, kg/m3
vf	=	constant phase velocity, m/s
${\mu }_f$	=	viscosity of the continuous phase, Pa$\cdot$s
Fex	=	particle’s additional source term, N
k	=	the kinetic energy of turbulent motion, J
ε	=	the rate of turbulent dissipation, J/s
Gk	=	the kinetic energy, J
Gb	=	the turbulent kinetic energy, J
Yk	=	the varying kinetic energy, J
pp	=	the solid pressure, Pa
$\overline{\stackrel{‾}{I}}$	=	the unit stress tensor
${\alpha }_p$	=	the percentage of the particle volume
μp	=	the shear viscosity, Pa$\cdot$s
λp	=	the bulk viscosity, Pa$\cdot$s
vp	=	the solid phase’s average velocity vector
Vp	=	the particle’s velocity, m/s
f(θ)	=	the impact angle function
et	=	the tangential bounce recovery factor
en	=	the bounce recovery factor for normal bounces

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Bo Ren

Bo Ren is a PhD student at the State Key Laboratory of Multiphase Flow in Power Engineering at Xi’an Jiaotong University, mainly engaged in numerical simulation of multiphase flow and heat transfer.

Yueshe Wang

Yueshe Wang is a professor at the State Key Laboratory of Multiphase Flow in Power Engineering at Xi’an Jiaotong University. His main research areas include: study on flow and heat transfer characteristics of gas-liquid two-phase flow, and high-efficiency thermal utilization of new energy and solar energy.

Xiaoqi Ma

Xiaoqi Ma is a PhD student at the State Key Laboratory of Multiphase Flow in Power Engineering at Xi’an Jiaotong University, mainly engaged in research on heat and mass transfer in gas-liquid two-phase flow.

Guohu Tong

Guohu Tong is a Master’s student at the State Key Laboratory of Multiphase Flow in Power Engineering at Xi’an Jiaotong University, mainly engaged in research on corrosion and protection of long-distance transportation pipelines.