204
K. Zhang et al.
where C μ = 0.0845. The term G k is defined as:
G k = −ρ g v i
g v
j
g
∂v
j
g
∂x i
(25)
The rate of strain (R ε ) in the ε equation is computed by:
R ε =
C μ ρ g η 3
1 − η/η 0
1 + βη 3
ε 2
k
(26)
where η 0 = 4.38, β = 0.012, and η is expressed as:
η =
k
ε
∂v i
g
∂x j
∂v i
g
∂x j
+
∂v
j
g
∂x i
1/2
(27)
2.6 Initial and Boundary Conditions
The physical model refers to a 3D horizontal eccentric annulus of 12 m in length as
shown schematically in Fig. 1. The diameters of the wellbore and drill pipe are devised
following the API standard, which are 244.5 and 127.0 mm, respectively. The drill
pipe eccentricity is 0.5 with a rotation speed of 120 rpm. The drill cuttings particle has
a diameter of 3 mm and density of 2600 kg/m 3 . The volume fraction of the injected
cuttings is constant with the value of 0.03. Nitrogen is used as the drilling fluid and its
velocity is a function of time, pulse amplitude, and pulse repetition frequency as follows:
Fig. 1. Schematic of horizontal annulus.
K. Zhang et al.
where C μ = 0.0845. The term G k is defined as:
G k = −ρ g v i
g v
j
g
∂v
j
g
∂x i
(25)
The rate of strain (R ε ) in the ε equation is computed by:
R ε =
C μ ρ g η 3
1 − η/η 0
1 + βη 3
ε 2
k
(26)
where η 0 = 4.38, β = 0.012, and η is expressed as:
η =
k
ε
∂v i
g
∂x j
∂v i
g
∂x j
+
∂v
j
g
∂x i
1/2
(27)
2.6 Initial and Boundary Conditions
The physical model refers to a 3D horizontal eccentric annulus of 12 m in length as
shown schematically in Fig. 1. The diameters of the wellbore and drill pipe are devised
following the API standard, which are 244.5 and 127.0 mm, respectively. The drill
pipe eccentricity is 0.5 with a rotation speed of 120 rpm. The drill cuttings particle has
a diameter of 3 mm and density of 2600 kg/m 3 . The volume fraction of the injected
cuttings is constant with the value of 0.03. Nitrogen is used as the drilling fluid and its
velocity is a function of time, pulse amplitude, and pulse repetition frequency as follows:
Fig. 1. Schematic of horizontal annulus.