156
R. Zhang et al.
If laminar or turbulence?
Yes
No
Gauss-Seidel iteration
Yes
Input basic parameter including the well structure,
thermal physical properties, fluid properties et al.
Dividing grid and determining time step length
Assuming the separation efficiency, injection
velocity of hollow glass ball and pump
Calculating the pressure drop and heat source
term and convective heat transfer coefficient in the
different section of the drill string and annulus
Laminar flow
Setting the initial and boundary
Calculating the node temperature
T i,j at t moment
Calculating the node temperature
Ti,j(t+ t) at (t+ t)moment
t=t+ t
Output calculation results of wellbore
and formation temperature
Turbulence
,
,
(
)
i j
i j
T t
t T
ε
+ Δ −
≤
Fig. 26. Flowchart of transient wellbore temperature calculation
A i (α ∗ ρ hgs v 2
hgs ) n
i − A i−1 (α ∗ ρ hgs v 2
hgs ) n
i−1 + A i−1 ((1 − α ∗ )ρ m v 2
m ) n
i − A i−1 ((1 − α ∗ )ρ m v 2
m ) n
i−1
z
− (f m ρ m
v 2
m
2
s m ) n
i
− (f hgs ρ hgs
v 2
hgs
2
s hgs ) n
i − A i g((1 − α ∗ )(ρ m ) n
i + α ∗ (ρ hgs ) n
i ) + (A i q hgs v hgs ) n
i
(A-17)
To make A i−1 /A i = Φ ,so the above equation can be changed to (Fig. 26)
(P n
i − φP n
i−1 ) = −
((1 − α ∗ )ρ m ν m ) n
i − ((1 − α ∗ )ρ m ν m ) n−1
i
+ (α ∗ ρ hgs ν hgs ) n
i − (α ∗ ρ hgs ν hgs ) n−1
i
z
t
(α ∗ ρ hgs v 2
hgs ) n
i − φ(α ∗ ρ hgs v 2
hgs ) n
i−1 + ((1 − α ∗ )ρ m v 2
m ) n
i − φ((1 − α ∗ )ρ m v 2
m ) n
i−1
− [(f m ρ m
v 2
m
2
s m ) n
i
− (f hgs ρ hgs
v 2
hgs
2
s hgs ) n
i − g((1 − α ∗ )(ρ m ) n
i + α ∗ (ρ hgs ) n
i ) + (q hgs v hgs ) n
i ]z
(A-18)
Nomenclature
A i
the area of the annulus
c p
specific heat capacity of the drilling fluid inside the drilling string, J/(kg·°C)
c a
specific heat capacity of the drilling fluid in the annulus, J/(kg·°C)
D
diameter, mm
f
friction efficient