Study on the Separation Technology of HGS and Its Effect
147
(2) Inside the lower part of drill string
π
4
D
2
pi
∂(ρ d
ml c d
ml T p )
∂t
= π D pi h
d
po (T a − T pi ) − (Q m + Q hgs (1−ε))
∂(ρ d
ml c d
ml T p )
∂z
+S
d
cp
(2)
3.2.2 In the Annulus
The heat transfer process in annulus is mainly the convection heat transfer between the
mixed fluid of drilling fluid and HGS and the outer wall of drill string and the wall of
wellbore, meanwhile, including the heat generated by the friction of mixed fluid. Because
of the separation efficiency varies with different situation, the number of HGS in the
upper annulus and the lower annulus is different. If the position of the separator is taken
as the reference point, the density, viscosity and other thermos-physical parameters of
the mixed fluid in the upper and lower parts of the annulus will also vary, thus having
different influences on the temperature and pressure distribution in the upper and lower
parts of the annulus. The heat transfer models of other parts of wellbore such as casing,
cement ring, seawater and formation, initial conditions and boundary conditions can be
referred to [26].
(1) In the upper part of annulus
π
4
(D 2
w − D 2
po )
∂(ρ u
ml c u
ml T p )
∂t
= π D pi h u
po (T a − T pi ) − (Q m + Q hgs ε))
∂(ρ u
ml c u
ml T p )
∂z
+S u
cp
(3)
(2) In the lower part of annulus
π
4
(D 2
w − D 2
po )
∂(ρ d
ml c d
ml T p )
∂t
= π D pi h d
po (T a − T pi ) − (Q m + Q hgs (1 − ε))
∂(ρ d
ml c d
ml T p )
∂z
+S d
cp
(4)
3.2.3 Continuity Equation and Momentum Conservation Equation
(1) continuity equation
∂(Aρ m α ∗ + Aρ hgs (1 − α ∗ ))
∂t
+
∂(Aρ m α ∗ ν m + Aρ hgs (1 − α ∗ )ν hgs )
∂z
= q hgs (5)
(2) momentum conservation equation
∂(A(1 − α ∗ )ρ m ν m + Aα ∗ ρ hgs ν hgs )
∂t
= −
∂(AP)
∂z
−
∂(Aα ∗ ρ hgs ν 2
hgs + A(1 − α ∗ )ρ m ν 2
m )
∂z
− f m ρ m
ν 2
m
2
s m − f hgs ρ hgs
ν 2
hgs
2
s hgs
− (A(1 − α ∗ )ρ m g + Aα ∗ ρ hgs g) + Aq hgs ν hgs
(6)
3.3 Model Verification
In this paper, the wellbore temperature calculation model of transient heat and mass
transfer was derived considering the separation efficiency of HGS under the condition
of multi-gradient pressure control drilling. The data listed in the following Table 1, 2,
147
(2) Inside the lower part of drill string
π
4
D
2
pi
∂(ρ d
ml c d
ml T p )
∂t
= π D pi h
d
po (T a − T pi ) − (Q m + Q hgs (1−ε))
∂(ρ d
ml c d
ml T p )
∂z
+S
d
cp
(2)
3.2.2 In the Annulus
The heat transfer process in annulus is mainly the convection heat transfer between the
mixed fluid of drilling fluid and HGS and the outer wall of drill string and the wall of
wellbore, meanwhile, including the heat generated by the friction of mixed fluid. Because
of the separation efficiency varies with different situation, the number of HGS in the
upper annulus and the lower annulus is different. If the position of the separator is taken
as the reference point, the density, viscosity and other thermos-physical parameters of
the mixed fluid in the upper and lower parts of the annulus will also vary, thus having
different influences on the temperature and pressure distribution in the upper and lower
parts of the annulus. The heat transfer models of other parts of wellbore such as casing,
cement ring, seawater and formation, initial conditions and boundary conditions can be
referred to [26].
(1) In the upper part of annulus
π
4
(D 2
w − D 2
po )
∂(ρ u
ml c u
ml T p )
∂t
= π D pi h u
po (T a − T pi ) − (Q m + Q hgs ε))
∂(ρ u
ml c u
ml T p )
∂z
+S u
cp
(3)
(2) In the lower part of annulus
π
4
(D 2
w − D 2
po )
∂(ρ d
ml c d
ml T p )
∂t
= π D pi h d
po (T a − T pi ) − (Q m + Q hgs (1 − ε))
∂(ρ d
ml c d
ml T p )
∂z
+S d
cp
(4)
3.2.3 Continuity Equation and Momentum Conservation Equation
(1) continuity equation
∂(Aρ m α ∗ + Aρ hgs (1 − α ∗ ))
∂t
+
∂(Aρ m α ∗ ν m + Aρ hgs (1 − α ∗ )ν hgs )
∂z
= q hgs (5)
(2) momentum conservation equation
∂(A(1 − α ∗ )ρ m ν m + Aα ∗ ρ hgs ν hgs )
∂t
= −
∂(AP)
∂z
−
∂(Aα ∗ ρ hgs ν 2
hgs + A(1 − α ∗ )ρ m ν 2
m )
∂z
− f m ρ m
ν 2
m
2
s m − f hgs ρ hgs
ν 2
hgs
2
s hgs
− (A(1 − α ∗ )ρ m g + Aα ∗ ρ hgs g) + Aq hgs ν hgs
(6)
3.3 Model Verification
In this paper, the wellbore temperature calculation model of transient heat and mass
transfer was derived considering the separation efficiency of HGS under the condition
of multi-gradient pressure control drilling. The data listed in the following Table 1, 2,