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R. Zhang et al.
3.2 Derivation of Heat and Mass Transfer Model
During multi-gradient pressure control drilling, the mixed fluid of HGS and drilling
fluid is injected into the drill pipe firstly. After flowing through the upper drill string,
then the mixed fluid reaches the separator, most of the HGS will be separated into the
annulus. The remaining HGS carried by the drilling fluid will enter into the lower part
of drill string, then go through the drill bit into the lower annulus, and finally the mixed
fluid in the annulus will be returned to the ground. Therefore, there is mass transfer
process between HGS with the drilling fluid during this process. At the same time, the
mixed fluid of drilling fluid and HGS inside the drill string will generate convection heat
transfer with the inner wall of the drill string, and axial heat conduction will be generated
between the inner wall and the outer wall of the drill string. In annulus, the mixed fluid of
drilling fluid and HGS generate convection heat transfer between the outer wall of drill
string and wall of the wellbore. What’ more, only radial heat transfer between annulus
fluid and seawater and formation is considered (Fig. 15).
Fig. 15. Physical model of heat and mass transfer in multi-gradient pressure control drilling
3.2.1 Inside the Drill String
Because the mixed fluid of HGS and drilling fluid were injected into the drill pipe, most
of HGS entering the separator will be separated into the upper annulus, and a small
amount of the unseparated HGS will be transferred into the lower string with the drilling
fluid, and then back into the lower annulus.
(1) Inside the upper part of drill string
π
4
D
2
pi
∂(ρ u
ml c u
ml T p )
∂t
= π D pi h
u
po (T a − T pi ) − (Q m + Q hgs )
∂(ρ u
ml c u
ml T p )
∂z
+S
u
cp (1)
R. Zhang et al.
3.2 Derivation of Heat and Mass Transfer Model
During multi-gradient pressure control drilling, the mixed fluid of HGS and drilling
fluid is injected into the drill pipe firstly. After flowing through the upper drill string,
then the mixed fluid reaches the separator, most of the HGS will be separated into the
annulus. The remaining HGS carried by the drilling fluid will enter into the lower part
of drill string, then go through the drill bit into the lower annulus, and finally the mixed
fluid in the annulus will be returned to the ground. Therefore, there is mass transfer
process between HGS with the drilling fluid during this process. At the same time, the
mixed fluid of drilling fluid and HGS inside the drill string will generate convection heat
transfer with the inner wall of the drill string, and axial heat conduction will be generated
between the inner wall and the outer wall of the drill string. In annulus, the mixed fluid of
drilling fluid and HGS generate convection heat transfer between the outer wall of drill
string and wall of the wellbore. What’ more, only radial heat transfer between annulus
fluid and seawater and formation is considered (Fig. 15).
Fig. 15. Physical model of heat and mass transfer in multi-gradient pressure control drilling
3.2.1 Inside the Drill String
Because the mixed fluid of HGS and drilling fluid were injected into the drill pipe, most
of HGS entering the separator will be separated into the upper annulus, and a small
amount of the unseparated HGS will be transferred into the lower string with the drilling
fluid, and then back into the lower annulus.
(1) Inside the upper part of drill string
π
4
D
2
pi
∂(ρ u
ml c u
ml T p )
∂t
= π D pi h
u
po (T a − T pi ) − (Q m + Q hgs )
∂(ρ u
ml c u
ml T p )
∂z
+S
u
cp (1)