Research on Wellbore Temperature Field in Deep-Water CML
217
(3) Calculation formula of sea water temperature
T sea = a + b/(1 + e
(h+c)/d
)
(10)
Where, h is the depth of seawater, m; Coefficient a = 39.4, b = 37.1, c = 130.1, d
= 402.7.
(4) Drilling fluid density, viscosity calculation formula
f (ξ ) = ξ 0 exp(A T (T − T 0 ) + A p (p − p 0 ) + A TT (T − T 0 ) 2 + A pp (p − p 0 ) 2 + A Tp (T − T 0 )(p − p 0 ))
(11)
Where, ξ is the drilling fluid density or viscosity;A T A TT , A p , A pp and A Tp were
obtained by multiple regression.
2.2.4 Initial and Boundary Conditions
(1) Initial conditions
1) Set the initial temperature of the whole system as formation temperature
T i (z, 0) = T s + Gz
(i = p, a, f )
(12)
2) Drill string wellhead temperature is injection temperature
T p (0, t) = T in
(13)
(2) Boundary conditions
1) Assume that at the bottom hole, the temperature in the drill string is equal to that
in the annulus
T p (L, t) = T a (L, t)
(14)
2) Set the surface boundary as an adiabatic boundary
∂T
∂z
z = 0
= 0
(15)
3) Assuming that the formation at a certain distance from the wellbore is not
disturbed, is the original ground temperature
∂T
∂r
r→∞
= 0
(16)
2.3 Solution Method
The whole wellbore system is uniformly dispersed in the axial direction and in evenly
dispersed in the radial direction. In order to improve the accuracy and stability of the
computation, Crank-Nicolson full implicit scheme was used to discrete the governing
equations. The linear equations obtained by discretization are solved by Gauss-Seld
iterative method [8–16].
217
(3) Calculation formula of sea water temperature
T sea = a + b/(1 + e
(h+c)/d
)
(10)
Where, h is the depth of seawater, m; Coefficient a = 39.4, b = 37.1, c = 130.1, d
= 402.7.
(4) Drilling fluid density, viscosity calculation formula
f (ξ ) = ξ 0 exp(A T (T − T 0 ) + A p (p − p 0 ) + A TT (T − T 0 ) 2 + A pp (p − p 0 ) 2 + A Tp (T − T 0 )(p − p 0 ))
(11)
Where, ξ is the drilling fluid density or viscosity;A T A TT , A p , A pp and A Tp were
obtained by multiple regression.
2.2.4 Initial and Boundary Conditions
(1) Initial conditions
1) Set the initial temperature of the whole system as formation temperature
T i (z, 0) = T s + Gz
(i = p, a, f )
(12)
2) Drill string wellhead temperature is injection temperature
T p (0, t) = T in
(13)
(2) Boundary conditions
1) Assume that at the bottom hole, the temperature in the drill string is equal to that
in the annulus
T p (L, t) = T a (L, t)
(14)
2) Set the surface boundary as an adiabatic boundary
∂T
∂z
z = 0
= 0
(15)
3) Assuming that the formation at a certain distance from the wellbore is not
disturbed, is the original ground temperature
∂T
∂r
r→∞
= 0
(16)
2.3 Solution Method
The whole wellbore system is uniformly dispersed in the axial direction and in evenly
dispersed in the radial direction. In order to improve the accuracy and stability of the
computation, Crank-Nicolson full implicit scheme was used to discrete the governing
equations. The linear equations obtained by discretization are solved by Gauss-Seld
iterative method [8–16].