Borehole Friction Factor
The borehole friction factor results from a complex interaction between the tubular string and the borehole. Its value depends primarily upon lithology. borehole surface configuration (washouts, keyseats. ledges, etc.). pipe surface configuration (centralizers, coating, etc.). casing, coupling size relative to the borehole size, and lubricity of drilling fluid and mud cake. Inasmuch as these parameters vary from well to well, it is not possible to determine any specific value of friction factor for a given well.
In a recent study, Maidla (1987) proposed the following mathematical model to estimate the borehole friction factor. /»,:
_ | Fh — FbUv ± Fvd |
h = Sl WMAUi ‘
where:
Fh — hook load, lbf.
Fbllb — vertical projected buoyant weight of pipe. lbf.
Fvi — hydrodynamic viscous drag. lbf.
Wd(L fb) — unit drag or rate of drag change, lb/ft.
I = length of pipe. ft.
I — measured depth, ft.
The unit drag force, И^(/,/4), is implicit in both depth, /, and friction factor, /(,, and, therefore, Eq. 4.65 cannot be solved explicitly.
The plus and minus signs in Eq. 4.65 relate to running in and pulling out situations, respectively. The term ‘hydrodynamic viscous drag’ represents the effect of surge and swab pressures associated with drilling fluid flow resulting from pipe movement in the borehole. Viscous drag can be quantified using the well known theory of viscous drag for Power-Law fluids in borehole (Fontenot and Clark, 1974; Burkhardt, 1961; and Bourgoyne et al.. 1985), which assumes the pipe is closed end and that the inertial forces and transient effects are negligible. Hence, the hydrodynamic viscous drag can be expressed in terms of viscous pressure gradient as:
For laminar flow: ^ /2 + 1/rt
dl 14.4 x 104 (dw — d0)1+n у 0.0208 J V ‘
For turbulent flow: — = —^ 1<XV /m— (4.67)
dl 21.1 (dw-d0) 1 ;
where:
К and n = Power-Law parameters.
7m = drilling fluid specific weight, lb/gal.
/ = flow frictional factor.
Vav — equivalent displacement velocity, ft/s.
The value for flow friction factor can be calculated by solving the Dodge and Metzner (1959) equation:
(/) = (W»,/«‘-"“’I(4.68)
where Л^е, the Reynolds number, is given by:
l + l/n j Equivalent displacement velocity can be calculated as follows:
(d0fdw)2
v~ = v> (4J0)
where:
|
TVD |
vp = velocity of the pipe, ft/s.
С с = clinging constant.
Clinging constant, Cc, which depends on the type of fluid flow and the ratio of pipe diameter to borehole diameter, can be expressed empirically as (Maidla, 1987):
For laminar flow:
|
(4.71) |
„ _ (d0/dw)2 — 2 (d0/dw)2 In dp/dy — I 2{l-(d0/dwY)lnd0/dw
|
For turbulent flow: (d0/dw)4 + d0/du |
|
(4.72) |
(d0/dw)2
(1 + d0/dw) (1 — (d0/dw)2)2J l — (da/dw)
|
Kickoff point |
5.000 ft |
|
Buildup rate (<7) |
2 °/100 ft |
|
End of buildup |
7.000 ft |
|
Inclination angle (r»i) |
40.0 degrees |
|
Dropoff point |
12.428 ft |
|
Dropoff rate (ab) |
1.5 7100 ft |
|
End of drop |
15.095 ft |
|
Inclination angle (o2) |
0.0 degrees |
|
Total measured depth |
20.638 ft |
Thus, from Eq. 4.65 it is evident that the borehole friction factor depends on drilling fluid properties, casing string composition, well profile, borehole geometry, hook loads (measured while running or pulling the casing), casing string velocity and the measured depth of the casing shoe. To determine the value of the borehole friction factor (BFF) one begins by assuming some initial value of the BFF and recurrently calculates the axial load from the casing shoe upward until the calculated hook load is determined. If the calculated hook load does not match the measured value, a new value of BFF is calculated and the procedure is repeated until the measured hook load is obtained.