Page 102 - Practical Well Planning and Drilling Manual

Section 1 revised 11/00/bc 1/17/01 2:56 PM Page 78

[ ] Well Design
1.4.13

The radius of the dogleg is calculated by 5730 ÷ dogleg severity
(DLS) in degrees per hundred foot; so the radius of curvature of the
casing center Rc is 2292 ft, assuming that the casing is perfectly cen-
tralized in the hole. The radius of curvature at the outside of the bend
is Rc (2292 ft) plus radius of casing (B to B¢ ft) = 2292.401 ft, which
is where the greatest strain will be. The circumference of these two
curves is 2pr and is 14,401.06 ft and 14,403.58 ft respectively. Strain
therefore is stretch ÷ original length or

e = 2.52 ÷ 14,401.06 = 0.000175

As 2p is a constant, the formula can be simplified to:

e = rc × DLS
5730

where Rc is the radius of the casing in feet and DLS is dogleg sever-
ity in ˚/100 ft.

Stress s = Young’s Modulus E x strain e, or

s = 30,000,000 x 0.000175 = 5248 psi, in the outer fibers due
to bending only.

Referring to the calculation above, the total tensile force at the top
of the kickoff point when bumping the plug to 3000 psi is calculated
using TVDs not measured depths due to the supporting effect of the
wellbore (see Fig. 1–14):

Tension due to casing weight below KOP without buoyancy =
14,000 ft (TVD) x 47 = 658,000 lbs.

Use TVD and actual ID/OD to calculate internal weights and exter-
nal buoyancy forces:

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