Drilling guides › Torque and drag basics: friction factors and hookloads
Torque and drag basics: friction factors and hookloads
In a vertical well, the hookload is simply the buoyed weight of the string. Once the hole is deviated, the pipe lies against the low side of the hole, and friction appears between the pipe and the wall. Friction adds to the load when pulling out, subtracts from it when running in, and resists rotation as torque. Torque and drag (T&D) analysis predicts those loads before a well is drilled, and compares them with what the rig sees while drilling, so that problems such as poor hole cleaning or a developing dogleg are spotted early.
The basic idea: normal force times friction factor
Any part of the string lying in an inclined hole pushes on the wall with a normal force. When the pipe slides, friction opposes the motion with a force equal to the normal force times a friction factor (μ). For a straight section, the buoyed weight of the pipe splits into two parts:
θ is the inclination and L the length of the section. The air weight should be the adjusted weight of the pipe including tool joints, from the pipe data sheet.
The friction factor is not a pure material property. It lumps together steel against casing or rock, the lubricity of the mud, cuttings beds, tool joint contact and other effects that the simple model does not describe. Values are therefore calibrated from offset wells or from the current well. As an order of magnitude, cased hole values are often quoted around 0.15 to 0.25 and open hole values around 0.2 to 0.4, with oil-based mud usually at the lower end. Use field-calibrated values for your area rather than these ranges.
Pick-up, slack-off and rotating loads
For a straight inclined section with a force Fbottom acting on its lower end (the load from the pipe below it), the force at the top of the section is:
When the pipe rotates, the friction acts around the pipe instead of along it, so the hookload approaches the free rotating weight and the friction shows up as torque instead. In practice, rotating while moving splits the friction between the two directions, which is why rotating while tripping reduces drag.
Notice the slack-off formula. If μ sin θ is greater than cos θ, the term becomes negative: the pipe in that section will not slide down under its own weight and must be pushed. That happens when tan θ exceeds 1 ÷ μ. With μ = 0.3, the critical angle is about 73°. Beyond it, weight must come from pipe higher in the well, which is why horizontal wells use HWDP in the vertical or build section to push the string.
The soft-string model
The model above is the simplest form of the soft-string model, which is the standard basis of most T&D software. It treats the string like a heavy cable: it follows the well path, has weight, tension and contact force, but no bending stiffness. The string is divided into short elements from the bit upwards, and the force at the top of each element is calculated from the force at its bottom, exactly as in the straight-section formulas.
The important difference in a curved section is that tension itself creates normal force. A string under tension pulled round a bend presses against the inside of the curve, like a rope over a pulley. So in a build or turn section, the drag depends on both the weight and the tension already in the pipe, and grows sharply with high tension and high dogleg severity. This is why a dogleg high in the well, where tension is greatest, often causes more drag and casing wear than the same dogleg deeper. In a straight section, by contrast, tension does not change the normal force. More advanced stiff-string models add the bending stiffness of the pipe and BHA, which matters in tight doglegs and for stiff assemblies.
Worked example 1: vertical well
10,000 ft of 5 in drill pipe, adjusted weight 22 lb/ft, mud 10.0 ppg, with a BHA whose buoyed weight is 30,000 lb.
In a truly vertical, straight hole the normal force is zero, so in theory pick-up, slack-off and rotating weights are all equal. Any difference seen at the rig comes from tight hole, doglegs, fluid drag or mechanical friction in the blocks, which is useful information in itself.
Worked example 2: a straight inclined section
A well has 3,000 ft of vertical hole, then (ignoring the short build section) a straight tangent of 5,000 ft at 45°. The string is the same 22 lb/ft pipe in 10.0 ppg mud, with no load at its lower end to keep the numbers simple. Friction factor 0.30, tool joint OD 6.625 in.
The drag of almost 20,000 lb either way is what the driller sees as the difference between rotating weight and pick-up or slack-off weight. Changing only the friction factor shows how sensitive the result is:
| μ | Pick-up (lb) | Slack-off (lb) | Torque (ft·lb) |
|---|---|---|---|
| 0.20 | 135,010 | 108,650 | 3,640 |
| 0.30 | 141,600 | 102,060 | 5,460 |
| 0.40 | 148,190 | 95,470 | 7,280 |
The rotating weight is the same in every case, about 121,830 lb. A real well would add the BHA, the build section with its tension-dependent drag, and the bit torque while drilling.
Broomstick plots
A broomstick plot shows predicted hookload against measured depth for pick-up, slack-off and rotating, each drawn for several friction factors. The lines spread out like the bristles of a broom as the well gets deeper and more deviated. During the job, the measured weights at connections are plotted on the same chart. If the readings follow one friction factor line, the hole is behaving as expected. If pick-up readings start to cross towards higher friction lines, or slack-off readings towards lower ones, something is changing: cuttings beds, swelling shale, a ledge or a developing key seat. The same idea is used for torque.
Broomstick plots are also used in planning, to check that the slack-off weight stays positive and above the buckling limits when running casing or liners, and that the pick-up load stays within the rig and pipe ratings with a margin for overpull.
Common mistakes
- Using air weight, or drill pipe body weight without tool joints.
- Reading pick-up and slack-off at different speeds or while the pumps are on and off. Take them the same way every time, ideally at the same speed with pumps off.
- Treating one friction factor as fixed for the whole well. Cased and open hole sections usually need different values.
- Forgetting the block weight, or zeroing the weight indicator inconsistently.
- Using planned surveys after the well is drilled. Rerun the model with actual surveys.
Metric notes
The formulas are unit-free. With buoyed weight in N/m (or daN/m), lengths in metres and radius in metres, forces come out in N and torque in N·m. 1 lb = 4.448 N and 1 ft·lb = 1.356 N·m.