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Understanding Torque and Drag

During drilling and completion operations in deviated wells, downhole assemblies experience forces that increase the tension and torque experienced at surface. In very deep or extended reach wells, these forces can exceed the capabilities of the pipe or prevent the string being run to bottom. For this reason, it is desirable to analyse these forces prior to; and during operations. Typically this analysis is performed by Torque and Drag Software.

What is Torque and Drag?

Drag is the frictional force acting against the movement of a downhole assembly in the axial direction.

Torque is produced by the frictional force acting against rotation.

These forces accumulate along the string to produce an overall force at surface. Frictional forces act against the direction of motion. This results in an increase in tension at surface due to drag when pulling pipe out of the hole and a decrease in tension when running in to hole.

What is Friction?

Friction is the force opposing motion between two surfaces sliding over one another. The friction experienced is proportional to the contact or normal force between the two surfaces. In the Torque and Drag model the frictional force is calculated as the normal or side force multiplied by the Friction Factor µ.

Frictional Force & Normal Force
Frictional Force & Normal Force

What is the Friction Factor?

The Friction Factor used in Torque & Dag is the number used to multiply the side force by to calculate the frictional force.

Friction in wellbore is caused by multiple physical processes and is dependent on the properties of the materials in contact, the fluids present, deviations in the wellbore, contact area, obstructions such as drilled cuttings and more.

In most cases the lubricating effect of the fluid is the most important factor in determining the friction factor to use. Typically, separate friction factors are used for Cased and Open hole.

Typical Friction Factors

Fluid Type

Cased Hole Friction Factor

Open Hole Friction Factor

























Combined rotating and axial friction

When pipe is run in hole whilst simultaneously rotating, the frictional forces are felt in both axial and rotational directions. The overall frictional force remains the same, but the fraction of the force experienced in each direction is proportional to the relative velocities in each direction.

From this we can see that increasing the rotating speed will reduce the frictional force in the axial direction. Since rotational velocities are typically much higher than axial velocities, rotation effectively reduces axial drag to negligible values.

What are the forces acting on a drill string?

The primary force acting a joint of pipe in a wellbore is the force due to gravity acting downwards.


A joint of pipe suspended in a wellbore containing drilling mud or other fluid will experience a buoyant force of the fluid acting against gravity. This will cause the pipe to appear to weigh less. This is the buoyed weight and is used to calculate side forces.

Side Force & Axial Force

In a perfectly vertical well there would be no lateral/side force and the buoyed weight acts in the axial direction.

Axial Force
Axial Force

If the well were inclined and pipe were to rest on the bottom of the hole, the buoyed weight can be split into axial and side force components. The side force component is termed Normal Force

Axial  &  Lateral Forces
Axial & Side Forces

At 90 degrees inclination the buoyed weight acts solely in the vertical direction and there is no force in the axial direction.

Lateral Forces
Side Forces

Capstan Effect

When pulling a drill string around a bend there will be increase the tension experienced. This is due to the Capstan effect.

The capstan effect explains the principle where the tension on one side a capstan is greater than the other due to the frictional force created by the change in angle or wrap, increased normal force and friction factor.

Capstan Force
Capstan Force

Location and relative magnitude of side forces in extended reach well
Location and relative magnitude of side forces in extended reach well


Buckling is the sudden change of the shape under compressive load due to stability failure. When a compressive load is applied to length of drill pipe it will buckle once the buckling limit is exceeded.

The first limit is the Sinusoidal limit when the pipe will take in the shape of a sinusoid Bending occurs is one plane.

Sinusoidal Buckling
Sinusoidal Buckling

Further compressive load will result in exceeding the Helical limit after which the pipe will take on the shape of a helix where bending occurs in two planes.

Helical Buckling
Helical Buckling

Once helical buckling has occurred, additional compressive load will be transferred to the sides of the wellbore in the form of additional side force which further increases drag. This will rapidly lead to lockup where the string cannot move any further into the hole.


We can create a plot of Tension or Axial Force against measured depth. A drill string with no additional forces acting upon it has an axial force or tension of zero at the bit. If we sum the axial force for each component from bit to surface, we can compute the tension.

Tension with no frictional forces
Tension with no frictional forces

If we were to move the string in an upwards direction, it would experience drag acting against the direction of motion. If we recalculate the tension to include the drag force, then we get a new tension curve that represents the tension condition when pulling out of hole.

Tension with frictional forces when pulling out of hole
Tension with frictional forces when pulling out of hole

Conversely if we were to move the string in a downwards direction, the drag force would act in the opposite direction and we can produce a curve that represents the tension when running in hole.

Tension with frictional forces when running in hole
Tension with frictional forces when running in hole

If the pipe were rotated whilst either moving up or down, the axial component of friction is reduced and as such the drag force is reduced to almost nothing.

Tension when rotating
Tension when rotating


If we sum up the torque experienced by each component due to the side force load from bit to surface, we can compute the torque in the string.

Tension & Torque
Tension & Torque

Differences in the side forces for each of the tension conditions results in different torque profiles.

Tension & Torque Limits

The Tension and Torque plots are useful to those designing downhole assemblies. To make use of the tension and torque values we need to know the tension and torque limits.

Tension limits

The string tension should remain between the compressive and tensile limits of the pipe. The compressive limit is usually defined by the buckling limit. This is the compressive load that will result in either sinusoidal or helical buckling of the pipe.

Tension with buckling and pipe yield limits
Tension with buckling and pipe yield limits

The tensile limit of the pipe is usually governed by the axial yield of the pipe body. The axial yield of the pipe can be reduced in the presence of torque or bending.

Torsional Limits

Typically, the limiting torque is governed by the make-up torque of the connections between pipe joints. Connections are made up to a specified torque that produces a desired stress in the connection threads. Exceeding this torque causes additional stress in the thread and can eventually cause damage or failure of the connection.

Torque with make-up torque and torsional yield limits
Torque with make-up torque and torsional yield limits

Hookload and Surface Torque

Typically, Torque & Drag results are presented in the form of Hookload and Surface Torque plots. These are produced by calculating the tension and torque at surface at various bit depths. To calculate the Hookload we must add the weight of the block/travelling assembly to the tension.

Hookload Limits

The upper limit for Hookload is usually defined by the maximum safe rig pull. This is usually a limit of the rig derrick or hoisting equipment. Another limiting factor maybe the tensile limit of the component at surface.

The lower limit is usually defined by the block weight. A Hookload lower than the block weight would indicate the string is in compression close to surface, which is usually undesirable due to low buckling limits in vertical hole.

Some torque and drag software also show a Buckling Hookload. This is the Hookload that would cause the string tension to drop below the helical buckling limit at some point in the wellbore.

Torque Limits

The limit for surface torque is usually defined by the maximum rig torque or the make-up torque of the surface component.

Other Forces

So far we have only accounted for frictional and gravitational forces on a drill string. However, there are more forces acting on the drill string that can be accounted for in our model.

Bit Torque

The additional reactive torque that occurs at the bit during drilling

Weight On Bit

The compressive load of the assembly at bit when drilling

Hydraulic/Viscous Forces

Pressure losses in the string and annulus result in additional hydraulic forces acting against the string. Depending upon the configuration of the string and wellbore this can lead to Hydraulic Lift or Weight On Bit

Piston Forces

Applied annular pressure at surface will result in an uplifting force being applied to the drill string

Sheave Friction

The frictional force experienced by the drilling line passing through the travelling block assembly. This results in lower or higher apparent measured hookloads when raising or lowering the pipe.

Friction Reduction Tools

Friction reduction tools can reduce the effective friction experienced by a given component. Running multiple tools on a drill string can reduce the overall frictional forces experienced by the drill string irrespective of the friction in the wellbore.

Sensitivity Plots

Since the friction experienced is due to multiple processes, it can change during drilling a well or hole section. For this reason, it is useful to calculate the tension or Hookload for a range of different friction factors.

When monitoring drilling operations, we often use a Sensitivity plot that shows Hookload or Torque calculated at various friction factors. This represents the overall friction experience by the drill string. By comparing the measured values with the predicted values, we can establish a trend of expected friction factor. We can use this trend to identify any deviation in the trend that might be caused by drilling problems such a poor hole cleaning or differential sticking.

Friction Factor Sensitivity Plot
Friction Factor Sensitivity Plot


If you would like to learn about these concepts and others in more detail along with how to solve issues like buckling using software, then contact us at to enquire about our training courses.


Looking for Torque & Drag software? Then check out S-Drill Torque and Drag Software and request a free 30 day trial.


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