Torque and drag are the result of frictional forces caused by contact forces along the wellbore. The Normal Force (F_{n}) is a product of the gravity force (F_{g}) and inclination. Drag (or torque) is a product of Normal Force and Friction Factor (smoothness of contact surface).

In the context of the calculation model, tension is positive (> 0) and compression is negative (< 0). Thus, compression is negative tension.

Where:

F_{g} : Gravity force

F_{n} : Normal force or contact force

F_{a} : Axial force (available string weight)

I : Inclination

F_{n} = F_{g} . sin I

F_{a} = F_{g} . cos I

The string is divided into segments (finite elements) of a specific step length and cumulative tension (or torque) is calculated at the top of each segment as depicted below.

There are 5 operational modes that can be applied to the drill string, each having its own set of calculation parameters:

1.Pick up without rotation (PU),

2.Pick up with rotation (PUR),

3.Slack off without rotation (SO),

4.Slack off with rotation (SOR),

5.Rotating off bottom (ROB),

6.Rotary drilling (ROT),

7.Oriented drilling (ORT).

For a free hanging string both tension and torque are zero at the bottom of the drill string. For the rotary drilling (ROT) and oriented drilling (ORT) modes, the model starts with the weight on bit (WOB) and bit torque specified in the parameters input for the model. The specified BHA drag or BHA torque will be applied to the starting values for all modes.

Then tension increase for each element is calculated from the axial force (F_{a}) for that element (corrected for the drilling fluid buoyancy factor). In addition, the drag force (F_{d}) is calculated from the normal force and the friction factor:

Depending on the operational mode, the drag force is added to, or subtracted, from the tension increment. When pulling out of hole (i.e. upwards), the drag force factor increases the tension (F_{drag} > 0), when running in hole (i.e. downwards) the drag force decreases the tension (F_{drag} < 0).

Torque is calculated from the normal force, friction factor and diameter of the string element. As torque increases with an increasing diameter, torque OD can be specified for each drill string element in the parameters input. This OD will be used for the torque calculation. Torque OD can never be smaller than the tool OD (the program will automatically correct this). The most frequent use of torque OD is for stabilizers and drill pipe (tool joint OD).

In the stiff string model, additional normal force results from the force required to bend the pipe (F_{b}). This additional force is added to the normal force before calculating the drag force.

It depends on the dimensions of the pipe and the curvature of the hole (DLS) before the bending force becomes a factor of importance (i.e. selecting stiff string giving different results). For example:

5" Drill pipe -> 16° per 30m (100ft)

3 1/2" Drill pipe -> 22° per 30m (100ft)

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