Calculating an equivalent ID

For certain tools, for example mud motors and MWD tools, the internal diameter (ID) may not be known or applicable. However, for the Torque & Drag model, a Tool ID value is required.

Based on an (estimated) relative stiffness, an equivalent ID can be calculated using the Moment of Inertia (I) formula:

An example

To calculate the equivalent ID of a 9 1/2" mud motor that has a relative stiffness of 95% of that of a 9 1/2" x 3" drill collar, the following calculation is made:

1. Calculate the Moment of Inertia for the drill collar:

2. Assuming the mud motor has a 95% relative stiffness, calculate its Moment of Inertia:

3. From the Moment of Inertia formula, back-calculate the equivalent ID of the mud motor: