Pressure and force relationship and applications

Pressure is force divided by cross section area (see an image below).

We normally use pressure in many units such as psi (pound per square inch), Pascal, kg/m3, etc.

In drilling operation, we mostly use circular area so area can be calculated by this formula;

Area = ¶ x (radius)² or ¶ x (diameter)²÷ 4

Where ¶= 22/7 = 3.143, so we can write a formula above in easy way

Area = 3.143 x (radius)² or 0.7857 x (diameter)²

Pressure = force ÷ (3.143 x (radius)²) or force ÷ (0.7857 x (diameter)²)

Let's try to apply pressure and force relationship in drilling operation. We plan to bullhead well and we still have drill string in the hole.

Drill string weight in the air = 45,000 lb
Mud weight in hole = 12.0 ppg
Bit size = 8.5"
Drill pipe size = 5″

What is the maximum pressure at surface you can apply before drilling string will be blow out due to bullheading pressure.

Buoyancy factor = (65.5 – 12.0) ÷ 65.5 = 0.817

Buoyed weight of drill string = 45,000 x 0.817 = 36,765 lb

Area = 0.7857 x (diameter)²= 0.7857 x (8.5)²= 56.77 square inch

Pressure = 36,765 lb ÷ 56.77 square inch= 647 psi.

In order to perform safe bullheading operation with drill string in hole, you need to apply bullheading pressure less than 647 psi on surface.

Please find Excel sheet for calculating force created by pressure.