Rig Derrick Load Calculation

The drilling line is reeved over a set of crow block and down to another set of sheaves known as travelling block. The hook connected to travelling block is used to suspend the drilling load. One end of drilling line is wound onto the drawworks and this line is called “Fast Line”. Other end of the drilling line is tied into an anchor point on the rig floor and this line is named as “Dead Line”. The drilling line is reeved around the blocks several times in order to meet required load.

According to the diagram above, we can use basic physic to determine derrick load.

Static Derrick Load

 Load Analysis Using Free Body Diagram on Travelling Block Under Static Condition

W = N x Tf

Tf = W/N

Where,

W – Hook load

N – Number of drilling lines in a travelling block

Tf = Td (Tf and Td are the same value because the same tension in the drilling line)

Load Analysis Using Free Body Diagram on Derrick Under Static Condition

Static derrick load equates to summation of fast line tension, dead line tension and hook load. We can describe into the following equation.

FD = Tf + W + Td

Where,

FD – Static derrick load

Tf – Fast line tension

Td – dead line tension

W – hookload

Note: Neglect a small effect of small angle of the fast line and the dead line.

FD = W/N + W + W/N

FD = (N+2) x W ÷ N

 Dynamic Derrick Load

Under dynamic condition, friction in sheave bearings and block lines make the fast tension higher than the dead line tension. It means that the fast line tension will increase under a dynamic condition; however, the dead line tension will remain the same because it is still in static condition.

The fast line tension under the dynamic environments can be described as the equation below;

Tf = W ÷ ( E x N )

Where,

Tf – The fast line tension.

W – Block weight

N – Number of lines

E – Efficiency

 Table#1 – Efficiency Factor for Wire Rope Reeving for Multiple Sheave Blocks (API RP9B)

Derrick load under dynamic condition is also equal to summation of hook load, dynamic fast line tension and dead line tension as described in the equation below

FD = Tf + W + Td

Exercise for Derrick Load Calculation

Buoyed weight of the drill string is 260,000 lb which will be pulled out of hole. Weight of travelling block and hook is 40,000 lb. The rig has 10 lines strung in crown block and travelling block.

Solution:

Efficiency of 10 lines = 0.811

Total hook load = 260,000 + 40,000 = 300,000 lb

The fast line tension:

Tt = 300,000 ÷ (10 x 0.811)

Tt = 36,991 lb

The dead line tension:

Td = 300,000 ÷ 10

Td = 30,000 lb

Derrick load under the dynamic condition:

FD = Tf + W + Td

FD = 36,991 + 30,000 + 300,000

FD = 366,991 lb

Derrick load in dynamic condition equates to 366,991 lb

Ref books: Lapeyrouse, N.J., 2002. Formulas and calculations for drilling, production and workover, Boston: Gulf Professional publishing.

Bourgoyne, A.J.T., Chenevert , M.E. & Millheim, K.K., 1986. SPE Textbook Series, Volume 2: Applied Drilling Engineering, Society of Petroleum Engineers.

Mitchell, R.F., Miska, S. & Aadny, B.S., 2011. Fundamentals of drilling engineering, Richardson, TX: Society of Petroleum Engineers.