This article will focus on block and drilling line calculations as block efficiency, drilling power input/output, etc. Additionally, there are some examples which will help you understand how the formulas work.

Block and drilling line efficiency formula is described below;

Power Output (Po) = F_{h} x V_{tb}

Power Input (Pi) = F_{f} x V_{f}

Where;

F_{h} is the hook load in lb.

V_{tb }is the velocity of the travelling block in feet per minute (fpm).

F_{f} is the fast line load in lb.

V_{f }is the velocity of the fast line in feet per minute (fpm).

The relationship between the fast line speed and the travelling block speed is listed below;

V_{f }= n x V_{tb}

Where;

n is number of lines strung between the travelling block and the crown block.

We can describe the hoisting efficiency into the following form.

**Example#1:** The maximum anticipated hook load is 500,000 and the travelling block velocity is 100 ft/minute. Hoisting efficiency is 85% and the drawworks efficiency is 75%. Based on the given information, what is the required horsepower for the drawworks for this situation?

Pi = 58,832,529 ft-lb/min

1 horsepower = 33,000 ft-lb/min

Pi = 58,832,529 ÷ 33,000 = 1,783 hp

We need to look at the drawworks. The drawworks output is the hoisting system output therefore we can figure out the horse power of the drawworks.

Pi = 2,377 hp

You need input horsepower of the drawworks of 2,377 hp.

**Example#2: **The string will be pulled out from 15,000 ft. The rig information is listed below;

Drilling lines: 12 lines

Hoisting efficiency: 70%

Drawworks: 1,200 hp

Drawworks efficiency: 80%

Expected hookload at 15,000 ft: 350,000 lb

What is the speed at which the first stand (90 ft stand) can be pulled out of hole based on the drawworks technical limit?

F_{f }= 41,667 lb

Fast line velocity (V_{f}) = Power Input (Pi) ÷ Fast line Load (F_{f})

Power Input (Pi) comes from the drawworks and we can determine it from the drawworks efficiency.

Power Input (Pi) = 0.8 x 1,200 = 960 hp

1 horsepower = 33,000 ft-lb/min

Power Input (Pi) = 960 x 33,000 = 31,680,000 ft-lb/min

Fast line velocity (V_{f}) = 31,680,000 ÷ 41,667 = 760 fpm

Travelling block velocity can be calculated by the following equation.

V_{f }= n x V_{tb}

V_{tb }= V_{f }÷ n

V_{tb }= 760÷ 12 = 63.3 fpm

The travelling block speed = 90 ÷ 63.3 = 1.42 minute.

The pulling speed for the first stand is 1.42 minutes.

**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.

There is a typing mistake. Instead of Power input it says Power Output.

Power Output (Pi) = Ff x Vf

Third line from the picture.

Rahul,

The typo mistake was corrected.

Regards,

Shyne

In Example 1 please check the block velocity. It should be 100 fpm according the solution.

Prashant,

Thanks for informing us. The typo error is fixed.

Regards,

Shyne.