Block and Drilling Line Calculation 

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.