Directional Drilling Calculations

I got the question from my friend, Nien, asking me about directional drilling calculation and the question is shown below:

Wellplanner is planning to design a deep kick-off well with a build section to by pass a salt dome section. He intends to achieve a horizontal departure of 1500 ft at the with the TVD at the target point to be 10,000 ft. Calculate the measure depth and build up rate.

 

Solution:
First thing, I would like to draw a trigonometry diagram like this.

Please keep in mind that this diagram I draw with the Power Point so I will not show good proportion but it can give you good idea on how to solve this problem.

The formula for radius build (Rb) and length of hole (L) are listed below respectively;





Where;
Rb = radius of build in ft
q = build rate degree/ft
θ = angle build in radius

Data given:

Total TVD = 10,000 ft

TVD in build section = 10,000 – 7,000 = 3,000 ft

The horizontal departure = 1500 ft

From the diagram,

Rb = 1500 + Rb x cos (θ)

1500 = Rb x (1- cos (θ)) -- >Equation 1

Use the trigonometric relationship

3000 = Rb x sin (θ) -- >Equation 2

Equation 2 ÷ Equation 1 so you will get like this

-- >Equation 3


Square the Equation 3 so you will get

-- >Equation 4

Arrange the Equation 4 and you will get like this:

-- >Equation 5

According to the trigonometry relationship


Therefore you can change the Equation 5 like this:



-- >Equation 6

Use the polynomial relationship to arrange the equation as shown below:


You will have two following answers:

cos (θ) = 3/5 and cos (θ) = 1

Then you need to check which answer is correct.

cos (θ) = 1 is unreal because θ = 0 degree.

Therefore, cos (θ) = 3/5 is the right answer for this case.





From the Equation 1, you will be able to get Rb via the Equation 1

1500 = Rb x (1- cos (θ)) -- >Equation 1

1500 = Rb x (1- cos (53.13))

1500 = Rb x (1 – 3/5)

Rb = 3750 ft

You can determine the length of build section via the equation below;





Total MD from the rig to end of the build section = 7000 + 3477.35 = 10,477.35 ft

Determine build rate via this following equation:





We can answer in degree/100 ft by multiplied 100 therefore you will get the answer like this.

q = 1.65 degree/100 ft

Conclusion of this question:

The measure depth of the well = 10,477.35 ft


The build-up rate = q = 1.65 degree/100 ft

Reference books: Drilling Formulas blog