Directional Drilling Survey Formulas

Survey calculation methods :

1) Average angle method

2) Tangential method

3) Balanced tangential method (rarely used)

4) Radius of curvature method; and 

5) Minimum curvature methods.

For any Survey calculations. first, please see following Diagram.

Lets understand this.

First start with line (1) to (2). this line is making inclination angle (α) with true vertical depth.

so, here

Sin(α) = X/MD,

So, X = MD*Sin(α)

Cos(α) = TVD/MD,

So, TVD = MD*Cos(α)

Now, look at line (1) to (3). this line is making Azimuth angle (β) with North direction.

so, here

Sin(β) = E/X, (and X = MD*Sin(α))

so, E = MD*Sin(α)*Sin(β)

Cos(β) = N/X , (and X = MD*Sin(α))

SO, N = MD*Sin(α)*Cos(β).

So, We have,

TVD = MD*Cos(α),

E = MD*Sin(α)*Sin(β),

N = MD*Sin(α)*Cos(β).

This is Tangential method of calculation. 

For all other methods, we use two inclination and azimuth angles. (one iis at upper point and one is at lower point). 

1) Average angle method:

we average angles.

α = (α1 + α2)/2

β = (β1 + β2)/2

2) Balanced Tangential:

We average sin or cosine terms.

TVD = MD*[Cos(α1) + Cos(α2)]/2,

E = MD*[Sin(α1)*Sin(β1) + Sin(α2)*Sin(β2)]/2,

N = MD*[Sin(α1)*Cos(β1) + Sin(α2)*Cos(β2)]/2.

3) Minimum Curvature:

We multiply RF (RF = Ratio Factor) in balanced tangential method.

TVD = RF*MD*[Cos(α1) + Cos(α2)]/2,

E = RF*MD*[Sin(α1)*Sin(β1) + Sin(α2)*Sin(β2)]/2,

N = RF*MD*[Sin(α1)*Cos(β1) + Sin(α2)*Cos(β2)]/2.

 and,

RF = tan(DL/2)/((DL/2))

DL = Dog Leg angle.

where,

Cos(DL) = Cos(α2 - α1) - Sin(α1)*Sin(α2)*[1 - Cos(β2 - β1)].

To watch in video, click here.

  

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