Modeling tortuosity to directional surveys

Hi folks,

Here's a challenge for you all.

Looking at some of the surveys for recent wells, and particularly vertical wells, it seems possible that the BHAs are producing spiraled well-bores that we cannot readily identify with MWD survey QA/QC standard techniques.

By analyzing torque and Drag data of actual versus theoretical there are sections where the friction factors change for no apparent reason. I looked at ways to apply a factor to the well path to simulate the actual surveys and bring friction factors back into line.

The standard formula for applying tortuosity I believe is;

Ť = (((Summation between n and j=1)(DL^2)) - ((Summation between m and i=1)(DL^2))) / MDj - MDi

This, however gives a very conservative result.

If a sine wave is applied, using the magnitude (amplitude) and period (wavelength) specified, then the angle change would be; M sin (MD/p)2p

Where M is measured depth, p is the period and M the magnitude of the maximum variation of angle to be applied to the inclination and azimuth value.

The only problem I have so far it that if the inclination is modified below zero, the equations don´t work.

Similarly, the survey depth should not be an exact multiple of the period as then sin(MD/p)2p = 0

New inclination and azimuth are as follows;

Inc2 = a a1

Azi2 = Azi1 a1 crv (cross vertical correction).

I applied the equations above and made a rough Excel sheet to convert actual surveys to correct to include the sine wave.

Magically - the corrected surveys normalise the friction factors and bring the Torque and drag model into line.

The grey areas are as follows;

• Amplitude of the sine curve - can we simply apply stabilizer size minus tubular size (similar as the calculations for minimum effective hole diameter.
• Period of the sine curve - my initial suggestion is as per stabilizer spacing (points on maximum diameter and so likely to follow a straighter trajectory); added to this is the effect of stabilizer blade length.
• How to eliminate the effect on negative inclination (though I suspect this is a matter of applying Algebraic logic to the argument).
• When the MD of the survey is an exact multiple of the period - how to avoid. As per point above, I suspect this can be cured by creative nesting in the calculation. (sin(MD/p)2p then becomes zero).
  

Does anyone have any suggestions...???
Thanks
Hendo

5 Answer(s)

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