METHOD FOR ESTIMATING THE PROBABILITY OF COLLISION BETWEEN WELLS

• US 20100169018A1
• Filed: 06/29/2009
• Published: 07/01/2010
• Est. Priority Date: 07/03/2008
• Status: Active Grant

• Current Assignee: Baker Hughes Incorporated (Baker Hughes Company)
• Original Assignee: Baker Hughes Incorporated (Baker Hughes Company)
• Inventors: Brooks, Andrew G.
• Granted Patent: US 8,447,522 B2
• Time in Patent Office: Days
• US Class Current: 702/9
• CPC Class Codes: E21B 47/022 of the borehole, e.g. using geomagnetism
• CPC Class Codes: E21B 47/09 Locating or determining the position of objects in boreholes or wells , e.g. the position of an extending arm; Identifying the free or blocked portions of pipes

Abstract

A method for drilling a well, the method including: identifying another well proximate to the well being drilled; collecting spatial information for at least a portion of the another well and the well being drilled; estimating a trajectory for at least a portion of the well being drilled and the another well; estimating an uncertainty in spatial information for each trajectory; estimating a probability of a collision with the another well during the drilling of the well by integrating a probability density function using the uncertainties and the trajectories; and performing the drilling in a manner that limits the probability of collision. A system and another method are provided.

Claims

1. A method for drilling a well, the method comprising:

identifying another well proximate to the well being drilled;

collecting spatial information for at least a portion of the another well and the well being drilled;

estimating a trajectory for at least a portion of the well being drilled and the another well;

estimating an uncertainty in spatial information for each trajectory;

estimating a probability of a collision with the another well during the drilling of the well by integrating a probability density function using the uncertainties and the trajectories; and

performing the drilling in a manner that limits the probability of collision.

2. The method as in claim 1, wherein the location information comprises a radius of the wellbore for each of the another well and the well being drilled.

3. The method as in claim 2, further comprising summing the radii, and assigning the summed value as the radius of the wellbore for one of the another well and the well being drilled.

4. The method as in claim 3, further comprising reducing the radius of the wellbore of the unassigned well to zero.

5. The method as in claim 1, wherein the probability density function comprises a Guassian distribution function.

6. The method as in claim 1, wherein the spatial information is expressed in at least one of a Mahalanobis space and a Cartesian coordinate system.

7. The method as in claim 1, wherein a result of the integrating represents a space mapped out by the representation of the relative position of the object well with respect to an origin point which progresses along the interval of interest in the reference well.

8. The method as in claim 1, wherein dimensions bounding a volume of the integrating are related to at least one of:

a locus of an interval of interest along at least one of the wells, a reversed path along the wellbore of at least one of the wells, and a sum of wellbore diameters for each of the wells.

9. The method as in claim 8, wherein the locus of the interval of interest is in a region of significant risk.

10. The method as in claim 1, wherein the integrating is performed using a Mahalanobis space.

11. The method as in claim 1, further comprising a transformation to a Mahalanobis space.

12. The method as in claim 1, wherein integration can be performed by breaking the volume of interest into volume elements, and summing the probability density function values corresponding to the centroids of those volume elements, weighted by volume of each volume element.

13. The method as in claim 1, wherein if one of the wells is straight within a region of significant risk, the integrating is performed for a two dimensional space normal to the other well.

14. The method as in claim 1, wherein integrating comprises numerically integrating.

15. A system for drilling a well, the system comprising:

a drilling apparatus for drilling the well, the apparatus adapted for receiving directional information from a processor and adjusting drilling according to the directional information;

the processor equipped for implementing instructions for avoiding collision during drilling of a well by performing a method comprising;

identifying another well proximate to the well being drilled;

collecting spatial information for at least a portion of the another well and the well being drilled;

estimating a trajectory for at least a portion of the well being drilled and the another well;

estimating an uncertainty in spatial information for each trajectory;

estimating a probability of a collision with the another well during the drilling of the well by integrating a probability density function using the uncertainties and the trajectories; and

performing the drilling in a manner that limits the probability of collision.

16. A method for estimating a probability of collision, P, between near-parallel wells, the method comprising:

obtaining separation information, S₀, and radius information, R₀, for a given depth, L; and

solving a relationship comprising;

$P=\frac{1}{\mathrm{\pi <br><br>}}·<br><br>{\sin }^{-1}<br><br>\left(\frac{R_0}{S_0}\right)·<br><br>\exp <br><br>\left[-\frac{\left(S_0^2-R_0^2\right)}{2}\right]+\frac{1}{\mathrm{\pi <br><br>}}·<br><br>{\int <br><br>}_{S_0-R_0}^{\sqrt{S_0^2-R_0^2}}<br><br>\left[{\cos }^{-1}<br><br>\left(\frac{S_0^2-R_0^2+x^2}{2·<br><br>S_0·<br><br>x}\right)·<br><br>x·<br><br>\exp <br><br>\left(-\frac{x^2}{2}\right)\right]<br><br><br><br><br><br>x;<br><br>$

where;

x represents a distance.

17. The method as in claim 16, wherein the estimating comprises:

solving the relationship at a first depth, L₁, and a second depth, L₂; and

determining a difference between a result for the first depth, L₁, and a result for the second depth, L₂.

18. The method as in claim 16, wherein separation information, S₀, comprises a dimensionless separation between the wells.

19. The method as in claim 16, wherein radius information, R₀, comprises a dimensionless sum of well radii.