1. Petroleum Engineering - 406 LESSON 19 Survey Calculation Methods

2. LESSON 11 Survey Calculation Methods  Radius of Curvature  Balanced Tangential  Minimum Curvature –Kicking Off from Vertical –Controlling Hole Angle (Inclination)

3. Homework READ: Chapter 8 “Applied Drilling Engineering”, (  first 20 pages )

4. Radius of Curvature Method Assumption: The wellbore follows a smooth, spherical arc between survey points and passes through the measured angles at both ends. (tangent to I and A at both points 1 and 2). Known: Location of point 1,  MD 12 and angles I 1, A 1, I 2 and A 2

5. Radius of Curvature Method I 2 -I 1 1 I1I1 A1A1  East  North North I2I2  MD = R 1 (I 2 -I 1 ) (rad) 2 East Length of arc of circle, L = R  rad A1A1 R1R1

6. Radius of Curvature - Vertical Section In the vertical section,  MD = R 1 (I 2 -I 1 ) rad  MD = R 1 ( ) (I 2 -I 1 ) deg I 1 I 2 -I 1  R 1 = ( ) ( )  MD R1R1  Vert I2I2

7. Radius of Curvature: Vertical Section  MD R1R1 R1R1 I1I1 I2I2 I2I2  Horiz

8. Radius of Curvature: Horizontal Section N A1A1 A2A2 L2L2  East 2  North R2R2 1 O A2A2 A 2 -A 1 A1A1 L 2 = R 2 (A 2 - A 1 ) RAD  East = R 2 cos A 1 - R 2 cos A 2 = R 2 (cos A 1 - cos A 2 ) so, DEG

9. Radius of Curvature Method  East = R 2 (cos A 1 - cos A 2 ) L2L2  East =

10. Radius of Curvature Method  North = R 2 (sin A 2 - sin A 1 ) L2L2  North =

11. Radius of Curvature - Equations With all angles in radians!

12. Angles in Radians If I 1 = I 2, then:  North =  MD sin I 1  East =  MD sin I 1  Vert =  MD cos I 1

13. Angles in Radians If A1 = A2, then:  North =  MD cos A 1  East =  MD sin A 1  Vert =  MD

14. Radius of Curvature - Special Case If I 1 = I 2 and A 1 = A 2  North =  MD sin I 1 cos A 1,  East =  MD sin I 1 sin A 1  Vert =  MD cos I 1

15. Balanced Tangential Method 1 I1I1  MD 2 I2I2 I2I2 I2I2 0 Vertical Projection  MD 2

16. Balanced Tangential Method NN EE A1A1 A2A2  Horiz.1  Horiz. 2 Horizontal Projection

17. Balanced Tangential Method - Equations

18. Minimum Curvature Method This method assumes that the wellbore follows the smoothest possible circular arc from Point 1 to Point 2. This is essentially the Balanced Tangential Method, with each result multiplied by a ratio factor (RF) as follows:

19. Minimum Curvature Method - Equations

20. Minimum Curvature Method P r O r RDL Q 2 DL =  S

21. Fig 8.22 A curve representing a wellbore between Survey Stations A 1 and A 2.   (A, I)

22. Tangential Method

23. Balanced Tangential Method

24. Average Angle Method

25. Radius of Curvature Method

26. Minimum Curvature Method

27. Mercury Method