The following are the two most commonly used methods to calculate directional surveys:
1. Angle Averaging Method
Fracture gradient (Ib/gal)
2. Radius of Curvature Method
North = MD(cos. I1 — cos. I2)(sin. A2 — sin. Al) (I2 — I1)(A2 — Al)
East = MD(cos. I1 — cos. I2)(cos. A2 — cos. Al) (I2 — I1)(A2 — Al)
where MD = course length between surveys in measured depth, ft
I1, I2 = inclination (angle) at upper and lower surveys, degrees A1, A2 = direction at upper and lower surveys
Example: Use the Angle Averaging Method and the Radius of Curvature Method to calculate the following surveys:
Survey 1 Survey 2
Depth, ft 7482 7782
Inclination, degrees 4 8
Azimuth, degrees 10 35
Angle Averaging Method:
North = 300 x sin (6) x cos. (22.5) North = 300 x .104528 x .923879 North = 28.97 ft
East = 300 x sin. (6) x sin. (22.5) East = 300 x .104528 x .38268 East = 12.0 ft
Vert. = 300 x cos. (6) Vert. = 300 x .99452 Vert. = 298.35 ft
Radius of Curvature Method:
North = 300(cos. 4 — cos. 8)(sin. 35 — sin. 10) (8 — 4)(35 — 10)
North = 300 (.99756 — .990268)(.57357 — .173648)
North = 0.874629 - 100 North = 0.008746 x 57.32 North = 28.56 ft
East = 300(cos. 4 — cos. 8)(cos. 10 — cos. 35) (8 — 4)(35 — 10)
East = 300 (99756 — .99026)(.9848 — .81915) 4 x 25
East = 0.36277 100
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