Formulas Average Angle.pdf

Formulas and Calculations

Figure 5-3 Eaton’s Fracture gradient chart

10.

Directional Drilling Calculations

Directional Survey Calculations The following are the two most commonly used methods to calculate directional surveys: 1. Angle Averaging Method North = MD x sin.(I1 + I2) x cos.(Al + A2) 2 2 East = MD x sin.(I1 + I2) x sin.(Al + A2) 2 2 Vert. = MD x cos.(I1 + I2) 2

147

Formulas and Calculations

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) Vert. = MD(sin. I2 — sin. I1) (I2 — I1) 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:

Depth, ft Inclination, degrees Azimuth, degrees

Survey 1

Survey 2

7482 4 10

7782 8 35

Angle Averaging Method: North = 300 x sin. (4 + 8) x cos. (10+35) 2 2 North = 300 x sin (6) x cos. (22.5) North = 300 x .104528 x .923879 North = 28.97 ft East = 300 x sin.(4 + 8) x sin. (10+35) 2 2 East = 300 x sin. (6) x sin. (22.5) East = 300 x .104528 x .38268 East = 12.0 ft Vert. = 300 x cos. (4 + 8) 2 Vert. = 300 x cos. (6) Vert. = 300 x .99452 Vert. = 298.35 ft

Radius of Curvature Method:

148

Formulas and Calculations

North = 300(cos. 4 — cos. 8)(sin. 35 — sin. 10) (8 — 4)(35 — 10) North = 300 (.99756 — .990268)(.57357 — .173648) 4 x 25 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 = 300 (0073) (.16565) 100 East = 0.36277 100 East = 0.0036277 x 57.32 East = 11.91 ft Vert. = 300 (sin. 8 — sin. 4) (8 — 4) Vert. = 300 (0.13917 — 0.069756) (8 — 4) Vert. = 300 x .069414 4 Vert. = 300 x 0.069414 4 Vert. = 5.20605 x 57.3 Vert. = 298.3 ft

Deviation/Departure Calculation Deviation is defined as departure of the wellbore from the vertical, measured by the horizontal distance from the rotary table to the target. The amount of deviation is a function of the drift angle (inclination) and hole depth.

The following diagram illustrates how to determine the deviation/departure:

149

Formulas and Calculations

DATA: AB = distance from the surface location to the KOP BC = distance from KOP to the true vertical depth (TVD) BD = distance from KOP to the bottom of the hole (MD) CD = Deviation/departure—departure of the wellbore from the vertical AC = true vertical depth AD = Measured depth Figure 5-4. Deviation/Departure To calculate the deviation/departure (CD), ft:

CD, ft = sin I x BD

Example: Kick off point (KOP) is a distance 2000 ft from the surface. MD is 8000 ft. Hole angle (inclination) is 20 degrees. Therefore the distance from KOP to MD = 6000 ft (BD): CD, ft = sin 20 x 6000 ft CD, ft = 0.342 x 6000 ft CD = 2052 ft From this calculation, the measured depth (MD) is 2052 ft away from vertical.

Dogleg Severity Calculation Method 1 Dogleg severity (DLS) is usually given in degrees/100 ft. The following formula provides dogleg severity in degrees/100 ft and is based on the Radius of Curvature Method: DLS = {cos.—1 [(cos. I1 x cos. I2) + (sin. I1 x sin. 12) x cos. (A2 — Al)]} x (100 ÷ CL) For metric calculation, substitute x (30 ÷ CL) i.e. DLS = {cos.—1 [(cos. I1 x cos. I2) + (sin. I1 x sin. 12) x cos. (A2 — Al)]} x (30 ÷ CL) where

Example:

DLS = dogleg severity, degrees/l00 ft CL = course length, distance between survey points, ft I1, I2 = inclination (angle) at upper and lower surveys, ft Al, A2 = direction at upper and lower surveys, degrees ^Azimuth = azimuth change between surveys, degrees

Survey 1

Survey 2

150

Formulas and Calculations

Depth, ft Inclination, degrees Azimuth, degrees

4231 13.5 N 10 E

4262 14.7 N 19 E

DLS = {cos.—1 [(cos. 13.5 x cos. l4.7) + (sin. 13.5 x sin. 14.7 x cos. (19 — 10)]} x (100 ÷ 31) DLS = {cos.—1 [(.9723699 x .9672677) + (.2334453 x .2537579 x .9876883)]} x (100 ÷ 31) DLS = {cos.—1 [(.940542) + (.0585092)]} x (100 ÷ 31) DLS = 2.4960847 x (100 ÷ 31) DLS = 8.051886 degrees/100 ft

Method 2 This method of calculating dogleg severity is based on the tangential method: DLS =

100 . L [(sin. I1 x sin. I2)(sin. A1 x sin. A2 + cos. A1 x cos. A2) + cos. I1 x cos. I2]

where DLS L Il, 12 Al, A2

= dogleg severity, degrees/ 100 ft = course length, ft = inclination (angle) at upper and lower surveys, degrees = direction at upper and lower surveys, degrees

Example: Depth Inclination, degrees Azimuth, degrees DLS =

Survey 1

Survey 2

4231 13.5 N 10 E

4262 14.7 N 19 E

100 . 31[(sin.13.5 x sin.14.7)(sin.10 x sin.19) + (cos.10 x cos.1l9)+(cos.13.5 x cos.14.7)]

DLS = 100 30. 969 DLS = 3.229 degrees/100 ft

Available Weight on Bit in Directional Wells A directionally drilled well requires that a correction be made in total drill collar weight because only a portion of the total weight will be available to the bit: P = W x Cos I where

P = partial weight available for bit I = degrees inclination (angle)

Example:

W = 45,000 lb

Cos = cosine W = total weight of collars

I = 25 degrees

151