Directional Survey Calculator (Minimum Curvature)
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52 rows x 13 columns
| A | B | C | D | E | F | G | H | I | J | K | L | M | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | Directional Survey — Minimum Curvature | ||||||||||||
| 2 | Blue cells on yellow are inputs. Overwrite the stations with your survey; for a shorter one, delete the unused rows rather than clearing them. | ||||||||||||
| 3 | |||||||||||||
| 4 | Survey Settings | ||||||||||||
| 5 | Vertical section azimuth | 45 | deg | ||||||||||
| 6 | Dogleg severity limit | 3 | °/100 ft | ||||||||||
| 7 | |||||||||||||
| 8 | Survey Stations | ||||||||||||
| 9 | MD (ft) | Inclination (°) | Azimuth (°) | Course (ft) | Dogleg (°) | DLS (°/100 ft) | Ratio factor | TVD (ft) | North (ft) | East (ft) | Vertical section (ft) | Dogleg check | TVD, plotted down (ft) |
| 10 | 0 | 0.00 | 0.00 | 0.0 | 0.0 | 0.0 | 0.0 | Tie-in | 0.0 | ||||
| 11 | 300 | 0.00 | 0.00 | 300 | 0.00 | 0.00 | 1.00000 | 300.0 | 0.0 | 0.0 | 0.0 | OK | -300.0 |
| 12 | 600 | 0.00 | 0.00 | 300 | 0.00 | 0.00 | 1.00000 | 600.0 | 0.0 | 0.0 | 0.0 | OK | -600.0 |
| 13 | 900 | 0.50 | 30.00 | 300 | 0.50 | 0.17 | 1.00001 | 900.0 | 1.1 | 0.7 | 1.3 | OK | -900.0 |
| 14 | 1,200 | 0.50 | 30.00 | 300 | 0.00 | 0.00 | 1.00000 | 1,200.0 | 3.4 | 2.0 | 3.8 | OK | -1,200.0 |
| 15 | 1,500 | 1.00 | 40.00 | 300 | 0.51 | 0.17 | 1.00001 | 1,500.0 | 6.5 | 4.3 | 7.7 | OK | -1,500.0 |
| 16 | 1,800 | 1.00 | 40.00 | 300 | 0.00 | 0.00 | 1.00000 | 1,799.9 | 10.6 | 7.7 | 12.9 | OK | -1,799.9 |
| 17 | 2,000 | 1.00 | 40.00 | 200 | 0.00 | 0.00 | 1.00000 | 1,999.9 | 13.2 | 9.9 | 16.4 | OK | -1,999.9 |
| 18 | 2,200 | 5.00 | 45.00 | 200 | 4.00 | 2.00 | 1.00041 | 2,199.6 | 20.7 | 17.2 | 26.8 | OK | -2,199.6 |
| 19 | 2,400 | 10.00 | 45.00 | 200 | 5.00 | 2.50 | 1.00064 | 2,397.8 | 39.2 | 35.7 | 52.9 | OK | -2,397.8 |
| 20 | 2,600 | 15.00 | 45.00 | 200 | 5.00 | 2.50 | 1.00064 | 2,593.0 | 69.8 | 66.3 | 96.2 | OK | -2,593.0 |
| 21 | 2,800 | 20.00 | 45.00 | 200 | 5.00 | 2.50 | 1.00064 | 2,783.7 | 112.3 | 108.8 | 156.3 | OK | -2,783.7 |
| 22 | 3,000 | 25.00 | 45.00 | 200 | 5.00 | 2.50 | 1.00064 | 2,968.4 | 166.4 | 162.9 | 232.8 | OK | -2,968.4 |
| 23 | 3,200 | 30.00 | 45.00 | 200 | 5.00 | 2.50 | 1.00064 | 3,145.7 | 231.7 | 228.1 | 325.1 | OK | -3,145.7 |
| 24 | 3,400 | 33.00 | 46.00 | 200 | 3.05 | 1.52 | 1.00024 | 3,316.2 | 304.9 | 302.7 | 429.6 | OK | -3,316.2 |
| 25 | 3,600 | 35.00 | 47.00 | 200 | 2.08 | 1.04 | 1.00011 | 3,482.0 | 381.8 | 383.8 | 541.4 | OK | -3,482.0 |
| 26 | 3,900 | 35.00 | 47.00 | 300 | 0.00 | 0.00 | 1.00000 | 3,727.8 | 499.2 | 509.7 | 713.4 | OK | -3,727.8 |
| 27 | 4,200 | 35.00 | 47.50 | 300 | 0.29 | 0.10 | 1.00000 | 3,973.5 | 616.0 | 636.0 | 885.3 | OK | -3,973.5 |
| 28 | 4,500 | 35.50 | 48.00 | 300 | 0.58 | 0.19 | 1.00001 | 4,218.5 | 732.4 | 764.2 | 1,058.3 | OK | -4,218.5 |
| 29 | 4,800 | 35.50 | 49.00 | 300 | 0.58 | 0.19 | 1.00001 | 4,462.8 | 847.8 | 894.7 | 1,232.1 | OK | -4,462.8 |
| 30 | 5,100 | 36.00 | 50.00 | 300 | 0.77 | 0.26 | 1.00002 | 4,706.2 | 961.7 | 1,028.0 | 1,406.9 | OK | -4,706.2 |
| 31 | 5,200 | 39.00 | 54.00 | 100 | 3.86 | 3.86 | 1.00038 | 4,785.6 | 999.1 | 1,075.9 | 1,467.3 | CHECK: over the DLS limit | -4,785.6 |
| 32 | 5,500 | 39.00 | 54.00 | 300 | 0.00 | 0.00 | 1.00000 | 5,018.7 | 1,110.0 | 1,228.7 | 1,653.7 | OK | -5,018.7 |
| 33 | 5,800 | 39.00 | 54.50 | 300 | 0.31 | 0.10 | 1.00000 | 5,251.9 | 1,220.3 | 1,381.9 | 1,840.1 | OK | -5,251.9 |
| 34 | 6,100 | 39.50 | 55.00 | 300 | 0.59 | 0.20 | 1.00001 | 5,484.2 | 1,329.9 | 1,536.9 | 2,027.1 | OK | -5,484.2 |
| 35 | 6,400 | 39.50 | 55.00 | 300 | 0.00 | 0.00 | 1.00000 | 5,715.7 | 1,439.3 | 1,693.2 | 2,215.1 | OK | -5,715.7 |
| 36 | 6,700 | 40.00 | 55.00 | 300 | 0.50 | 0.17 | 1.00001 | 5,946.3 | 1,549.4 | 1,850.4 | 2,404.0 | OK | -5,946.3 |
| 37 | 7,000 | 40.00 | 55.50 | 300 | 0.32 | 0.11 | 1.00000 | 6,176.1 | 1,659.3 | 2,008.8 | 2,593.7 | OK | -6,176.1 |
| 38 | 7,500 | 40.00 | 55.50 | 500 | 0.00 | 0.00 | 1.00000 | 6,559.2 | 1,841.3 | 2,273.7 | 2,909.7 | OK | -6,559.2 |
| 39 | 8,000 | 40.50 | 56.00 | 500 | 0.60 | 0.12 | 1.00001 | 6,940.8 | 2,023.1 | 2,540.7 | 3,227.1 | OK | -6,940.8 |
| 40 | 8,500 | 40.50 | 56.00 | 500 | 0.00 | 0.00 | 1.00000 | 7,321.0 | 2,204.7 | 2,809.9 | 3,545.9 | OK | -7,321.0 |
| 41 | |||||||||||||
| 42 | Survey Summary at TD | ||||||||||||
| 43 | Total depth (MD) | 8,500 | ft | ||||||||||
| 44 | TVD at TD | 7,321.0 | ft | ||||||||||
| 45 | North at TD | 2,204.7 | ft | ||||||||||
| 46 | East at TD | 2,809.9 | ft | ||||||||||
| 47 | Vertical section at TD | 3,545.9 | ft | ||||||||||
| 48 | Closure distance | 3,571.6 | ft | ||||||||||
| 49 | Closure azimuth | 51.88 | deg | ||||||||||
| 50 | Highest dogleg severity | 3.86 | °/100 ft | ||||||||||
| 51 | Courses flagged | 1 | |||||||||||
| 52 | Dogleg check | CHECK: 1 course(s) flagged in the check column | |||||||||||
| 53 | |||||||||||||
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| 62 |
| Name | Refers To | Comment |
|---|---|---|
| _PO.DE.Dir.DoglegSeverity | =LAMBDA(Inc1_deg, Azi1_deg, Inc2_deg, Azi2_deg, dMD_ft, DEGREES(2 * ASIN(SQRT(MIN(1, SIN(RADIANS(Inc2_deg - Inc1_deg) / 2)^2 + SIN(RADIANS(Inc1_deg)) * SIN(RADIANS(Inc2_deg)) * SIN(RADIANS(Azi2_deg - Azi1_deg) / 2)^2)))) * 100 / dMD_ft) | Dogleg severity in degrees per 100 ft between two directional surveys, from the inclinations, azimuths and course length. |
| _PO.DE.Dir.RatioFactor | =LAMBDA(Dogleg_deg, IF(Dogleg_deg < 0.000001, 1, 2 / RADIANS(Dogleg_deg) * TAN(RADIANS(Dogleg_deg) / 2))) | Minimum curvature ratio factor from the dogleg angle over a course, degrees (1 for a straight course). |
| _PO.DE.Dir.MinCurv.dTVD | =LAMBDA(Inc1_deg, Inc2_deg, dMD_ft, RF, dMD_ft / 2 * (COS(RADIANS(Inc1_deg)) + COS(RADIANS(Inc2_deg))) * RF) | Minimum curvature TVD increment, ft, over a course. |
| _PO.DE.Dir.MinCurv.dNorth | =LAMBDA(Inc1_deg, Azi1_deg, Inc2_deg, Azi2_deg, dMD_ft, RF, dMD_ft / 2 * (SIN(RADIANS(Inc1_deg)) * COS(RADIANS(Azi1_deg)) + SIN(RADIANS(Inc2_deg)) * COS(RADIANS(Azi2_deg))) * RF) | Minimum curvature north increment, ft, over a course. |
| _PO.DE.Dir.MinCurv.dEast | =LAMBDA(Inc1_deg, Azi1_deg, Inc2_deg, Azi2_deg, dMD_ft, RF, dMD_ft / 2 * (SIN(RADIANS(Inc1_deg)) * SIN(RADIANS(Azi1_deg)) + SIN(RADIANS(Inc2_deg)) * SIN(RADIANS(Azi2_deg))) * RF) | Minimum curvature east increment, ft, over a course. |
| _PO.DE.Dir.VerticalSection | =LAMBDA(North_ft, East_ft, VSAzi_deg, North_ft * COS(RADIANS(VSAzi_deg)) + East_ft * SIN(RADIANS(VSAzi_deg))) | Vertical section, ft: the horizontal displacement projected onto the vertical section azimuth. |
| _PO.DE.Dir.ClosureDistance | =LAMBDA(North_ft, East_ft, SQRT(North_ft^2 + East_ft^2)) | Closure distance, ft: the straight-line horizontal displacement from the surface location. |
| _PO.DE.Dir.ClosureAzimuth | =LAMBDA(North_ft, East_ft, IF(AND(North_ft = 0, East_ft = 0), 0, MOD(DEGREES(ATAN2(North_ft, East_ft)), 360))) | Closure azimuth, degrees from north (0-360), of the horizontal displacement from the surface location. |
| SVY_VSAzi | $B$5 | Vertical section azimuth, deg |
| SVY_DLSmax | $B$6 | Dogleg severity limit, °/100 ft |
Description
Works a directional survey by minimum curvature. Enter MD, inclination and azimuth for each station below a tie-in. The sheet returns, for every course, the course length, dogleg angle, dogleg severity and ratio factor, and for every station the TVD, north and east coordinates and vertical section. Courses over the DLS limit are flagged. At TD it summarises the TVD, coordinates, vertical section, closure distance and azimuth, and the highest dogleg. Plan-view and vertical-section charts show the well path.
Parameters:
- Vertical section azimuth: Direction the vertical section is projected onto (deg)
- DLS limit: Highest acceptable dogleg severity (°/100 ft)
- Tie-in: MD, inclination and azimuth, plus TVD, north and east, of the station the survey starts from (surface by default)
- Stations: MD (ft), inclination and azimuth (deg). Thirty example stations ship. For a shorter survey, delete the unused rows rather than clearing them. To add stations, insert rows inside the table, above its last row. Either way the summary and charts follow the rows that remain. A station whose MD does not increase is flagged rather than calculated.
Method: Dogleg β = 2 arcsin √[sin²((I₂ − I₁)/2) + sin I₁ sin I₂ sin²((A₂ − A₁)/2)]. This is the haversine form of the usual arccos expression, and unlike arccos it stays exact when a course barely changes direction. DLS = β × 100 / ΔMD. The ratio factor is RF = (2/β) tan(β/2), or 1 for a straight course. Then ΔTVD = ΔMD/2 (cos I₁ + cos I₂) RF, ΔN = ΔMD/2 (sin I₁ cos A₁ + sin I₂ cos A₂) RF and ΔE = ΔMD/2 (sin I₁ sin A₁ + sin I₂ sin A₂) RF. Vertical section = N cos(VSA) + E sin(VSA). Closure is the distance and azimuth of (N, E). The vertical-section chart plots TVD downward. The formulas are the sheet's own _PO.DE.* LAMBDAs, so it calculates with no add-in installed.
Example: A well kicked off at 2,000 ft and built to about 40° toward the north-east, surveyed to 8,500 ft MD. A 100 ft course at 5,100–5,200 ft adds 3° of inclination and 4° of azimuth, about 3.86°/100 ft, and is the one course flagged against the 3°/100 ft limit.
How to use this blueprint
- In Excel, go to the Petroleum Office ribbon tab and click Blueprint Manager
- Search for Directional Survey Calculator (Minimum Curvature)
- Click on the blueprint to preview
- Click Insert to place it into your worksheet. Modify the input values to match your data.