This article demonstrates how to design the well trajectory in J-shape from the surface location to the required target depth (TD).

**Information Given**

- The surface location coordinate of Well-A is 6,543,065.00N 416,695.00E and the target is located at 6,542,213.00N 415,456.00E and the UTM zone is 31N.

- Kick off depth = 4,200’MD/4,200’TVD
- Planned build up rate = 2 degree/100 ft
- Well profile = J-profile (build and hold)

The surface location coordinate of Well-A is 6,543,065.00N 416,695.00E and the target is located at 6,542,213.00N 415,456.00E and the UTM zone is 31N. Therefore, the surface and the target for Well-A can be illustrated is Figure 1.

**Distance from Surface Location to Target**

ΔN = 6,542,213.00 – 6,543,065.00 = – 852 m

ΔE = 415,456.00 – 416,695.00 = -1,239 m

Map Distance = 1503.671 m

**True Distance**

This distance must be applied the scale factor in order to get the true distance.

True Distance (m) = Map Distance ÷ scale factor

True Distance (m) = 1503.671 ÷ 0.999685 = 1504.144 m

Convert from meter to feet

True Distance (ft) = True Distance (m) x 3.281

True Distance (ft) = 1504.144 x 3.281

True Distance (ft) = 4934.86 ft

The true distance is the horizontal displacement referencing from surface location to the target.

**Target Azimuth**

The target in reference to the surface location is located in 3rd quadrant; therefore the target azimuth is calculated by the following relationship;

Target AZI = 180 + tan-1(ΔE÷ΔN)

Target AZI = 180 + tan-1((-1,239) ÷ (-852))

Target AZI = 235.486 degree

**Directional Plan and Calculation**

In order to design well trajectory for this well, the illustration (Figure 3) is made to determine all required parameters.

**Calculations**

Radius build (ft) = (180 ÷ ϖ) × (100 ÷2)

Radius build (ft) = 2,864.79 ft

**a = TVDtarget – TVDkop**

a = 9,500- 4,200 = 5,300 ft

**b = Horizontal Displacement to Target – Radius Build**

b = 4,934.86 – 2,864.79= 2070.07 ft

**c = (a^2 + b^2)^1/2**

c = (5,300^2 + 2,070.07^2)^1/2 = 5,689.92 ft

**d= (c^2 – e^2)^1/2**

d= (5,689.92^2 – 2,864.79^2)^1/2 = 4916.11 ft

**e = Radius build**

e = 2,864.79 ft (Radius build)

**f = g ÷ cos(θ1)**

f = 750÷ cos(51.565) = 1,206.52 ft

**g = Planned Depth TVD– Target Depth TVD**

g = 10,250 – 9,500 = 750 ft

**h = g × tan(θ1)**

h = 750 × tan(51.565) = 945.09 ft

**θ1 = 180- ?1- α1**

θ1 = 180 – 59.769 – 68.665 = 51.565 degree

**θ2 = 90- θ1**

θ2 = 90- 51.565 = 38.435 degree

**Distance build (ft) = Change in Inclination ÷ Build Rate**

Inclination increases from 0 degree to 51.57 degree at the end of build

Distance build = 51.57 degree ÷ (2 degree/100ft) = 2578.27 ft

**Measured Depth at End of Build = Kick of Depth + Distance Build**

Measured Depth at End of Build = 4,200 + 2,578.27 = 6,778.27 ft MD

**TVD at End of Build = Kick of Depth TVD + Radius of Build x sin (θ1)**

TVD at End of Build = 4,200 + 2864.79x sin (51.57) = 6,444.04 ft TVD

**Horizontal departure at EOB = Radius Build × (1- cos(θ1))**

Horizontal departure at EOB = 2864.79x × (1- cos(51.57)) = 1083.98 ft

**Horizontal Departure at TD = Horizontal Departure at Target + h**

Horizontal Departure at TD = 4,934.86 + 945.05 = 5879.91 ft

Figure 4 illustrates all calculated parameters for Well-A

**North-South and East-West Calculation**

Since there is no change in Azimuth direction, North-South and East-West can be calculated by the following equations

**North-South = Horizontal Departure x cos (Wellbore Azimuth)**

East-West = Horizontal Departure x sin (Wellbore Azimuth)

**North-South and East-West at Kick Off Point (KOP)**

At KOP, there is not horizontal departure so North-South and East-West direction are 0.

**North-South and East-West at End of Build (EOB)**

North-South = Horizontal Departure at EOB x cos (Wellbore Azimuth)

North-South = 1083.98x cos (235.49) = -614.20 ft

East-West = Horizontal Departure at EOB x sin (Wellbore Azimuth)

East-West = 1083.98 x sin (235.49) = -893.18 ft

**North-South and East-West at Target**

North-South = Horizontal Departure at Target x cos (Wellbore Azimuth)

North-South = 4934.86 x cos (235.49) = -2,796.16 ft

East-West = Horizontal Departure at Target x sin (Wellbore Azimuth)

East-West = 4934.86 x sin (235.49) = -4,066.24 ft

**North-South and East-West at Total Depth (TD)**

North-South = Horizontal Departure at TD x cos (Wellbore Azimuth)

North-South = 5879.95x cos (235.49) = -3,331.66ft

East-West = Horizontal Departure at TD x sin (Wellbore Azimuth)

East-West = 5879.95x sin (235.49) = -4,844.98ft

Figure 5 shows the plan view of Well-A and Table 1 demonstrates all critical points.

**Calculation Summary**

Well-A is planned for 2-D well design with a J-shape trajectory plan. The well will be drilled vertically to 4,100’ MD/4,100’ TVD. Then, the kick off starts at 4,200’ MD/4,200’ TVD (100 ft below 16” shoe) in a firm shale zone and the designed build up rate is 2 degree/100 ft. End of build depth is 6,778’MD/6,444’TVD. The target depth is 11,694’MD/9,500’ TVD KRB and the target depth of the well is 12,901’MD/10,250’ TVD KRB.

**Reference** – https://www.linkedin.com/pulse/well-trajectory-j-profile-example-directional-suwat-pongtepupathum

Hello,

Thanks for this. Please, what would the azimuth be if the target reference is in the 1st, 2nd or 4th quadrant?

It is in the 3rd quadrant.

Wow, good job, this is an eye opener. Thanks for sharing, keeping the good job rolling.

Hello, I hope you guys fix the picture cuz all of them are not showing