In a well site, a directional drilling is planned. The reference points are given in the table below. Depth (m) 1000 200 |(surface) 50 400 600 800 1200 (target) 400 Lateral Offset (m) 200 300 350 375 A) According to this data, design a trajectory for the drilling by using a 6th order interpolation polynomial to estimate the lateral offsets from the well site at given depths. B) Verify the interpolation polynomial at least at two reference points. C) Estimate the lateral offsets from the well site for 300 m and 500 m depths. D) Plot the reference points and the interpolation ploynomial (the trajectory) on the same graph (choose a scale of 1:1).

In a well site, a directional drilling is planned. The reference points are given in the table below. Depth (m) 1000 200 |(surface) 50 400 600 800 1200 (target) 400 Lateral Offset (m) 200 300 350 375 A) According to this data, design a trajectory for the drilling by using a 6th order interpolation polynomial to estimate the lateral offsets from the well site at given depths. B) Verify the interpolation polynomial at least at two reference points. C) Estimate the lateral offsets from the well site for 300 m and 500 m depths. D) Plot the reference points and the interpolation ploynomial (the trajectory) on the same graph (choose a scale of 1:1).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

In a well site, a directional drilling is planned. The reference points are given in the table
below.
Depth (m)
200
400
600
800
1000
1200
(surface)
(target)
400
Lateral
50
200
300
350
375
Offset (m)
A) According to this data, design a trajectory for the drilling by using a 6th order interpolation
polynomial to estimate the lateral offsets from the well site at given depths.
B) Verify the interpolation polynomial at least at two reference points.
C) Estimate the lateral offsets from the well site for 300 m and 500 m depths.
D) Plot the reference points and the interpolation ploynomial (the trajectory) on the same
graph (choose a scale of 1:1).

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