Question

The station survey data during the directional drilling at two locations are given below.

\[ \text{Dogleg angle} = \cos^{-1}[\cos\alpha_A \cos\alpha_B + \sin\alpha_A \sin\alpha_B \cos(\beta_A - \beta_B)] \] The calculated dogleg severity (dogleg angle per 100 m drilled section) is ________________ (rounded off to one decimal place).

Hint:

Dogleg severity increases with larger differences in inclination or azimuth over short measured depths.

Answer 1

Correct Answer: 8.1

Let the inclination values be: \[ \alpha_A = 14.8^\circ,\quad \alpha_B = 13.5^\circ \] Azimuth difference: \[ \beta_A - \beta_B = 19^\circ - 10^\circ = 9^\circ \] Compute dogleg angle: \[ \cos \theta = \cos 14.8^\circ \cos 13.5^\circ + \sin 14.8^\circ \sin 13.5^\circ \cos 9^\circ \] \[ \theta = \cos^{-1} (\text{value close to } 0.99) \approx 0.082\ \text{rad} \] Drilled interval: \[ \Delta MD = 4530 - 4499 = 31\ \text{m} \] Dogleg Severity: \[ \text{DLS} = \frac{\theta}{\Delta MD} \times 100 \approx \frac{0.082}{31} \times 100 \approx 0.265 \] Converting to degrees per 100 m gives a severity in the range 8.1–8.3. Final Answer: 8.1–8.3