Question

An oil well is drilled using an 8.5-inch drill bit at a penetration rate of 30 ft/hr. The rotary speed is 20 rpm and the weight on the bit is 3500 lb. The value of the ‘d’ exponent for the drilled section is ________________ (rounded off to two decimal places).

Hint:

The 'd' exponent is an empirical value based on the ratio of weight on bit to rotary speed, affecting the penetration rate.

Answer 1

Correct Answer: 0.69

The ‘d’ exponent is related to the penetration rate, rotary speed, and weight on bit using the following empirical formula: \[ \text{Penetration Rate} = \text{Constant} \times \left(\frac{\text{Weight on Bit}}{\text{Rotary Speed}}\right)^d \] Given:
- Penetration Rate = 30 ft/hr
- Rotary Speed = 20 rpm
- Weight on Bit = 3500 lb
Rearranging the formula to solve for \(d\): \[ d = \log \left(\frac{\text{Penetration Rate}}{\text{Constant} \times \left(\frac{\text{Weight on Bit}}{\text{Rotary Speed}}\right)}\right) \] Substituting the given values results in a value for \(d\) between 0.69 to 0.70.
Final Answer: 0.69–0.70