Certainly! Let's walk through the steps to calculate the gradient of the influx given the parameters provided:
1. Given Values:
- Mud weight: 12.5 pounds per gallon (ppg)
- Surface Indicated Drill Pipe Pressure (SIDPP): 800 psi
- Surface Indicated Casing Pressure (SICP): 1025 psi
- Annulus capacity: 0.292 barrels per foot (bbl/ft)
- Influx volume: 12 barrels (bbl)
2. Calculate the Pressure Difference:
- [tex]\( \text{Pressure difference (psi)} = \text{SICP} - \text{SIDPP} \)[/tex]
- [tex]\( \text{Pressure difference} = 1025 \text{ psi} - 800 \text{ psi} \)[/tex]
- [tex]\( \text{Pressure difference} = 225 \text{ psi} \)[/tex]
3. Convert Mud Weight to psi/ft:
- The conversion factor from ppg to psi/ft is 0.052.
- [tex]\( \text{Mud weight in psi/ft} = 12.5 \text{ ppg} \times 0.052 \)[/tex]
- [tex]\( \text{Mud weight in psi/ft} = 0.65 \text{ psi/ft} \)[/tex]
4. Calculate the Gradient of the Influx:
- The formula is:
[tex]\[
\text{Influx gradient} = \text{Pressure difference} + \left(\text{Mud weight in psi/ft} \times \left(\frac{\text{Influx volume in bbl}}{\text{Annulus capacity in bbl/ft}}\right)\right)
\][/tex]
- Plugging in the values, we get:
[tex]\[
\text{Influx gradient} = 225 \text{ psi} + \left(0.65 \text{ psi/ft} \times \left(\frac{12 \text{ bbl}}{0.292 \text{ bbl/ft}}\right)\right)
\][/tex]
- First, calculate the volume term:
[tex]\[
\frac{12 \text{ bbl}}{0.292 \text{ bbl/ft}} \approx 41.0959 \text{ ft}
\][/tex]
- Then, multiply by the mud weight in psi/ft:
[tex]\[
0.65 \text{ psi/ft} \times 41.0959 \text{ ft} \approx 26.7123 \text{ psi}
\][/tex]
- Finally, add the pressure difference:
[tex]\[
\text{Influx gradient} = 225 \text{ psi} + 26.7123 \text{ psi} \approx 251.7123 \text{ psi}
\][/tex]
5. Choose the Closest Option:
- Among the provided choices, none of them exactly matches our calculated value of approximately [tex]\(251.7123 \text{ psi/ft}\)[/tex]. This suggests there might be a mistake in the given choices or in their descriptions.
However, based on our detailed calculations, the gradient of the influx is approximately [tex]\(251.7123 \text{ psi/ft}\)[/tex].
Given the lack of matching choices, verify the numbers and possible typo in the available options or re-evaluate the problem constraints.
