Question

\( C_1, C_2, \) and \( C_3 \) are the Dietz shape factors of three reservoirs with circular, square, and rectangular shape of drainage area, respectively. The well is located at the geometric center of the reservoir. Which ONE of the following options is CORRECT about the shape factors?

• A. \( C_3<C_2<C_1 \)
• B. \( C_2<C_1<C_3 \)
• C. \( C_1<C_2 = C_3 \)
• D. \( C_1 = C_2 = C_3 \)

Hint:

In reservoir engineering, the shape factor is important for accounting for the effects of reservoir geometry on pressure and flow calculations. Circular reservoirs generally have the highest shape factor, while rectangular ones have the lowest.

Answer 1

The Correct Option is A

The Dietz shape factor (\( C \)) is a dimensionless factor that depends on the shape of the drainage area of the reservoir. It is used in reservoir engineering to correct for the geometry of the reservoir when calculating pressure or flow rates.
For different shapes of the drainage area:
- For a circular reservoir, the shape factor \( C_1 \) is the largest because a circular shape offers the most efficient drainage.
- For a square reservoir, the shape factor \( C_2 \) is smaller than \( C_1 \), but larger than \( C_3 \) due to the more irregular shape compared to a circle.
- For a rectangular reservoir, the shape factor \( C_3 \) is the smallest because a rectangular shape is the least efficient in terms of drainage.
Thus, the correct order of the shape factors is: \[ C_3<C_2<C_1 \] This corresponds to option (A).