\(C_1, C_2,\) and \(C_3\) are the Dietz shape factors of three reservoirs with circular, square, and rectangular drainage areas, respectively. The well is located at the geometric center of the reservoir.
Which ONE of the following options is CORRECT about the shape factors?
Show Hint
- \(C_3 < C_2 < C_1\)
- \(C_2 < C_1 < C_3\)
- \(C_1 = C_2 = C_3\)
- \(C_1 = C_2 < C_3\)
The Correct Option is A
Solution and Explanation
Step 1: Concept of Dietz shape factor.
Shape factor accounts for reservoir geometry effect on well productivity index. Higher symmetry (more compact shape) → higher shape factor. Step 2: Order of compactness.
- Circle is most compact, has the highest symmetry → highest shape factor. - Square is less compact than circle → lower than circle. - Rectangle (elongated) is least compact → lowest shape factor. Step 3: Establish order.
Thus, \[ C_{\text{rectangle}} < C_{\text{square}} < C_{\text{circle}}. \] Or, \[ C_3 < C_2 < C_1. \] Final Answer: \[ \boxed{C_3 < C_2 < C_1} \]
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