Question

The formation volume factors of oil and water are \(B_o\) and \(B_w\), respectively. The CORRECT relationship between the fractional water cut at the surface condition \(f_{ws}\) and the fractional water cut at the reservoir condition \(f_w\) is:

• A. \( f_{ws} = \frac{B_o f_w}{B_w + B_o} \)
• B. \( f_{ws} = \frac{B_o f_w}{B_w + B_o f_w} \)
• C. \( f_{ws} = \frac{B_w}{B_o \left( \frac{1}{f_w} - 1 \right) + B_w} \)
• D. \( f_{ws} = \frac{B_o}{B_w \left( \frac{1}{f_w} - 1 \right) + B_o} \)

Hint:

In reservoir engineering, the formation volume factor is key in determining the volume changes from reservoir to surface conditions. Ensure to account for both water and oil formation volume factors when calculating fractional cuts.

Answer 1

The Correct Option is D

Step 1: Understand the formation volume factor.
The formation volume factor relates the volume of a substance in the reservoir to its volume at the surface condition. The fractional water cut \(f_w\) and its relation to \(f_{ws}\) at different conditions are crucial for material balance in reservoir engineering.
Step 2: Analyzing the given options.
- Option (A): This is not correct because the fractional water cut does not consider the changes in both water and oil factors in the denominator.
- Option (B): This option is also incorrect as it does not appropriately represent the relationship between the water cut and formation volume factors.
- Option (C): This option involves a formulation that doesn’t account for the appropriate fraction of water cut considering both \(B_o\) and \(B_w\).
- Option (D): This option correctly models the relationship between the surface and reservoir fractional water cut by taking into account both \(B_o\) and \(B_w\) in the denominator.
Thus, the correct answer is (D).