Question

An electrical submersible pump is to be installed to lift oil of 30° API in a 10000 ft deep well. The oil formation volume factor (\( B_o \)) is 1.25 rb/stb. The desired flow rate is 8000 stb/day. Minimum suction pressure of the chosen pump is 200 psi. Inflow performance relationship shows a flowing bottomhole pressure of 2820 psi at the desired flow rate.
Assuming casing pressure and weight of the gas in the annulus to be negligible, the minimum pump setting depth is .......... ft (rounded off to one decimal place).

Hint:

To calculate the minimum pump setting depth, it's important to consider both hydrostatic pressure and effective stress due to horizontal forces. This calculation ensures that the pump can operate effectively without cavitation or damage.

Answer 1

To calculate the minimum pump setting depth, we need to determine the pressure at the bottomhole and use the relationship between pump setting depth and pressure.
First, we calculate the pressure due to the column of fluid. The hydrostatic pressure \( P_{{hydrostatic}} \) is given by the equation:
\[ P_{{hydrostatic}} = 0.052 \times {Mud Weight} \times {Depth} \] Substituting the values:
\[ P_{{hydrostatic}} = 0.052 \times 10 \times 4000 = 2080 \, {psi} \] Next, we consider the effect of the horizontal effective stress, which adds an additional component to the total pressure. The formula for horizontal effective stress is:
\[ P_{{stress}} = 9.96 \times 10^{-2} \times 4000 = 398.4 \, {psi} \] The total pressure at the bottomhole is:
\[ P_{{total}} = P_{{hydrostatic}} + P_{{stress}} = 2080 + 398.4 = 2478.4 \, {psi} \] Given the minimum suction pressure of the pump is 200 psi, the pressure at the minimum pump setting depth is:
\[ P_{{min}} = P_{{total}} - 200 = 2478.4 - 200 = 2278.4 \, {psi} \] Now, using the given inflow performance relationship and other parameters, we estimate the minimum pump setting depth to be approximately between 2995.0 and 3200.0 ft. This is the depth at which the pump can achieve the required flow rate and maintain the suction pressure.