Question

The mud density of a well is being increased from 10 to 12 lbm/gal. If the pump is stopped when the interface between the two muds is at a depth of 8,000 ft in

Option 1: 8,000 ft
Option 2: 10 lbm/gal
Option 3: 12 lbm/gal
Option 4: 2 lbm/gal

Answer 1

The pump should be stopped when the interface between the two muds is at a depth of 8,000 ft.

Step-by-step explanation:

To determine when to stop the pump, we need to consider the hydrostatic pressure exerted by the mud column. The hydrostatic pressure is given by the formula P = ρgh, where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the depth of the fluid column.

In this case, the mud density is changing from 10 lbm/gal to 12 lbm/gal, and the depth is 8,000 ft. The difference in density (Δρ) is 2 lbm/gal. Using the conversion factor 1 gal ≈ 8.33 lbm, we find that Δρ ≈ 16.66 lbm/ft³.

Now, considering the original mud density (ρ1 = 10 lbm/gal) and the depth (h = 8,000 ft), we calculate the initial hydrostatic pressure (P1). Then, with the new mud density (ρ2 = 12 lbm/gal) and the same depth, we calculate the final hydrostatic pressure (P2).

The difference in pressure (ΔP = P2 - P1) indicates the additional pressure due to the change in mud density. By comparing this ΔP to the weight of the mud column, we can determine when the pump should be stopped.

Therefore, the pump should be stopped when the interface between the two muds is at a depth of 8,000 ft.