# Buoyancy Factor with Two Different Fluid Weights in The Well

Buoyancy Factor is the factor that is used to compensate loss of weight due to immersion in drilling fluid and you can find more information from this article > buoyancy factor calculation .  In that article, it demonstrates the buoyancy formula only for one fluid in the wellbore. However, this time, we will have the details about buoyancy factor when inside and outside fluid are different.

Buoyancy factor with different fluid inside and outside of tubular is listed below;

Where;

Ao is an external area of the component.

Ai is an internal area of the component.

ρo is fluid density in the annulus at the component depth in the wellbore.

ρi is fluid density in the component depth in the wellbore.

ρs is steel weight density. Steel density is 65.4 ppg.

If you can the same mud weight inside and outside, the equation 1 will be like this

Let’s take a look at the following example to get more understanding.

Example

13-3/8” casing shoe was at 2,500’MD/2,000’TVD

9-5/8” casing was run to 6,800’MD/6,000 TVD.

9-5/8” casing weight is 40 ppf and casing ID is 8.835 inch.

Current mud weight is 9.5 ppg oil based mud.

The well bore diagram is show below (Figure 1).

Figure 1 – Wellbore Diagram

The well is planned to cement from shoe to surface and the planned cement weight is 14.0 ppg. The displacement fluid is drilling mud currently used.

• Air weight of casing string
• Buoyed weight of casing in drilling mud
• Buoyed weight of casing when cement is inside casing and drilling mud is outside casing
• Buoyed weight of casing when cement is outside casing and drilling mud is inside casing

Air weight of casing string

Air weight of casing string, lb = length of casing, ft x casing weight, lb/ft

Air weight of casing string, lb = 6,800x 40 = 272,000 lb

Buoyed weight of casing in drilling mud

Figure 2 – Buoyed Weight When Submersed In Drilling Mud

Buoyed weight = Buoyancy Factor (BF) X Air Weight of Casing

Buoyancy Factor (BF) = 0.855

Buoyed weight = 0.855 X 272,000 = 232,489 lb

Buoyed weight of casing when cement is inside casing and drilling mud is outside casing

Figure 3 – Buoyed weight of casing when cement is inside casing and drilling mud is outside casing

We will apply the Equation-1 for this case.

Ao is an external area of the component.

Ao = π x (Outside Diameter of casing)2 ÷ 4

Ao = π x (9.625)2 ÷ 4 = 72.76 square inch

Ai is an internal area of the component.

Ai = π x (Inside Diameter of casing)2 ÷ 4

Ai = π x (8.835)2 ÷ 4 = 61.31 square inch

ρo = 9.5 ppf (mud in the annulus)

ρi = 14.0 ppg (cement inside casing)

ρs = 65.4 ppg.

Buoyancy Factor (BF) = 1.22

Buoyed weight = 1.22 X 272,000 = 331,840 lb

Buoyed weight of casing when cement is outside casing and drilling mud is inside casing

Figure 4 – Buoyed weight of casing when cement is outside casing and drilling mud is inside casing

We will apply Equation-1 for this case as well.

All the calculation parameters are the same.

Ao = π x (9.625)2 ÷ 4 = 72.76 square inch

Ai = π x (8.835)2 ÷ 4 = 61.31 square inch

ρo = 9.5 ppf (mud in the annulus)

ρi = 14.0 ppg (cement inside casing)

ρs = 65.4 ppg.

Buoyancy Factor (BF) = 0.42

Buoyed weight = 0.42 X 272,000 = 114,240 lb

Conclusion: At different stage of the well, you may have different buoyed weight depending on density of fluid inside and outside of the component and it is not always that buoyed weight is less than air weight.

Reference book => Formulas and Calculations for Drilling Operations

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### 5 Responses to Buoyancy Factor with Two Different Fluid Weights in The Well

1. George Heckler says:

An interesting excercise, but there is one additional thing that needs to be considered during a cementing job and that is the differential forces acting across the closed end of the shoe. These act either positively or negitively and could in the worst case cause the pipe to almost float or overload the top casing connections and running equipment. One of the problems I have with recipocating the pipe during a cement job where you also have to add the drag forces.

I understand that you are trying to present a concept, but there are these other considerattons. Keep up with your good work in highlighting drilling engineering concepts.

• George,

Thanks for your comment and it is very useful for everybody.

Regards,
Shyne.

2. Thomas says:

The weight should only be the vertical component (ie TVD instead of MD).

• Thomas,

Weight must be calculated based on measured depth of the string. TVD will be used for hydrostatic pressure calculation.