Volume Capacity and Displacement




Open Hole








Pump Output




Strokes per Minute






pi (3.14159265)


Stroke Length




Pump Efficiency




Pump Liner Inside Diameter




Pump Rod Diameter






1. Mud System Volume - The total mud system volume may be calculated with the drill string either in or out of the hole.

Total Mud Volume = Pit Volume + Hole Volume

2. Pump Output Volume - Pump output tables must be adjusted for estimated or measured pump efficiencies. Triplex pumps usually have an efficiency between 90-98%. Double action duplex pumps usually have an efficiency between 85-95%.

The following two equations calculate pump output at 100% volumetric efficiency. The constant, K, may be changed to obtain units of bbl/STK, gal/STK, or Liter/STK.

Pump Constant, K

Pump Type




Duplex Pump




Triplex Pump




See Appendix, for Pump displacement tables.

3. Mud Pit Volume - The same capacity equations shown in Dilution of Water-Based Muds hold true for volume. Depth will be the actual depth of mud in the mud pits.

Capacity (Mud Pits) 1. Rectangular Mud Pits

Mud Pitcap, bbl

L = Length, ft W = Width, ft h = Height, ft 2. Sloping Sided Mud Pits

Mud Pitcap, bbl

  1. 6146 ft3/bbl Average width
  2. Horizontal Cylindrical Mud Pit

Mud Pitcap, bbl

R2 arccos


  • R - h)J2Rh - h2)
  • 5.61460

Note: Calculator must be set for degrees for above equation. If you wish to use radians on the calculator, simply remove (57.296) from the above equation.

4. Upright Cylindrical Mud Pits

Mud Pitcap, bbl

5.6146 ft3/bbl

Capacity and Displacement (Drill String and Hole)


Outside diameter, in.


Inside diameter, in.


Hole diameter, in.


Annular outer pipe diameter, in.


Annular inner pipe diameter, in.


Closed-ended pipe


Open-ended pipe


1. Capacity - Capacity, as related to drill pipe, drill collars and other tubulars is the volume of fluid the pipe can contain. The internal pipe diameter, ID, (inches) is used in the equation shown below.


Capacity of a wellbore, either cased or open hole, is the volume of fluid the hole can contain. The hole diameter, Dh, or casing ID are used in the equation above.

2. Displacement a. Open-End Pipe - Displacement, as related to drill pipe, drill collars and tubulars is the volume of fluid that the pipe will displace if placed into fluid open ended to allow it to fill inside. The displacement volume equals the volume of metal in the pipe. The pipe's outside diameter, OD, and inside diameter, ID, are used in the equation below.

Displacement/OE, bbl/ft

3. Closed-End Pipe - Displacement, as related to drill pipe, drill collars and tubulars is the volume of fluid that the pipe will displace if placed into fluid with the lower end closed to allow no fluid inside. The pipe's outside diameter, OD, is used in the equation below.


Annulus Capacity and Multiple-Pipe Annulus Capacity

1. Annulus Capacity -Annulus capacity, (Anncap) is the volume contained between two cylinders - one inside the other, such as casing with drill pipe inside. The casing ID, drill pipe OD are used in the calculation.

Annulus capacity, bbl/ft = [(-D),,-.-„iOD') -y y 1029.4

Annulus capacity of pipe or casing in an open hole of diameter, Dh, is calculated using Dh (instead of ID) and OD of the pipe or casing using the equation above.

2. Multiple-Pipe Annulus Capacity -An annulus may contain more than one pipe inside a casing or open hole. To calculate the fluid volume in a multiple annulus use the equation below, which assumes all pipes are the same OD (n = number of pipes in annulus.) When interior pipes are of different sizes, the individual ODs must be squared and summed and the sum subtracted from the ID2 value in the numerator of equation below.

Multiple annulus capacity, bbl/ft = [(ID)2~"(OD)2] K 1029.4

For an open hole with multiple pipes, annulus capacity is calculated based on hole diameter, Dh in equation above, substituting Dh for ID.

Conversion to Other Units

Below are equations that allow annulus capacity and displacement volume calculations to be made in other useful units. In these equations, "D" represents the larger diameter and "d" represents the smaller diameter.

Note: For multiple-pipe annulus volumes substitute the value n(d2) for d2 in equations above when pipes are all same diameter. If not all same diameter, the OD of each pipe must be squared, summed and the sum subtracted from the value of ID2 in the numerator of the appropriate equation above.

Tabulated Capacity and Displacement Data

Tabulated values for capacity and displacements of various sizes, weights and tool-joint tubular goods is found in the Appendix of this Manual.

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