Drill Pipe

21 minutes read

Capacity and Displacement

Capacity is the amount of fluid that can be contained in a pipe or an annulus; it is generally expressed as volume per unit length (e.g., barrels per foot). Displacement is expressed either as the length of pipe required to displace a unit volume of fluid (e.g., feet per barrel), or the volume of fluid displaced by a unit length of pipe (e.g., barrels per foot).

These quantities are fundamental to well planning and operations, particularly with respect to drilling fluids, well control and cementing. They can be determined using formulas or read from service company charts or tables.

Capacity and Displacement Formulas

The following formulas are adequate for quick calculations. But because they are based only on the pipe body diameters and do not account for upsets and tool joints, they are approximations only, and should be used with some caution.

$\textrm{Pipe Capacity} = \dfrac{\pi }{4}\cdot ID_{pipe} ^{2}$

$\textrm{Annular Capacity} = \dfrac{\pi }{4}\cdot \left (D_{hole}^2 - OD_{pipe}^2 \right )$

$\textrm{Displacement } = \dfrac{\pi }{4}\cdot \left (OD_{pipe}^2 - ID_{pipe}^2 \right )$

where

ID_pipe= inside diameter of pipe;

OD_pipe= outside diameter of pipe;

D_hole= hole diameter

(Note: in a cased hole, casing ID replaces hole diameter)

With pipe diameter expressed in inches and capacity or displacement expressed in barrels per foot, the constant (π/4) is replaced by 0.0009714, or (1/1029).

For example:

The internal capacity of 4.5 inch, 16.60 lb/ft, plain-end drill pipe (inside diameter of 3.826 inches) is

$\quad 0.0009714\cdot 3.826^2 = 0.0142\, \tfrac{bbl}{ft}$

The annular capacity in an 8.5-inch diameter hole would be

$\quad 0.0009714\cdot (8.5^2 - 4.5^2) = 0.0547\, \tfrac{bbl}{ft}$

Its displacement is

$\quad 0.0009714\cdot (4.5^2 - 3.826^2) = 0.00545\, \tfrac{bbl}{ft}$

Tables

Tabulations of pipe capaciity and displacement are usually included in engineering data books published from oil field service companies and pipe manufacturers. These data books are available in hardcopy and digital formats. Some of the digital versions—notably Halliburton’s eRedbook (a downloadable version of its classic Cementing Tables – include built-in calculators and other interactive applications.

When using these tables, it is important to note the assumptions (for example, the type of upset or tool joint) under which the calculations were made.