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50 Part I Liquid Drilling Systems

Calculating surge and swab pressures can be a complex undertaking,
depending on the pipe configuration and the hole geometry. Burkhardt
(1961) developed a relationship between well geometry and the effect of
the fluid being dragged by the pipe. Based on Burkhardt’swork,the
effective annular velocity is equal to
(2.80)
v e = v m − κv p
where

v e = effective annular velocity, ft/s or m/s
v m = mud velocity, ft/s or m/s
v p = pipe velocity, ft/s or m/s

and κ is referred to as the clinging constant, which is a function of
annular geometry. Burkhardt presented a chart for determining the value
of κ in both laminar flow and turbulent flow. We found that the chart
can be replaced by the following correlations with minimal error. For
laminar flow, the correlation is

d p
κ = 0:275 + 0:25 (2.81)
d h
where

d p = outer diameter of pipe, in or mm
d h = hole diameter, in or mm
For turbulent flow, the correlation is

d p
κ = 0:1 + 0:41 (2.82)
d h
For closed-end pipes, such as a casing string with a float shoe, the mud
velocity can be calculated by
2 !
d
p
v m = − v p 2 2 (2.83)
d − d
h p
For open-end pipes, the mud velocity can be calculated by

2 2 4 !
4d ðd h − d p Þ − 3d
p p
v m = − v p 2 2 (2.84)
2
2
4d ðd h − d p Þ ðd − d Þ + 6d 4
p h p p