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Mud Hydraulics Fundamentals 27

2.3.1 Flow Regimes
The regimes most commonly encountered in drilling are laminar, turbulent,
and transitional. In a laminar flow, the fluid behaves like a series of parallel
layers moving at uniform or near-uniform velocity. There is no large-scale
movement of fluid particles between layers. The fluid layers nearest the
center of the pipe or annulus generally move faster than the layers adjacent
to the pipe wall or wellbore. Turbulent flow is characterized by velocity
fluctuations among the fluid stream particles, both parallel and axial to the
mean flow stream. These fluctuations break down the boundaries between
the fluid layers, resulting in a chaotic flow pattern.
Transitional flow exhibits characteristics of both laminar and turbulent
regimes. It describes the often hard-to-define region where flow is neither
completely laminar nor completely turbulent. Also reported in the literature
is an additional fluid regime called plug flow. It describes the low-velocity,
sublaminar condition of a fluid moving as a homogeneous, relatively
undisturbed body. This flow regime has not been found in normal drilling
conditions.
It is usually preferred to see laminar flow in the annulus to move
cuttings up the hole and to prevent erosion. Turbulent flow, on the
other hand, is more desirable at the bottom of the hole because it pro-
motes cleaning and cuttings removal. While they are conceptually easy to
visualize, flow regimes may be difficult to identify. Not only does fluid
behavior vary within the circulating system, but more than one flow
regime may exist at the same point in the system. For example, while
the main flow stream in the annulus may exhibit laminar behavior, the
adjacent fluid at the pipe boundary may be in turbulent flow.

Newtonian Fluids
The most common method for determining a fluid’sflowregimeisby
calculating its Reynolds number. For Newtonian fluids inside pipe, the
Reynolds number is defined as
ρvd
N Re = (2.15)
μ
where
3
ρ = fluid density, kg/m
d = inside diameter of pipe, m
μ = fluid viscosity, Pa-s