Page 226 - Introduction to Petroleum Engineering

SINGLE‐PHASE FLOW IN PIPE 213
11.4 SINgLE‐PHASE FLOW IN PIPE

Pipes are used extensively to move oil, gas, and water on the well location and from
the location to gathering facilities. We introduce the factors that influence fluid
flow in pipe by considering the relatively simple case of single‐phase flow in pipe.
Flow downstream from the separator should be single‐phase flow.
The movement of fluid in pipe can be laminar or turbulent flow. In laminar fluid
flow, fluid moves parallel to the direction of bulk flow. By contrast, fluid moves in all
directions relative to the direction of bulk flow when fluid flow is turbulent. For a
fluid with a given density and dynamic viscosity flowing in a tube of fixed diameter,
the flow regime is laminar at low flow velocities and turbulent at high flow velocities.
One parameter that is often used to characterize fluid flow is Reynolds number N .
Re
Reynolds number expresses the ratio of inertial (or momentum) forces to viscous
forces. For fluid flow in a conduit, the Reynolds number is
vD
N Re (11.16)

where ρ is the fluid density, v is the bulk flow velocity, D is the tube inner diameter
for flow in a tube, and μ is the dynamic viscosity of the fluid. The choice of units
must yield a dimensionless Reynolds number. In Système Internationale (SI) units,
3
a dimensionless Reynolds number is obtained if fluid density is in kg/m , flow
velocity is in m/s, tube diameter is in m, and dynamic viscosity is in Pa⋅s. Note that
3
1cp 1mPas 10 Pa s.
The Reynolds number for flow in a cylindrical pipe can be written in terms of
volumetric flow rate q. The bulk flow velocity v of a single‐phase fluid flowing in the
cylindrical pipe is related to volumetric flow rate q by

q 4 q
v (11.17)
A D 2
Substituting Equation 11.17 into 11.16, then

vD 4 q
N Re (11.18)
D
Fluid flow in cylindrical pipes is laminar if N Re 2000, and it is considered turbulent
at larger values of the Reynolds number.

Example 11.6 Reynolds Number
Suppose oil is flowing through a circular pipe with volumetric flow rate q 1000
3
/
.
barrels/day. The oil density is 09 /gcc 900kgm and the dynamic viscosity
.
of oil is 2cp 0 002 Pa⋅s. The pipe has a 3 in. inner diameter. Calculate
Reynolds number.