Page 227 - Introduction to Petroleum Engineering

214 UPSTREAM FACILITIES

Answer
First express all variables in SI units. The inner diameter in SI units is

D 3in.. 0 0762m
0 0254min/.
.
Volumetric flow rate in SI units is
3
3
.
.
q 1000 barrels/day 0 159 m/barrel 1day/ 86400 sec 0 00184 m //s
Reynolds number is
3
.
4 q 4 900 kg/m 3 0 00184 m /s
N 13 3800
Re
.
D 0 002 Pa s 0 0762 m
.
The relationship between fluid flow velocity and pressure change along the
longitudinal axis of the cylindrical pipe is obtained by performing an energy balance
calculation. Figure 11.5 shows the geometry of an inclined cylindrical pipe with length
L along the longitudinal axis and angle of inclination θ. The single‐phase fluid has
density ρ and dynamic viscosity μ. It is flowing in a gravity field with acceleration g.
We make two simplifying assumptions in our analysis that allow us to minimize
external factors and consider only mechanical energy terms. We assume that no
thermal energy is added to the fluid and that no work is done on the system by its
surroundings, for example, no mechanical devices such as pumps or compressors are
adding energy to the system. An energy balance with these assumptions yields the
pressure gradient equation

p p p p (11.19)
L L PE L KE L fric
where p is the pressure. We have written the pressure gradient along the longitudinal
axis of the pipe as the sum of a potential energy term
p gsin , (11.20)

L PE

L
A

V

FIgURE 11.5 Flow in an inclined cylindrical pipe.