Pressure Drop Evaluation Along Pipelines
Pressure Drop Evaluation Along Pipelines
Pressure Drop Evaluation Along Pipelines
The simplest way to convey a fluid, in a contained system from Point A to Point B, is by
means of a conduit or pipe (Fig. 1).
Contents
1 Piping design
2 Bernoulli equation
6 Multiphase flow
o 6.1 Flow regimes
6.1.1 Bubble
8 Nomenclature
9 References
11 External links
12 See also
Piping design
The minimum basic parameters that are required to design the piping system include, but are
not limited to, the following.
The distance between Point A and Point B (or length the fluid must travel) and
equivalent length (pressure losses) introduced by valves and fittings.
These basic parameters are needed to design a piping system. Assuming steady-state flow,
there are a number of equations, which are based upon the general energy equation, that can
be employed to design the piping system. The variables associated with the fluid (i.e., liquid,
gas, or multiphase) affect the flow. This leads to the derivation and development of equations
that are applicable to a particular fluid. Although piping systems and pipeline design can get
complex, the vast majority of the design problems encountered by the engineer can be solved
by the standard flow equations.
Bernoulli equation
The basic equation developed to represent steady-state fluid flow is the Bernoulli equation
which assumes that total mechanical energy is conserved for steady, incompressible, inviscid,
isothermal flow with no heat transfer or work done. These restrictive conditions can actually
be representative of many physical systems.
The equation is stated as
(Eq. 1)
where
Z
V
g
and
HL
=
=
=
=
pressure, psi,
density, lbm/ft3,
velocity, ft/sec,
gravitational constant, ft/sec2,
=
=
=
=
V
g
P
and
d
=
=
=
=
velocity, ft/sec,
gravitational constant ft/sec2,
pressure drop, psi,
density, lbm/ft3,
D
V
and
=
=
=
density, lbm/ft3,
pipe internal diameter, ft,
flow velocity, ft/sec,
viscosity, lbm/ft-sec.
d
SG
Ql
and
V
=
=
=
=
viscosity, cp,
pipe inside diameter, in.,
specific gravity of liquid relative to water (water = 1),
liquid-flow rate, B/D,
= velocity, ft/sec.
d
S
= viscosity, cp,
= pipe inside diameter, in.,
specific gravity of gas at standard conditions relative to air (molecular weight divided
=
by 29),
and
Qg = gas-flow rate, MMscf/D.
The Moody friction factor, f, expressed in the previous equations, is a function of the
Reynolds number and the roughness of the internal surface of the pipe and is given by Fig. 3.
The Moody friction factor is impacted by the characteristic of the flow in the pipe. For
laminar flow, where Re is < 2,000, there is little mixing of the flowing fluid, and the flow
velocity is parabolic; the Moody friction factor is expressed as f = 64/Re. For turbulent flow,
where Re > 4,000, there is complete mixing of the flow, and the flow velocity has a uniform
profile; f depends on Re and the relative roughness (/D). The relative roughness is the ratio
of absolute roughness, , a measure of surface imperfections to the pipe internal diameter, D.
Table 9.1 lists the absolute roughness for several types of pipe materials.
Table 1
If the viscosity of the liquid is unknown, Fig. 4 can be used for the viscosity of crude oil, Fig.
5 for effective viscosity of crude-oil/water mixtures, and Fig. 6 for the viscosity of natural
gas. In using some of these figures, the relationship between viscosity in centistokes and
viscosity in centipoise must be used
(Eq. 7)
where
and
SG
=
=
specific gravity.
=
=
=
=
=
(Eq. 9)
where
HL
L
C
d
Ql
and
gpm
=
=
=
=
=
Table 2
Pressure drop can be calculated from
(Eq. 10)
(Eq. 11)
where
w
g
A
V1
f
L
D
P1
and
P2
=
=
=
=
=
=
=
=
Simplified equation
For practical pipeline purposes, Eq. 11 can be simplified to
(Eq. 12)
where
P1
P2
S
Qg
Z
T
f
d
and
L
=
=
=
=
=
=
=
=
= length, ft.
All three are effective, but the accuracy and applicability of each equation falls within certain
ranges of flow and pipe diameter. The equations are stated next.
Weymouth equation
This equation is used for high-Reynolds-number flows where the Moody friction factor is
merely a function of relative roughness.
(Eq. 13)
where
Qg
d
P1
P2
L
T1
S
and
Z
=
=
=
=
=
=
=
Panhandle equation
This equation is used for moderate-Reynolds-number flows where the Moody friction factor
is independent of relative roughness and is a function of Reynolds number to a negative
power.
(Eq. 14)
where
E
efficiency factor (new pipe: 1.0; good operating conditions: 0.95; average operating
conditions: 0.85),
= gas-flow rate, MMscf/D,
= pipe ID, in.,
= upstream pressure, psia,
= downstream pressure, psia,
= length, miles,
= temperature of gas at inlet, R,
= specific gravity of gas,
=
Qg
d
P1
P2
Lm
T1
S
and
Z = compressibility factor for gas, dimensionless.
Spitzglass equation
(Eq. 15)
where
Qg
hW
and
d
=
=
Assumptions:
f
T
P1
Z
and
P
=
=
=
=
< 10% of P 1 .
The Spitzglass equation is recommended for low-pressure vent lines < 12 in. in diameter (P
< 10% of P1).
The petroleum engineer will find that the general gas equation and the Weymouth equation
are very useful. The Weymouth equation is ideal for designing branch laterals and trunk lines
in field gas-gathering systems.
Multiphase flow
Flow regimes
Fluid from the wellbore to the first piece of production equipment (separator) is generally
two-phase liquid/gas flow.
The characteristics of horizontal, multiphase flow regimes are shown in Fig. 8. They can be
described as follows:
Bubble: Occurs at very low gas/liquid ratios where the gas forms bubbles that rise to
the top of the pipe.
Plug: Occurs at higher gas/liquid ratios where the gas bubbles form moderate-sized
plugs.
Stratified: As the gas/liquid ratios increase, plugs become longer until the gas and
liquid flow in separate layers.
Wavy: As the gas/liquid ratios increase further, the energy of the flowing gas stream
causes waves in the flowing liquid.
Slug: As the gas/liquid ratios continue to increase, the wave heights of the liquid
increase until the crests contact the top of the pipe, creating liquid slugs.
Spray: At extremely high gas/liquid ratios, the liquid is dispersed into the flowing-gas
stream.
Fig. 10Two-phase-flow patterns in vertical flow (courtesy of AMEC Paragon).
Bubble
Where the gas/liquid ratios are small, the gas is present in the liquid in small, variablediameter, randomly distributed bubbles. The liquid moves at a fairly uniform velocity while
the bubbles move up through the liquid at differing velocities, which are dictated by the size
of the bubbles. Except for the total composite-fluid density, the bubbles have little effect on
the pressure gradient.
Slug flow
As the gas/liquid ratios continue to increase, the wave heights of the liquid increase until the
crests contact the top of the pipe, creating liquid slugs.
Transition flow
The fluid changes from a continuous liquid phase to a continuous gas phase. The liquid slugs
virtually disappear and are entrained in the gas phase. The effects of the liquid are still
significant, but the effects of the gas phase are predominant.
Annular mist flow
The gas phase is continuous, and the bulk of the liquid is entrained within the gas. The liquid
wets the pipe wall, but the effects of the liquid are minimal as the gas phase becomes the
controlling factor. Fig. 11[2] shows the various flow regimes that could be expected in vertical
flow as a function of the superficial velocities of gas and liquid flow.
Fig. 11Vertical-multiphase-flow map (after Taitel et al.).[2]
Table 3
f
L
W
M
and
d
=
=
=
=
=
=
=
=
=
There are several notable characteristics associated with pressure drop because of elevation
changes in two-phase flow. The flow characteristics associated with the elevation changes
include:
In downhill lines, flow becomes stratified as liquid flows faster than gas.
The depth of the liquid layer adjusts to the static pressure head and is equal to the
friction pressure drop.
In low gas/liquid flow, the flow in uphill segments can be liquid "full" at low flow
rates. Thus, at low flow rates, the total pressure drop is the sum of the pressure drops
for all of the uphill runs.
With increased gas flow, the total pressure drop may decrease as liquid is removed
from uphill segments.
The pressure drop at low flow rates associated with an uphill elevation change may be
approximated with Eq. 19.
(Eq. 19)
where
PZ = pressure drop because of elevation increase in the segment, psi,
SG = specific gravity of the liquid in the segment, relative to water,
and
Z = increase in elevation for segment, ft.
The total pressure drop can then be approximated by the sum of the pressure drops for each
uphill segment.
Resistance coefficients
The head loss in valves and fittings can be calculated with resistance coefficients as
(Eq. 20)
where
HL
Kr
D
and
V
=
=
=
velocity, ft/sec.
Table 4
Table 5
Table 5 (Cont'd)
Table 5 (Cont'd)
Table 5 (Cont'd)
Flow coefficients
The flow coefficient for liquids, CV, is determined experimentally for each valve or fitting as
the flow of water, in gal/min at 60F for a pressure drop of 1 psi through the fitting. The
relationship between flow and resistance coefficients can be expressed as
(Eq. 21)
In any fitting or valve with a known CV, the pressure drop can be calculated for different
conditions of flow and liquid properties with Eq. 22.
(Eq. 22)
where
QL
and
SG
Again, the CV is published for most valves and fittings and can be found in Crane Flow of
Fluids,[3] Engineering Data Book,[4] Cameron Hydraulic Data Book,[5] as well as the
manufacturers technical data.
Equivalent lengths
The head loss associated with valves and fittings can also be calculated by considering
equivalent "lengths" of pipe segments for each valve and fitting. In other words, the
calculated head loss caused by fluid passing through a gate valve is expressed as an
additional length of pipe that is added to the actual length of pipe in calculating pressure
drop.
All of the equivalent lengths caused by the valves and fittings within a pipe segment would
be added together to compute the pressure drop for the pipe segment. The equivalent length,
Le, can be determined from the resistance coefficient, Kr, and the flow coefficient, CV, using
the formulas given next.
(Eq. 23)
(Eq. 24)
and
(Eq. 25)
where
Kr
D
f
d
and
CV
=
=
=
=
Table 6 shows equivalent lengths of pipe for a variety of valves and fittings for a number of
standard pipe sizes.
Table 6
Nomenclature
Z
P
V
g
HL
f
L
D
P
SG
Ql
T
PZ
Z
HL
Kr
CV
Kr
= operating temperature, R,
= pressure drop because of elevation increase in the segment, psi,
= increase in elevation for segment, ft.
= head loss, ft,
= resistance coefficient, dimensionless
= flow coefficient for liquids, dimensionless.
= resistance coefficient, dimensionless,