Iranian Journal of Chemical Engineering

Vol. 7, No. 1 (Winter), 2010, IAChE

Resea rch note

Looped Pipeline System for Increasing the Capacity

of Natural Gas Transmission
M. A. Fanaei∗, M. Niknam

Department of Chemical Engineering, Faculty of Eng., Ferdowsi University of Mashhad, I. R.Iran

Abstract
At present, gas engineers use the simple Campbell’s equation to determine the proper
length of parallel gas pipelines. The Campbell’s equation was proposed for horizontal
pipelines with the assumption that the gas compressibility factor and temperature
throughout the pipeline are constant. Therefore, the Campbell’s equation has a notable
error for an inclined pipeline. In this paper, the Campbell’s equation was extended in a
way that it can be used for inclined pipelines. In order to make a comparison between
the extended and original equations, a pipeline with different slopes was used. The
results show that in the case of using a pipeline with more than 2 degrees in slope, the
resultant error is increased to 11 percent by using the original Campbell’s equation.
For validation of the extended Campbell’s equation, the results of this equation are
compared to the results of HYSYS software (version 3.1) in which the temperature and
gas compressibility factor are not considered constant. The results indicate that the
average error of the extended equation is less than 2 percent.

Keywords: Natural Gas pipeline, Looped Pipeline, Optimization

1. Introduction Mass balance equation

In the past, the gas pipeline networks were
∂ρ ∂(ρ u) (1)
designed based on a simple formula such as + =0
∂t ∂x
Weymouth and Panhandle [1, 2], but in
recent years the use of engineering software Momentum balance equation
such as PIPEPHASE [3], PIPESYS [4] and
HYSYS [5] has increased. In general, for the ∂( ρ u ) ∂( ρ u 2 + P) fρ u u
+ = − ρ g sin θ − 2 (2)
prediction of flow rate, pressure and ∂t ∂x D
temperature variation of gas along the
Energy balance equation
pipelines, three equation of mass, momentum
∂ ⎡ ⎛ u2 ⎞⎤
and energy balances should be solved qρ Ad x = ⎢( ρ Ad x )⎜⎜ C v T + + gz ⎟⎟⎥
∂t ⎢⎣ ⎝ 2 ⎠⎥⎦
simultaneously [6]. These equations for a (3)
pipeline with angle θ from horizontal are as ∂ ⎡ ⎛ u2 P ⎞⎤
+ ⎢( ρ Au d x )⎜⎜ C vT + + gz + ⎟⎟⎥
follows: ∂ x ⎢⎣ ⎝ 2 ρ ⎠⎥⎦

∗ Corresponding author: fanaei@um.ac.ir

76
 Looped Pipeline System for Increasing the Capacity of Natural Gas Transmission

In the above equations, the density of the real presented article, Campbell’s equation is
gas could be estimated as follows. extended in a way that it can be used for
inclined pipelines as well.
P
ρ= (4) This article is arranged as follows. First, the
ZRT accuracy of Campbell’s equation is compared
with the results of HYSYS software (in
Different numerical methods such as explicit
appendix, an algorithm is proposed for
and implicit finite difference, the method of
simulation of looped pipelines with given
characteristics and the method of lines [7]
diameter and unknown length in HYSYS
can be used to solve the above mentioned
software). In the next part of this article, after
equations. At steady state the above partial
presenting the way of extending the
differential equations (2 and 3) are converted
Campbell’s equation for inclined pipelines,
to ordinary differential equations and an
the angle range of inclined pipelines for
initial value method such as Euler and
which the extended equation must be used, is
Runge-Kutta can be used for the calculation
determined. Then, two real pipeline case
of pressure and temperature along the
studies are used for comparison of original
pipeline. In HYSYS software, the explicit
and extended Campbell’s equations. Finally,
finite difference method is used for dynamic
a method is presented for the determination
gas pipeline and the Euler method is used for
of optimal length and diameter of parallel
steady state gas pipeline calculations [5].
pipelines using the original or extended
One of the most important difficulties for gas
Campbell’s equation.
transport companies in recent years has been
the increase of gas pressure drop results from
2. Campbell’s equation
the increase of gas flow rate through the
In a looped pipeline system, which is shown
pipeline network. In order to solve this
in Fig. 1, the length of the parallel pipeline
problem the establishment of new pipelines,
(B) is determined in a way that, in spite of
the increase in the number and capacity of
the increase in gas flow rate, the amount of
compressor stations, and strengthening of the
pressure drop in the main pipeline (A+C)
old gas pipelines using a parallel pipeline are
was not changed. Of course, it should be
applied [1].
pointed out that the length and diameter of
The strengthening of gas transport pipelines
the parallel pipeline are interrelated. In other
by using parallel pipes known as looped
words, only the length or the diameter of the
pipelines was first investigated by Campbell.
pipeline can be considered as a design
The results of these investigations are
parameter.
available in most gas engineering textbooks
[1, 2, 8]. In the equation presented by
Campbell to determine the pipelinelength,
the assumptions of horizontal pipelines,
isothermal flow, and constant gas
compressibility factor are used. In the Figure 1. Looped pipeline system

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 Fanaei, Niknam

Campbell was the first one to present an Before extending the Campbell’s equation,
equation to determine the length of the its accuracy was compared with the results
parallel pipeline in a loop system [8]. In obtained from HYSYS software. For this
Campbell’s equation, some assumptions like purpose a horizontal pipeline with a length of
horizontal pipeline, isothermal and steady 107.4 kilometers, diameter of 54.76 inches,
state flow, and constant gas compressibility inlet pressure of 1000 psia, inlet temperature
factor are applied. In the case of using of 45 oC and flow rate of 80 million standard
Weymouth formula to determine the friction cubic meters per day (MMSCMD) is
factor, Campbell’s equation will be as simulated (Fig. 2). The steps used for
follows [1]: simulation of a looped pipeline in HYSYS
software are illustrated in the appendix. The
Qnew 2 composition of the inlet gas is shown in
1− ( )
xf =
Qold (5) Table 1. Then, in order to increase the gas
1
1− flow rate up to 110 MMSCMD, a parallel
DB 8 / 3 2
[1 + ( ) ] pipeline with a 42 inch diameter is used. By
DA
using Campbell’s equation and HYSYS
Where xf represents a fraction of the length of software, the length of the parallel pipeline is
calculated as 89.68 and 91.77 kilometers
the main pipeline (A+C) which is looped
respectively. The resulting error from using
with a parallel pipe B, Qold is the old gas flow
Campbell’s equation in comparison to
rate and Qnew is the new (increased) gas flow
HYSYS software is about 2.3 percent.
rate. xf is defined as follows: Therefore, we can conclude that, in the case
that changing the height of the pipeline is
LA ignorable, Campbell’s equation can be used
xf = (6)
L A + LC with acceptable accuracy.

Figure 2. The simulated diagram of a looped pipeline system.

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 Looped Pipeline System for Increasing the Capacity of Natural Gas Transmission

Table1. The mole percent of inlet gas

Methane Ethane Propane i- Butane n-Butane i-Pentane

88.3 3.84 1.18 0.24 0.33 0.13

Carbon
n-Pentane Hexane n-Heptane Nitrogen
monoxide
0.09 0.09 0.16 5.58 0.06

3. Generalization of Campbell’s equation governing the inclined pipelines network

As it has already been discussed in the (Fig. 3), while considering the isothermal and
previous section, Campbell’s equation can be steady state flow, and assuming the constant
used for horizontal looped pipeline systems gas compressibility factor is as follows [1].
with desirable accuracy. But the most
important question is how the accuracy of the 16 ρ sc2 Q 2 Z avTav R f
P1 = e S Pn2+1 + (
2
) Le (7)
Campbell’s equation is changed with π 2 gc D5M
changing the pipeline slope. To answer this
question, first the Campbell’s equation is where
extended for inclined pipelines. Then the i −1

accuracy of the Campbell’s equation and ∑Sj

n
(e Si − 1)e j =1
extended equation are compared by using an Le = ∑ Li (8)
i =1 Si
inclined pipeline with different angles.
In general, the equations governing the
2 M g zi
inclined pipelines are different from the Si = (9)
equations of horizontal pipelines. In the g c Z av Tav R
calculation of inclined pipelines, the concept
n
S = ∑ Si
of equivalent length (Le) instead of real
(10)
length (L) is used. Briefly, the equation i =1

Figure 3. A typical network of inclined pipelines

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 Fanaei, Niknam

The extended Campbell’s equation is Table 2, we can conclude that, when the
obtained if the length of pipeline A and C is slope of the pipeline is less than 0.5 degrees,
replaced by the equivalent lengths (LAe and the resulted error of Campbell’s equation will
LCe) in equations 5 and 6. Therefore the be less than 3 percent. Therefore, for an
fraction of the equivalent length of the main inclined looped pipeline with angles less than
pipeline (xfe) that must be looped with a new 0.5 degrees, the changes in the elevation of
parallel pipeline can be calculated by the the pipelines can be ignored. However, for
following equation. inclined pipelines with more than 2 degrees,
the resulted error will increase to more than
Qnew 2 11 percent if we ignore the changes in the
1− ( )
L Ae Qold elevation of the pipelines. Therefore, in this
x fe = = (11)
L Ae + LCe 1−
1 case, the extended Campbell’s equation is
D advisable. In addition, as in the previous
[1 + ( B ) 8 / 3 ]2
DA section, the accuracy of the extended
Campbell’s equation was compared to the
Having used the above equation and results of HYSYS software. The results show
determined the equivalent length of the that, the average error of the extended
required parallel pipelines, the real length of equation is less than 2.3 percent.
the parallel pipeline can be calculated by trial
and error and by using equation 8.
The results of Campbell’s equation and its
extended form are compared for an inclined
pipeline with different angles. For this
purpose, a pipeline with the length of 100
kilometers, 40 inch diameter, inlet pressure
of 1200 psia and inlet temperature of 50 oC is
considered. Moreover, a parallel pipeline Figure 4. The diagram of inclined looped pipeline
with a 35 inch diameter is used to remove the
problem of pressure drop created due to the
increase of flow rate from 50 to 60 4. Case studies
MMSCMD. The general perspective of the In this section the results of original and
mentioned pipeline is shown in Fig. 4. The extended Campbell's equations are compared
calculations for angles from zero to 50 for two real gas transport networks of Iran.
degrees are repeatedly done and the obtained The first case study is a part of the gas
results are shown in Table 2. It is necessary pipeline between Tehran and Qum, and the
to mention that, in all calculations, the gas second is the gas transport pipeline from
compressibility factor is considered to be Aliabad Katol to Shahrood. The second case
equal to 0.9, average temperature of gas study pipeline has the higher elevation
equal to 40°C, and molecular weight equal change compared to the first one.
to 16.04. With regard to the offered results in

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 Looped Pipeline System for Increasing the Capacity of Natural Gas Transmission

Table 2. The obtained lengths of parallel pipeline for an inclined looped pipeline system with different angles.
Length of parallel pipeline Resulted error in comparison to
Angle (degree)
(km) horizontal looped system (%)

0 46.700 --------------------

0.25 47.430 1.54

0.5 48.162 3.03

1 49.623 5.90

2 52.540 11.12

3 55.403 15.70

5 60.836 23.20

10 71.856 35.00

20 83.673 44.19

30 88.682 47.34

50 92.599 49.57

4.1. Gas transport pipeline between Tehran Campbell’s equation and its extended form,
and Qum the calculated length of the parallel pipe will
This pipeline has a length of 107.4 km and be 63.67 and 64.23 kilometers, respectively.
average inside diameter of 55 inches (Fig. 5). As it can be observed, the length of the
Other specifications of the selected pipeline parallel pipeline obtained through these two
which included six pipe segments are equations will be almost the same. The first
presented in Table 3. The mole fraction of reason is that the elevation changes for all
gas transmitted in this pipeline is also pipelines are small, and the second reason is
presented in Table 1. To increase the that the elevation changes of some pipes are
capacity of the network from 80 to 100 positive and the others are negative. The
MMSCMD, a parallel pipeline with an inner former reason causes the effects of the slope
diameter of 45 inches is used. The length of on calculations for the length of the parallel
the needed parallel pipeline is calculated first pipelines to be neutralized (Fig. 5).
by Campbell’s equation, while ignoring the Therefore, when the changes in the elevation
changes in the elevation of each pipe, and of the pipes are rather low, the application of
then by using the extended Campbell’s Campbell’s equation with regard to its
equation, while the real slope of each pipe is simplicity is more preferable than the
taken into consideration. In the case of using extended form.

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 Fanaei, Niknam

600

500

400

Elevation (m)
300

200

100

0
0 20 40 60 80 100 120
Length (km)

Figure 5. Gas transport pipeline between Tehran and Qum.

Table 3. Specification of the gas transport pipeline between Tehran and Qum.

Slope from
Pipe number Length (km) Elevation change (m) Average temperature (oC)
horizontal (degree)

1 56 -386 45.0 -0.395

2 6.2 -50 44.1 -0.462
3 9.0 -30 43.45 -0.190
4 16.8 70 42.3 0.239
5 10.2 61 41.2 0.343
6 9.2 211 40.45 1.314

4-2. Gas transport pipeline between Aliabad is calculated by using Campbell’s and
Katol and Shahrood extended Campbell’s equations, is 42.49 and
This pipeline has a length of 69 km and an 44.28 km respectively. As it can be observed,
average inside diameter of 15 inches (Fig. 6). the calculated length of the parallel pipeline
Other specifications of this pipeline, which by using the Campbell’s equation has about 4
included five pipe segments, are presented in percent error in comparison to extended
Table 4. The mole fraction of gas transmitted Campbell’s equation. Therefore, for this
in this pipeline is shown in Table 5. To pipeline, which has an average slope of about
increase the capacity of the pipeline from 2.0 0.75 degree, the use of extended Campbell’s
to 2.5 MMSCMD, a parallel pipeline with an equation is more preferable than the
inner diameter of 12.0 inches is used. The Campbell’s equation.
length of the needed parallel pipeline, which

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 Looped Pipeline System for Increasing the Capacity of Natural Gas Transmission

1400

1200

1000

Elevation (m) 800

600

400

200

0
0 20 40 60 80
Length (km)

Figure 6. Gas transport pipeline between Aliabad and Shahrood.

Table 4. Specification of the gas transport pipeline between Aliabad and Shahrood.

Average Slope from

Pipe number Length (km) Elevation change (m)
temperature (oC) horizontal (degree)

1 12.9 193.3 14.28 0.859

2 10.10 45.8 12.52 0.257

3 16.9 1070 8.69 3.630

4 12.20 -270.4 7.54 -1.270

5 16.9 77.25 9.47 0.262

Table 5. The mole percent of inlet gas

Methane Ethane Propane i- Butane n-Butane i-Pentane

98.510 0.669 0.079 0.020 0.073 0.026

Carbon
n-Pentane Hexane+ Nitrogen
dioxide

0.020 0.095 0.480 0.028

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 Fanaei, Niknam

5. The optimization of looped pipeline has an optimal diameter of 42 inches. The

system length of this pipeline, according to equation
As previously mentioned, in the looped 11, is almost 70.2 km.
pipeline system, in order to determine the
length of the parallel pipeline, the diameter 6.5

of the parallel pipeline is considered as an 6.45

independent variable. In other words, in the

CB /Cp x 107
6.4
case of changing the diameter of the parallel
pipeline, its length will also be changed 6.35

according to equation 5 or 11. In this section,

6.3
a method is introduced for the determination
of the optimal diameter (and length) of the 6.25
35 37 39 41 43 45
parallel pipeline. For this purpose the total Inner Diameter (in)
cost of purchasing and installing the parallel
pipe are considered as an objective function. Figure 7. Values of the objective function versus the
The purchasing and installation costs of diameter of the parallel pipeline

pipelines with a diameter of more than one

inch can be calculated as follows [9]: 6. Conclusions
The Campbell’s equation is a simple and
1.5 popular equation for calculating the length of
⎛ DB ⎞
CB = CP ⎜ ⎟ LA (12) horizontal looped pipelines. Before
⎝ 0.0254 ⎠ extending the Campbell's equation, its
accuracy was compared to HYSYS software.
In this equation, Cp represents the purchasing The obtained results show that the
price and the installation cost of steel Campbell’s equation has the acceptable
pipelines with a one inch inside diameter and accuracy in determining the length of the
one meter length, and DB is the inner parallel pipeline used in horizontal networks
diameter of the looped pipeline. The inner (the obtained error is less than 2 percent).
diameter of the parallel pipeline must be But with increasing the slope of the pipeline,
determined based on the minimization of the the accuracy of the Campbell's equation was
objective function. Of course, with regard to decreased. In the next step, the Campbell’s
the dependence of the length and diameter of equation was extended in a way that it can be
the parallel pipeline (referring to equation 5 used for inclined pipelines. The comparison
or 11), the optimization should be carried out between the extended Campbell's equation
numerically or graphically. For example, the and HYSYS software show that the obtained
values of the objective function versus the error in calculating the length of the parallel
inner diameter of the parallel pipeline for the pipeline is less than 2 percent. In addition,
gas transport network explained in section the results show that when changes in the
4-1 are shown in Fig. 7. As it can be seen, for elevation of the pipelines are rather low (the
the mentioned network, the parallel pipeline average slope is less than 0.5 degree), the

84 Iranian Journal of Chemical Engineering, Vol. 7, No. 1

 Looped Pipeline System for Increasing the Capacity of Natural Gas Transmission

application of Campbell’s equation with Appendix: Proposed algorithm for

regard to its simplicity is more preferable simulation of looped pipelines in HYSYS
than the extended form (the obtained error is When the diameter of the parallel pipeline is
less than 3 percent). known, the following algorithm is used for
simulation of the looped pipeline system
Notation using the HYSYS software:
A Cross-sectional area of pipe (m2)  First, the main gas pipeline is simulated
CB Purchase and installation cost of pipe without increasing the gas flow rate (Q
CP A constant equal to the purchase and = Qold). To do so, the PIPE SEGMENT
installation cost of a 1-in diameter of a or PIPESYS elements in the HYSYS
steel pipe per meter of pipe length software must be used [4, 5]. Of course,
CV Specific heat at constant volume (J/kg it is necessary to simulate the main
K) pipeline by using two separate pieces of
D Inner diameter of the pipe (m) pipe known as A and C.
f Moody friction factor  A pipeline B (parallel pipeline) with a
g Gravitational acceleration (m/s2) known diameter is added to the above
L Length of the pipe (m) system. Then by using two SET (an
M Molecular weight of the gas (kg/kmol) element of HYSYS software [5]) the
P Pressure (Pa) pipeline B and pipeline A with the same
Q Gas flow rate at standard condition length is set, the length of pipeline C is
(MMSCMD) set equal to the total length of the main
q The added heat per unit mass per unit pipeline minus the length of pipeline A.
time (W/kg) Now, the input of gas flow rate is set
R Gas constant (J / kmol K) according to the new amount (Q= Qnew).
T Gas temperature (K)  By using the ADJUST element of the
t Time (s) HYSYS software [5], the gas flow rate
u Gas velocity (m/s) between the pipelines A and B is divided
xf Fraction of the length of the main into such a way that the pressure of the
pipeline which is looped with a parallel two pipelines is the same at the junction.
pipe  Now, by using another ADJUST
Z Gas compressibility factor element, the length of pipe A should be
z Elevation change of the pipeline (m) changed in a way that the outlet pressure
 Angle of pipeline from horizontal of pipeline C is the same as the main
 Gas density (kg/m3) pipeline before increasing the gas flow
Subscripts rate.
s.c Standard condition The diagram of the mentioned algorithm in
a.v Average HYSYS is shown in Fig. 2.
i i th pipe segment
e Equivalent

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 Fanaei, Niknam

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Pipeline design and construction, American [8] Campbell, J. M., Gas Conditioning and
Society of Mechanical Engineers, 2th Processing, Vol. 1, Campbell Petrolum
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[4] Pipesys User Guide, Aspen Technology, engineers, McGraw-Hill, New York, 5th
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