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This research work on “Modelling and Simulation of Leakage-Induced Pressure drops along oil
and gas pipelines tends to develop flow equations that can detect and localize leakages in oil
and gas pipelines by modifying the Darcy-weisbach equation for liquid/oil flow, and the
Panhandle B equation for natural gas flow in pipelines. These modified equations were
simulated using matlab to show how flow rate values for the oil and gas pipelines vary when;
the pipeline is working at full capacity, ie no leak, when the pipe is opened, ie with leak, at
different leak diameters, and when a host is inserted into the pipeline for oil/gas
bunkering.The natural gas used is methane while the oil is gasoline.
This research work was necessitated by the reports that the United States of America lost
approximately $6.75B to pipeline incidences between 1986-2012. Nigeria also lost $10.9bn to
oil theft(bunkering) and vandalism between 1999 to 2011. Thus, owing to the fact that there is
increasing demands for oil and gas products, and their bye products all over the world cum the
climatic changes, distortion of aquatic ecosystems, the environmental degradation, property
damages and the billions of dollars spent in cleaning up these spill, there is great need for all
hands to be on deck to checkmate this ugly trend. Hence, the need for leakage detection and
localization cannot be over-emphasized.
The materials used in this work were obtained from the databases of oil companies in Nigeria,
oil spill intelligence report, shell, oil and gas journals, U.S institute of standards and safety, etc.
The simulation results for oil and gas follow similar trend and shows that; the flow rate is
inversely proportional to pipeline lengths, the flow rate decreases as leak diameter increases.
Above all, this project discovered from the simulation result that if a long and wide host is
inserted into a pipeline for oil bunkering, the difference in flow rates is infinitesimal that control
room engineers term it “small leak”when huge quantities of oil or gas is being taken away from
the pipeline.
It is recommended that pipeline engineers should treat small variations in flow parameters
with all urgency and alacrity instead of terming it small leak.




Title page i
Approval page ii
Certification page iii
Dedication iv
Acknowledgement v
Abstract vi
Table of contents vii
List of Figures xii
List of Tables xiv
List of Graphs xv
List of Abbreviations xvi
Appendixes xviii
1.1 Background of the study 1
1.2 Significance of the study 5
1.3 Problem statement 5
1.4 Objectives of the project 5
1.5 Scope of the study 6
1.6 Thesis structure or organisation 6
2.0 Oil exploration and production in Nigeria 7
2.0.1 Natural gas exploration and production 9
2.0.2 Downstream operations 10
2.0.3 Upstream operations 10
2.0.4 Production capacity and supply 11
2.1 Pipelines for oil and gas 12
2.1.1 Pipeline operations 13
2.1.2 Components of a pipeline 14
2.1.3 Maintenance of pipeline 18
2.2 Pipeline failures in the oil and gas industries in the Niger Delta area
of Nigeria. 18
2.3 Pipeline Leak detection techniques 20
2.3.1 Biological methods 21
2.3.2 Hardware-based methods 21
2.3.3 Software-based method 22
2.3.4 Comparison of key attributes of different methods 23
2.4 Communication systems for pipeline protection 25
2.4.1 Fibre optical cable 25
2.4.2 Scada system 27
2.4.3 Monitoring of gas leak detection 30
2.5 Basic fluid analysis and properties 31
2.6 Newton’s law of viscosity 31
2.7 Newtonian / non-newtonian fluids 33
2.8 Pressure 35
2.9 Uniform flow, steady flow 35
2.10 Compressible or incompressible 37
2.11 Three-dimensional flow 37
2.12 Mass flow rate 38
2.13 Volume flow rate – discharge 38
2.14 Bernoulli’s equation 38
2.15 Real fluids 40
2.16 Laminar and turbulent flow 41
2.17 Pressure loss due to friction in a pipeline 44
2.18 Pressure loss during laminar flow in a pipe 46
2.19 Pressure loss during turbulent flow in a pipe 47
2.20 The value of f for laminar flow 48
2.21 Colebrook- white equation for frictional factor f 48
2.22 Moody equation and diagram/chart 48
2.23 Density and specific gravity of liquids 51
2.24 Specific gravity and compressibility factor of gas 52
3.1 Pipeline design,equation and modeling 53
3.2 Pressure drop for gas flow in pipes 54
3.3 Practical equation for gas flows in pipeline 55
3.4 The Weymouth equation 57
3.5 Panhandle A equation 57
3.6 Panhandle B equation 58
3.7 Application of the formulas 59
3.8 Modification of panhandle B equation for leak detection in gas pipeline 60
3.9 Materials and method 61
3.10 Matlab simulation parameters and programs for natural gas(methane) 63
3.11 Pressure drop for liquid (oil) flow in pipes 69
3.12 Modification of the Darcy- weisbach equation for leakage detection in oil pipeline 63
3.13 Matlab simulation of the modified liquid (gasoline) flow in pipeline 71
4.1 Results and Analysis 75
5.1 Conclusion 86
5.2 Recommendations 87



Pipeline networks are the most economic and safest mode of transportation for oil, gases and
other fluid products. As a means of long-distance transport, pipelines have to fulfill high
demands of safety, reliability and efficiency. If properly maintained, pipelines can last
indefinitely without leaks. Most significant leaks that do occur are caused by damage from
nearby excavation equipment. Therefore, it is critical to call authorities prior to excavation to
assure that there are no buried pipelines in the vicinity. If a pipeline is not properly maintained, it
can begin to corrode slowly, particularly at construction joints, low points where moisture
collects, or locations with imperfections in the pipe. However,these defects can be identified by
inspection tools and corrected before they progress to a leak. Other reasons for leaks include
accidents, terrorism,or earth movement ,or sabotage[1].
In Nigeria, the Department of Petroleum Resources(DPR) estimated 1.89 million barrels of
petroleum were spilled into the Niger Delta region of Nigeria between 1976 and 1996 out of a
total of 2.4 million barrels spilled in 4,835 incidents(approximately 220 thousand cubic
metres)[2]. A UNDP(United nations Development programme) report states that there have
been a total of 6,817 oil spills between 1976 and 2001, which account for a loss of three million
barrels of oil, of which more than 70% was not recovered[3]. Most of these spills occurred offshore
(69%), a quarter was in swamps and 6% spilled on land. Some spills are caused by
sabotage and thieves, however most are due to poor maintenance by oil companies (4).
The Nigerian National Petroleum Corporation places the quantity of petroleum spilled into the
environment yearly at 2,300 cubic metres with an average of 300 individual spills annually[5].
However, because this amount does not take into account “minor” spills, the World Bank argues
that the true actual of petroleum spilled into the environment could be as much as ten times the
officially claimed amount. The largest individual spills include the blowout of a Texaco offshore
station which in 1980 dumped an estimated 400,000 barrels (64,000 m3) of crude oil into the
Gulf of Guinea and the Royal Dutch Shell’s Forcados Terminal tank failure which produced a
spillage estimated at 580,000 barrels (92,000 m3)[6]. In 2010, Baird reported that between 9
million and 13 million barrels have been spilled in the Niger Delta since 1958[7]. Junger even
calculated that the total amount of petroleum in barrels spilled between 1960 and 1997 is
upwards of 100 million barrels (16,000,000 m3[8].
Oil spills in Nigeria are a common occurrence; it has been estimated that between 9 million to
13 million barrels have been spilled since oil drilling started in 1958[5]. The government
estimates that about 7,000 spills occurred between 1970 and 2000[5]. Causes include corrosion
of pipelines and tankers (accounts for 50% of all spills), sabotage (28%), and oil production
operations (21%), with 1% of the spills being accounted for by inadequate or non-functional
production equipment. A reason that corrosion accounts for such a high percentage of all spills
is that as a result of the small size of the oilfields in the Niger Delta, there is an extensive
network of pipelines between the fields. Many facilities and pipelines have been constructed to
older standards, poorly maintained and outlived their estimated life span[4]. Sabotage is
performed primarily through what is known as “bunkering”, whereby the saboteur taps a
pipeline, and in the process of extraction sometimes the pipeline is damaged. Oil extracted in this
manner can often be sold for cash compensation. Nigerian regulations are weak and rarely
enforced allowing oil companies, in essence, to self-regulate.
Sabotage and theft through oil siphoning has become a major issue in the Niger River Delta
states as well, contributing to further environmental degradation. Damaged lines may go
unnoticed for days, and repair of the damaged pipes takes even longer. Oil siphoning has
become a big business, with the stolen oil quickly making its way onto the black market. While
the popularity of selling stolen oil increases, the number of deaths are increasing. In late
December 2006, more than 200 people were killed in the Lagos region of Nigeria in an oil line
explosion[9]. Nigerian regulations of the oil industry are weak and rarely enforced allowing, in
essence, the industry to self-regulate. However, these defects can be identified by inspection
tools and corrected before they progress to a leak. Other reasons for leaks include accidents,
terrorism, earth movement, or sabotage.
Appendix A describes succinctly number of pipelines by diameter, a summary of the various
causes of pipeline failure, number of oil spill by location and failure rates for the six Niger Delta
states of Akwaibom, Crossriver, Bayelsa, Delta, Edo and River states.
On a global scale, the story is the same. On April 20, 2010, the Deepwater Horizon offshore
drilling rig exploded in Gulf of Mexico, killing 11 people. Two days later, the rig sank, causing
the riser (a 5,000-foot-long pipe that connects the wellhead to the rig) to detach and start leaking
oil. Shortly thereafter, U.S. Coast Guard investigators discovered a second leak in the wellhead
itself. For weeks, as much as 60,000 barrels of oil per day leaked into the water, threatening
wildlife along the Louisiana Coast. To date, it is the largest oil spill in U.S. history[10].
On Nov. 1, 2007, a 12-inch-diameter pipeline segment operated by Dixie Pipeline Co. was
transporting liquid propane when it ruptured in a rural area near Carmichael, Mississippi. The
resulting gas cloud expanded over nearby homes and ignited, creating a large fireball that was
heard and seen from miles away. About 430,626 gallons of propane were released. As a result of
the ensuing fire, two people were killed and seven people sustained minor injuries. Four houses
were destroyed, and several others were damaged. About 71.4 acres of grassland and woodland
were burned. Dixie Pipeline Co. reported that property damage resulting from the accident,
including the loss of product, totaled $3,377,247[10].
In Scotland, On July 6 1988, around 10 pm,in North Sea off Scotland, a gas leak on pump on
Occidental Petroleum’s Piper Alpha rig caused a fire. The fire spread, resulting in a series of
explosions that eventually caused much of the offshore drilling rig to collapse, killing 166
On August 19, 2000, a 30-inch-diameter natural gas transmission pipeline operated by El Paso
Natural Gas Co. ruptured next to the Pecos River near Carlsbad, New Mexico. The released gas
ignited and burned for 55 minutes. Twelve people who were camping under a concrete-decked
steel bridge that supported the pipeline across the river were killed and their three vehicles
destroyed. Two nearby steel suspension bridges for gas pipelines crossing the river were also
extensively damaged. According to El Paso Natural Gas Co., property and other damages or
losses totaled $998,296[10].
In Brazil, On Jan. 18, 2000, a ruptured pipeline owned by government-owned oil company
Petrobras spewed 343,200 gallons of heavy oil into Guanabara Bay just outside Rio de Janeiro,
In Africa, the Chad-Cameroon petroleum development and pipeline project( runs a pipeline that
stretches 890km of the total 1,070km) has witnessed pipeline oil spill since construction. The
most recent occured on April 22, 2010 at the transfer site eleven miles off the shore of
Cameroon affecting aquatic lives and water bodies[11].
The Jebel al Zayt oil spill in Egypt occurred north of the red sea on june 16,2010.It is
considered to be the largest offshore spill in Egyptian history. The spill polluted around
100miles(160km) of coastline including tourist beach resorts[12]
This research work is basically a leak detection method aimed at detecting leaks earlier thereby
preventing the environmental degradation associated with it. The primary purpose of leak
detection systems (LDS) is to assist pipeline controllers in detecting and localizing leaks.
LDS provides an alarm and display other related data to the pipeline controllers in order to aid in
decision-making. Pipeline leak detection systems are also beneficial because they can enhance
productivity and system reliability thanks to reduced downtime and reduced inspection time.
LDS Systems are therefore an important aspect of pipeline structural integrity and technology.
According to the API document “RP 1130”, LDS Systems are divided into internally based
LDS Systems and externally based LDS Systems[13]. Internally based systems utilize field
instrumentation (for example flow, pressure or fluid temperature sensors) to monitor internal
pipeline parameters. The externally based systems also utilize field instrumentation (for
example infrared radiometers or thermal cameras, vapor sensors, acoustic microphones or
fiber-optic cables) to monitor external pipeline parameters.
Although this research work did not design a physical leak detection system, it x-rayed the
various detection techniques used in the oil and gas industry and most importantly carried out a
matlab simulation of a pipeline using modified panhandle B equation of flow for natural
gas(methane) and modified darcy weisbach equation for oil(gasoline). The pipe is then opened
and a drop in gas and oil flow rate suggests that a leak had occurred. The flow rate was found to
be inversely proportional to the diameter of the leaks by the simulation results. The simulation
results also showed that if a wide and long host is inserted into the pipeline, the variation in flow
rate is small even though large quantities of oil and gas is being taken away from the pipeline.
Any of the detection technique mounted on the pipeline can detect this leak.
1.The main significance of this project is to model flow equation for oil and gas pipelines and
using simulation to show when there is a leak by differential pressure in pipeline.
2.It modified the panhandle B and Darcy weisbach equations for leakage detection in
gas(methane) and oil(gasoline) pipelines respectively.
3.It is also an eye opener for pipeline monitoring technicians and engineers not to neglect
any drop in flow parameters eg, pressure, flow rate etc, (no matter how infinitesimal) because
this work reveals that if the pipeline vandals use long and wide host to tap oil or gas from the
pipeline, the flow rate is nearly unchanged from the simulation result. This may go unnoticed for
some days.
1.Nigeria has lost billions of dollars on pipeline leakages, so there is great need for effective
monitoring of leakages along the length of pipelines to detect leakages early enough.
2.United States of America lost $6.75B between 1986 to 2011 to oil and gas pipeline leakages.
2.Because of high viscosity of some fluid especially oil, pressure varies greatly along oil and gas
pipelines. However, the high rate of vandalisation of oil and gas pipelines has also doubled
the demand for accurate pipeline monitoring, not only in Nigeria but the world over.
1.To simulate a pipeline (using matlab) showing when the pipe is working at full capacity and
when there is leak using the panhandle B equation for natural gases(methane). Any of the leak
detection system mounted at such length of a pipe can detect leakages.
2.To simulate a pipeline (using matlab) showing when the pipe is working at full capacity and
when there is leak using the darcy weisbach equation for liquid products(gasoline). Any of the
leak detection system mounted at such length of a pipe can detect leakages.
This research work deals with pressure and flow rate measurement of oil and gas in pipelines. It
modified the panhandle B and the darcy weisbach equation for natural gas and gasoline oil
respectively. Thus, it can detect leakages in pipeline by comparing the flow rate with and without
leakages and using the difference to detect and localize leakages on time .
The project is organized in chapters. Chapter one deals with the aim, scope and background of
study. It introduces briefly the incidences of pipeline leakages in Nigeria, Africa and the world.
Chapter two, the literature review discusses in detail oil and gas discovery,exploration and
production in Nigeria, pipeline components, compressor stations, leak incidences in Niger
Delta,communication systems for pipeline protection, basic fluid mechanics, pressure loss in
pipes etc.
Chapter three,the methodology deals with pipeline design,modelling and equations. The
modified Panhandle B and Darcy equation for leak detection.
Chapter four is data presentation and analysis. The simulation results for gas and oil pipeline
is presented. Graphs for flow rates versus; pipe length, leak diameter and inserted host length
are ploted for oil and gas. Chapter five is conclusion of the work and recommendation.
There is also appendixes on; pipeline terminology, leak incidences and causes in Nigeria Niger
Delta and the United States of America, Data on density of liquids, density, viscosity, specific
gravity and compressibility factor for natural gases.