In the design of pipeline filled with flowing fluid, it is imperative that the vibration properties of the pipeline are analyzed to prevent excessive vibration of the pipelines as this could cause damages to the pipeline and even to the tie – in equipment such as pumps, compressors, heat exchangers, vessels and even tanks. On the other hand, vibrations of pipeline are also important as it dampens the vibration wave that would have otherwise passed on to the equipment. The vibration of pipeline could be as a result of so many factors which include, Coriolis Force.

The Coriolis Force is a force that causes the deflection of a moving object such as ocean currents moving in a straight path relative to the Earth’s surface. Its strength is proportional to the speed of the earth's rotation at different latitudes but it has an impact on moving objects across the globe. The deflecting objects moving in a strength path are viewed from a rotating reference frame, the Coriolis effects is caused by the Coriolis forces, which appeared in the equation of motion of an object in a rotating frame of reference. Sometimes this force is called a fictitious force (or pseudo force), because it does not appear when the motion is expressed in an inertial frame of reference. The motion of an object is explained by the real impressed forces, together with inertia. In a reference frame with clockwise rotation, the defection tends to the left of the motion of the object, in one with counter-clockwise rotation, the deflection tends to the right.

In rotating frame, the Coriolis force depends on the velocity of the moving object or fluid and the centrifugal force which are not needed in the equation to correctly describe the motion.

The most commonly encountered rotating references frame is the Earth. The Coriolis Effect is caused by the rotation of the Earth and the inertia of the mass experiencing the effect. Because the Erath completes only one rotation per day, the Coriolis force is quite small and its effects generally become noticeable only for motion occurring over large distance and long periods of time, such as large scale movement of air inthe atmosphere or water in the ocean. Such motions are constrained by the surface of earth, so only the horizontal component of the Coriolis force is generally important. This force causes moving objects on the surface of the Earth to deflect in a clockwise sense (with respect to the direction of travel) in the Northern Hemisphere and in a counter clockwise sense in the Southern Hemisphere. Rather than flowing directly from area of high pressure to low pressure, as they would in a non-rotating system. Then winds and currents tend to flow to the right of this left of this direction North of the Equator and to the left of this direction South of it. This effect is responsible for the rotation of large cyclones.

1.2 HISTORICAL BACKGROUND OF THE RESEARCH

Pipeline network are used to transport fluid such as stabilized crude oil, gas, water and even steam. Stabilized crude oil and liquefied natural gas are usually transported from the point of production (that is the point of drilling) to the point where it is required for refining. The refined products (Petrol (PMS), Kerosene, Diesel etc) could also be transported from these refineries to location where they are shipped out of the country. Pipeline network are also used to transport these fossil fluid from the point of production to across West Africa countries, this pipeline project are current run by a company called West Africa Gas Pipeline Company (WAPCO) with headquarters in Ghana.

1.3 THE ORIGIN OF PIPE LINE NETWORK

The use of pipes for oil transportation started far back in 1859 after the first commercial oil well was drilled by Colonel Edward Drake in Titusville Pennsylvania. The first oil pipes were short in length and were used to channel oil from the drill holes to a nearby local refineries or tanks where the crude oil were locally refine into the kerosene and other product, kerosene been the mostly demanded product. A rapid increase in the demand for kerosene led to the drilling of more oil well and there was an increase in need to transport the product to the nearest market.

Before the advent of pipe in the transportation of oil, Teamster Wagon carries the oils in whiskey barrels and transported them by horse to rail station from where they are distributed to various locations. The first pipeline of about 9 miles in length was built of wood in 1865 to break the oil transportation monopoly of Teamster Wagon. About this same period, John Rockefeller acquires many refineries for producing kerosene which was in high demand but his method of transportation was by rail which had some limitations.

However, the first crude oil trunk line called “Tide water” was built in 1879 by some oil men to compete with John Rockefeller in the area of transportation and within a year this pipe lines were laid to Philadelphia, Buffalo, Cleveland and New York in the USA.

1.4 VIBRATION OF PIPELINE

One of the operational challenges faced by pipeline operator is the vibrations of pipelines. Vibrations in pipelines can sometimes be of importance to plant equipment such as pumps, compressors, heat exchanger etc as it dampens the wave that would have been passed to these equipment. However, depending on the amplitude of the vibration, pipelines can be damaged.

Excessive piping vibration can cause real problems. Threaded connections can cause real problems, threaded connections can loosen, flanges can start leaking. Pipes can be knocked off their supports. And in extreme cases, a pipe fatique failure can occur. But when vibration is excessive, vibration is obviously causes a failure.

1.5 TYPES OF PIPING VIBRATION

There are two major categories of piping vibration and several vibration types within each category. An Engineer must know the type of piping vibration being dealth with before the vibration can be treated effectively. In other words, what is causing the vibration and what are its characteristics?

The two major vibration categories are steady-state and transient.

Steady-State Vibration is forced, repetitive and occurs over a relatively long period of time. The force causing the vibration can be generated by rotating or reciprocating equipment, pressure pulsations, or fluid flow (liquid or gaseous). Excessive-Steady Vibration can cause a fatique failure in the pipe due to a large number of high stress cycles. This failure will probably occur at stress vibration can also cause concentration point (e.g, branch connection,) threaded connection, fillet weld, elbow etc). steady-state vibration can also cause failures at small diameter connections and tubing (e.g instrument lead lines) of cause flange leakage due to loosing of the studs.

When compared to Steady State vibrations, transient vibrations occur for a relatively short period of time and are usually caused by large exciting forces. Pressure pulses travelling through the fluid are the most common cause of transient vibration in piping systems. These pressure pulses exert unbalanced dynamic forces on the pipe that are proportional to the straight length of pipe between bends. A common transient piping vibration is water hammer that may be caused by rapid pump starts or stops or by quick valve closing or opening.

If the vibration is at the Natural frequency of the pipeline, the pipeline tends to absorb the cyclic stresses. On the other hand, if there is a Forcing frequency which tends to cause vibration above the Natural frequency of the pipeline then Resonance will occur. Resonance can break the bearings and impellers of a pump, when the pump is pushed so hard by overstressed pipe, thereby forcing the pump’s Natural frequency to coincide with the Forcing frequency. Resonance can reduce the rotational speed of pump than what was originally designed for.

Transient is known as Free Vibration and in free vibration, the pipeline is said to vibrate at its Natural frequency in its static equilibrium position. Steady State Vibration is known as forced vibration. At forced vibration, the pipeline will tend to vibrate at its Natural Frequency as well as to follow the frequency of the excitation force. As a result, the system will vibrate at the frequency of the excitation force regardless of the initial conditions or the Natural Frequency of the System.

As the vibration of the pipeline continues, the pipeline deflects as a result of external forces.

1.6 CORIOLIS FORCE

Coriolis Force originated from the inventor, a French Mathematician called Gaspard Gustave Coriolis (1792 – 1843). On the rotating earth, the Coriolis Force acts to change the direction of a moving body plane in the Northern Hemisphere to the right and change the direction of the moving body placed in the Southern Hemisphere to the left. The deflection is not only instrumental in the large – scale Atmospheric circulation, Sea – breeze circulation and Storm development ( Simpson 1985; Neumann 1984; Atkinson 1981) but can even affect the outcome of a baseball tournament. For example, a ball thrown at 25m/sec (100m in 4 sec ) in the United State of America which is in the Northern Hemisphere will deviate about 1.5cm to the right due to the effect of Coriolis Force.

Generally, the flow velocity in pipelines and vessels is low and thus the effects of Coriolis force would either be negligible or would not be there at all. There are times when the velocity of flow is high especially during operations in flare up gas flow, stream out condition, purging condition etc, so there are some operations such as process plant operation where flows are continuously at high velocities. At these high flow velocities, the pipeline and even pressure vessels have been noticed to experience vibrations which has been analyzed and found to be due to Coriolis Force. Generally, in the industries such vibration problems are solved by working round them, if the vibration cannot be ignored. “The earth’s pull downwards along with its angular velocity, w_e which results in the expression 2ω_ex v_r. This term is called the Coriolis acceleration” (Persson, 1998). When mass, m is multiplied with the Coriolis acceleration, we have the term 2mω_e x v_r which is called the Coriolis Force.

1.7 SCOPE OF THE RESEARCH

This research presents a framework system dynamics model that will evaluate and investigate the effect of Coriolis force in the vibration of pipeline containing flowing fluid (crude oil).The model would highlight possible factors such as Deflection, Frequencies at various Speeds, Force and Moment using fixed ends condition, a case when the pipeline is empty and when the pipeline is filled with flowing fluid at different velocities. Analytical method would be used to obtain the Results. An Industrial pipeline project designed by a Consulting firm called Delta Afrik Engineering Limited is used as case study, where its data would be utilized.

1.8 AIM OF THE RESEARCH

In the dynamics of pipelines, deflections, Natural frequency and Normal modes of empty pipes, fluid filled pipe and pipe with fluid flowing velocity is considered. The deflection and frequencies obtained when the pipe is empty and when the pipe is filled with flowing fluid at various velocity using Textbook methods, Industrial method with Coriolis force are compared to know the extent of deviation. The introduction of Coriolis force in the mathematical model is compared with ANSYS analyses and the other methods, this shall clearly show the effect of Coriolis force in the vibration of pipelines with fixed ends conditions.

1.9 SIGNIFICANCE OF THE RESEARCH

The vibration of pipelines is the centre focus of all pipelines problem in most of the oil companies in the world and it is very important to solve the vibration problem so as to preserve the life of the pipeline and the tie – in equipment. In solving this vibration problem, different numerical methods are used ie Mathematical Method. It is very significant to know the degree to which the pipeline carrying flowing fluid is vibrating or deflecting which may be as a result of the effect of Coriolis force, as this will aid the pipeline design Engineers in solving pipeline vibration problems.

Furthermore, the extent to which Coriolis force can cause vibration in the pipelines can only be appreciated as it will help to reduce the failure of the pipelines due to excessive vibration as currently experienced in the country today. Oil spillage in the Niger Delta area today are not only caused by pipeline vandalisation but also by some factor that were not put in place by most pipeline design Engineers as this results to the build up of stresses in the pipeline which can eventually lead to the failure of the pipelines causing oil spillage in this area. The pipeline design Engineers will have to put the effect of Coriolis force into consideration when designing any pipelines depending on the kind of fluid to be transported through the pipelines.