The Impact of Pipeline Bend on Bi-directional Pig and the Theories for the Optimal Pig Design

Zhu Xiaoxiao Zhang Shimin Wang Deguo Wang Wenming Liu Shuhai

School of Mechanical and Transportattion Engineering China University of Petroleum Beijing

18 Fuxue Road, Changping, Beijing China 102249 {zhuxiaoxiaovip & zsm7481976 }@163.com

Abstract-As a kind of pipeline robot, pig is needed to perform

operations such as dewatering, cleaning and internal inspecting to improve the efficiency and ensure the safety of oil and gas pipeline. A pig with improper geometry will easily get stuck in the pipeline and the attached electrical equipments may also be damaged by the crash, especially when passing through pipeline bends or elbows. This is not only harmful for the pig itself, but also threatens the transportation security of pipeline. In this paper, avoiding getting stuck in the pipeline bend, the detail process when the bi-directional pig passing through pipeline bend is discussed. The proper method for determining the geometry size of the pig body is proposed and displacement of the bi-directional pig when passing the bend is presented after a force analysis of the sealing discs. The related theories for the pig design can provide some references to determine the size of pig body and make an appropriate setup of discs.

Index terms- pipeline inspection gauge, bi-directional pig, pipeline bend, passing ability, design method

I. INTRODUCTION

Pipeline transportation is now the most safe and efficient way to deliver fluids such as oil and gas products to users. After a long term run of these pipelines, problems like wax plug, cracking and corrosion may damage these pipelines and reduce their lives [1]. As a kind of pipeline maintenance tool, pipeline inspection gauge (PIG) is widely used to perform operations such as cleaning, batching and inspection. Regularly pigging can remove wax in oil pipeline and swab liquid hold-up in gas pipeline, which can prevent the pipeline from defects like cracking and corrosion. Pigging with advanced pig can detect defects and their positions, aimed to provide important information for repair work.

Before pigging, selecting a pig with proper size will be significant to the final performance. Pig is often got stuck, stalled or damaged in the pipeline because of the complicated pipeline route. As the boosting needs of pigging operation, these accidents increase in relevant and the cost of shut-down due to a stuck can be extremely large.

Results of research on the design of the pig are scarcely found in the literatures. Due to the absence of design information, most of the available knowledge is based on field experience and selecting the best pig may often involve some guesswork and consequently, a high degree of uncertainty [2-5]. As the result, the research on the methods or theories of designing or selecting a pig is needed, avoiding any stuck or

damage during pigging.

In this paper, the aim is to discuss the possible problem when the pig passes through the pipeline bend in oil and gas pipeline and find the impact of the bend on running pig. The analysis and calculating methods are proposed for designing or selecting a proper pig, which can prevent it from getting stuck in the pipeline bend.

II. THE IMPACT OF PIPELINE BEND ON RUNNING PIG

Constrained by the environment, pipelines can not always be straight from the beginning to the terminal. Bends are always used to avoid villages, rivers and the like. Unfortunately, the pig with improper geometry will easily get stuck at the pipeline bends. Even worse, the attached detectors and the pig itself will be damaged, as it is showed in Fig.1.

Till now, most of the researches are focus on modeling pig motion in the pipeline [6-10], while it is still not clearly that how geometry affects the pig steady state motion, especially when the pig passing through the bend. There is also no theories or methods to define the suitable size of physical modification. Physical modification often have to be used to pig the pipeline before the real pigging, avoiding any possible accidents. As the result, the relevant theoretical researches are urgently needed for the pigging guide.

III. THE THEORIES AND METHODS IN DESIGNING

The method by using the software of CAD and theoretical calculation is introduced to design the pig body. The theories to make appropriate setup of sealing discs are also proposed in this part.

Fig. 1. The interaction between detectors and pipe inner wall

Fig. 2. The schematic diagram of pig body

A. The Impact on the Pig Body and Design Theory for it Though it is a simple structure (which is showed in Fig.2), a

pig body with improper length or width will cause unexpected problems in the pipeline. There is few research papers deal with the specification for how to design the pig body. According our experience, two points should be known in the designing.

1) The pig body should be strong enough to endure the impaction during pigging in the pipeline.

Usually, when pigging the pipeline, there is no large force acting on the pig body. However, if the pig get stuck or stalled in the pipeline, another pig need to be sent to drive it out, and the acceleration of the back pig will be large, which lead to a seriously crash into the front one. The front pig may also undergo a large pushing force when entering in the pig launcher and hit onto the blank cover at the effect of back pig. These two situations will always lead to the deformation of the pig body.

This problem can be easily solved by increasing the wall thickness of pig body. The impact force on the pig body can be general calculated by using Newton's second law:

=F m a⋅ (1)

Where, m is the mass of the pig, a is the acceleration of the

pig and the value can be assumed according the real pigging condition.

The compressive stress can be written as:

=F/Aσ (2)

Where, A is the cross sectional area of pig body. The calculated result can be compared with the allowed

stress of the material used for pig body. Of course, a nondestructive inspection on the welding parts

of pig body should be taken for avoiding any flaws, or the pig body allowed stress will be far less than the material it should be. Another way is to improve the safety factor, which means a larger increase on the wall thickness of pig body.

2) The pig body should be small enough to go through the pipeline bends.

Fig. 3. The schematic diagram of the pig when passing pipeline bends, the axis

of pig body tangent to the middle diameter of the annular pipeline

In order to make sure the pig can go through the pipeline bends freely, theoretical calculation combined with a graphical analysis is often used in the designing. Now, there are two ways can be used to calculate the size of pig geometry. These two ways will be described in the following respectively and the results will be compared.

a) The first case: the axis of the pig is tangent to the middle diameter of the pipeline bend

As it is showed in Fig.3, an annular pipeline was draw by using CAD with the minimum size of the bend in the whole pipeline. The rectangle in the annular pipeline represented the steel pig body and its axis is assumed to tangent to the middle diameter of the annular pipeline. L is the length of pig body and W is the outer diameter of pig, which is the extreme dimension without considering cups. R is the curvature of the bend. D is the internal diameter of the pipeline.

To ensure the pig body can pass the bend freely, the size of pig body should be limited in the bend.

in Fig.3, + / 2OA R D= , + / 2OB R W= The equation 2 2 2+OA AB OB= in the triangle OAB can be

written as Eq. (3):

( ) ( ) ( )2 2 2/ 2 + +W/2 + / 2L R R D= (3)

From Eq. (3), we can get the maximum length of the pig body is:

( )( )max - + +4L D W D W R= (4)

b) The second case: the axis of the pig is not tangent to the middle diameter of the pipeline bend

In some research papers, the axis of the pig body was not assumed to tangent to the middle diameter of the annular pipeline in the calculation and the there may be also some problems with the calculation results [11-12]. Now, the correct result will be proposed and a comparison between these two results will be made as below.

The pig body

The sealing disc The guide disc

Fig. 4. The schematic diagram of the pig when passing pipeline bends, the axis

of pig body do not tangent to the middle diameter of the annular pipeline

In this case, as it is showed in Fig.4, the calculation is also divided it into two cases: (a) the outer diameter of pig W is relatively smaller than its length L and both ends of the segment are located on the straight parts of the pipelines. (b) Both ends of the segment are located on the curved part of the pipelines [13-14]. However, the fact is that if the pig with the limited size of W and L can pass the annular pipeline, it can certainly pass the pipeline bend with straight parts. So, we do not need to divide the calculation work into two cases and the first case may not happen in oil and gas pipeline because of the large curvature of the bend, and this will also be proved in the following.

The axis of the pig body does not tangent to the middle diameter of the annular pipeline and the equation 2 2 2+OA AB OB= in the triangle OAB will be written as Eq. (5), which is a little different from Eq. (3):

( ) ( ) ( )2 2 2/ 2 + - / 2+ + / 2L R D W R D= (5)

And we can get:

( )( )max' 2 - +2L D W W R= (6)

c) A result comparison between these two cases Under the two cases, maxL and '

maxL , the maximum length of the pig, are all obtained.

Then,

( ) ( ) ( )( ) ( )( )2 2max max- ' - + +4 -4 - +2 - -4 -3L L D W D W R D W W R D W D R W= =

Because the curvature of piping bend is larger than the

internal diameter of the pipeline, which means D R< , together withW D< , we can get:

2 2

max max- ' <0L L (7)

And then, we can get from Eq. (7): max max< 'L L (8)

So, the maximum length of the pig body when the axis of

pig body is tangent to the middle diameter of the annular pipeline is smaller than that the axis does not tangent to the annular pipeline middle diameter. Actually, in the designing, we prefer a more safety value and as the result, the first method will be more reliable. Also, if the pig body axis is tangent to the middle diameter of the annular pipeline when the pig passing through the pipeline bend, the detect sensors circumferential arranged will have the opportunity to be in the middle of the pipeline and may do not have a seriously offset or an impact with the pipeline wall during pigging, which is better for the safety and excellent performance of these detect sensors. The proper size will provide the conditions for the further designing work to keep the pig stay in the middle of the pipeline bend.

The electrical equipments, such as date collection system and the power module, are usually placed inside the pig body. As the result, W is an important parameter in the designing and it determines the volume of the pig body. So, W will be usually defined at first.

Then, L can be defined by

( )( )max - + +4L L D W D W R≤ =

Finally, the restriction of the length and width of pig body

can be written as:

( )( )0< - + +4L D W D W R≤

(9) 0<W<D

And finally, L and W can be written as:

max=L Lξ , =W Dζ

Where 0<ξ <1, 0<ζ <1. In order to express the value range of L and W with a better

illustration, the Eq. (9) can be written as:

( ) ( )2 222 + 2 ,0 , 0W R L D R W D L+ ≤ + < < > (10)

As the Fig.5 shows, the area with section line is the allowable range to define the value of W and L.

Fig. 5. The value range of W and L

Though the value of W ranges from 0 to D, not all the values in this range are suitable for designing. The wider the pig body, the shorter it will be. There is a principle in the designing is that as long as W can fulfill the requirement, we should choose the minimum value, because the smaller the W is, the better passing ability the pig will have. In some papers, the value of W from 0.5D to 0.9D is suggested in the designing [15].

B. The Impact on Sealing and Guide Discs and Theories for the Appropriate Setup

Sealing disc is an important part of pig, which is used to building the differential pressure over the pig for providing the driving force. As the result, it is also called drive disc. The number, thickness and hardness of these sealing discs will affect the pig performance. Guide discs are used to keep the pig close to the centerline of the pipeline. Whether the pig can get stuck is not only depends on the size of pig body, but also determines by the setup of discs or cups.

Unfortunately, it can hardly find any research papers dealing with guide discs and sealing discs, not mention to the method on how to make an appropriate setup of these discs. The most basic questions regarding pig differential pressure, leakage and other parameters can only be guessed at [16].

Though the discs are complicated to model during pigging, there are still some methods can be summarized according our design experience.

1) The number of sealing discs When the pig passes through pipeline bend, we should

know the effort of the pig’s gravity and centripetal force.

a) The effort of the pig’s gravity The gravity of the pig acting on the sealing discs is

complicated, and the deformations are also non-uniform. In this paper, In order to simplify calculating, the gravity of the pig is assumed to be uniformly acting on the lower half parts of these discs, and lead to an elastic deformation, as the Fig.6 shows.

In the calculating, the sealing disc is divided into infinitesimal parts, then, a force calculation is taken for each infinitesimal part, and finally with an integration. So, we can get:

Fig. 6. The schematic diagram of the force analysis for sealing discs

0sin /GE Rl d G N

πε θ θ⋅ =∫ (11)

And then, from Eq. (11), we can know:

( )/ 2mg NERlε = (12)

Where m is the mass of the pig; g is the acceleration of

gravity; N is the number of sealing discs; E is the Young's modulus of sealing discs; R is the curvature of the bend and l is the thickness of each sealing disc.

In order to get a maximum deformation, take an inspection pig in the Φ1016 pipeline for example. The inspection pig is the heaviest pig with the mass of nearly 4000kg, and g=9.8m/s2, R is usually equal to 6D, which is about 6.096m, and l=0.05m. The minimum number of sealing discs N=2, and E=1MPa.

According these dates, we can get:

( ) ( )6/ 2 4000 9.8 / 2 2 10 6.096 0.05 =0.032G mg NERl mε = = ⋅ ⋅ ⋅ ⋅ ⋅

Though 32mm is not large compared with the size of pig, we can still reduce the effort of the gravity. Improving the value of N, E and l are widely used in the designing, and actually, more than four sealing discs are often used in the pigging, also, the Young's modulus is far bigger than 1MPa. With the proper setup of these parameters, we can find that the gravity of the pig will have little effect on its passing ability.

b) The effort of centripetal force The centripetal force will be exerted by the outside inner

wall of pipeline bend when the pig passing through it and the centripetal force is:

2 /CF mV R= (13)

And the force all acts the sealing discs and we can get:

C CF E Nl Rε π= (14)

Fig. 7. The ideal force diagram of bidirectional pig when passing through the

pipeline bend

Where Cε is the sealing disc deformation caused by centripetal force.

Combined with Eq. (13) and Eq. (14), we can get:

( )2 2/C mV ENl Rε π= (15)

Where, V is the tangential velocity of the pig. In the designing, combined with Eq. (12), we can choose

the relative suitable value to reduce the deformation.

2) The fixed position of the discs The bidirectional pig is commonly used for heavy duty

pigging jobs and it can perform effective cleaning work with guide discs and sealing discs. Compared with the pig using cups, the bidirectional pig is more likely to be stuck in the pipeline bend. So, take the bidirectional pig for example, a detail analysis will be given below.

As it is showed in Fig.6, the setup of the discs is random. When the bidirectional pig running through the straight pipeline, the sealing discs attached on this pig are all deformed and contact with inner wall of the pipeline tightly, while the guide discs do not have any deformation because the diameter of these guide discs is a little smaller than the inner diameter of the pipeline. When the pig passing through the pipeline bend，the guide discs may be also deformed as the reason of geometry restriction. During this stage, the pig subjects the force of F1, F2, F3 and F4. In the straight pipeline, we can get that F1=F3 and F2=F4. However, in the pipeline bend, when the pig is moving forward, geometric constrained by inner wall of the pipeline bend, the deformed area S1 and S4 is increasing and S2 and S3 is decreasing, which is showed in Fig.7 and Fig.8. So, the force of F1 and F4 will be increased, while F2 and F3 will be decreased respectively and we can get F1>F3 and F4>F2. At the effort of torque leading by unbalanced force, the pig will have an anti-clockwise turning. That’s the reason why the sealing pig can turn over the pipeline bend. As it is showed in Fig.9, the longer the pig body is, the larger areas that guide discs and sealing discs will be deformed. In the rectangular box, there is a shorter pig and outside the rectangular box there is a longer pig. The red areas represent the deform parts of these discs. From this figure, we can see A1>A2.

Fig. 8. The partial enlarged detail of the deformed sealing discs

Fig. 9. The deformation area of the guide discs and sealing discs

As the result, the longer pig may have a larger offset than

the shorter pig from the outer bend to the inner bend at the effort of the force exerting by the outer bend. Actually, the deformation caused by centripetal force can offset some displacement of the pig caused by the geometry restriction. However, in the designing, it is not a good idea to utilize it because the deformation of the sealing discs caused by centripetal force is unstable and can not be predicted accurately.

We can see from Fig.9 that it is impossible for the pig to stay at the middle of the pipeline bend during passing regardless of the displacement caused by centripetal force, unless the pig is compressed into a plane. Because the hardness or thickness of guide discs is always larger than sealing discs, the guide discs usually do not have too much deformation at the pipeline bend. In order to calculate the maximum displacement of the pig at the pipeline bend, we can assume that the top of the front and rear guide discs are all just contact with the pipeline inner wall and do not have any deformations when passing the bend.

So, the maximum offset is:

( ) ( ) ( )2 2max = / 2 / 2 / 2G GR W R D Lε + − + − (16)

Where, GW is the out diameter of guide disc, which is

usually depend on the situation of the pipeline, GL is the separation distance between the front and rear guide disc.

In the designing, we often have some requirements about offsetε , combined with Eq. (16), the value can be determined.

From Fig.10, we can also find the minimum offset is the displacement of the backmost sealing disc at the front half part of the pig, towards the inner wall of pipeline inside ring.

Fig. 10. The offset of pig when passing the pipeline bend

( ) ( ) ( )2 2min = / 2 / 2 / 2S SR W L R Dε − + − − (17)

Where, SW is the out diameter of sealing disc, SL is the

separation distance between backmost sealing disc at the front half part of the pig and foremost sealing disc at the rear part of the pig.

With the help of Eq. (16) and Eq. (17), we can properly determine the fixed position of these discs and make the pig pass through pipeline bend with a better pose.

IV. CONCLUSION

In this paper, in order to make the pig to have the best passing ability and pigging performance at the pipeline bend, the impact of the bend on running pig is discussed and the conclusions are as follows:

(1) After comparing two calculation methods for determining the geometry of the pig body, the calculation result based on the assumption that the axis of the pig body tangent to the middle diameter of the annular pipeline is preferred and the result is more reliable.

(2) The theories on how to make an appropriate setup of the discs are proposed after a detail force analysis, which can provide some references for choosing the number, Young's modulus, and the thickness of the sealing discs. The effect of pig gravity and its centripetal force when passing through the pipeline bend can be reduced

(3) These methods and theories proposed for designing or selecting a proper pig can not only prevent it from getting stuck in the pipeline bend, but also provide the possibility of the excellent pigging performance with a better pigging pose at the bend.

ACKNOWLEDGMENT

We appreciating that this paper is supported by the National Natural Science Foundation of China (Grant No. 51175514). We should also acknowledge the support of the Australian and Western Australian Governments and the North West Shelf Joint Venture Partners, as well as the Western Australian Energy Research Alliance.

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