Prediction of residual pipeline resource taking into account the operation loading conditions
An effective energy approach to the evaluation of the residual service life of a pipe of oil pipeline containing a crack on its inner surface for the two-frequency loading mode of biaxial tensioncompression has been proposed. The two-frequency variations of pressure in the pipe are caused by the tur...
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
2009
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| Цитувати: | Prediction of residual pipeline resource taking into account the operation loading conditions / Yu.V. Banahevych, O.E. Andreykiv, M.B. Kit // Проблемы прочности. — 2009. — № 1. — С. 44-52. — Бібліогр.: 8 назв. — англ. |
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irk-123456789-484772013-08-20T07:31:57Z Prediction of residual pipeline resource taking into account the operation loading conditions Banahevych, Yu.V. Andreykiv, O.E. Kit, M.B. Научно-технический раздел An effective energy approach to the evaluation of the residual service life of a pipe of oil pipeline containing a crack on its inner surface for the two-frequency loading mode of biaxial tensioncompression has been proposed. The two-frequency variations of pressure in the pipe are caused by the turbulence of the flow of oil (highfrequency), opening and closing of the gate valves, and the shutdowns of the pumps (low frequency). Предложен эффективный энергетический подход к оценке остаточного эксплуатационного ресурса нефтепровода с трещиной на внутренней поверхности трубы, подвергаемой двухчастотному биаксиальному нагружению растяжением-сжатием. Двухчастотный режим изменения давления в трубопроводе обусловлен турбулентностью потока нефти (высокочастотная составляющая), открыванием и закрыванием задвижек, а так же отключением нефтенасосов (низкочастотная составляющая). 2009 Article Prediction of residual pipeline resource taking into account the operation loading conditions / Yu.V. Banahevych, O.E. Andreykiv, M.B. Kit // Проблемы прочности. — 2009. — № 1. — С. 44-52. — Бібліогр.: 8 назв. — англ. 0556-171X http://dspace.nbuv.gov.ua/handle/123456789/48477 en Проблемы прочности Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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Научно-технический раздел Научно-технический раздел Banahevych, Yu.V. Andreykiv, O.E. Kit, M.B. Prediction of residual pipeline resource taking into account the operation loading conditions Проблемы прочности |
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An effective energy approach to the evaluation of the residual service life of a pipe of oil pipeline containing a crack on its inner surface for the two-frequency loading mode of biaxial tensioncompression has been proposed. The two-frequency variations of pressure in the pipe are caused by the turbulence of the flow of oil (highfrequency), opening and closing of the gate valves, and the shutdowns of the pumps (low frequency). |
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Article |
| author |
Banahevych, Yu.V. Andreykiv, O.E. Kit, M.B. |
| author_facet |
Banahevych, Yu.V. Andreykiv, O.E. Kit, M.B. |
| author_sort |
Banahevych, Yu.V. |
| title |
Prediction of residual pipeline resource taking into account the operation loading conditions |
| title_short |
Prediction of residual pipeline resource taking into account the operation loading conditions |
| title_full |
Prediction of residual pipeline resource taking into account the operation loading conditions |
| title_fullStr |
Prediction of residual pipeline resource taking into account the operation loading conditions |
| title_full_unstemmed |
Prediction of residual pipeline resource taking into account the operation loading conditions |
| title_sort |
prediction of residual pipeline resource taking into account the operation loading conditions |
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Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| publishDate |
2009 |
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Научно-технический раздел |
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http://dspace.nbuv.gov.ua/handle/123456789/48477 |
| citation_txt |
Prediction of residual pipeline resource taking into account the operation loading conditions / Yu.V. Banahevych, O.E. Andreykiv, M.B. Kit // Проблемы прочности. — 2009. — № 1. — С. 44-52. — Бібліогр.: 8 назв. — англ. |
| series |
Проблемы прочности |
| work_keys_str_mv |
AT banahevychyuv predictionofresidualpipelineresourcetakingintoaccounttheoperationloadingconditions AT andreykivoe predictionofresidualpipelineresourcetakingintoaccounttheoperationloadingconditions AT kitmb predictionofresidualpipelineresourcetakingintoaccounttheoperationloadingconditions |
| first_indexed |
2025-07-04T09:00:00Z |
| last_indexed |
2025-07-04T09:00:00Z |
| _version_ |
1836706276136976384 |
| fulltext |
UDC 539.4
Prediction of Residual Pipeline Resource Taking into Account the
Operation Loading Conditions
Y u. V. B anahevych ,a O. E. A ndreyk iv ,b an d M . B. K itb
a Department of Main Gas Pipelines “Lvivtransgas,” Lviv, Ukraine
b Franko National University, Lviv, Ukraine
An effective energy approach to the evaluation o f the residual service life o f a pipe o f oil pipeline
containing a crack on its inner surface fo r the two-frequency loading mode o f biaxial tension-
compression has been proposed. The two-frequency variations o f pressure in the p ipe are caused by
the turbulence o f the flow o f oil (high frequency), opening and closing o f the gate valves, and the
shutdowns o f the pumps (low frequency).
K e y w o r d s : residual service life o f a pipeline, block loading, fatigue crack
propagation, energy approach.
In tro d u c tio n . Based on the energy approach developed in [1-4], we propose
a m ethod for the determination o f the residual service life o f structural elements
w ith cracks under block loading by bilateral tension-compression. The proposed
m ethod is applied to the evaluation o f the residual service life o f a pipe with
surface crack subjected to longitudinal bilateral tension-com pression caused by
the processes o f heating and cooling o f the pipe, its squeezing by the soil, and the
action o f internal pressure formed in the process o f oil pumping. The
two-frequency variations o f pressure in the pipe are explained by the turbulence
o f the oil flow (high frequency), closing and opening o f the gate valves, and
shutdowns o f the pumps (low frequency).
M odel of L oad ing of a P ipe. The oil pressure in the m ain pipelines can be
quite high to guarantee their high throughput capacity. The deviations o f working
pressure caused by the startups and shutdowns o f the pump stations can be as
large as 2 -3 M Pa [5]. In case o f successive pumping o f different types o f oil,
these deviations do not exceed 1 MPa, the deviations caused by the startups and
shutdowns o f separate aggregates vary w ithin the range 0 .5-1.0 MPa, and the
deviations caused by the pollution o f the pipeline and formation o f air blocks, as a
rule, do not exceed 0.5 MPa.
Due to the oil flow turbulence, a disbalance o f the pumps, and the flow
frequency oscillations, the pressure in the pipeline deviates from its m ean value
by 0.2-0.3 M Pa [6 ]. The design-basis pressure for the reinforcement o f pipelines
at the intermediate pump stations is usually set equal to 4 M Pa because a pressure
close to this level is formed after the shutdown o f this station.
The restriction imposed on the input pressure o f the station, i.e., 2.1 MPa, is
connected w ith the action o f a regulating valve o f the protective system o f the oil
main. The rate o f pressure increase depends on the response time o f the pump
rotor. Thus, the steepness o f the shock wave decreases as the indicated response
time increases. In the course o f closing o f a gate valve, the level o f pressure
specified by the flow interruption rate rapidly increases. The pressure wave
© Yu. V. BANAHEVYCH, O. E. ANDREYKIV, M. B. KIT, 2009
44 ISSN 0556-171X. Проблемы прочности, 2009, № 1
Prediction of Residual Pipeline Resource
propagates w ith the sound speed toward the previous pump station, reflects from
it, and, thus, leads to the formation o f a wave o f lower pressure. The amplitude of
the pressure waves formed in the process of closing of gate valves can be as high
as 4.44 M Pa [5]. Thus, pressure variation in the pipes o f oil mains is, in fact,
two-frequency and can be simulated by block loading.
The experimental graphic dependence o f pressure variations in a pipe in the
process o f repumping o f oil [5] is qualitatively similar to the m odel diagram.
As a result o f the increase in the diameters o f oil mains, pressure, and
tem perature o f oil products, the levels o f stresses formed in the walls o f the pipes
become m uch higher, especially in the longitudinal direction. The changes in the
properties o f soil along the route o f the pipeline result in different conditions of
its squeezing. This m ay lead to the formation o f significant longitudinal stresses
Q between fixed points o f the pipeline. These stresses depend on tem perature and
pressure and can be found by using the following formula [7]:
0.3 p d
Q = a E ( M ) - ,
where a = 12-10 6 deg 1 is the coefficient o f linear therm al expansion o f the
pipe metal, d 2 = 2 r 2 and d 1 = 2r1, are, respectively, the inner and outer diameters
o f the pipe, p is the pressure o f oil products, E is the elastic modulus,
AT = Tm — Te , and Tm and Te are the temperatures o f the pipeline in the
processes o f installation and operation, respectively.
We consider a pipe containing a surface semielliptic crack (Fig. 1).
Fig. 1. Schematic diagram of loading of a cracked pipe.
According to the data o f in -s itu observations, the level o f stresses Q caused
by the variations o f temperature in the walls o f the pipe restrained by soil can be
as high as 200 M Pa [7]. Variations o f pressure p can be mathematically
described as follows. The high-frequency oscillations o f pressure p are
represented by the m ajorant
p 1 = a 1 + b 1 sin rn1t , ( 1)
where, according to the data o f the in -s itu observations [5], the measured
quantities a 1, b 1, and « 1, have the following values: a 1 = 1 MPa, b 1 = 0.2 MPa,
and « 1 = 0.6 Hz. The oscillations o f pressure caused by the delays in the process
o f oil pumping due to the shutdowns o f pumps, closing o f gate valves, etc. are
also described by a majorant sinusoidal cyclic curve o f the form
ISSN 0556-171X. npoôëeMbi npounocmu, 2009, N 1 45
Yu. V. Banahevych, O. E. Andreykiv, and M. B. Kit
P 2 = a 2 + b 2 sin m 21, (2)
where a 2 = 3.5 MPa, b2 = 1 MPa, and m 2 =1.3 M Hz [6 ]. Hence, pressure
variations in the pipeline p ( t ) are described by the superposition o f relations ( 1)
and (2 ).
Since ®i is m uch lower than m 2 , the period o f subcritical growth o f the
semielliptic crack is determined by the num ber o f cycles N 2 = t/1 2 of
low-frequency oscillations.
C om p u ta tio n a l M odel o f F atigue C rac k P ropaga tion . To determine the
residual service life o f the pipeline (the time to its depressurization), we propose
computational models o f the development o f defects and determine the time of
their penetration through the wall (Fig. 1).
Assume that the process o f crack propagation is continuous. By analogy with
[2 ], we write the equation o f energy balance o f the body at any time t in the form
A = W + r , where A is the work o f external forces, W is the energy of
deformation o f the body, W = W e + Wp(1)(S ) + Wp2) ( t ) ~ w P3>( t ), W e is the
elastic component o f W , Wp(1)( S ) is the w ork o f plastic strains depending only
on the area o f the crack S , Wp(2)( t ) is the w ork o f plastic strains caused by the
external forces for a constant area o f the crack during the incubation period of
preparation to its jum p depending only on time t, Wp(3)( t ) is the w ork o f plastic
strains in the process o f compression o f the process zone (caused by the release o f
potential energy o f the body also for a constant area o f the crack during the
incubation period o f preparation to its next jum p) depending only on time t , and
r is the fracture energy o f the body depending solely on the area o f the crack.
Since the requirem ent o f energy balance is satisfied, the following condition of
balance o f the rates o f variation o f energy is also true:
d[T - (A - W e - WP1 - W P2 + W P3 )] d S
d S d t
d (A - W e - w P r> - W P2> + Wp(3))
d t
= 0. (3)
M ultiplying Eq. (3) by T2 and differentiating the result w ith regard for the
dependences o f the functions on S and t , we arrive at the following relation for
the crack propagation rate V = d S / dt:
i d L = _ W 1 _ (4)
d N 2 (y - Y s )
where N 2 is the num ber o f blocks o f loading (low-frequency cycles), y is the
density o f fracture energy o f the m aterial [2, 3], y s is the density o f potential
energy in the process zone for the m axim um level o f stresses in a cycle, and
46 ISSN 0556-171X. npo6n.eMH npounocmu, 2009, N9 1
Prediction of Residual Pipeline Resource
W ^ 1 is the cyclic component o f the dissipation o f energy in the process zone for
one package o f loading w ith T2 = 2xa> — 1.
Since the thickness o f the wall o f the oil main h i = r 2 — r is m uch smaller
than the radius o f the pipe r , for the sake o f simplicity, we assume that the crack
propagates in an infinite plate under the action o f the static stresses Q and
variable loading p .
The quantities y , y s , and W ^ are determined as follows [2, 3]:
£ fc
s
f d x 5 ° 0 f ° max( 1 > x ) d | > Y = 0-75 a 0 f £ f c ,
° f c AS L 0 (5)
1 £ fc N' /2 lf
W C1 = ° ^ f dy f d x f a 0 f [° max(1 > x , y ) - ° min (1 , x , y ) ] d | ,
° fc 0 L 0
-c
W C2 = £ f c ° - c f f a 0f [°max( 1 , x , 0) - ° Imin (1 , x , 0 )]d x d |,
0 L
s
where o of is the m ean level o f stresses in the process zone under the loads p
and Q , A S is the area o f the process zone near the crack contour, y is the
num ber o f cycles o f oscillations o f pressure p ( t ) for the period T2, d max and
d min are, respectively, the m axim um and minimum values o f the opening
displacement o f the m odel cut along the process zone [2 ], d f c is its critical value
for the critical strain e f c under cyclic loading, is an increment o f arc length
along the crack contour L , l f and l s are the widths o f the cyclic and static
process zones, respectively, and l c is the critical value o f l s .
By using the H uber-M ises condition o f plasticity, we determine the quantity
o o f as follows [3]: _________________
o of = 0-5[Q + V( o s + o p )2 — 3Q 2 ^ (6)
where o s and o p are, respectively, the ultimate and yield strengths o f the
material.
To simplify the solution o f the problem, we assume that the quantity
^ max — ^ mm is identical in the course o f increase and decrease in the load, which
is used to compute the num ber o f cycles to failure. Thus, by using the results
obtained in [2, 3], we find
= 2 = 0 .5 K ̂ ( l — R ) 2
^ max ^ min = 0' 5 ̂ max (i — R ) 2 = -
E ° 0 f
0.1KI2max(1 - R ) 2
l f - 0.25 ls(1 - R ) 2 = ----------- 2----------- ,
a 0 f
ISSN 0556-171X. npoöxeMbi npounocmu, 2009, N 1 47
Yu. V. Banahevych, O. E. Andreykiv, and M. B. Kit
where R = p p max is the load ratio. Note that R is a function o f N j. These
relations and the results presented in [2, 3] enable us to rewrite relations (5) in the
form
(1) 0.0368ajfc fc r (1) 4
WC2 = — 2------- f - f [KI(m)ax(« , 0) - K Imin (« , 0)]4 d« ,
K f c ° 0 f L
0.2944£ fc r (2) 4
r K 2 ( A e f ( K imax( « . ° » 4 d« •
K fc ( A S )<7 0 f L
0.3927 r (2) 2
AS = ^ - f (K immx(« ,0 ) ) 2 d « ,
(8)
„ 0 f L
N 1 /2
W C1 = 0.0368« ^ £ fcK - „ - f1 f d« f 2 [K imax(« , y ) - K Imin (« . y )]4 dy .
L 0
where K Imax(« , 0) and K Imjn (« , 0) are the m aximum and m inim um values of
K I for cycles o f the second type and K Imax(« , y ) and K Imjn (« , y ) are the
m aximum and m inim um values o f K i for cycles o f the first type.
We apply the m ethod o f equivalent areas [2, 3, 8], according to which the
increm ent o f the area o f a fatigue crack o f a given configuration is approximately
equal to the increment o f the area o f a circular crack o f radius a (o f the same
area). This enables us to write the approximate values o f K Imax(« , 0), K Imjn (« , 0),
K Imax(« , y ), and K Imin (« , y ) by analogy with the case o f a plate with surface
semicircular crack stretched by the uniform ly distributed stresses „ = r1 h - 1 p ( t )
as follows:
K I(m x(« ,0 ) = 2 r1h - V -1/2 a 1/2( a 2 + b 2 + ( - 1 ) % ) ( i = 1,2),
K Imax(« , 0) = 2^ - 1/2r1h -1 a 1/2(a 2 - b 2 - b 1) ,
K Imax(« , y ) = 2n - 1/2r h - 1a 1/2 [a2 + b 1 + b2 sin(2n y / N 1 - n / 2 )],
K Im x (« , y ) = 2 n - 1/2r1 h --1a 1/2 [a2 - b 1 + b2 s in (2 n y /N 1 - n / 2)].
(9)
Further, we substitute relations (9) in (8) and then, together w ith (5), in (4).
This yields
d a 1.3ay3a2r 1 h 4 [b2 + bj4N 1]
d N 2 „ 0 f [ K f - 1.2732a r12h - 2 ( a 2 + b2 + b 1) 2 ]
( 10)
Thus, we have deduced the differential equation (10) for the evaluation of
subcritical crack growth in the case where the pipe is depressurized. This equation
describes only the kinetics o f fatigue crack propagation. To com plete the
m athem atical model, we supplement it with the following initial and final
conditions [2, 3]:
48 ISSN 0556-171X. npoôëeMbi npounocmu, 2009, N 1
Prediction of Residual Pipeline Resource
N 2 = 0, '- = i o , ( 11)
N 2 = N g a = h 1, ( 12)
where S o is the area o f the initial crack. For small surface elliptic cracks [3], the
ratio o f the semiaxes a o and bo o f the ellipse takes the following approximate
value: x = b 0 / a 0 ~ 0.7 and, hence, N 2 = 0 and a = 1.2a0 , where 2 a 0 is the
length o f the crack on the surface o f the pipe wall.
Thus, the m athematical m odel used to predict the operation period prior to
the depressurization o f a pipe o f oil m ain includes relations ( 10)—(12). The
material constants a , i , K f c , and a o f are determined experimentally [2, 3].
P ipe R esidual Life A ssessm ent. Integrating the differential equation of
growth o f a fatigue crack ( 10) w ith initial (11) and final ( 12) conditions, we get
C 3C 2 ( 1 1
N = — | ----------- .
g C 1 ( a o h 1 ) C 1 ̂h 1
+ — ln | — (13)
where
C 1 = 1.2726 a ß r 4 h f 4 ( b? + b? N 1), C 2 = a 2 f K0 f K f c ,
C 3 = 1.2732 a 2 f r12 h f 2 ( a 2 + b 2 + b1)2 .
We now substitute the data obtained for the pipe o f the Krem enchug-
Kherson oil m ain [3], i.e., a x = 0, a 2 = 3.5 MPa, b^ = 0.15 MPa, b 2 = 1 MPa,
r = 0.5 m, h 1 = 0.012 m, Q = 200 MPa, o Y = 420 MPa, o s = 880 MPa, N 1 =
= 28• 104 cycles, K f c = 86 M PaVm , and ay3 = 3 • 10_4 cycle- 1 , in relation (13).
This yields
N g = 7.13(a-1 - 83.33) + 46.07 ln(83.33a0 ). (14)
In the absence o f longitudinal tension-com pression o f the pipe, i.e., for a = 0,
we find
N g = 5 .7(a -1 - 54.82) + 36.88ln(a 0 ). (15)
Further, in the absence o f both longitudinal tension-com pression o f the pipe
( a = 0) and hydraulic oscillations o f pressure ( b1 = 0 , N 1 = 0), we obtain
N g = 814.66(a-1 - 56.57) + 4930.36ln(a 0 ). (16)
Relations (14)-(16) are used to construct the dependences o f the residual
service life N g on the size o f the initial defect a 0 on the inner surface o f the oil
pipeline (Fig. 2).
In the case where the longitudinal tension-com pression o f the pipe and
hydraulic oscillations o f the pressure o f oil are neglected, the residual service life
o f the pipe specified by relation (16) is too long to be regarded as realistic.
ISSN 0556-171X. npoôëeMbi npounocmu, 2009, N9 1 49
t, years
Yu. V. Banahevych, O. E. Andreykiv, and M. B. Kit
Fig. 2. Dependences of the residual life of the pipe on the initial size of the defect Oq computed
according to relations (14) (curve 1) and (15) (curve 2).
tg , years tg , years
3
Fig. 3 Fig. 4
Fig. 3. Dependence of residual lifetime of pipe tg on the defect initial size a0 at the change of
frequency n of bolts opening-closing [(/) n = 30; (2) n = 40; (3) n = 50; (4) n = 73].
Fig. 4. Dependence of residual lifetime tg of pipe on the defect initial size ao at the change of
pressure p amplitude b on flow turbulence [(/) b = 0.05; (2) b = 0.1; (3) b = 0.15].
O p tim um O p era tio n P a ra m e te rs fo r Oil R epum ping . For the choice of
optimum operating parameters o f repumping oil, which could provide reliable
lifetime o f pipe o f oil pipeline with set imperfectness, we study the effect o f each
o f such parameters on the period tg o f subcritical crack propagation in a pipe.
For this purpose, w e’ll take advantage o f dependences (13) and for each o f such
parameters we will write down these dependences in such kind:
change o f frequency n in the pipe o f oil pipeline o f closing and opening of
bolts per year
N g
t g = ----- , where n = 3 0 ,4 0 ,5 0 ,7 3 , (17)
g n
change o f amplitude b 1 o f pressure in a pipe at turbulence o f oil flow
N g ( b i )
t g = ----------- , where b 1 = 0 .0 5 ,0 .1 ,0 .1 5 , (18)
50 ISSN 0556-171X. npoôëeMbi npounocmu, 2009, N9 1
tg , years
Prediction of Residual Pipeline Resource
Fig. 5. Dependence of residual lifetime tg of pipe on the defect initial size a at the change of size
of tensions Q in a pipe under its squeezing by the soil [(/) Q = —150 MPa; (2) Q = —100 MPa;
(5) Q = —50 MPa].
change o f size o f tensions o in the wall o f pipe from its squeezing by the soil
N g ( Q )
t g = — ------, where Q = —150, — 100, —50. (19)
45 n
Graphic dependences o f the residual lifetime o f pipe o f oil pipeline on the
above parameters are presented in Figs. 3 -5 using formulas (17)-(19).
Conclusions. From the analysis o f graphic dependences (see Fig. 3 -5 ) it is
possible to draw the following conclusions:
(i) the decrease o f a num ber o f the bolts closing-opening increases the pipe
lifetime;
(ii) presence o f turbulence o f the oil flow in the pipe decreases its lifetime,
which requires best synchronization o f pum ps’ operation;
(iii) the decrease o f p ipe’s squeezing by the soil results in the increase o f the
pipe lifetime.
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the-art,” M a te r . S c i., 39, No. 3, 7 -27 (2003).
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o f M a te r ia ls a n d S tre n g th o f S tr u c tu re s [in Ukrainian], Issue 2, Kamenyar,
Lviv (1999), pp. 141-148.
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Yu. V. Banahevych, O. E. Andreykiv, and M. B. Kit
5. V. M. Agapkin and B. L. Krivoshein, M e th o d s f o r th e P r o te c t io n o f
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Received 11. 06. 2008
52 ISSN 0556-171X. npo6n.eMH npounocmu, 2009, N 1
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