GROUP ASSIGNMENT Pipeline Upheaval Buckling Analysis and Design
Chomphoonuch Waisayaphan
ABERDEEN UNIVERSITY
Ergin Salihoglu
SUBSEA ENGINEERING
Hamidreza Yeganeh
MSc Program 2011-2012
Kingsley Sunday Placid Ihuoma
EG55F2&G2 Course Coordinator Dr Alfred Akisanya
PIPELINES and SOIL MECHANICS
Contents ABSTRACT
1
INTRODUCTION
1
1.0
2
SOIL PROPERTIES AND CHARACTERISTICS
(Manager: Sunday, Kingsley)
2.0
POSITIONING ON THE SEABED AND TRENCHING PO
3
(Manager: Sunday, Kingsley)
3.0
SUBSEA FACILITIES
4
(Manager: Waisayaphan, Chomphoonuch) Chomphoonuch)
4.0
PIPELINE MATERIAL
5
(Manager: Ihuoma, Placid)
5.0
UPHEAVAL BUCKLING ANALYSIS
8
(Manager: Yeganeh, Hamidreza)
6.0
PIPELINE CROSSING
13
(Manager: Salihoglu, Ergin)
7.0
SAFETY AND ENVIRONMENTAL CONSIDERATIONS
17
(Manager: Waisayaphan, Chomphoonuch) Chomphoonuch)
8.0
CONCLUSION AND RECOMMENDATION
18
REFERENCES
18
APPENDIX
20
MANAGERS OF THIS DESIGN This Pipeline Pipeline design was done by members of Group four (4). With respect to major sections, the manager of each section is as presented presented above, below the section(s) section(s) managed towards making this design a success; success; other sections sections comprising the Abstract, introduction, conclusion, recommendation and arrangements were handled by the group as a unit.
Disclaimer: The design was carried out in accordance to industrial standards and international standard code of practi practices ces and papers, papers, aimed aimed towards towards the achiev achievemen ementt of MSc Subsea Subsea Engine Engineeri ering, ng, Univer Universit sity y of Aberdeen Aberdeen;; However, it does not in any way represent any real life project(s) and as such the data and assumptions made herein should not be relied upon or transferred in any form to any real practical project(s) with or without notice to the designers. i
ABSTRACT Following the assessment, analysis and design of the pipelines using various pipeline design considerations, a detailed upheaval buckling analysis and design was provided for both pipeline A and pipeline B connecting the BLP. Major design factors considered are pressure, temperature variation, and seabed imperfections along the pipelines route. The results yielded a rock-dump height for pipeline A between the ranges of 0.11m - 0.75m maximum for imperfections of 0.3m to 0.5m respectively; and the crossings required rock-dumps of 0.96m and 0.03m at KP 4Km and 8Km respectively. The design also gave requirements of rock-dumps for pipeline B as between the ranges of 0.2m – 1.53m maximum for imperfections of 0.1m to 0.5m (higher due to single pipe, less weight); note that the rock-dump also varies due to imperfections. Other aspects of the design such as geotechnical investigation gave an approximate soil bearing capacity of
2
KN/m , and the verification of the soil type and properties
closely agrees with the CPT results in the design spec (not included in this report). The pipelines material was also found to be adequate in terms of pressure containment (burst) and collapse, considering reellay installation method. Furthermore, the design considered subsea facilities selection such as manifolds, templates, subsea trees and pipeline ancillaries, etc, with respect to design data, environmental factors and reasoned assumptions. Finally, safety guidelines and environmental factors that were taken in account during the design and also additional to be adhered during installation, conforming to standards and legislations were also outlined herein as part of the design. INTRODUCTION This design aims to provide assessment, analysis and design against upheaval buckling of two major subsea pipelines tiebacks: Pipelines from both drill centre C and from drill centre S to Bridge Linked Platform (BLP). Both Reservoirs are being considered by a major field operator as two oil and gas fields, however, they are both connected to the same production platform called the Bridge Linked Platform (BLP) as their estimated reserves does not justify the installation of a standalone production platforms at their respective locations, thus, the two fields are developed as tie-backs to a new platform (BLP) adjacent to an existing production platform. Drill centre C and drill centre S are located at 10km and 17km respectively away from the BLP. The water depth for this project was estimated at 95m, and three major crossings are expected, two for the pipeline from drill centre C to BLP and one for the pipeline from drill centre S to BLP. The main production Pipeline from drill centre C to the BLP shall be an 8”/14” pipe-in-pipe with aerogel insulation and with design life of 15years; and is expected to transport production products from up to three separate wells from C reservoir to the BLP, this pipeline shall hereafter be referred to as pipeline A. On the other hand, the main production pipeline from drill centre S to the BLP shall be a 10” wet insulated single pipeline with design life of 20years; and is expected to transport production products from up to five separate wells from S reservoir to the BLP, hereafter be referred to as pipeline B. The design scope is expected to cover aspects of site investigation and geotechnical analysis, positioning on the seabed, subsea facilities selection, pipelines material checks, upheaval buckling, crossings, safety and environmental considerations. Detailed specifications for this project are presented in the design specification manual (not included in this report). 1
1.0
SOIL PROPERTIES AND CHARACTERISTICS
Following the CPT results from the geotechnical investigation, the following deductions, verifications and recommendations are can be derived using simplified chats from Robertson and Campanella, 1984, and Searle, 1979 as presented in Figure 1.0A and Figure 1.1A respectively in appendix A. A summary of the original results from the soil report and the verification is as presented in Table 1.0 appendix A: Assuming undrained condition which is true for the case of a completely Submerged soils (Subsea soils) as pore water remains in position during the early years of loading. Thus, angle of internal Friction,
, and the ultimate bearing capacity equation becomes; q U = c.NC = 5.14CU +
for trenched condition, then q U =5.14CU yields
KN/m2 for CU
2
vo,
and
vo=0
approximately [2, 3].
The verification of the CPT results along both routes from both drill centres to BLP using a combination of Fig. 1.0A and Fig. 2.0A, the results generally conforms to the representation from the CPT results and thus can be relied upon. The soil along both routes showed identical soil properties and characteristics; the first 1m depth is generally dominated by loose to dense silty SAND which is usually underlain by a thick layer of soft to firm silty CLAY to complete CLAY soil, occasionally by dense SAND [1, 2, 3]. The profile showed an average range of effective angle of internal friction of
-
which will yield
reasonable shear resistance value, while the majority of the soil layer dominated by CLAY with undrained cohesion value generally less than 10KN/m2 which will yield low bearing capacity ( KN/m2) and represents soft to very sensitive clay are will be susceptible to settlements upon loading from pipeline. Furthermore, this loading may also induce differential settlements which will result to free-spanning or buckling of the pipeline depending on the amount of settlements and other contributing factors [1, 2]. 1.01
Placement of Pipelines on Seabed and On-Bottom Analysis
The laying of the pipelines on the seabed shall be done with Reel-Lay method to further buttress the pipelines thicknesses specified for Reel-lay method of installation. However, a pre-installation survey shall be carried out to account for any seabed changes due to dwell time from the initial survey; also a preparation for the pipeline crossing shall be made. Trenching of both pipelines has greatly reduced the On-bottom analysis issues such as wave, currents, lateral stability, and other hydrodynamic forces. The lateral friction can be calculated from the angle of internal friction, shear strength and the side-slope angle of the trench. A predominant stability issue associated with trenched pipe is upheaval buckling as the pipeline will be laterally and downwardly restrained, thus, the only alternative is Upheaval Buckling (addressed later, herein) [2, 3]. 1.02 Recommendations Following the available data from the CPT test and its inconsistency in test depths, there is need to carry out Vibrocore test to enable intact/un-remoulded soil for accurate determination and identification of soils, unit weight of the soil, consolidation and settlement, shear strength, Atterberg limit and moisture content test, grain size distribution, carbonate content, lateral angle of friction for excavation and burial operations, Metocean survey for hydrodynamics and erosion issues, corridor width for safe installation operation. 2
2.0 POSITIONING ON THE SEABED AND TRENCHING Following the soil analysis from the CPT results, it was derived that the soil bearing capacity was 2 predominantly yields KN/m2 for CU approximately. Also majority of the soil was dominated by CLAY mostly overlaid by Silty Sand. Positioning on the seabed and trenching will be very much controlled by the soil characteristics, properties and behaviour upon loading which have been to an extent determined above. The trenching operations and appropriate tools/equipments based on the soil analysis shall also be looked into, and appropriated recommendations made thereafter [2, 3]. 2.01 Positioning on The Seabed Prior to installation as mentioned earlier, it is recommended to perform pre-installation route survey to enable correlation with the previous survey, considering amount of dwell time from original survey. Also, a systematic analysis of equipment and installation operations shall be performed in order to identify possible critical items or activities which could cause or aggravate a hazardous condition, and to ensure remedial measures are taken. Special attention shall be given to the crossing sections of the pipelines. This operation will include seabed preparation, especially for the pipelines crossings [3]. S-Lay and Reel-Lay are both suitable methods for this project (with no restraint from NB and water depth), but a more suitable one will be selected following pipeline design considerations, economical and laying speed. S-Lay method with an average laying speed/rate of 4 – 5 Km/day (approximately say, $350K/day) stands advantageous over Reel-Lay considering Reeling of the Pipe-in-Pipe and the induced stresses associated with Reeled PIP. However, the S-lay method is without flaws compared to the ReelLay method highlighted thus; the operation method of S-lay of offshore welding will pose a quality assurance and financial problem considering quality assurance of the PIP welding. Furthermore, the Reel-lay method (onshore weld) offers a faster laying rate of approximately 1 – 2km/hr and about $200K/day (can take advantage of short weather windows). Following the above consideration, it is clear that both Pipelines A and B shall be installed using the ReelLay method as it offers advantages of laying speed, cost, and onshore quality assurance, while still accommodating the Outer diameters of the pipelines within its Reeling limits; Thus, installation shall be performed with Reel-Lay method which agrees with specified thicknesses based on Reeling. 2.02 Trenching Trenching of the pipelines offers protection (against dropped objects, fishing gear, etc) and reduced onbottom stability issues of the pipelines. This is further enhanced by backfilling. Basically, the various trenching methods used for subsea pipeline operations are [1,4]:
Jetting, Dredging (with cutter heads), Mechanical cutters Ploughing.
3
The soil bearing capacity is a key to selecting of the trenching method. From the geotechnical consideration of the soil properties and behaviour considered earlier, it was ascertained that the soil bearing capacity is KN/m2, and this may fall significantly lower as the frequency of the CPT results may not represent the entire soil properties along the route as soil properties can change significantly with history. Assuming this is not the case, and the data we obtained are through representative data, then jetting and Ploughing will be the most suitable for this project considering the soil type (soft Clay with layers of silty Sand), properties (undrained), water and trenching depth. We shall go further to narrow our trenching selection based on certain consideration as will be presented. Ploughs work most effective in sands and clays giving good performance rates with minimal maintenance time, although their capability in rocks is highly dependent on fracture spacing and strength. From literature, the plough performance prediction from standard CPT is difficult; however, ploughing rates of 400-450m/hr can be achieved for loose/very soft soils, pitched to be consistent with the low bearing capacity of the underlying soil [4]. Jetting on the other hand employs water jets to cut or liquefy the soils around and in front of the pipeline practicable for both cohesive and cohesionless soils. It can achieve a jetting speed of about 200350m/hr for CU
2
at 1000psi, for the same jetting pressure at CU
2
the trenching
speed can drop significantly. Cohesionless soils (loose sands and silts) are generally easy to cut and may only require low jetting pressure (say 130psi), although difficult due to shallow slope (
-3 ) [4].
Thus, following analysis for both trenching methods, the ploughing trenching method shall be used for this project. The seed ploughing compared to jetting speed offers financial advantage, and reduces the risk liquefaction and cavitation from jetting upon sudden excess overburden pressure from the equipment, and possibly shearing and failure of the soil related to permeability to relieve pore pressure. Care should be taken in refilling the trench with the disturbed soil as the characteristics will be different. The trenching method shall be performed as post-lay trenching considering soil and pipeline properties [2]. 3.0
SUBSEA FACILITIES
This section will present the subsea system designed and selected for both pipelines; challenging seabed characteristics and system availability are the major considerations for choosing and designing appropriate devices. The following criteria will be used in deciding:
All subsea production systems are designing for a 15-year design life;
Maximum design water depth is 95m and design temperature is 120 degree Celsius;
3.01
Subsea Manifold: for the commingling of produced fluids and distribution of control fluids.
According to this field conditions, there are two lines which are oil and gas lines. From design consideration, two subsea manifolds were selected, one each for the oil and gas drill centres to reduce associated flow assurance problems; Multiphase flow comes with increased flow assurance problems, and maintenance difficulties and will incur more cost Therefore, this project is designed to use two manifolds for each oil and gas lines [5,7]. 4
3.02
Subsea Trees: Horizontal subsea trees were selected for this project to enable easy
maintenance and access to tubing during work-over operations. The main functions of subsea tree are: direct the produced fluid from well to the flowline or inject protection fluid such as inhibitor downhole; monitor well parameters such as pressure and temperature and regulate the fluid flow via a choke [5, 7]. 3.03
Production Rise: rigid risers shall be used for project, considering a fixed platform with
insignificant movements (6 DOF). Rigid risers are economical and less complex compared to flexible. Other equipments that may interface with the riser system are, bend stiffeners and Riser Anchor [5, 7]. 3.04
Subsea umbilical and Jumper (or spool piece): Umbilical was selected to ensure control of
drill centres, supply of control fluids, and chemicals injection. A Jumper is a short pipe connector used to transport fluid from one subsea component to another subsea component such as tree and manifold. Jumpers/flying leads shall be required [5, 7]. 3.05
Template: The main purposes for deploying templates is are to protect the subsea equipments
from accidental loads such as dropped objects and fishing gear impacts (overtrawlable design). In addition, regarding flow monitoring and maintenance, this structure will make such operation easy and less expensive as equipments are closely housed [6]. 3.06
Pipeline Ancillary Equipment Flanges and connectors use to provide the pressure containing connection between two parts of pipeline. A compact flanges shall be deployed as they are small, light and guaranteed seal integrity. A collet type connector will be employed for small-bore connections whilst, a clamp type connector will be deploying for large bore connections [8].
Tie-in Spools, Tie-in systems and intervention tools : Tie-in Spools are used to connect one part of subsea system to another and relieve axial stresses. The flow-lines and umbilicals will be connected to the production manifolds by means of field proven and remotely operated tie-in tools [8].
4.0
PIPELINE MATERIAL
4.01
PIPE A (PIP) - INNER PIPE MATERIAL DATA
Do=
NB- 8” = 203.2mm;
Di = D o - 2t = 203.2 - [2x29] = 145.2 mm
Pi = Design internal pressure of the pipe, which is 525bar = 52.5 MPa; Assuming P O = , considering negligible effects from external pressure on inner pipe as this is taken up by the carrier pipe. 4.01.1 The Hoop Stress Analysis [For Elastic Deformation] Verifying wall thickness region, From hoop stress equation, we have;
, since t= 29 =
7.26 the pipe is considered thick. (52.5) = 162.051 MPa
Populating the equation for various SMYS rating w.r.t. temperature and checking to verify if the pipeline satisfies the hoop stress equation shown in the Table 1.0 as presented below; 5
Table 1.0: Hoop Stress Analysis for Pipeline A T o ( C) 20 50 100 150
SMYS (Y) (MPa)
ƒ 1
ƒ 2
ƒ 1 ƒ 2Y (MPa)
450 450 420 400
0.77 0.77 0.77 0.77
1 1 1 0.867
346.50 346.50 323.40 267.04
(MPa) 162.051 162.051 162.051 162.051
0.468 0.468 0.501 0.607
The maximum operating temperature of the fluid in the pipe is given as 112oC, hence to capture this temperature we worked with the temperature effect at 150 o C, as well as analysed the effect at various temperature variations. From the analysis it was ascertained that the pipeline properties satisfies the DNV elastic deformation equation. Hence the material grades of the pipe DNV SMLS 450 is adequate based on hoop stress requirements [10]. 4.02
PIPE A (PIP) - CARRIER PIPE MATERIAL DATA
Do= NB- 14” = 355.6mm; t = thickness = 18mm; D i= D o - 2t = 355.6 - [2x18] = 319.6 mm Assuming internal pressure, P i =0 (assumed to be taken up by the internal pipe); P O = 0.955 MPa 4.02.1 Collapse Check Design: Using (eqn. 3, 4, and 5), we have; Table 1.1: Collapse Check Pipeline A o
T ( C)
Y (MPa)
3
E (GPa = MPa x 10 )
PEC (MPa)
PY (MPa)
PC (MPa)
P
Y m .Y sc . P o
i
P C
20 75 125 150
360 320 300 290
207 206 203 200
60.25 59.97 59.09 58.22
36.45 32.40 30.37 29.36
31.19 28.51 27.01 26.22
0.0401 0.0438 0.0463 0.0477
From the analysis on table 3, it was ascertained that the pipeline properties satisfies the collapse overpressure criterion, Hence the material grades of the pipe DNV SMLS 360 is suitable as a carrier pipe for the proposed project operation to withstand collapse [10]. 4.03
Pipe BMaterial Data (In accordance to DNV OS F101)
D0= NB- 10” = 254mm ; = 1MPa );
PO =
Di = D o - 2t = 254 - [2x22] = 210 mm;
Pi , = 300 bar = 30 MPa ( I0 bar
gh , 1025 x 9.81 x 95 = 0.955 MPa. Considering a medium class safety factor as
trenching have reduced the hazard level; we have,
sc =
1.138,
m
= 1.15, and
u=
1, chosen to obtain an
allowable hoop stress of 96% of SMYS (from DNV F101 section5 306, pg 45) 4.03.1 The Hoop Stress Analysis [For Elastic Deformation] ≤ 1 f 2
Y;
– Hoop stress design criterion
(eqn. 1); Y is specific minimum yield stress
f 1, 2 – are various design factors to account for variability in strength and temperature.
6
f 1 =
= 1/(1.138 x 1.15) = 0.77. However, DNV recommends use of SMTS instead of
SMYS i SMTS/ 1.15 is less than SMYS. f 2 = 1 for temperatures < 120oC. t (thickness)
for thin pipe, else considered as thick; but, 22
, since t= 22
12.7, then the
pipe is considered a thick walled pipe [10]. Calculating The Hoop Stress Fo Thick Pipe As Given By DNV-OS-F101 =
(eqn. 2);
(pi -po )MPa,
=
(30 - 0.955)MPa = 154.523 MPa
Checking for hoop stress satisfaction at various temperature in accordance to (eqn. 1) Table 1.2: Hoop Stress Analysis for Pipeline B o
T ( C)
SMYS (Y) (MPa)
ƒ 1
ƒ 2
ƒ 1 ƒ 2Y (MPa)
20 50 100 150
450 450 420 400
0.77 0.77 0.77 0.77
1 1 1 0.867
346.50 346.50 323.40 267.04
(MPa) 154.523 154.523 154.523 154.523
0.446 0.446 0.478 0.579
Given the maximum operating temperature of the fluid in the pipe as 110 oC, this was taken care of with temperature effect at 150o C, with other temperature effects analysed. From the analysis it was ascertained that the pipeline properties satisfies the DNV elastic deformation equation. Hence the material grades of the pipe DNV SMLS 450 satisfies hoop stress requirements. 4.03.2 Collapse Check Design Considering external overpressure of the pipeline during installation, collapse assessment will be performed to withstand the imposed load from the external overpressure using the equations [10, 11]: Collapse pressure,
P C
1 1 2 2 P EC P Y
Elastic collapse pressure,
P EC
Yield external over pressure,
0.5
2 E
(eqn. 2), t
3
; 1 v 2 Do
P
Y
(eqn. 3 )
2t
(eqn. 4)
Do
But, PO = gh, 1025 x 9.81 x 95 = 0.955 MPa, v = 0.33; Young’s Modulus = E;
m
= 1.15;
SC
= 1.138
Table 1.3: Collapse Check Pipeline B o
T ( C) Y (MPa)
3
E (GPa = MPa x 10 )
PEC (MPa)
PY (MPa)
PC (MPa)
P
Y m .Y sc . P o
i
P C
20 50 100 150
450 450 420 400
207 207 204 200
30.19 30.19 29.75 29.17
77.95 77.95 72.76 69.29
28.15 28.15 27.54 26.88
0.0444 0.0444 0.0454 0.0465 7
4.04
Maximum Strain In The Reel Pipeline
Considering the Reel-lay installation method and speed of operation, a first level reeling baseline strain (PIP) to be referenced is as presented thus; =
; Do = outer diameter of pipe; Rdrum = radius of the reel drum (Assuming 8m = 8000mm).
And 5.0
, where t is the pipeline wall thickness.
UPHEAVAL BUCKLING ANALYSIS
As the lateral soil resistance in a buried pipeline is higher than the vertical resistance, so the vertical movement of the pipeline should be considered as a main cause of buckling which is called upheaval buckling [13]. The aim of the following calculation is that to investigate whether the 1 meter suggested backfill soil is enough for both routes or not. Then there are some recommendations for each KP of both pipelines. 5.01
Pipeline A
In order to calculate the upheaval buckling, DNV has introduced the below equation to obtain the Effective Axial Force weather it is the thick or thin pipeline: (DNV-OS-F101:2007 Eq.4.11)
. To obtain the total effective axial force of pipeline A both effective axial forces of inner and carrier pipes should be considered per each kilometre (KP). To clarify the results all related calculations are presented in appendix B and an example for KP number 1 has been shown in below:
To prevent the upheaval buckling the principal issue is the weight of pipeline. It should be considered that the pipeline is submerged so the weight in the water is lower than the air according to the below calculations:
Table 2.0: Pipeline Weight computation 1220.584
1470.15
13.1
24.298
998.633 8
In the next stage by employing the industrial equation the length of imperfection can be calculated. Due to %10 inaccuracy in survey equipments (%10 will be added to the imperfection heights, H). Using a common industrial equation presented below [17], length of imperfection is calculated thus:
Table 2.1: Computation of length of imperfection Frequency(Imperfection Number of imperfections Imperfection height per kilometer) in 10 Km H (m) 50 5 0.1 15 1.5 0.2 6 0.6 0.3 8 0.8 0.4 4 0.4 0.5 To find the upheaval buckling weight DNV and lecture notes referred to Palmer described as below [12]:
The corresponding
Length (m)
23.45 27.89 30.87 33.17 35.07 function which is
values are calculated
in Table 2.1B, of appendix B. By using the below equation the value of which is the amount of up heaval buckling will be found for each imperfection. For example the amount of up heaval buckling weight for the lower imperfection H=0.1 is about
,
On the other hand by comparing the total apparent weight of pipeline which is calculated in previous section, the height of required soil in each kilometre can be calculated from below equation. It should be mentioned that the is a submerged unit weight of soil in route A and is 8 KN/m3 . Also the which is the peak up lift resistance factor is equal to 0.4 in route A.
9
So for the first KP: Detailed calculation is presented in Table 2.2 below. Table 2.2: Computation of weight and height of soil required for Pipeline A K.P
1 2 3 4 5 6 7 8 9 10
W (KN)
W (KN)
W (KN)
W (KN)
W (KN)
H(soil)
H(soil)
H(soil)
H(soil)
H(soil)
H=0.11 4.19 3.99 3.88 3.69 3.52 3.41
H=0.22 6.05 5.92 5.90 5.77 5.64 5.61
H=0.33 8.80 8.35 8.20 7.90 7.60 7.46
H=0.44 11.17 10.77 10.58 10.19 9.81 9.62
H=0.55 13.96 13.46 13.22 12.74 12.26 12.03
H=0.11 0.54 0.51 0.49 0.46 0.43 0.41
H=0.22 0.53 0.52 0.51 0.50 0.49 0.49
H=0.33 1.11 1.06 1.05 1.01 0.98 0.97
H=0.44 1.33 1.29 1.28 1.24 1.21 1.19
H=0.55 1.56 1.52 1.50 1.46 1.42 1.40
3.18 3.08 2.92 2.77
5.37 5.34 5.20 5.05
7.03 6.89 6.62 6.35
9.07 8.89 8.68 8.33
11.34 11.12 10.85 10.41
0.36 0.34 0.31 0.28
0.47 0.47 0.46 0.45
0.92 0.90 0.87 0.84
1.13 1.12 1.10 1.06
1.35 1.33 1.30 1.26
It should be mentioned that as there is no seabed profile, so the exact location of the imperfection cannot be calculated. On the other hand due to 1 meter suggested backfill, there are different comments and heights for each KP and related imperfections. For example for the first KP and the lowest imperfection H=0.10 m there is no need of rock dumping (the submerged unit weight of rock=9.5 and should be applied). Table 2.3: Computation of height of rock-dump required for Pipeline A K.P
H(Rock)
H(Rock)
H(Rock)
H(Rock)
H(Rock)
0 1 2 3 4 5 6 7
H=0.11 -0.24 -0.32 -0.34 -0.36 -0.39 -0.41
H=0.22 -0.17 -0.22 -0.22 -0.23 -0.24 -0.24
H=0.33 0.29 0.26 0.25 0.23 0.21 0.20
H=0.44 0.52 0.50 0.48 0.46 0.44 0.42
H=0.55 0.75 0.72 0.71 0.68 0.66 0.64
-0.44 -0.46 -0.49 -0.52
-0.26 -0.26 -0.27 -0.28
0.17 0.16 0.13 0.11
0.39 0.38 0.36 0.34
0.60 0.59 0.57 0.55
8 9 10
10
Figure 1.0: Presentation of rock-dump requirement in each KP for Pipeline A. 5.01.1 Analysis of results for pipeline A So by attention to the heights of the back fill of the soil, pipe diameter and the suggested height of backfill, it is clear that 1 meter backfill soil is not net and sufficient for the whole pipeline route A. It is recommended to rock dump for imperfection 0.3 meters and higher. (DNV recommends a safety class for rock dumping and the lower one is one for the covered rock.DNV-RP-F110-page 32). As it indicates, the maximum height of Rock dump is required is 0.75 m for the 0.55 m imperfection height in K.P 1. 5.02 Pipeline B Similarly, the occurrence of up heaval buckling for the pipeline B will be calculated. In first stage, the effective axial force in each kilometre is calculated as presented in Table 2.2B, appendix A, and the length of imperfections are presented in Table 2.4 below: Table 2.4: Computation of length of imperfections for Pipeline B No in 17 Km H (m) Length (m) 85 0.10 17.49 25.5 0.20 20.80 10.2 0.30 23.02 13.6 0.40 24.74 6.8 0.50 26.16 Furthermore, Using palmer equation and graph, the functions of Φι and Φw have been calculated and presented in Table 2.3B, appendix B [12]. Again by comparing the total apparent weight of pipeline which is described in previous section, the height of required soil in each kilometre can be calculated as presented in Table 2.5, and the required height of rock-dump is calculated in Table 2.6. is 7.5 and
is 0.3.
Table 2.5: Computation of weight and height of soil required for Pipeline B W W W W W K.P H(soil) H(soil) H(soil) (KN) (KN) (KN) (KN) (KN) 0 H=0.11 H=0.22 H=0.33 H=0.44 H=0.55 H=0.11 H=0.22 H=0.33 1 6.88 16.42 20.63 27.51 33.27 1.16 2.17 2.51 2 6.66 16.12 19.99 26.65 32.24 1.13 2.15 2.46 3 6.56 15.82 19.35 26.22 31.22 1.11 2.12 2.41 6.45 15.77 19.04 25.80 30.71 1.09 2.12 2.39 4 6.29 15.45 18.42 25.16 29.71 1.07 2.09 2.34 5 6.23 15.13 17.82 24.48 28.73 1.06 2.06 2.29 6
H(soil)
H(soil)
H=0.44 2.99 2.94 2.91 2.88 2.84 2.79
H=0.55 3.35 3.29 3.23 3.19 3.13 3.07 11
7 8 9 10 11 12 13 14 15 16 17
6.02 6.19 6.06 5.93 5.83 5.62 5.49 5.46 5.33 5.20 5.09
14.81 14.74 14.41 14.07 13.99 13.65 13.30 13.05 12.56 12.08 11.84
17.50 17.20 16.60 16.02 15.74 15.17 14.85 14.57 14.02 13.48 13.22
23.81 23.55 22.88 22.21 21.95 21.29 20.63 20.37 19.72 19.07 18.81
27.77 27.30 26.36 25.43 24.98 24.08 23.20 22.77 21.91 21.07 20.65
1.03 1.06 1.04 1.02 1.00 0.97 0.95 0.94 0.92 0.90 0.88
2.03 2.02 1.99 1.96 1.95 1.92 1.89 1.87 1.82 1.77 1.74
2.26 2.24 2.19 2.14 2.11 2.06 2.03 2.01 1.96 1.91 1.88
2.74 2.72 2.68 2.63 2.61 2.56 2.51 2.49 2.44 2.39 2.37
3.01 2.98 2.92 2.85 2.82 2.76 2.70 2.67 2.61 2.54 2.51
Table 2.6: Computation of height of rock-dump required for Pipeline B K.P H(Rock) H(Rock) H(Rock) H(Rock) H(Rock) H=0.11 H=0.22 H=0.33 H=0.44 H=0.55 1 0.14 0.73 0.97 1.28 1.53 2 0.12 0.72 0.94 1.25 1.49 3 0.12 0.71 0.92 1.24 1.46 4 0.11 0.70 0.90 1.22 1.44 5 0.10 0.69 0.88 1.20 1.41 6 0.09 0.67 0.85 1.17 1.38 7 0.07 0.66 0.84 1.15 1.35 8 0.09 0.65 0.83 1.14 1.33 9 0.08 0.64 0.80 1.11 1.30 10 0.07 0.62 0.77 1.09 1.27 11 0.06 0.62 0.76 1.08 1.25 12 0.04 0.60 0.73 1.05 1.22 13 0.03 0.58 0.72 1.03 1.18 14 0.03 0.57 0.70 1.02 1.17 15 0.02 0.55 0.68 0.99 1.13 16 0.00 0.52 0.65 0.96 1.10 17 0.00 0.51 0.64 0.95 1.09 5.02.1 Analysis of results for pipeline B Considering to the required backfill soil for the pipeline B indicates that the amounts of required soil vary between 0.88 and 3.35 m for different K.P, depending on the height of imperfections. Considering maximum 1.14 m backfill soil which does not provide sufficient weight for the pipeline B in imperfection 0.1, thus, rock dumping is needed. From the Table 2.6, the suggested rock dumping height has been recommended for different imperfections and K.P. The analysis showed that more rock dumping is required for the first K.P which has a higher effective force due to higher temperature. On the other hand the interesting result is that the maximum height of required rock dumping is 1.53 m where the height of imperfection is 0.5 m in K.P number 1. It means that usually with higher imperfection needs higher rock dumping. Finally by considering the frequency of each imperfection easily the total number of each imperfection can be achieved in whole route to forecast the volume and the cost of rock dump. It should be mentioned as we haven’t the seabed profile, we cannot give a more precise recommend for the rock dumping analysis. 12
Figure 2.0: Presentation of rock-dump requirement in each KP for Pipeline B. 5.03 Results interpretations Considering to the results from pipeline A and B, indicates that with close apparent weight, the pipeline A needs a very lower rock dumping rather than pipeline B. This is occurred from increase in the total second moment occasioned by the carrier pipe of pipeline A. It should be mentioned that he principal benefit of using a carrier pipe refers to the flow assurance aspect. On the other hand a high rock dump is needed due to the small diameter for pipeline B in larger imperfections. 6.0
PIPELINE CROSSING
The geometry of the each crossing along Pipeline A and B will be defined by the following criteria:
Vertical clearance between crossing and crossed pipelines minimum 300mm as defined in DNV OS F101.
Prelay and post lay rockdump required at each crossing location to support the crossing pipeline. Allowable Free-span limits should be calculated according to the DNV RP F105. As we don’t consider the current velocities and the pipeline at the crossing location covered with rockdump, we do not provide the calculation for free span limits for VIV considering the operation end of life condition.
We consider that the crossing is 2 section realised to reduce the imperfection height and to have a smooth transition length and to be comply the with safety of the existing pipeline. In order to reduce the imperfection height and to keep the safety distance to the existing pipeline, crossing pipeline will be taken out of the trenching 50 -70 m earlier and laid on the seabed then elevated at the calculated crossing length to cross the existing pipeline. In a real case scenario, for the both sections an independent upheaval buckling check must be carried out. In our project we carry the upheaval buckling check just for the second part where the pipeline is elevated to cross the existing pipeline. Upheaval buckling check is provided due to the out of straightness configuration of the pipeline at each crossing point. Buckling failure defined as an ultimate limit state (ULS). Due to insufficient data and general concept of this assignment we do not provide all checks required in the codes. Regarding the exiting codes pipeline needs to be designed considering the following load cases: • Pipeline Hydrotest; • Pipeline Empty; • Pipeline Flooded;
• Pipeline in Operation (start of live and end of live); 13
The following detailed checks not covered here are recommended in accordance to DNV Codes;
Local buckling checks for combined loading criteria; Detailed geotechnical investigation at the crossings; Crossing Support Sliding Overturning Checks.
Table 2.7: Crossing details for Pipeline A and Pipeline B Crossing
Description
details
Oil pipeline, pipe in pipe
Pipeline A Crossing
from Reservoir C to BLP. Gas trunk line 40 mm
Pipeline OL Existing
coating
Pipeline MU Existing
Oil pipeline
Oil pipeline, wet insulation
Pipeline B Crossing
from Reservoir S to BLP.
Pipeline MU Existing
Oil pipeline
Size
Length
(Inch)
(km)
14”/8”
10
Status
Location
Crossing Angel
Buried
44”+40mm Unknown Exposed 24”
Unknown Buried
10”
17
24”
Unknown Buried
4 km from C drill Centre 7,9 km from C drill Centre
56.60 600
Buried 14,5 km from S drill Cent.
55.60
Under certain pressure and temperature loads a pipeline will buckle when the effective force reaches a critical value. At very small imperfections the buckling will take place as a dynamic “snap” resulting in an instant drop in the axial effective force with an lateral or vertical (upheaval) deflection. We treat the pipeline crossing area as imperfection and carry out upheaval buckling calculation as the pipeline buried and laterally restrained. Pipeline A, Pipeline Data Crossed Pipeline 1: OL pipeline OD=44” and 40 mm Concrete coating, exposed on the seabed Crossed Pipeline 2: MU pipeline OD=24” and, buried and depth is unknown. Crossing Pipeline : Pipe in pipe ND: 14” / 8” ti = 29 mm, to = 18 mm, Total length= 10 km,
LO pipeline Crossing Point: km 4.00, MU pipeline Crossing Point: km 7,9 Pdesign = 525 bar, Pipeline is trenched and buried, H backfill =1.00 m Inner Pipe Grade DNV SMLS 450, assumed E= 200 GPa, Y= 420 MPa, Outer Pipe Grade DNV SMLS 360, assumed E= 203 GPa, Y= 300 MPa, o
o
3,
Inner pipe T: 105 C, Sea Temp.: 4 C , ρcontent= 150 kg/m Hwater = 91m at Cross. Points 6.01
Upheaval Buckling Calculation , ,
,
, ,
14
29 mm
29 mm > 17.78 mm inner pipe considered as thick pipe
18 mm
18 mm > 15.98 mm inner pipe considered as thick pipe
,
Hoop stress
,
Radial stress
, 6.02
,
Pipeline A Crossing at K.P.=4 km crossed OL pipeline, D= 44”+40 mm coating ;
Pa;
Safety margin for temperature 1.15, -4,889,59 KN;
L = 90 m assumed,
H= 1.1976+0.30 =1.50 m;
24.15,
;
W-Wpipe= 7.359 -1.729 = 5.63 KN/m; Hrock =0.96 m Using the Palmers graph and to find the download parameter Parameter”
we find first the “Length
= 22.45. This figure falls in the area in which a corresponding figures for
is not to determine. We assume that the graph for the assumption we can determine the corresponding
is linear decreasing. Based on our in Palmers graph. Our assumption is
based on several papers attached in annex. 6.03
Pipeline A Crossing at K.P.=8 km crossed MU pipeline, D= 24” ; ;
16.73; 6.04
Pa;
-4,500.10 KN; H= 0.40; L = 65 m assumed ;
W-Wpipe= 3.559 -1.729 = 1.83 KN/m;
Hrock =0.03 m
Pipeline B, Pipeline Data
Crossed Pipeline 2 : MU pipeline OD=24” and, buried and depth is unknown. Crossing Pipeline : Wet insulated Single pipeline, ND: 10” t = 22 mm, Total length= 17 km, MU pipeline Crossing Point: km 14,5 Pdesign = 300 bar, Pipeline is trenched and buried, H backfill =1.00 m Single Pipe Grade DNV SMLS 450, assumed E= 203 GPa, Y= 420 MPa, Inner pipe T: 86oC, Sea Temp.: 4 oC , ρcontent= 850 kg/m3, H water = 91m on Cross. Point In project speciation is indicated that existing pipeline is a buried 24” MU pipeline and trenching depth is not specified. Considering the worst case scenario, assumed that the exiting MU pipeline buried at the nearest point of seabed meaning MU pipeline has no soil backfill. ;
;
15
, 22 mm
22 mm > 12.7 mm pipe is considered as thick pipe
Pipeline B Crossing at K.P.=14.5 km crossed MU pipeline D= 24”
; ; 10.11;
K . P
T Pipeline
-1067.34 KN;
H= 0.40 m;
W-Wpipe= 2.0997- 0.4897 = 1.61 KN/m;
∆T Inner
Feff
∆T
(inner pipe)
Carrier
KN
Feff KN
Carrier
F eff KN
Pa,
total
H
L
(m)
(m)
L = 35 m assumed Hrock =0.00 m
Φι
Φw
e p i p
HRock W (m) - ) N K W (
Pipeline A Pipeline A Pipeline A Pipeline A Pipeline A 4 105 116,5 -3,731,81 25.59 -1,157,78 -4,899.59 1.50 90 24.15 0.014 5.63 0.96 8 98 108.1 -3,433.38 23.58 -1,066.72 -4,500.10 0.91 85 21.88 0.019 3.40 0.41 Pipeline B Pipeline B Pipeline B Pipeline B Pipeline B 1 4 86 94.3 -1,067.3 -1067.34 0.91 57 16.46 0.027 1.70 0.01 Recommendations : In order to reduce the rockdump height, based on global upheaval buckling failure along the pipeline A and B, we recommend reducing operation temperature through water cooling circuit or concrete coating as additional weight on pipe. That would have an effect on reducing the axial effective force which creates upheaval buckling.
16
7.0
SAFETY AND ENVIRONMENTAL CONSIDERATIONS
According to the standards and legislations, which have been chosen for designing the pipeline positioning on seabed, upheaval buckling design analysis, the crossing, pipeline material selection and subsea facility selections, the following safety and environmental considerations have and shall be adhered to: 7.01
Offshore Standard DNV-OS-F101 Submarine Pipeline Systems
Safety Philosophy Health, safety and environment, the entire process, which starts from the design process until decommission, must be done in compliance with national legislations and company policy with respect to health, safety and environmental aspects.
Concept development and design premises There are significant numbers of the areas, which need to be taken into account, such as subsea integrity. This area needs to consider the transport capacity and the flow assured. Moreover, inspection and monitoring during operation, for example, threat parameters to the pipeline need to be monitor and prevented.
Loads Generally, functional loads can classify from loads arising from the physical existence of the pipeline system. During both the fabrication and the operational process, all functional loads which are essential for ensuring the integrity of the pipeline system, shall be taken into account.
Design-Limit state criteria The minimum vertical distance, which is separately crossing pipelines, is 0.3 m. The unacceptable harm due to dropped objects, fishing gear, ships and anchoring, has to be prevented. Such potential damages might be protected from one of these approaches o
Concrete coating
o
Burial
o
Cover (e.g. sand, gravel, mattress)
o
Other mechanical protection
Local buckling Pipe wall buckling implies gross deformation of the cross section. The following criteria shall be fulfilled: o
system collapse (external pressure only)
o
propagation buckling
o
combined loading criteria, i.e. interaction between external or internal pressure, axial force and bending moment
Pipe soil interaction In order to treat pipelines accordingly, all relevant parameters and the uncertainties, shall determine limited states influenced by the interaction between the pipelines. Typically, pipeline soil interaction depends on the characteristics of the soil, the pipeline, and the failure mode in question, which shall all be properly accounted for in the simulation of the detailed pipeline-soil interaction. 17
Material Engineering The high priorities of submarine pipeline material selection are the type of the fluid, loads, temperature and possible failure modes during the entire operation. What is more, the compatibility ensure of all components of the pipeline system is also crucial[10]. 7.02 DNV-RP-F110 Global Buckling Of Submarine Pipelines Structural Design Due To High Temperature/High Pressure
Global bucking Buckle globally has been caused by fundamentally 2 factors, which are temperature and pressure and on the seafloor installed pipeline and left exposed have a potential to buckle globally. The force major to initiate global buckling is the effective axial force, S, which represents the combined action of pipe wall force, N, internal and external pressures. The level of axial force to initiate this global buckling depends on: o pipe cross section properties o lateral resistance o out-of-straightness in the pipeline o lateral triggering force (e.g. trawling)[13] 7.03
DNV-OSS-306, Verification of Subsea Facilities
This standard is used to verify subsea facilities. There are typically 9 subsea systems needed to be verified, such as subsea downhole system, manifold, foundation and template etc[5]. 8.0
CONCLUSION AND RECOMMENDATION
The work specification of this project was divided into various sections as presented in the main report. The upheaval buckling is the basis on which this design was carried out, however, pipeline design cannot be considered complete without other sections presented herein, such as soil/geotechnical investigation and design, subsea equipment selection, pressure containment and collapse checks, crossings, safety and environmental considerations. Pipeline A was found to be more stable (buckling resistance) than pipeline B due to additional weight from the carrier pipeline. Also less rock dump requirement was obtained for the crossing of the buried pipeline. The specified pipeline materials and wall thicknesses were also found adequate with respect to pressure containment and collapse. Although, the data provided from soil investigation was not sufficient, a soil bearing capacity was established. Finally, considering the success achieved in this design, we shall recommend a detailed soil investigation (pre-lay), engineering critically assessment (ECA), detailed installation analysis to include crossings (strain control), effect of environment and fatigue, maintenance of tight tolerance, adherence to safety and risk assessment.
REFERENCES [1] Meigh, A. C., 1987. Cone Penetration Testing Methods and Interpretation. In: Butterworths, ed., London, Buston, and Dubia. Great Britain: Adlard & Son Ltd. [2]
Poulos, H. G., 1988. Marine Geotechnics. London: Unwin Hyman Ltd, pp. 168 – 202.
[3] Tirant, L. P., 1979. Seabed Reconnaissance and Offshore Soil Mechanics for the Installation of Petroleum Structures. In: Technip, ed., Paris, France. Pairs: Imprimerie Louis-Jean, pp. 140-249, 485-507. 18
[4] Allan, P. G., SEtech Ltd, Society of Underwater Technology, 1998. Offshore Site Invesitgation and Foundation Behaviour: Geotechnical Investigation For Performance of Submarine Trenching Ploughs, London, UK. 22-24 September 1998. [5]
Offshore Service Specification, 2004.DNV-OSS-306 Verification of Subsea Facilities. DNV
Standards
Online
[online]
Available
through:
http://exchange.dnv.com/publishing/Codes/ToC_edition.asp [Valid from April 2012]. Services Limited. Subsea Templates and Manifolds. [Online] Available [6]
FLTC
at:
[Accessed October 20010]. [7]
Thomas B., Hydro ASA, Offshore Technology Conference, 2004. Subsea facilities, Houston, Texas,
U.S.A., 3–6 May 2004. [8]
Scott, W., 2012. Pipeline Ancillary Equipment, EG55F2/EG55G2 Pipeline and Soil Mechanics.
University of Aberdeen, unpublished. [9] Ana, I., 2012. On Bottom Stability,EG55F2/EG55G2 Pipeline and Soil Mechanics. University of Aberdeen, unpublished. [10]
Offshore Standard, 2010.DNV-OS-F101 Submarine Pipelines Systems.DNV Standards Online
[online] Available through: http://exchange.dnv.com/publishing/Codes/ToC_edition.asp [Valid from April 2012]. [11]
Alfred, A., 2012. Stress Analysis Based Design of Pipelines 2,EG55F2/EG55G2 Pipeline and Soil
Mechanics. University of Aberdeen, unpublished. [12]
Alfred, A., 2012. Buckling and Collapse of Subsea Pipelines,EG55F2/EG55G2 Pipeline and Soil
Mechanics. University of Aberdeen, unpublished. [13]
Recommended Practice, 007.DNV-RP-F110 Global Buckling Of Submarine Pipelines, Structural
Design Due To High Temperature/High Pressure.DNV Standards Online [online] Available through: http://exchange.dnv.com/publishing/Codes/ToC_edition.asp [Valid from April 2012]. [14]
Recommended Practice, 2006.DNV-RP-F105 Free Spanning Pipelines.DNV Standards Online
[online] Available through: http://exchange.dnv.com/publishing/Codes/ToC_edition.asp [Valid from April 2012]. [15]
Subrata K.C., 2005. Handbook of Offshore Engineering Vol2 chapter 11.Oxford: Elsevier.
[16]
Scott, W., 2012. Pipeline Routing and Free Spanning, EG55F2/EG55G2 Pipeline and Soil
Mechanics. University of Aberdeen, unpublished. [17]
Common industrial equation from pipeline department in Technip Company, unpublished.
19
APPENDIX Appendix A – Soil Analysis Table 1.0A: Conservative/representative estimates from CPT results through Drill Centres to BLP CPT No. C to BLP
Depth range (m)
Soil type
CPT-01
0 - 0.5
Very loose silty SAND
0.5 – 4.91
Soft CLAY with a thick lamination of SAND at 2.58m
0 -1.0
Loose to dense slightly silty SAND
Medium SAND
1.0 – 5.03
Soft CLAY
Soft to sensitive CLAY
0 – 0.5
Loose slightly silty SAND
Loose Silty SAND
0.5 – 1.31
Dense to very dense SAND with rare gravel
Medium dense Gravelly SAND
CPT -10B
0 – 0.85
Loose to dense silty SAND
Very loose Silty SAND
CPT-15
0 – 0.88
Loose to medium dense slightly silty slightly clayey SAND
Very loose Silty gravelly SAND
0.88–3.03
Dense to very dense silty SAND with thin bedded soft CLAY at 1.58m
Medium dense gravelly SAND with thin layer of CLAYEY sandy silts at 1.58m
CPT-16A
0 – 1.42
Loose to very dense silty SAND
Medium SAND
CPT No. S to BLP
Depth range (m)
Soil type
CPT-01
0 - 0.28
Medium dense to dense silty SAND Very soft CLAY underlaid by firm slightly sandy CLAY underlaid by Firm CLAY Medium to dense silty SAND
CPT - 04
CPT–09A
0.28–5.09
CPT - 05
0 -0.33
Cone resistance , q t (MPa)
Verification of Soil type
Undrained Cohesion, CU 2 (KN/m )
Angle of internal Friction, ()
Undrained Cohesion, CU (KN/m2)
Angle of internal Friction, ()
Loose to very Loose SANDY silts and Silts Very soft CLAYEY Silts and Silty Clays
Cone resistance , q t (MPa)
dense
dense
silty
silty
Verification of Soil type
Loose Silty SAND Very sensitive/soft CLAY underlaid by loose silty SAND underlaid by silty CLAY Medium dense silty SAND 20
CPT–10
CPT -15
CPT-20
CPT-26
CPT-27A
0.33-4.28
Soft to firm sandy CLAY with sand bed
Soft to firm Sandy Silty CLAY with sand bed
4.28-5.19
Medium to dense silty SAND Loose to medium dense silty SAND
Medium to dense Silty SAND Loose to dense gravelly silty SAND
1.0-2.48
Firm to soft silty sand CLAY
Soft to firm Silty sand CLAY
2.48–5.17
Soft to firm sandy CLAY with a bed of a thin bed of sandy SILT
Soft to firm sandy silt
0 – 0.37
Loose to medium dense silty SAND
Very loose to loose SANDY silt and silt
0.37-1.81
Soft CLAY
Sensitive CLAYEY silt
1.81-5.21
Loose to medium dense silty SAND Loose silty SAND
Loose to medium dense Silty SAND Very loose silty SAND to Clay
0.19–3.78
Very soft becoming soft CLAY
Sensitive silty CLAY
3.78-4.65
Loose to dense silty SAND with a bed of sandy CLAY Loose to very dense silty SAND
Loose to dense silty SAND with a bed of clay
1.24-5.00
Very soft to soft sandy CLAY
Very sensitive to sensitive sandy CLAY
0-1.0
Loose to very dense silty SAND
Loose to very dense silty SAND to gravelly SAND
0 – 1.0
0 – 0.19
0 – 1.24
CLAYEY
Medium to dense silty gravelly SAND
Figure 1.0A: Soil identification (after Robertson and Campanella, 1983) and Figure 1.1A: Soil identification (from Searle, 1979) Courtesy of [1]
21
Appendix B – Soil Analysis Table 2.0B: Effective Axial Force for Pipeline A T Pipeline F(eff inner ∆T(Inner ) ∆T(Carrier ) K.P A( ) pipe)KN 0 112
F(eff Carrier)KN
F(eff total)KN
1
110
108
-4234.53
24.00
-1,051.95
-5,286.47
2
109
106
-4161.62
23.50
-1,030.03
-5,191.65
3
107
105
-4125.16
23.25
-1,019.07
-5,144.23
4
105
103
-4052.25
22.75
-997.16
-5,049.41
5
104
101
-3979.34
22.25
-975.24
-4,954.58
6
101
100
-3942.89
22.00
-964.28
-4,907.17
7
100
97
-3833.52
21.25
-931.41
-4,764.93
8
98
96
-3797.07
21.00
-920.45
-4,717.52
9
96
94
-3724.16
20.50
-898.54
-4,622.69
10
94
92
-3651.25
20.00
-876.62
-4,527.87
Table 2.1B: Computation of the functions of Φι and Φw for Pipeline A K.P Φι Φι Φι Φι Φι Φw Φw 1 2 3 4 5 6 7 8 9 10
Φw
Φw
Φw
H=0.11 6.56 6.50 6.47 6.41 6.35 6.32
H=0.22 7.80 7.73 7.69 7.62 7.55 7.51
H=0.33 8.63 8.55 8.51 8.44 8.36 8.32
H=0.44 9.27 9.19 9.15 9.06 8.98 8.94
H=0.55 9.81 9.72 9.67 9.58 9.49 9.45
H=0.11 0.090 0.089 0.088 0.087 0.086 0.085
H=0.22 0.065 0.066 0.067 0.068 0.069 0.070
H=0.33 0.063 0.062 0.062 0.062 0.062 0.062
H=0.44 0.060 0.060 0.060 0.060 0.060 0.060
H=0.55 0.060 0.060 0.060 0.060 0.060 0.060
6.23 6.19 6.13 6.07
7.40 7.37 7.29 7.22
8.19 8.15 8.07 7.99
8.81 8.76 8.67 8.58
9.31 9.26 9.17 9.08
0.084 0.083 0.082 0.081
0.071 0.072 0.073 0.074
0.062 0.062 0.062 0.062
0.060 0.060 0.061 0.061
0.060 0.060 0.061 0.061
Table 2.2B: Effective Axial Force for Pipeline B ∆T ( ) F(eff pipe)KN K.P T Pipeline B( ) 0 110.00 108.00 106.00 -4,684.00 1 2 106.00 104.00 -4,610.40 105.00 102.00 -4,536.80 3 4 103.00 101.00 -4,500.00 101.00 99.00 -4,426.40 5 6 99.00 97.00 -4,352.80 7 98.00 95.00 -4,279.20 8 96.00 94.00 -4,242.40 9 94.00 92.00 -4,168.80 22
10 11 12 13 14 15 16 17
93.00 91.00 89.00 88.00 86.00 84.00 83.00 81.00
90.00 89.00 87.00 85.00 84.00 82.00 80.00 79.00
-4,095.20 -4,058.40 -3,984.80 -3,911.20 -3,874.40 -3,800.80 -3,727.20 -3,690.40
Table 2.3B: Computation of the functions of Φι and Φw for Pipeline B Φι Φι Φι Φι Φι Φw Φw K.P 0 H=0.11 H=0.22 H=0.33 H=0.44 H=0.55 H=0.11 H=0.22 8.11 7.17 7.93 8.53 9.01 0.062 0.074 1 2 8.05 7.11 7.87 8.46 8.94 0.062 0.075 7.99 7.06 7.81 8.39 8.87 0.063 0.076 3 7.95 7.03 7.78 8.36 8.84 0.063 0.077 4 7.89 6.97 7.71 8.29 8.76 0.064 0.078 5 6 7.82 6.91 7.65 8.22 8.69 0.065 0.079 7 7.76 6.85 7.58 8.15 8.62 0.065 0.080 8 7.72 6.82 7.55 8.11 8.58 0.068 0.081 9 7.66 6.76 7.48 8.04 8.50 0.069 0.082 10 7.59 6.70 7.42 7.97 8.43 0.070 0.083 11 7.55 6.67 7.38 7.94 8.39 0.070 0.084 12 7.48 6.61 7.32 7.86 8.31 0.070 0.085 13 7.42 6.55 7.25 7.79 8.24 0.071 0.086 7.38 6.52 7.21 7.75 8.20 0.072 0.086 14 7.31 6.46 7.15 7.68 8.12 0.073 0.086 15 7.24 6.40 7.08 7.60 8.04 0.074 0.086 16 7.20 6.36 7.04 7.57 8.00 0.074 0.086 17
Φw
Φw
Φw
H=0.33 0.062 0.062 0.062 0.062 0.062 0.062 0.063 0.063 0.063 0.063 0.063 0.063 0.064 0.064 0.064 0.064 0.064
H=0.44 0.062 0.062 0.063 0.063 0.064 0.064 0.064 0.065 0.065 0.066 0.066 0.066 0.067 0.067 0.068 0.068 0.068
H=0.55 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060
23
