Saudi Aramco DeskTop Standards Table of Contents 1 Introduction................................................. 2 2 Applicable Codes and Standards............... 2 3 Production Data.......................................... 3 4 Pipeline Routings........................................ 4 5 Pipeline Wall Thickness Calculations (Best Practice 1).................................. 5 6 Allowable Bending Stresses (Best Practice 2)........................................... 7 7 Corrosion Allowance................................... 8 8 Determination of Concrete Weight Coating (Best Practice 3)..................... 8 9 Preparing Data for Pipeline Free Spans, Crossings & Other Miscellanies Calculations.......................................... 9 10 Maximum Allowable Free-Spans (Best Practice 4)................................. 10 11 Revising Maximum Allowable Free- Spans (Best Practice 5)..................... 10 12 Pipeline Crossing (Best Practice 6)........... 11 13A Installation Stresses (Best Practice 7)...... 12 13B Shear Stresses Between the Concrete and Corrosion Coatings (Best Practice 7).......................................... 14 14 Flange Selection (Best Practice 8)........... 15 15 Pipeline Scraping and Hydrotesting......... 16 Appendix-A........................................................ 18 Appendix B........................................................ 21 Appendix-C........................................................ 23
Document Responsibility: Piping SABP-L-002 Issue Date: 19 May 2007 Next Planned Update: TBD Design of Submarine Pipelines
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1 Introduction
There are 5 major constraints involved in Sub-Sea Pipeline Design.
Environmental, these required the definition of currents, waves, mudslides, fault movements, soil profiles and bathymetry, which could affect the stability and integrity of the pipeline during its economical life.
Constructional, fabrication and installation equipment, the specification of the pipeline steels, welding and quality controls, and pipeline bidding, backfill and protection.
Operational and Maintenance, these must consider the need for tie-in points, flow-rates, pressure and temperature profiles and the corrosivity of transported fluids, methods of pipeline surveillance and monitoring, the need for maintenance possibly repair, means of controlling fluid escape and emergency procedure.
Design, method of analysis to be used, route guidelines, regularity requirements and codes, allowable stresses and factors of safety.
Economics, cost of construction, operation, surveillance, maintenance, failure and repair. Furthermore, the potential effects of the pipeline on other systems must be fully explored for their economic, political, environmental and social effects, especially when these are related to pipeline failure.
2 Applicable Codes and Standards
As per Saudi Aramco standards, the selection of material and equipment, and the design, construction, maintenance, and repair of equipment and facilities covered by this standard shall comply with the latest edition of the references listed below, unless otherwise noted.
2.1 Saudi Aramco References
Saudi Aramco Engineering Procedure
SAEP-302 Instructions for Obtaining a Waiver of a Mandatory Saudi Aramco Engineering Requirement
Saudi Aramco Engineering Standards
SAES-H-002 Internal and External Coatings for Steel Pipelines and Piping
SAES-H-202 Storage, Handling and Installation of Weight Coated Pipe
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SAES-L-100 Applicable Codes and Standard for Pressure Piping System
SAES-L-109 Metallic Flanges Gaskets and Bolts
SAES-L-310 Design of Plant Piping
SAES-L-410 Design of Pipeline
SAES-L-850 Design of Submarine Pipelines and Risers
SAES-L-133 Corrosion Protection Requirements for Pipelines/Piping
SAES-W-012 Welding Requirements for Pipelines
SAES-X-300 Cathodic Protection of Marine Structures
09-SAMSS-090 Shop Applied Extruded P. E. external Coating
2.2 Industry Codes and Standards
American Petroleum Institute
API RP 1111 Design, Construction, Operation and Maintenance of Offshore Hydrocarbon Pipelines
American Society of Mechanical Engineers
ASME B31.4 Liquid Petroleum Transportation Piping System
ASME B31.8 Gas Transportation and Distribution Piping System
3 Production Data
Please refer to Saudi Aramco standard SAES-L-410 for the particulars of each oil field. As an example, this data sheet provides generalized design criteria for design of new oil flowlines and trunklines. Since field conditions can vary, Area Production Engineers should be requested to provide information on the most recent field conditions.
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FIELD SAFANIYA
Present SIWHP, Kpa (ga) (psig) 2070-4830 (300-700) as of 12/97. See Note #2
Maximum Expected SIWHP, Kpa (ga) (psig): With full gas column At reservoir maint. pressure
N/A (See Note #1) 4658 (675)
Maximum flowing surface temp. deg C 66 Normal flowing pressure:
Flowline design pressure, Kpa (ga) (psig) 5175 (750) Flowline design temperature deg C 66
NOTES: 1) No full gas column is expected. 2) Natural aquifer support maintains Reservoir pressure at or near the bubble point pressure. 3) Given shutin pressure data excludes Ratawi rsvr wells which currently have SIWHPs as high as 6210 Kpa
(ga) (900 psig). No Ratawi producing wells planned to be drilled in the foreseeable future. 4) The maximum injection pressure of future gas lift system is 12400 Kpa (ga) (1800 psig). 5) All offshore flowlines and trunklines are protected by ESD systems and a well and tie-in platforms. 6) Consult E&P Facilities & Technology Department for details of any further updates before final design.
4 Pipeline Routings
Preliminary pipelines routes shall be selected by studying the geophysical and bathymetric survey (drawings can be obtained from the Saudi Aramco Hydrographic Survey unit (HSU)). These routes shall be reviewed and approved by the Marine department and proponent before they become final. Also the construction contractor shall be responsible for performing a pre-construction survey of the route to identify any obstruction which might affect the rout. Universal transverse Mercator (UTM) is used for coordinates referencing.
4.1 Route Selection
Offshore routing shall be selected to avoid potential hazardous areas such as pock marks, cap rock, and coral out-cropping; also efforts should be made to avoid the need to trench pipelines in order to reduce cost and impact to the environment.
Also future expansions of offshore oil fields and associated subsea pipelines net work should be taken into consideration.
4.2 Route Criteria
As each routing normally has its own particular peculiarities, each pipeline and power cable installations should be reviewed and approved on a case by case basis by Marine Barge and Rig Operation Division's. This should be done at the very early stage to avoid late and expensive modifications.
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Following is a typical schematic illustrating pipelines and cables going to an offshore jacket. There are three unobstructed sides that should be left for the safe approach of:
1) Producing Department's well service, testing and maintenance jack-up barges.
2) Drilling department's drilling and Work-Over rigs.
5 Pipeline Wall Thickness Calculations (Best Practice 1)
The pipeline stresses calculation will start by identifying the followings:
1 Required Nominal outside Diameter of the Pipeline (OD) this is produced after pipeline hydraulic simulation analysis is done utilizing special software.
2 Field Design Pressure (P), operating Temperature, product density and water cut as a percentage (%) this can be obtained from current field data.
Offshore Jacket
60-200 meters Pipelines and/or Cables Corridor
Clear Area = Circle with 60-200 meters Radius
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3 Location design factors (F) refer to ASME-B31.8 table 841.114A per Saudi Aramco standards (F=0.72 for pipeline and F=0.5 for Riser), longitudinal Joint quality factors (E) refer to ASME-B31.8 table 841.115A and Temperature de-rating factors (T) refer to ASME-B31.8 table 841.116A.
4 Specified Minimum Yield Strength (SMYS) for example using grade B, X-42, X-52 or X-60 etc.
In summary:
Field Design Pressure Pf
Outside Diameter of Pipe OD
Specified Minimum Yield Strength S.M.Y.S
Location Design Factor F
Joint Quality Factor E
Temp. De-rating Factor T
The formula for calculating the minimum wall thickness per ASME-B31.8 paragraph 841.11.
min. wt. =P * OD/(2*F*E*T*SMYS) psi (2-1)
The above calculated wt. is the minimum; however in selecting the appropriate wall thickness for the pipe, one should consider other parameters that affect the wall thickness. For example pipe laying stresses, corrosion allowances, design life of the pipe and potential change in operating pressure and temperature by introducing different artificial lefts. However, per Saudi Aramco standards and guidelines the minimum wall thickness is 0.375-in for sub-sea Pipeline and 0.5-in for Riser.
Based on the selected wall thickness, the Maximum Allowable Operating Pressure should be calculated.
Max. Allow. Op. Pr. (M.A.O.P.) = 2*SMYS*wt.selected*F*E*T/OD psi (2-2)
Also, based on the selected wall thickness, the hydrotest pressure for the pipeline should be calculated.
This is derived from the hoop stress formula, σH=PD/2t, D is = OD, please refer to Appendix “A” to see how to drive hoop stress σH=PD/2t
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Hoop stress for the selected wall thickness should be calculated for both operation and hydrotest pressures; this will be utilized when calculating the allowable bending stress for the pipe.
Thermal Stress due to operational temperature should be calculated. This also will be utilized. In order to be more Conservative the Corrosion Allowance should not be included when Hoop Stress SH Due to Operational or hydrotesting Pressure is obtained, this will REDUCE the Allowable bending Stress SB.
Formula (2.4) will become
Hoop stress (SH) =P * OD/ (2* (wt.selected – Cor)) psi (2.4.1) P is the selected Hydrotest or operation pressure.
The formula to calculate Thermal Stress
St =Thermal Stress = E * α * ΔT psi (2-5)
E = Modulus of Elasticity of Steel psi (MPa)
α Thermal Coefficient of Expansion in. /in. /F (mm/mm/C)
SAX = Residual axial Stress Due to Pipe lay tension psi (MPa). Please note that Axial Tension due to the lay tension SAX increases the allowable bending stress. SAX is unknown, for conservative approach it can be considered to be = 0.0
7 Corrosion Allowance
Corrosion allowance will not reduce the corrosion rate of the piping material. However, the extra wall thickness of the pipe may provide a longer service life if the mode of attack is uniform general corrosion.
Corrosion allowances are not effective against localized corrosion, such as pitting. Please refer to SAES-L-133.
However, Excess pipe wall above the minimum wall thickness is considered as corrosion allowance.
SAES-L-133 Par. 7.1. Recommend (3.0 mpy) 76 μm/yr. if a need is there. 1.6 mm Corrosion Allowance. Based on this it is recommended to subtract these corrosion allowances from the selected pipe wall thickness when calculating pipeline free-spans and crossings.
8 Determination of Concrete Weight Coating (Best Practice 3)
The Pipe Research Committee International (PRCI) and American Gas Association (AGA) Level-2 analysis computer program should be used to analyze the subsea stability of the pipelines.
Analysis should be performed in accordance with SAER-5711, SAES-L-850 and Arabian Gulf Hind-cast study to determine the required concrete weight coating thickness to prevent pipeline movement during storms conditions.
An adequate number of points along each pipeline route should be analyzed to determine the most severe combination of storm direction, tide and water depth.
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Stability analysis for each selected point should be run for one (1) year storm with the pipeline empty and for (100) year storm with the pipeline full of product.
The design density of the concrete coating for stability analysis should not be less than 3044 kg/m^3 (190 lbs/ft^3). This value dose not includes water absorption.
9 Preparing Data for Pipeline Free Spans, Crossings & Other Miscellanies Calculations:
Input data:
The following is an example of the required information that is required to generate data for further calculations, please note that 3" of concrete is used based on stability analysis that should be done once the selected wall thickness has been established.
1 Field Name SFNY 2 Field Design Pressure P 750 psi 51.7 bar 3 Field Design Temperature f 150.8 deg F 66.0 deg C 4 Nominal Diameter of Pipe N P D 20 in 508.00 mm 5 Outside Diameter of Pipe D 20.000 in 508.00 mm 6 Pipe Wall Thickness wt 0.625 in 15.88 mm 7 Corrosion Coat Thickness FBE tcc 0.020 in 0.51 mm 8 Corrosion Coat Density FBE ρcc 100.00 lb/ft^3 1.602 g/cm^3 9 Concrete Coat Thickness twc 3.00 in 76.20 mm 10 Density of Concrete Coat ρwc 190.00 lb/ft^3 3.044 g/cm^3 11 Density of Product ρp 24.00 lb/ft^3 0.384 g/cm^3 12 Density of Sea water ρsw 64.50 lb/ft^3 1.033 g/cm^3 13 Density of Steel ρs 0.28356482 lb/in^3 7.8490 g/cm^3 14 Pipeline Length L 17139.1 ft 5224.0 mt
Based on the above data one should be able to calculate the submerged weight of the pipe with hydrocarbon product or with hydrotest water and the weight of the displaced sea water. Also this calculation will provide the volumes of Oxygen Scavenger and bactericide as required by SAES-A-007 sections 5.5.1 and 5.5.2.
CONCRETE COATING PIPELINE
WALL+ CC
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Please note that Oxygen scavenger is required whenever water is introduced to the piping system either for lay-up or hydrotesting. Bactericide is only required if the lay up period is greater than > 90 days. The PPM (part per million) changes as a function of time. The Sea Dye is required to be added to hydrotesting water in order to ease locating any potential subsea leak.
10 Maximum Allowable Free-Spans (Best Practice 4)
Base on the calculated allowable bending stress for the subject pipeline, the freespans should be calculated for the subject pipeline for two conditions:
1) Max straight free-span during operation.
2) Max curved free-span during operation.
3) Max straight free-span during hydrotesting.
4) Max curved free-span during hydrotesting.
The calculation should also define the Vortex Shedding frequencies envelop for the straight freespans. Curved pipe will not be subject to Vortex Shedding.
11 Revising Maximum Allowable Free-Spans (Best Practice 5)
The pipeline calculated allowable freespan should be reevaluated due to concentrated load additions such as, set of flanges or Instrument scrapers load moving through the pipe span or both.
These additional loads will subject the pipeline at the freespan to bending stresses beyond the allowable. Therefore to bring the bending stresses within the allowable limits, the freespans need to be revised; this will result in shortening the allowable free span.
Sub-sea pipeline Instrument scraper
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12 Pipeline Crossing (Best Practice 6)
Engineering of Submarine pipeline crossings profile will require the following:
1) % of Embedment of Crossed Pipe below seabed at location of crossing or height of Crossed Pipe above seabed.
4) Separation between top of crossed pipe and bottom of new pipe. According to the standard it should not be less than 12 inches.
5) Maximum Allowable Bending Stress of the new pipe.
6) Maximum Allowable Free spans during operations and hydrotesting.
7) Height of new pipe from Seabed +new pipe (Concrete coating+ OD/2) = height of neutral axis, all pipeline profile calculation will be done with reference to neutral axis.
8) Determination of the "Hypothetical Unit Weight": This is not the real unit weight of the line. It is the unit weight resulting from limiting the bending stress in the Hypothetical Weight Calculation so that it will not exceed the Maximum Allowable Bending Stress during operation or hydrotest of the pipeline. This is used for calculating the profile of the crossing and required support heights. Hypothetical weight = (min(sb)*Z/1.414213562)^2*(1/ (E*I*h)) -- refer to Appendix "C" equation # (10) to see the derivation of the subject equation.
9) Calculating of the load reaction at the ridge (Crossing) "Bo". The load reaction at ridge resulting from the pipeline spanning over a ridge used only for calculating the profile of the span assuming a single support in middle of span at which the Maximum Allowable Bending Stress will not be exceeded. Bo = 3.883934 *[(E*I*w*h)^0.25 (w)^0.5], please refer to Appendix "C" equation # (5) for the derivation of the subject equation.
touchdown Existing Pipeline
Max. Crossing Height
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10) "L" Distance from center of crossing (Ridge) to touchdown point of the pipe. The equation # is (6.6.5 in SAER-5711); please refer to Appendix "C" equation # (6) for the derivation of the subject equation.
11) Deflection of the pipeline with respect to the reference crossing height can be calculated by the following equation:
)11()430.(,)
241
121
643(1
3
4432 −−≥≤+−= αααα where
wBo
EIY
for the derivation of the subject equation, please refer to Appendix "C" equation # (11). Alpha (α) is the deflection variable, its range is from "0" zero which is the value @ central of the crossing to "3/4" at which the pipeline makes a touchdown. Equation # (11) will be utilized to calculate the height of the submarine pipeline from the seabed at any distance from the crossing as a function of [F (α)].
12) The required height of pipe support can be calculated by subtracting (1/2 of pipe O D + the thicknesses of the concrete weight coating) from the height of the neutral axis above the seabed. Please note that, when this value reaches zero (0.0) this will indicate the concrete weight coating touchdown point.
13) Distance from the support to the center of the crossing of the pipeline with respect to the reference crossing point can be calculated by the following equation
43,),1( === αα whenL
wBodoafrom
For the derivation of the Subject equation; please refer to Appendix "C" equation # (1 &1a). Alpha (α) is the deflection variable, its range is from "0" zero which is the value @ central of the crossing to "3/4" at which the pipeline neutral axis makes a touchdown. Equation # (1a) will be utilized to calculate the distance from the center of the submarine pipeline crossing to concrete coating touchdown and/or any supports of any height from the seabed as a function of (α).
13A Installation Stresses (Best Practice 7)
There are various methods of submarine pipeline installations including the lay-barge, reel, bottom–pull, tow, and other methods. Some of these methods are more suited for a particular application than others.
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Certain installation method such as reel is particularly suited for small diameter pipe with no concrete weight coatings; others are particularly suited for big diameter pipe and deepwater installations.
Generally in the Arabian Gulf area the most common and predominate method for submarine-pipeline installations is the lay-barge. There are three different types of lay-barges exist, including conventional box hull, ship-shaped barge, and semi-submersible.
The above conventional box-hull type is used in the Gulf area; the maximum depths to which conventional lay-barges can operate are governed by:
1) Capacity of the barge mooring system. 2) Stinger size. 3) Tensioner system capacity. 4) Pipe diameter, wall thickness and steel grade. 5) Pipe concrete weight coating.
Traditional marine pipeline design often assumes that the dynamic stresses which occur during installation will not exceed one third of the static stresses. As the industry moves into more exacting environments, this assumption become less tenable and careful analysis of the dynamic stresses becomes essential in order to define the limiting weather conditions which could result in failure and overloading of a pipeline.
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Therefore pipelay dynamic stress analysis shall be done to insure that the submarine pipeline do not exceed the allowable stress limit during installation. The combined lay stresses shall not exceed (80%) of the Specified Minimum Yield Strength (SMYS) of the pipe.
Because stress analysis is a function of the lay-barge's particularities, the dynamic lay stress analysis should be performed by the Construction/Installation contractor utilizing sophisticated finite element method based computer programs such as OFFPIPE or Dynamic Seapipe, that been specifically developed for the modeling and structure analysis of nonlinear problems encountered in the installation of offshore pipelines.
The pipe string extending from tentioner/s on the lay barge to the seafloor is subject to dynamic actions due to barge motions and to direct hydrodynamic action on the pipeline and the lay barge stinger.
In summery there are (6) possible dynamic motions of the pipe Lay-Barge (surge, heave, sway, roll, yaw and pitch).
13B Shear Stresses Between the Concrete and Corrosion Coatings (Best Practice 7)
One of the important issues during subsea pipe lay is the shear stresses between the corrosion coating (Fusion Bond Epoxy (FBE)) and the concrete weight coating.
SURGE
SWAY
HEAVE
YAW
ROLL
PITCH
Lay barge Center of Gravity
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Therefore in order to prevent breaking the bond between the concrete and the pipe corrosion coatings during installation, the maximum tensioning force that the pipe can be subject to shall be calculated as a function of; FBE coated section area that has been covered by the linear tensioner and the maximum allowable shear stresses between the corrosion and the concrete coatings in kips/ft2 or kN/m2.
PIPING TENSIONER
Calculation for a 20 inch pipe with 0.02 inch FBE corrosion coating
Linear Tensioning Pipe OD + CC = D + 2 * tcc ODC 20.040 in 0.5090 mt length of Concrete Coated Section L 39.0 ft 11.8872 mt
Area of coated section A = ODC * L* π A 204.612 ft^2 19.01 mt^2
Mean Shear Stress between the Concrete and Corrosion Coatings (TESTED VALUE) S 1.09 kips/ft^2 52.24 kN/m^2 Max Shear Stress for the Total Pipe Length =A*S 223.24 kip 993.03 kN
Concrete Section Length covered by the linear pipe tensioner (FUNCTION OF TENSIONER) LT 18.0 ft 5.49 mt
Area of coated section Covered by tentioner AT AT=ODC*LT*π 94.436 ft^2 8.77 mt^2 Max Allowable Applied Shear Stress =S*AT 103.4 kip 458.32 kN
14 Flange Selection (Best Practice 8)
Ring joint weld neck flanges are used for offshore piping system. Selecting the appropriate flange should be in accordance to ASME/ANSI B-16.5 (PIPE FLANGES AND FLANGE FITTINGS), SAES-L-109 (Metallic flanges, Gaskets and Bolts for
Effective length of linear tensioner “LT”
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Low and Intermediate Temperature Service) AND 02-SAMSS-001 (Forged Steel Weld Neck Flanges for Low and Intermediate Temperature Service).
The following items control the selection:
A) System design pressure and temperature; based on the field design pressure and temperature the appropriate flange CLASS can be selected using ASME/ANSI B-16.5 Table-2 (Pressure-temperature ratings). for example to decide the proper flange for MARJAN offshore oil field that suitable for:
1) 2800 psi design pressure,
2) 150.8ºF operating temperature,
3) 20" inch size X60 pipe with 0.75" wt (assuming that, the pipe design is already done for the subject pressure and temperature)
From ASME/ANSI B-16.5 Table-2, Class 1500 flange is the one which meet the above requirements, however there are material group No's that need to be chosen from. Go to B.
B) Pipe size and pipe material grade; such as grade B, X42, X52, X60, etc; based on both, pipe size and pipe material grade, flange Material CODE & GROUP can be selected according to 02-SAMSS-001 Table-1 and/or SAES-L-109 Table-3. Back to the above example, Class 1500 Flange with 20 inch X60 pipe material grade will result in Material CODE K and ASME B16.5 Material GROUP 1.7.
C) Based on ASME B16.5 Table-2, Class 1500 flange with Material GROUP 1.7 and 150.8ºF operating temperature will give a pressure rating of 3750 psi; this is the maximum operating pressure for the giving temperature.
D) The Hydrotest pressure for the subject flange can be calculated by multiplying the operating pressure at ambient temperature time 1.5, for the case in hand the operating pressure at ambient temperature as per ASME B16.5 Table-2 is also 3750 psi, this will result 3750*1.5 = 5625 psi Hydrotest pressure.
E) Please note that if the calculated Hydrotest pressure for example came to be 5557 then this should be round up to the next 25 i.e. it will be 5575 and so on.
15 Pipeline Scraping and Hydrotesting
All submarine pipelines with associated corridor and tie-ins spools shall be cleaned and gauged with scraper after installations. This to assure that they are free of debris and pipe buckles. The scraper shall be selected to be able to negotiate the 3d bends. Gauging plats should have a diameter ½ inch less than the minimum inside diameter along the pipeline system taking manufacturing tolerances into consideration. One
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should refer to the appropriate pipe, flange and fitting standards to determine the allowable manufacturing tolerances for wall thickness and diameter. For cleaning and gauging temporary launchers and receivers shall be provided for each pipeline size.
If the gauging plate shows the existence of any obstruction or pipeline damage, the obstruction or damage shall be located and repaired as necessary. A scraper with a gauging plate shall be passed through the pipeline again after the repair has been completed. This sequence shall be repeated until the scraper passes through the pipeline with the gauging plate undamaged.
During the pipeline scraping/gauging operation the line will be filled with water containing dye and oxygen scavenger. Bactericide shall be added where specifically required for pipe lay-up. The concentrations of these additives shall be in accordance with SAES-A-007.
For Hydrotesting pressure please refer to section five (5) for Hydrotesting and hoop stress calculations, the strength test pressure shall be maintained for two hours in compliance with SAES-A-004. Also baseline instrument scraping is also required.
Revision Summary 19 May 2007 New Saudi Aramco Best Practice.
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Appendix-A
Hoop & Longitudinal Stresses Formulas:
Hoop Stresses:
The ratio of pipe wall thickness to the radius t/r is < 1/10, therefore if the circumferential strain is uniform, an analysis of the above free body diagram will show the relationship between applied pressure and circumferential stress.
σc= Circumferential Stress (σH Hoop Stress) due to internal pressure.
The integration from (-π/2) to (π/2) of; the internal gage pressure P, multiplied by (*) the arc length (r dθ) * L * Cos θ , will result in the Σ of the perpendicular vector components of the pressure in the pipe with respect to Areas 1 & 2 plan.
The force on # 1& 2 steel edges due to hoop strain = 2 * σc* t *L
The integration of (Cos) is (Sin)
π/2
-π/2
Steel Edge Area1 = t * L
Steel Edge Area 2 = t * L
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The integration of [(P L r d θ) Cos θ] from (-π/2) to (π/2) will result in P L r * (Sin (π/2) - Sin (-π/2)) = P L r * {(1) - (-1)} = 2 P L r
Thus, Σ F = 0
Therefore, 2 P L r - 2 * σc* t *L = 0 2 P L r = 2 * σc* t *L
σc = 2 P L r /2 * t *L σH = σc = P * D /2 * t (1)
Longitudinal Stresses
In Closed end system and contain a fluid under a pressure P, the wall of the Vessel will have longitudinal stress as well as circumferential stress.
P = Inside pipe Pressure t = pipe wall thickness D average approximately = D internal when t is very small when comparison with D internal
Pipe average Circumference = π D average
Pipe Cross Section Steel Area = π D average * t And σL= Longitudinal Stress due to internal pressure.
Σ Forces = 0
Inside Pipe Area =
((π/4)*D2)
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Thus, P * ((π/4)*D2) = σL* π D average * t
Since D average approximately = D internal when t is very small when comparison with D internal.
σL= P * ((π/4)*D2) / (π*D*t) P *D / (4*t) (2) From (1) & (2) it can be seen that: Longitudinal Stress = 0.5 Hoop Stress
σL= P *D / (4*t) = 0.5 σH = 0.5 P * D /2 * t
Document Responsibility: Piping SABP-L-002 Issue Date: 19 May 2007 Next Planned Update: TBD Design of Submarine Pipelines
E = Modulus of Elasticity of Steel psi (MPa) α = Thermal Coefficient of Expansion in. /in. /F (mm/mm/C) ΔT = T2–T1 (Operating Temp. – Surrounding SEA Temp.) °F / °C ν = Poisson's Ratio = 0.3 for steel SB = Allowable bending Stress psi (MPa). SAX = Residual axial Stress Due to Pipe lay tension psi (MPa).
This formula is for an element at the top of the pipeline
0.9 SMYS >= SH + E * α * ΔT – ν * SH + SB – SAX
Therefore:
SB <= 0.9 SMYS – SH – E * α * (T2–T1) + 0.3 * SH + SAX
SB <= 0.9 SMYS – 0.7 SH – E * α * (T2–T1) + SAX
It can be seen from the equation, that Axial Tension due to the lay tension SAX increases the allowable bending stress.
SAX is unknown, for conservative approach it can be consider to be = 0.0
SB <= 0.9 SMYS – 0.7 SH – E * α * (T2–T1) + 0.0
Un-Restrained pipelines – Operating Case:
Per ASME B-31.4, Para.402.3.2 (D) & 419.6.4(C)
The allowable stress range is SA= 0.72 SMYS, also the sum of the longitudinal stresses due to pressure SL, and other sustain external loadings SB shall not exceed 0.75 SA .
Document Responsibility: Piping SABP-L-002 Issue Date: 19 May 2007 Next Planned Update: TBD Design of Submarine Pipelines
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i.e. 0.75 SA >= SL+ SB
0.75 SA = 0.72 SMYS * 0.75 = 0.54 SMYS
SL = PD/ (4 * wt) = SH /2 = 0.5* SH
Therefore 0.54 SMYS >= 0.5* SH+ SB
And SB <= 0.54 SMYS - 0.5* SH
Restrained pipelines – Hydrotesting Case: SAX is unknown, for conservative approach it can be consider to be = 0.0
During hydrotest T2=T1 and E * α * (T2–T1) = 0.0
SB <= SMYS – 0.7 SH – 0.0 + 0.0
Un-Restrained pipelines – Hydrotesting Case:
SMYS >= SH - SL + SB
SMYS >= SH - 0.5* SH + SB And SB <= SMYS - 0.5* SH
Document Responsibility: Piping SABP-L-002 Issue Date: 19 May 2007 Next Planned Update: TBD Design of Submarine Pipelines
Page 23 of 27
Appendix-C Crossing
Assumptions:
1) The deflection angle of the pipe is small 2) The Bottom (SEABED) is flat
From differential equation of the Elastic Curve REA (Research & Educational Association) page 573.
E.I.Y"= M = E.I/R
Where
Y"= 1/R, where R= the radius of curvature, Y"=d2y/dx2
E = Modulus of Elasticity = LengthUnitPernDeformatio
AreaUnitPerStress⋅⋅⋅
⋅⋅⋅
I = Moment of Inertia. M = Bending Moment, which is causing the deformation.
do
y δ
y
x
SEABED
Moment at ridge = Mo
Deflection at X
Bo/2 reaction at ridge
Sub-Sea Pipeline crossing profile
Touchdown Point
Y = Distance from Seabed to Pipe Centerline
do = distance from Crossing to Touchdown Point
Document Responsibility: Piping SABP-L-002 Issue Date: 19 May 2007 Next Planned Update: TBD Design of Submarine Pipelines
Page 24 of 27
E.I = Stiffness (rigidity) of the pipe. w = Submerged unit weight.
For the pipeline going over a ridge in the above diagram the following equation apply:
2
21
2''.. wxxBoMoYIE +−=
At x = 0 and x = do,
)1......(0..21.
2''.. 2 =+−== dowdoBoMoMYIE
Solving Equation # (1)
By integrating EIY'', will get Y' which is the slope of the pipe curvature:
( )
LdoxatandxatCY
dxwx xx
=====→
−−−++−=
+−= ∫
,.,0..0&0'
)2(Cwx61x
4BoMoxY'I*E*
21
2ΒοΜοY'Ι*Ε*
32
2
0
)1(..34
.).1(323
),1(.4
.3
2
cwdoBo
andbw
BoMo
aw
Bodo
−−−=
−−−⋅
⋅=
−−−−=
Document Responsibility: Piping SABP-L-002 Issue Date: 19 May 2007 Next Planned Update: TBD Design of Submarine Pipelines
Page 25 of 27
Also, by integrating E.I.Y' will get Y which is the deflection of the pipe.
Substitute with (1a) and (1b) into (3) above.
From (4) above one can get
010.@0
)3(1.241
122..
.61.
4...
432
0
32
=→==
−−−++−=
⎟⎠⎞
⎜⎝⎛ +−= ∫
CxY
CxwxBoxMoYIE
dxxwxBoxMoYIEx
)4(16144
276144
276144
8127*827*66144
8176827
102427
43.,
43
3
4
3
4
3
4
3
4
3
4
3
4
2
−−−−==∴
=+−
=
+−=
==
EIwBoYdeflection
wBo
wBo
wBo
wBo
wBoEIY
wBoMoand
wBodo
( )
)6(*27
6144*43.9129506.2
*883934.3*43
43),1(
)5(.883934.3
276144
276144
444
4 3
4 3
4 3434
−−−==
===
−−−−−−−−−−=
=→=
wEIY
wEIYL
wYEIw
wBoLdoafrom
YEIwBo
YEIwBoYEIwBo
Document Responsibility: Piping SABP-L-002 Issue Date: 19 May 2007 Next Planned Update: TBD Design of Submarine Pipelines
Page 26 of 27
Formula # (6) is the free span length that has been used in SAER-5711
From equation (1)
)7(34,,
43
−−−−=∴=→= LwBodoLletw
Bodo
Substitute with (7) above into (1b)
Formula # (8) is the maximum bending moment that has been used in SAER-5711
)9(.6
2...
2
−−−−−−==
=
ZwL
ZMStress
DIZModulusSectionElastic
From equation (6) substitute for L in (9) one can obtain the maximum bending stress σb.
σb)10(414265.1
6)9129506.2(
22
−−=== EIwYZw
EIYZw
ZM
Formula # (10) is the maximum bending stress that has been used in SAER-5711.
In order to determine the deflection of the submarine pipeline as a function of the touchdown point at a distance L from the crossing point and as a function of α the deflection variable.
)8(69
16**323
).1(32
3
222
2
−−−==
−−−⋅
⋅=
wLwLw
Mo
bw
BoMo
Document Responsibility: Piping SABP-L-002 Issue Date: 19 May 2007 Next Planned Update: TBD Design of Submarine Pipelines
Page 27 of 27
The maximum for do is L.
43,),1( === αα whenL
wBodoafrom
Let α = deflection variable where )430( ≥≤ α
Substitute the value of do from (1a) and the value of Mo from (1b) into Equation (3)
)11()430.(,)
241
121
643(1
*241**
121*
323*
21
)3(.241.
121.
21
3
4432
4
44
3
33
2
22
2
432
−−≥≤+−=
+−=
−−−−−−+−=
αααα
ααα
wherewBo
EIY
wBow
wBoBo
wBo
wBoEIY
dowdoBodoMoEIY
Equation (11) will be utilized to determine the height of the submarine pipeline from the SEABED at any distance from the crossing.
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