Offshore Pipeline Hydraulic and Mechanical Analyses
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Hydraulic and Mechanical Analysis of Offshore Pipeline...
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Part I – Pipeline Alternative
Hydraulic and Mechanical Analysis
CHAPTER 1 Pipeline Hydraulic and Mechanical Design
1
Part I – Pipeline Alternative 1
Hydraulic and Mechanical Analysis The continuity equation for steady state is:
Pipeline Hydraulic and Mechanical Design
1.1
Overview
dm
T
1.2
. m constant ρ A u ρ A u ρAu 1 1 1 2 2 2 For a constant diameter pipe: . m ρu C A Where C is a constant 1.2.2
The energy equation
The energy equation applied on gas flow between sections 1 and 2 is in the form: u M C 2 ln u 1 P 2 P 2 2 2R Z T 1 ave ave 2 M 2 Pave2 H H 2 2 f C2 L 1 D R 2 Tave2 Zave2
This equation is a general equation that can be used in Imperial or S.I. units, for any size or length of pipe, for laminar, partially turbulent or fully turbulent flow and for low, medium or high pressure systems.
Hydraulic Design:
As we mentioned before the target of the hydraulic analyses is to select a suitable standard diameter that satisfies the pipeline requirements. The major tool used in the analysis is the energy equation which relates the pressures at the start and end of a pipe with the flow rate passing through the pipe and other pipe and flow parameters. 1.2.1
0
dt
he target of the hydraulic design is to get the range of suitable diameters for the pipeline to satisfy the outlet pressure and flow capacity requirements, while the mechanical design defines the minimum acceptable thickness for the pipeline. This chapter discusses some of the important concepts of gas flow study. It shows the equations governing the compressible flow in pipes with brief explanations for the different terms of each equation and its physical meaning. We will go through the diameter selection criteria for gas pipelines. The mechanical design is based on the DNV 2000 rules for submarine pipeline systems. Also we will discuss the Enby Excel sheet which is a professional mechanical design program based on the DNV 2000. We are going to show the solution algorithm for both hydraulic and mechanical design and the flow chart of V.B.Net program for hydraulic and mechanical design of gas pipelines. The chapter is concluded with the results of V.B.Net program for the EgyptCyprus pipeline. The analyses are obtained using Imperial units.
Definition of parameters:
u1 & u2 flow velocities at sections 1 and 2 respective ly, ft/sec P1 & P2 pressures at sections 1 and 2 respective ly, psia Pave average pressure between sections 1 and 2, psia
The continuity equation:
Consider pipeline that transports a compressible fluid (e.g. natural gas). For any two sections 1 and 2 along a gas flow pipe;
Pave
P P 2 P1 P2 1 2 3 P1 P2
T1& T2 temperatures at sections 1 and 2 respective ly, R
1
P1, u1 T1, H1 Z1, A1 ρ1
Tave average temperature between sections 1 and 2, R
2
T T2 Tave 1 2
P2, u2 T2, H2 Z2, A2 ρ2
R universal gas constant 10.73 , (psia ft3 / lb moles R) M gas molecular weight, (lbm / lb moles)
P = gas pressure u = gas velocity A = pipeline cross sectional area ρ = gas density
Zave compressib ility factor C constant
2
Part I – Pipeline Alternative
C
. m A
Hydraulic and Mechanical Analysis 1.2.3 Determination of the compressibility factor:
4Q MP b b πR T Z D b b
2
There are two main methods for the determination of the compressibility factor; compressibility factor chart and the equations of state
Qb = standard flow rate, MMSCFD or MCF/HR The standard volume is the gas volume at the standard or base conditions (Tb, Pb and Zb) that have the same mass of the actual gas volume. That is; . m Qb ρb Q ρ
1.2.3.1
Compressibility factor chart:
As we can see, to get the compressibility factor from the chart we have to get the pseudo reduced pressure, Pr and the pseudo reduced temperature, T r.
Pb P Q Z b R Tb ZR T Pb pressure at base condition, 14.7 psia
Pr
Pave PC
Tb temperature at base condition, 520 R
Tr
Tave TC
Qb
Zb compressib ility factor at Pb and Tb, ˜ 1 D inside diameter of the pipe, inch
Where, PC = pseudo critical pressure TC = pseudo critical temperature The pseudocritical values for a gas mixture such as the natural gas can be obtained with Kay's rule as follows: T'C = TCA . yA + TCB . yB + TCC . yC + … P'C = PCA . yA + PCB . yB + PCC . yC + … T'C = average pseudocritical temperature of the gas P'C = average pseudocritical pressure of the gas TCA, TCB, TCC,. = critical temperature of each component PCA, PCB, PCC,. = critical pressure of each component yA, yB, yC,. = mole fraction of each component
G gas gravity The gas gravity is the ratio between the gas molecular weight and the air molecular weight = M / Mair, Mair ≈ 29 lbm / lb moles Z = compressibility factor at Pave and Tave H1H2 = the elevation change, ft L = pipe length, ft or mile
The pseudo critical properties for the different gases forming the natural gas mixture are listed in the following table.
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Part I – Pipeline Alternative
Hydraulic and Mechanical Analysis
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Part I – Pipeline Alternative
Hydraulic and Mechanical Analysis
Compound
Molecular Weight
Critical Temperature(R)
Critical Pressure (psia)
C1
16.043
343
666
C2
30.07
550
707
C3
44.097
666
617
iC4
58.124
734
528
nC4
58.124
765
551
iC5
72.151
829
491
nC5
72.151
845
489
nC6
86.178
913
437
nC7
100.205
972
397
nC8
114.232
1024
361
nC9
128.259
1070
332
nC10
142.286
1112
305
nC11
156.302
1150
285
nC12
170.338
1185
264
N2
28.016
227
493
CO2
44.01
548
1071
H2S
34.076
672
1300
O2
32
278
731
H2
2.016
60
188
H2O
18.015
1165
3199
Air
28.96
238
547
He 4 9 Where, C1 is the single carbon atom alkane, methane CH4, C2 is the double carbon atom alkane, ethane, C2H6…etc. Also "i" refers to the ISO structure while n refers to the normal structure. 1.2.3.2
33 The CNGA equation is used to determine the compressibility factor for natural gas with 90% methane by volume. The equation is valid when the average gas pressure Pave is greater than 100 psig. For pressures less than 100 psig, the compressibility factor can be taken as 1.00. Note that the pressure used in the CNGA equation is the gage pressure not the absolute pressure.
Equations of state
Several equations can be used to determine the compressibility factor like the CNGA equation and the Vander Waals equation.
Vander waals equation
CNGA equation:
Z
a P 2 v b RT v
1
P 344400 10 1.785G 1 ave 3.825 T
2 2 27R TC RTC a &b 64PC 8PC
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Part I – Pipeline Alternative
Hydraulic and Mechanical Analysis For internally uncoated commercial pipes, the value of Ke is normally measured in the range of 650750 μ inches. Erosion, corrosion, contamination and other factors cause a yearly increase in Ke by 3050 μ inches. Internal coating of pipes with a material such as epoxy/polyamide reduces the surface roughness to within a range of 200300 micro inches so the pressure drop decreases and correspondingly the compressor power. The deterioration also decreases the rate of deterioration per year by 5075 microinches for every five years.
This equation was the first attempt to correct the ideal gas law, but its accuracy is law. 1.2.4
Flow regimes
There are two main types of flow; laminar and turbulent flow. The regime of flow is defined by the Reynolds number, which is a dimensionless expression:
Re
ρDu Getting Reynolds number: ρDu Re μ
μ
Where ρ fluid density, lbm/ft
3
u
D pipeline internal diameter, ft u fluid average velocity, ft/sec μ fluid viscosity, lbm/ft.sec For Reynolds numbers less than 2,000 the flow is normally laminar or stable. When the Reynolds number exceeds 2,000, the flow is turbulent or unstable. In highpressure gas transmission lines with moderate to high flow rates, only two regimes of flow exist: partially turbulent flow (rough pipe flow) and fully turbulent flow (smooth pipe flow).
Re
ρb D Qb ρDQ 2 2 μ πD 4 μ πD 4 ρb
Pb M Z b R Tb
Z b 1, M 29G
Re
The transmission factor for fully turbulent flow can be calculated from the Nikuradse equation as follows:
4Q b 29G Pb μ π D R Tb
Once the actual Reynolds number is determined, the flow regime can be determined from Prandtl Von Karman equation which defines border line between partially and fully turbulent flow:
3.7D 1 4 log10 f Ke Ke = effective roughness, inch which is comprised of the following terms: Ke = K s + Ki + K d Where Ks = surface roughness Ki = interfacial roughness Kd = roughness due to bends, welds, fittings, etc. Usually in highpressure gas transmission lines with high flow rates where the flow regime is fully turbulent and the natural gas is almost dry, the values of Ki and Kd are negligible. The values of Ks or Ke is important in fully turbulent flow because the laminar sublayer, the surface roughness of the pipe plays an important role in determining the flow and pressure drop in the pipe. Laminar sublayer
R 1 4log10 e f 1 f
0.6
Partially Turbulent Zone Border Line Prandtl Von Karman Equation Fully Turbulent Zone 10000
Partially turbulent flow
Q 2 πD 4
Fully turbulent flow
6
100000 Re (in Log Scale)
1000000
Part I – Pipeline Alternative
Hydraulic and Mechanical Analysis
If the actual Reynolds number is greater than the Reynolds number obtained from Prandtl Von Karman Equation, the flow is fully turbulent. Otherwise, the flow is partially turbulent. 1.2.5
These equations are especially suitable for the design of gas transmission lines having large diameters and high pressures. Only ColebrookWhite can be used for both partially and fully turbulent flow regimes, Panhandle A and AGA partially turbulent equations are used in the partially turbulent flow regime while the remainders are used in the fully turbulent flow regime. For AGA partially turbulent equation, D f is the drag force that compensates for the inefficiencies due to bends, welds, fittings, etc., and has a numerical value in the range of 0.92 to 0.97. The Panhandle B equation is normally suitable for largediameter (i.e., pipes larger than NPS 24). The Weymouth equation tends to overestimate the pressure drop predictions, and contains a lower degree of accuracy relative to the other equations. Weymouth is commonly used in distribution networks for the sake of safety in predicting pressure drop. Both the AGA fully turbulent and the ColebrookWhite introduce the effect of the pipe effective roughness, Ke.
Widely used steadystate flow equations
A more simplified form of the general energy equation in Imperial units can be written as follows:
1
2 2 Tb 1 P1 P2 E 2 2.5 Q b 38.744 D Pb f GLTave Z ave E = potential energy term 2
E 0.0375G ΔH
Pave TaveZave
Qb gas flow rate at base conditions, SCF/D Tb = temperature at base condition, 520 R Pb = pressure at base condition, 14.7 psia
1 = transmission factor, dimensionless f P1 = gas inlet pressure, psia P2 = gas exit pressure, psia
G = gas gravity, dimensionless H = elevation change, ft Pave = average pressure, psia Tave = average temperature, R Zave = average compressib ility factor, at Pave Tave, dimensionless L = pipeline length, miles D = pipeline inside diameter, inch The different flow equations differ in the value of the transmission factor. The general form of all the equations is: d b Tb P12 P2 2 E e Q b a D P G c LT Z ave ave b Where a, b, c, d, e are constants that have different values in each equation. The values of a, b, c, d, e for some of the most common steadystate flow equations are listed in the table below.
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Part I – Pipeline Alternative
Equation Panhandle A
Transmission factor,
6.872 R e
Hydraulic and Mechanical Analysis
1 f
Re 4D f log10 1.4126 F
Panhandle B
Qb G 16.70 D
Colebrook White
1.2.6
b
c
d
e
435.83
1.078 8
0.853 9
0.539 4
2.618 2
R e 38.774 4D f log10 1 1.4126 f
1
1
0.5
2.5
737.02
1.02
0.961
0.51
2.53
432.7
1
1
0.5
2.667
1
1
0.5
2.5
1
1
0.5
2.5
0.07305
AGA Partially Turbulent
Weymout h AGA Fully Turbulent
a
0.01961
1 11.19 D 6
3.7D Ke
4 log10
3.7D Ke
38.774 4 log10
1 1 1.4126 1.4126 Ke Ke f f 38.774 4 log10 4 log10 3.7 D 3.7 D Re Re Concrete coating Conduction
Temperature profile:
Temperature is very important parameter in the design of pipelines and related facilities. The temperature has major effect on gas properties and hence gas transportation in pipeline. Many gas properties depend on temperature, such as gas viscosity, density and specific heat. As gas temperature increases, its viscosity increases which results in the increase in pressure drop and hence power loss. The temperature change in a pipeline has three main reasons; heat transfer between gas and surrounding, isenthalpic gas expansion due to friction which is expressed by the JouleThompson effect and isentropic gas expansion caused by elevation change. 1.2.6.1
Plastic coating Conduction
1.2.6.1.1 wall:
Gas flow Convection Pipe thickness Conduction
Surrounding Convection and Radiation
Heat transfer between gas and pipe
This is held by convection, the heat transfer coefficient can be calculated from DittusBoelter equation:
Heat Transfer in gas pipelines
Heat is transferred between gas and surrounding among three stages; heat transfer by convection between gas and pipe wall, heat transfer by conduction through pipe wall, insulation and concrete and heat transfer by convection and radiation between pipe wall and surroundings.
h f 0.023kf Where hf kf Cpf μf ρf
8
0.6 C pf
μ f
0.4
ρf Vf 0.8 D
0.2
= heat transfer coefficient, Btu/hrf2R = gas thermal conductivity, Btu/hrftR = gas specific heat, Btu/lbmR = gas dynamic viscosity, lbm/fthr = gas density, lbm/ft3
Part I – Pipeline Alternative Vf D
Hydraulic and Mechanical Analysis
= flow velocity, ft/hr = internal pipe diameter, ft
Re number range 40,000
This equation is suitable for turbulent flow in pipes where, Re > 10,000 and Prandtl number between 0.7 and 160. The internal heat transfer resistance, Ri, can then be calculated from the equation:
Ri
1 hf π L D
i
1 UA
1.2.6.1.2 Heat transfer through pipe wall, insulation and concrete:
1.2.6.2
The heat transfer through solids occurs by conduction, the total thermal resistance can be calculated from the equation:
JouleThompson Effect
ΔT j
or
ΔT j
ΔP L m C p dT U dA T Tsurround m C p j dL
By integration we yield:
T Tsurround j/a T2 1 Tsurround j/a a L e
Heat may be transferred between pipe wall and the surrounding by conduction, convection and radiation; this depends on what kind of environment surrounds the pipe. For an aboveground or offshore pipeline placed in a blowing fluid environment, the heat transfer coefficient can be calculated from the equation:
T1 = inlet gas temperature, R T2 = exit gas temperature, R Tsurround = surrounding temperature, R j = JouleThompson coefficient, (sometimes R/psi) a = constant πDU = , ft1 m C p L = pipe length, ft
k m n h surr surr C R e, surr Pr Dout Where ksurr = thermal conductivity of the surrounding fluid, Btu/hrftR Dout = outer diameter of the pipeline, e.g. concrete outer diameter, ft Re,surr = Reynolds number of the surrounding fluid C, m and n are constant that are given in the following table. The corresponding heat resistance can be given as follows:
h surr πLD
R i R s R surr
j
1.2.6.1.3 Heat transfer between pipe and surrounding:
1
n 1/3 1/3 1/3 1/3 1/3
The JouleThompson effect describes the temperature loss due to the pressure drop that occurs when gas expands in a pipeline. The JouleThompson factor can either be related to the pressure drop or pipe length as following:
Where Di, Dp, Dins, Dc are the internal and external diameters of pipe, external diameter of insulation and external diameter of concrete respectively. While kp, kins and kc are the thermal conductivities of pipe, insulation and concrete respectively.
R surr
m 0.33 0.385 0.466 0.618 0.805
Then, the overall heat transfer coefficient is determined from the equation:
, R hr/Btu
ln D /D ln D /D ln D /D p i ins p c ins Rs 2π L k 2π L k 2π L k p ins c
C 0.989 0.911 0.683 0.193 0.027
R/ft
Notes: 1. For an underground pipeline, heat transfers by conduction through the soil. The amount of heat transfer through soil is calculated using the following equation: q k soil S T Tg
Where q = heat transfer rate, Btu/h ksoil = soil thermal conductivity, Btu/hftR S = conduction shape factor for buried pipelines, ft
, R hr/Btu c
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Part I – Pipeline Alternative
Hydraulic and Mechanical Analysis
T = pipe wall temperature, R Tg = soil (ground) temperature, R The conduction shape factor for buried pipelines is given as:
S
1.2.7.1
Qs ρs Q b ρ b
2 L 1 h cosh D out/2
ρs
P Ts Zs b ρs Ps Tb Z b 2 πD A 4
2.
Heat transfer by radiation from pipe to the surroundings can be given as: 4 4 q ε σ Asurface Tsurface Tsurround Where ε = surface emissivity of the pipe σ = Boltzman constant = 5.67×108 Btu/hrft2R4 Asurface = pipe surface area, ft2 Tsurface = pipe surface temperature, R Tsurround =surrounding temperature, R
Pb M Ps M ; ρb Zs R Ts Z b R Tb ρb
Where L = pipe length, ft h = distance from center of pipe to the ground surface, ft Dout = pipeline outer diameter, ft
1.2.7
Pipeline gas velocity Q us s A
us
Pb Ts Zs 2 P T Z πD s b b
Qb
4 Substitute, Pb = 14.7 psia, Tb = 520 R, Zb = 1 3 Q b Ts Zs u s 1.44 10 2 D Ps Where us = gas velocity at any segment, ft/sec Qb = gas flow rate at base condition, ft3/hr P = pressure at any section, psia Ts = temperature at any section, R D = pipeline diameter, inches
Diameter selection criteria:
The diameter selection in fluid transmission pipelines is usually based on the fluid velocity. For liquid transmission pipelines, the pipeline diameter is selected such that the liquid velocity in the pipeline ranges between 1 and 3 m/s. If the liquid velocity exceeds 3 m/s, the pressure drop in the pipeline will be very large, while a low velocity flow allows precipitation of solids carried with fluid.
1.2.7.2
Erosional velocity
The velocity that can cause erosion to the pipeline can be calculated from the following equation: C ue 0.5 ρ Where, in Imperial Units, ue = erosional velocity, ft/sec ρ = gas density, lbm/ft3 C is a constant defined as 75 < C < 150. The recommended value for C in gas transmission lines is C = 100. 100 ue 0.5 P 29G ZR T In the above equation: ue = erosional velocity, ft/sec G = gas gravity, dimensionless P = pipeline minimum pressure, psia Z = compressibility factor at the specified pressure and temperature, dimensionless T = flowing gas temperature, R R = 10.73 (ft3 × psia/lb moles × R)
In gas pipelines, the gas velocity is limited by the erosional velocity. If a fluid flows in a pipeline with a high velocity it can cause both erosion and vibration in the pipeline. This will reduce the life of the pipeline. So it is always necessary to control gas velocity in gas transmission pipelines to prevent it from rising above the erosional velocity.
The recommended value for the gas velocity in gas transmission mainlines is normally 40% to 50% of the erosional velocity; this means a flow velocity in
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Part I – Pipeline Alternative
Hydraulic and Mechanical Analysis
the range of 3343 ft/sec (1013 m/sec). This value could be increased to 1517 m/sec for nonmajor lines or laterals. Note that a very low velocity ratio means that the pipeline is very extremely large which means a high capital cost.
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Part I – Pipeline Alternative 2 2.1
Hydraulic and Mechanical Analysis cross section; collapse, localized wall wrinkling and kinking are examples thereof. 10. Safety class(SC): in relation to pipelines; a concept adopted to classify the significance of the pipe line system with respect to the consequences of failure 11. safety class resistance factor: Partial safety factor which transform the lower fractile resistance to a design resistance reflecting the safety class 12. Reliability: the probability that a component or a system will perform its required function without failure, under stated conditions of operation and maintenance and during a specified time interval
Mechanical Design Objectives
The objectives of this standard are: Provide an international acceptable standard of safety for submarine pipeline system by defining minimum requirements for the design, materials, fabrication installation, testing, commissioning, operation & repair. Serve as technical reference document in contractual matters between purchaser and contractor; and Serve as guideline for designers, purchaser, and contractors 2.2 Definitions 1. Erosion: Material loss due to repeated impact of sand particles liquid droplets. 2. Fabrication: Activities related to the assembly of objects with a defined purpose. In relation to pipelines, fabrication refers to e.g. risers, expansion loops, bundles, reels, etc. 3. Fabrication factor: factor on the material strength in order to compensate for material strength reduction from cold forming during manufacturing of line pipe. 4. Failure: An event affecting a component or system and causing one or both of the following effects: Loss of component or system function; or Deterioration of functional capability to such an extent that the safety of the installation , personal or environmental is significantly reduced
Pressure definitions 1. Pressure collapse: characteristic resistance against external over pressure 2. Pressure design: In relation to pipelines this is the maximum internal pressure during normal operation, referred to a specified reference height, to which the pipeline or pipeline section shall be designed. The design pressure must take account of steady flow conditions over the full range of flow rates, as well as possible packing and shutin conditions, over the whole length of the pipeline or pipeline section which is to have a constant design pressure. 3. Pressure incidental: In relation to pipelines this is the maximum internal pressure the pipeline or pipeline section is designed to withstand during any incidental operation situation, referred to the same reference height as the design pressure. 4. Pressure propagation: the lowest pressure required for a propagating buckle to continue to propagate. 5. Pressure containment : is the maximum internal pressure causing failure
5. Fatigue: cyclic loading causing degradation of material. 6. Limit state: A state beyond which the structure no longer satisfies the 2.3 DESIGN PHILOSOPHY requirements. The following categories of limit states are of relevance for pipeline 2.3.1 Location class systems: SLS= Serviceability L.S. ULS=Ultimate L.S FLS=Fatigue L.S ALS= Accidental L.S 7. Ovalisation: the deviation of the perimeter from a circle. This has the form of an elliptic section. 8. Buckling, global: Buckling mode which involves a substantial length of the pipeline, usually several pipe joints and deformations of the cross section; upheaval buckling is an example thereof.
9. Buckling local: Buckling mode confined to a short length of the pipeline causing gross changes of the
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Part I – Pipeline Alternative 2.3.2
Safety classes
2.3.3
Categorization of fluids
Hydraulic and Mechanical Analysis Effects from the following phenomena are the minimum to be considered when establishing functional load: Wight External hydraulic pressure; Temperature of continent Reaction from component(flanges, clamps etc) Cover (soil, rock, mattresses); Internal pressure during operation Reaction from sea floor(friction &rotational stiffness) Prestressing Permanent deformation of supporting structure Permanent deformations due to subsidence of ground, both vertical and horizontal Possible loads due to ice bulb growth around buried pipelines near fixed points ( in line valves tees, fixed plants etc) Loads included by frequent pigging operations 2. Environmental loads : Are defined as ;those loads on a pipeline system which are caused by the surrounding environment, and that are not otherwise classified as functional or accidental loads Hydrodynamic loads: are defined as flow induced loads caused by the relative motion between the pipe and the surrounding water. When determining the hydrodynamic loads the relative liquid particles velocities and accelerations used in the calculations shall be established, taking into account contributions from waves, current and motions if significant. The following hydrodynamic loads shall be considered but not limited Drag and lift forces which are in phase with the absolute or relative water particles velocity Inertia forces which are in phase with the absolute or relative water particle acceleration 3. Accidental loads Loads which are imposed on a pipeline system under abnormal conditions shall be classified as accidental loads. Typical accidental load can be caused by: Vessel impact or other drifting items (collision , grounding, sinking); Dropped objects; Mud slides Explosion Fire and heat flux Dragging anchors
According to previews classifications in our case:Fluid category is:  B Location type: 2 So safety class would be: High Loads: Loads shall be classified as follows:1. Functional loads: Loads arising from the physical existence of the pipeline system and its intended use shall be classified as functional loads All functional loads which are essential for the pipe line system, during both the construction and the operational phase, shall be considered
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Part I – Pipeline Alternative
Hydraulic and Mechanical Analysis The pressure containment resistance, pb (t), is given by: The minimum between Yield limitstate & the bursting limitstate. Yield limit state is 2t 2 Pb ,s (t) fy Dt 3 The bursting limitstate is
2.4
Design Calculations Limit states: As minimum requirement, risers and pipelines shall be designed against the following potential modes of failure: 1. serviceability limit state Ovalisation / Ratching limit state; accumulated plastic strain limit state damage due to , or loss of, weight coating. 2. Ultimate limit state Bursting limit state; Ovalisation / Ratching limit (if causing total failure) Local buckling limit state (pipe wall buckling limit state); Global buckling limit state (normally for loadcontrolled conditions); Unstable fracture and plastic collapse limit state; and Impact 3. Fatigue limit state Fatigue due to cyclic loading. 4. Accidental limit state All limit states shall be satisfied for all specified load combinations; the limit state may be different for the load controlled condition and the displacement controlled condition All limit states shall be satisfied for all relevant phases and conditions. Typical conditions to be covered in the design are: Installation As laid System pressure test Operation and Shutdown
Pb ,u (t)
fu 2t 2 D t 1.15 3
t : Wall Thickness D: outer Diameter Fy: Yield Stress to be used in design Fu: Tensile Strength to be used in Design
2. Collapse Pressure:
(PC Pe1 ) (PC2 PP2 ) PC Pe1PP f 0 Pe1
t 2E D 1 ν2
3
D t
t PP 2 f y α fab D D max D min f 0 ovality, 1 D
THE DESIGN WILL BE ACCORDING TO [ULS] The design load can generally be expressed in the following: 1.
Pressure containment
Pli Pe
Pb (t) γ SC γ m
Not to be taken < 0.005 (0.5%) The external pressure along the pipeline shall with the Following collapse check:
Pe
Pc : Collapse Pressure Pe1 : Elastic Collapse Pressure E : young’s modulus ( Pipe Material) ΰ : Poisson’s ratio PP : Plastic Collapse Pressure UO: Pipe Fabrication process for welded pipes UOE: Pipe Fabrication process for welded pipes, Expanded TRB: Three roll bending
High safety class during normal operation:
Pli 1.05Pi Pe Z.g.ρ w
PC 1.1 γ SC γ m
Pe: External pressure Z : water height G : proportionality constant Pi : internal pressure : sea water denisity. w
3. Local buckling The check is:2 2 2 S ΔPd ΔPd Md 1 γSC γ m d γSC γ m 1 αcM P α c SP α c Pb t α c Pb t
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Part I – Pipeline Alternative
Hydraulic and Mechanical Analysis γf
γE
γA
γp
SLS&
1.2
0.7

1.05
ULS
1.1
1.3

1.05
FLS
1.0
1.0

1.0
ALS
1.0
1.0
1.0
1.0
For Pi>Pe S [γ SC γ m d α cSP
2
Md γ SC γ m αcM P
2 P ] [γ SC γ m e Pc
2 ] 1
For Pe>Pi
Sd SF γ F γ C SE γ E Md M F γ F γ C M E γ E SP πD t f y t M P D t f y t 2
ΔPd γ P (Pld Pe ) SF α EAsT Pi (1 2νν)(π/4) i2 Pe (1 2νν)(π/4) 02 L
P1d : Local design Pressure , The internal pressure at any point in the pipeline system for corresponding design pressure or incidental pressure Sd: Design Effective Axial Force SF: Functional Axial Force= Residual lay tension+ Thermal Expansion Force + Internal Pressure force A: Pipe steel cross section Area L: Residual lay tension SE: Environmental Axial Force Coefficient of thermal expansion Md : Design bending moment MF: Functional bending moment ME: Environment bending moment SP: Characteristic plastic axial force resistance MP: plastic Moment resistance PdDesign differential overpressure
4. Propagation buckling:The external pressure along the pipeline shall be checked with the following Propagation check:
Pe
PPr 35
PPr
m
SC
f y fab
m SC
(
t 2.5 ) D
Safety class resistance factor γsc Safety class low Normal High Pressure 1.046 1.138 1.308 containment Other
1.04
1.14
1.26
Load effect factor and load combinations Limit state
Functional EnvironAccidental Pressure loads Mental loads loads load
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Part I – Pipeline Alternative
Hydraulic and Mechanical Analysis
Conditions load effect factor γc γc
Condition
Pipe line resting on uneven seabed or in 1.07 a snaked condition Continuously supported .82 System pressure test
.93
Otherwise
1
Material resistance factor γm Limit state SLS/ULS/ALS FLS category γm 1.15 1 5. The Drag Force:
FD 0.5DCDU 2 c The Lift Force:
FL 0.5ρ.5
L
U2c
The Inertia Force:
FI
π ρ.D 2 .C M 4
ρ the density of sea water, D is is the pipe diameter UC is the steady state current velocity averaged over the pipe diameter. CD and CL are the nondimensional force coefficient for drag and lift. CM : Inertia coefficient
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Part I – Pipeline Alternative 3 3.1
VB.NET Program algorithm Inputs
Input data
Load Data Bases
3.2
Hydraulic and Mechanical Analysis
Pipe Length, Flow Rate Supply/Discharge Pressure & Temperature Surrounding Temperature Steel Grade Number of Segments ZFactor Equation & Pressure Equation Allowable Range for Velocity Ratio & Allowable Pressure Drop Gas Composition Concrete/Insulation Thickness and conductivity, Surface Emissivity Environmental Conditions; contours of: depth, wave and current speed & direction Properties of Gas components at the different pressures and temperatures, ρ, Pr, μ, Cp, k, JouleThompson Molecular weight, critical pressures and temperatures of different gas components Standard diameters and thicknesses from the API Yield and tensile strengths of the different steel grades
Outputs
Tables
Graphs
Acceptable diameters according to each equation o Outlet/Inlet pressure and temperature o Pressure drop o Power lost in the line o Velocity ratio Required thicknesses in each contour according to the pressure drop calculated by each equation Line chart o o Bar chart o o o
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Pressure plot Temperature plot Velocity ratios Powers Pressure drop
Part I – Pipeline Alternative 3.3
Hydraulic and Mechanical Analysis
Processing Loop all solution equations Loop all API diameters Defining the flow regime; partially turbulent or fully turbulent flow NO Equation Suits Flow regime Yes Loop all pipe segments Find suitable thickness for this pipe segment according to DNV code
Calculate compressibility factor
Calculate segment temperature according to heat transfer (convection and radiation) and gas expansion (JouleThompson) effect
Calculate pressure using the selected solution equations
Calculate power loss in segment
End of loop Diameter satisfies requirements Yes End of loop Calculate local to erosion velocity ratio at pipe end Calculate total pressure drop along pipeline Calculate total power lost in the pipeline
End of loop
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NO
Part I – Pipeline Alternative 3.4
Hydraulic and Mechanical Analysis
Program Interface
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Part I – Pipeline Alternative 4 4.1
Hydraulic and Mechanical Analysis
EgyptCyprus Pipeline
Pipeline requirements:
The proposed EgyptCyprus pipeline is 680 km (422.6 mile) long. The demand is 4 MMSCM/Day. The discharge pressure is 1,015 psi (70 bar). The discharge temperature and the surrounding temperature are equal and supposed to be 20 (C). The gas consists mainly of methane (90%) and ethane (10%). 4.2
Solution bases
Solve using both CNGA equation and Vander Waals equation Solve using all the energy equations, Panhandle A, AGA partially turbulent, Panhandle B, AGA fully turbulent, Weymouth and ColebrookWhite Divide the pipeline into 1000 segments. Accept only diameters that give outlet local velocity ranging between 3050% of the erosional velocity Limit pressure drop to 1,500 psi Ignore heat transfer The selected pipe material is steel X80. Concrete thickness = 15 cm
4.3 Results: 4.3.1 Solution using CNGA equation Selected diameters D(in) 14
P1(psi) 2359.27
T1(F) 111.2475
D(in)
P1(psi)
T1(F)
D(in) 12.75 14
P1(psi) 1709.595 1482.561
T1(F) 93.16087 85.60558
D(in) 12.75 14
P1(psi) 1746.229 1513.105
Panhandle B % us/ue Pressure Drop (psi) 35.25817 1344.27 Weymouth % us/ue Pressure Drop (psi)
AGA fully turbulent % us/ue Pressure Drop (psi) 43.37388 694.5952 36.26622 467.5608 ColebrookWhite T1(F) % us/ue Pressure Drop (psi) 94.33281 43.32061 731.2288 86.65953 36.22514 498.1049
Selected thicknesses 12.75" Contour (mile) Thickness(in) 435.0528 427.6569 0.281 427.6569 263.642 0.312 263.642 147.4829 0.33 147.4829 46.55065 0.344 46.55065 0 0.375
14" Contour (mile) 435.0528 399.8135 399.8135 147.4829 147.4829 0
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Power loss(HP) 3729.771 Power loss(HP)
Power loss(HP) 2269.894 1638.808 Power loss(HP) 2364.554 1728.601
Thickness(in) 0.312 0.344 0.375
Part I – Pipeline Alternative 4.3.2
Hydraulic and Mechanical Analysis
Solution using Vander Waals equation Selected diameters D(in) 14
P1(psi) 2386.581
T1(F) 111.8889
D(in)
P1(psi)
T1(F)
D(in) 12.75 14
P1(psi) 1713.575 1483.859
T1(F) 93.2877 85.65056
D(in) 12.75 14
P1(psi) 1750.842 1514.654
Panhandle B % us/ue Pressure Drop (psi) 36.48789 1371.581 Weymouth % us/ue Pressure Drop (psi)
AGA fully turbulent % us/ue Pressure Drop (psi) 43.77462 698.5751 36.42109 468.8585 ColebrookWhite T1(F) % us/ue Pressure Drop (psi) 94.48033 43.76394 735.8423 86.71336 36.39981 499.6541
Selected thicknesses 12.75" Contour (mile) Thickness(in) 435.0528 427.2219 0.281 427.2219 252.7657 0.312 252.7657 129.6457 0.33 129.6457 23.0578 0.344 23.0578 0 0.375
14" Contour (mile) 435.0528 397.2032 397.2032 125.7303 125.7303 0
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Power loss(HP) 3782.823 Power loss(HP)
Power loss(HP) 2280.264 1642.656 Power loss(HP) 2376.35 1733.113
Thickness(in) 0.312 0.344 0.375
Part I – Pipeline Alternative 4.3.3
Hydraulic and Mechanical Analysis
Pressure plot vs. pipe length Solution using CNGA equation
Solution using Vander Waals equation
Panhandle B
Panhandle B
AGA Fully Turbulent equation
AGA Fully Turbulent equation
ColebrookWhite
ColebrookWhite
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Part I – Pipeline Alternative 4.3.4
Hydraulic and Mechanical Analysis
Temperature plot vs. pipe length
Solution using CNGA equation
Solution using Vander Waals equation
Panhandle B
Panhandle B
AGA Fully Turbulent
AGA Fully Turbulent
ColebrookWhite
ColebrookWhite
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Part I – Pipeline Alternative
Hydraulic and Mechanical Analysis
Discussion of results: As we can see the use of Vander Waals equation results in slightly higher pressure drop The in the selected diameters is fully turbulent, so the solution is based on equations: Panhandle B, AGA fully turbulent, Weymouth and ColebrookWhite. The power lost is calculated by summation of the power lost in each segment of the pipe. P ZT Power losshp Q b SCF/hr b ΔP psi P Z b Tb
Temperature Gas Temperature
Surrounding Temperature Distance
Temperature
144 Gas Temperature
3600 550
The reason why we do not include the effect of heat transfer can be interpreted as following: due to heat transfer, the temperature drops along the pipeline. For long pipelines, such as our case the temperature reduces till reaching the temperature of the surrounding, then the pipe become "thermally insulated" and the temperature become constant for the remainder of the pipeline. If we had to solve the problem from the last segment to the first one backward solution, there will be no way to determine the point when the pipe become isothermal so the backward solution is not possible
Surrounding Temperature
Small number of segments
Gas Temperature Surrounding Temperature
Distance
Gas Temperature
Moderate number of segments
Distance
Temperature
Temperature
Surrounding Temperature
Large number of segments
Distance
The number of segments in the forward solution should be selected in proportional to the pipe length since a small number of segments for a long pipeline may result in a great error calculation of the heat transferred.
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The program determines the minimum required thickness in each pipe contour. For liquid pipelines it is possible to use more than one thickness which greatly reduces the total cost of the pipeline. However, in gas pipelines we can only use one thickness which is certainly the largest one. But studying the variation in thicknesses along the pipeline, gives an indication to the factors affecting the mechanical design of the pipeline, which may be the pressure if the thicknesses are descending along the pipe or the water head if the largest depth is associated with the largest thickness. Selected diameter: Due to the proceeded selection criteria there are two acceptable diameters 12.75" and 14". We decide to use the 14” diameter as most flow equations decide this diameter. The specifications are summarized in the table below:
Part I – Pipeline Alternative
Hydraulic and Mechanical Analysis
D(in)
Thickness (in)
P1(psi)
T1(F)
% us/ue
14
0.375
1482.561
85.60558
36.26622
25
Pressure Drop (psi) 467.5608
Power loss(HP) 1638.808
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