Subsea Pipelines

In-field flowlines transfer production among subea wells to the production facilities. The processed hydrocarbons will be transferred to the shore through the export pipelines. The subsea flowline or pipeline is installed on the seabed and is subjected to wave and current loading.

The main scope to design a pipeline system is presented below.

• Wall Thickness Sizing: Provide sufficient pipe wall thickness to resist internal and external pressure loads
• On-Bottom Stability: Ensure pipe vertical stability in water to avoid floatation and lateral stability
• Free Spanning: Fatigue screening and ultimate limit state (ULS) design due to in-line and cross-flow VIV, as well as direct wave loading
• CP Design: [will be uploaded in 1Q 2025]
• Thermal Expansion and Lateral Buckling: [will be uploaded in 3Q 2025]

Pipeline Sizing

Pipeline design begains with material selection and pipe sizing to withstand the inernal or external overpressure. When the pipe diameter is selected for the flow consideration, the pipe wall thickness is designed for internal pressure containment, which is to prevent the pipe burst failure due to the internal pressure. Pipe should also be designed to prevent the collpase and propagating buckling failure due to the external over pressure.

Burst: Internal Pressure Design

30 CFR 250 has the following formulation for internal pressure design: \[P = {2\cdot S\cdot t \over D}F\cdot E\cdot T \tag{1}\label{eq1} \] where

• P = internal design pressure,
• S = specified minimum yield strength,
• t = pipe nominal wall thickness,
• D = pipe nominal outside diameter,
• F = design factor (0.6 for riser component),
• E = longitudinal joint factor, and
• T = temperature derating factor.

30 CFR 250 uses Barlow's Equation to calculate the internal design pressure that a pipe can withstand to its dimensions and the strength of its material. The design factor of 0.6 indicates the the hoop stress due to the internal design pressure should be limited to 60% of yield strength for riser component.

The Federal Regulations codes and industrial standards employ Barlow's Equation to calculate the internal design pressure that a pipe can withstand, considering its dimensions and material strength. A constant hoop stress along the wall thickness is calculated, which should be less than 72% of the yield strength. The required wall thickness based on ASME codes is typically less than that required by CFR codes. ASME codes use the differential pressure, whereas CFR codes consider the internal design pressure only. The formula for riser wall thickness internal pressure design (burst) is presented below in Table 1.

Table 1: Different Formula of Pipeline Wall Thickness Calculation for Pressure Design

Pipeline	Code	Formula	Design Factor F	Pressure
DOI Pipelines	30 CFR 250.1002	t=PD/(2SEFT)	0.72	Internal
	API RP 1111	pb=k(S+U)ln(D/Di), p<F*pb	0.72	Differential
DOT Pipelines (Liquid)	49 CFR 195.106	t=PD/(2SEF)	0.72	Internal
	30 CFR 250.1002	t=PD/(2SEFT)	0.72	Internal
	B31.4 A402.3.2	t≥pD/(2FS)	0.72	Differential
	API RP 1111	pb=k(S+U)ln(D/Di), p<F*pb	0.72	Differential
DOT Pipelines (Gas)	49 CFR 192.105	t=PD/(2SEFT)	0.72	Internal
	30 CFR 250.1002	t=PD/(2SEFT)	0.72	Internal
	B31.8 A842.2.2	t≥pD/(2FST)	0.72	Differential
	API RP 1111	pb=k(S+U)ln(D/Di), p<F*pb	0.72	Differential

Where S - yield strength, U - tensile strength, E - longitudinal joint factor, F - design factor, T - temperature derating factor, D - pipe nominal outer diameter, Di - pipe inside diameter, t - wall thickness, P - internal design pressure, p - differential design pressure, pb - specified minimum burst pressure of pipe, and k - constant (0.45 or 0.5).
DOI pipelines and DOT pipelines are defined in 30 CFR 250.1001. Usually production risers connecting subsea wells to platform are categorized as DOI pipelines, and export risers belong to DOT pipelines.

API RP 1111 presents the formula to calculate the pipe burst pressure and set up the 72% of the burst pressure as the limit of the design pressure. The burst pressure formula from pipe testing or can be verified using finite element analysis method (von Mises stress at the outfer reaches the yield strength). It's worth noting that calculations based on CFR using Barlow's Equation are often conservative for thick-walled pipes. A request to use API RP 1111 to determinethe wall thickness is an alternate compliance from requirment of 30 CFR 250 per BSEE NTL 2009-G28.

Collapse: External Pressure Design

Pipe collpase pressure are calculated based on pipe material and size. API RP 1111 utilizes a collapse factor of 0.7 (limiting the external overpressure to 70% of the collapse pressure) for seamless or ERW pipe, while applies a collapse factor of 0.6 for cold expanded pipe, such as DSAW pipe.

Propagating Buckles

Pipeline is also checked for propagating buckling due to the external hydrostatic pressure. The propagating buckling case is checked exclusively at the maximum water depth, where the maximum net external overpressure are located, assuming a minimum internal pressure of zero. As the pressure requried to start a propagating buckling is smaller than the pressure required to initiate collapse, it is often not economical to prevent the propagating buckling by increasing the pipe wall thickness, epsecially for deepwater pipelines. Instead, Buckle arrestors may be used if external overpressure exceeds 80% of propagating pressure per API RP 1111.

On-Bottom Stability

The pipeline is installed on the seabed and is subjected to wave and current loading. The assessement of on-bottom stability includes both vertical and lateral stability design. Three methods for lateral stability are considered:

• Absolute static stability
• Virtual stability design
• Limited accumulated displacement design

Before pipeline stability is assessed, the following parameters, such as pipe weight, penetration, and enviromental loads must be determined.

Pipe Weight

The pipe weight calculation includes the pipe metal, coatings (anti-corrosion, insulation, or concrete weight coating), contents, and marine growth. The calculation is performed for three conditions: installation, embedment, and operation. The weight difference arises from varying fluid contents. Pipe metal loss due to corrosion is only considered at the operational stage.

Pipe Penetration

The initial penetration, z_pi, is due to the self-weight of the pipe prior to lateral movement. This value can either be provided or calculated using the following models. An iterative procedure is performed to determine the initial pipe embedment after laying, based on the equilibrium between the pipeline's contact force and the bearing capacity of the soil. The initial penetration in clay can be calculated using the Verley and Lund model, while the initial penetration in sand can be calculated using the Verley and Sotberg model.

The initial penetration will be added to the penetration caused by dynamics during laying, penetration due to pipeline movement under waves and current, and penetration due to piping to calculate the total pipeline penetration, z_p.

The hydrodynamic load reductions due to pipeline penetration and trenching are applied to the absolute stability calculations. Load reduction due to a permeable seabed is not considered in this assessment.

Environments at the Pipeline Level

Two basic wave parameters, significant wave height H_s and peak wave period T_p, are provided. The JONSWAP or other spectrum is applied as the appropriate spectral density function. The significant flow velocity amplitude \(U_s\) and the mean zero up-crossing period \(T_u\) of the oscillating flow at the pipeline level can be calculated using the spectral moment. The spectrally derived characteristics - oscillatory velocity, period and the associated steady current velocity V - are the main paramters for the generalized lateral stability assessment.

Stability Design Criteria

Stability design criteria provide methods and acceptance standards for the vertical and lateral stability of pipelines. Vertical stability ensures that flotation in water is avoided. The submerged weight of the pipeline must exceed the safety factor on buoyancy, which usually is a value of 1.1. If the pipeline's submerged weight does not satisfy this criterion, a concrete weight coating should be added to increase the pipeline's specific gravity to at least the safety factor.

An example is shown in the table below to check the pipe vertical stability in water (to avoid floatation). Initially, no concrete weight coating is specified. Since the pipe's specific gravity of 1.146 without the coating is greater than or equal to the required buoyancy safety factor of 1.1, the submerged weight of pipeline meets the vertical stability criterion to avoid floatation.

Concrete Weight Coating (CWC)	CWC Thickness, mm	Pipeline Specific Gravity
Existing	0.0	1.146

Absolute static stability is a simplified and conservative approach based on the quasi-static equilibrium of forces, aimed at ensuring that the pipeline will experience no break-out under the design extreme single wave-induced oscillatory cycle in the sea state.

Virtual stability design allows for displacement of less than approximately half a diameter under the largest waves in a sea state. In this condition, the pipeline is considered virtually stable and will not experience break-out. This optimized approach may also benefit from the build-up of passive resistance.

Limited accumulated displacement design permits accumulated displacement of up to 10 hydrodynamic pipeline diameters. Under this design, the pipeline will break out of its cavity multiple times during the sea state, and the calculated displacement should be assumed to be proportional to time.

For a pipeline on sand, the minimum pipeline weights required to achieve virtual stability and to limit lateral displacement to 10D during a three-hour stormshould be determined using database solutions. For a pipeline on clay, the significant weight parameters that satisfy the virtual stability criterion and the 10D criterion are defined using emprical equations.

The stability utilization ratio (UR), defined as the ratio of the required submerged weight for stability to the actual submerged weight, should be less than or equal to 1.0 to meet the stability requirements. An example is shown in the table below to check the pipe absolute static stability & generalized stability. As illustrated in the previous table, no concrete weight coating is required to avoid floatation. However, the stability does not meet either the absolute static stability or generalized lateral stability requirements without concrete weight coating, as the URs exceed 1.0. The required concrete weight coating thickness is calculated to meet the stability criteria. For example, to reduce the 10D displacement stability UR of 1.515 to 1.0 and meet the limited displacement stability criterion, the required concrete weight coating thickness must be increased to 29.9 mm.

To Meet Stability Criterion	Required CWC Thickness, mm	Absolute Static Stability		Generalized Stability
		Vertical UR	Lateral UR	Virtual Stability UR	10D Disp. Stability UR	Generalized Stability Applicable?
Vertical stability in water	0.0 (Existing)	1.501	1.961	1.636	1.515	Yes
Absolute static vertical	31.6	1.000	1.961	1.636	1.515	Yes
Absolute static lateral	323.4	0.437	1.000	0.277	0.372	Yes
Virtual stability	32.3	0.994	1.702	1.000	0.976	Yes
10D Displacement	29.9	1.017	1.718	1.028	1.000	Yes

To meet the stability requirements, the pipeline should be designed with a concrete weight coating thickness as summarized in the following table. The required CWC thickness for absolute static stability is not feasible since it exceeds the maximum applicable thickness, usually 150 mm.

To Meet Stability Criteria	Pipe Allowable Movement	Required Concrete Coating Thickness, mm
Absolute Static Stability	No movement	323.4 (not feasible)
Virtual Stability	Less than half the pipeline's diameter	32.3
Limited Displacement Stability	Up to 10x pipeline's diameter	29.9

Free Spanning

The pipeline is installed on the seabed and may have the fee spans. The pipeline free spanning assessment addresses fatigue screening and ultimate limit state (ULS) design due to in-line and cross-flow VIV, as well as direct wave loading. Three key design considerations are evaluated based on the following criteria:

• VIV Avoidance Criteria: Determination of the span length for the onset of in-line and cross-flow VIV
• Screening Fatigue Criteria: Determination of the allowable span length to achieve a fatigue life exceeding 50 years
• Combined Loading Criteria Local buckling assessment for the observed span under combined loading conditions

Pipe Weight

The pipe weight calculation for the free spanning assessment is similar to the weigth calculation for pipeline stability assessment. The submerged pipe weight and specific gravity for each phase are calculated and provided for the pipeline free spanning assessment.

Flow Velocity

The flow velocity at the pipe level is calculated similar to those calculated for pipeline stability assessment. The main wave parameters, including significant wave height H_s, peak wave period T_p, and wave direction θ, are provided. The spectrally derived significant wave velocity \(U_s\), wave period \(T_u\) and the current velocity \(U_c\) are key paramters for the pipeline free spanning assessment. The significant flow velocity amplitude and the mean zero up-crossing period of oscillating flow at the pipeline level can be calculated using the spectral moment. The sea state paramters (Hs, Tp, θ) are transformed into (Us,Tu) at the pipe level.

Pipe Tension

The pipe effective tension (axail force) is used to calculate the pipe fundamental natural frequency. The pressure and temperature difference from the installation phase is used to calculate the effective axial force. The effective axial force can be estimated using non-linear finite element analysis and input to this module, or by applying the simplified formulas for thin-walled pipes and thick wall pipe.

In-Line VIV Onset and Screening

When the lowest (fundamental) natural frequencies in the in-line direction for a given free span exceed the VIV onset frequencies, the onset of in-line VIV is not expected to occur. When the lowest (fundamental) natural frequency in the in-line direction for a given free span exceed the VIV screening frequency, a fatigue life of more than 50 years is expected. If the VIV screening criteria are violated, a full fatigue analysis should be performed. The following figure shows the pipe natural frequency and in-line VIV onset and screening for operation phase.

For operation phase, in-line VIV is not expected if the span length is less than the VIV onset length of 20.9m. If the span length is more than the VIV onset length of 20.9m, in-line VIV is possible. The fatigue life due to in-line VIV is in excess of 50 years if the span length is less than the VIV screening length of 22.1m. If the span length is more than the VIV screening length of 22.1m, the fatigue life due to in-line VIV is less than 50 years and more detailed fatigue analysis should be performed.

Cross-Flow VIV Onset and Screening

When the lowest (fundamental) natural frequencies in the cross-flow direction for a given free span exceed the VIV onset frequencies, the onset of cross-flow VIV is not expected to occur. When the lowest (fundamental) natural frequency in the cross-flow direction for a given free span exceed the VIV screening frequency, a fatigue life of more than 50 years is expected. If the VIV screening criteria are violated, a full fatigue analysis should be performed. The following figure shows the pipe natural frequency and cross-flow VIV onset and screening for operation phase.

For a span in the effectve range shown in Figure 2, the minimum structural frequency is 1.94Hz when the span length is 18.8m. The cross-flow onset frequency is 0.96 Hz and the cross-flow screening frequency is 0.70 Hz, which are independent of the span length. Since the cross-flow onset frequency is less than the minimum structural frequency, no cross-flow VIV onset is expected. Since the cross-flow screening frequency is less than the minimum structural frequency, a fatigue life in excess of 50 years is exprected for cross-flow VIV.

Response Mode

The response model is applied to estimate the magnitude of the dynamic response in a free span. For in-line VIV, the maximum steady-state amplitude response primarily depends on the reduced velocity and the stability parameter. The amplitude response for cross-flow VIV is a function of the reduced velocity. The cross-flow response model is also applied for low KC regimes under current-dominant conditions. The response model is applied to estimate the magintude of dynamic response in a free span, which will be used for VIV-induced bending calculation. One example of an in-line respsone model (normalized amplitdue as a fucntion of reduced velocity) is shown in Figure 3.

For an observed span of 20.0m, the reduced velocity for opertion phase is 1.25. There is no in-line VIV respsone.

One example of an cross-flow respsone model is shown in Figure 4.

For an observed span of 20.0m, the reduced velocity for opertion phase is 0.78. There is no cross-flow VIV respsone.

ULS Criterion

The design bending moment is the resultant of the two static moments (horizontal and vertical) and the two dynamic moments due to in-line and cross-flow VIV. The pipe, subjected to the design bending moment, effective axial force, and pressure, should satisfy the local buckling combined loading criteria.

References

1. API RP 1111, 5th Edition, September 2015 - Design, Construction, Operation, and Maintenance of Offshore Hydrocarbon Pipelines (Limit State Design)
2. DNV-ST-F101: Submarine pipeline systems, 2021
3. 30 CFR 250: Oil and Gas Sulphur Operations in the Outer Continental Shelf
4. BSEE NTL 2009-G28: Alternate Compliance and Departure Requests in Pipeline Applications
5. 49 CFR 192: Transportation of Natural and Other Gas by Pipeline: Minimum Federal Safety standards
6. 49 CFR 195: Transportation of Hazardous Liquids by Pipeline
7. ASME B31.4, 2019 - Pipeline Transportation Systems for Liquids and Slurries
8. ASME B31.8, 2018 - Gas Transmission and Distribution Piping Systems
9. DNV-RP-F109 On-bottom Stability Design of Submarine Pipelines
10. DNV-RP-F105 Free Spanning Pipelines
11. DNV-RP-F114 Pipe-soil Interaction for Submarine Pipelines