1. Purpose of Calculation

For the FSRU Gas Compressor Retrofit Project, a preliminary finite element stress analysis is conducted on a highly representative core cryogenic liquid piping segment within the system.

Strictly complying with DNV maritime codes, this analysis takes a typical piping segment (Line No.: LNG-Pipe-Demo-01, refer to Appendix Figure 1) as an example to verify the structural integrity and safety of the pipeline under combined extreme loads. These loads include internal high operating pressure, extreme cryogenic temperature gradients (-165°C), 6-DOF dynamic ship motion accelerations in severe sea states, and hull deflection deformations of the FSRU vessel. Furthermore, it aims to provide accurate ultimate support reaction data for the structural design of the deck pipe supports.

2. Abbreviations and Acronyms

3. Codes and Standards

The finite element modeling, load application, and stress evaluation in this report are strictly executed in accordance with the following codes and project-specified documents:

1. ASME B31.3 (2024) - Process Piping
2. DNV-RU-SHIP (2025) / DNV-OS-D101 (2025)
3. H2189-PYT-BAS-005_01 - General Piping Specification
4. H2189-PYT-BAS-006_01 - Pipe Thickness Calculation

4. Calculation Conditions

4.1 Structural Dimensions and Layout

The specific structural configuration of the piping for this FSRU gas compressor retrofit project is detailed in the design drawing specifications. The process piping material is ASTM A312 TP316 / 316L. The pipeline adopts a design with a cryogenic insulation layer. The piping model is constructed based on the design drawings, and envelope calculations are performed for evaluation.

4.2 Design Environment and Operating Loads

The core computational load data extracted from the project specification are shown in Table 4-1 below:

Table 4-1 FSRU Piping System Design Load Data

4.3 Piping Material and Property Parameters

The property parameters of the main piping material ASTM A312 TP316L under the extreme design temperature (-165°C) and the target evaluation codes are shown in Table 4-2.

Table 4-2 Piping Material Property Parameters

5. Finite Element Calculation Model and Load Case Setup

5.1 Model Generation and Element Selection

The advanced finite element calculation platform developed by ANSYS, Inc. (USA) is adopted as the calculation software.

• Piping Body: Simulated using the PIPE288 3D pipe element, accurately defining the inner/outer diameters and insulation layer thickness, with the LNG fluid density applied in the cross-sectional properties.
• Elbow Distortion: For prefabricated elbows (1.5D) with a nominal diameter larger than DN40, "Pipe Idealization" is enabled. The underlying element utilizes the ELBOW290 advanced elbow element to accurately capture the cross-sectional ovalization/flattening effect under complex marine torsional loads.
• Valve/Instrument Simulation: Point Mass is utilized to accurately apply the valve weight, restoring the actual eccentric bending moments exerted on the pipeline.
• Description of Pipe Support Boundary Conditions and Constraints Simulation: To realistically reflect the constraint effects of on-site pipe supports on the pipeline, this analysis abstracts the physical supports into mathematical boundary conditions in ANSYS according to the actual process layout drawings. The specific correspondences are shown in Table 5-1.

Table 5-1 Correspondence between Typical Piping Support Types and FEA Boundary Conditions

5.2 Comprehensive Calculation Load Case Setup

To satisfy DNV's comprehensive review requirements for both normal process conditions and extreme sea states, this analysis establishes the following 6 core computational load cases using a step-by-step load superposition approach (detailed in Table 5-2).

Table 5-2 FSRU Piping Static and Dynamic Analysis Load Case Combinations

Load Component Definitions:

• G (Gravity): Includes empty pipe dead weight, insulation weight, eccentric load of flange/valve assemblies, and the weight of the full LNG fluid medium, applied vertically downward.
• T1 (Thermal Contraction): Simulates the massive overall cryogenic contraction effect when the entire pipe wall temperature drops to the extreme cold limit after entering the stable operating phase.
• T2 (Transient Thermal): Simulates the cross-sectional and axial temperature gradients caused by localized liquefaction inside the pipe during the initial cool-down phase (e.g., inlet at -165°C, outlet at ambient temperature).
• Acc (Marine Dynamic Load): The immense dynamic inertial force induced by the total mass of the system when the FSRU experiences 6-DOF motions (such as rolling and pitching) in rough seas.
• SAM (Hull Deflection Load): The forced pulling and compressing displacements exerted on the connected piping due to the relative movement of deck supports when the FSRU undergoes global hogging or sagging bending in waves.

6. Stress Analysis and Evaluation

6.1 Evaluation Criteria and Allowable Stress Calculation (ASME B31.3)

To scientifically and accurately assess the structural safety of this pipeline under complex marine conditions, this analysis strictly complies with the ASME B31.3 code. Primary stress (to prevent plastic rupture) and secondary stress (to prevent fatigue failure) are decoupled, and their respective acceptance criteria are established.

6.1.1. Primary Stress Evaluation Criteria:

6.1.2. Secondary Stress Evaluation Criteria:

6.1.3. Bellows Expansion Joint Evaluation Criteria (EJMA Standard):

6.2 Stress Calculation Results Summary Table

Computed by the ANSYS solver, the maximum nodal stress extractions and the latest baseline evaluations for each load case are summarized below:

Table 6-1 Maximum Combined Stress and Evaluation Results of Piping under Various Load Cases

6.3 Displacement Evaluation of Bellows Expansion Joints

For the cryogenic bellows in the system, a finite element equivalent substitution has been performed based on the stiffness parameters (axial and lateral stiffness matrices) provided by the vendor. Under the extreme envelope load case, the relative deformations extracted at both ends of the bellows are as follows:

Table 6-2 Relative Displacements and Evaluation of Bellows under Extreme Load Case

6.4 Displacement Analysis of Key Piping Nodes

To ensure that the movement trajectory of the pipeline under extreme sea states and cryogenic conditions does not clash with other hull structures, and that the displacement travel of various sliding supports remains within the safe range of the base plates (to prevent slip-off), the directional displacements of key nodes under the most severe load case are extracted as follows:

Table 6-3 Summary of Extreme Displacements at Key Piping Nodes

7. Ultimate Support Reaction Load Extraction

In accordance with DNV code requirements stipulating that "pipe support foundations must be capable of withstanding dynamic load impacts," the ultimate reaction loads transmitted from the pipeline to various support points are extracted under the most severe LC6 (Ultimate Extreme Envelope Case).

The following data is formally submitted as critical interface information to the overall structural discipline for the final strength verification and welding design of the deck support frames and hull base structures.

Table 7-1 Summary of Maximum Piping Support Reaction Loads under Ultimate Envelope Case (LC6)

8. Conclusion

Multi-case calculations verify that the FSRU gas compressor retrofit process piping system, under the combined effects of extreme internal pressure and heavy eccentric loads from flange/valve assemblies, exhibits primary sustained stresses far below 115 MPa. This fully satisfies the basic ASME requirements for tensile and rupture prevention.

Upon superimposing the DNV-mandated extreme full-pipe cryogenic contraction, ultimate ship motion accelerations (Acc), and forced hull bending displacements (SAM), the maximum ultimate dynamic and thermal stresses generated by the piping system are strictly controlled within the safe envelope of the 231.8 MPa secondary allowable stress, as calculated per the ASME B31.3 code.

In conclusion: The routing layout and the guide/sliding constraint design of the support system for this pipeline are highly rational. Under various extreme sea states and severe process operations of the FSRU, the system demonstrates excellent anti-fatigue flexibility as well as robust anti-motion rigidity. The structural integrity completely meets the standard requirements, proving to be safe and reliable.

The relevant ultimate support reaction loads have been fully detailed in Section VI, providing sufficient and conservative interface data for the subsequent detailed structural engineering of the deck pipe supports.

9. Appendix Documents

Appendix A: Stress Calculation Result Contour Plots for FSRU Retrofit Liquid Piping

Figure 1: Isometric View of FEA Model for Piping (Line No. CL4009-SS150-50-23)

Figure 2: Stress Contour Plot of Piping under LC1

Figure 3: Stress Contour Plot of Piping under LC2

Figure 4: Stress Contour Plot of Piping under LC3

Figure 5: Stress Contour Plot of Piping under LC4

Figure 6: Stress Contour Plot of Piping under LC5

Figure 7: Stress Contour Plot of Piping under LC6

Figure 8: Total Displacement Vector Plot of Piping under LC6