# Flowline - Pipeline Thermal Expansion Calculation ### 1. SUMMARY

Flowline/Pipeline Thermal/Pressure Expansion can be developed for submarine pipelines (both single pipe and Pipe-in-pipe) expansion assessments due to pressure and temperature, refer to References below. In addition, the effective force along a flowline can be calculated of the flowline end displacements.

This procedure performs the expansion calculation considering the following two scenarios:

• The flowline ends are free to move
• The flowline ends overcome a constant force to displace, for example, due to Pipeline End Terminal (PLET) frictions

The calculation can also consider the effect of a seabed slope to the flowline end displacements.

The spreadsheet also considers either a residual flowline lay tension or a zero lay tension.

Assumptions listed below are to ensure the validity of this procedure:
• Both single pipe and Pipe-in-Pipe (PiP) cases are included in this procedure, with PiP system being treated as an equivalent pipe. Thus, the frictional loads between the inner pipe and the outer pipe are not considered.
• The seabed profile needs to be flat and the flowline assumes straight; flowline feed-in to the spans is not considered.
• No lateral buckling or flowline walking is considered.
• The flowline outer temperature the same as the ambient.
• The flowline inner pressure is constant.

### 2. REFERENCE

 Document Document Title DNV RP F110 Global Buckling of Submarine Pipelines SafeBUCK III JIP Safe Design of Pipelines with Lateral Buckling, Design Guideline API RP 1111 Design, Construction, Operation and Maintenance of Offshore Hydrocarbon Pipelines

### 3. THEORY   The friction lengths are limited by the virtual anchor length, Lhot and Lcold.

The effective force of the fully restrained flowline and the friction force along a typical flowline can be illustrated in Figure 3‑1, where the red curve represents the Seff,res and the blue line represents the friction force along the flowline length.

The friction eventually intersects with the Seff,res at the point A and B for the hot end and cold end, respectively. The slope of the friction force is equal to μ·WPiP, i.e. the pipe / soil axial friction force per unit length. At the section between the points A and B (virtual anchors), the flowline expansion load is balanced by the friction force. Thus, the flowline of the section A-B is fully restrained, and there is no expansion in this section. This scenario is often referred as “long” flowline. Another flowline expansion scenario is illustrated in Figure 4‑2, where the friction force does not intersect with the Seff,res, and the friction forces of the hot end and the cold end are balanced with each other. In this case, the entire “short” flowline is mobilized by expansion and there is no virtual anchor restricting the flowline growth.  ### 4. FEATURES OF THE PROCEDURE

#### 4.1 General

The major sections in the procedure include Data Input, Calculation, and Results Summary as detailed in the following sections.

#### 4.2 Data Input

The required design data are directly input in this section. The following input is to be given:
• Pipeline Data: Pipeline length, type (single pipe or pipe-in-pipe), dimensions, material grade, coating data, etc.
• Operational Data: Operational temperature/pressure, content density, residual lay tension, etc.
• Soil Data: axial pipe/soil friction coefficient.
• Environmental Data: Water depth (profile), ambient temperature, Sea water density, etc.

#### 4.3 Viewing Results

Effective forces and the flowline growth along the flowline are shown in Figure 4‑1 and Figure 4‑2 as examples.  