Steel catenary riser (SCR) is a costeffective riser system that is widely used in deepwater offshore oilfields development. During SCR Jlay installation, the movement of pullhead must be carefully controlled to ensure riser safety. Since the SCR installation path calculation through numerical simulation software is usually timeconsuming, this paper has established a mechanical model for SCR installation by making use of homotopy analysis method (HAM) to simplify its analytical solution, and dimensional analysis was considered in making initial guess solution. Based on this analytical solution, a program within the framework of MATLAB was developed to predict the twodimensional riser behavior during installation, and a sensitivity analysis for different values of the control variables was carried out. Engineers may efficiently optimize the installation path by the application of this technique.
In response to increasing global demand of energy from fossil fuels and the replacement of depleting oil and gas reserves in most matured fields in the world, operating companies in the oil industry are expanding their exploration and production operations into deepwater. In deepwater exploration, SCRs are widely used as a costeffective riser system which is connecting offshore platforms and subsea production systems. During SCR installation as shown in Figure
SCR installation procedure.
The shape of SCR will be affected by the route of pullhead during installation controlled by both the A&R and the pullin wire, and the maximum stresses to be encountered during the transfer process must be obtained before installation [
The structural model presented in this paper is a simple and practical method to obtain the static configuration and the mechanical load parameters for SCR transfer process. The bending stiffness and large deformation of the part suspended in water are taken into consideration. The governing equation system is derived and the analytical approximate solution is obtained by means of HAM. Compared with the available commercial software such as OrcaFlex, the calculation of the present model has the advantage of high stability and being timesaving. A series of parameters such as initial installation angle, maximum lower depth of pullhead, water depth, and distance between installation vessel and offshore platform are considered during the stress analysis of SCR installation.
The mechanical model used to simulate the behavior of transfer process during SCR installation is composed of two parts, as presented in Figure
The dynamic movement of the installation vessel and platform are not considered.
The gravitational and hydrostatic forces are the only loads upon the riser during installation operations.
The SCR material is linear elastic, and the behavior of SCR is modeled as a twodimensional beam subjected to axial and bending deformations. Torsional and shear deformation are not considered.
The seabed is rigid. Two parts of the model are solved in the local coordinate system X′O′Y′, respectively and transformed to the global coordinate system XOY, finally. The TDP of SCR is the origin of local coordinate system X′O′Y′.
Mechanical model for transfer process of SCR installation.
The location of pullhead is important for SCR shape control. It is controlled by the length of A&R wire from installation vessel and pullin wire from platform. Based on catenary theory as shown in Figure
Catenary axis and forces.
The transfer process is typically carried out by two steps. The first step is to lower the pullhead by increasing the length of A&R wire from installation vessel, and the second step is to pullin the pullhead by decreasing the length of pullin wire from platform.
The geometrical relationship in lowering step is shown in Figure
Geometrical relationship for lowering step.
Based on (
The geometrical relationship in pullin step is shown in Figure
Geometrical relationship for pullin step.
By combining (
An infinitesimal element with length
Forces on a large deformation beam segment
According to large deformation beam theory, the curvature
By simplifying (
The boundary condition at top point of riser is
Equation (
Perturbation technique has been widely used for nonlinear problem [
For the nonlinear differential equations with general form:
Thus, as
Assuming that
Differentiating the zeroorder deformation equation (
A dimensionless parameter
Assuming that
Thus, zeroorder deformation equations can be obtained as follows:
Applying (
The
We select the nonzero auxiliary function as
Referring to the catenary equation, we select the initial guess solution
If we select the length of riser
Considering the boundary conditions at TDP
When the nonzero auxiliary parameters are selected as
In order to implement the SCR installation model as described above, a computer program has been developed within the framework of MATLAB language program. The efficiency and accuracy of this model is verified by comparison with the numerical results of OrcaFlex. The parameters of SCR used for verification and analysis are detailed in Table
Parameters of SCR.
Parameter  Value 

Outer diameter (m)  0.3048 
Inner diameter (m)  0.2743 
Flexural rigidity (N·m^{2}) 

Weight submerged (N/m)  350.59 
Density (kg/m^{3})  7850 
The overall configuration and axial tension calculated by the proposed method and OrcaFlex are compared as shown in Figures
Critical results.
Item 















HAM  297.97  499.41  217071  545.43  1004.09  429937  1050.67  2006.54  859997 
OrcaFlex  299.89  499.91  214430  546.57  1002.77  428228  1056.20  2003.68  853240 
Difference  0.64%  −0.1%  −1.23%  0.21%  −0.13%  −0.4%  0.53%  −0.14%  −0.79% 
Configuration results comparison between HAM and OrcaFlex in different water depth.
Axial tension results comparison between HAM and OrcaFlex in different water depth.
Postlay method is selected for SCR installation parameters analysis. In this method, the offshore platform is on site. When SCR is laid near to the offshore platform by installation vessel, SCR pullhead is firstly connected to the A&R wire and the cable from offshore platform, which is lifted only by the A&R wire. Increase the length of A&R wire to lower pullhead to the maximum depth and then decrease the length of cable from offshore platform until pullhead is finally lifted to the hangoff position. Note that the dynamic positioning (DP) system always maintains the installation vessel and offshore platform position in the original place during SCR installation.
The safety of SCR during installation is affected by many factors. The most important one is that the variation of SCR maximum stress caused by the change of installation shape should be within the allowable stress. In order to investigate the influence of the initial installation angle, the maximum lower depth of pullhead, water depth, and the distance between installation vessel and offshore platform, the parameters shown in Table
Assume that the initial installation angle is
Assume that the horizontal position of pullhead is
Assume that the vertical position of pullhead is
The maximum stress results under different conditions are summarized in Table
Maximum stress results.






8  30  1000  35  169.37 
10  30  1000  35  215.15 
12  30  1000  35  273.91 
10  33  1000  35  218.09 
10  36  1000  35  221.10 
10  35  1000  35  219.98 
10  35  1500  35  135.79 
10  35  2000  35  100.23 
10  35  1000  30  217.84 
10  35  1000  40  222.21 
Usually, deepwater SCR is installed by Jlay vessel, and the installation angle (the angle between the Jlay tower and the vertical direction) will affect the SCR installation shape. Under the conditions that
Maximum stresses in different
Under the condition that
Maximum stresses in different
Under the condition that
Maximum stresses in different
Under the condition that
Maximum stresses in different
A simple model for analyzing the static behavior of the deepwater SCR during installation is proposed, while the nonlinear large deformation beam theory is applied and HAM is used to obtain an analytical approximate solution for this model. This model has the main advantage of timesaving and its practicality. In comparison with the results calculated using the software OrcaFlex, a positive agreement is obtained, which demonstrates that the analytical approximate solution is reliable.
The presented model is applied to analyze the influence of different parameters. Some valuable conclusions can be drawn as follows.
Larger initial installation angle causes higher maximum stress during SCR installation, and the Jlay tower is preferred to be placed in an almost vertical position during SCR installation in order to reduce the initial installation angle.
The maximum stress during SCR installation increases with the lower depth of pullhead. The pullhead should be controlled at the minimum lower depth to keep the safety of SCR during installation.
As water becomes deeper, the maximum stress during SCR installation becomes smaller, which is beneficial to the safety of SCR. However, the increasing axial tension induced by its selfweight brings higher requirements on the capacity of the installation vessel.
A longer distance between the installation vessel and the offshore platform can cause a little increase in the maximum stress during SCR installation. To avoid the interference between the installation vessel and the offshore platform, a smaller distance between them is preferred for SCR installation.
This paper reports reasonable approach to the deepwater SCR installation analysis. However, as some assumptions are made for simplifying the investigation, further work needs to be carried out to integrate these assumptions, such as the effect of pipesoil interaction.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This paper is financially supported by the National Natural Science Foundation of China (Grant no. 51349002), the China National Science and Technology Major Projects on Pipe Laying and Lifting Vessel (Grant no. 2011ZX05027002), and the Higher Education Specialized Research Fund for the Doctoral Program (Grant no. 20130007120009). Sincerely, the authors’ thanks also go to colleagues in the COOEC Ltd. and Offshore Oil/Gas Research Centre of CUP, who are involved in this wide range of researches. The authors also highly appreciate the reviewers and the editors’ careful checking and valuable comments on this paper.