INTRODUCTION
Oil industry needs to venture into deep and ultra-deep waters, marking a new stage in oil development and boosting economic growth. For this reason, the generation of high potential technology is required to be implemented in these depths and to be able to access to new resources in a safe and efficient way.
In recent years, various studies have focused on sandwich pipes Kyriakides y Netto (2004); Kardomateas y Simitses (2005); Arjomandi y Taheri (2010a, 2010b, 2011, 2012); Xu et al. (2016),These pipes equipped with thermal insulation, offer better flow assurance from the deposit to the production platforms and systems Netto et al. (2002), thus, the existing deficiencies of single wall pipes are overcome (Castello & Estefen, 2008). Therefore, it is vital to know the behavior of these pipelines, which will be exposed to severe operating conditions, since in deep water, the deposit fluids are warmer than the sea water, generating thermal shock (Su et al., 2003; Castello & Estefen, 2008; An et al., 2012, 2014).
It is of great importance for precision agriculture of high productivity, the study of the structural integrity of the pipelines used for irrigation with groundwater Llamas & Martínez (2005) and Paneque et al. (2018), because in their trajectory, they are exposed to different conditions such as terrain where high pressures and high temperatures may exist. Therefore, the knowledge of their behavior through an analytical and numerical model is very useful (Arjomandi & Taheri, 2011).
According to the above, the objective of this work is to investigate by means of finite element analysis the influence of the thermal gradient in the operation of the proposed sandwich pipes, considering different annular materials and variations in their thickness.
METHODS
Analytical Model of Critical Pressure (buckling pressure)
Based on Arjomandi & Taheri (2011), the critical pressure for the proposed sandwich pipes is calculated, using polypropylene annular material. This equation (1) is only applicable for soft cores and considers the imperfection existing in the sandwich pipes, as well as the annular thickness:
With
Where Pcr is the critical pressure (buckling pressure) for the sandwich pipes, Pcrs is the external pipe buckling pressure, k, α, γ, ξ are constants calculated in Arjomandi &Taheri (2011), used to obtain the pipeline pressure. These constants were obtained through a numerical model using Matlab and the restricted nonlinear regression algorithm recommended by Gill et al. (1986), with a sequential quadratic programming method. Parameters ψ1 and ψ2 represent the effect of the core and internal pipeline, respectively, Ep and Ec are the elastic modulus of steel and annular material, respectively, υp and υc are Poisson’s ratio, te and ti are external and internal thickness of steel and Re and Ri are external and internal radius of the steel pipelines.
Numerical Simulation
In order to know the behavior of sandwich pipes before the effect of temperature in deep and ultra-deep waters, modeling was performed through the Finite Element Method. Four X-60 steel sandwich pipes were analyzed, for which dimensions and annular material were varied (polypropylene (PP) and cement). The analyzed pipeline model was reduced to a two-dimensional model without losing accuracy according to Estefen et al. (2005) y Chen et al. (2013), meanwhile computational costs were reduced. The objective is to propose to the oil industry a sandwich pipe with the required dimensions and the most feasible annular material, according to the severe operating conditions at these depths (Table 1).
TABLE 1.
Sandwich pipes dimensions
The sandwich pipes are composed of two layers of X-60 steel and an annular material (Figure 1).
FIGURE 1.
Sandwich pipe model.
The mechanical properties according to Estefen et al. (2005); Castello & Estefen (2008); Castello (2011) and thermal properties according to (Xu & Chung, 2000; Castello & Estefen, 2008), used for the numerical analysis of sandwich pipes are shown in Table 2, for each material.
TABLE 2.
Properties of the materials
Perfect adhesion between the steel layers and the annular material through joined contact elements, which do not allow the separation of the layers, was considered. Two types of elements were used: a) CONTA172 contact elements and b) TARGE169 type elements.
Boundary conditions were applied such as the restriction of movement on the y-axis, allowing the free x-axis, as the first condition and the second condition was the restriction of movement of the x-axis, allowing the y-axis free. The axial compression load, referring to the external pressure was applied over the entire outer surface of the sandwich pipe (Figure 2). With this, it is possible to obtain the collapse pressure. Finally, temperatures were applied, external (4oC) and internal (90oC), according to Castello & Estefen (2008) and the stress-strain curves of each material, according to Souza et al. (2007), were used for the correct simulation.
FIGURE 2.
Boundary conditions applied to sandwich pipes for simulation
The generation of a suitable mesh is a decisive factor in the simulation (Figure 3), to obtain reliable results, for this, the second order Plane 183 element was defined, which has the ability to be hyper elastic.
FIGURE 3.
Sandwich pipe mesh.
RESULTS AND DISCUSSION
Results of Thermal Analysis
The temperature profile was obtained for each sandwich pipe with each annular material analyzed (Figures 4 and 5), observing that for the PP the temperature in the external pipe decreases more than in the case of the sandwich pipe with cement. The temperature decreases (from the inner pipe to the outer pipe) as the thickness increases (Souza et al., 2007; Castello & Estefen, 2008).
FIGURE 4.
Temperature profile for the IPP and IIPP pipelines, respectively.
FIGURE 5.
Temperature profile for the IC and IIC pipelines, respectively.
Numerical Results of the Collapse Pressure under the Effect of Temperature
Figures 6 and 7 show the results of thermal analysis and buckling for the sandwich pipes analyzed. The collapse pressure was obtained for each sandwich pipe, under the influence of a thermal gradient. Figure 6 shows the sandwich pipes with polypropylene annular material, observing that, with the increase of the annular thickness and the decrease of the layers of steel, a decrease of the collapse pressure is generated.
FIGURE 6.
Collapse pressure under the thermal gradient for the IPP and IIPP pipelines, respectively.
In the case of sandwich pipes with cement annular material (Figure 7), a behavior similar to that of sandwich pipe with polypropylene was obtained, where the influence of the increase in annular thickness on the decrease in collapse pressure become remarkable once again.
FIGURE 7.
Collapse pressure under the thermal gradient for the IC and IIC pipelines, respectively.
According to the results obtained, the sandwich pipes with cement annular material have higher collapse pressure and, in turn, more stiffness than the polypropylene pipes, since the latter is less resistant to thermal gradient than cement (Castello & Estefen, 2008). Based on these results, it can be established that the cement pipeline offers greater potential for operation in ultra-deep water for a thin annular material as for a greater thickness.
Comparison of Collapse Pressure (buckling pressure) Results
In order to know the effect of temperature on the collapse pressure, the sandwich pipes with and without the effect of the thermal gradient were also analyzed in finite elements (Figure 8).
FIGURE 8.
Collapse pressure comparison under thermal gradient.
In this way, it was possible to compare and observe the difference in the behavior of the collapse pressure (Table 3). The thermal gradient generates a decrease in the collapse pressure in the four sandwich pipes analyzed, resulting in vulnerability in its resistance (Souza et al., 2007). However, despite the effect of temperature, sandwich pipes provide better performance than single wall pipes (Souza et al., 2007). It was obtained that, for the pipes with greater core thickness, the temperature influenced in a smaller proportion the results of collapse pressure, probably achieving with this technology the flow assurance, due to the benefits offered by the thermal insulation.
TABLE 3.
Collapse pressure comparison
Comparison of Analytical and Numerical Results
The critical pressure of each polypropylene sandwich pipe was calculated through Equation 1. It was compared to the numerical results and similar values were obtained for both cases (Table 4).
TABLE 4.
Comparison of analytical and numerical results
| Pcrit (MPa) | ||
|---|---|---|
| Model | Analytical (Equation 1) | Numeric (Finite Element) |
| IPP | 200.97 | 200.15 |
| IIPP | 108 | 107.32 |
CONCLUSIONS
The sandwich pipes were analyzed by finite element under the effect of the thermal gradient and taking into account variations in the annular material and its thickness. The stiffness of the system is affected due to the thermal shock generated in deep water. Numerical and analytical analyses threw similar results, both for deep-water applications and for irrigation with groundwater. With the increase in the annular thickness, both, in the case of cement and polypropylene, a decrease in collapse pressure occurs. It was also obtained that the sandwich pipes with cement core present greater resistance than the pipes with polypropylene before the operating conditions analyzed. The polypropylene sandwich pipe with greater annular thickness does not meet the requirements to be implemented in deep water. For this reason, it can be argued that the sandwich pipe of cement annular material, despite also presenting a decrease in stiffness, offers high potential to be implemented in deep and ultra-deep waters. With the thermal insulation provided by sandwich pipes technology, the existing deficiencies in the oil industry in single wall pipes are overcome.