ORIGINAL ARTICLE

Influence of Temperature in Sandwich Pipes Subjected to High Pressures

MSc. Dayvis Fernández Valdés^I 

Dr. Alberto Omar Vázquez Hernández^II 

Dr. José Angel Ortega-Herrera^I 

MSc. Minelkis Machado Molina^III 

Dr. Arturo Ocampo Ramirez^{IV  *} 

^ISEPI-ESIME, Instituto Politécnico Nacional, Ciudad de México, México.

^IILloyds Register, Ciudad de México, México.

^IIIUniversidad Agraria de La Habana, Facultad de Ciencias Técnicas, San José de las Lajas, Mayabeque, Cuba.

^IVUnidad de Simulación e Ingeniería Mecánica Estructural - GrupoSSC, Ciudad de México, México.

ABSTRACT

Nowadays, there is a great global development of infrastructure for the extraction, exploitation and transport of hydrocarbons in deep-waters, due to the decrease of existing resources in shallow waters. The objective of this research is to propose a sandwich pipe with thermal insulation, capable to operate in deep water under the effect of the thermal gradient that occurs at these depths and flow assurance guaranteeing. This is also of great importance in agriculture for irrigation with groundwater, where it is necessary to guarantee the structural integrity of the pipelines that transport the fluid through land where high pressures and high temperatures may exist. Therefore, 4 sandwich pipes were analyzed in finite elements, considering high fluid temperatures and low seawater temperatures, as well as variations in the annular material (cement and polypropylene) and the thicknesses. It was obtained that the greater the thickness the lower the stiffness of the system. However, the thermal effect does not significantly influence the resistance of the pipes with greater core thickness, due to the thermal insulation offered by the annular material. The sandwich pipe with cement annular material offers greater potential to be implemented as it presented greater collapse pressure than the pipe with polypropylene.

Keywords: sandwich pipe; thermal gradient; finite elements

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:

$P_{cr}=k{P}_{crs}+E_p\left(1+{\alpha }_1{\upsilon }_c^2\right){\left(\frac{t_e}{R_e}\right)}^{{\alpha }_2}\left({\psi }_1+{\psi }_2\right)$ (1)

With

$P_{crs}=\frac{E_p}{4\left(1-{\upsilon }_p^2\right)}{\left(\frac{t_e}{R_e}\right)}^3$ (2)

${\psi }_1={\gamma }_1{\left(\frac{E_c}{E_p}\right)}^{{\gamma }_2}{\left(1-\frac{R_i}{R_e}\right)}^{{\gamma }_3}$ (3)

${\psi }_2={\xi }_1{\left(\frac{E_c}{E_p}\right)}^{{\xi }_2}{\left(1-\frac{R_i}{R_e}\right)}^{{\xi }_3}{\left(\frac{t_i}{R_i}\right)}^{{\xi }_4}$ (4)

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 

	Sandwich pipe with PP annular material		Sandwich pipe with cement annular material
Dimensions (mm)	I PP	II PP	I C	II C
External diameter	359	359	359	359
Internal diameter	290	290	290	290
Internal thickness	14	5.5	14	5.5
External thickness	14	5.5	14	5.5
Annular thickness	6.5	23.5	6.5	23.5

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 

Properties	X-60 Steel (Multilinear Isotropic Hardening Model)	PP (Hiperelastic Arruda-Boyce Model)	Cement (Isotropic Hardening Model)
Elastic modulus (GPa)	206	-	5.78
Poisson’s ratio	0.3	-	0.15
Density (kg/m^3)	7850	700	1666
Thermal conductivity (W/mºC)	54	0.17	0.53

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 (4^oC) and internal (90^oC), 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 

Pco (MPa)
Model	No thermal gradient	With thermal gradient
IPP	47	34.5
IIPP	20.5	14.8
IC	56	50
IIC	35.8	33

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.

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⁷The mention of trademarks of specific equipment, instruments or materials is for identification purposes, there being no promotional commitment in relation to them, neither by the authors nor by the publisher.

Received: July 15, 2019; Accepted: December 19, 2019

^*Author for correspondence: Arturo Ocampo Ramirez, email: [e-mail]

Dayvis Fernández Valdés, doctorante de SEPI-ESIME, Instituto Politécnico Nacional, Ciudad de México, México, e-mail: [e-mail]

Alberto Omar Vázquez Hernández, investigador, Lloyds Register, Ciudad de México, México, e-mail: [e-mail]

José Angel Ortega-Herrera, investigador, de SEPI-ESIME, Instituto Politécnico Nacional, Ciudad de México, México, e-mail: [e-mail]

Minelkis Machado Molina, doctorante, profesora, Universidad Agraria de La Habana, Facultad de Ciencias Técnicas, San José de las Lajas, Mayabeque, Cuba, e-mail: [e-mail]

Arturo Ocampo Ramírez, investigador, Unidad de Simulación e Ingeniería Mecánica Estructural-GrupoSSC, Ciudad de México, México, e-mail: [e-mail]

The authors of this work declare no conflict of interests.