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LUCIENE ALVES et al.: TRANSIENT THERMAL EFFECTS AND WALKING IN SUBMARINE PIPELINES 37

Abstract— The discovery of new oil fields, many of them in deep and ultra deep waters, has taken the rigid and flexible pipelines operating in extreme conditions. As a consequence, the lateral buckling and walking become crucial in the process of designing products. In particular, the phenomenon of walking is intrinsically linked to transient flow. In this paper, we present a numerical tool for analysis of heat transfer in transient flow in pipelines. This numerical tool was associated with a structural model based on finite element method, which allowed a better understanding of the phenomenon of walking in rigid pipes by conducting a case study. The results showed that cycles of heating and cooling pipes, expanding it and contracting it, respectively, significantly influence in its initial configuration, increasing its length and causing axial residual throughout. This cumulative displacement is known as walking and may compromise structurally the pipeline.

Index Terms — Walking, Transient thermal analysis,

Conduction and convection heat.

I. INTRODUCTION

HEN a pipeline is laid on the seafloor and is heated by passing a hot fluid, it tends to expand. This expansion is

resisted by the friction generated by contact with the seabed. When the product is cooled, it contracts, but the effects of friction of the seabed on the pipe causes it not to contract to its original position. With subsequent cycles of heating and cooling, is accumulating a shift towards the hot end (near end of the pit) to the cold end (opposite end) of the pipe. This shift is called the accumulated walking and can be critical for the structure, since many cycles of heating and cooling pipe can lead to considerable shifts, compromising it.

The walking, so it is a continuous phenomenon and occurs in each thermal cycle (heating and cooling). While walking to start the first cycle, is the second and subsequent cycles that dominate the process.

The walking mechanism is dominated by the transient phase of loading and is therefore understood by examining the relationship between the transient thermal profile of force, and displacement of the pipeline in each cycle of time during the process of heating and cooling.

Manuscript received March, 29, 2012.

Different authors have studied the phenomenon of walkingin recent years. Reference [7] conducted a large number of non-linear structural analyses models based on finite element method. Through these models, we calculated the axial displacements of the pipeline after several cycles of loading and unloading of line considering the transient flow. Two different types of behavior were observed: the product of "long" and pipe "short." Thermal expansion in a pipe "long", with constant temperature and pressure, is contained due to a balance between the axial forces generated by the frictional resistance and the sum of the efforts of the load from heat, pressure and other loads imposed on the pipe causing that expansion occurs only at the ends of the pipe. In the case of a pipeline "short", the thrust generated by the friction forces are not able to balance these efforts led to the expansion of the pipeline. [4] study the phenomenon of walking using both numerical models and simplified analytical models. Through a parametric study, the authors point out that the main parameters related to the phenomenon of walking are: the friction in the axial direction of the soil with the pipe, the transient thermal gradient, the conditions of operation in steady state, which define the variation of force effective along the pipeline, the possible tilt of the sea floor, and pull the top of the shaft imposed by the possible presence of an SCR (Steel Catenary Riser).

This study aims to evaluate the effect of walking on the structural response of offshore pipelines, by testing with thermal and structural models.

First, it solved the problem of heat transfer in the transient regime in pipes and then the bases of the computer program built for the solution of this problem are presented. The proposal is also a numerical model based on finite element method for structural analysis of this phenomenon.

It is a case study conducted with some thermal analysis in a typical submarine pipeline (short pipe), considering different conditions of pump oil and get the response for these thermal conditions.

II. STRUCTURAL AND THERMAL MODEL

A. Heat transfer transient in the radial direction of the pipe

The differential equation governing the one-dimensional problem of transient conduction in a solid cylindrical geometry is [5]:

0),,(*1),(

*1

²²

),(²),(*

1

rtrgkr

trT

rr

trT

t

trT

(1)

Transient Thermal Effects and Walking in Submarine Pipelines

Luciene Alves, José R. M. Sousa and Gilberto B. Ellwanger

[email protected], [email protected], [email protected]

Federal University of Rio de Janeiro, Civil Engineering Department, Rio de Janeiro – RJ

W

INTERNATIONAL JOURNAL OF MODELING AND SIM ULATION FOR PETROLEUM INDUSTRY, VOL. 6, NO. 1, JUNE 2012 38

Where T is the temperature at the solid wall, t is the time step, r is the distance in radial direction in relation to the cylinder axis; is the thermal diffusivity, k is the thermal conductivity, and g (r, t) is a function of internal heat generation.

In this work, will be considered for the analysis of heat conduction, a pipeline consisting of N cylindrical and concentric layers, as shown in Fig. 1. Each layer is considered as homogeneous, isotropic and constant thermal properties. Considering also that the adjacent layers are in perfect thermal contact and there is no internal heat generation (g (r, t) = 0). Under these conditions, the differential equation governing heat transfer in the radial direction of the pipe is expressed by [5]:

Nirrr

r

trT

rr

trT

t

trT

ii

iii

i

,,1

,),(

*1

²²

),(²),(*

1

1

(2)

Where ),( trTi is the temperature in the i-th layer at time t.

Fig. 1. Multilayer pipe.

Are considered also the following boundary conditions and

interface [1]:

11111

1 rrinThThr

Tk f

(3)

1

NaNaN

n rrinThThr

Tk (4)

j

ii

j

ii r

Tk

r

Tk

1

1 (5)

0,)0,( 11 trrrinTrT N (6)

Where 1h is coefficient of heat transfer between the inner

layer of pipe and the internal fluid, and ah is transfer

coefficient heat between the outer layer pipe and external fluid.

Equations (3) and (4) are related therefore to convection on the walls internal and outside the pipe, respectively. Equation (5) provides the perfect thermal contact between the layers and (6) establishes that all layers at the beginning of pumping, are in same temperature as the surrounding medium.

Equation (2) as well as their boundary conditions and interface is solved using the finite difference method of second order Crank-Nicolson [1].

B. Transfer transient heat in the fluid transported

For the solution of the energy equation, it is considered a flow stationary, fully developed, of a fluid production with constant properties being transported through a pipe with circular cross section, as demonstrated in Fig. 2, at an average speed . According to [7], the energy equation for one-dimensional transient fluid production is:

pff

rff

cr

q

x

Tv

t

T

1

12

(7)

)( 111 rfr TThq (8)

Where is average speed of fluid of production; 1rq is

thermal flow on the inner surface of the conveying line; 1r is

internal diameter of pipe; f is density of the fluid

production; pc is specific heat; 1h is coefficient heat transfer

between the fluid and the inner wall in line; fT is fluid

temperature transported; 1rT is temperature on the inner wall

production line.

Fig. 2. Cross section of a production line circular [6].

Equation (7) will be settled with the distribution of initial

temperature ))0,(( xTf of the fluid throughout the pipe, and

assuming that the pipe entrance remains with temperature constant and equal to inlet temperature oil, i.e.:


)()0,( 0 xTxT ff (9)

finf TtT ),0( (10)

The discretization of (7) is done using the method of

second-order central difference Crank-Nicolson [1].

C. Program verification

The numerical solution to the mathematical model described in items a and b, was implemented in a computer program called TRANSIENT [1], developed in Fortran90.

The flowchart of Fig. 3 shows in summary the procedures developed.

The analysis begins with reading a file with the following information: number of layers, number of divisions longitudinal, total time of analysis, number of intervals time, number of divisions of each layer, temperature of the medium external, temperature of the fluid in the inlet pipe, mass flow, density and specific heat of the internal fluid, conductivity of the fluid internal and external, the internal diameter pipe and the total length pipe, the density, the specific heat, the thermal conductivity and thickness of each layer of the pipe.

After reading the above data, the program calculates the longitudinal spacing ( x ), time interval ( t ), inner area

( A ), and the stream velocity ( ). After this information is made to read the boundary conditions for heating or closing the pipe and calculated radial conduction in each layer with the resolution of the system of nonlinear equations and calculation of the transient convection (outlet temperature of the oil).

Fig. 3. Flowchart of the program developed in Fortran90.

D. Structural model – Finite Element Model

The finite element model proposed in this work in order to predict the phenomenon of walking considers non-linearity on the contact interaction between soil and pipe due to the structure heating. This model, if necessary, can also consider

the nonlinear behavior of the pipe material as well as geometric nonlinearity. The transient variation of temperature in the pipe wall and your weight are also considered submerged.

The finite element mesh generated is analyzed using the commercial finite element program ANSYS® [2], and the types of elements were chosen:

BEAM188 - element three-dimensional non-linear gantry, used to represent the pipeline.

COMBIN39 - non-linear spring element used to represent the interaction between soil and pipe.

Fig. 4 shows the finite element model, developed for this work from the elements described above, is represented with the geometric properties expanded.

Fig. 4. Finite element model developed to predict the phenomenon of walking (extended geometric properties).

III. CASE STUDY

A. Description

As an example of application of the methodology described above, was considered a rigid pipe 6.625'' internal diameter. This pipe own two layers: the first (innermost) carbon steel with 1'' thick; and an insulating layer of polypropylene with 2.36'' thick.

The length of the pipe is 6km, it is assumed located at 1500m depth with water temperature in the leasing of 277.15 K and the fluid inlet temperature of 363.15 K

The geometric properties and thermo physical pipe are provided in Table 1 and Table 2 respectively, and the properties of the fluid are in Table 3.

TABLE I GEOMETRIC PROPERTIES OF THE PIPE

Symbol Quantity Units SI

in Inner diameter of the 0,16827m


pipe e Thickness of the

polypropylene 0,060m

Rin Inner radius 0,08415m R2 Average radius 0,10955m R3 Out radius 0,16955m

TABLE II THERMAL PHYSICAL PROPERTIES OF THE PIPE


ρsteel ρPP Cp_steel Cp_PP Ksteel KPP esteel ePP

Specific weight - steel Specific weight – polypropylene Specific heat - steel Specific heat - polypropylene Thermal conductivity - steel Thermal conductivity - polypropylene Thickness of the polypropylene Thickness of the polypropylene

7700 kg/m³ 775 kg/m³ 486 J/kg.K 2000 J/kg.K 54 W/m.K 0,17 W/m.K 0,0254m 0,060m

TABLE III PROPERTIES OF THE FLUID


Tfin Mflow Cp_fluid ρfluid h1 ha U

Temperature Mass flow Specific heat - fluid Specific weight – fluid transfer coefficient heat transfer coefficient heat Thermal transmittance

363,15 K 16,1024 kg/s 2700 J/kg.K 875 kg/m³ 100 W/m.K 500 W/m.K 4,47 W/m².K

In Table 1, Rint corresponds to a radius, found in Fig. 5, measured from the center until the layer 1, R2 is measured from the center the layer 4 and R3 of center to layer 14. In the analysis, the thermal model was discretized into 500 elements with 12m each. The load thermal is applied in increments of time of 18s.

To obtain the temperature distribution along the cross section pipe in each of the mesh points thermal elaborate, were adopted radial divisions illustrated in Fig. 4. The steel layer with 25.4 mm thick was divided on 3 isotherms concentric away from 8.46 mm, while the polypropylene layer, with 60mm thick, was divided into 10 isotherms concentric 6mm. How can be observed in Fig. 5, the isotherm 1 is the inner wall of pipe, namely, is in contact with the internal fluid, the isotherm 4 is the outer wall of layer steel, being the isotherm in contact with the polypropylene . The isotherm 10 is located on medium line of polypropylene layer and isotherm 14 is situated in external wall of the pipe, namely, is in contact with the external fluid, the seawater.

Fig. 5. Division of the layers of pipe to calculate the temperatures along their cross sections.

The finite element mesh used in the structural analysis has a

total length of 6000m, with 1002 elements and 1002 nodes, 501 finite element space frame for the representation of the pipeline and 501 non-linear spring elements to represent the friction of the soil.

B. Analysis of results

Transient thermal analysis

In a first analysis, we adopted the time of 10 hours for heating (pump) and 15 hours for cooling (stop pumping), resulting, therefore, for each cycle, a period of 25 hours. Seven cycles were considered and examined the response of the pipe during these cycles. The Fig. 6 shows the time course of heating the product examined, as well as the steady state temperature during pumping. This figure shows that the fluid initially has its temperature sharply reduced due to the low temperature of the pipeline, but will gradually warm up. The fluid reaches the far end of the pipe after approximately three hours and the steady state pumping down to about 10 hours after pumping.


Fig. 6. Variation of temperature along the internal fluid pipe at different instants of time.

The Fig. 7 illustrates the variation of temperature in the

layers of the last pipe section (output) as a function of time. It can be observed in this graph, the temperature in isotherm 1 is very close to isotherm 4 since it the steel is an excellent conductor of heat. In the isothermal 10, the temperature drops sharply and the temperature isotherm 14 is almost equal to the temperature of sea water. Thus, it is confirmed the efficiency of heat insulating material such as polypropylene. The fluid, therefore, had a small fall in temperature over time when it reaches the steady state, thus avoiding the formation of hydrates and paraffins in the pumping phase.

Fig. 7. Temperature layers of the last section of the pipe as a function of time.

In the graph of Fig. 8 shows that the temperature of the

fluid along the pipe falls off linearly with time after stopping the pump. After 15 hours the temperature of the fluid is 28.40 C, the critical temperature for the start of formation of paraffin.

Fig. 8. Temperature during stop pumping.

An important observation is the outlet temperature of the oil

after the pumping stage (10 hours) and restarting the pump (25 hours). These temperatures are 334.75 K and 301.55 K, respectively, are above the precipitation of wax and hydrates

( CThydrate 25 according [3]). This shows the efficiency of

the thermal insulation offered.

C. Structural analysis

The Fig. 9 and Fig. 10 show the effective axial force developed after the first cycle of heating / cooling pipe, respectively.

When the product is heated, the axial force grows along its length until the pipe is completely mobilized by the temperature, which for this example was after 3 hours (yellow line - Fig. 6). After that time, it formed a "virtual anchor" (peak axial force) in the middle of the pipe, which expands toward the hot end and cold end. The expansion of the product remains, there is no change in the force profile over 10 hours of pumping, as shown in Fig. 9.

When the product cools, shrinkage takes place at a uniform rate over its entire length and from the central peak, as shown in Fig. 10.

Therefore, the uniform cooling pipe, which occurs after stopping the pump, it takes the friction force to reverse in response to contraction of the pipeline, and compression force observed becomes an effective traction force, which will be changing the from the virtual anchor.


Fig. 9. Effective axial force along the pipe for heating in the first cycle.

Fig. 10. Effective axial force along the pipe for cooling the first cycle

The effect of thermal loading in the movement of the pipe can be understood by considering a cumulative axial displacement means of each time increment. Fig. 11 shows the graph of extension movement through the pipe during the first heating cycle.

Fig. 11. Expansion of the pipe during heating - first round.

With the heating pipe, a non-uniform expansion is evident.

The region of the pipe close to the hot end tends to expand toward this end, while the rest of the pipe moves to the cold end. With continuous heating pipe, the displacement increases and remains zero only in the central section of the pipeline when it becomes fully mobilized. Thereafter, the subsequent expansions are centered at this point.

From the complete mobilization of the pipe, that is, when the fluid travels along its entire length, the cold end begins to expand with the continuous increase in temperature. In this example, particularly the final expansion was 2.50 m.

On the other hand, when the product cools in a uniform manner, the discharge pipe symmetrically about its center. The axial displacement during unloading can be seen in Fig. 12.

Fig. 12. Contraction of the pipe during cooling - the first cycle.

From the second cycle, the strength of the product will

grow in a manner different from that shown in Fig. 10 due to the axial residual force in the pipeline after the end of the first cooling cycle, as shown in Fig. 13. This is due to the fact that


the pipeline does not return to its original size due to the restriction caused by friction.

Fig. 13. Effective axial pipe - the second heating cycle.

At the beginning of the second heating cycle, the product is

pulled and with the heating, the product begins to expand from the hot forming an anchor point (A1) and that expansion occurs in the direction of hot tip between A1 and A0. In order to maintain balance force, a second anchor (B1) is at the other end. With the heating pipe, the location of these anchors will be changing toward the midpoint of the shaft, which is its peak. After the formation of virtual anchor in the center section of the pipeline, there is no change in the axial forces along their length.

When the product cools along its length, it can no longer return to its original length, with a remaining displacement accumulated. When the product is re-heated, the process begins again, only now with the new settings of the pipe. The Fig. 14 shows the second heating cycle of the pipe and Fig. 15 the second cooling cycle.

Fig. 14. Graph of displacement during the second heating cycle.

Fig. 15 – Graph of displacement during the slowdown in the second cycle.

Thus, each cycle the pipeline "walk" toward the cold end.

This is the phenomenon of walking. The Fig. 16 shows how the center and ends of the pipe

expand and contract with temperature changes through the profile of heating and cooling. This clearly shows how the repeated cycles lead to deformation of the pipe.

Fig. 16. History of displacement after seven cycles of heating / cooling.

With uniform cooling of the line, the drag friction is

maintained in equilibrium about the midpoint of the pipe, causing the core does not move axially. In Table 4 are the values of the walking at the midpoint of the walking pipe in which it can be seen that the displacement accumulated is fixed, the amount of 140mm in any heating and cooling cycle.


TABLE IV

VALUE OF WALKING AT THE MIDPOINT OF THE PIPE 6KM EXTENSION

Walking - Midpoint

cycles Displacement

(m) Cumulative displacement

(mm)

1 0,0027 -

2 0,14 140

3 0,29 140

4 0,43 140

5 0,57 140

6 0,71 140

7 0,85 140

IV. CONCLUSION

In this work we present a numerical tool for analysis of heat transfer in transient flow in pipelines used in the production of hydrocarbons in deep and ultra deep water.

As an application of this tool, a typical rigid pipe was studied. Temperatures were observed throughout the structure and these temperatures were carried out for structural analysis of a model-based Finite Element Method (FEM).

The results showed that cycles of heating / cooling pipe, the expanding and contracting it, respectively, significantly influence in its initial configuration, increasing the axial length and resulting waste in all its extension. This shift is known as the accumulated walking and may compromise the structural pipe.

It can be observed in the analyses, the formation of a virtual anchor due to the heating pipe, showing that, on heating, the product tends to expand causing a compressive force along its entire length. This force has a peak in the virtual anchor, in the case of the free ends of the pipe is formed at its center. With cooling, the compressive force is decreased until it becomes a tensile force, since the pipe is contracted with decreasing temperature. This change in force occurs from the center to the ends of the pipe.

The problem of walking could be reduced by more gradual warming of the pipe in order to control the slope of the profile of the thermal transient. However, this is often not possible for operational reasons and reluctance to extend the time of recovery from the production stop.

Another way to control the walking installing anchors it in the pipes at the end of the extension of the pipe, but the charges can be as high as the frictional force along the whole axial length of the pipe. This loading would therefore be reduced by an anchor in the middle of the length of the pipe, but the design and installation of these anchors can become a challenge.

In future work we intend to do a parametric study of the phenomenon of walking with the following cases of sensitivity coefficient of friction between soil and pipe; effect of thermal gradient, effect of a spring on top of the shaft, representing a possible PLET (Pipe Line end Termination).

REFERENCES [1] L.S. Alves, “Transient thermal effects on walking and submarine

pipelines,” M.S. thesis, Dept. Civil. Eng., UFRJ, Rio de Janeiro, Brazil, 2009.

[2] Ansys, 2007, ANSYS Reference Manual (Version 11.0), ANSYS, Inc. [3] J.S. Baioco, C.A. Santarem, R.B. Bone, V.J.M. Ferreira. “Economic

Costs and Benefits of Technology Natural Gas Transportation in Brazil”. 40 PDPETRO, Campinas, SP, Brazil, 2007.

[4] M. Carr, F. Sinclair, D. Bruton. “Pipeline Walking – Understanding the Field Layout Challenges, and Analytical Solutions Developed for the SAFEBUCK JIP”. OTC 17945, Houston, Texas, USA, May 2006.

[5] M.N. Özisik. “Finite Difference Methods in Heat Transfer”. Ed. CRC Press, North Carolina State University, Raleigh, North Carolina, US, April, 1994.

[6] Su, J., Cerqueira, D. R., 2001. “Simulation of Transient Heat Transfer in Multilayered Composite Pipeline”. In: Proceedings of 20th International Conference on Offshore Mechanics and Arctic Engineering, OMAE 2001–4126, Rio de Janeiro, June.

[7] Tornes, K., Ose, B. A., Jury, J., Thomson, P., 2000. “Axial Creeping of High Temperature Flowlines Caused by Soil Ratcheting”. OMAE2000/PIPE-5055, New Orleans, LA, 2000.

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