cilamce2007_contato

7/30/2019 CILAMCE2007_contato

1/17

CMNE/CILAMCE 2007

Porto, June 13th

to 15th, 2007

APMTAC, Portugal 2007

A CONTACT MODEL FOR THE SIMULATION OF LINE COLLISION

IN OFFSHORE OIL EXPLOITATION

Danilo M. L. Silva1*, Antonio C. P. Pereira1 and Breno P. Jacob1

1: LAMCSO Laboratory of Computational Methods and Offshore Systems

Graduate Institute of the Federal University of Rio de Janeiro COPPE / UFRJ

e-mail: [email protected]

[email protected]; [email protected]

Keywords: Contact Model, Line Collision, Offshore Oil Explotation.

Abstract. Deepwater offshore oil exploitation activities have been requiring the use of a

sophisticated computational tool to predict the behavior of floating offshore systems under

the action of environmental loads. Nowadays, it has been recognized that such tool shouldbe able to perform coupled dynamic analysis, considering the non-linear interaction of the

hydrodynamic behavior of the platform with the structural/hydrodynamic behavior of the

mooring lines and risers.

In this approach, the structural behavior of the lines is represented by Finite Element

models. Traditionally, the implementation of the analysis tools considers the coupling of

the equations of motion of the FEM model with the 6-DOF equations of motion of the

platform hull. However, this approach has a limitation for model some situations in

offshore operations, it does not rigorously consider the contact between the lines in the

model.

Therefore, the objective of this work is to present a tool that improve the coupled analysismodel described above and make it capable to model the collision involving the lines of

the system (mooring lines and risers). Such tool includes a search algorithm for the

automatic determination of the contact point. The contact point can, depending on the

situation, slip on each line and no limitation is made related to the position of this point

along the lines.

Some physical considerations are made to model the behavior of the lines during the

period of impact and during the period of deformation/restitution. The velocities and

directions of collision are used to take into account the impulsive force acting on each line

due the impact with another line.

The application of the presented contact model is demonstrated by case studies ofapplications for offshore systems. The collision between a drilling riser and a mooring

line is analyzed.

1. INTRODUCTIONTop-tensioned risers are subject to displacement by platform motions, excitations by wave


2/17

Danilo M. L. Silva, Antonio C. P. Pereira and Breno P. Jacob

2

loading, and vortex induced vibrations (VIV) by current loads. Such non-deterministic

loading may cause a riser to move into the vicinity of another and provide conditions

where interference or clashing may occur. The consequences of impact between risers can

be dents to the pipe, damage to attachments (such as anodes, buoyancy modules, strakes,etc.), or even tearing of the coatings.

In shallow water, the risers can be spaced so that this condition does not occur, but as oil

exploration and production moves towards deeper water, it becomes unfeasible to provide

the well spacing on the top-sides necessary to prevent interference. Consequently, some

interference and impacts may have to be accepted in order to avoid impractical riser

spacing.

Clashing or colliding between marine risers is an issue of considerable interest in the

design of deep sea floating oil and gas production systems. The problem is that static

deflection of a marine riser due to drag is proportional to the square of its length, when

other parameters are kept constant. This implies that risk of clashing and collision

increases dramatically with respect to water depth. A second factor that contributes to this

concern is that the number of marine risers suspended from offshore structures increases

with the growing use of subsea production systems.

Of course the collision between lines is an important issue not only for production risers

but also in other types of lines and in different situations of installation and accidents. For

instance, in drilling operations, when a dynamic positioning (DP) drilling unit is close to

other production unit, the unit may lose its capacity to maintain position and must

disconnect the drilling rigid riser column at the seabottom. In such situation, the unit drifts

with the riser hung from the hull through the tensioning system, and may follow a

trajectory that may lead to the collision of the riser column with a mooring line of a nearby

production unit.Therefore, the objective of this work is to present a tool that improve the coupled analysis

model, and make it capable to model the collision involving the lines of the system

(mooring lines and risers). Such tool includes a search algorithm for the automatic

determination of the contact point. The contact point can, depending on the situation, slip

on each line and no limitation is made related to the position of this point along the lines.

The proposed contact model has been incorporated into the Prosim computer program for

the coupled nonlinear static and dynamic analysis of floating platforms [1]. The program

is integrated to a pre and pos-processing interface called SITUA, that generates the models

(including the FE meshes) and visualizes the results. The SITUA-Prosim system has been

developed since 1997 [1], in cooperation by Petrobras and LAMCSO (Laboratory of

Computational Methods and Offshore Systems, at the Civil Eng. Dept. of COPPE/UFRJ,Federal Univ. of Rio de Janeiro).

Modules have been incorporated to the SITUA-Prosim system to allow generation and

analyses of several installation and operational procedures in offshore oil explotation

[2,3].


3/17


3

2. TYPICAL CONTACT SITUATIONS2.1.Contact involving adjacent risersFor deep sea systems the relatively small difference in static deflection may lead to

mechanical contact between adjacent risers. The situation is illustrated in Fig.1. The

downstream riser, R2, is sitting in the wake of an upstream riser, R1. The effective inflow

velocity, and thus the static deflection, of R2 will be reduced relative to R1. Depending on

pretensions, spacing, and other geometrical parameters there is the possibility of clashing

or collisions between the risers. So far, the tendency has been to consider such collisions

as unacceptable in practical design, due to the possible damage of the risers that they may

cause.

Figure 1. Physics of riser collision.

Due to the complexity of the physics of riser collisions, this is indeed a very challenging

task. First of all one has to predict the traditional VIV response of the risers. Then one hasto understand and predict the low frequency, stochastic motion response which is typical

for the downstream risers [4]. In the end the possible damage mechanisms have to be

predicted, combining all the relevant processes in a statistical model.

Whether collision between two adjacent risers will occur or not, depend on many factors

such as:

loading environment; hydrodynamic interaction comprising wake induced oscillations (WIO) including

shielding effects and vortex induced vibrations (VIV);

riser spacing at floater and seafloor terminations; top-tension, and different dynamic properties of the risers due to differences in mass, diameter,

effective weight, applied top-tension or effective tension-distribution etc.

Structural interference is a complex phenomenon involving different time scales. The

initial impact duration between two bare risers experiencing contact is typically a small

fraction of a second. The maximum collision load effects normally occur at the very

beginning of the impact. Only a small segment of the riser participates to the local


4/17


4

collision load effects such as stresses and strains.

The peak stresses, and the number of peaks, are strongly affected by local dynamics of the

risers. The riser tube is significantly stiffer in circumferential direction than in

longitudinal direction. Hence, the hoop stress will be larger than the longitudinal stresses.The structural response is highly centralized around the contact point both in

circumferential and longitudinal directions. Coating might effectively be used as a bumper

to reduce the peak stresses [5]. However, coating must be designed to withstand the

impact that might occur over the lifetime.

2.2.Contact involving risers and mooring linesMany important operations in offshore oil industry such as drilling, completion or

workover are being performed in congested areas, with increasing proximity between

dynamic positioning (DP) drilling units and other production units based on ships or

platforms.The collision between the drilling riser of a DP unit and a mooring line can occur when

the DP unit loses its capacity to maintain position, due to some failure of the electric

system, thrusters or the control system. In such situations, it must disconnect the drilling

rigid riser column at the seabottom, retaining the device known as Low Marine Riser

Package (LMRP) still coupled to the base of the riser.

Thus, the DP unit drifts with the riser hung from the hull through the tensioning system,

and follows a trajectory that may lead to the collision of the riser column with a mooring

line of a nearby production unit, with the possible consequences of material loss and

financial damage due to the need of replacement and reinstallation operations. This

situation is illustrated in Figure

Figure 2. Collision between a drilling riser and a mooring line.

The study of the collision between a rigid riser and mooring lines has been involved is one

the main objectives of Petrobras, the Brazilian state oil company, which is to develop oil

exploration and production activities regarding environmental and human safety. These, in

accordance with the current world demands, are indispensable factors for any enterprise

that may present environmental impact.


5/17


5

In fact, drilling, completion and workover activities are being performed in congested

areas, with crescent proximity between dynamic position floating units and other

production installations. As a consequence, the risk of accidents may become high if

effective safety procedures are not adopted.Several issues may be addressed amongst the possible results of the collision between a

rigid riser and a mooring line [6,7]:

The drilling riser can become engaged to the mooring line; this may be due to the factthat the LMRP device at the bottom of the riser has specific weight and diameter

values considerably larger than those of the riser, In this case, either the line or the

riser can rupture.

The pull capacity of the anchor can be exceeded; The riser can slip along the mooring line. In this case the line can serve as a guide

leading to the collision between the DP unit and the production unit.

3. COMMENTS ON GLOBAL ANALYSES MODELSThe purpose of global riser analysis is to predict global structural response, e.g. bending

moments, effective tension, displacements and curvature, in a stationary environmental

load conditions. Such analyses are performed by the Prosim finite element computer code

using 3D beam elements with specified bending-, axial- and torsional properties.

For direct modelling of interference and collision between lines, the global dynamic

analyses should include:

a hydrodynamic interaction model, and

a global contact model, that may include the modeling of dynamic effects of impact, and

also the global rebound effects of the collision.This paper deals with the latter aspect. Of course, a comprehensive approach for

interference and collision of lines should include both aspects, although hydrodynamic

interaction models are useful to represent some of the causes of line collision, but not all.

For instance, in some installation procedures and accidental situations such as the

described in the previous section, hydrodynamic interaction could be disregarded.

4. MODELLING AND ASSESSING IMPACT ON LINESConventionally, engineers employ a concept, such as kinetic energy, to calculate the

impact damage when two bodies collide. The problem can be simplified by reducing the

impactor as a single degree of freedom object and the total energy absorption by the targetwould be estimated by factoring the initial energy of the impactor. All the other structural

quantities, such as strains and stresses, would be calculated based on the energy absorbed

by the target structure [8,9].

In order to apply kinetic energy as the governing dynamic parameter in impact of risers

and other types of lines, the mass of the line involved in the impact and the velocity

profile along the effective length need to be known. One of the main challenges in


6/17


6

estimating impact energy in collisions between marine risers and lines is the assessment of

the mass involved in the collision. One of the simplifications and assumptions made in this

paper is to use a constant mass term in the energy calculations. The assumption of a

constant mass during the impact is not self evident, but it is made to obtain suitableengineering solutions to this challenge. This constant mass term is denoted participating

mass.

Basic assumptions and simplifications

1. The participating mass m is constant during the duration of the impact time.

2. The exchange of momentum takes place over a very short interval, hence the global

riser shape will not be altered during the impact.

3. The impact energy loss is negligibly. All impact energy is absorbed by deformation and

velocities. This assumption is reasonable and conservative due to the very short collision

time, hence there is very little time for the energy to dissipate out from the system due to

internal or external damping.

4.1.Analysis Method for Collision EnergyThe impulse force is here defined as the integral of the force signal,

Fdt (1)

where F is force and tis time, the integration performed over the duration of the collision.

The basic law of nature controlling the relationship between force, mass, and acceleration

is

F = d(mv)/dt (2)

Where m is mass and v is velocity. Integrated over the duration of the collision

Fdt= d(mv) = mdv+vdm (3)

Let us now assume that it is possible to define an effective mass meff which does not

change during the collision. This makes the second integral on the right hand side above

equal to zero, and m can be placed outside the integral sign of the first one. This leads to

Fdt= meffdv (4)

Now, since dv =adt, wherea is acceleration,

meff = Fdtadt (5)

The acceleration and the collision force are obtained from dynamic simulation of the riser

behavior. The acceleration at the contact point is easily obtained from equation of motion.

The collision force is not evident once this force depends on inertial effects, which means

it depends on the mass and velocity. Here, the value of the collision force is approximated

by the resultant force at the contact point immediately before collision. Thus, the inertial


7/17


7

effects are considered without explicit use of the participating mass.

It should be noted that in problems involving collision/impact two types of effects take

place: a) effects due impact, such as impulse forces or high frequencies vibrations , which

take place in a very short period of time and (b) effects just due the contact, which meansno inertial effects involved. In that sense, the contact can be seemed as an impact with a

very low velocity and during a long period of time which make inertial effects not

significant.

Thus, by Eq.(5) above an effective mass of the riser can be determined, referring to the

collision.

4.2.Conservation of energyThe Principle of conservation of energy states that the energy is conserved trough the

impact:

12( )m1vi1

2 +m2vi22 = 12( )m1vf1

2 +m2vf22 (6)

The subscripts i and f refer to just before and just after the impact respectively and the

subscripts 1 and 2 refer to mass and velocities of riser 1 and 2.

4.3.Conservation of momentumThe conservation of momentum states that:

m1vi1+m2vi2 = m1vf1+m2vf2 (7)

where again the subscripts i and f refer to the states before and after the impact.

5. COMPUTATIONAL IMPLEMENTATION OF THE CONTACT MODEL5.1.Distance Between Two Line Segments in 3DMathematical Formulation

The problem is to compute the minimum distance between points on two line segments

L0 =B0+sM0 for s [0,1], and L1 =B1+sM1 for t [0,1]. The minimum distance iscomputed by locating the values s [0,1] and t [0,1] corresponding to the two closest

points on the line segments [10].

The squareddistance function for any two points on the line segments isQ(s,t) = |L0(s) -L1(t) |2 for (s,t) [0,1]2. The function is quadratic in s and t,

Q(s,t) = as2+ 2bst+ct2+ 2ds+ 2et+f (8)

Where a =M0M0, b = -M0M1, c =M1M1, d=M0(B0-B1 ), e = -M1(B0-B1),and f= (B0-B1) (B0-B1). Quadratics are classified by the sign ofacb2. For functionQ,


8/17


8

acb2 = (M0M0 )(M1M1 ) - (M0M1 )2 = |M0M1 |2 0 (9)

If acb2> 0 then the two line segments are not parallel and the graph of Q is aparaboloid. Ifac

b2 = 0, then the two line segments are parallel and the graph of Q is a

parabolic cylinder.

In calculus terms, the goal is to minimize Q(s,t) over the unit square [0,1]2. Since Q is a

continuously differentiable function, the minimum occurs either at an interior point of the

square where the gradient Q = 2(as+bt+d, bs+ct+e) = (0,0) or at a point on theboundary of the square.

The unit square [0,1]2 is shown in Figure 3. The central square labeled region 0 is the

domain of Q, (s,t) [0,1]2. If (s, t) is in region 0, then the two closest points on the 3Dline segments are interior points of those segments.

Figure 3. Partitioning of the st-plane by the unit square.

Nonparallel Line SegmentsWhen acb2> 0 the line are segments are not parallel. The gradient of Q is zero onlywhen s = (be-cd) / (ac-b2) and t= (bd-ae) / (ac-b2). If (s, t) [0,1]2 then we havefound the minimum of Q. Otherwise, the minimum must occur on the boundary of the

square.

Parallel Line Segments

When acb2 = 0 the gradient of Q is zero on an entire st-line, s = (bt-d) / a for all t. If any pair (s,t) satisfying this equation is in [0,1], then that pair leads to two points on

the 3D lines that are closest. Otherwise, the minimum must occur on the boundary of the

square.

ImplementationThe implementation of the algorithm is designed so that at most one floating point division

is used when computing the minimum distance and corresponding closest points.

Moreover, the division is deferred until it is needed. In some cases no division is needed.

Quantities that are used throughout the code are computed first. In particular, the

quantities computed are a, b, c, d, e,f. It is also needed to determine immediately whether

or not the two line segments are parallel. The quadratic classifier is d = acb2 and is also


9/17


9

computed initially. The code actually computes d = | acb2 | since it is possible for nearlyparallel lines that some floating point roundoff errors lead to a small negative quantity.

Finally, d is compared to a floating point tolerance value. If larger, the two line segments

are nonparallel and the code for that case is processed. If smaller, the two line segmentsare assumed to be parallel and the code for that case is processed.

General Case Nonparallel Line Segments

In the theoretical development, it was computed s = (be-cd) / d and t= (bd-ae) / d sothat Q(s,t^) = (0,0). The location of the global minimum is then tested to see if it is in the

unit square [0,1]2. If so, then it was already determined what it needs to compute minimum

distance. If not, then the boundary of the unit square must be tested. To defer the division

by d, the code instead computes s = (be-cd) and EQ t= (bd-ae) and tests forcontainment in [0, d]2. If in that set, then the divisions are performed. If not, then the

boundary of the unit square is tested. The general outline of the conditionals for

determining which region contains (s,t) is

det = a*c- b*b; s = b*e- c*d; t = b*d- a*e;i f ( s >= 0 ) t hen

i f ( s = 0 ) t hen

i f ( t = 0 ) t hen

i f ( t = 0 ) t hen

i f ( t


10/17


10

Region 0

i nvDet = 1/ dets = s * i nvDett = t * i nvDet

Region 1

! F(t) = Q(1,t)

! F(t) = 2*((b+e)+c*t)

! F(T) = 0 when T = -(b+e)/c

s = 1;t mp = b+e;i f ( t mp > 0 ) t hen

t = 0 !T < 0el se i f ( - t mp > c ) t hen

t = 1 !T > 1el se

t = - t mp/ c !0


11/17


11

6.1.The contact modelThe problem to be solved here consists of two perpendicular beams as shown in Figure 4.

The two beams have the same physical and geometrical properties. Initially the two beams

are very close but not in contact; then a displacement is applied to each beam as shown in

Figure 4.

Figure 4. Perpendicular beams Contact Model.

Thus the problem is symmetric and can be seen as a simple problem in strength of

materials: a supported beam with concentrated load. The solution of this problem is easily

obtained and is shown besides the mathematical model in Figure 5.

Deflection =PL3

48EI

Moment=PL

4

Figure 5. Simple supported beam and analytical solution.

The material and geometrical parameters are selected as follows:

E = 70 GPa;r = 2680 kg/m3; L = 1200 mm; d= 20 mm.Thus, the load P and moment M depends on the value of the displacements u applied to the

beams. If u1 = u2, the maximum deflection PL3 / 48EI is known and it is just u. For

u = d/ 4 = 5 mm: P = 0.076 KN and M = 0.023 KN m

In order to avoid influence of inertial effects due to impact when the two beams intersect,

the displacement u is applied slowly. The velocity of movement is less than 0.0005 m/s.

Several different finite element meshes were used, with element lengths ranging from

0.02m (60 elements) to 0.6 (2 elements). Also, the analyses were performed for severaltime steps, from 0.1 seconds to 0.0001 seconds. The results were the same for all these

parameters.

The Figure 6 shows the vertical reaction and moments at the midpoint of beam 1 (blue)

and 2 (red).


12/17


12

- 0. 08

- 0. 06

- 0. 04

- 0. 02

0. 00

0. 02

0. 04

0. 06

0. 08

0. 0 3. 0 6. 0 9. 0 12. 0 15. 0Tempo (s)

Vertical

Rea

ction

(KN)

Beam 1

Beam 2

- 0. 08

- 0. 06

- 0. 04

- 0. 02

0. 00

0. 02

0. 04

0. 06

0. 08

0. 0 3. 0 6. 0 9. 0 12. 0 15. 0

Tempo (s)

Mom

ent

(KN.m)

Beam 1

Beam 2

Figure 6. Vertical reaction and moment midpoint beams 1 (blue) and 2 (red).

From these graphs one can see that the computed solution agree with the analytical

solution, thus demonstrating that the contact model represents the physical event withsufficient accuracy.

6.2.The Impact modelIn an impact problem, the ratio of the magnitudes of the impulses corresponding,

respectively, to the period of restitution and to the period of deformation is called the

coefficient of restitution and is denoted by . The coefficient of restitution is the ratio ofthe relative velocities before and after impact. The value of is always between 0 and 1and depends to a large extent on the two materials involved. However, it also varies

considerably with the impact velocity and the shape and size of the two colliding bodies.

When = 0, the impact is perfectly plastic. There is no period of restitution, and bothbodies stay together after impact. When = 1, the impact is perfectly elastic. The relativevelocities before and after impact are equal. The impulses received before by each body

during the period of deformation and during the period of restitution are equal. In other

words, the bodies move away from each other after impact with the same velocity with

which they approached each other before impact.

The determination of from experiments is conveniently accomplished by dropping asphere on a massive plane plate of the same material from a height h and observing the

rebounding height h*.

The energy loss is then given by

DE = mg(h-h*) (10)

and using the equation of free fall, v = 2gh, and the definition of the coefficient of

restitution, yields

= h* / h (11)

Thus, when a body is in free fall, as shown in Figure 7, and collides with a plane surface

(which can be seen as another much bigger body ), if the impact is perfectly elastic, than


13/17


13

there is no loss of energy, = 1 and h* = h.

Figure 7. Impact after free fall coefficient of restitution.

The free fall problem shown in Figure 7, in which a body collides with another very rigid,

bigger body, was modeled using 2 beam elements with circular cross-section to represent

the small body, and 10 beam elements to represent the larger body. Some parametricstudies were done varying the finite element mesh and time step, as well as the specific

weight of the two bodies, and the results were the same since the target body still is very

rigid in comparison to the impactor body.

The material and geometrical parameters are selected as follows:

E = 70 GPa;r = 2680 kg/m3; L1 = 10000 mm; d1 = 10000 mm, L2 = 10 mm; d2 = 10 mm.The initial height is h = 4.85 m, and from Eq 11, it is possible to compute the value ofh*.

For values of = 1.00, = 0.90, = 0.75 and = 0.50, Eq.11 gives h* = h = 4.85,h* = 3.9285, h* = 2.7281 and h* = 1.2125 respectively.

Figure 8 shows the computed response. It can be seem that the results agree with

analytical predictions. There is no dissipation for = 1.00, thus h* = h = 4.85, and forothers values of the computed h* are also equal to the analytical h*.

- 5. 0

- 4. 5

- 4. 0

- 3. 5

- 3. 0

- 2. 5

- 2. 0

- 1. 5

- 1. 0

- 0. 5

0. 0

0. 0 1. 0 2. 0 3. 0 4. 0 5. 0 6. 0 7. 0 8. 0 9. 0 10. 0

Tempo (s)

Height

(m)

e = 1. 00

e = 0. 90

e = 0. 75

e = 0. 50

Figure 8. Perpendicular beams Contact Model.

7. APPLICATION FOR OFFSHORE SYSTEMSAs mentioned previously, the proposed contact model has been incorporated into a

computer program for the coupled static and dynamic analysis of floating offshore


14/17


14

systems. Several small preliminary problems have been run to test the validity of the

algorithms as shown in section 6. A variety of actual applications for offshore systems

involving complex configurations and nonlinear boundary conditions were also analyzed,

including those presented in this section.

7.1.Collision of Drilling Risers with Mooring LinesThe drilling column of a DP unit is contained in a rigid riser, connected to a wellhead on

the sea bottom. If, as mentioned before, for some reason a DP unit operating near to a

production unit loses control of its position, it disconnects the riser from the wellhead and

may follow a trajectory that leads to the collision of the riser with a mooring line of the

production unit.

Table 1 summarizes the general data.

Table 1. General data.

Depht 345m

Mooring Radius 1000m

Initial Tension 55 t

Line Lenght 1130m

Line Sections Chain (76mm)

Wire rope (96 mm)

Chain (76 mm)

Riser Lenght 335 m

Riser Diameter 18 pol

The complete study of the collision should consider not only the assessment of the

consequences of a collision between the rigid riser of a DP unit and a mooring line of a

production unit, but also the consequences of the collision between both units, and also of

the collision of the rigid riser with the sea bottom, in situations when the DP unit derives

towards shallower waters.

The numerical simulation of such situation was performed by generating models with the

SITUA-Prosim system [1], illustrated in Figure 9. The simulation consists of leaving the

DP unit to drift under environmental loadings, with the riser hung. The environmental

condition was set intentionally to make the unit follow a trajectory that lead to the

collision of the riser column with a mooring line of the nearby production unit.

Table 2. Environmental conditions applied on the system.

Current ProfileDepth (m) Speed (m/s) Azimuth (degrees)

0.0 1.0 225

345.0 0.2 225

Regular Wave

H Tp Azimuth (degrees)

2.0 10.0 25

The finite element meshes were modeled using nonlinear frame elements, 100 elements


15/17


15

were used to model the riser and 200 elements to model the mooring line. The total

simulation time was 200 seconds, with time step 0.01 seconds.

Figure 9. Generated Model Initial Position.

Figure 10. Deformed Position.

Figure 11 shows the XY plane (horizontal plane) displacement for the DP unit and the

contact point in the drilling riser and Figure 12 shows the resultant change in bending

moment at the contact point.


16/17


16

Displacements (m)

- 140. 0

- 120. 0

- 100. 0

- 80. 0

- 60. 0

- 40. 0

- 20. 0

0. 0

- 15. 0 - 10. 0 - 5. 0 0. 0 5. 0 10. 0 15. 0 20. 0 25. 0 30. 0 35. 0 40. 0 45. 0 50. 0

Direction X

Dir

ection

Y

DP uni t

Contact Poi nt

Figure 11. Plane Displacement DP unit and contact point.

- 50. 0

- 25. 0

0. 0

25. 0

50. 0

75. 0

100. 0

125. 0

150. 0

175. 0

200. 0

0. 0 25. 0 50. 0 75. 0 100. 0 125. 0 150. 0 175. 0 200. 0 225. 0 250. 0 275. 0 300. 0 325. 0 350. 0

Riser Lenght (m)

Moment(KN

m)

Moment Y ( Gl obal )

Moment X ( Gl obal )

Figure 12. Moment in the Riser.

From Figure 11, one can see the abrupt change in trajectory of the riser after the

collision with the mooring line. At this point there is a change in bending moment, leading

to the peak shown in Figure 12.

8. FINAL REMARKSThis work presented a tool intended to improve the applicability and accuracy of

coupled analysis of offshore floating units, making the simulations more realistic. Such

tool represents, during the dynamic analysis, the contact involving different lines in the

model. The generalized contact model presented here avoids some limitations of the

computational tools traditionally used for the static and dynamic analysis of offshore

structures. Also, this tool provides the engineer with several relevant information at

preliminary design stages.

In summary, the presented contact algorithm was shown to be quite efficient and


17/17


17

robust, and comprises an important contribution to the analysis and design of offshore

systems with flexible lines such as mooring lines, risers and hoses. The resulting

numerical tool is able to provide valuable knowledge for the design of safe offshore

operations.

REFERENCES

[1] B. P. Jacob, I.Q. Masetti, PROSIM Coupled Numerical Simulation of the

Behavior Of Moored Semisubmersible Units COPPETEC-Petrobras Internal

Report, Rio de Janeiro, 1997.

[2] D. M. L. Silva, B. P. Jacob, M. V. Rodrigues,Implicit and Explicit Implementation

of the Dynamic Relaxation Method for the Definition of Initial Equilibrium

Configurations of Flexible Lines. 25st International Conference on Offshore

Mechanics and Arctic Engineering OMAE, June 4-9, Hamburg, Germany (2006).[3] D. M. L. Silva, F. N. Corra, B. P. Jacob,A Generalized Contact Model for Nonlinear

Dynamic Analysis of Floating Offshore Systems. 25st International Conference on

Offshore Mechanics and Arctic Engineering OMAE, June 4-9, Hamburg, Germany

(2006).

[4] E. Huse, G. Kleiven, F. G. Nielsen, Large Scale Testing of Deep Sea Risers, Paper

No.8701, Offshore Technology Conference, Houston, USA, (1998).

[5] A.J. Kalleklev, K.J. Mrk, N. Sdahl, M.K. Nygrd, A.M. Horn,,Design Guideline

for Riser Collision, Paper No.15383, Offshore Technology Conference, Houston,

USA, (2003).

[6] S. F. Senra, Numerical Simulation of the Collision of Drilling Risers with Mooring

Lines for Offshore Oil Exploration, M.Sc. Thesis (in Portuguese), UFRJ/COPPE,Civil Eng. Department, Rio de Janeiro, Brazil (1998).

[7] S. F. Senra, B. P. Jacob,Numerical Simulation of the Collision of Drilling Risers

with Mooring Lines in Offshore Oil Exploration. 19th International Conference on

Offshore Mechanics and Arctic Engineering OMAE, February 14-17, New Orleans,

LA (2000).

[8] S.R. Wilmshurst, H.H. Chan, C.P. Ellinas, T Moros,Deepwater Riser Systems: Riser

Local Impact. 19th International Conference on Offshore Mechanics and Arctic

Engineering OMAE, May 28-June 2, Seattle, USA (2000).

[9] S.R. Wilmshurst, H.H. Chan, C.P. Ellinas, T Moros, Local Riser Impact: The Effect

of Neoprene Coatings. 20th International Conference on Offshore Mechanics and

Arctic Engineering OMAE, June 17-22, Stavanger, Norway (2001).

[10] D. Eberly, Distance between two line segments in 3D, Geometric Tools, Inc.,

http://www.geometrictools.com (2005).

[11] I. Babuska, J. T. Oden, Verification and validation in computational engineering

and science: basic concepts, Computer methods in applied mechanics and

engineering, vol. 193, pg 4057-4066 (2004).

cilamce2007_contato

Documents