Numerical Multiple-Body Simulations of Side-by-Side ... - CiteSeerX

Proceedings of the Eleventh (2001) International Offshore and Polar Enghleering Conference Stavanger, Norway, June 17-22, 2001 Copyright © 2001 by The International Society of Offshore and Polar Engineers ISBN1-880653-51-6 (SeO; ISBN 1-880653-52-4 (VoL I); ISSN 1098-6189 (SeO

Numerical Multiple-Body Simulations of Side-by-Side Mooring to an FPSO Bas Buchner, Adri van Dijk and Jaap de Wilde Maritime Research Institute Netherlands (MARIN) Wageningen, The Netherlands

ABSTRACT

offloading option in areas with relatively calm seas, because it allows conventional LNG loading arms to be used.

A numerical time domain simulation model has been developed for the prediction of the hydrodynamic response of an LNG FPSO with an alongside moored LNG carrier. The model has been validated using the findings of dedicated basin model tests. The hydrodynamic response of two bodies in close proximity is a complex hydrodynamic interaction problem. Three influencing factors showed to play an important role on the quality of the results: the use of a free surface lid in the multiple-body diffraction analysis for accurate calculation of the drift forces; the use of accurate input data on relative viscous damping in the horizontal plane for the correct prediction of the low frequency motion response, and the use of the complete matrix of retardation functions for the correct prediction of the heave and pitch motions. -

-

-

KEYWORDS: Multiple-body simulations, diffraction analysis, FPSO, side-by-side mooring, offioading, LNG Figure 1. Impression of the Shell Floating LNG System.

INTRODUCTION Background

Technical Objectives of the Paper

Shell is developing a Floating LNG System to economically produce and process gas in remote offshore locations. The system can be used in remote oil developments, or in green field gas cases. In remote oil developments, the floating LNG system converts the problem of associated gas disposal into a moneymaking opportunity. In the green field gas case, the Floating LNG System is an economical means to develop remote offshore gas fields. The Floating LNG System (see Fig. 1) consists of a barge type LNG FPSO with accommodations, an external turret, a gas preconditioning and liquefaction plant, a number of LNG storage tanks and offioading facilities. It is positioned over the reservoir and replaces the offshore platform, the pipeline to shore, the onshore LNG plant and the jetty. When sufficient LNG is accumulated in the storage tanks, it is offioaded to a LNG carrier and shipped to the customer. Side-by-side mooring of the LNG carrier is being considered as the preferred

To determine the feasibility of the concept and to minimize the downtime of the offioading operation, the Maritime Research Institute Netherlands (MARIN) developed a numerical model for the time domain simulation of a side-by-side offioading operation. The developed model was based on an existing numerical model developed earlier for multiple body lift operations offshore (Van Oortmerssen, 1981). However, it was identified that a further extension of this model was necessary to model the side-by-side situation accurately. This mainly related to the fact that in this situation the two floating bodies are in real close proximity, resulting in a strong and complex hydrodynamic interaction. Recently Inoue and Islam (1999) and Teigen (2000) also performed interesting studies in this field, with the main focus on numerical aspects. The objective of the study was to develop and validate a numerical multiple body simulation model for the reliable prediction of relative motions and mooring loads during side-by-side offloading operations. During the study the numerical model was extended step by step,

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making use of the results of dedicated model tests. The present paper describes this development. First the paper summarizes the existing numerical model; secondly the model tests performed are described. After that the development of the improved numerical model is described: the damping model, the improvement of the drift force prediction and the use of the complete matrix of retardation functions in the time domain. Finally the results of the developed model will be presented and discussed. Although wind and current are also important for side-by-side offloading, they are outside the scope of the present paper.

displacement at t = 0 by a constant velocity v, during a short time At yields: Ax = vAt, with:

lim v = 2 At--->0

(5)

During the impulse the water velocity field related to the hydrodynamic reaction forces may be described by: qb = vgt

DESCRIPTION OF EXISTING NUMERICAL MODEL

(6)

where uj is a normalized velocity potential fulfilling the fluid boundary conditions. After the impulse the radiated disturbing wave may be described by a potential proportional to the displacements because of the assumed linearity of the system:

The response of a floating structure to waves in the frequency domain is generally described by means of a mass-spring system. Assuming a linear system in 6 degrees of freedom, such analysis represents the equations of motions as:

qb = Z(t)AX

(7)

6

~] (Mkj + akj)2j + bkjZ~j + CkjXj = Fk

k =1, 2 . . . 6

For the total impulse at an arbitrary time t, due to an arbitrary motion, it now follows that:

(1)

j=l

where: k,j =

t

subscripts of hydrodynamic property in the k-mode as a result of motion in the j mode Mkj = mass of structure akj = added mass matrix bkj = damping matrix Ckj = hydrostatic restoring matrix F k = external force in the k-th mode. Non-linearities related to moored structures, such as the non-linear force-displacement characteristics provided by a mooring system, do not allow the linear frequency domain approach, nor the direct use of Eq. (1) in the time domain. To overcome these problems, use can be made of the impulse response theory to describe the fluid reactive forces (Cummins, 1962) and (Van Oortmerssen, 1973). A brief description of this approach is given below.

q~(t) = 5 ~ + [

m

~gnds (9)

R(t)

=pll 0Z(t) n d s Sw

where n is the normal vector. By applying Newton's law to these quantities, together with the hydrostatic restoring forces and the external loads, the equations of motion for six degrees of freedom can be derived: 6

t

Z ( M k j + m k j ) X j + j" R k j ( t - ' 0 x j ( x ) d l : + C k j x j = F k ( t ) j=l -oo

(2)

where: xj = Fk(t) =

(3)

-

-

or:

-

t

x ( t ) = I F(x) R ( t - x ) d x

(4)

-

--o0

This formulation is known as the Duhamel, Faltung or convolution integral. The impulse response theory has been used by Cummins (1962) to formulate the equations of motion in the time domain for floating structures. Assuming the hydrodynamic reaction forces to be linear, according to Cummins the reaction forces due to the water velocity potential may be derived by the impulse response theory by considering the vessel's velocity as system input. An impulsive

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motion in j-direction arbitrarily in time varying extemal force in the k-mode of motion: first order wave forces low frequency drift forces wind forces non-linear viscous damping forces interaction forces between (three) rigid bodies current forces mooting line forces Mkj = inertia matrix mkj = added inertia matrix Ckj = matrix of hydrostatic restoring forces Rkj = matrix of retardation functions k,j - mode of motion. As derived above, the frequency independent coefficients of inertia and the retardation functions can be computed from the velocity potential. By substitution of a harmonic motion into the time domain equations and comparison with the frequency domain equations,

Owing to the linearity of the system, the response to an arbitrary force F(t) may be found by superposition:

lim ~ F(x) R ( t - ~ ) A~ Ax-~O

=oil Sw

When the response R(t-'0 of a linear system to a unit impulse at the time t = x is known, the response of the system due to an arbitrary impulse 5 is:

x(t) =

(8)

By integration of the linearized hydrodynamic pressure, obtained from Bernoulli's theory over the wetted surface, the hydrodynamic reaction quantities are found:

Equations of Motion in Time Domain

x(t) = 5 R ( t - "c) = F(x) A~ R ( t - x)

z ( t - ~) :~('c) dx

--o(3

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Ogilvie (1964) has derived the relationship between the time domain and frequency domain quantities:

M 11

0

0

0

M 22

0

0

0

M 33

~2

oo

akj

= m k j - - - - _[ Rkj(t)__ sin o t dt 0) o

(11)

oo

bkj

= ~ Rkj(t ) c o s c o t d t o

i

Rll( t

.1 x

~)

o

where: akj = frequency dependent bkj = frequency dependent o = circular frequency. From these relationships added inertia coefficients transformation:

t

I R22 (t o

added mass coefficient damping coefficient

t

the retardation function and the matrix of may be found by inverse Fourier-

mkj

=--2 ~ bkj(O) cos o t d o 7~0

i T

= akj(O') + ~ o'0

.2 x

~) I R33 (t o

C~

0

0

0

C2

0

0

0

C3

1

X

oo

Rkj(t)

5~3

(12)

x

X2

~)

F1 F2

(X 1. ~1. X2,~2 . . x 3 , _~3 ,t)

Rkj(~ ) sin o ' t d~

Apparently the retardation functions and the coefficients of added inertia can be derived from frequency dependent damping values and the added mass at one frequency. Once the system of coupled differential equations is obtained, arbitrary in time varying loading such as wave excited forces, current forces, non-potential fluid reactive forces and non-linear mooring forces may be incorporated as external force contributions. The solution may be approximated by numerical methods such as the finite difference technique. Knowing the displacement and its time derivatives until a certain time, the simulation may be continued with a small time step predicting the velocity from the acceleration and the known time histories by use of time series expansions. The new position may then be predicted by numerical integration of velocities.

3 X

F3

(13) Eq. 13, implemented in the numerical code, is given for 3 bodies, whereas the present problem of side-by-side offioading involves 2 bodies only. In essence there are no restrictions to the number of bodies. Summary of Calculation Procedure To perform a multiple body time domain simulation, the steps below are necessary. In essence they fill the multiple body equation of motion (Eq. 13) step by step: A multiple body diffraction analysis in the frequency domain to determine the inertia, added inertia, damping, wave force RAOs (Response Amplitude Operators) and wave drift force QTFs (Quadratic Transfer Functions). The drift forces were calculated with the direct pressure integration method (Pinkster, 1980). Preparation of the hydrostatic terms of all bodies. Calculation of the retardation functions in the time domain from the added mass and damping values in the frequency domain. Preparation of the stiffness, damping and friction effects of the mooring system. Calculation of the time traces of the wave frequency wave forces (from the wave force RAOs) and the low frequency drift forces (from the wave drift force QTFs) in a certain realization of the wave spectrum. These time traces are calculated prior to the simulation runs and read by the program during the simulation itself. Performance and analysis of the simulation in the time domain.

Multiple Body Simulations In the case of multiple bodies which are hydrodynamically and/or mechanically coupled, the approach mentioned above needs to be solved in a coupled matrix equation. In the case of a 3-body system, this system has 18 degrees of freedom. All 3 bodies can be subject to wave-induced forces, hydrodynamic reaction forces and mechanical coupling effects (either linear or non-linear), see below, with: M ''j = inertia and added inertia matrix of body i as a result of motions of body j R id - matrix of retardation functions of body i as a result of motions of body j Ci = matrix of hydrostatic restoring forces of body i xi = motion vector of body i F' = vector of external forces on body i, including wave forces and wave drift forces. The inertia and added inertia matrices and also the matrices of the retardation functions are derived from multiple body diffraction analysis in the frequency domain. Therefore matrices such as M ~'l and R 1'1 and the vector of external wave forces m F 1 are determined with the other two bodies present in the diffraction analysis. This implies that, for instance, wave shielding of one body behind another body is taken into account. The present formulation does, however, not include hydrodynamic cross coupling between the motions of the bodies: when one body moves, the other bodies do not start to move as well as a result of wave radiation.

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The model lines were made of steel wire with a linear spring. The fenders were modeled by means of a stiff rod pivoting around a fixed rotation point on the deck of the FPSO. The required horizontal stiffness of the fenders was obtained by means of a linear spring connected to a cantilever on the other end of the rotation point. A low friction roller was mounted at the free end of the rod, providing a low friction contact between the fender and the shuttle tanker. In the model the stiffness and pretensions of the mooring lines and fenders were chosen in such a way that the horizontal stiffness parameters of the actual mooring system were as accurately as possible reproduced. The stiffnesses (C) and pretensions (T) of the mooring lines and fenders in the model can be found in the Table 2.

MODEL TESTS The model tests were carried out to validate, and where necessary extend, the numerical model and to determine the important viscous damping terms that cannot be calculated with state-of-the-art calculations tools. The model tests were performed with a schematical set-up, focussing on the main issues for validation. Therefore a soft spring setup with a fixed heading in the basin was chosen instead of a real weathervaning system around the turret of the LNG FPSO. Also a simplified side-by-side mooring system was used with 2 fenders and 4 mooring lines. Finally only waves were considered, not wind and current.

Table 2 The stiffnesses (C) and pretensions (T) of the mooring lines and fenders.

Models All models were made according to Froude scaling at a scale of 1:50. A barge type LNG FPSO was used with a rectangular hull and a tapered bow. Bilge keels were not present. A typical 130,000 m 3 LNG shuttle tanker was used in the tests. The main dimensions of the two vessels are given in Table 1.

Mooring lines in model ,,

Designation L1 L2 L3 L4

Table 1 Main dimensions of LNG FPSO and LNG shuttle carrier. LNG shuttle tanker

LNG FPSO Length between perpendiculars (Lpp) Beam (B) Draft (t) Displacement

[m]

332.0

[m] [m] [t]

C [kN/m]

Aft breast line Aft spring line Fore spring Line Fore breast Line

919 1000 1000 919

401 306 306 401

T [kN] 919 919

C [kN/m] 1839 1839

,.

Fenders in model Designation

274.0

70.0 14.42 331,693

Type

T [kN]

F1 F2

44.2 11.0 99,548

Type Aft fender Fore fender

Considering a pretension of 919 kN on each fender and a fender stiffness of 1839 kN/m, a fender compression of approximately 0.5 m can be calculated. This results in an initial clearance between the two ships of approximately 4.5 - 0.5 = 4.0 m. In the initial position the shuttle midship was shifted 15 m backwards with respect to the FPSO midship.

The schematized mooring system consisted of 2 lateral breasting lines, 2 longitudinal spring lines and 2 fenders in the waterline. The layout of the mooring system in the model is presented in Fig. 2.

Coupled and Uncoupled Test Set-Up FPSQ .

.

.

.

.

FPSO

] .~

.

.

.

Both a coupled and an uncoupled situation of the side-by-side offioading configuration have been tested (see Fig. 2). In the coupled situation all relevant hydrodynamical and mechanical interactions were taken into account. In the uncoupled situation only the hydrodynamical coupling was present. All tests were carried out with the LNG FPSO in a soft mooring system. The 2 x 2 soft spring mooring lines of 400 m length were located between the bow and the stem of the FPSO and fixed poles at 45 degrees angle in the basin. Horizontal linear springs of 1,275 kN/m and 10,055 kN pretension were used. In this way the heading of the vessel was fixed in the basin, expect for the low frequency yaw motions allowed by the soft mooring system. In the uncoupled tests the shuttle tanker was kept in its own soft mooring system. The 325 m mooring lines were connected to the bow and the stem and were placed in-line with the longitudinal axis of the ship. The spring stiffness and pretension were the same as for the FPSO soft mooring.

.

i I

s~~

L

~~'f.

.........

"

Wave Conditions

Figure 2. Test set-up and layout of the mooring system in the tests. (coupled set-up above and uncoupled set-up below)

The tests were carried out in a water depth of 50.0 m in different irregular sea and swell conditions. In the present paper the test results in a high sea of Hs=3.0m and Tp=7s (JONSWAP spectral shape, y=0.93) are considered.

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This resulted in the following additional damping terms in the coupled equation of motions for the shuttle tanker:

Sign Conventions The motions are positive in the following directions: positive positive positive positive positive positive

surge sway heave roll pitch yaw

(x) (y) (z) (q~) (0) (~)

: : : : : :

.__yl-By-b(y1 - __y2).Bry

towards the bow towards port side upwards starboard side down bow down bow towards port side

(14)

~_~_..B,+(li/1 ~t -k~/2)-Br~g Results with the Existing Model

The environmental headings are defined as follows: 0.degrees heading 90.degrees heading 180.degrees heading 270.degrees heading

: : : :

Using the new damping tests and simulations with conditions (180 degrees) in summarizes the results. Time

stem on starboard side on bow on port side on

Table 4 Comparison of standard deviations of the most important signals from the tests and the existing numerical model.

DEVELOPMENT OF IMPROVED MODEL Damping Model

Relative motion x at midships Relative motion y at midships z shuttle at center of gravity Roll shuttle Pitch shuttle Yaw shuttle Mooring line 3 (spring line) Mooring line 4 (breasting line)

Sway motion

(y) Yaw motion

(v)

By-- 1236

[kNs/m]

By= 1.18,106 [kNms]

[m] [m]

0.17

0.32

0.22

0.90

0.07

0.20

0.15 0.09 0.11

0.19 0.13 0.25

[m] [deg] [deg] [deg] [kN]

54

100

[kN]

159

469

The following can be observed from this comparison: Even in a head wave condition, the transverse motions (sway, yaw) are significant in both the model tests as well as calculations. This is a result of the waves that run in the area between the shuttle bow and the FPSO: they reflect on the side of the shuttle bow and result in strong oscillating relative wave motions. The wave drift forces are strongly coupled to these relative wave motions, see for instance Pinkster (1980). The resulting drift forces in the yaw and sway direction result in low frequency motions of the FPSO and shuttle at the natural periods of the side-by-side mooring system. This effect is observed in both the model tests as well as in the calculations. However, it can also be observed from Table 4 and Fig. 3 that these relative motions and resulting mooting line loads are significantly overpredicted by the existing numerical model (relative y motion of 0.89m instead of 0.22 m measured). Also the wave frequency dominated heave (z) motion and pitch motions seem to be overpredicted significantly. This lead to the conclusion that the existing model is not able to predict the low frequency motions and the wave frequency motions accurately enough. Based on this conclusion it was decided to investigate the background of the differences and improve the numerical model step by step.

Table 3 Derived linear damping coefficients for the (relative) sway and yaw motions. Damping coefficient shuttle with fixed FPSO 3003 [kNs/m] 1.89,107 [kNms]

Standard deviation With existing In model tests numerical model

Signal

One of the most important issues in the study of the motions of moored vessels, is the viscous damping of the low frequency motions due to the low frequency viscous reaction forces. For a single moored vessel, this problem has been studied in detail by Wichers (1987). This resulted in a complex model for the viscous damping in both still water and in current, making use of oscillation tests of tanker models in the horizontal plane. For the present study the situation is even more complex, because of the interaction between the two bodies. With relative sway and yaw motions between the LNG FPSO and the shuttle, the water in the small area between the two vessels is oscillating in and out at the bottom and at the sides. This results in large water velocities around the sharp bilges of the FPSO and along the bilge keels of the shuttle. The resulting vortex shedding results in an important viscous damping contribution. For the present problem no oscillation tests have been performed yet, but decay tests in the horizontal plane (sway and yaw) have been carried out for the following situations: a. Shuttle alone b. Shuttle alone, with fixed FPSO present. Based on these tests linear damping coefficients have been determined and are summarized in Table 3 below.

Damping coefficient shuttle alone

terms a comparison was made between the existing model for the head wave the high sea (Hs=3.0m). Table 4 below traces of these signals are given in Fig. 3.

Derived relative damping coefficient Bry = 1767 [kNs/m] Brv = 0.71,107 [kNms]

By subtracting the damping of the shuttle alone (By, By) from the damping of the shuttle next to the fixed FPSO, the relative damping coefficient was estimated (Bry, Brv).

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Improvement of Drift Force Prediction with Free Surface Lid

Multiple-Body Simulations of Side-by-Side M o o t i n g to an FPSO High (180 deg) - C O M P U T A T I O N S WITH EXISTING NUMERICAL MODEL

Sea

To investigate the overpredicted low frequency sway and yaw motions, the drift force quadratic transfer functions (QTFs) of the mean surge, sway and yaw mode in head waves were studied: the QTFs give the mean wave drift force or moment in regular waves per meter wave amplitude squared (kN/~ 2 or kNm/~2). The drift forces were calculated with the direct pressure integration method (Pinkster, 1980). They are shown in Fig. 4.

T E S T NO. 9020031

U~ -~f~'iM,'\,;~,~;'\~'#

x=~,=,,o =°~i,,_~,,' ~'~v~vWJw;~