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Marine Systems & Ocean Technology
Journal of SOBENA
www.sobena.org.br/ms&ot
Adress: Av. Presidente Vargas, 542 - Grupo 709 a 713 - Centro - Rio de Janeiro - RJ - Brasil - CEP 20071-000
Telephones: [+55](21) 2283-2482 - Telefax: [+55] (21) 2263-9079 - E-mail: [email protected] - Site: www.sobena.org.br
List of Editors
Celso Pupo Pesce
Universidade de São Paulo, Brazil (Chief-Editor)
[email protected]
Clóvis de Arruda Martins
Universidade de São Paulo, Brazil
[email protected]
Marcelo de Almeida Santos Neves
Universidade Federal do Rio de Janeiro, Brazil (Chief-Editor)
[email protected]
Júlio Romano Meneghini
[email protected]
José Augusto Penteado Aranha
[email protected]
Torgeir Moan
Norwegian University of Science and Technology, Norway
[email protected]
Michael M. Bernitsas
University of Michigan, USA
[email protected]
Helio Mitio Morishita
[email protected]
Belmiro Mendes de Castro Filho
[email protected]
Celso Kazuyuki Morooka
Universidade de Campinas, Brazil
[email protected]
Günther Clauss
Technical University of Berlin, Germany
[email protected]
Kazuo Nishimoto
[email protected]
Paulo de Tarso Temístocles Esperança
Universidade Federal do Rio de Janeiro, Brazil
[email protected]
Apostolos Papanikolaou
National Technical University of Athens, Greece
[email protected]
Segen Farid Estefen
[email protected]
Floriano Carlos Martins Pires Jr
[email protected]
Odd Faltinsen
Norwegian University of Science and Technology, Norway
[email protected]
Claudio Ruggieri
[email protected]
Jeffrey M. Falzarano
Texas A&M University, USA
[email protected]
Claudio Mueller Prado Sampaio
[email protected]
Antonio Carlos Fernandes
[email protected]
Turgut Sarpkaya
Naval Postgraduate School, USA
[email protected]
José Alfredo Ferrari Jr
Petrobras, Brazil
[email protected]
Sergio Hamilton Sphaier
[email protected]
Carlos Guedes Soares
Universidade Técnica de Lisboa, Portugal
[email protected]
Célio Taniguchi
[email protected]
Liu Hsu
[email protected]
Atilla Incecik
Universities of Glasgow & Strathclyde, UK
[email protected]
Breno Pinheiro Jacob
[email protected]
Jan Otto de Kat
A. P. Moeller-Maersk, Denmark
[email protected]
Carlos Antonio Levi da Conceição
[email protected]
Armin Walter Troesch
University of Michigan, USA
[email protected]
José Márcio do Amaral Vasconcellos
[email protected]
Dracos Vassalos
University of Strathclyde, United Kingdon
[email protected]
Murilo Augusto Vaz
[email protected]
Ronald W. Yeung
University of California at Berkeley, USA
[email protected]
Volume 5
Number 1
December 2009 / June 2010
Chief-Editors
Marcelo de Almeida Santos Neves
Universidade Federal do Rio de Janeiro
Celso Pupo Pesce
Universidade de São Paulo
JOURNAL OF
SOBENA
Sociedade Brasileira de Engenharia Naval
Aims and Scope
The design process of marine systems is one of formulation, evaluation and modification. Very often the problems confronting the
designer are effectively complex problems, particularly on the technical side. Analytical models have to be invoked and applied together
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In the past these difficulties have been more concentrated on few particular types of marine vehicles and systems. In particular,
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Some excellent periodicals are dedicated to the coverage of researches and developments in this sector.
More recent technological developments, particularly in the offshore industry, have challenged this knowledge, introducing many,
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Marine Systems & Ocean Technology is an editorial initiative jointly coordinated by SOBENA and CEENO. SOBENA is an
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Systemic modeling and logistic planning in the petroleum supply chain
Rui Carlos Botter1 and Ricardo Terumichi Ono1
1
Department of Naval and Ocean Engineering of Polytechnic School of the University of São Paulo Av. Prof. Mello Moraes,
2231, São Paulo, SP, Brasil, Emails: [email protected], [email protected]
Abstract
The study of the petroleum supply chain involves several subsystems that interact among themselves in the exploration processes,
transportation to the terminals, storage in tanks and transference to the refineries. In this context, this paper aims to study the
characteristics of the main subsystems that compose the upstream segment, which ranges from petroleum production in the
platforms to the shipment to oil refineries, with special attention to the transportation subsystem. The adopted methodology
compatibilizes decisions based on distinct levels of hierarchical planning, initially attempting to identify the main resources
dimensioning on a strategic basis and afterwards, programming them on a tactic/operational level. Computational models were
developed using ARENA software, version 5.0. CPLEX, version 10.0, was used to develop simulation and optimization models. The
optimization model was adopted to rectify or improve the result presented by the simulation model, completing the decisionsupporting tool that enables to analyze each scenario and compose the project of the petroleum supply chain.
Keywords
Offshore logistics; Downstream Distribution; Simulation and Optimization
1
Introduction
The study of the petroleum supply chain involves a series of subsystems that interact among themselves in the processes of
exploration, petroleum transference to the terminals, storage in tanks and transference to the refineries to finally initiate the
refining and production processes of petroleum derivates. Such subsystems must be studied in detail so that it is possible to elucidate
the main characteristics governing each process, attempting to identify ideal, optimum conditions, and mainly the interferences
that occur inside and among each one of them.
The petroleum exploration and production has been a focus of major relevance in the area of energy, since the country aims more
and more to augment its productive capacity pursuing a condition of self-sustainability. In this context, the development policy that
has been adopted in the sector, for two decades, has gradually attempted to deregulate the sector through opening the market,
spurring the entrance of new conglomerates in order to break the monopoly of the sector, whose immediate consequence is the
increase of foreign investments.
In this context, the present article aims to examine in detail the characteristics of the main subsystems that compose the petroleum
supply chain, which ranges from the production of the platforms in the Campos Basin to the shipment of the petroleum to the oil
refineries through ducts.
The aggregation value chain of petroleum needs to be constantly monitored and reviewed because it is the key of the success of the
whole process. In order to have this control, there must be decisions support systems (DSSs) able to provide information so that the
decision is made correctly. The decision variables that influence in this macro process may be summarized in: what products and in
which quantities they will be made or purchased; sold or stored, transferred or consumed; finally, when and how all this must occur.
The combination of these decision variables is what will provide enough subsides for a good follow-up and management of the
petroleum chain. Thus, a system able to acquire information, integrate data adequately and evaluate the capacities of the resources
must be a great triumph for this field of study.
Submitted to MS&OT on Nov 23 2009. Revised manuscript received Jun 02 2010. Editor: Celso P. Pesce.
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Vol. 5 No. 1 pp. 5-22 December 2009/June 2010
Systemic modeling and logistic panning in the petroleum supply chain
Rui Carlos Botter and Ricar
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The problem to be studied consists of the petroleum supply
chain, the upstream segment, delimited by the subsystem of
petroleum exploration and production in the platforms, the
petroleum discharge by a shipping fleet, its reception by the
terminals located on the coast and the oil pumping to refineries.
The system of storage in the refineries is not part of the scope
studied. Figure 1 illustrates the scope of the problem
approached.
Fig. 1
chain that will contemplate the scenario to be
evaluated. The main and most usual criterion in the
production process is to avoid operational losses in
the platforms, i.e. make sure the platforms produce
petroleum continuously, non-stop. Such premise is
adopted in the study's development.
Problem description
c.
Terminals: Located on the coast, they represent the
discharge points of the petroleum extracted in the
maritime units. Each terminal possesses enough service
infrastructure to receive the vessels and pump to
refineries. There are restrictions concerning the
number and extension of berths, which limits the
class of the vessel. Storage tanks are interconnected
through ducts for the discharge of the ships, whose
discharge fee is determined and constant. The tanks
are dedicated by type of petroleum, i.e. there must not
be mixtures in order not to interfere with the physicchemical characteristics of petroleum. The tanks'
release is done through pumping directly to the
refineries, conducted as "sequences of hits" defined by
the kind of petroleum, the time interval of pumping
and the corresponding outflow. Analogous to the
criterion established for the platforms, the
unavailability of petroleum in batch condition results
in operational loss and necessity of interrupting the
pumping, having to be avoided in any level of
planning.
d.
Refineries: Located near the terminals and
interconnected to these by land ducts. They represent
the industrial plants for processing the oil received by
the terminals. The scope of the present paper is limited
to the pumping process of the oil to the refinery. The
storage systems of petroleum in the refineries are not
treated here. The subjects of pumping by the terminals
are considered as demand of the refineries.
e.
Meteorological conditions: Environmental factor that
restricts the continuity of the operations of receiving
ships in the platforms and terminals. Especially in the
platforms, the meteorological conditions impede or
retard the procedure of berthing and connecting the
relief oversleeves of the ship. This way, platforms and
terminals are subject, in different degrees, to reception
restrictions, which will be considered in the study.
f.
Vehicles: The main link of the supply chain is attributed
to the ships, which perform the task of discharging the
petroleum between platforms and terminals. The ships
that conduct this operation are classified according to
physical characteristics, among which are: dimensions,
capacity of the holds, speed and daily costs. The details
of the characteristics and their functions are treated
in BORGES (2000). The central focus of the present
article covers the dimensioning and further
programming of the ships fleet necessary for serving
the conditions of demand determined by the platforms
and terminals. The goal is to plan the ships' trips as
adequately as possible, aiming for the best fleet use in
Scope of the problem
The approach adopted for the problem may be divided in
three aspects: environment and infrastructure, vehicles, and
operation and control:
a.
Environment and infrastructure: Consists of the
specification of the main resources involved in this
scope and the operational conditionants to which the
activities are submitted.
b.
Maritime units (platforms): Located in deep water,
they work on the exploration, production and storage
of petroleum. Maritime units may or may not possess
storage tanks. Units that maintain low production are
connected through maritime ducts to the nearest
platform for storage of its production, or the release is
done only at the vessel reception. The platform
produces a single type of petroleum, determined by
soil characteristics and the depth at which it is located.
The decision of production initially goes through
detailed evaluations of risk and economic-operational
viability, when studies are raised on seismic conditions,
physic-chemical characteristics of the petroleum reserves, production and discharge potentialities. Such
decision still contemplates the volume to be produced
during the planning horizon, considering accelerating
or retarding the production, through the increase or
decrease of wells to be drilled. The activities inherent
to the decision of drilling and exploration are not
contemplated in this study. Further decisions, as
definition of the volumes to be produced by each
platform, selection of the applicant platforms, under
the criterion of logistic discharge are objects of this
study; i.e. from a previously studied or existing
configuration, it will be possible to study the supply
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petroleum discharge. The trips of the ships are not
restricted to trips between platforms and terminals;
there may also be trips between platforms and between
terminals. That is, there could be conditions in which
the trips are designated to carry out multiple cargos
between terminals, with the possibility of carrying even
distinct kinds of petroleum. Similarly, there may be
trips between terminals for fractionated deliveries or
of distinct kinds of petroleum. With a pre-determined
configuration of a ships fleet, there are innumerable
possibilities of load allocation and trips for meeting
the established demand. Thus, the study intends to
explore a group of viable solutions for adequate
planning of dimensioning and programming the ships.
g.
Operation and control: The operations that involve
petroleum discharge and that will be explored in the
present work consist in the activities of production
and storage of petroleum and ships programming. The
discharge of petroleum is done primarily aiming to
minimize the incidence of losses, which may occur in
terminals and platforms: the first, when the petroleum
is unavailable for pumping and the second, due to the
excess of petroleum produced and unavailability of its
storage. In order to avoid such situations, it is necessary
to maintain an adequate configuration when
dimensioning the resources involved: platforms,
terminals and ships fleet so that the tanks' levels remain
within the acceptable and safe upper and lower limits.
The safety levels in the tanks are defined by the
denomination "TOP", which delimits the maximum
adverse condition of safe operation. It consists in the
levels close to the tanks' capacity in the platform and
the levels close to the minimum of the tanks in the
terminals. Regarding the ships operation and control,
the focus of the problem lies in their programming,
which aims to look for the trips routes at the lowest
cost, maintaining the tanks' levels under safe
conditions.
Concerning the evaluation in strategic level:
•
Analysis of Capacity of Resources - evaluate the necessity
of fleet increase, land and submarine ducts, maritime
terminal and others from the projection of production
growth in the following years, i.e. of the forecast and
ongoing development projects;
•
Analysis of the Impact of Policies / Operational
Procedures - policies may be evaluated as, for example,
test the policy of zero tolerance regarding the
environment in the required size of the fleet, test the
maintenance of a minimum stock of petroleum higher
in the refineries evaluating the level of service obtained
by the logistic system, verify the change of petroleum
mixture allocated to the refineries focusing on the
unfoldings in the performance of the logistic system,
among others;
•
Propose and Test Limiting Parameters or Benchmarking
- for the various standard-operations of the stages of
supply, determine the parameters of productivity under
certain conditions, such as tying/untying ships to the
monobuoys, FSO and FPSO, according to weather and
sea conditions.
Concerning the evaluation in tactic/operational level:
•
Optimum Programming of the Fleet - enable shortterm logistic planning, through the identification of
the ideal configuration to serve the proposed demands,
establishing the characteristics of the trips to be executed
by the fleet aiming the operationalization of the
solution.
The schematic figure 2 illustrates the attributions of the two
levels of planning and the respective objectives.
Therefore, the petroleum supply chain, which is the
focus of the present paper, covers the operations
involved in the discharge of petroleum, from the
platforms to the pumping to refineries, excluding the
system of storage in refineries.
Fig. 2
3
Objectives
In this context, the objective of this work is to present a
developing methodologically and systematically tools for
integrated logistic planning of the upstream activities that
involve the supply chain, aiming to establish the project of the
supply chain, composed of planning and programming.
From this general view of the processes involved in the
petroleum supply to the refineries, it is possible to highlight
the following objectives:
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Objectives
The set of models developed will result in a tool for planning
and analysis, whose users could be the sectors of strategic,
tactic and even operational planning of the company that
detains the controls of the main assets involved and the mature
fields. The article is intended to bring valuable contribution
for the regulating agency (ANP) as well in order to offer a tool
of control and analysis of the productivity in any of the processes inserted in the chain and mainly for future planning
and establishment of new production and oil discharge goals.
Table 1 shows succinctly the characteristics and attributions
of each model.
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Table 1 Attribution of Techniques
4
Methods for system solution
The resolution of a problem adopting the methodology of
systemic approach requires a differentiated and specific
approach for each of the subsystems considered. Such individual considerations of the subsystems naturally enable to explore in detail the processes that sustain them, initially
permitting to raise all of the possible restrictions that affect
the problem, without worrying about the relevance in the
global system.
The individual analysis of each subsystem may and will usually
prompt errors or inconsistencies because in many cases the
delimitation of the boundaries of the region of control of the
system is not clearly defined.
In this context, the methodology of simulation allows a discreet
approach of the events through individual modeling of the
subsystems and further integration according to the viability
of the data and the responses required for utilization in the
optimization modules.
The mathematical modeling adopted for the resolution of the
present problem may be divided in two major stages, according
to the criterion of the modeling technique: the probabilistic
simulation and the linear programming. As described in the
chapter regarding the methodology, the first stage of the thesis
consists in the development of a computational model of
simulation whose main objective is to understand the
interferences among the subsystems and to identify the
bottlenecks through scenario analyses from a set of preestablished data.
From the simulation model, it will also be possible to evaluate
how relevant each of the entry parameters is and the impacts
in modifying them. For example, to know what would be the
impact in the chain of an increase in demand of a certain type
of petroleum in a certain refinery, and in parallel, which
subsystems, new bottlenecks, new restrictions would be
affected. Besides that, it will be possible to evaluate such
occurrences quantitatively.
Afterwards, from the analyses of the parameters, we will be
able to define clearly the variables of decision that will compose
the optimizing model.
4.1
4.2
The conceptual model
The simulation model developed is composed of approximately
fourteen routines or logics of decision, each one with its
respective function, which as a whole presents a global model
of the petroleum supply chain in Campos Basin. The fourteen
routines may be subdivided in two big categories, as follows:
•
Routines inherent to data preparation, updating and
attribution of external conditions to which the entities
will be exposed: initial data reading and recording,
meteorological conditions, determination of
operational hours (day/night) and results printing.
•
Routines of the processes that compose the supply chain:
ships reception, processes of petroleum production in
the platforms, transport, ships reception and petroleum
pumping to the refineries.
This technique presents the following advantages:
• Systemic analysis (considers all the interrelations of
several subsystems and components of the logistic
system);
The Simulation Model
The modeling using the technique of probabilistic simulation
proved to be the most adequate due to the characteristics of
the problem and the objectives proposed. According to (PIDD,
1989), among the main forms of modeling, the simulation
must be applied in the cases when the system to be studied
presents a dynamic, interactive approach, subject to the
variation of the conditions in weather. According to the author,
when there is not an explicit linearity of the processes of the
system, the activities can occur simultaneously and interfere
with each other. This linearity is complex in terms of the
problem's dimension, with a vast load of information, rules
and specific procedures that must be modeled. In the
simulation model, the size of the model and the number of
variables is entered differently from the heuristic and linear
programming models. In other terms, the date associated to a
variable or parameter may be vectorial and stored in alternative
forms as, for example, through attributes, variables and/or
simple or compound expressions. According to (Nersesian;
Swartz, 1996), the model developed may be called combined,
for the fact that it makes use of expressions to define some
variables of the process. Thus, in the simulation model, we
define the term entity, which corresponds to the object or
being that will receive instructions and attributions in the
modeled logic of the system. The entity may "carry"
information that is used throughout the decisions that compose
the logic of the model. The methodology to be adopted in the
development of the current stage will follow renowned the
methodology of (Pedgen et al,1995), which comprises the stages
of problem definition, project planning, system definition,
design of conceptual model, preliminary project, data analysis,
model translation, verification and validation, final project,
experimentations, results analysis and interpretation,
implementation and documentation.
• Evaluates every and any modification that may
possibly be made to the system;
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• Identifies bottlenecks in the processes and among
subsystems;
• Incorporates dynamic characteristics and randomness
of the processes.
Figure 3 illustrates the scenario of animation of the simulation
model developed.
Fig. 4
Cost distribution of the ships
Fig. 5
Tanks' behavior in the platform and the terminal
Fig. 3 Model animation
4.3
Results to be evaluated
The immediate and possible results to be verified at the end of
the execution of the model regard the dimensioning of the
ships fleet and the capacities and subdivisions of the storage
tanks in the platforms and land terminals. We were able to
verify that the bottlenecks found here are dynamic and often
multiple, i.e. the interrelation among the subsystems makes
the bottlenecks come up in distinct places many times identified
indirectly through some anomaly or inconformity in a further
subsystem. For example, when a result presents a large amount
of losses in a certain platform, it may be suggested that the loss
is caused by the lack of vessels to release the petroleum.
Nevertheless, the scenario might have an overdimensioned fleet
as well. Which would be the bottleneck of the system and how
is it possible to reduce or stop such losses? In this case, one of
the possibilities is that the excess of vessels would be provoking
a long waiting line in the loading points of the platforms and/
or unloading at the land terminals, which by themselves, may
be obstructing the reception of a ship with a certain type of
petroleum. Similarly, the inexistence of a certain type of
petroleum in the terminal automatically impedes conducting
the pumping sequence, causing a second global loss in the
pumping of the other kinds of petroleum.
The stage of model validation consisted of analyses of sensitivity
of the main dimensioning parameters of the resources. The
results of the scenarios were analyzed, with gradual modifications
of increase or decrease of: tanks' capacity in the platforms,
afterward in the terminals, rate of pumping to the refineries,
fleet size and features, among others. The simulation model
allows, thus, to evaluate new reception policies, test alternative
scenarios and evaluate the impact that this alteration provokes
in the whole system. The figure 6 below shows an example of
dimensioning analysis of the terminals' tanks, through the
productivity indicator.
A second very usual situation identified throughout the study is
the great difficulty to ideally dimension the tanking capacity of
the land terminals. It was verified that a simple increase of
capacity in the tank that stores a certain kind of petroleum in
an "A" terminal increases the space availability, and
consequently, in permanent regime, this terminal obtains a
priority of reception over the other terminals. Therefore, this
reflects directly in the dimensioning of the fleet and mainly in
the necessity to restructure the pumping policy of the other
terminals.
Figures 4 and 5 present the graphs of tank level in a platform,
the tank levels in the terminals and the cost distribution of the
ships.
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Fig. 6
Productivity
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4.4
Considerations on the simulation
model
The original proposal of the present work, in summary, is to
study and analyze the petroleum supply chain, making possible
to evaluate and adequately dimension the resources involved
in various subsystems, enable the evaluation of policies and
operational procedures and finally attempt to establish the
limiting parameters in a creative and effective way.
The simulation model developed meets integrally the
requirements proposed, taking into account the range of
modeled subsystems and the versatility that the simulation
technique offers. It also performs the task of adequate
dimensioning for each operation condition and presents the
problem limiting and conditioning. On the other hand, the
policies for the model may be tested through the modification
of parameters.
However, the simulation technique, as intrinsic characteristic,
does not aim to look for a good solution or an effective strategy
in supply chain management. Building a simulation model
necessarily implies in the adoption of certain rules or premises
which are considered beforehand and in the fact that in certain
situations, the decisions made cause distortions that may
disregard alternatives of more plausible and realistic solutions.
The development of a simulation model includes the adoption
of a technique to build events that serve an entity. This model
has in its composition a set of events that define the way the
entity will follow. Naturally, there is a wide range of possibilities
and functionalities that may be attributed throughout this
"way", which will allow its construction in an unlimited form.
Nonetheless, the process of construction of the "way" itself
prompts strict and defined rules to be attributed to the entities,
without the possibility of changes initially unforeseen.
An example of this conditionant is the fact that the entity
that covers a certain stretch of the simulation model carries
along the main attributes, but does not carry "in its memory"
the variables which changed or will change it throughout the
stretch. The immediate and direct consequence is that the
decisions made along the entity took into account only just
factors associated to the events modeled in that stretch or in a
more complex model, the main value of global variables. Hardly
ever will the simulation model make a decision based on all
variables involved.
Therefore, the details of the operations and the range of the
systemic approach attained by the simulation model are valid
and extremely powerful when the focus is the validation of
certain policies and operational conditions and, especially,
when they aim comprehension, localization and quantification
of the impacts generated by the variables that form the supply
chain. For the objectives initially proposed to be integrally
reached effectively and satisfactorily, it is necessary to
complement the study with a new approach for the problem,
one that guarantees the correct dimensioning of the system.
Facing the exposed problem, it is imperative for the simulation
model to integrate into an optimizing approach, especially for
the main subsystems that form the petroleum supply chain.
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The optimization model
This stage consists of developing the optimizing model, whose
main objective is to attempt to find subsidies in the formulation
of the project of the petroleum supply chain together with the
simulation model. The latter proved that the modeled system
presents high complexity in the interrelation among the
subsystems, concerning the adopted parameters and, therefore,
must be analyzed under a global approach, intended by the
optimizing model.
In the simulation model, the sensitivity analysis consisted of
studying how relevant are the main parameters of the model;
nevertheless, the results represent solely a specific case of the
analyzed scenario. The optimizing model proposed must
establish the project of the petroleum supply chain and pursue
results that will provide subsidies to plan this chain. The model
will be tactic and, thus, the answers must define the best
configuration of the main resources of the system within the
established restrictions.
This way, the optimizing model aims, as a result, for adequate
conditions to achieve the established goal. Adequate conditions
are defined as the configuration of the logistic system of the
chain in terms of quantities of productive resources and forms
of transference of the produced petroleum to the refineries.
The flows and optimal conditions of storage may guide the
search for the optimum solution.
The simulation model proved that the level of service associated
to the modeled system is preponderantly related to the offer
of resources, i.e. the availability of an adequate ships fleet, in
terms of quantity and capacity as well as the fundamental
correct dimensioning of the storage tanks in the platforms,
terminals and refineries.
The sensitivity analyses showed that such resources define a
rational discharge without losses in all subsystems. However,
correct dimensioning is associated to the adequate
configuration of resources and their respective employments,
the combination of the fleet characteristics, their allocation
and the levels of each of their tanks. It is necessary to highlight
the differences and similarities of the modeling proposed to
AL-KHAYYAL, of (Hwang, 2007), briefly cited in the chapter
regarding bibliographical revision. The referred article presents
the programming modeling of a bulk carriers fleet that do the
oil discharge in the region of the Pacific. The modeling regards
a single type of binary variable for the arches existing between
the loading and unloading points, i.e. it does not consider the
possibility of making trips between loading points and between
unloading points. The consideration of the load also differs
because it enables the occupation of the ships by different
kinds of products, simultaneously, cramped by the individual
holds of the vessels. The attributions of knot berthing were
the same used in the modeling proposed; however, the
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consideration of demand by quantity of berths is distinct. In
the article, the demands are determined by minimum and
maximum limits of the storage tanks, directly. Such
consideration implies in the manipulation of initial data so
that the model does not result in basic null solution. The
introduction of a time window is an unprecedented approach
in the modeling proposed and not considered by ALKHAYYAL. Procedures of linearization of the restrictions that
bond the arches are similar.
costs related to the ships' trips to be made.
5.1
The model in mixed linear programming to be presented
involves a model of routes programming (scheduling) of the
petroleum platforms reception service. It is, in fact, a model
with multiple origins and multiple destinations, served by a
heterogeneous fleet (ships of different capacities) for discharge
of a single type of petroleum, in a horizon of finite time
(parameter).
Description of the optimization
model
The mathematical model in linear programming, here
proposed, consists in programming a ships fleet dedicated to
the operation of petroleum discharge produced by the
platforms, to be transported to the terminals on the coast, for
further pumping to the refineries.
The set of production platforms that compose the scenario of
the analyzed system will produce a single type of petroleum
controlled by daily and constant individual production rate.
In the other edge of this chain, there are terminals that receive
petroleum through the ships and pump them to the refineries,
also under a daily and constant individual rate.
The routines to be followed by the ships and load allocations
(volumes to be loaded and unloaded) are the main variables of
decision and the ones which will determine the best fleet
programming. It is a set of multiple origins and multiple
destinations because both the set of platforms and the set of
terminals represent points of load and unload (origins and
destinations).
The decisions inherent to routinization of the ships are
conditioned to the maintenance of the levels in the tanks of
platforms and terminals, whose lower and upper limits are
pre-determined.
The model must find the optimum programming solution
during the period necessary to accomplish the pre-determined
berths, i.e. the demand of reception at the platforms and
terminals will be modeled according to the number of berths
that must occur with the minimum lot of load/unload during
the planning horizon. As the volumes of load/unload may be
bigger than the minimum, the finishing instants of the trips
will necessarily occur after the instant of the planning horizon.
That is, the extension of the period is associated with load
allocation to accomplish the pre-determined berths.
The number of necessary berths will be calculated according
to the rates (production for platform and pumping for
terminals), the initial stocks, the tanks' limiting (upper for
platforms and lower for terminals), the minimum lot of load/
unload and the planning horizon. The calculation consists in
determining the minimum number of berths that must occur
in each platform and terminal, adopting the premise of
minimum lot so that the levels of the stocks remain satisfactory.
The function objective of the model must be the reduction of
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The decision variables will comprise the flows between each
platform and each terminal, by type of ship, as well as the
associated time, the volumes of loaded and unloaded petroleum
in each place and the tanks' levels in the terminals and
platforms.
5.2
The conceptual model
The production platforms possess tanks that store petroleum.
Its extraction or production tends to occur following a constant
production rate and are adopted as parameters of the model.
Terminals have similar characteristics: they possess their own
tanks and the consumption, regarding the pumping to
refineries, is simplified through a consumption rate, also
constant and chosen as parameter of the model. Each tank, in
platforms or terminals, is characterized by parameters for their
capacities (upper limit) and lower limits. The programming
and allocation of the ships' routes are done through attributions
of binary variables, chosen according to the function objective
of reducing operational costs. Routes designation is composed
of a set of arches that enables origins and destinations in
platforms and terminals, also enabling ships to make trips
between terminals and between platforms.
The dimension of time in the model is regarded through
enumerating possible berthing sequences in the horizon of
pre-established time: for each berthing point (terminal or
platform) and ship, there will be the attribution of a sequential
value that corresponds to the order of berthing (m or n). Such
order dissociates the time spent in loading and unloading
operations during the ship's berthing. This approach dismisses
time discretization and, consequently provokes a reduction
in the quantity of variables of the model. The chronological
order is guaranteed through restrictions of time windows due
to the growing sequences of berthing. Time windows are
dynamic and calculated from the quantity loaded in the
platforms and unloaded in the terminals. The trip time of
each ship are considered as parameters of the model.
The allocations to the routes are done through binary variables,
which correspond to arches between the origin terminal and
destination terminal, or the origin platform and destination
platform, each one following the berthing sequences of each
terminal (m) and platform (n), conducted by ship v. The main
restrictions aim to compatibilize the existence of the arch
with the operations of loading/unloading, the possible
allocations according to the availability in ships' holds and
storage tanks, the time windows and the restrictions of
minimum and maximum level of tanking in terminals and
platforms.
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of time (last instant) is calculated, i.e. the maximum instant
at which the berthing must occur so that the tank level remains
within the limits established. In further berthings, the
maximum instants are calculated according to the lot loaded/
unloaded in the previous berthing and the tank's conditions
in the previous berthing.
Fig. 7
Example of viable configuration
The decision of ship allocation to the loading or unloading
point presupposes the existence of storage tanks of the type of
petroleum to be loaded or unloaded. Besides the necessity of
this compatibility of type of petroleum to be loaded/unloaded
by the ship and the existence of the corresponding tank, we
have the restriction of the volume to be transferred, according
to the restrictions of capacity of the ship and the space
availability in the tanks of the terminals and platforms. Such
availability is calculated according to the production rates in
the platforms and the pumping rates in the terminals. The
(lower and upper) limits are informed to the model through
parameters.
Figure 7 shows an example of a viable configuration in a reduced
scenario, with two terminals, one platform, two ships and
three possible berthing sequences in each terminal and
platform. The numeric indications represent the rates of the
places and the rate of the number of berthing. In this example,
the first ship starts the operation with terminal 1 as destination,
in berthing 1 (1, 1). The first arch has the platform as
destination, in sequence 1 (1, 1). Next, it heads for terminal
2, in sequence 1 (2, 1), comes back to the platform, in sequence
3 (1, 3), heads again for terminal 1, in sequence 3 (1, 3) and
ends the trip in terminal 2, in sequence 3 (2, 3). The second
ship starts its trip to platform 1, in sequence 2 (1, 2), and
heads for terminal 1, in sequence 2 (1, 2). Next, it heads for
terminal 2, in sequence 2 (2, 2), when it concludes the trip.
Each position, composed of the pair place-sequence of berthing,
must receive only one berthing. The decision of ship allocation
to the loading or unloading point presupposes space availability
in the storage tank of petroleum to be loaded or unloaded,
respecting the limits imposed to the tanks. Such availability is
calculated according to the production rates in the platforms
and consumption rates (pumping) in the terminals and to the
(lower and upper) limits calculated by the dynamic time
windows.
The time windows indicate the maximum instant when there
must be berthing so that the conditions imposed by the tanks
are respected. To do so, the first berthing takes into account
the parameters of the initial conditions of the tanks: initial
level, upper and lower limits, the minimum lot of loading/
unloading and the rates of production/consumption. Based
on the data referring to the initial conditions, the upper limit
Regarding the demand, one must comprehend the attribution
of this reception applied to this problem. It is necessary for the
platforms to have conditions to produce petroleum at the
production rate indicated during the planning horizon.
Concomitantly, the terminals need to be capable of pumping
the petroleum at the consumption rate indicated. Thus, the
model presents two similar sets of equations, referring to
serving the demand, for the platform and the terminal.
For the production and consumption rates to be maintained
and respected, the volumes of petroleum available in the tanks
have to remain within the range established between the upper
and lower limits of the tanks: for the case of the platform, it is
necessary that releases or ships' discharge occur for the
maintenance of the production rates; for the terminals,
adequate load reception is essential in order to enable the
consumption. Thus, one of the ways to ensure the continuity
is the formulation of the restriction to serve the demand through
the number of berthings.
The number of berthings that each platform or terminal must
receive is calculated in relation to the minimum lot, which is
the parameter. The calculation presupposes the quantity of
berthings necessary during the programmed time horizon so
that the tanks' levels allow the regularity of the production
and consumption rates. After the first berthing, the quantity
of petroleum to be produced or consumed until the time
horizon, divided by the minimum lot, results in the maximum
quantity of berthings necessary.
5.3
Model formulation
5.3. (a) Indexes
• i,g...to represent the terminal;
• j,a...to represent the platform;
• m, m´... to represent the order of berthing sequence in the
terminal;
• n, n´... to represent the order of berthing sequence in
the platform;
• v... to represent the ship;
5.3. (b) Sets
• V={1,2,...,nV}... to represent the set of ships;
• I={1,2,...,nI} ... to represent the set of terminals;
• J={1,2,...,nJ} ... to represent the set of platforms;
• M(i) ... to represent the set of berthings in terminal i;
• N(j) ... to represent the set of berthings in platform j;
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5.3. (c) Parameters
• TVGTg,i,v … Trip time taken by ship index v between
terminal index g and terminal index i;
The parameters used in the mathematical model are
described below:
• TVGPa,,j,v … Trip time taken by ship index v between
platform index a and platform index j;
Regarding costs:
• TVG0T,i,v … Initial trip time taken by ship index v to
terminal index i;
• CX i, j,v … cost in R$ of the trip of ship index v between
terminal index i and platform index j;
• TVG0P,j,v … Initial trip time taken by ship index v to
platform index j;
• CZ j,i,v … cost in R$ of the trip of ship index v between
platform index j and terminal index i;
• CTE g,i,v … cost in R$ of the trip of ship index v between
terminals indexes g and i;
• CPA a,j,v … cost in R$ of the trip of ship index v between
platforms indexes a and j;
•
... Number of berthings in
terminal index i;
• C0T i,v … cost in R$ of the initial trip of ship index v to
terminal index i;
•
• C0P j,v … cost in R$ of the initial trip of ship index v to
platform index j.
platform index j;
Regarding tanks:
... Number of berthings in
5.3. (d) Decision variables
• SMNTi … Minimum level of the storage tanks in
terminal index i;
Regarding the global system: CT ... total cost;
• SMXTi … Maximum level of the storage tank in
terminal index i;
Regarding the flows:
• SMNPj … Minimum level of the storage tank in platform
index j;
• SMXPj … Maximum level of the storage tank in platform
index j;
• ISTi … Initial level of the storage tank in terminal
index i;
• ISPj … Initial level of the storage tank in platform index j;
• QIv … Initial level of the tank of ship index v;
• CAPv … Capacity of the storage tank in the hold of ship
index v;
• G ... Largest loading/unloading lot among the capacities of
the tanks of ships, terminals and platforms;
• QMIN ... Minimum lot of release or discharge.
Regarding rates:
• RPj … Production rates in platform index j;
• RTi … Consumption rates (pumping) in terminal index i;
• Ximjnv : =1, if ship v conducts berthing order m in t e r minal i and heads for platform j where it will conduct
berthing order n;
: = 0, otherwise;
• Zjnimv : = 1, IF ship v conducts berthing order n in platform
j and heads for terminal i where it will conduct berthing
order m;
: = 0, otherwise;
• Wgmímv : = 1, if ship v conducts berthing order m´ in
terminal g and heads for another terminal i where it will
conduct berthing order m;
: = 0, otherwise;
• Uan´jnv : = 1, if ship v conducts berthing order n´ in platform
a and heads for another platform j where it will conduct
berthing order n;
: = 0, otherwise;
• VITimv: = 1, if ship v makes the initial trip to terminal i in
berthing order m;
: = 0, otherwise;
• VIPinv: = 1, if ship v makes the initial trip to platform j in
berthing order n;
: = 0, otherwise;
• TQPj … Loading rate in platform index j;
• TQTi … Unloading rate in terminal index i;
Regarding time:
• T… Planning horizon for calculation of number of
berthings;
• TVGi,,j,v … Trip time taken by ship index v between
terminal index i and platform index j and between platform
index j and terminal index i;
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Regarding berthings:
• VFTimv: = 1, if ship v makes the final conclusion trip from
terminal i in berthing order m;
: = 0, otherwise;
• VFPjnv: = 1, if ship v makes the final conclusion trip from
platform j in berthing order n;
: = 0, otherwise;
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loaded or unloaded, respecting the minimum and
maximum lots. Besides these, it establishes the demand in
the terminal and platforms, according to pre-determined
quantities of berthings.
• Yv: = 1, if ship v does not make any trip;
: = 0, otherwise;
Regarding loading/unloading operations:
• qTim ... load volume unloaded in terminal index i in
berthing order m;
• qPjn ...load volume loaded in platform index j in berthing
order n;
• lTimv ...petroleum volume contained in the tank of ship
index v when leaving berthing order m in terminal index i;
• lPjnv ... petroleum volume in the tank of ship index v
when leaving berthing order n in platform index j;
Regarding time:
• tTim ... time instant of berthing order m in terminal index i;
• tPjn ... time instant of berthing order n in platform index j;
• lsTim ... upper limit of time window for berthing order m
in terminal index i;
• lsPjn ... upper limit of time window for berthing order n in
platform index j;
• Regarding time Windows: set of restrictions that calculate
the upper limits of the time windows according to the
characteristics of the tanks' levels.
• Regarding time: instants of berthing in platforms and
terminals that are established originating in all the possible
origin conditions and which establish the increasing order
of berthings.
• Regarding tanking in terminals and platforms: set of
restrictions which calculate the values of the tanks' levels
in platforms and terminals, establishing them within the
limits determined.
• Regarding tanking in the ships: set of restriction that defines
the tank's volume in the ships' holds, after the berthings,
conditioning them to the existence of the arches and the
limits of the ships' capacity.
• Regarding the non-negativities of the binary and real
variables.
Regarding the flow
Regarding tanking:
• sTim ... level of the tank in terminal index i at the initial
instant of berthing order m;
• sPjn ... level of the tank in platform index j at the initial
instant of berthing order n;
5.3. (e) The objective function
The objective function is to minimize the total cost of the
trips made by the ships fleet. All the possible arches are included:
• Between terminals and platforms (Ximjnv) and the inverse
arch (Zjnimv);
• Between terminals (Wgmímv) ;
• Between platforms (Uan´jnv) and
• Initial trips to platforms and terminals (VIPjnv e VITimv).
• Initial Condition of the ships:
(1)
Expression 1 guarantees that each ship allocates a single initial
arch, by a platform (VIPjnv), by the terminal (VITimv) or does
not allocate any trip (Yv). In case this last variable is selected,
there will not be any intermediate arch until the closing.
• One arch of departure at most from each platform with
destination to some terminal or platform:
(2)
Expression 2 guarantees that for any platform (j) and any
berthing sequence (n), there is at most a single arch with
destination to some terminal or platform.
• One arch of departure at most from each terminal w i t h
destination to some platform or terminal:
(3)
The equation of this function objective is shown below:
Expression 3 guarantees that for any terminal (i) and any
berthing sequence (m), there is at most a single arch with
destination to some platform or terminal.
• Continuity in the platform:
5.3. (f) Restrictions
(4)
Restrictions were subdivided in the following categories:
• Regarding the flow: set of restrictions that create a single
initial arch per ship, and then ensure its continuity until
the final trip.
• Regarding the receptions in platforms and terminals: set
of restrictions that establish the loading volumes to be
Expression 4 establishes the continuity of arches in the
platform (j) and berthing (n). The flows of arrival come
from terminals (Ximjnv), other platforms (Uan´jnv) or the
initial condition (VIPjnv). The flows of departure are the
ones with destination to one of the terminals (Zjnimv), one
of the platforms (Ujnan´v) or to the final arch (VFPjnv).
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time interval between berthings, and finally subtracted
from the lower limit of the tank.
• Continuity in the terminal:
• Maximum lot in the terminal's release:
(5)
(11)
Expression 5 establishes the continuity of the arches in
the terminal (i) and berthing (m). The flows of arrival
come from platforms (Zjnimv), other terminals (Wgmímv) or
the initial condition (VITimv). The flows of departure are
the ones with destination to one of the platforms (Ximjnv),
one of the terminals (Wimgm´v) or the final arch (VFTimv).
• Final condition of the ships:
(6)
Expression 6 ensures that each ship v ends the mission in
a single position: in terminal i and berthing m, in platform
j and berthing n or in the initial condition, without trips.
Regarding the receptions in platforms and terminals
• Minimum lot in the platform's release:
(7)
(12)
Expressions 11 and 12 calculate the volumes to be unloaded
in the terminal. Expression 11 is attributed to the initial
condition, whose volume to be unloaded must not go over
the volume equivalent to the maximum stock, subtracted
from the initial volume available and the volume pumped
(consumed) until the moment of berthing. Expression 12
recalculates the volumes to be unloaded, starting with the
second berthing, which is equivalent to the maximum stock
subtracted from the level in the previous berthing, the volume
unloaded in the previous berthing and the volume pumped
during the time interval between the berthings.
• Release lot in the platform, conditioned to the existence
of the initial arch to the platform, the arch b e t w e e n
platforms and the arch from the terminal to the platform:
(13)
• Minimum lot in the terminal's unloading:
(8)
Expressions 7 and 8 establish the minimum lot, defined as
parameter for loading in the platform and unloading in
the terminal, conditioned to the existence of their
respective arches. The value must be respected as condition
to guarantee the demand of the number of berthings
forecast for each terminal and platform, calculated
according to initial conditions of the minimum and
maximum levels of the tanks.
• Unloading lot in the terminal, conditioned to the
existence of the initial arch to the terminal, the arch
between terminals and the arch from the platform to the
terminal:
(14)
Expressions 13 and 14 have functions to set a condition
between the existence of the loading or unloading lots to
the existence of the arch that will originate the berthing.
• Reception of Demand in the Platforms:
• Maximum lot in the platform's release:
(15)
(9)
• Reception of Demand in the Terminals:
(10)
Expressions 9 and 10 calculate the volumes to be loaded in
the platform. Expression 9 is attributed to the initial
condition, whose volume to be loaded must not go over
the initial volume available, added up to the volume
produced until the moment of berthing and subtracted
from the volume equivalent to the lower limit of the tank.
Expression 10 recalculates the volumes to be loaded, starting
with the second berthing, when the stock levels in the
previous berthing are considered, subtracted from the part
of the volume loaded in the beginning of the previous
berthing, added up to the volume produced during the
15
(16)
Expressions 15 and 16 consist in restrictions that set as
mandatory the existence of berthings. Indirectly, it can be
denominated as reception of demands. The calculation of
the number of berthings of each terminal or platform
took into account the fulfillment of the upper and lower
levels of the tanks, through minimum and maximum time
intervals for a lot of minimum load, in order to respect
the imposed conditions.
• Operation Time of berthing index m in terminal index i:
(17)
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• Operation Time of berthing index n in platform
index j:
Regarding time
(18)
Expressions 17 and 18 establish the operation time in
terminals and platforms, calculated according to the lot
to be unloaded or loaded, divided by the loading and
unloading rates.
• Berthing instant in the platform for a ship coming from
the initial condition:
(25)
a terminal:
Regarding the time window
(26)
• Upper limit of time window in platform index j in berthing
index n:
another platform:
(19)
(20)
Expressions 19 and 20 determine the upper limits of
berthings in the platforms. For the first berthing, equation
19 calculates the time interval elapsed until the tank's
level reaches its upper limit. For the other berthings, this
time is calculated based on the conditions of the previous
berthing: instant, tank's level and volume released.
• Upper limit of the time window in terminal index i in
berthing index m:
(27)
Expressions 25, 26 and 27 allocate the time associated to
the trip and reception, to the berthing instants,
conditioned to the existence of the arches. Expression 25
considers only the trip time to get to the platform, when
variable VIPjnv is selected. Expression 26 considers trip
time from terminal index i and berthing index m for
platform index j and berthing index n, berthing instant
index m, reception time in the terminal, all conditioned
to the existence of arch Ximjnv. Expression 27 is analogous
to the previous one, considering the origin of the arch is
another platform.
• Berthing sequences in the platform:
(21)
(28)
(22)
Expressions 21 and 22 are analogous to the previous two
and determine the upper limits of the instants of berthings
in the terminals. The upper limiting of the berthing instant
for the terminal is dictated by the minimum level of the
tank because the terminal consumes the petroleum and
therefore, the tank's level decreases. For the first berthing,
equation 21 calculates the time interval elapsed until the
tank's level reaches the lower limit. For the other berthings,
this time is calculated based on the conditions of the previous
berthing: instant, tank's level and volume unloaded.
• Imposition of the upper limit of the time window in
terminal index i in berthing index m:
Expression 28 reinforces the need for increasing
ordination of berthings over time and ensures the
beginning of berthing occurs only after the time of
reception of the previous berthing. That is due to the
possibility of having consecutive berthings for the same
terminal or platform.
• Berthing instant in the terminal, coming from the
initial condition:
(29)
• Berthing instant in the terminal, coming from a platform:
(30)
(23)
• Imposition of the upper limit of the time window in
platform index j in berthing index n:
• Berthing instant in the terminal, coming from another
terminal:
(24)
Expressions 23 and 24 complete the set of restrictions of
time windows, establishing the maximum berthing instants
to be reached until the upper limits calculated.
(31)
Equations 29 to 31 are analogous to equations 25 to 27,
oriented to terminals.
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• Berthing sequences in the terminal:
(32)
Regarding tanking in terminals and platforms
• Minimum stock in each platform index j in the beginning
of each berthing:
(33)
• Minimum stock in each terminal index i in the beginning
of each berthing:
(34)
• Stock in the platform index j in the beginning of berthing n:
(35)
(36)
Expressions 35 and 36 calculate the values of tanks' levels
in the beginning of each berthing. For the first berthing,
initial conditions are considered. For the others,
conditions of the previous berthing are considered: tank's
level, volume released by the ship and volume produced in
the time interval between the berthings.
Linearization is done through the reformulation of
equations for a set of whole-mixed equivalent equations,
according to Sherali, H.D. (1998), who exposes the
structure of a non-linear problem, delimited by the viable
region as follows:
where f(y) is the function of domain Y. For the specific
case, taking equation 41 as an example, it is possible to
and
adopt x as the binary variable VIPjnv and y as
f(y) as
.
Considering the set
where
is compact, i.e. there are lower and upper
limits [I,S] that satisfy:
Hence, set T is equivalent to:
Function f(y)=
is linear and parameters -G
and G are valid as lower and upper limits, respectively.
Using the proposition resulting from the linearization
given by T' from the previous demonstration and
substituting the variables, we have:
(39a)
• Stock in terminal index i in the beginning of berthing m:
sT = IST − tT * RT
im
i
im
i
, ∀i ∈ I , m ∈ M (i ) : m = 1
sTim = sTim −1 + qTim −1 − (tTim - tTim −1 ) * RTi
(37)
∀i ∈ I , m ∈ M (i ) : m > 1
(39b)
Similarly, we have the other equations applied to the other
two binary arches:
(38)
(40a)
Equations 37 and 38 are analogous to the previous ones,
applied to terminals.
(40b)
Regarding to tanking in the ships
(41a)
• Volume of petroleum in the hold of ship v after berthing
order n in platform j:
(41b)
(39)
(40)
• Volume of petroleum in ship v's tank after berthing order
m in terminal i:
(41)
Analogous to what was shown for calculation of the stocks in
the platform, the same structure can be applied for the case of
the ship's stocks in the departure of the terminal, hence:
Equations 39, 40 and 41 determine the values of the
volumes in the ships' holds when leaving the reception in
platform index j in berthing index n. Equations are
conditioned to the arches of the initial trip, for the first
berthing, arches from terminals and arches from other
platforms, respectively. Equations are non-linear and,
therefore, must be transformed in linear equations.
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(42a)
(42b)
(43a)
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(43b)
(44a)
(44b)
• Maximum stock of the ship in the departure of the
platform:
(45)
• Maximum stock of the ship in the departure of the
terminal:
(46)
Expressions 45 and 46 limit the amount of load present in
the ship up to its capacity.
5.3. (g) Non-negativity of the variables
• Binary: Ximjnv , Zjnimv , Wgmímv , Uan´jnv , VIPjnv,VITimv , Yv ,
VFPjnv , VFTimv;
6
Results
In order to test and validate the responses of the model, as well
as to evaluate the computational effort and the optimality degree
of the solution, we present below the results of a small-sized
fictional case.
The elevated complexity of the model makes the conceptual
validation difficult, which reinforces the need to conduct
tests through the elaboration of several kinds of scenarios,
trying to analyze the responses according to the modifications
carried out, assimilate and comprehend the reasons of the
solution presented. To achieve this objective, several scenarios
were tested, among which, there is one, of reduced scale, but
which presents enough solutions to understand the problem
and the potentialities of the model.
The model presented totals 2915 restrictions with 1080
variables, among which 882 are binary. The optimum solution
was found in around 64 minutes, using the standard
configuration of CPLEX 10.0 search parameters. The ships
presented the trips programming according to the table and
figure below:
Table 2 Programming
• Real: qTim, qPjn, lTimv , lPjnv , tTim , tPjn, lsTim, lsPjn, sTim, sPjn.
5.4. Computional implementation and
results
The optimization model was developed in linear mixed
programming and the computational implementation in
mathematical language C++ and VBA. The formulation of
the model caused the elevated quantity of classes of restrictions
and the adoption of high quantity of binary variables, mainly
related to the arches, which contain preponderantly five
indexes. The size of the model and its possible potential of
difficulties in the execution were fundamental for the selection
of the computational package to be used in the
implementation. Two great problem-solving tools for linear
programming are available for the author: software GAMS,
general system of algebraic modeling, in version 20.0, whose
resolution algorithm uses CPLEX, in version 7.0, and the direct
utilization of algorithm CPLEX, in version 10.0.
The implementation in CPLEX 10.0 requires the creation of
the mathematical model in language C++, whose data reading
routines, equation reading, execution and results presentation
are standardized, what largely facilitates its creation. The model
generation was made using the resources of Microsoft Excel,
especially through the creation of Macros in VBA language.
Parameters were defined in spreadsheets according to the data
categories and, through routines in VBA, the model's sets of
equations were created. Thus, the generation of scenarios, with
modification of some characteristic of the model's parameters,
is made through Microsoft Excel itself. The computers used
for the execution of the models possess Pentium IV processors,
1.7 GHz, 512 MB RAM memory and 40 GB HD.
Fig. 8
Routes
From the Table 2 and Figure 8, it is possible to observe that
the ships started the routes from the platforms (1,1 and 2,1).
The first ship ended the route in terminal 3, after completing
ten berthings, as well as the second ship, which conducted
the same number of berthings, ending in terminal 2. It is
18
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also observed that, in both routes, there were arches between
the terminals. The details of the operations carried out by
ship 1 is presented on Table 3.
Table 3 Results of the hypothetical model of optimizationShip 1
resources available.
Tables 3 and 4 present the results based on the berthings
conducted by the ships. Regarding the behaviors of the tanks'
levels of the platforms and terminals, it is necessary to consider
the initial conditions and the berthing instants, regardless of
the ship, associated to the loading/unloading volumes,
production rates, pumping and the overflow. The results are
presented below:
Table 3 shows the characteristics of the berthings conducted
by ship 1. The first two columns present the place and the
sequence of berthing. On the third column, the values of the
tank's levels are presented at the moment of berthing; on
the fourth column, the volume loaded or unloaded by the
ship and, on the next column, the volume of load left in the
ship's hold, at the end of the reception. The sixth column
shows the instant at which the berthing occurred and the last
column shows the instants of the upper limits of each
berthing.
This table already points out some important conclusions of
the scenario evaluated. It is observed that, on the column
referring to the load volume, the minimum attributed
volume (minimum lot) was allocated five times and that, in
just one trip, the full capacity of the ship was used. It is also
possible to verify that the tanks' levels in the platforms
remained high and, on the other hand, the tanks' levels in
the terminals remained low, many times near the lower limit.
In great part of the itinerary, the ship's hold was unoccupied
and the berthing instants occurred much before the upper
limits, consequence of the minimum loading established.
Table 4 shows the characteristics of the berthings conducted
by ship 3.
Table 4 Results of the hypothetical model of optimization Ship 2
The programming completed by ship 2 follows the restrictions
of the model together with ship 1 and, similarly, the behavior
is analogous, also with the occurrence of unoccupied trips.
Thus, the results presented allow us to conclude that the
configuration of the scenario presents deficiencies in the
allocation of loads and in the trips, and a low usage of the
19
Fig. 9
Platforms' tanks
Figure 9 presents the behaviors of the tanking levels in the
platforms. The results reflect truthfully the conditions required
for the control of the levels. The platform produces or extracts
a volume of petroleum according to a constant rate, which
establishes a time window for release or reception by ship
necessary to obey the upper limit. In case of platform 1, it is
observed that the initial stock was 45,000 m3 and the first time
window was established in [3, 7] days. That is, the first berthing
must occur between the instants referring to days 3 and 7. In
fact, it occurred on day 3, when the curve starts to be decreasing.
The end of the berthing occurred on day 5, when the curve
retakes the increasing behavior, or of production.
After determining the volume of release, the new time window
is recalculated for the following berthing, what occurs again on
the lower limit (day 9). The third berthing in this platform
occurs at the instant on day 14 and the load volume released is
enough to significantly postpone the date of the next berthing,
which occurred only on day 35, whose limits were [34, 38].
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petroleum pumping, in an integrated way. The study of
petroleum supply chain proved to be quite broad and
complex in the sense that the systemic approach desired
from a global and concise approach requires unlimited efforts
in the search for effective and tangible results in the process
of planning and management.
The simulation model presented the possible impacts that
may occur to a certain link of the chain, from perturbations
in the system originated in links adjacent or distant from
this one. This corroborates the importance of understanding
adequately the amplitude or range of the boundary of the
system to be studied.
A systemic approach needs mainly the evaluation and
framing of the problem in hierarchical levels of decision. In
the process of modeling, the task of aggregation/
disaggregation of the events and the associated data must be
cautiously thought over and adjusted according to what is
desired as an answer.
Fig. 10 Terminals' tanks
The figures above illustrate the behaviors of the tanks' levels in
the terminals. Naturally, the behavior is the inverse of the
observed in the platforms, in which, from the initial condition,
the curve is decreasing because it is associated to the pumping
rate or petroleum consumption. The berthings are defined by
the time windows, calculated according to the necessary time
for meeting of the lower limit.
The set of figures allows the visualization of the time Windows,
which are dynamic and recalculated according to the volumes
loaded and unloaded, always trying to obey the restrictions of
upper limits of the tanks.
7 Conclusions
The opportunities of improvements may be defined from
the execution of integrated planning and the petroleum
supply chain management in order to try to employ
efficiently and rationally the resources involved.
The research has shown that a complex system of this nature
requires systemic treatment, through studies of each
subsystem individually and their further integration with the
purpose of quantifying and analyzing the interaction existing
in all the supply chain.
Therefore, the present article provides a contribution to a
systemic and broad approach, considering links of
production, storage, transport, ships' reception and
In terms of contributions in academic ambit, it is important
to emphasize the success obtained in systemic modeling from
two modeling techniques: simulation and optimization.
Simulation considers and models a high quantity of events,
with the exploration of the main technical advantage:
modeling of stochastic events. Variations in associated time,
random conditions, drawing probabilities in decisions of
petroleum production, pumping and the maintenance of
ships fleet are some of the modeled examples.
Concerning the optimization, modeling for obtaining ships
programming subject to restrictive trip and stock conditions
on the two edges, modeling a variable demand and dynamic
time windows are odd characteristics.
In summary, the objectives proposed were achieved
successfully, bringing valuable contribution both for the
academic environment and for the petroleum sector, which,
day by day, wonders the necessity of excellence not only in
technological terms, but also in effective management in
planning of its operations. For the academic community, a
problem of ships programming in distinct routes involving
multiple origins and multiple destinations, serving a
dynamic time window to maintain satisfactory tanking levels
on the two edges had ever been solved successfully. For the
sector, more specifically for the managers of mature fields
(existing infrastructure), the study brings significant
contribution to enable discerning evaluation of the strategies
employed and offer alternatives of increment in the services,
or even serve as theoretical basis to rectify the programming
system of the fleets in a tactic plan of resources allocation.
The most valuable product of the present paper involves a
form of approach that enables not only the application in
the segment of petroleum supply chain, but also in similar
systems in which a high quantity of processes must be
concomitantly evaluated.
20
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Acknowledgements
This research was developed with the support of the National
Agency of Petroleum (Agência Nacional do Petróleo -ANP)
and the Financier of Studies and Projects (Financiadora de
Estudos e Projetos - FINEP) through the Human Resources
Program of ANP for the Sector of Petroleum and Natural Gas
- PRH-ANP/MME/MCT.
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22
Bifurcation analysis of unstable ship motions resulting from strong nonlinear
coupling
Marcelo A. S. Neves1, Jerver E. M. Vivanco2 and Claudio A. Rodríguez3
1 LabOceano, COPPE/UFRJ, [email protected]
2 COPPE/UFRJ, [email protected]
3 LabOceano, COPPE/UFRJ, [email protected]
Abstract
The present paper employs modern nonlinear dynamics tools in order to investigate the dynamic characteristics governing the
complex coupling of the heave, roll and pitch modes in head seas at some regions of the numerical stability map of a fishing vessel.
Bifurcation diagrams and Poincaré mappings are computed and employed to investigate the appearance of multistability and chaos
associated with increased values of the selected control parameter, the wave amplitude. The connection between these nonlinear
characteristics and the coupled nature of the mathematical model are analyzed.
Keywords
Ship stability; Parametric rolling; Nonlinear dynamics; Bifurcations
Nomenclature
Aw
wave amplitude
Fn
Froude number
Jxx
transversal mass moment of inertia
Jyy
longitudinal mass moment of inertia
m
ship mass
z
heave non-linear motion
ζ
wave elevation
θ
pitch non-linear motion
φ
roll non-linear motion
ZW
heave external excitation
K W roll external excitation
M W pitch external excitation
χ
wave incidence
ωe
ω n4
roll natural frequency
1
Introduction
encounter frequency
It is well known that parametric rolling in head seas may lead to large roll angles and accelerations in few cycles. Even though many
studies on the subject simplify the analysis to a single degree of freedom, there is nowadays a wide acceptance of the relevance of the
nonlinear coupling of the roll mode with heave and pitch for a better physical modeling of intense parametric amplification.
In previous studies Neves and Rodríguez (2005, 2006) have introduced a mathematical model in which the heave, roll and pitch motions
are nonlinearly coupled to each other. Using this model they investigated the occurrence of head seas parametric rolling on a small fishing
Submitted to MS&OT on Nov 23 2009. Revised manuscript received Jul 12 2010. Editor: Celso P. Pesce.
23
Bifurcation analysis of unstable ship motions resulting from strong nonlinear coupling
Marcelo A. S. Neves, Jerver E. M. Vivanco and Claudio A. Rodríguez
vessel. They showed, by means of numerical simulations,
comparable to experimental results, the occurrence of strong
dependence of the roll responses in head seas conditions to initial
conditions, Neves and Rodríguez (2007b).
In order to investigate the quantitative and qualitative changes
of parametric rolling with respect to the encounter frequency
tuning and wave amplitude, Neves and Rodríguez (2007a,b)
proposed the computation of analytical and numerical maps
representing the boundaries of stability of the nonlinear system.
The numerical maps aggregate information not only on the
boundaries of stability, but also on the amplitude of roll response
in the whole region of parametric amplification.
In order to get a deeper insight into the nonlinear characteristics
of the solutions, the present paper investigates in greater detail
the dynamics governing the complex coupling of modes at
some regions of the numerical stability map. Bifurcation
diagrams and Poincaré mappings, Guckenheimer and Holmes
(1983), Seydel (1988) are employed in order to investigate the
appearance of multistability and chaos associated with increased
values of the control parameter, wave amplitude. The
connection between these nonlinear characteristics and the
coupled nature of the model are analyzed.
2
Mathematical model
Employing Taylor series expansions up to third order, Neves and
Rodríguez (2005, 2006) expressed restoring actions in the heave,
roll and pitch modes in a nonlinear coupled way. Wave actions
are taken into consideration not only in the Froude-Krilov plus
diffraction first order forcing functions, but also in second and
third order terms resulting from volumetric changes of the
submerged hull due to vertical motions and wave passage effects.
The model corresponds to an extension, both in the order of
non-linearities and in the levels of coupling, of the model
introduced by Paulling and Rosenberg (1959) and Paulling (1961).
The equations are taken here in their explicit form described in
detail in Neves and Rodríguez (2005, 2006). Thus, the non-linear
heave, roll and pitch equations are introduced as:
is considered in equation (2). The terms associated with
variables z,φ,θ and wave elevation ζ(t) correspond to the
non-zero linear and non-linear (up to third order)
coefficients due to hydrostatic and wave pressure effects
analytically derived by Neves and Rodríguez (2005, 2006),
dependent on hull characteristics and on wave amplitude,
frequency and time. On the right hand side of Eqs. (1-3),
[ZW(t) KW(t) MW(t)]T represent linear wave excitation. Due to
the particular wave incidence considered, KW = 0 has been
assumed in Eq. (2). Once all the coefficients in Eqs. (1-3)
are known, this set of three equations may be numerically
integrated without difficulty.
3
Numerical simulations
Numerical simulations have been performed in the case of a
fishing vessel denominated TS, see Fig. 1 and Table 1. Parametric
rolling of this fishing vessel has been experimentally and
numerically examined in detail in Neves and Rodríguez (2005,
2006), Neves et al. (2002). Figures 2 and 3 show comparisons of
numerical simulations performed using the equations (1-3) with
experimental results for two wave conditions and ship speeds
corresponding to quite intense roll amplifications. In both cases
the encounter frequency was equal to twice the roll natural
frequency, which corresponds to the exact Mathieu tuning ratio
at the first region of instability, we / wn4 = 2.0. The comparisons
allow one to conclude that the mathematical model has good
capabilities for modeling intense parametric rolling for the
fishing vessel under investigated.
(1)
Fig. 1
(2)
Hull form of transom stern (TS) fishing vessel.
Table 1 Ship main characteristics
(3)
On the left hand side of Eqs. (1-3) added masses and wave
damping terms are assumed linear. A quadratic roll damping
24
Fig. 2
Roll motion, Fn= 0.20, Aw = 0.60m, w e / w n4 = 2.0.
Fig. 3
Roll motion, Fn =0.30, Aw = 0.78m, w e / w n4 = 2.0.
4
Numerical limits of stability
As demonstrated in the previous section the transom stern
fishing vessel employed in the present investigation is quite
prone to strong parametric rolling in head seas.
It is important to investigate parametric rolling not only at
the exact encounter frequency tuning we / wn4 = 2.0. In fact,
large amplifications may take place in a quite broad spectrum
of excitation frequencies. In order to comprehensively
investigate the unstable regions Neves and Rodríguez (2007b)
proposed the computation of numerical maps representing
the boundaries of stability but containing information on the
amplitude of roll response in the whole region of parametric
amplification. Figure 4 shows the limits of stability of the
fishing vessel in head seas at Fn = 0.30, corresponding to the
first region of instability. The mapping is constructed by
numerically computing the roll amplitude for different
encounter frequencies and wave amplitudes. All points of the
map are computed for the same set of initial conditions. The
intensity of the final steady roll amplitude is indicated by the
color scale displayed on the right hand side of the figure.
It is interesting to notice that the colour scale in Figure 4
indicates that for small wave amplitudes the roll amplitude
tends to grow slowly (blue to light-blue colours) and also that
on the contrary, for large wave amplitudes, strong
nonlinearities show their effect: the upper limits of the domains
of parametric amplification, for the whole spectrum of
frequencies, reflect the existence of jumps (fold bifurcations)
from large roll amplitudes to equilibria (no roll amplifications).
Four important features of the new limits of stability are:
• appearance of upper boundaries, indicating that for
increased wave amplitudes, parametric rolling may
not necessarily increase; in fact, it tends to disappear.
• general tendency of the unstable area to bend to the right,
indicating that the exact tuning we / wn4 = 2.0 is not
necessarily the one with stronger amplification.
• smooth growth of roll amplitude at lower level of boundaries,
abysmal (sudden) decrease in the upper boundaries.
• larger area of instability as the roll initial conditions were
modified.
A more detailed discussion of these features may be found in Neves
and Rodríguez (2007a). These four characteristics point out to
complexities and intricacies that demand further investigations.
In the next section some numerical tools of nonlinear dynamics
will be employed in an attempt to clarify some of these topics.
25
Fig. 4
Ship TS, Fn=0.30. Limits of stability (upper), wave
amplitude effect on roll amplitude (lower).
5
Bifurcation diagrams
In Figure 4 (upper) the whole spectrum of exciting frequencies
was explored. It has been observed that distinct characteristics
are revealed. It is now desirable to get an in depth knowledge
of dynamical characteristics as the parameter wave amplitude
AW is increased. So, if previously we have been more interested
in the limits of stability as a whole, now we wish to have a
closer look at some domains inside the unstable area. For this
purpose, we will investigate the changes in dynamic
characteristics as we cross the area inside the limits. A limited
region of the map of limits of stability will be explored, that is,
we will follow a vertical line defined at the tuning
in Figure 4. Aiming at demonstrating the influence of initial
conditions on the solutions corresponding to points inside
the area of the limits of stability we developed a brute-force
algorithm for capturing the branching of solutions for a
specified set of initial conditions.
Thus, using the AW parameter, the type of roll bifurcation
diagram is obtained as shown in Figure 5. The adopted mapping
period is the encounter frequency. Thus, given the low cycle
character of parametric rolling for
there exist
positive and negative branches for the roll bifurcation diagram.
Two interesting characteristics, not observable in the numerical
limits of stability, are revealed by this bifurcation analysis. After
a first range in which the roll amplitudes tend to increase almost
linearly, in the short second range of AW defined by 0.6037 <
Aw< 0.6129 one observes the appearance of a solution with 3
periods that ends with a sudden appearance of a burst of nonperiodic solutions. The period-3 solutions of heave, roll and
pitch motions are illustrated in Figures 7-9, respectively. In each
of them, time history, phase plane and Poincaré map are shown.
The appearance of non-periodic solutions is illustrated in Figure
10 which shows the roll time series, the corresponding phase
diagram and Poincaré map for Aw= 0.6129 m.
8
Fig. 5
Roll bifurcations, w e/wn4 = 2.0.
In order to get a better understanding of the coupling between
the heave, roll and pitch motions it is important to observe
the bifurcations taking place in these three modes. These are
developed for the same set of initial conditions used in the
mapping of the limits of stability presented in Figure 4. The
bifurcation diagrams for the heave, roll and pitch motions are
shown in Figures 5 and 6. In Figure 6 the negative branch for
the roll motion is not plotted in the figure; otherwise, with the
heave and pitch bifurcation diagrams, the figure would be
overloaded with graphs and its scale would result inadequate
for clarity. Figures 5 and 6 reveal the branching structure for
distinct ranges of wave amplitude. Seven ranges with distinct
qualitative and quantitative types of responses are noticed.
These are subsequently discussed in detail.
Fig. 6
Heave, roll and pitch bifurcation diagrams, Fn=0.30.
Fig. 7
Heave motion, phase plane and Poincaré map, period-3
solution, Aw=0.605 m.
26
Fig. 8
27
Roll ( φ max=24.18°), phase plane and Poincaré map,
period-3 solution, Aw=0.61 m.
Fig. 9
Pitch motion, phase plane and Poincaré map, period-3
solution, Aw=0.605 m.
show that this is not the case. In fact the roll solutions in
this third range of Aw are period-1, but as illustrated in
Figures 11 and 12, the solutions continuously alternate, at
each new value of the parameter Aw, from one attractor to
another one which is situated close by. In other words, roll
motion either lives in one attractor or in the other, but
always with a single period. Subsequently, for higher wave
amplitudes, flip bifurcation will take place together with
multistability: period-2, 4 and 8 solutions will appear in
sequence, ending in chaos.
Fig. 11 Roll motion: (a) Aw=0.639 m, (b) Aw=0.6391 m.
Multistability for two neighboring points.
It is interesting to observe that in this third range of Aw (0.6130
- 0.6626) the roll motion undergoes multistability with period1 solutions, as shown in Figures 11 and 12. But in this same
range, the vertical motions have already undergone a period
doubling bifurcation. This is shown in Figures 13 and 14 for
heave and pitch, respectively. Another aspect worth noting is
that the alternating process illustrated in Figures 11 and 12 for
the roll motion does not contaminate the heave and pitch
modes, Vivanco (2009).
Fig. 10 Roll motion, phase plane and Poincaré map,
Aw=0.6129m. Non-periodic solutions.
The second interesting characteristic encountered is
multistability with associated alternance of values. This
dynamical feature arises immediately after the occurrence of a
burst of non-periodic solutions, as shown in Figures 5 and 6,
that is, in the range 0.613m < Aw< 0.626m. In the bifurcation
diagram one may get the impression that the roll motion has
migrated to a period-2 solution, but a detailed analysis will
Subsequently, in the fourth range of Aw (0.6627 - 0.6758) the
roll motion continues with multistability but responding with
period-2 solutions, as shown in Figure 15, whereas the heave
and pitch motions now respond with period-4 solutions. The
sequence of flip bifurcations soon leads the coupled system to
respond with chaotic motions. Figure 16 illustrates the period4 roll motion and finally, Figure 17 shows the chaotic behaviour
for Aw=0.683m. The region with chaotic behaviour ends
abruptly at the wave amplitude corresponding to the upper
limit of stability of Figure 4.
28
Fig. 13 Heave time history, phase plane and Poincaré map,
Fig. 12 Roll phase planes: (a) Aw=0.639 m, (b) Aw=0.6391 m.
Multistability for two neighboring points.
Fig. 14 Pitch time history, phase plane and Poincaré map,
29
Fig. 16 Roll motion ( φ max==24.73°), phase plane and
Poincaré map, period-4 solution for Aw=0.678 m
Fig. 15 Roll motion ( φ max==24.27°), phase plane and
Poincaré map, period-2 solution for Aw=0.67 m.
30
Authors also acknowledge financial support from CAPES,
FAPERJ and LabOceano. Thanks are due to Prof. Marcelo
A. Savi for many fruitful discussions.
References
G U C K E N H E I M E R , J., and Holmes, P.(1983). - “Nonlinear
Oscillations, Dynamical Systems and Bifurcations of Vector
Fields”. Applied Mathematical Sciences, vol. 42, SpringerVerlag.
Fig. 17 Roll motion ( φ max=25°), phase diagram and Poincaré
map, chaotic behaviour for Aw=0.683 m.
6
N EVES , M.A.S. and Rodríguez, C. (2005) - “A Nonlinear
Mathematical Model of Higher Order for Strong Parametric
Resonance of the Roll Motion of Ships in Waves”. Marine
Systems & Ocean Technology - Journal of SOBENA, Vol. 1
No. 2, pp. 69-81.
NEVES , M.A.S. and Rodríguez, C. (2006) - “Unstable Ship
Motions Resulting from Strong Nonlinear Coupling”.
Ocean Engineering, vol. 33, pp. 99-108.
Conclusions
Numerical limits of stability for a fishing vessel at Fn=0.30
undergoing strong parametric rolling in head seas have
been computed for a range of encounter frequencies. The
main dynamical characteristics of these limits have been
discussed.
For the encounter frequency tuning corresponding to the
first region of instability of the Mathieu stability map,
bifurcation diagrams for the heave, roll and pitch motions
have been computed considering wave amplitude as control
parameter.
Interesting phenomena such as coexistence of attractors
with period-3 solutions, appearance of a burst of nonperiodic solutions, multistability with alternance, fold and
flip bifurcations and chaos have been identified.
The phase planes and Poincaré mappings showed that the
period-3 solutions and burst of non-periodic solutions
are common to the three modes of motion considered.
On the other hand, multistability with alternance only
takes place for the roll motion.
It is relevant to observe that unique insights on the complex
nature of strong coupling between the heave, roll and pitch
motions are gained from this nonlinear dynamics analysis
presented in the paper. Future work on this subject must
consider ways for on-line detection and possible mechanisms
for the control of parametric rolling in rough seas.
N EVES , M.A.S. and Rodríguez, C. (2007a) - “Influence of
Nonlinearities on the Limits of Stability of Ships Rolling
in Head Seas”, Ocean Engineering. v.34, p.1618 - 1630.
NEVES, M.A.S. and Rodríguez, C. (2007b) - “An Investigation
on Roll Parame tric Resonance in Re gular Waves”.
International Shipbuilding Progress, Vol 54, pp. 207-225.
NEVES, M.A.S., Pérez, N.A. and Lorca, O. (2002) - “Experimental
Analysis on Parametric Resonance for Two Fishing Vessels
in Head Seas”. 6th International Ship Stability Workshop,
Webb Institute, New York, USA.
PAULLING, J.R. and Rosenberg, R.M. (1959) - “On Unstabl e
Ship Motions Resulting from Nonlinear Coupling”. Journal
of Ship Research 3 (1), 36-46.
PAULLING, J.R. (1961) - "The Transverse Stability of a Ship in a
Longitudinal Seaway", Journal of Ship Research, vol. 4, no.
4 (Mar.), pp. 37-49.
S EYDEL R. (1988) - "From Equilibrium to Chaos: Practical
Bifurcation and Stability Analysis", Elsevier Science
Publishing Co., Inc., NY.
VIVANCO, J.E.M. (2009) - “Parametric Rolling of a Fishing Vessel Nonlinear Dynamics”. M.Sc. Dissertation, COPPE/UFRJ,
Jan (in Portuguese).
Acknowledgements
The present investigation is supported by CNPq within
the STAB project (Nonlinear Stability of Ships). The
31
Parametric study on the axial vibrations of riser suspended and moored by chains
(RSAA) configurations
Claudio Marcio S. Dantasa,*, Marcos Q. de Siqueiraa, Victor Milanez da S. Pereiraa,
Fernando Jorge M. de Sousaa, José Renato M. de Sousaa and Isaías Q. Masettib
a
COPPE/UFRJ, Department of Civil Engineering - LACEO: Laboratory of Analysis and Reliability of Offshore Structures
*e-mail: [email protected]
b TRANSPETRO/GETID/TN
Abstract
Recently, in order to minimize the influence of the vertical motions in the risers and consequently allow the utilization of FPSOs
in deep waters, a new riser configuration called RSAA (riser suspended and moored by chains - in Portuguese), composed of a rigid
vertical riser, flexible structures and mooring line segments (top and bottom) was proposed. This configuration presents solutions
to the most critical points in a riser design: the top tensions are dissociated from the bending moments at the top region, and the
curvatures at the TDP are reduced by utilization of floaters.
Feasibility analyses have shown that the vertical riser is the most critical part of the proposed system due to the FPSO high level of vertical
motions. These motions are transmitted by the top chains, leading to high levels of axial stress variation due to dynamic tension. Faced
with this, a parametric study is vital in order to understand the system's behavior as well as to establish the main parameters which
influence its structural behavior. Analytical methods may require some slight simplifications of the problem to be applicable, but they
generally lead to very compact formulae that do explain which parameters influence the results and why and how it does so.
Considering some simplifying hypotheses, this work proposes an analytical model to determine axial stress and tension variations
at the top of the vertical riser. Neglecting some non-linearities but considering the coupling between axial and transversal vibrations,
a random dynamic analysis in the frequency domain can be performed to evaluate the maximum stresses and tensions levels with
considerably lower computational costs.
Keywords
Axial vibrations, analytical formulation, dynamic analysis
1
Introduction
Nowadays, the use of FPSOs in ultra deep waters and under severe environmental conditions is limited by several issues:
• The inexistence of flexible risers qualified to operate at such depths;
• High tensions and stresses at the top connections of steel catenary and lazy wave risers, due to the weight of the structures;
• High stresses at the TDZ (Touch Down Zone) due to the vertical motions developed by FPSOs;
• Fatigue, mainly at the TDP region of steel risers, both for the catenary and lazy wave configurations;
• Catenary and lazy wave steel risers need a great segment in contact with the soil to avoid tension at the wellhead. This fact may
present a problem if the platform has too many lines, or in the case of two platforms operating close.
The confirmation of the Pre-Salt reservoirs and PETROBRAS option for FPSOs, however, is forcing the development of new solutions
to the aforementioned problems. One of these solutions is a new riser conception, called RSAA (riser suspended and moored by chains
- in Portuguese), that allows the utilization of rigid risers associated with FPSOs. The main advantages of the proposed model are the
Submitted to MS&OT on Sep 11 2009. Revised manuscript received Apr 29 2010. Editor: Celso P. Pesce.
33
Parametric study on the axial vibrations of riser suspended and moored by chains (RSAA) configurations
Claudio Marcio S. Dantas, Marcos Q. de Siqueira, Victor M. da S. Pereira, Fernando Jorge M. de Sousa, José Renato M. de Sousa and Isaías Q. Masetti
dissociation of high tension and bending moments at the top
connection of the rigid riser (Sousa et al 2009, Dantas et al
2009 and LACEO 2009) and the reduction of the vertical
motions influence on the curvatures at the TDP region, due to
the use of floaters. Feasibility analyses have shown that the
vertical risers are the most strained parts due to the high level of
vertical motions of the FPSO transmitted by the top chains,
leading to accentuated levels of axial stress variation due to
dynamic tension (Masetti et al 2009).
Faced with this, a parametric study is vital in order to
understand the system's behavior as well as to establish the
main parameters which influence its structural behavior.
Analytical methods may require some slight simplifications of
the problem to be applicable, but they generally lead to very
compact formulae that do explain which, why and how
parameters influence results. Therefore, the main objective of
this work is to propose an analytical model to determine axial
stress and tension variation at the top of the vertical riser. The
analyses showed that the system has a linear behavior, and, in
this case, during the design phase, a random dynamic analysis
in the frequency domain can be performed to evaluate
maximum stresses and tensions levels acting on the system.
This methodology, which has lower computing costs when
compared to random simulations in time domain, allows the
fast assessment of the system response. Considering the
random characteristics of the environmental loads,
methodologies based on deterministic procedures can lead to
unrealistic dynamic responses, as the dynamic response is
dependent on the analysis period. The dynamic analysis
methodology in the frequency domain has already been
consolidated in SCR fatigue analyses (Dantas, 2004a, 2004b,
2005a and 2005b), helping as a tool for identifying the most
critical sea states for the structure. Only for these identified
sea states, non linear dynamic analyses are performed in time
domain to determine fatigue damage.
In this way, initially, the analytical solution that allows the
evaluation of the axial behavior of a fixed vertical riser is
presented. After that, the differential equation solution that
establishes the axial vibrations of hung-off risers considering a
concentrated mass at the lower end is deduced.
From these solutions, a procedure to evaluate the tension
variation of a vertical riser is proposed. Analytical results are
compared to ones obtained from non linear numerical analyses
in time domain considering several vertical motions levels,
periods and varying some parameters of riser's definition.
The analyzed examples consider the variation of several vertical
riser definition parameters, such as: installation depth, vertical riser
length, total mass per unit length (structure plus internal fluid),
vertical motion level and excitation periods. The vertical motion
levels considered are related to centenary waves acting on the FPSO.
All analyses performed in the parametric study considered
dynamic vertical motion as the only source of incident input
loading on the system. However, in a real world, riser designers
may consider several input loads acting on the structure, such
as current loading, static offset, wave loading acting directly
on the riser and finally the body floating motions from six
degrees of freedom. In this context, the use of an analytical
formulation may be an inadequate tool to predict the realistic
structural behavior. Therefore, as the structural behavior of the
proposed systems seems to be linear, the determination of the
riser response by random dynamic analysis in frequency
domain, considering all inputs loads, is convenient.
Random dynamic analyses both in time domain and frequency
domain were carried out considering current loads, static offset,
wave loading acting directly on the system and dynamic
motions from six degrees of freedom of the FPSO. The
obtained results demonstrated good agreements among these
random dynamic analysis methodologies.
The analyses performed showed that the proposed system does
not have any resonant frequency within the commonly
encountered wave frequency range. In certain circumstances, a
hung off riser may present axial resonant behavior amplifying the
structural response. For a 20in vertical riser Chung (1991) showed
that the natural periods may occur within wave period range.
2
System description
The proposed configuration is constituted by a steel vertical
riser that is supported by a mooring line segment and
connected to the FPSO through a flexible jumper, as shown in
Figure 1. The transmission of bending moments to the steel
riser is consequently minimized, reducing the stresses at the
top of the riser. In the same way, the steel riser is connected to
the flowline by another flexible structure or a bundle of flexible
structures, as indicated in Figure 2; in this case, floaters help to
reduce bending moments at the TDZ. At the bottom
connection of the vertical riser, a slack mooring line segment
helps to keep the system correctly positioned and increase
restoring forces when the vertical riser moves upward. This
chain segment length has to be dimensioned not to stretch
the system even in the farthest position, but just enough to
keep the system in the same position under strong sea currents.
Finally, the connections between the flexible structures and
the vertical riser and between the mooring line segments and
the vertical riser, are made by steel connectors ("Y" shape)
(Sousa et al 2009, Dantas et al 2009).
Fig. 1
Main components of the original proposed system.
34
3
Axial vibrations of vertical risers
Analytical methods may require some slight simplifications
of the problem to be applicable, but they generally lead to
very compact formulae that do explain which, why and how
parameters influence the structure response. Furthermore,
those compact formulae are often very simple to program
and hence can be useful for preliminary analyses. Those two
reasons are the main motivations to the application of
analytical methods.
3.1
Axial vibrations of fixed risers
Figure 3-a shows a vertical uniform riser subjected to a topend sinusoidal movement of amplitude U0 and frequency
w, where u is the dynamic vertical displacement and, hence,
du/dx is the dynamic strain.
Figure 3-b shows the internal dynamic axial forces acting on a
short element of length δx and mass m per unit length. The
dynamic axial force is related to the local strain by:
(1)
where E is the riser material Young modulus and A is the
cross-sectional area. Since the mass-acceleration of the element
is equal to the applied force, from figure 3-b,
(a)
(2)
Hence,
(3)
Equation (3) is the wave equation, which can be written as:
(4)
where c is the celerity, speed of transmission of axial stress
waves in the riser, which, from Equations (3) and (4) can be
expressed as:
(5)
Note that if the riser mass is entirely structural, with no
additional mass in the form of buoyancy modules, then
and
, where is the mass density of the riser
material.
For the configuration shown in Figure 3-a, the vertical
displacement at distance x below the top end is given by the
solution to Equation (4) which yields:
(b)
(6)
Fig. 2
35
RSAA system composed by only 1 line (a) and
configured as a bundle (b)
The dynamic tension is related to the local strain by Equation
(1). By differentiating Equation (6) and considering Equation
(1), the dynamic tension is given by:
(7)
Hence, the amplitude of the top-end (x = 0) dynamic tension is:
(8)
Axial resonance occurs when the denominators of Equations
(6) and (7) are zero, for frequencies wn given by Equation (9)
for which sin(wnL / c) = 0, where n is the mode number:
3.1.1 Numerical analysis
Analyses were performed considering the structure showed
in Figure 4. The results obtained from analytical Equation
(7) were compared to the ones considering non linear
dynamic analyses using the finite element method (ANFLEX,
2008). The riser was modeled considering three-dimensional
beam elements and the non linear analysis was carried out
according to the Newton Raphson method adapted to
dynamic problems.
(9)
Since wn= 2π/Tpn, where Tpn is the period of the vibration for
mode n , resonance occurs for natural periods Tpn given by:
(10)
(a)
Fig. 4
Axial vibrations of fixed risers - analyzed case.
The main characteristics of the problem are:
• Riser length • Young's modulus of steel:
• Mass per unit length:
(b)
(structural and internal
fluid)
• Celerity:
• Sinusoidal movement of amplitude:
• Periods:
Fig. 3
Axial vibrations of fixed risers and internal forces.
Figure 5 shows the dynamic tension results at the top of the
fixed vertical riser obtained from both analytical and numerical
36
procedures. This figure indicates excellent agreement between
the obtained results.
Analysis of axial vibrations of hung off risers is more complicated
than for fixed risers for several reasons. First, the risers generally
have a large concentrated mass at the lower end in the form of
a lower marine riser package (LMRP) or blowout preventer
(BOP). Second, the resonant response depends on short period
heave of the vessel and on the riser axial damping, both of which
are difficult to determine precisely.
Nevertheless, a similar approach to the fixed riser can be used
to determine resonance frequencies and understand the
parameters influence on the results
3..2.1 Uniform riser
Fig. 5
Axial Vibrations of fixed risers - Analyzed case.
3.2
Axial vibrations of hung-off risers
Axial vibration is of particular concern for drilling risers
hung off drilling vessels in storm conditions. In such
conditions, hung off risers are subjected to axial excitation
induced by the floating body. The problem is that
unacceptably large axial forces may be induced in the riser,
which may even lead to dynamic buckling. The subject has
been treated in a number of publications in recent years
(Sparks, 2007). Figure 6 shows three riser models that can be
studied analytically.
Figure 6a shows a uniform riser, which can be analyzed very
easily by using equations similar to those of the previous problem.
In this case, the tension TL at the riser bottom end is always
zero. Hence, from the tension-strain relationship, Equation
(1),
. Therefore, the wave equation yields
the following solutions for the displacement u(x,t) and the
dynamic tension T(x,t) at distance below the top end:
(11a)
and
(11b)
Axial resonance occurs for
. Since the period
resonance occurs at periods given by:
, for which
,
(12)
M
where n is the mode number and n=1 denotes the
fundamental. The fundamental resonant period is therefore
equal to 4L/c, which is the time taken by the axial stress wave
to run four times the length of the riser.
3.2.2 Uniform Riser with Concentrated Mass at
Lower End
For a riser with a concentrated mass M at the lower end,
Figure 6b, the analysis is more complicated. The wave equation
is satisfied by:
(13)
where B0 is a constant that depends on the concentrated
mass at the lower end. The constant B0 can be determined
by considering the forces that act on the concentrated mass
at the lower end, as given by:
Fig. 6
37
(14)
Analytical hung off riser models.
where the left-hand side of the equation is the force
resulting from the riser dynamic strain and the right-hand
side is the inertial force of the concentrated mass.
Substitution of Equation (13) into Equation (14) leads to
the value of B0:
where is the mode number. The resonance period is given by:
(15)
(23)
The constant B0 can be expressed in terms of a new constant
defined by:
Hence, the fundamental resonant period Tp1 is equal to the
time taken by an axial stress wave to run four times the riser
equivalent length .
(16)
Substitution for B0 in Equation (15) then leads to:
(17)
(22)
For the structure shown in Figure 7 several analyses were carried
out in which different relations between the concentrated
mass M and the total riser mass were considered. The total
riser mass is given by MRiser = m.L. The analytical results
considering M = 0 are given by Equation (12) while for
Equations (17) and (19) are employed.
Substitution of B0 into Equation (13) leads to Equation (18)
for the axial displacement at distance x from the top end.
(18)
Since
, the dynamic tension is given by:
(19)
By comparison of Equations (11b) and (19), it can be seen
that is an equivalent length of uniform riser, as shown in
figure 6c. Note that for small angles, Equation (17) can be
written as:
(20)
and
(21)
Fig. 7
Axial vibrations of hung off risers - analyzed case.
The riser behaves as if its length were extended by M/m.
Equation (21) gives the maximum value of . As the frequency
increases, the precise value of is reduced. From Equations
(18) and (19), resonance occurs for
hence, for values of
given by:
The main characteristics of the problems analyzed are:
• Riser length -
and,
• Young's modulus of steel:
38
• Mass per unit length:
(structural and
internal fluid)
• Concentrated mass:
systems. This can be observed at Figure 10 and Table 1.
That condition is required to avoid a great lateral response
on the riser if parametric instability occurs;
d) The suspended mass of the flexible riser and bottom chain
do not vary so much when compared to the total mass of
the system. In this way, the expressions established for a
hung off vertical riser with a concentrated mass M at the
lower end can be employed .
;
(20% of the riser mass) ;
(40% of the riser mass)
• Celerity:
• Sinusoidal movement of amplitude:
In the simplified structural model, the bottom arrangement is
represented by a static tension acting at the lower end of the
vertical riser, as in Figure 9b. In this way, the expressions
established for a hung off vertical riser with a concentrated
mass M at the lower end, can be employed considering the
definition of an equivalent mass M given by:
• Periods:
Figure 8 shows the dynamic tension results at the top of the vertical
riser obtained from both numerical and analytical procedures. This
figure points excellent agreement between all results.
(24)
where g is the gravitational acceleration.
Due to the vertical dynamic motions originated by the incident
waves in the floating production system, the tension T is
influenced by dynamic effects and by the vertical force that
the bottom arrangement provides to the system. As the
variation of the resistance force is small when compared to
the total tension at the top of the vertical riser, it is possible to
consider it as a constant (static) value and propose a procedure
to determine the tension variation at the top of the vertical
riser. This procedure has demonstrated excellent agreement
when compared to the numerical results obtained considering
the full structural model using a FEM program.
Fig. 8
Axial vibrations of hung off risers - analyzed case.
3.3
Axial Vibrations of the Proposed
System
The comparative analyses were performed considering several
variations of the system configuration parameters. In this
parametric study the following modeling and loading
parameters were varied: vertical riser length and water depth;
mass per unit length of the vertical riser including structural
and internal fluid mass; vertical amplitude motion; and vertical
period motion.
Figure 9 shows the proposed system configuration. Under some
considerations, the main point here is to establish an analytical
formulation to allow the evaluation of the dynamic tension
level at the top of the vertical riser.
3.3.1 Basics hypotheses
a) Although the vertical riser is not directly connected to the
floating system, the vertical motions imposed by the
floating are completely transmitted by the top chain to the
top riser (the top chain is always tensioned);
(a)
b) The analytical model ignore the coupling between axial
and transversal vibrations, which can be a potential source
of non linear behavior;
c) The heave periods are not close to natural periods of the
39
(b)
Fig. 9
Non linear dynamic analyses were performed considering the
original structural model shown in Figure 9a. From Equations
(19), (21) and (24), the analytical procedure was applied to
evaluate the simplified structural model shown in Figure 9b.
The tension T and the related concentrated mass M, calculated
by Equation (24), have the same values presented in Table 1.
Figure 11 shows the dynamic tension at the top of the vertical
riser, considering the original system configuration and varying
the riser mass per unit length. Figure 12 shows both numerical
and analytical results considering the original model (M2)
and varying the water depth.
Axial vibrations of the proposed system.
The amplitudes and periods of the vertical motions considered
in this example are related to centenary waves with periods
from 5.0 seconds to 19.0 seconds acting on the FPSO,
producing the results shown in Figure 10. This figure shows
that the vertical amplitude values are varying from zero to
13.0m, whilst the vertical period values are varying from 6.5
seconds to 15.0 seconds. In this item, six riser models were
analyzed and the riser modeling data are shown in Table 1.
Fig. 11 Results for M2 models, see table 1
Fig. 12 Results for M1, M2, M3 and M4 riser models, see
table 1.
Fig. 10 Amplitudes of the vertical movements.
Table 1 - Description of the risers.
Figures 11 and 12 indicate that, even for high levels of vertical
movements, the results provided by the analytical model agree
quite well with the ones from the numerical model. Hence, it
can be concluded that, under the simplifying hypotheses
assumed, the proposed analytical model is a helpful and reliable
tool to account for a number of parameters in the analysis of
RSAA configurations.
4
Frequency domain analysis
Agreement among results from both analytical and numerical
procedures shows that the system behavior does not present
significant non linearities. It suggests that the dynamic analysis
40
in frequency domain can be performed during the riser design
phase. This analysis methodology allows consideration of a
complete set of environmental loading cases, keeping their
random nature, however with low computing costs. The FEM
used in this methodology allows consideration of coupling
between axial and transversal vibration due to beam matrix.
The use of the frequency domain analysis is well established
for SCR fatigue analyses. One o its most important applications
is the identification of the most critical analysis loading cases,
avoiding a high computer time for processing all loading cases
and, consequently, reducing the impact on the design schedule.
The dynamic finite element equations of motions are typically
expressed in matrix form as:
(25)
where the symbols in uppercase bold letters denote matrices
and in lowercase letters vectors. The major dynamic
contribution to the force vector comes from wave forces and
from vessel motions imposed at the top of the risers.
In general, Equation (25) has no closed form solution for
the dynamic response x(t), so the solution must be found
numerically in either the time or in the frequency domain.
The frequency domain approach demands linearization
techniques, implying in a certain lack of quality in results,
but it is attractive due to the lower computer time demanded
and because there is no "statistical uncertainty" associated
with the results of the random sea analyses, since the input
and output are respectively wave and response spectra. The
frequency domain derivation assumes that the inputs and
outputs are sinusoids or summations of sinusoids if the
procedure is random analysis. So for an irregular wave with
frequencies wn:
and
(26)
where and are complex vectors, with both amplitude and
phase information. Differentiating for
and
and
replacing into equation (25) gives:
(27)
Canceling
for .
from both sides, equation (27) can be solved
(28)
Notice that, in deriving Equation (27), it is assumed that
M, C and K do not vary with time. This assumption is not
valid when geometric nonlinearities are important or when
intermittent effects, such as seabed interaction, occur.
A major difficulty with the above derivation is that Equation
(26) for f(t) is not valid for the drag force in Morison's equation.
The drag is nonlinear (proportional to the square of the relative
velocity), but a drag linearization technique can be used to
derive a reasonable approximation.
41
The first studies dealing with linearization techniques applied
on risers were conducted for two-dimensional problems with
and without current velocity and without considering
structural velocity. After that, Krolikowisk and Gay
(Krolikowisk,1980) extended the model considering
excitations of random and deterministic nature taking into
account the relative fluid-structure velocity for vertical
structural elements. For two-dimensional problems the
linearization process of the drag force is resumed into the
linearization of a scalar, since the incident loading is aligned
in one of the normal directions of the analyzed element.
A proposal that allowed considering the linearization and also
addresses the distribution of the excitation was conducted by
Langley (Langley, 1984) and later by Rodenbusch (Rodenbusch
et al, 1986). Bernt J. Leira (Leira, 1986, 1987) proposed another
linearization technique that developed even more Langley's
expression for dynamic linearization coefficients using the
results obtained by Atalik (Atalik et al, 1976). These methods
are also presented and discussed by Dantas (Dantas 2000,
2004a). The structural analysis program (ALFREQ, 2008) used
in the linear dynamic analyses conducted in this work allows
the consideration of several 3D linearization methods (Dantas
et al, 2004b).
All the previous analyses considered dynamic vertical motion
as the only source of incident input loading on the system.
However, in a real world, riser designers may consider several
input loads acting on the structure, such as current loading,
static offset, wave loading acting directly on the riser and
finally the body floating motions from six degrees of freedom.
In this context, the use of an analytical formulation may be
an inadequate tool to predict the realistic coupling between
axial and transversal behavior. Therefore, as the structural
behavior of the proposed systems seem to be linear, the
determination of the riser response by random dynamic
analysis in frequency domain, considering all inputs loads, is
convenient.
Random dynamic analyses were carried out considering
current loads, static offset, wave loading acting directly on the
system and dynamic motions from six degrees of freedom of
the FPSO. The waves considered here are the same centenary
ones considered above. The analyses performed in time domain
considered 1200 seconds of time simulation, each one
demanding 9 hours of computer processing time. The analyses
performed in frequency domain employed an iterative
procedure due to the relative velocity fluid-structure present
in the Morrison equation, and each one demanded 15 minutes
of computer processing time.
Figure 13 shows the results in terms of axial stress standard
deviation at the riser top considering the centenary waves
with period varying from 5.0 seconds to 19.0 seconds. We can
observe excellent agreement within results, demonstrating that
the dynamic frequency domain methodology can be a helpful
tool to predict the structural behavior of the proposed system
during the design phase.
In a future work, this linear procedure will be employed to
perform random dynamic analyses of the proposed system
considering several loading cases and the obtained results will
be compared to the ones obtained from random dynamic
analysis in time domain.
analytical model is a helpful and reliable tool to account for a
number of parameters in the analysis of RSAA configurations.
Furthermore, these results showed that if the structural behavior
of the proposed system does not present significant non
linearities, a random frequency domain methodology can be
applied during preliminary feasibility analyses. This
methodology, due to its lower computing costs, can be applied
to explore a range of alternatives, vary several parameters which
define the system, and consider all the input loads.
In the near future, this linear procedure will be applied to
perform random dynamic analyses of the proposed system
considering several loading cases and the obtained results will
be compared to ones obtained in non linear random dynamic
analysis in time domain.
Fig. 13 Axial stress standard deviation at the top riser.
5
Concluding remarks
The system called RSAA (riser suspended and moored by chains
- in Portuguese) is composed by a rigid vertical riser, flexible
structures and mooring line segments (top and bottom).
Feasibility analyses have shown that the vertical riser is the
most critical part of the system due to the high level of vertical
motions of the FPSO transmitted by the top chains, leading
to high levels of axial stress variation due to dynamic tension.
Faced with this, some analyses were performed in order to
understand the system's behavior as well as to establish the
main parameters which affect its structural behavior and why
and how it does so. The main objective of this work was to
propose an analytical model to determine axial stress and
tension variation at the top of the vertical riser.
In this work the axial stress wave equation has been derived,
and the axial displacements and dynamic tension equations
have been deduced for both fixed and hung off risers. Several
examples were analyzed and excellent agreement between
numerical and analytical procedures was observed. From these
equations and assuming some conditions, an analytical
procedure to determine the dynamic axial stress and tension
variation throughout the vertical riser of the RSAA was
proposed. Analytical results have been compared to ones
obtained in non linear numerical analyses in time domain
considering several vertical motion levels, periods and some
riser models. The examples considered the variation of several
vertical riser definition parameters, such as: installation depth,
vertical riser length, total mass per unit length (structure plus
internal fluid), vertical motion level and excitation periods.
These analyses indicated that, even for high levels of vertical
movements, the analytical model showed agreement with the
numerical results. The maximum observed differences were
of the order of 10%.
Under the simplifying hypotheses assumed, the proposed
Acknowledgments
The authors thank PETROBRAS for sponsoring this work and
allowing us to publish this paper. The authors would like to
thank also some post-graduating students from LACEO/
COPPE/UFRJ - Laboratory of Analysis and Reliability of
Offshore Structures of the Engineering Post-Graduating
Coordination of the Federal University of Rio de Janeiro, for
their contribution performing computer analyses.
References
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43
Evolution of the MPSO (monocolumn production, storage and offloading system)
Rodolfo T. Gonçalves, Fabio T. Matsumoto, Edgard B. Malta, Guilherme F. Rosetti,
André L. C. Fujarra and Kazuo Nishimoto
TPN - Numerical Offshore Tank
Department of Naval Architecture and Ocean Engineering, Escola Politécnica - University of São Paulo, Brazil
[email protected], [email protected], [email protected], [email protected], [email protected],
[email protected]
Abstract
One of the most difficult challenges in the offshore industry is to reduce hydrocarbon production costs, which increase as exploration
advances to deeper water regions. Most of the Brazilian oil companies demand the use of a conventional ship-shaped FPSO
(Floating Production, Storage and Offloading System) as a solution for offshore production due to the lack of pipelines, soft local
environmental condition, and the characteristics of the oil fields. However, the small roll damping and the relatively large heave
motions of the FPSO pose some limits to the use of rigid risers and nearly forbid the use of dry tree completion system facilities.
In order to make the application of rigid risers and dry tree completion feasible on an FPSO, Brazilian universities and research
institutes, in a partnership with Petrobras, have developed a new concept of a hydrocarbon exploration and production platform –
the MPSO (Monocolumn Production Storage and Offloading System) – which is a floating unit based on a monocolumn with a
moonpool.
The development of the MPSO concept was focused on reducing the motions, keeping storage capability and allowing the use of
rigid risers. Furthermore, recent studies have pointed towards the possibility of using dry tree completion system in MPSO.
Considering this scenario, the MPSO concept evolution in which the hull forms and hydrodynamic appendages were developed,
always aiming at motions mitigation, is presented herein. Initially, the MPSO was proposed to operate in the Campos Basin (Brazil)
and, after new design considerations, it is being adopted to operate in the Gulf of Mexico (USA) at a no pipeline area. Thus, the
MPSO solution proved to be versatile enough to be adapted to any location, including the pre-salt in Brazil.
Keywords
MPSO (Monocolumn Production, Storage and Offloading System), offshore platform, hydrodynamic behavior, platform design,
new platform concept
1
Introduction
In the last few years, an increasing number of gas and oil production platforms have been developed in order to obtain more
efficient floating systems, capable of operating in deep (>500m) and ultra-deep (>1700m) waters and with a greater capacity for
storing and processing oil and gas.
There are several distinct types of oil platforms, employed according to the characteristics and needs of the field where they are
installed. Platform types range from conventional ship-shaped FPSO to innovative concepts such as monocolumn platforms. A
summary of these systems evolution is found in Clauss (2007). That text presents the characteristics of fixed, semisubmersible, TLP
(tension leg platform), spar and monocolumn platforms. Examples of such types of platforms are presented in Figure 1. petroleum
chain. Thus, a system able to acquire information, integrate data adequately and evaluate the capacities of the resources must be a
great triumph for this field of study.
Submitted to MS&OT on Nov 11 2009. Revised manuscript received Jul 12 2010. Editor: Celso P. Pesce.
45
Rodolfo TT.. Gonçalves, Fabio TT.. Matsumoto, Edgar
me FF.. Rosetti, André L. C. Fujar
Edgardd B. Malta, Guilher
Guilherme
Fujarra
ra and Kazuo Nishimoto
The aim is to summarize, into a single work, the most
important developments of the MPSO, mainly involving
aspects such as geometry, hydrodynamic behavior, stability and
mooring/risers design, over the past 10 years of research. This
new concept has incorporated technological solutions as no
other similar work in the world, including the recognition of
more than one related patent.
Fig. 1
Thereby, section 2 presents the monocolumn concept with
further details on its geometry and features. Section 3
demonstrates its evolution on hydrodynamic behavior. Section
4 provides a general view on its stability characteristics and
section 5 on riser and mooring systems. Finally, section 6
presents some conclusions about monocolumns.
Examples of offshore oil exploration systems
[Gonçalves et al. ( 2007)].
To summarize, the basic idea behind floating systems is to
provide a system with natural periods of motion as far as
possible from the wave power spectrum peak at the location
where it will be installed, in order to avoid high motion levels
suited for the sea. For example, an easier way to better
understand this strategy is to compare the natural heave motion
period of the unit with the energy wave spectrum of the region
where it is installed. In Figure 2, three typical sea spectra regions
where a great part of offshore producing systems is concentrated
are presented: the Campos Basin (Brazil) and the Gulf of
Mexico (USA). In the same figure, the typical heave motion
natural periods of typical units are also included.
2
Considering its geometry with a cylindrical shape, the
monocolumn with a moonpool hereafter called MPSO is
similar to the spar platform, as can be exemplified in works by
Rueda et al. (2006), Campos (2008) and Matsumoto et al.
(2008), and seen in Figure 3. However, an important difference
can be found between the aspect ratios (L/D, length/diameter);
mainly because the spar platform has a large value of L/D,
while the MPSO has a small one (smaller draft and larger
diameter). Additionally, compared to the spar, the MPSO due
to its large displacement can support heavier process plants
and greater production storage.
Fig. 3
Fig. 2
Comparison between the resonance of systems and sea
spectrums [Malta (2009)].
As can be observed in Figure 2, the RAO (response amplitude
operator) of the TLP, monocolumn and spar platforms are
detuned from the wave energy spectrum, which, in this case,
implies the decrease of the heave motion. These conditions
allow the employment of dry completion systems.
Since floating unit motions due to waves, currents and winds
can damage equipment that would be launched towards the
oil wells, reduced motions are desirable. Regarding these aspects,
the monocolumn concept was developed: a platform with
high natural motion periods, outside the high energy density
region in the wave spectrum and with a relatively simple
geometry – as can be seen in Figure 2, illustrating the MonoBR,
a monocolumn platform with a moonpool, appropriately
design to operate at the Campos Basin, in Brazil.
Monocolumn with a moonpool
concept
Examples of MPSO platforms (a) cylindrical hull
[Campos (2008)], (b) polygonal hull [Rueda et al.
(2006)] and (c) cylindrical hull with hydrodynamic
appendages [Matsumoto et al. (2008)].
A practical function of the moonpool is to allow free access of
risers and umbilical cables from the field to the process plant,
and the large volume of the moonpool takes an important
role in the MPSO dynamic behavior, acting as passive motion
absorber; the works by Torres et al. (2004a-b), Barreira et al.
(2005), Cueva et al. (2005), Malta et al. (2006), Sphaier et al.
(2007) and Torres et al. (2008b) are examples in which the
moonpool geometry were studied.
Figure 3c shows the internal moonpool with hydrodynamic
appendages at the bottom, details about the hydrodynamic
appendages can be found further on in this text and especially
in the works by Masetti (2007) and Matsumoto et al. (2008).
Also, Figure 3c illustrates the internal tank arrangement
composed by internal and external ballast tanks and central
46
Guilherme
Fujarra
oil storage tanks, making this conception totally double hull.
Discussions about the stability advantages to use this type of
tank arrangement were presented in Rueda et al. (2006) and
Santos et al. (2006). Besides the dynamic features and storage
capability, the MPSO has a great reserve of stability, not only
because of the large water area but also because of this area
distribution along the hull. The moonpool leads the water area
to an external region increasing the moment of area and,
consequently, the metacentric height. Another characteristic of
the MPSO is its low construction cost due to the simplified
geometry concept; however, it demands larger shipyards for its
construction, due to its large diameters; more characteristics of
the MPSO concept can also be found, for example, in Costa et
al. (2005), Reyes et al. (2007) and Masetti & Malta (2009).
Historically, the monocolumn concept considering a
moonpool was initially developed by the University of São
Paulo and Petrobras, as the main design objective for the
vertical motion mitigation.
The first MPSO project presented a cylindrical shape, as
illustrated by Masetti & Malta (2009) in Figure 5, with a simple
radial symmetry, which enables great inertia at the waterline
implying stability reserve for the unit. Furthermore, the circular
shape makes hydrodynamic and stability analysis easier.
However, due to a circular geometry with diameter around
100 meters, the difficulty of construction makes this solution
less feasible in economic terms.
Several types of hulls, with different motion and stability
responses, can be designed from the monocolumn main
concept. There are some examples with circular or polygonal
transversal sections created to be employed according to the
operation type at a given field. Also, there is the possibility of
designing monocolumn platforms without a moonpool, such
as the ones installed by the Sevan Marine Company.
In a partnership with Petrobras, the Sevan Marine Company
commissioned the SSP-Piranema, a first monocolumn
production unit without a moonpool, see Figure 4b. The SSPPiranema has a production capacity of 30 thousand barrels of
oil per day and storage capacity for 300 thousand barrels of oil
in water depth of 1100 to 1600 m; details of the unit can be
seen in Saad et al. (2009). Another monocolumn without a
moonpool was also created by Sevan Marine to operate in the
North Sea, as illustrated in Figure 4a. It is important to point
out that these platforms do not have moonpools, and therefore
they present motions equivalent to a conventional FPSO, as
well as restriction of storage capacity and difficulties to operate
under severe sea conditions.
Fig. 5
Based on this argument, it was proposed that the MPSO could
present a square transversal section, making its construction
process easier. However, regarding hydrodynamic effects, a
square hull presents worse results when compared to a circular
hull. After some analysis, it was confirmed that the MPSO
shaped, illustrated by Masetti & Malta (2009) and shown in
Figure 6, even with rounded edges, increases the drag due to
the current caused by the platform, which damages the risers
and mooring system, and can cause unwanted production
interruptions. Another drawback of a square hull is the loss of
the valuable axial symmetry.
Fig. 6
Fig. 4
47
Installed monocolumn platforms: (a) FPSO Sevan
Hummingbird and (b) FPSO Sevan Piranema. Pictures
taken by the Sevan Marine company.
MPSO example with cylindrical shape [Masetti &
Malta (2009)].
MPSO example with a square shape and rounded edges
[Masetti & Malta (2009)].
A compromise solution was found based on a multifaceted polygonal shape, as seen in Masetti & Malta
(2009) and in Figure 7. The construction problem was
solved and the platform has practically kept all the
advantages of a circular hull. Following the definition of
the external geometry of the MPSO hull, the next step
was to improve the unit hydrodynamic characteristics by
studying hydrodynamic appendages and the moonpool
geometry.
Guilherme
Fujarra
on the system. The use of a moonpool as a passive damper of
monocolumn motions has been studied for years. Concerning
the tests using small-scale models in test tanks, as can been seen
in Figure 9, the works by Torres et al. (2004b), Barreira et al.
(2005) and Sphaier et al. (2007) can be cited; and concerning
numerical/mathematical models to represent the moonpool
behavior, the works by Torres et al. (2004a), Cueva et al. (2005),
Malta et al. (2006) and Torres et al. (2008a-b) can be cited.
Fig. 7
MPSO example with a 16 side polygonal shape
[Masetti & Malta (2009)].
3
Hydrodynamic characteristics
The employment of devices to minimize motion such as
moonpools, skirts and beaches, see Figure 8, has been studied
in order to reduce the platform motion without the need to
increase its displacement. These devices have as main function
to introduce viscous damping and to modify the natural
frequency of the system, displacing it to a region outside the
high energy wave spectrum, as presented in Figure 2.
The characteristics of these devices and studies on them are
detailed separately in this paper, as well as other solutions such
as one to mitigate the vortex-induced motions (a phenomenon
that may amplify surge and sway motions) and another hull
inside the moonpool to allow the application of dry tree
completion. These two latter solutions are good examples of
the mentioned innovation concerning the MPSO concept.
Fig. 8
Devices employed to improve the hydrodynamic
performance of monocolumns: a) Moonpool, (b) Skirt
and (c) Beach [Campos et al. (2004b)].
3.1
The moonpool
The moonpool is an opening inside the hull, platform or
chamber giving access to the water below and allowing
technicians or researchers to lower tools and instruments into
to the sea, see Figure 8a. Moreover, studies, such as the work by
Nishimoto et al. (2001), investigated the use of the moonpool
as a passive tank to reduce vertical platform motions modifying
its aspect ratio (ratio between the moonpool diameter and the
external platform diameter). In a MPSO, the moonpool
geometry was designed to have a resonant period far from the
sea energy spectrum. The moonpool resonant period is mainly
defined by the relation between its diameter and height,
although the moonpool can be modified by introducing a
restriction near the bottom that increases the viscous dissipation
Fig. 9
Examples of reduced scale models of MPSO platforms:
a) wave tests [Campos (2008)] and (b) current tests
[Fujarra et al. (2009)].
Studies such as Torres et al. (2004b), Barreira et al. (2005) and
Sphaier et al. (2007) show a series of experimental results for
the evaluation of the moonpool diameter with regards to the
heave motions of a monocolumn. In those tests, variations in
moonpool diameter (D) are evaluated for a fixed waterline
area of the unit, see details in Figure 10.
The results of the vertical motions presented by Sphaier et al.
(2007) demonstrated that it is possible to modify the natural heave
motion period of the MPSO by altering the opening of the
moonpool. Thus, there is an optimum relation in which the motions
decrease, as can be verified in Figure 10 by the green line.
Fig. 10 Heave motion RAO for different openings of a
moonpool [Sphaier et al. (2007)].
48
Guilherme
Fujarra
Another alternative to decrease the vertical heave motion of
the unit is to change the entrance geometry of the moonpool.
In the study by Barreira et al. (2005), this change is suggested
by changing the reentrance and therefore the water flow through
it; see details in Figure 11a. The results have shown that such a
modification is not as efficient in changing the entrance of
the moonpool to a cross-like format as shown in Figure 11b.
the works by Masetti et al. (2007) and Matsumoto et al.
(2008). Figure 8b and Figure 12c show the structures used as
bilge keel located on the external side of the hull and inside
the moonpool; hereafter these structures are denominated
external and internal skirt, respectively.
Fig. 12 Influence of skirt types on MPSO motion [Matsumoto
et al. (2008)]: (a) heave RAO (b) pitch RAO.
Fig. 11 Heave motion RAO for different types of moonpool
entrances [Barreira et al. (2005)]. (a) Internal
reentrance and (b) Cross shaped restriction.
For the format shown in the Figure 11b, the results present a
reasonable heave motion decrease. However, this solution
presents difficulties to construction.
Aside those minor aspects, the conclusion concerning the
monpool issue is that alterations in its geometry are absolutely
important to minimize the heave motion of the unit, which is
another requirement to be taken into account during the
preliminary design stages.
3.2
The skirt
The bilge keel is commonly used to add viscous damping to a
ship-shaped vessel. The bilge keel efficiency is a compromise
between the decrease in roll motion amplitude and the increase
of the resistance introduced by additional wetted surface.
However, offshore production systems such as MPSO are
stationary and appendages similar to bilge keels can be used
without forward speed resistance concerns; see for example
49
As can be seen in Figure 12, both external and internal skirt
have a tumbled “T” geometry such that a portion of water can
be confined leading to an increase of two hydrodynamic effects:
added mass and viscous damping.
Studies regarding the influence of skirt type appendages on a
MPSO hydrodynamic behavior were carried out by Masetti et al.
(2007) and also by Matsumoto et al. (2008). Particularly in the
latter work, tests were performed with small-scale models
presenting the following configurations: SS (MPSO without
appendages), SR (MPSO with internal skirt only), CS (MPSO
with external skirt only) and CR (MPSO with external and
internal skirts). Configuration details are presented in Figure 12.
The principal results obtained by Matsumoto et al. (2008)
showed that the use of this type of hydrodynamic appendage
has the ability to significantly modify the natural period of
vertical motions: heave and pitch, shown in Figure 12a and
Figure 12b, respectively. This effect is mainly due to the change
in the added mass contributions caused by the presence of the
appendage.
Consequently, the design of the skirts also becomes an
important issue in a MPSO design, in order to minimize the
unit motions.
Guilherme
Fujarra
3.3
The beach
The beach is a “quasi” horizontal level formed by reducing the
MPSO hull in diameter near the waterline area; see details in
Figure 8c. The main objective of this reduction is to modify
the natural period of the vertical motions (heave, roll and
pitch) by decreasing the waterline area. If damage occurs in
tanks, the increase in the waterline area obtained due to the
change in diameter can also contribute to the stability.
Numerical studies to determine the characteristics of the beach,
such as its angle and position in relation to the waterline, are
presented in Torres et al. (2004b). According to the authors, it
is very important to consider this hydrodynamic element in a
MPSO design because it is possible to decrease the heave exciting
forces by up to 40%.
3.4
spoiler plates decreases the motion amplitudes probably
due to the break in the correlation of the formation of
vortex shedding. However, as in the case of strakes normally
utilized on spar type platforms, e.g. Roddier et al. (2009),
different configurations of spoiler plates should be tested
to prove their efficiency in mitigating the VIM
phenomenon on a MPSO.
3.5
Two bodies
A new MPSO system concept with two bodies was proposed
by Gonçalves et al. (2008). This innovative offshore platform
combines characteristics of storage capacity and dry tree
completion system.
Spoiler plates
The VIM (Vortex-Induced Motion) is a self-excited
phenomenon, likely to occur on bluff bodies immersed and
free to oscillate in specific fluid flow caused by ocean current,
resulting in offset amplitudes similar to the unit diameter; see
details about the phenomenon in Gonçalves et al. (2009b).
Thus, on spar and monocolumn type platforms, the VIM
causes greater offsets, eventually having consequences, such as
extreme tensions and early fatigue of the mooring lines and
risers; see details in Sagrilo et al. (2009).
Fig. 13 (a) Example of a MPSO with the presence of spoiler
plates (b) Motion on the MPSO horizontal plane,
without the presence of spoiler plates, submitted to the
VIM phenomenon (c) Motion on the MPSO
horizontal plane, with the presence of spoiler plates,
submitted to the VIM phenomenon [Fujarra et al.
(2009)].
The spoiler plates are flat structures fixed on the side of the
platform aiming to minimize the effects of the VIM
phenomenon. They can be arranged, e.g. in triple helicoid
along its depth, as observed in Figure 13a, this solution is
patented. These appendages demonstrated great efficiency in
mitigating motions of high amplitude caused by the VIM,
according to the results seen in Cueva et al. (2006), Gonçalves
et al. (2009a) and Fujarra et al. (2009).
In Figure 13b, the motion tests results in the horizontal plane
of a MPSO submitted to the VIM phenomenon are presented.
In the graph, Vr is the reduced velocity, the radius represents
the MPSO offset and the angles represent the current
incidence. Figure 13c presents the results of the same platform
with spoiler plates. It can be observed that the presence of
Fig. 14 General view of the MPSO concept with dry
completion and two bodies (a) taken from Gonçalves
et al. (2008) and (b) taken from Reyes et al. (2009).
In order to have these characteristics, the new concept
comprises two floating units, one inside the other. The external
one, called main body, has storage capacity; supports the process
plant, the accommodations and the well intervention tower.
The internal unit, called inner body, is designed to support the
well heads, the tensioners and riser connectors, as presented
in Figure 14. It is important to point out that one of the many
advantages in dry tree completion systems is to avoid umbilicals
for intervention, manipulation and control.
The inner body heave motion is mechanically uncoupled from
the main unit, resulting in smaller motions, which allows for
dry tree completion facilities and lower operational system
cost. Both works by Gonçalves et al. (2008) and by Reyes et al.
(2009) demonstrated the concept feasibility, thus allowing
this prospective system to be used for the new well explorations
in the pre-salt of the Santos basin, Brazil.
50
Guilherme
Fujarra
4
Stability characteristics
The MPSO with moonpool, as described earlier, presents a
great reserve of stability, mainly due to the increase of area and
area inertia in the waterline provided by the beach in heel
situation - see Figure 15b - and discussed in details in Torres et
al. (2004b). Although standard rules for MPSO are not
consolidated by classifications societies, the stability can be
evaluated by the requirements used in other floating systems,
such as column-stabilized and self-elevating units, as in Campos
et al. (2004a) and Campos et al. (2008). In another work,
Santos et al. (2006) employed the ABS rules for column
stabilized units to evaluate MPSO stability showing that this
conception was approved in all requirements, even for damage
conditions.
maintain the platform in even keel position, as the operation
illustrated in Figure 17. The works by Campos et al. (2004a),
Santos et al. (2006) and Rueda et al. (2006) evaluated a damage
analysis for a MPSO platform and the results showed the
feasibility of the concept.
Fig. 17 MPSO platform with one tank damaged: (a) without
damage compensation and (b) with damage
compensation [Santos et al. (2006)].
5
Fig. 15 Example of the restoring arm in the analysis of MPSO
system stability [Campos et al. (2008)].
Due to the MPSO symmetrical geometry, the tank
arrangements can also simplify the ballast operation and
number of pumps. For example, in MPSO designed for the
Gulf of Mexico - GoM, one of most important premises was
that in case of hurricane the platform should reach a survival
draft only with ballast operation in any oil loading condition.
Also, it is important to note that MPSO hull can be flexible
enough to assemble different tank arrangements including
double hull, as required in that area of gas and oil production.
Initially, the MPSO tank subdivision was defined based on
analyses of similar systems such as spars. Nowadays even for
platform operating out of GoM, the common solution is the
double hull due to the legislation on oil spills. As an example
of the citation above, Figure 16a shows tanks with radial
bulkheads (as the standard spar platforms); Figure 16b shows
tanks with conventional subdivision and Figure 16c shows
double hull configuration.
Riser and Mooring System
Because of its axial symmetric design and the hydrodynamic
devices for motion mitigation discussed before, the MPSO
has great versatility in mooring arrangements for each
installation field. The work developed by Rampazzo et al.
(2008) evaluates different mooring designs for a MonoBR
platform. According to this work, an example of a possible
MPSO mooring configuration is presented in Figure 18.
These arrangements allow a MPSO to offer extremely favorable
conditions for the operation of umbilicals and risers,
particularly the SCRs (steel catenary risers). Another important
characteristic concerns the fairlead positions of risers, which
are well protected inside the moonpool, hence facilitating
and guaranteeing greater integrity in MPSO units.
Fig. 16 Types of MPSO tank subdivision: (a) Sectional
[Campos et al. (2008)] (b) Conventional [Campos et
al. (2008)] and (c) Dual tank [Reyes et al. (2009)].
Ballast and oil tank subdivision is essential for damage stability
analysis. For that reason, the MPSO tank subdivision is capable
of guaranteeing the viability of the unit according to
classification societies. The subdivision design also makes the
project more stable, including the possibility of damage
compensation by transferring water between ballast tanks to
51
Fig. 18 Example of a riser and mooring system for the MPSO
[Rampazzo et al. (2008)].
Guilherme
Fujarra
6
Conclusion
The challenge to obtain a production system with storage and
vertical motion equivalent to spar platforms was accomplished
with the development of a MPSO with a moonpool. Due to
its geometric form, the construction process and structural
resistance are superior compared with a conventional FPSO.
In comparison, for monocolumns without the presence of a
moonpool, the vertical motions can be similar to the shipshaped FPSO because of the similar natural frequency of the
heave motion, which cannot allow the use of rigid risers and/
or dry completion.
However, a MPSO with a moonpool, beach, skirt and spoiler
plates results in minimized vertical motions, then the use of
rigid risers and dry completion systems are allowed providing
this kind of platform with an enormous advantage when
compared with others.
For that reason, the MPSO concept associated with a
moonpool and other already studied hydrodynamic devices
undoubtedly makes it one of the best solutions for the
exploration of new fields in the pre-salt area of Brazil and also
in the area of severe sea conditions.
Acknowledgements
The authors are indebted to the Department of Naval
Architecture and Ocean Engineering of the University of São
Paulo, to the TPN (Numerical Offshore Tank) Laboratory of
the University of São Paulo and to Petrobras for supporting
these researches.
References
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Armazenamento com Completação Seca (in portuguese)”.
Final Degree Work, University of São Paulo, São Paulo.
GONÇALVES, R. T., Matsumoto, F. T., Medeiros, H. F., Brinati,
H. L., Nishimoto, K., & Masetti, I. Q. (2008) - “Conceptual
Design of a Floating Production and Storage with Dry Tree
Capability”. 27 th International Conference on Offshore
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BARREIRA, R., Sphaier, S. H., Masetti, I. Q., Costa, A. P. S., &
Levi, C. (2005). “Behavior of a Monocolumn Structure
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Cueva, M., & Siqueira, E. F. (2009) - “Vortex-Induced Motion
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CAMPOS, F. C. R., Cueva, M., Nishimoto, K., & Costa, A. P. S.
(2004). “Stability Criteria and Analysis of a Monocolumn
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GONÇALVES, R. T., Rosetti, G. F., Fujarra, A. L. C., Nishimoto,
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para Projetos de Plataformas do Tipo Monocoluna (in
portuguese)”. Master Degree Thesis, University of São Paulo,
São Paulo.
M ALTA , E. B. (2009) - “Métodos e Processos para a Análise
Experimental de Sistemas Oceânicos de Produção de
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University of São Paulo, São Paulo.
52
Guilherme
Fujarra
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MASETTI, I. Q., Costa, A. P. S., Matter, G. B., Barreira, R. A., &
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OMAE2007-29024.
SANTOS, B. M. R., Rueda, G. E., Matsumoto, F. T., Campos, F.
C. R., Costa, A. P. S., & Nishimoto, K. (2006) - “Stability
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OMAE2006-92276.
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Sevan Marine ASA: http://www.sevanmarine.com/
index.php?option=com_frontpage&Itemid=1
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F., Nishimoto, K., & Masetti, I. Q. (2008) - “The Influence
at Vertical First Order Motions Using Appendages in a
Monocolum Platform”. 27 th International Conference
on Offshore Mechanics and Arctic Engineering.
OMAE2008-57410.
SPHAIER, S. H., Torres, F. G., Masetti, I. Q., Costa, A. P., & Levi,
C. (2007) - “Monocolumn Behavior in Waves: Experimental
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August 2007.
NISHIMOTO, K., Videiros, P. M., Fucatu, C. H., Matos, V., Cueva,
D. R., & Cueva, M. (2001) - “A Study of Motion minimization
Devices of FPDSOS”. 20th International Conference on
Offshore Mechanics and Arctic Engineering.
T ORRES , F. G., Cueva, M., Malta, E. B., Nishimoto, K., &
Ferreira, M. D. (2004) - “Study of Numerical Modeling of
Moonpool as Minimization Device of Monocolumn Hull”.
23 rd International Conference on Offshore Mechanics
RAMPAZZO, F. P., Masetti, I. Q., & Nishimoto, K. (2008) - “The
Mooring System Design of MONOBR Platform for Harsh
Environmental Conditions (GoM)”. 20th Ocean Engineering
Symposium.
REYES, M. C. T., Kaleff, P., Masetti, I., & Costa, A. P. S. (2007) “Construction Issues of Mono-Column Type FPSO
Newbuildings”. 2007 RINA International Conference
Design & Construction of Floating Units.
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Operating in Ultradeep Waters”. 28 th International
OMAE2009-79586.
RODDIER, D., Finnigan, T., & Liapis, S. (2009) - “Influence of the
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T ORRES, F. G., Alho, A. T. P., Sales, J. S., Sphaier, S. H., &
Nishimoto, K. (2008) - “Experimental and Numerical
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Moonpool”. 27th International Conference on Offshore
TORRES, F. G., Nishimoto, K., Malta, E. B., & Masetti, I. Q.
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F. T. (2006) - “Influence of the Ballast Tanks Loading on the
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OMAE2006-92275.
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R. Z. M., Lopes, C., & Gioppo, H. (2009) Motion Behaviour
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53
MS&OT – Guidelines for Authors
Title of paper
First Name Surname, Organisation, Address of corresponding author (including e-mail)
Abstract
The abstract should be a brief description of the scope of the paper, not exceeding 100 words in length
Keywords: at least 3 suitable words for indexing purposes
Nomenclature
A nomenclature is required for papers using a large number of symbols, abbreviations and acronyms. Where possible, these should
be ordered alphabetically.
Symbol 1 Definition
Symbol 2 Definition etc.
E.g.:
α
ρ
λ
Angle of attack
Density of water
Wave length
1. Introduction
This is normally the first section in the main body of the text. Please note that this section and all subsequent sections and
subsections are numbered. All main headings should be typed in bold as shown below.
2. Heading
2.1 Sub-heading
Each Section may have sub-headings. Sub-headings should be numbered and typed using lower case as above.
2.2 Sub-heading
2.2 (a) Further subsidiary heading
The sub-sections can be further divided up as above. Further subsidiary headings not in bold in lower case.
3. Manuscript format conventions
3.1 Font
The fonts to be used are the same that have been used for this page, Times New Roman and Arial. The title of the paper should be
in 12 point bold capitals. Authors names should be in 10 point bold, with affiliation in 10 point regular. The rest of the paper should
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3.2 Page setup
The final manuscript should use the style used in this template. The margins are as follows for both A4 and US letter style in order
that Acrobat versions of the manuscript can be printed on either A4 or 8.5x11 inch paper:
A4
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Top
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54
3.3 Page numbers
Please put page numbers on manuscript at bottom center. This will be redone by the editors in the final printed version. Total height
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3.4 (a) General guidelines
w All illustrations should be clearly referenced in the text
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w Figures may be in color or in black and white. If you use color graphics please check the graphic in black and white to see
if shading or hatching is needed. Wherever possible, figures will be in black and white.
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3.4 (b) Figure format
Figures should be produced electronically where possible, in .wmf, .eps, .jpg, .cdr, .gif, or .tif formats. Excel charts should be copied
and pasted to Microsoft Word. Save another copy of each individual graphic in separate file (Fig1, Fig2, etc.) in addition to the
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Please ensure that the lettering used in the artwork/illustrations does not vary too much in size. The final font size should be about
6-8 point. Make sure that the physical dimensions of your artwork match the dimension of A4 paper.
4. Submission requirements
Authors must submit their paper IN ELECTRONIC FORMAT in word processor or Acrobat format. They must be sent to one of
the Editors.
w Papers should be sent as e-mail attachments if each file is no larger than 3MB.
w If larger than 3MB, a CD should be sent to the Editors.
w Maximum length of paper 20 pages (above 20, with editors approval).
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5. Additional information for authors
5.1 Liability
Authors are responsible for obtaining security approval for publication from employers or authorities where necessary. If they so
wish, authors should include a disclaimer at the end of the paper stating that the opinions expressed are those of the author and not
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6. Conclusions
The main body of the text should end with the conclusions of the paper.
Acknowledgements
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References
References should be listed alphabetically with the year of publication just after the author’s last name aand referred to in the text
as Firth (1989):
Firth, S. (1989) - “Investigation into the Physics of Free-Running Model Tests”. SNAME Transactions, pp. 169-212.
55
Calendar of Events
PRADS 2010
OTC 2011
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and Other Floating Structures
Rio de Janeiro, 19-24 September 2010
www.prads2010.org.br
41st Offshore Technology Conference
Houston, USA, 2-5 May 2011
www.otcnet.org/2011
OMAE 2011
FPSO Research Forum 2010
25 FPSO JIP Week
Aberdeen, Scotland, 11-15 October 2010
www.fpsoforum.com/upcoming.html
30th International Conference on Ocean, Offshore and Arctic
Engineering
Rotterdam, Netherlands, 19-24 June 2011
www.asmeconferences.org/omae2011
LNG Tech Global Summit 2010
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Rotterdam, Netherlands, 19-20 October 2010
www.lngsummit.com/
21st International Offshore and Polar Engineering Conference
Maui, Hawai, USA, 19-24 June 2011
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SOBENA 2010
XXIII Brazilian Conference on Maritime Transport,
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Rio de Janeiro, Brazil, 25-29 October 2010
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ITTC 2011
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56
SOBENA
Sociedade Brasileira de Engenharia Naval
The Sociedade Brasileira de Engenharia Naval (SOBENA)
is the Brazilian forum for exchange of theoretical and
practical knowledge amongst naval architects and marine
engineers. It was founded in the beginning of the modern
phase of Brazilian naval construction, in 1962, with the
aim of bringing together engineers, technicians and other
professionals involved in activities as: shipbuilding and
ship repair, design and other engineering services,
maritime transportation, waterways, ports, specialized
cargo terminals, ocean and river transportation
economics, marine environmental protection, offshore
support bases, offshore logistics, naval aspects of offshore
exploration and production, construction and
conversion of platforms and other offshore vessels.
SOBENA is a non-profit civil society, declared a federal
public utility by Decree No. 97589/89, which since its
foundation is aimed at promoting technological
development in the above activities through courses,
conferences, seminars, lectures and debates. SOBENA
is a source of reference called upon to provide its opinion
on matters of public interest and has also been politically
active, expressing its views concerning topics of national
relevance related to its areas of activity.
Following the evolution of the industry in the past years,
SOBENA has started to include activities related to
offshore oil exploration and production, holding events
for professionals of those areas. As a member of the
Mobilizing Committee of the National Petroleum
Industry Organization (ONIP), SOBENA has been taking
part in various subcommittees which are seeking to create
conditions to promote the development of the Brazilian
naval and offshore construction industry.
SOBENA has signed affiliation agreements with the
Institute of Marine Engineers (IMarEST), with
headquarters in London, England and cooperative
agreement with The Society of Naval Architects and
Marine Engineers (SNAME), from the United States of
America.
President
Alceu Mariano de Melo Souza
Vice-President
Floriano Carlos Martins Pires Jr.
Regional Director - Bacia de Campos
Aribel de Oliveira Lopes
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Fábio Ribeiro de A. Vasconcellos
Administrative Director
Ana Paula dos Santos Costa
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Luiz Sérgio Ponce
Technical Director
Luis Felipe Assis
Associated Directors
Francisco Roberto Portella Deiana
Luiz Carlos de A. Barradas Filho
Anderson Mariano Carvalho
Address:
Av. Presidente Vargas, 542 - Gr. 713
Centro - CEP 20071-000
Rio de Janeiro - RJ - Brasil
Telephones: [+55](21) 2283-2482
Telefax: [+55] (21) 2223-3440
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CEENO
Centro de Excelência em Engenharia Naval e Oceânica
The Centre of Excellence in Naval Architecture and Ocean Engineering (CEENO) was created in
1999 as a result of a joint initiative of four Brazilian institutions (COPPE, IPT, PETROBRAS and
USP), traditionally involved in scientific and technological development applied to marine activities.
As a Centre of Excellence, CEENO aims to integrate facilities and human resources, developing
theoretical and experimental methods, giving strong support for consolidation, expansion and
improvement of the maritime activities in Brazil and worldwide.
CEENO has been involved in relevant projects on Offshore Engineering and Ship Design &
Construction.
S O B E N A

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