Subsea Tree Frame Weight Optimization and Preliminary Study

(1)

Università degli Studi di Pisa

Dipartimento di Ingegneria Civile ed Industriale

Corso di Laurea Magistrale in Ingegneria Meccanica

SUBSEA TREE FRAME WEIGHT

OPTIMIZATION AND PRELIMINARY STUDY

Supervisors:

Candidate:

Prof. Eng. Leonardo Bertini

Filippo Ceccanti

Eng. Francesco Sorbo

Eng. Tommaso Bagnoli

(2)

(3)

My gratitude goes to the Florence GE Subsea Engineering Office. I wish to acknowledge every person which has helped me in my work.

In particular, I’d like to thank my supervisors near the office: Francesco, for the opportunity which has given me and Tommaso, for all of the notions taught and for all of the time spent for my work.

I wish, moreover, acknowledge all of the people which have shared with me their time and have helped and supported me in my work; thank you Giordano, Christian, Maurizio, Enrico, Giacomina and all of the rest of the people to which I am grateful.

(4)

(5)

Abstract

The purpose of this work is to develop an APDL tool, suitable in the conceptual and preliminary design phases of a Subsea Christmas Tree (XT in the following), which has to perform preliminary structural assessments and weight optimization of the structure’s frame.

The tool has been developed as a sequence of organized APDL macros with a layout to grant general applicability to the tool.

This circumstance implies that different structure can be processed with the tool without any changes in its structure and in its core functionalities.

All of the customization operations required for the application of the tool on a specific structure result simple and quick to carry out, in particular if compared with the time needed for the definition of a tool for the preliminary assessment and weight optimization dedicated for a specific structure.

The tool needs, as input, simplified representations of frames, and performs linear elastic structural assessments on the resultant FE model.

All of the choices regarding the properties of the geometrical model and the type of analysis performed by the tool are in line with its intended purposes.

The definition of the simplification procedure needed for the building up of the geometrical model of the frame has been carried out as integral part of the work.

Once defined, the tool has been tested on two different XT frames.

For each of these, detailed structural assessment results are already available. These ones are referred to frame models made of solid elements and have been taken as reference.

The first frame has been represented using a geometrical model made of lines and areas. The resultant FE model contains both beam and shell elements.

Structural assessment results have been compared with those ones coming from the reference model; this operation is called benchmark phase.

Benchmark phase highlights that the frame representation used is too much approximate.

Accordingly, the second frame has been represented with a geometrical model made of areas only, which generates a FE model containing only shell elements.

With this simplification strategy, the benchmark phase better validates the model.

Despite the discrepancies highlighted for the first simplification strategy adopted, the weight reduction procedure has been applied on both frames.

Weight reduction obtained is about 25% of the original weight for the first frame, and about 16% for the second one.

Thanks to the optimization restraining, weight reduction results are conservative.

This implies that the frame redesign which follows the indications suggested by the tool should satisfy every structural requirement in final detailed design verification phase.

As future developments, the tool can be applied on structures different from XT frames, such as manifold frames; on XT frame analysis, the introduction of large bore piping allows the assessment of structural interactions which are not considering with these models.

Moreover, the implementation of a more effective and efficient optimization criteria will make the developed tool more suitable for the purpose of the weight optimization.

(6)

(7)

5.1.1.3 Connections ... 44 Mesh ... 46 5.1.2. Load Cases ... 51 5.1.3. Structural Assessment ... 60 5.1.4. Post Processing ... 75 5.1.5. 5.2. BENCHMARK ... 77 5.3. OPTIMIZATION ... 82 Structure ... 82 5.3.1. Hypothesis... 83 5.3.2. Constraints ... 86 5.3.3. 5.4. OPTIMIZATION OUTPUT INTERPRETATION... 87

6. RESULTS ... 88

7. TOOL GENERAL VALIDITY TEST (DHXT FRAME #2) ... 102

7.1. TEST EXPLANATION ... 103 7.2. FEA ... 104 Model Modification ... 104 7.2.1. Load Cases ... 111 7.2.2. Structural Assessment ... 117 7.2.3. Post Processing ... 123 7.2.4. 7.3. BENCHMARK ... 124 7.4. OPTIMIZATION ... 129

7.5. OPTIMIZATION OUTPUT INTERPRETATION... 130

(9)

LIST OF FIGURES

FIGURE 2-1: SUBSEA PLANT ... 13

FIGURE 2-2: FROM TOP LEFT: A) TLP B) PRODUCTION PLATFORM C) SPAR D) FPSO ... 14

FIGURE 2-3: ROV ... 15

FIGURE 2-4: FLOWLINE ... 16

FIGURE 2-5: MARINE RISER ... 16

FIGURE 2-6: FROM LEFT: A) BUOYANCY TANK B) BALLAST ... 17

FIGURE 2-7: FPSO TURRET ON THE LEFT SIDE ON PICTURE ... 18

FIGURE 2-8: UMBILICAL CABLE ... 19

FIGURE 2-9: SUCTION PILE ... 20

FIGURE 2-10: XT ... 22

FIGURE 2-11: MVB ... 24

FIGURE 2-12: FCM ... 25

FIGURE 2-13: CONNECTION SYSTEM (IN PARTICULAR, A VCCS) ... 25

FIGURE 2-14: ANODES ... 26

FIGURE 2-15: XT FRAME ... 27

FIGURE 4-1: GENERAL TOOL FLOW DIAGRAM ... 34

FIGURE 4-2: FLOW DIAGRAM OF A SPLITTED OPTIMIZATION ROUTINE ... 39

FIGURE 5-1: REFERENCE FRAME USED FOR FIRST TOOL TEST ... 40

FIGURE 5-2: GEOMETRICAL MODEL OF THE DHXT FRAME #1 ... 41

FIGURE 5-6: MESH OF DHXT FRAME #1 ... 47

FIGURE 5-10: MESH OF DHXT FRAME #1, DETAIL ... 49

FIGURE 5-14: LIFTING OF A XT ... 52

FIGURE 5-15: LC_1 EXTERNAL LOADS AND BOUNDARY CONDITIONS... 55

FIGURE 5-22: LC_10 EXTERNAL LOADS AND BOUNDARY CONDITIONS ... 59

FIGURE 5-23: LC_12 EXTERNAL LOADS AND BOUNDARY CONDITIONS ... 59

FIGURE 5-24: LC_1 STRESS DISTRIBUTION ... 61

FIGURE 5-25: LC_1 TOTAL DISPLACEMENT ... 62

(10)

FIGURE 5-50: CONTROL POINTS USED FOR DHXT FRAME #1 BENCHMARK ... 77

FIGURE 5-55: FIRST FRAME OPTIMIZATION ROUTINE STRUCTURE ... 83

FIGURE 5-56: VCCS CONNECTION PLATE ... 84

FIGURE 5-57: FCM CONNECTION PLATE ... 85

FIGURE 5-58: MVB CONNECTION RING ... 85

FIGURE 6-1: LC_1 STRESS DISTRIBUTION IN THE OPTIMIZED DESIGN ... 88

FIGURE 6-2: LC_1 TOTAL DISPLACEMENT IN THE OPTIMIZED DESIGN ... 89

(11)

FIGURE 7-15: LC_4 EXTERNAL LOADS DETAIL ... 114

FIGURE 7-17: LC_5 EXTERNAL LOADS DETAIL ... 115

FIGURE 7-31: CONTROL POINTS USED FOR LC_1 BENCHMARK ... 124

FIGURE 7-34: CONTROL POINTS USED FOR LC_4 AND LC_5 BENCHMARK ... 126

FIGURE 7-35: CONTROL POINTS USED FOR LC_4 AND LC_5 BENCHMARK ... 126

(12)

(13)

LIST OF TABLES

TABLE 5.1-1: MAIN MASSES ... 44

TABLE 5.1-2: LOAD CASES ... 54

TABLE 5.2-1: BENCHMARK ... 80

TABLE 7.2-1: MAIN MASSES ... 109

TABLE 7.2-2: LOAD CASES ... 112

(14)

(15)

ABBREVIATION AND SYMBOLS

𝑪𝒇 Design condition factor

COG Center of Gravity

CRA Corrosion Resistant Alloy

DDVC Deep Draft Caisson Vessel

DHXT Deepwater Horizontal XT

DOF Degree of Freedom

FCM Flow Control Module

FE – FEA Finite Element - Finite Element Analysis

FTA Flowline Termination Assembly

FPSO Floating Production Storage and Offloading

𝒈 Acceleration of gravity

HCCS Horizontal Clamp Connection System

HXT Horizontal XT

LF Load Factor

MVB Master Valve Block

PLET Pipeline End Termination

ROV Remote Operating Vehicle

𝒓𝒔 Section radius

𝑹𝑼𝑪 Ultimate capacity

𝑺𝒂 Applied load effect

SCM Subsea Control Module

𝑺𝒅 Design load effect

𝑺𝒚 Specified minimum yield strength

𝒕 Wall thickness

TLP Tension Leg Platform

UTA Umbilical Termination Assembly

VCCS Vertical Clamp Connection System

VXT Vertical XT

XT Christmas Tree

𝝈 Stress

𝝈𝒃 Bending stress

𝝈𝒆 Allowable Von Mises stress

𝝈𝒎 Membrane stress

𝝈𝑽𝑴 Design Von Mises stress

𝝈𝒚 Specified minimum yield strength

(16)

(17)

1. Introduction

1.1. Scope of Work

The scope of this work is to develop an APDL tool that has to perform both preliminary structural assessments and the weight optimization of a XT frame.

The tool intended use is the preliminary design phase, so it has to work on a draft of the frame and has to give, as output, indication about which are the solutions that allow a weight reduction with a high confidence on the fact that all of the final design structural assessments (which are necessary for the documentation relative to each XT) will check every requirements.

The tool has to have also a general validity, so it has to be applied on different kind of frames with only a little customization for each specific structure.

This requirement implies that the tool has to be modular.

The tool has to work on a simplified model of the frame; the structuralization of the simplification process that produces the frame geometrical model is also part of the work.

The frame model simplification process (or model adjustment process) consists in a structurized procedure (the organization of which is, as said, integral part of the work) that has the specific scope to produce, starting from a CAD representation of the considered structure, a geometrical model suitable to be used as tool input.

The optimization process has to be based on the main load cases that involve XT frame (specific for each frame considered).

1.2. Work Overview

This short paragraph is written with the specific scope to make clear the comprehension of the various steps of the work.

Every part of the work will be widely explained in next chapters. First of all, the structure of the tool has been defined.

With “tool structure” reference is made to how the tool manages the information coming from all of the macros that compounded the tool.

Tool structure has been thought considering the modularity of the tool, and trying to maximize this aspect.

The modularity is represented by the tool attitude to allow, as input, different structures (encoded in the appropriate way).

Once defined the tool structure, a first XT has been considered; hence a simplified geometrical model of the frame has been build up, and the structural assessment has been performed.

The simplified model used in the first test is a mixed one, made of both beam and shell elements. All of the results obtained from the structural assessment have been compared with those ones obtained with a model made of solid elements (used for the design verification and took as reference). The comparison carried out (called benchmark phase) has the scope to demonstrate the validity of the simplified model through confronting of the results of the two models and taking as reference that one made of solid elements.

(18)

After the model validation, the weight reduction routine has been performed on the structure.

Once obtained a lighter design, because of the fact that the benchmark phase demonstrated that a shell and beam representation of the frame generate a model which is not a good approximation of the structure, a different procedure for the creation of the simplified model has been defined.

This second methodology adopted for the building up of the simplified geometrical model of the frame is based on the use of only areas for the representation of the structure. The use of areas only in the geometrical model implies the creation of a FE model made of only shell elements, which has structural behaviours closer to the reference (if compared with the previous FE model).

Structural assessments have been carried out, and all of the results obtained from them have been used for the benchmark of the simplified model.

The comparison between the structural assessment results of the simplified model obtained with the new simplification strategy and the reference shows a high level of agreement; this means that the model made of only shell elements is validate.

(19)

2. Subsea

In this chapter is described how a subsea oil or gas production site works.

2.1. The Cluster

Around the world there are a lot of different subsea production site, each of which has a specific and characteristic layout.

In this chapter will be described how a typical deepwater production site is made and works.

Figure 2-1: Subsea plant

On the surface of the water there is, in general, a production rig or vessel, which is connected with a subsea production, injection and export system by a series of risers.

(20)

Typical examples of production rig or vessel are:

 FPSO

 TLP

 Production Platform

(21)

Considering a deep-water or an ultra-deep-water site (which are installed more than 2000 m deep), the plant is handled with particular devices, called ROV; these are controlled and moved from a control room on the surface.

Figure 2-3: ROV

A single production rig or vessel is able to serve simultaneously up to four or five fields.

Every field can produce oil and/or gas from different and separate reservoirs; for this reason, every field can has several production and injection wells.

In general every field has an independent production, water and gas injection and service and utility system.

The production system transports production fluids from the production well to the rig (or vessel); the water injection and gas injection systems are used to provide pressure support into the reservoirs. Not every reservoir needs water or gas injection.

The service line is used to flush and clean the production system as required.

Electrical power, hydraulics and a range of different chemicals are delivered to each field by dedicated umbilical.

The production well can be deviated to the target area into the reservoir drilling a channel up to several kilometres long.

Reservoir fluids, once the channel is opened, reach the production tree and from they are channelled towards the production manifold.

Each of the tree contains a flowmeters, which provide continuous information to update the reservoir model.

(22)

Fluids then passed through FTA and then into the production flow lines.

Figure 2-4: Flowline

In general the production flow lines have a pipe in pipe construction, in order to maintain the production fluid temperature.

In between each of the pipes, a layer of insulation is putted to minimize the ocean water cooling effect.

Fluids continue to the end of the flow line; then into another FTA, and then to the surface though a riser.

(23)

The riser is held in constant tension by driven piles, with ballast at the bottom and buoyancy tanks at the top.

Figure 2-6: from left: a) buoyancy tank b) ballast

The last 300 m to the surface are covered with flexible risers, made flexible to allow for the motion of the current and tides.

(24)

They carry the fluids into an externally bonded turret on the FPSO (or in another equivalent production rig or vessel).

Figure 2-7: FPSO Turret on the left side on picture

The produced fluids then pass into a separation system, in which water and gas are removed from the oil for further processing.

The processed oil is stored in cargo tanks, waiting the trading tank; it take on the oil every six or seven days inasmuch, indicatively, an FPSO has a store capacity of about 1.8 million barrels of oil. The produced water that was removed from the oil is cleaned, mixed with seawater and then passed through a sulphate reduction plant.

The produced gas that is removed from the reservoir fluid is cleaned and compressed.

The water and gas then travel through the turret before going subsea to be re-injected into the reservoir to maintain the pressure support.

(25)

The umbilical is a cable with different cables and tubes inside.

Figure 2-8: Umbilical Cable

Inside the umbilical, there are up to ten power and signal cables and up to sixteen tubes for delivery of hydraulic fluids and the various chemicals required to operate the subsea systems.

Within the dynamic section at the umbilical there are also carbon fibre inserts or steel wires; these increase its strength to allow for movement of the FPSO.

On the surface, while the FPSO’s turret is fixed to the seabed, the vessel is free to weather vane around it.

The power generation on-board is provided by gas turbine generators, which can generate several hundred of MW.

(26)

The turret is hold in place by chains which are moored in place thanks to suction piles installed on the seabed and on which the chains are linked.

Figure 2-9: Suction Pile

To look in more detail at the other subsea structures, the base of the vertical risers are hold in place by drilled piles.

The top of the buoyancy tanks are held about one hundred meters from the surface.

The tanks generate over 600 tons uplift to support the weight of the rigid riser pipe beneath.

The manifolds are supported of the seabed by the manifold support structure, which is held in position by suction piles.

Considering, instead, in more detail the component of the production plant object of this work, the most important things to consider is represented by the fact that every XT has the primary function to control the production of oil and gas from the well.

In a simplified way, indeed, a XT can be described as a series of gate valves that are used to open or close the flow of the well.

(27)

Each XT is fitted also with one SCM; this component provides communication between the XT and the control room on the top side production unit.

Every XT is connected with the manifold with jumpers, which are short (flexible or rigid) pipes used to connect subsea structures located close to one another.

The manifold is placed in the centre of the cluster (or drill centre) and the wells are, in general, located around the manifold.

Typically four to six wells are drilled and installed around a single manifold, and the maximum distance from the manifold to a XT is approximately 20 m.

A manifold lands on a foundation structure that provides stability even on a soft seabed.

The purpose of the manifold is to gather the production from the well connected; for this purpose, the manifold is designed with several valves and connection points.

Hubs not connected are protected by pressure caps and anodes are used to avoid severe corrosion on the structures.

Manifold can also contains small bore piping and valves for the distribution of the hydraulic fluid and other chemical needed by each XT; this is handled by a separate bundle jumper.

The electrical communication is provided with specially built electrical cables. An ROV with special tooling is used to install the connection system.

The ROV can also be used to connect jumpers and cables to the XT.

One large bore connection runs from the manifold to the pipeline end termination (all the PLET). This pipe is typically 16-20 inches (400-500 mm) in diameter.

Pressure rating can be up to 690 bar, but 345 bar is more common.

The umbilical is connected to the manifold by a specially built umbilical termination assembly (UTA). UTA is the end termination that is design to fit the umbilical

Dedicated vessels are used to install the flow line to the PLET. Jumpers connect the pipeline and PLET to the manifold.

This field layout represents the state of the art technology for the development of deepwater oil and gas fields.

(28)

2.2. XT

As said, a XT is the site component that explains the interface function between the well and the external world.

Figure 2-10: XT

A subsea XT monitors and controls the production of a subsea well.

Fixed to the wellhead of a completed well, subsea trees con also manage fluids or gas injected into the well (in fact, there are different kind of XTs, which are described later).

(29)

The differences between the two types of XTs regard several aspects and field, ranging from a different installation procedure until different performance in terms of reliability and maintenance. In this work are considered only horizontal XT (HXT), but it shall be easily extended to VXTs.

As mentioned before, in a plant, in general, four kinds of XTs are used together each of which explains a specific function.

The four XT kinds are:

 Oil production

 Gas production

 Water injection

 Gas injection

Oil and Gas production XTs manage the flow of production oil or gas from the well to a receiving unit (that can be a fixed or floating vessel or a produced via pipeline to shore, depending from the plant structure).

Water and gas injection, indeed, manage the flow of water or gas into its respective well from a process installation off- or on-shore.

A XT, independently from the specific function, is made by several fundamental components, such as:

 MVB

 FCM

 Connection system (VCCS or HCCS)

 SCM

 Cathodic protection system

 Frame

(30)

The MVB is, maybe, the most important part of a XT.

Figure 2-11: MVB

It’s made by a forged element, coated with specific CRAs. On MVB are housed all of the most important valves of the tree.

(31)

The FCM is a component that is not present in every XT.

Figure 2-12: FCM It’s made by several valves that explain a flow managing function.

The connection system is a component with which the XT is connected with other part of the plant. According with the geometry of the connection system (horizontal or vertical) and with the type of tree (production or injection), on this component acting loads that are dimensioning for the frame.

(32)

The SCM is the component that allows the communication between the control room and the XT. It is necessary for the remote actuation of valves (without the intervention of a ROV).

The Cathodic protection system consists in a series of elements that protect the main XT parts from the corrosion.

Figure 2-14: Anodes

The cathodic protection system is made by a set of anodes (dimensioned specifically for each XT), the material of which have a potential reduction lower than that of steel.

Anodes are placed in many parts of the XT and, thanks to their chemical composition (that causes a potential reduction lower than that of steel), the corrosion induced by the environment is concentrated on those elements; anodes are dimensioned to protect the XT for the whole XT design life.

(33)

2.3. XT Frame

As mentioned before, one of the elements that compose a XT is the frame.

Figure 2-15: XT Frame

The frame is a component that has the only scope to group and hold in place all of the XT components.

The task required implies that the frame has to be dimensioned considering the loads acting on its various parts and the maximum allowable displacements of every component.

The main loads acting on the frame are:

 The connection loads, coming from the connection between the XT and other part of the plant;

 The weight of all of the XT components.

XT frame load are static and constant (so they are not fatiguing loads).

Considering that the most onerous loads in terms of structural strength acting on the frame comes from the effect of the interaction of the mass with accelerations (vertical, in the case of XT own weight and lifting and horizontal in case of lateral acceleration, which occurs during the transportation of the XT to the field) and considering that all of the most intense load case occurs a little number of times, the frame represent a component which introduced mass that results unused for the almost whole tree life.

(34)

Considering moreover the fact that an higher mass of a XT imply high costs (high raw materials costs, high handling costs, high transportation costs, high manufacturing costs etc…) the XT components weight reduction make more competitive the XT on the market.

(35)

3. Theory

In this chapter will be presented the main hypothesis on which the work has been developed.

3.1. Structural Assessment Hypothesis

As said, a linear elastic FE calculation will be performed as the frame structural assessment.

This kind of analysis has been chosen because of its little computation resources requirement; with this calculation methodology, the structural assessment will be faster than a nonlinear or an elastic-plastic analysis.

The frame has been represented with a simplified geometrical model; the simplification strategy adopted for the representation of the frame will be illustrates in the following chapters.

The geometrical model has been meshed both with shell and beam elements.

In particular, shell181 has been chosen as shell element, and beam188 as beam element.

Shell181 is an ANSYS plane element that is represented through four nodes per elements (for the quadrilateral elements); nodes are placed on the vertexes of the quadrilateral

Shell181 elements have six degrees of freedom at each node: translations in the x, y and z axes, and rotations about the x, y and z axes.

The element formulation is based on logarithmic strain and true stress measures.

Shell181 uses a penalty method to relate the independent rotational degrees of freedom about the normal (to the shell surface) with the in-plane components of displacements.

Shell181 includes the effects of a transverse shear deformation.

Shell181 uses an advanced shell formulation that accurately incorporates initial curvature effects. The calculation for effective shell curvature change accounts for both shell-membrane and thickness strains. The new formulation generally offers improved accuracy in curved shell structure simulations. The effects of pressure load stiffness are automatically included for this element.

Beam188 is an ANSYS line element that is represented though two nodes (that delimit the element); these nodes have six degrees of freedom each one.

These DOF includes include translations in the x, y and z directions and rotations about the x, y and z axis.

With the keyoption 3 is possible to define the shape function order; it’s possible to use linear, quadratic and cubic shape function along the element length.

Beam188 is based on Timoshenko theory, which is a first-order shear-deformation theory; transverse shear strain is constant through the cross-section (that is, the cross sections remain plane and undistorted after deformation).

The element can be used for slender and stout beams. Due to the limitation of first-order shear-deformation theory, slender to moderately thick beams can be analysed.

Beam188 are provided with section relevant quantities (area of integration, position, Poisson function, function derivatives, etc.) automatically at a number of section points by the use of section

(36)

commands. Each section is assumed to be an assembly of predetermined number of nine-node cells; each cell has four integration points.

Thanks to the integration points, it is possible retrieve information about, for example, the stress distribution on the cross-section (despite beam188 is a line element).

3.2. Optimization Theory

Terminology

3.2.1.

Design Variables (DVs) are independent quantities that are varied in order to achieve the optimum design. Upper and lower limits are specified to serve as "constraints" on the design variables. These limits define the range of variation for the DV. DVs will be indicated with {𝑥} in the following passages. State Variables (SVs) are quantities that constrain the design. They are also known as "dependent variables," and are typically response quantities that are functions of the design variables. A state variable may have a maximum and minimum limit, or it may be "single sided," having only one limit. The Objective Function is the dependent variable that you are attempting to minimize. It should be a function of the DVs, that is, changing the values of the DVs should change the value of the objective function. Objective function will be indicated with 𝑊({𝑥}) in the following.

The design variables, state variables, and objective function are collectively referred to as the optimization variables. In an ANSYS optimization, these variables are represented by user-named variables called parameters. The user must identify which parameters in the model are DVs, which are SVs, and which is the objective function.

A design set (or design) is simply a unique set of parameter values that represents a particular model configuration. Typically, a design set is characterized by the optimization variable values; however, all model parameters (including those not identified as optimization variables) are included in the set. A feasible design is one that satisfies all specified constraints-constraints on the SVs as well as constraints on the DVs. If any one of the constraints is not satisfied, the design is considered infeasible. The best design is the one which satisfies all constraints and produces the minimum objective function value. (If all design sets are infeasible, the best design set is the one closest to being feasible, irrespective of its objective function value.)

Optimization 3.2.2.

The optimization of a structure is a process in which all of the DVs (chosen by the analyst) are varied in order to define the best design, which consist in the DVs set that match all of the constraints (so is a feasible design) and minimize the objective function.

(37)

Each optimization loop generates a new data point, and the objective function approximation is updated. It is this approximation that is minimized instead of the actual objective function.

State variables are handled in the same manner. An approximation is generated for each state variable and updated at the end of each loop.

The Subproblem Approximation Method, in order to consider the constraints, performs a conversion of the constrained problem in an equivalent unconstrained problem.

A general formulation for the various constraints can be 𝑔𝑗({𝑥}) ≥ 0

The conversion is done by adding penalties to the objective function approximation to account for the imposed constraints (this technique I called penalty functions method).

Defined the objective function 𝑊({𝑥}), the new objective function, coming from the conversion of the constrained problem in an equivalent unconstrained one is

𝑊∗_{({𝑥}) = 𝑊({𝑥}) + ∑ 𝑝} 𝑗({𝑥}) 𝑗 Where 𝑝𝑗({𝑥}) are the penalty functions.

A specific objective function will be defined for each constraint of the optimization problem. 𝑔𝑗({𝑥}) ≥ 0 → 𝑝𝑗({𝑥})

Penalty functions, in general, have the following formulation

{_𝑝𝑝𝑗({𝑥}) ≥ 0 𝑖𝑓 𝑔𝑗({𝑥}) ≥ 0 𝑗({𝑥}) → ∞ 𝑖𝑓 𝑔𝑗({𝑥}) < 0 Generally penalty functions have a polynomial formulation.

At the end of each loop, a check for convergence (or termination) is made. The problem is said to be converged if the current, previous, or best design is feasible and any of the following conditions are satisfied:

 The change in the objective function from the best feasible design to the current design is less than the objective function tolerance;

 The change in the objective function between the last two design is less than the objective function tolerance;

 The changes in all design variables from the current design to the best feasible design are less than their respective tolerance;

 The changes in all design variables between the last two designs are less than their respective tolerances.

The First Order Method, differently from the Subproblem Approximation Method, minimizes the actual value of the objective function (so doesn’t consider an approximation).

This method uses gradient of the dependent variables with respect to the design variables. For each iteration , gradient calculations (which may employ a steepest descent or conjugate direction method) are performed in order to determine a search direction, and a line search strategy is adopted to minimize the unconstrained problem.

(38)

Thus, each iteration is composed of a number of sub iterations that include search direction and gradient computations. That is why one optimization iteration for the first order method performs several analysis loops.

First order iterations continue until either convergence is achieved or termination occurs. The problem is said to be converged if, when comparing the current iteration design set to the previous and best sets, one pf the following conditions is satisfied:

 The change in objective function from the best design to the current design is less than the objective function tolerance;

 The change in objective function from the previous design to the current design is less than the objective function tolerance

It’s also a requirement that the final iteration used a steepest descendent search, otherwise additional iterations are performed.

Compared to the Subproblem Approximation Method, the First Order Method is seen to be more computationally demanding and more accurate.

(39)

4. Tool

In this chapter are described all of the aspects of the tool that perform the structural assessment and the weight optimization of a XT frame.

4.1. Requirements

The tool has to be developed a series of APDL macros, which performs structural assessments and the weight optimization on a frame design, given to the tool as input. The frame is represented though its geometrical model and a set of parameters which defines every thickness and cross sectional dimensions.

The tool has to be able to work on different kind of frame; so its validity has to be general.

The final scope of the tool is to give, as output, an optimized design of the input frame in input; this output will be consider as a guideline for the sizing of the beam cross-sectional dimensions and of the plates thicknesses.

Indeed, the output of the tool has to be the dimensions of the main XT frame components, which are all of the beams and plates that compound the frame.

The optimization process is structured and designed considering the intended use of the tool, which is the preliminary/conceptual design phase.

The consideration of this aspect is more relevant in terms of how to structure the optimization process, because it involves the magnitude of the weight reduction generate with the procedure. Considering the preliminary/conceptual design phase in which the tool will be applied, the magnitude of the weight reduction is not heavy, but it has only the scope to highlight and identify all of the XT frame components that are oversized.

The identification of the areas of the frame in which there are too much material allows the definition of a weight reduction plan, which has to be suggested by the optimized design founded by the tool. An important aspect which affects the conservative approach adopted for the weight reduction is represented by the XT working environment, which develop on the structure loads that are not easily foreseeable. In addition, the long life required at these structures (20 or 25 years) expose them to unpredictable working conditions.

These circumstances impose, as said, a conservative approach in subsea structure design, such as XTs.

On the other hand, a too much safe design brings at the definition of heavier structures, which present several problems, such as high costs, handling troubles and high load on the structure (considering that the main loads acting on a XT frame come from the own weight).

The scope of the work is to find out the main oversized components of the frame, in order to redefine the design of these components in the early design phase of the project.

The design philosophy, however, remain conservative.

(40)

4.2. Tool Structure

Here is reported the general tool flow diagram (Figure 4-1); general refers to the fact that the flow diagram in Figure 4-1 shows the internal architecture of the tool. In other words, Figure 4-1 shows how the tool works, without any reference to a specific application of it on a structure (hence are not considered all of the customization needed for the application of the tool on a specific frame).

This diagram illustrates how the information are used from the tool, where information have to be provided and what kinds of information are necessary.

This general scheme has the scope to explain how the tool works from a general point of view; every detailed explanation will be provided in the next paragraphs and chapters.

(41)

4.3. Tool Description

The architecture of the tool is based on a core macro that reads and edits sub-macros; each of these accomplishes specific tasks (such as parameters input, meshing, mass adding, etc.).

In order to provide the required generality (and then to make easy the application of the tool on a specific structure), these macros have to have a specific layout and are organized in a particular way. First of all, macros have been subdivided in two main categories:

 Editable macros

 Non-editable macros

From a general point of view, editable macros define the frame on which the tool has to work; some of these macros will be substitute with other input file (such as a processed CAD model) for the application of the tool on a general structure (different from the reference frame). Editable macros also perform the conversion of the geometrical input in an encoded one, without any geometrical reference and defined the load cases.

The advantage of the use of an encoded input (which is created through the definition of the

components) without geometrical references is represented by the fact that if the input changes (so a

different kind of frame is considered) the tool will work fine despite the changing of geometry.

Non-editable macros work on the encoded input, and perform all of the operation required to the tool. Specifically, editable macros provide in:

 Definition of all parameters

 Creation of the geometrical model (if an external geometrical model does not exist)

 Definition of the masses of the main components of the XT (see paragraph 5.1.1.2 for more details)

 Component creation (if they are not included in geometrical file)

 Load cases definition

Components are ANSYS entities that associate a group of elements, geometrical (such as area, lines

and points) and not (such as nodes and elements) with a code; they are, in other words, the entities by which are possible the separation of geometry and data, and by which is possible structure the tool to work with code.

The use of components allows, hence, to define a structure of the tool which is completely independent from the geometry of the frame; every frame, encoded in the appropriate way, will be indistinguishable for the tool.

(42)

Non-editable macros, instead, accomplish the following tasks:

 Mesh the structure

 Mesh the mass elements

 Link mass elements with the frame

 Perform structural assessment

 Perform post processing of the FE results calculation

 Perform frame weight optimization

The automation of all of these operations is made possible by the structure of the tool, which is based on the use of the components instead of geometrical references.

(43)

4.4. How the Tool Works

Even considering Figure 4-1, in this paragraph will be explained in details how the tool works. The first box represents a file in which are defined all of the analysis global parameters, such as

 Load cases considered in the analysis

 LF for each load case (which depend from the load case nature, such as normal operation load, accidental load, etc.)

 Number of shell, beam and mass components considered in the FE model

 Material density (which is set in order to adjust the COG position with the real one)

Defined these parameters, if an external geometrical model is available, it has to be imported and on it the components have to be defined.

If, on the contrary, an external geometrical model does not exist, additional files have to be arranged in order to allow ANSYS APDL environment to create the model inside itself. On the builded model, the components have to be defined.

With both geometrical model and components defined, a database is then created (called geometrical database). Geometrical database contains information about geometrical model and components defined on it.

At this point, the main macro starts writing a separate one, which will be used by the optimization routines.

Simultaneously, the main macro meshes the structure and all of the masses, defines all of the connection between the various part of the FE model and performs the structural assessments, considering every load cases specified.

The structural assessments are performed retrieving the FE model produced after the mesh of the structure, the creation of all the connection between the various parts of the frame and applying, for each load case, the loads through which they are defined. Results coming from the structural assessment are then saved in a file, then the solver is cleaned and the procedure restarted.

Mesh operation is managed through a file containing all of the parameters required for the definition of the structure (then the Young Modulus of each frame components, the cross sectional dimensions of each beam, the thickness of each plate, etc.).This file is red from the macro after the resuming of the geometrical database and defines the parameters used for the creation of the elements of the FE model.

When the tool performs the structural assessments (before the starting of the optimization routine), this file contains the parameters that define the unoptimized structure (the original design).

During the weight reduction procedure, a similar file will be created and updated during each iteration. This file will be the reference for design definition during the weight optimization.

Once resumed the geometrical database and red the parameters file, the model is meshed, load cases are solved and the post processing phase is performed.

Structural assessment results of the original design are automatically saved as RST file; this expedient allow the tool to be used as a preliminary structural assessment procedure.

(44)

Post processing consist in the evaluation of a series of parameters (state variables) on which the optimization process will be based; in particular, as said, state variables constrain the optimization process. State variable values are stored in memory and used in the following optimization procedure. The end of the post processing phase coincides with the interruption of the automatic macro creation. Automatically created macro is here used for the optimization procedure; the macro, essentially, contains all of the commands that allow the FE solver to perform a structural assessment of the considered structure.

Optimization procedure starts creating a new set of design variables, which are automatically written in a parameters file. This file is red from the software after the resuming of the geometrical database. The new parameters file define, combined with the geometrical model of the structure, a new frame, different from the original design thanks to the different set of parameters which define it. On the new frame the structural assessment and post processing phases are performed; state variables are defined and stored in memory and the optimization routines, relying on the new data, define a new set of design variables.

This procedure is iterated until the convergence criterion is satisfied.

As said in paragraph 4.2, here is explained what is the logic of the tool, and here is explained how the tool works from a general point of view.

Considering the application of the tool on a specific structure, the most important limitation is represented by the maximum design variables number that the FE solver allows.

When the number of design variables to be considered exceeds the limit (this circumstance has occurred in each test) the optimization procedure has to be subdivided in an appropriate number of steps.

In these cases, is important to choose in an appropriate way the portions of the structure the weight of which will be reduced, in order to maintain a reasonable structural behaviour of the structure.

(45)

An example of a subdivided optimization process is reported in the following picture.

Figure 4-2: Flow Diagram of a Splitted Optimization Routine

Referring to the example in Figure 4-2, the process is subdivided in two steps of optimization, in each of which a different portion of the structure is considered. The general approach that has been ever adopted consists in the consideration, in the first optimization step, of the upper part of the frame, in order to reduce the weight of the vertical columns. The following steps (one in the example) consider, instead, the lower parts of the frame.

This choice comes from the necessity to maintain, during the weight optimization procedure, a coherent structural behaviour of the structure.

(46)

5. Tool Test Application (DHXT Frame #1)

In this chapter will be described the application of the tool on the first frame considered.

Figure 5-1: Reference Frame used for First Tool Test

5.1. FEA

In this paragraph are described all of the aspects regarding the structural assessments performed on the first frame considered.

Structural assessments can be used both for the simple preliminary analysis of the structure’s behaviours of a frame layout and for the definition of the state variables used in the weight optimization procedure.

(47)

In the following images represent the first DHXT frame geometrical model (areas are in cyan and lines are in all the other colours).

Figure 5-2: Geometrical model of the DHXT Frame #1

(48)

(49)

5.1.1.2 Masses

In the previous paragraph is illustrated the representation of the XT frame; on the structure, obviously, are attached several massive components (such as MVB, SCM, spools, VCCS, etc.), a representation of them is fundamental.

One of the most important reason why a representation of the main XT components is necessary is represented by the fact that the weight of them represents some of the main loads acting on the structure.

An accurate representation of these components is too much expensive both from the modelling time and for the calculation time required; XT components are then replaced with point masses, placed in the estimated COG position of each one.

This choice implies that the structural contribution of these components has to be introduced in the model with an approximation; this approximation is represented by the use of contact elements (see paragraph 5.1.1.3) for the connection of frame and masses; the behaviours of these components have been defined through the setting of specific options.

(50)

In Table 5.1-1 is reported the list of the XT components replaced with point masses and their position in the frame.

Table 5.1-1: Main Masses Component name Treehead SCM Counterweight 1 Counterweight 2 Counterweight 3 Counterweight 4 Counterweight 5 Stabplate Mounting Panel

Panel 1 Panel 2 Panel 3 Counterweight 6 Counterweight 7 Counterweight 8 Counterweight 9 Counterweight 10 Flow Control Module

Hub

Production/Injection Hub VCCS Permanent Cap

Production Isolation Valve Block Assembly Spool A143338-4 Accumulators Metering Valves Panel 4 Panel 5 Panel 6

(51)

 Rigid connections between beam and masses

 Deformable connections between beam and masses

Connections between shell and beam are realized with the common node technique; for the implementation of this solution is necessary the predisposition of shared geometrical entities (such as lines or areas) in all of the portion of the structure in which have to be meshed common nodes. This expedient has the scope to force the ANSYS meshing system to create nodes in every shared geometrical entity; this cause the connection of the interested portion of the frame.

Common node technique is chosen because of the little computation cost required; the use of this technique allows the tool to obtain results in less time than using a connection strategy based on the use of contact elements.

Connections between frame and point masses are created, on the contrary, using bonded contact elements.

CONTA174 and TARGE170 are used to connect shell and masses; specific keyoptions are used to define the behaviour of contact (rigid or deformable).

Beam-masses connections are realized, instead, with CONTA175 and TARGE170 contact elements; even in this case, specific keyoptions are used to specify the behaviour of contact.

Various contact pairs are meshed with the opportune feature thanks to the codification of each contact. The codification allows the user to specify all of the keyoptions that define the behaviours of each single contact pair.

Referring to the paragraph 5.1.1.2, contact pairs, in addition with the realization of the connection between masses and structure, have to simulate the structural contribution of the components replaced with point masses.

As said, the replacements of the XT components with point masses connected with the structure through contact elements implies that the structure behaviours will be only an approximation of the real one; this assumption is, however, in line with the structural assessment methodology adopted for the official reports.

Contact pairs can have, as said, a rigid or a deformable behaviour.

The use of a rigid connection between frame and mass define a rigid region in the structure. Specifically, the rigid region will be created in the portion of the frame on which the mass is attached. On the contrary, the use of a deformable contact pair for the connection of mass and frame create a low stiffness connection between the two components. The stiffness of the connection is automatically set by ANSYS and its value is chosen in such a way that does not modify local stiffness of structure. The choice of the contact behaviour is based on how various components are actually attached on the frame.

An important factor is represented by the simplified way with which the frame model is made, that is line and areas.

As said, a model made of lines and areas will be meshed with, respectively, beam and shell elements. Connecting a mass with a beam imply that the whole beam cross section on the node on which the contact element will be meshed will be influenced by the contact element behaviour.

(52)

If the contact element has a deformable behaviour, locally the beam stiffness will not be influenced by the presence of the contact element. On the contrary, if the contact pair is a rigid one, locally the whole beam cross section acquired a rigid behaviour.

This aspect implies that, for this first model made by shell and beam elements, most of the contact pairs are deformable; this circumstance implies that the model is not able to transfer some action (this fact will be demonstrated in paragraph 5.2).

Mesh 5.1.2.

Mesh process is managed by the ANSYS meshing system.

Elements dimensions are chosen in order to obtain a total number of nodes of about 25000. As sum up, during the meshing phase are generated elements of the following types:

 SHELL181  BEAM188  CONTA174  CONTA175  TARGE170  MASS21

For the mesh of the contact pairs is required the existence of a meshed FE model; for this reason is necessary to mesh in a first step every line, area and point (in which are placed mass elements). Then, on the nodes defined during this first meshing phase, contact elements will be meshed (so contact elements are located on the node of a pre-existing meshed model).

(53)

The following pictures represent the meshed structure. Note that Figure 5-10, Figure 5-11, Figure 5-12 and Figure 5-13 represent the same FE model shown in Figure 5-6, Figure 5-7, Figure 5-8 and Figure 5-9, with ESHAPE option activated (ESHAPE command show shape and dimensions of all simplified elements in the model, that is, in this case, shell and beam).

(54)

(55)

Figure 5-9: Mesh of DHXT Frame #1

(56)

(57)

Figure 5-13: Mesh of DHXT Frame #1, detail

Load Cases 5.1.3.

As mentioned before, all of the load cases which have to be considered and included in the analysis have to be defined in a specific file; this file is a editable macro, so it has to be edited for the customization of the tool for its application on a specific structure.

For the first test, the following load cases are considered:

 Normal operation load cases

 Lifting load case

 In place load cases

 Transportation load cases

Normal operation load cases represent the loads coming from the XT ordinary work; loads are generated from the connection between the XT with the rest of the cluster and from the XT own weight.

Normal operation loads are simulated with two different load cases, in which a remote force and a remote moment are applied on the VCCS and the XT weight is considered.

Two different load cases are necessary for the representation of the normal operations because of the fact that two different combinations of force and moment have to be considered.

(58)

Lifting load case represents the lifting phase of the XT; here only XT weight is considered, but it is multiplied by 2.5, in order to consider the inertial load due to lifting action, wave on the ocean surface, ocean streams, etc.

Figure 5-14: Lifting of a XT This load case is simulated with a single combination of loads. In place load cases represent the XT weight action on the frame.

Two configurations are considered (so two different load cases are necessary to cover this load case): XT leaned on the wellhead and XT standing on feet.

Obviously only XT weight is considered.

The configuration in which the XT is leaned on the wellhead has to be considered because, being a normal operation load case, it has, if compared with lifting load case, a different load factor (lifting load case presents same loads multiplied for a 2.5 factor; then, is more conservative).

In transportation load cases are considered all of the combination of vertical and horizontal inertial loads developed during the shipping from the factory to the installation site (which occurs, in general, by boat).

(59)

The first one uses LINK180 elements, with tension only option activated, combined with PRETS179 elements.

These elements have the specific function to include in a component of the structure a defined pretension; this solution is highly accurate and simulates well the effects of a pretension in the chain. On the other hand, this solution is highly non-linear (because of the presence of PRETS179, the LINK180 tension only behaviour and the non-linear geometry analysis required from these elements) and the time necessary to obtain the optimized frame is about 100 hours.

The other solution, more simple, uses a linear analysis; the calculation time, hence, results strongly reduced (for the tested frame is about 8 hours).

In this solution, for each load case (so for each accelerations combination), are included in the model only the chains that actually work (so the only ones facing the horizontal acceleration).

Obviously this solution produces different results if compared with the first one, but it allows to consider chains effects and, considering the intended use of the tool, the solution produced with this simplified method is acceptable.

Another reason why this approximation is acceptable is represented by the high uncertain degree which characterized the transportation.

This load case depends on a lot of factors, the most important of which are:

 Vessel used

 Marine survey indications

 Shipping skid geometry

 Agreements with the customers

 Etc.

All of this ambiguity results in the necessity to indicate the customer only a tested configuration of the tree for the shipping.

In general transportation load cases are not considered in the preliminary design because of these factors (in the next test, in fact, transportation load cases are omitted); in general transportation load cases are considered only in the last part of the design phase.

For this reason, transportation load cases will not be included in the analysis of the second frame considered.

(60)

Table 5.1-2 lists all of the load cases considered with a short description, loads and LFs (on the allowable stress).

Table 5.1-2: Load cases

Name Code Loads Accelerations Constraints LF

Normal Operation

LC_1 Horizontal Force _Moment 1g vertical MVB displacements _{and rotations} 2/3 LC_2 Horizontal Force _Moment 1g vertical MVB displacements _{and rotations} 2/3

Lifting LC_3 None 2.5g vertical MVB displacements

and rotations 0.85

In Place

LC_4 None 1g vertical MVB displacements

and rotations 2/3

LC_5 None 1g vertical Foot displacements 2/3

Transportationa

LC_6 None 1g horizontal _{0.7g vertical} Foot and chains _{displacements} 0.85 LC_7 None 1g horizontal _{1.3g vertical} Foot and chains _{displacements} 0.85 LC_8 None 1g horizontal _{0.7g vertical} Foot and chains _{displacements} 0.85

LC_9 None 1g horizontal

1.3g vertical Foot and chains displacements 0.85

LC_10 None -1g horizontal

(61)

In the following images are represented accelerations, constraints and external loads for each load case.

(62)

(63)

Figure 5-18: LC_4 external loads and boundary conditions

(64)

(65)

Figure 5-22: LC_10 external loads and boundary conditions