Top Tensioned Riser Layout Design Optimization

Yongjun Chen, Peimin Cao SBM Atlantia, Inc. Houston, TX USA

ABSTRACT Dry tree production platform becomes more and more popular due to its low OPEX and ease of well intervention. For TTR layout design, there are minimum spacing requirements for both deck wellbay and seafloor. There are also constraints on the deck spacing and the riser offset at seafloor relative to the wellbay location, i.e. riser vertical angle. For fields with substantial reserve, the number of TTRs may become large; and thus the TTRs may cluster together, which makes the riser layout design very complex, and may require exhaustive design iterations. In order to solve the problem, this paper presents a novel optimization approach called Equilateral Triangle Grid method. Based on the predefined deck wellbay layout, the method guarantees the minimum spacing requirement at seafloor while tries to minimize the riser vertical angle. KEY WORDS: TTR Layout; Dry-Tree System; Optimization INTRODUCTION Dry tree production systems, such as TLPs and Spars, are continuously being designed and installed for deepwater developments worldwide, especially for reservoirs with large reserves. This is because dry tree systems offer direct access to the development wells, and thus reduces the cost associated with drilling and well intervention. Top tensioned risers (TTRs) installed on the dry tree production system provides the shortest flow path, which reduces flow assurance problem and increases recovery rate from the reservoir. The TTR layout design includes both deck wellbay layout and seafloor well layout. The deck wellbay layout is generally governed by the deck space, equipment handling, jumper/tree clashing requirement, and operational limitations. The seafloor well layout is generally governed by the riser clashing requirements, riser deployment and stab-in requirements, and ROV access. For equipment handling and riser clashing, the distances between risers

at the deck wellbay and at the seafloor should be maximized. However, the riser spacing at deck wellbay is restrained by the overall deck design and layout, and is normally pre-defined. If it is not pre-defined, this methodology still can be used to evaluate various deck layout options. The riser spacing at the seafloor is restrained by the riser vertical angle required by the installation and well operations. In addition, in order to reduce TTR stroke, the offset of well at seafloor level should be minimized from the riser slot at the deck level in any direction, i.e. the riser vertical angle should be minimized. The most preferable layout is that all TTRs being installed without offset, which is easy for installation, well operation, and induces no geometric stroke. However, for clustered and large fields with 20+ wells, running all TTR straightly vertical down is difficult, or even impossible, to achieve and the TTR layout design becomes very complex and may require extensive design iterations. This paper presents a novel optimization method Equilateral Triangle Grid for TTR layout design for clustered wells. For a predefined deck wellbay layout, the method first puts all the seafloor wellheads on an equilateral-triangle grid, which maintains the wellhead seafloor spacing as the required; it then shifts and rotates the grid to minimize the riser vertical angle. This method has been applied to a case study, and its results are compared to a commercial optimization program. PHYSICAL MODEL DESCRIPTION The TTR layout design includes both deck wellbay layout and seafloor well layout. The deck wellbay layout is generally governed by the deck space, equipment handling, jumper/tree clashing requirements, and operational limitations. Therefore the deck wellbay layout is normally predefined. The seafloor well layout is generally governed by the riser clashing requirements, deployment and stab-in requirements, and ROV access. The seafloor well layout is normally determined and optimized by the engineering design. Under sufficient tension, each TTR can be simplified as a straight line-pipe connecting two nodes, one at the deck (tensioner ring, air can, or guide structure), and the other at the seafloor (wellhead tie-back

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Proceedings of the Twenty-first (2011) International Offshore and Polar Engineering ConferenceMaui, Hawaii, USA, June 19-24, 2011Copyright 2011 by the International Society of Offshore and Polar Engineers (ISOPE)ISBN 978-1-880653-96-8 (Set); ISSN 1098-6189 (Set); www.isope.org

connector). Figure 1 shows a typical TTR and connections (Rainey, 2002); Figure 2 shows a typical deck wellbay layout (Jordon, Otten, Trent, and Cao, 2004), with tensioner, jumper, and trees are shown; and Figure 3 shows a typical riser layout, both at deck wellbay and at seafloor.

Figure 1. Typical TTR and Connection

Figure 2. Typical Deck Wellbay Layout

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Figure 3. Typical TTR Layout

For the seafloor well layout design, the following constraints should be considered: 1) The spacing between any pair of wellheads should be not less than

a threshold value set by the installation, drilling and ROV access requirements;

2) The offset of riser wellhead relative to the riser slot at the deck in any direction, i.e. riser vertical angle, should be limited to no greater than a certain value set by deployment and final stab-in angle requirements;

3) There is no clashing between risers under extreme environment with the consideration of wake effects.

Normally constraint 1) is a mandatory requirement which can not be relaxed or design around; while constraints 2) and 3) can be achieved through engineering design and optimization. Constraints 1) and 3) require large seafloor spacing; on the contrary, constraint 2) requires small seafloor spacing. This creates an optimization problem minimize riser the vertical angle while satisfy the seafloor spacing and no clashing constraints. MATHEMATICAL MODEL DESCRIPTION There are two sets of nodes, A and B, each has N nodes. The positions of A nodes (A1, A2 ) are predefined (deck); while the positions of B nodes (B1, B2 ) need to be determined (seafloor). Nodes Ai and Bi are considered as one pair, and connect them forms the ith riser. Definitions:

DAB(i) horizontal distance between nodes Ai and Bi, offset for the ith riser.

DBB(i,j) - distance between any two nodes (Bi, Bj) within set B Known Variables: Ai(x), Ai(y) - position of all nodes within set A DBB0 - a preset threshold value Decision Variables: Bi(x), Bi(y) - position of all nodes within set B Optimization Target: Minimize the maximum value of all N DAB values Constraints:

DBB(i,j) DBB0 (for all i and j, i j) Figure 4 illustrates the optimization problem.

Figure 4. Mathematical Model Illustration

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This optimization problem has 2N decision variables and N*(N-1)/2 constraints. When the number N becomes large, such as 20+, the problem becomes very complex and needs special program to handle. EQUILATERAL TRIANGLE GRID METHOD In order to simplify the above problem, the first task is to reduce the number of decision variables and/or constraints. Since the distance between any two nodes within set B should be not less than a certain value; if all the B nodes are chosen from an equilateral triangle grid (grid spacing = DBB0) as shown Figure 5, then all the constraints (DBB(i,j) DBB0) are satisfied.

Figure 5. Equilateral Triangle Grid By choosing B nodes from an equilateral triangle grid (grid spacing = DBB0), the distance between any pair of B nodes is guaranteed not less than the required value of DBB0. In addition, for any equilateral triangle grid, the location of all nodes can be determined based on the following three variables (as shown in Figure 5). (BX1, BY1) - the position of the starting node - the initial heading of the first grid line i.e. BXi = f (BX1, BY1, ) BYi = f (BX1, BY1, ) Therefore, the original optimization can be simplified as: Minimize the maximum value of all N DAB values by adjusting decision variables (BX1, BY1) - shift the grid and adjusting decision variable - rotate the grid This simplified optimization problem only has three decision variables without constraints, and thus is much easier to handle than the original problem. Please bear in mind that the solution space for the simplified problem is only a subset of the original problems solution space, and thus the optimal solution for the simplified problem may not be the optimal solution for the original problem. The general procedure for design/optimize the TTR layout design is:

1. Random select a starting point (normally one of the center nodes) and initial heading angle (Figure 6)

2. Generate an equilateral triangle grid which covers all the A nodes (Figure 7)

3. Pick up B nodes from the grid, and pair/connect them with the closest A node (Figure 8)

4. Calculate the distance for all pairs of AB nodes, and then calculate the maximum distance

5. Minimize the maximum distance DAB by shifting/rotating the grid 6. Report the positions of B nodes

Figure 6. Step 1 - Select Starting Point and Initial Heading

Figure 7. Step 2 - Generate Equilateral Triangle Grid

Figure 8. Step 3 - Pick B Nodes and Connect to A Nodes

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IMPLEMENTATION USING EXCEL For the simplified optimization problem, Microsoft Excel is the best tool to implement the Equilateral Triangle Grid method. The implementation includes 4 sections. Section 1 provides user interface for input design requirements, decision variables, and target values; as shown in Figure 9.

Design Requirement:Required Dist. DBB0 = 20.00Calculated DBB-min = 20.00Meet Requirement? Y

Decision VariablesInitial Heading = 0.175Starting Node BX1 0.000Starting Node BY1 0.000

Target Value - MinimizeMax of DAB 27.04

TTR Layout Design Optimization - Using Equilateral Triangle Grid Method

Figure 9. Implementation in Excel Users Input Section 2, as shown in Figure 10, is the table for TTR node coordinates, which includes both the deck nodes (set A, known) and the seabed nodes (set B, unknown). The coordinates of set B are calculated based on BX1, BX2, and equilateral equation. The distance between each pair of nodes (DAB) is also calculated in the table, and the max DAB is highlighted. The distance between any two nodes within set B (DBB) are calculated and listed in Section 3 (DBB table) as shown in Figure 11. The minimum distance values are highlighted. Section 4 provides the plot for user to view the layout results. After the above initial set up, Solver add-in in Excel can be used to search the best solution. The Solver set up is:

Set Target Cell: Max of DAB

Equal To: Min

By Changing Cells: Initial Heading , Starting Node BX1, BY1 Subject to the Constraints:

It is unnecessary to add constraints on DBB DBB0 since the equilateral triangle grid method guarantees this requirement. In order to speed-up the search process, user may add constraints on the values of , BX1, and BY1

Figure 12 shows the Solver setup in Excel.

DABBX (ft ) BY (ft ) AX (ft ) AY (ft ) S-play

01 -24.06 -55.88 -18.00 -47.50 10.3402 -24.76 -35.89 -18.00 -28.50 10.0103 -25.46 -15.90 -18.00 -9.50 9.8304 -26.16 4.09 -18.00 9.50 9.7905 -26.86 24.08 -18.00 28.50 9.9006 -27.56 44.06 -18.00 47.50 10.1607 -7.10 -45.28 -6.00 -47.50 2.4808 -7.80 -25.29 -6.00 -28.50 3.6809 -8.50 -5.30 -6.00 -9.50 4.8910 -9.20 14.69 -6.00 9.50 6.1011 -9.90 34.68 -6.00 28.50 7.3012 -10.60 54.66 -6.00 47.50 8.5113 10.56 -54.66 6.00 -47.50 8.4914 9.86 -34.68 6.00 -28.50 7.2815 9.16 -14.69 6.00 -9.50 6.0716 8.46 5.30 6.00 9.50 4.8717 7.76 25.29 6.00 28.50 3.6618 7.06 45.28 6.00 47.50 2.4619 27.52 -44.06 18.00 -47.50 10.1220 26.82 -24.08 18.00 -28.50 9.8721 26.12 -4.09 18.00 -9.50 9.7622 25.42 15.90 18.00 9.50 9.8023 24.72 35.89 18.00 28.50 9.9924 24.02 55.88 18.00 47.50 10.31

Ris e r IDSe abe d - Unknown De c k - Known

Figure 10. Implementation in Excel Coordinates Table

DBB 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

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10 72 53 35 20 20 35 60 40 2011 92 72 53 35 20 20 80 60 40 2012 111 92 72 53 35 20 100 80 60 40 2013 35 40 53 69 87 106 20 35 53 72 92 11114 40 35 40 53 69 87 20 20 35 53 72 92 2015 53 40 35 40 53 69 35 20 20 35 53 72 40 2016 69 53 40 35 40 53 53 35 20 20 35 53 60 40 2017 87 69 53 40 35 40 72 53 35 20 20 35 80 60 40 2018 106 87 69 53 40 35 92 72 53 35 20 20 100 80 60 40 2019 53 53 60 72 87 104 35 40 53 69 87 106 20 20 35 53 72 9220 60 53 53 60 72 87 40 35 40 53 69 87 35 20 20 35 53 72 2021 72 60 53 53 60 72 53 40 35 40 53 69 53 35 20 20 35 53 40 2022 87 72 60 53 53 60 69 53 40 35 40 53 72 53 35 20 20 35 60 40 2023 104 87 72 60 53 53 87 69 53 40 35 40 92 72 53 35 20 20 80 60 40 2024 122 104 87 72 60 53 106 87 69 53 40 35 111 92 72 53 35 20 100 80 60 40 20

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Figure 11. Implementation in Excel DBB Table

Figure 12. Implementation in Excel Solve Setup

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CASE STUDY A deepwater dry tree facility is designed with 24 well slots. The well pattern is 6 rows in North-South direction with 4 wells each row (East-West). The well spacing is 19-ft along both North-South direction and 12-ft along East-West direction. At seabed, the minimum distance between wells is 20-ft. To facilitate riser installation, drilling and well intervention, the riser vertical angle with respect to the vertical direction for the bottom connection shall be not more than 2.0 degrees, and this includes the wellhead inclination tolerance that is 1.0 degree. So, for installation, the maximum angle with respect to the vertical direction is 1.0 degree. The water depth at the field is 1500-ft. The problem was modeled in Microsoft Excel using Solve feature. It took less than one minute to find an optimal solution. Figure 13 shows the optimal solution from the Equilateral Triangle Grid method with three decision variables having values:

BX1=-8.50; BY1=-5.30; =2.0 degrees The optimized/minimized maximum distance of all AB pairs (DAB) is 10.34-ft, this occurs at both the bottom-left node and the top-right node.

TTR Layout Optimization

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Figure 13. Case Study Solution To show effectiveness of the method, the problem was also solved using the commercial optimization software LINGO from LINDO SYSTEMS. LINGO is a comprehensive tool (modeling language) designed to make building and solving Linear, Nonlinear (convex and non-convex / global), Quadratic, Quadratically Constrained, Second Order Cone, Stochastic, and Integer optimization models faster, easier and more efficient. User does not need to specify which solver to use; the LINGO automatically selects the appropriate solver based on users model and formulation.

The model of the problem consists of 48 nonlinear decision variables, 276 constraints. Both Non-Linear Programming and Global Solver are employed. It took several hours to find a global optimal solution. Figure 14 shows the solution from LINGO. The optimized/minimized maximum distance of all AB pairs (DAB) is 9.69-ft.

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Figure 14. Case Study Solution from LINGO By comparing Figure 13 with Figure 14, it can be found that the optimal solution from the Equilateral Triangle Grid method is very close to the global optimal solution from LINGO, for both seafloor layout pattern and minimized DAB value. CONCLUSION AND DISCUSSION An Equilateral Triangle Grid method was proposed to optimize the TTRs layout design for the dry tree facilities with clustered risers. The method provides the most compact grid for searching the solution. A case study was examined and the result demonstrates that the solution from the proposed method could be close to the global optimal solution. Due to the extra constraints introduced into the simplified problem, i.e. all nodes are on the equilateral triangle grid; the solution space of the simplified problem is only a subset of the solution space for the original problem. Therefore the optimal solution from the method may not be the global optimal solution of the problem. However, the method is still a very useful tool because of its ease to model, quick to find solution, and the solution can be very close to the global optimal solution. For projects with special requirements on the deck and seafloor well layout to assist a certain installation or drilling sequence, such as all wells are required to be on concentric circles or on straight lines, the proposed method may not provide a good feasible solution. However, by employing the same principle and procedure, Concentric Circle

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Grid, Rhombus Grid, or Square Grid method can be used to search the best solution meeting the project requirements. For projects with strict requirements on the riser vertical angle and spacing, multiple grid methods can be used simultaneously and select the best solution among all sub-optimal solutions. ACKNOWLEDGMENTS The authors would like to acknowledge the management of SBM Atlantia for allowing this paper to be published. The valuable comments and advice from S. Schuurmans of SBM are also greatly appreciated.

REFERENCES Rainey RM, (2002), Brutus Project Overview: Challenges and

Results, Proc of Offshore Tech Conf, Houston, USA Jordon R, Otten J, Trent D, Cao P, (2004), Matterhorn TLP Dry Tree

Production Risers, Proc of Offshore Tech Conf, Houston, USA LINDO SYSTEMS website: http://www.lindo.com

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