The objective of this study is to explore the opportunity to improve the design and sizing of mudmat for subsea structures, such as Pipeline End Termination (PLET). This is done by comparing the traditional approach following the limit equilibrium methods in API RP 2GEO with a more rigorous simplified integrated analysis approach that involves a single finite element analysis (FEA) model that includes both the pipeline and jumpers together along with the soil-mudmat interaction modeled as non-linear springs, and to quantify any conservatism inherent in the traditional approach. A mudmat design with aspect ratio of 1:2 was considered for detailed analysis. Initially, jumper and pipeline loads were determined by imposing artificial boundary conditions at the hubs and end terminals. Using analytical methods and considering a total dead (submerged) weight of the mudmat and superstructure, a mudmat size was determined per the American Petroleum Institute (API) approach. Factor of Safety (FOS) for bearing and sliding loads were also determined. Thereon, using this mudmat size, the FOS for bearing and sliding were determined using the simplified integrated approach with non-linear springs representing soil-mudmat interactions. The FOS values using the simplified approach were observed to be higher than those obtained using the traditional approach. This provides an opportunity for a “leaner” design, especially as new high pressure, high temperature (HPHT) fields are made feasible where the mudmat size, if designed with conservatism in API RP 2GEO, may be impractically large for installation.

1. FEA BASED SIMPLIFIED INTEGRATED ANALYSIS
FOR MUDMAT DESIGN
Dr. A. Chakraborty, Dr. S. Srigiriraju, Dr. B. Ozturk, Devvrat Rathore
Virtual Integrated Analytics Solutions (VIAS)
1400 Broadfield Blvd. Suite 325, Houston TX 77084
Phone : +1 (832) 301-0881
www.viascorp.com
Contact Person: Dr. A. Chakraborty – achakraborty@viascorp.com
June 09 - 14, 2019 | Glasgow, Scotland, UK

2. © 2019 Virtual Integrated Analytics Solutions Inc.
Agenda
2
• VIAS Introduction
• Background & Objective
• Methodologies of Mudmat Design
• Design Basis
• Conventional Approach
• Proposed Simplified Integrated Approach
• Comparison of Two Approaches
• Conclusions

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Who We Are
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• Provide AM Simulation and 3D Printing Services

4. BACKGROUND & OBJECTIVE

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Background
5
• Loads on PLET:
• Weight of components
• Ocean currents
• Thermal expansion of pipeline
• Mudmat
• Provide bearing strength
(weight of components)
• Skirt of mudmat
• Provide resistance to lateral
movement on seabed
• Current Standard Practice in Design
• API – focus of this work
• ISO
• DNV
A typical subsea production system (Yong Bai, Qiang Bai)

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Background
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• Design of mudmat
• Too large a size – fabrication & installation cost and feasibility
• Too small a size – low bearing strength
• Very important for high pressure and high temperature (HPHT) deep water
wells
Installation of PLET (Courtesy: Allseas)

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Objective
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• Propose an integrated solution for mudmat design considering high
fidelity numerical simulation but capable of providing a time efficient
approach for project team.

8. METHODOLOGY

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Conventional Approach
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• Pipeline loads including
thermal expansion
• Jumper loads including
thermal expansion
• Assume mudmat size and
evaluate FOS using API
• Iterate until the sizing
process until the design
criteria is satisfied and
mudmat size is as small as
possible

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Proposed Simplified Integrated Analysis Approach
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• Use the mudmat size of
conventional approach
• Develop soil-mudmat
interaction as nonlinear
springs in FEA
• Use mudmat, jumpers and
nonlinear springs in FEA to
evaluate new factors of
safety.

11. DESIGN BASIS

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Mudmat, Soil and Jumpers
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Nominal geometric and material properties
were used
Mudmat and Soil features and properties Two jumpers’ dimensions
Jumpers features and properties

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PLET
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• Pipeline length of 5km was considered
• Soil friction of 0.5 was used in
conventional approach
• The pipeline end structure was
allowed a sliding distance of before it
gets locked into mudmat to make
them a single rigid body.
PLET elevation and plan views

14. MUDMAT DESIGN
CONVENTIONAL APPROACH

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Pipeline Design Analysis
• Step-1: Lay the straight pipe under gravity
• Step-2: Push the PLET end of the pipe up
(away from seabed) by 30 inches
• Step-3: Activate buckling modes if applicable
• Step-4: Apply internal pressure on ID
(content pressure = 10 ksi) and external
pressure on OD (2667 psi @ depth of 72000
in)
• Step-5: Apply temperature (250 F, initial
temperature=39.2 F) with buckling active at
the locations of imperfections
Pipeline
Seabed
Pipeline FEA Model

16. © 2019 Virtual Integrated Analytics Solutions Inc.
Pipeline Design – Axial Displacement of PLET
with/without Buckling in Pipeline
# Buckling
Locations
Displacement
(in)
Displacement
(ft)
0 115.97 9.66
1 65.77 5.48
2 46.50 3.88
3 36.58 3.05
4 30.57 2.55
Number of buckling locations chosen for axial force calculation: 4
End displacement of pipe with 4 buckling locations = 30.57” (2.55ft –
close to design criteria of free expansion of PLET end).

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Pipeline Design – Axial Force for various Sliding
Distances with Four Buckling Locations
Stop
Distance (in)
Axial Force
(kips)
3 209.69
2 144.66
1 72.52
Sliding distance was kept at 29.57” (1” Stop Distance) to have a reasonable size of mudmat.
Axial force exerted on mudmat after slider locks PLET to mudmat = 72.52 kips
Stop Distance = Free Expansion (without slider) – Sliding Distance (with slider)
Free Expansion = 30.57”
Choose an appropriate sliding distance (judiciously)
Stop Distance was varied as given below:
Introduce slider mechanism on mudmat – PLET end locks up after sliding certain distance

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• Initial Temperature = 39.2 oF
• Step-1: Gravity loading
• Step-2:
• Internal Pressure = 10000 psi @
ID
• External Pressure = 2667 psi @
OD
• Step-3: Operating Temperature = 250
oF
• Step-4: Deflection of 29.57 in at PLET
end and the other end is fixed
Jumper Analysis
Jumper-100 Jumper-150
Force along the length (lbf) 13592 1148
Vertical (lbf) 7553 7526
Lateral Force (lbf) 153 240
Max. Deflection (in) 31.21 34.30
VM Stress (ksi) 41.97 31.29
Results:
PLET Ends
Along Length
Fixed
Ends
PLET Ends

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Mudmat Analytical Design (2:1 ratio) 70x35
Iteratively, arrive at minimum mudmat size that passes the FOS of bearing and
sliding capacities as per API RP 2GEO
Factors of Safety:
Undrained bearing capacity = 2.86598
Undrained sliding capacity = 2.04772

20. MUDMAT DESIGN
SIMPLIEFIED INTEGRATED
APPROACH

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Total ShearStrain Plastic Shear Strain Shear Stress (psi)
0 0
1.00E-04 0.255569307
0.005 0 8.604166667
0.01 0.0025 12.90625
0.02 0.01 17.20833333
0.03 0.01875 19.359375
0.04 0.028 20.65
0.05 0.0375 21.51041667
0.1 0.086363636 23.46590909
0.15 0.1359375 24.19921875
0.2 0.185714286 24.58333333
Mudmat-Soil Interaction – Develop Nonlinear Springs
• Mohr-Coulomb Plasticity model was used for soil
• Undrained Shear Strength (Su) = 40 + 7z (“z” is depth in ft)
• At any depth:
• Shear Stress/Su = min{1.05*r/(0.01+r),1} (“r” is shear strain)
• Shear Modulus of soil was chosen as ratio of shear stress to shear
strain @ 0.5% shear strain.
• Young’s Modulus = 3 *Shear Modulus (incompressible)
• Friction and Dilation Angles were chosen to be 0.
• Stress-plastic strain data were evaluated to give as input to Abaqus
Total ShearStrain Plastic Shear Strain Shear Stress (psi)
0 0
1.00E-04 0.002887789
0.005 0 0.097222222
0.01 0.0025 0.145833333
0.02 0.01 0.194444444
0.03 0.01875 0.21875
0.04 0.028 0.233333333
0.05 0.0375 0.243055556
0.1 0.086363636 0.265151515
0.15 0.1359375 0.2734375
0.2 0.185714286 0.277777778
At Depth
z=0
At Depth
z=6000 in
E=58.14 psi
E=5145.29 psi

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Automation of Creation of Mudmat-Soil FEA Model
A meshed FEA model of any mudmat and soil block dimensions can be generated.

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Mudmat-Soil FEA Model – Develop Nonlinear Springs
Rigid Body
Symmetry conditions
• Mudmat not physically
included in the model.
The effect of presence
of mudmat was
modeled by rendering
the volume of the soil
occupied by the
mudmat as rigid.
• The reference node of
this rigid body was at
the mudmat center (at
z=0 soil line).

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Mudmat-Soil FEA Results – Nonlinear
Spring Behavior Along the Long Edge
Mises Contour Plot
and Deformed
Configuration
Von Mises in psi
Evaluate non-linear soil spring in each of the six DOF by moving the mudmat in each of
the six directions

25. © 2019 Virtual Integrated Analytics Solutions Inc.
Mudmat-Soil FEA Results – Nonlinear
Spring Behavior Along the Long Edge
Mises Contour Plot
and Deformed
Configuration
Von Mises in psi
Evaluate non-linear soil spring in each of the six DOF by moving the mudmat in each of
the six directions

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Simplified Integrated FEA Model
Rigid
connections
• Connectors used to connect PLET,
mudmat and jumpers
• Mudmat Center is connected to ground
with soil springs in 6 DOF.
Mudmat CoG
Jumper fixed
ends
Rigid seabed surface not shown
Pipe left end fixed

27. © 2019 Virtual Integrated Analytics Solutions Inc.
Simplified Integrated FEA – Free Expansion of Pipe
End
• Recalculate the PLET end displacement
of pipe in this new model with no stop
• Initial Temperature = 39.2 oF
• Same steps as Pipeline FEA analysis:
• Step-1: Laying of a straight pipe under
gravity
• Step-2: Pushing the PLET end of the pipe up
(away from seabed) by 30 in
• Step-3: Activate Buckling modes if
applicable
• Step-4: Applying internal pressure on ID
(content pressure = 10 ksi) and external
pressure on OD (2667 psi @ depth of 72000
in)
• Step-5: Applying Temperature (250 F, initial
temperature=39.2F) with buckling active at
the locations of imperfections
Free Expansion of pipe end in Integrated Model: 29.82”
Difference from conventional approach free expansion – due to addition of soil springs
and jumpers

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Simplified Integrated FEA
• Use same stop distance of 1”
as in conventional approach
• Sliding Distance = 28.82 in
(difference between Free
Expansion of 29.82 in and
Stop Distance of 1”)
• Activate the stop
• Run the analysis
Pipeline Load at PLET End: 50.71 kips

29. COMPARISON OF TWO
APPROACHES

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• The below loads are along the length and lateral of the respective jumpers.
• Values of jumper analysis and integrated model are shown for comparison.
Jumper Loads – PLET End
Jumper-100
Conventional
Approach
Jumper-100
Integrated Model
Reduction %
Force along the length (lbf) 13592 13430 1.19
Lateral Force (lbf) 153 154 -0.65
Jumper-150
Conventional
Approach
Jumper-150
Integrated Model
Reduction %
Force along the length (lbf) 1148 1095 4.62
Lateral Force (lbf) 240 239 0.42
Most jumper loads are reduced in the Simplified Integrated Model

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Loads at PLET end for Standalone Pipeline FEA and Integrated Analysis
Pipeline Loads – PLET End
Stand-alone Pipeline FEA
(Conventional Approach)
Simplified Integrated
Model
Force along the length of the pipe (kips) 72.52 50.71
PLET
Ends
Pipeline Load reduced by 30%!

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Mudmat Size & Loads
Per API RP 2GEO
Integrated Model Conventional Approach
60 x 30 ft.Minimum allowable mudmat size 62 x 31 ft.

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FOS (2:1 Mudmat size ratio: 70x35 ft)
Per API RP 2GEO
FOS Integrated
Model
Conventional
Approach
Percent
Change
Bearing
Capacity
3.05 2.87 6.29
Sliding
Capacity
3.23 2.05 57.85
Calculation of FOS for loads from Integrated Model

34. CONCLUSIONS

35. © 2019 Virtual Integrated Analytics Solutions Inc.
Conclusions
• Traditional approach of mudmat design based on API RP 2GEO gives a
conservative estimate of mudmat size and FOS.
• Simplified integrated model that involves the pipeline, jumpers, and soil-
mudmat interaction in a single model gives more accurate estimate of the
forces/moments on mudmat.
• Using simplified integrated approach, mudmat design can be directly based on
soil failure behavior – relevant for brown field assets.

36. FUTURE WORK

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Future Work
• Validation with field data
• Use the current approach to develop a surrogate model to be use in a data
driven framework

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Thank you