Design optimisation of swellable elastomeric sealsusing advanced material modelling and FEM simulations

Yevgen Gorash , Alan Bickley and Francisco Gozalo1 2 3*

1 – Dep. of Mechanical & Aerospace Engineering, University of Strathclyde, Glasgow G1 1XJ, UK2 – Weir Advanced Research Centre, Technology and Innovation Centre, Glasgow G1 1RD, UK

3 – Weir Oil & Gas, Weir Rubber Engineering, Salt Lake City, UT 84119, USAyevgen.gorash@strath.ac.uk, alan.bickley@weir.co.uk, francisco.gozalo@weirminerals.comEmails:

Advanced Research Centre

the placeof usefullearning

RobustSimulation

of SwellablePackers

• Standard Water Swell (SSW) Series• High Salinity Water Swell (SHSW) Series• Hybrid Oil and Water Swell (SHYB) Series• Stampede™ Sleeve (SSLV) Series• Standard Oil Swell (SSO) Series

Available Options:

Design Features and Benefits:

High-quality elastomersthat are critical to thelife of the packer

Multiple set screwsand end ring designprevents extrusion

�

�

�

Proprietary elastomer compound provides predictable swell when in contactwith well fluids and with changes in temperature.Robust end ring design, with multiple set screws, protects the rubber during run-in, and provides a barrier against extrusion.Elastomer is vulcanized to the base pipe, allowing the packer to have oneeffective annular seal.

Stampede™ Swellable Packers

1

[1] Lou, Y. & Chester, S. (2014) "Kinetics of swellable packers under downhole conditions." : 1450073.Int. J. Appl. Mechanics 06

[2] Flory, P.J. & Rehner Jr., J. (1943) "Statistical mechanics of cross-linked polymer networks: II. Swelling." : 521–526.

[3] Dassault Systèmes (2015) Providence, USA

[4] Treloar, L. R. G. (1944) “Stress-strain data for vulcanised rubber under various types of deformation.” : 59–70.

[5] Wagner, N. & Helfrich, R. (2016) "Topology and Shape Optimization of Structures under Contact Conditions.", 12-13 October 2016, Manchester, UK

J. Chem. Phys.

SIMULIA Abaqus 2016 Documentation,

Trans. Faraday Soc.

European Conference:Simulation-Based Optimisation

11

40

References

Planned Research Outcomes

�

�

�

�

�

�

�

�

�

Design and manufacturing of tools for mechanical testing ofswellable elastomeric specimens and mechanical behaviour ofpackers in conditions resembling downhole operation.

Mechanical characterisation of swellable elastomers used byWeir Oil & Gas USA for packers through experimental studies inAdvanced Materials Research Laboratory (AMRL) in theUniversity of Strathclyde ( )

Implementation of an advanced material model ofhyperelasticity with moisture swelling in FE-code andidentification of corresponding material constants for it.

Linking of moisture swelling with the fluid pressure penetrationfeature in order to simulate realistic non-uniform materialexpansion, which is more intensive on the areas that are incontact with fluids.

Development of an optimisation procedures for available FEApackages (ABAQUS, ANSYS, MSC.Marc etc.) based onpackers downhole behaviour simulation using an advancedmaterial model.

Implementation of parametric optimisation - to find an optimallength of a packer, and non-parametric (shape and topology)optimisation - to find an optimal packer profile. For this purposeIsight (parametric) and Tosca Structure (non-parametric)optimisation engines will be used.

Optimised packers geometry is obtained by running theoptimisation studies on the regional supercomputer centre atthe Un ivers i t y o f S t ra thc lyde – ARCHIE-WeSt( ).

Provision of packers design recommendations and optimaldesigns based on a number of optimisation studies for variety ofdownhole conditions in form of tables and/or mathematicalrelations.

Delivery of the ABAQUS plugin to Weir industrial partners as aconventional tool for simulation-based design analysis andimprovement.

https://www.strath.ac.uk/amrl/

https://www.archie-west.ac.uk

Discussion

1. for fluid pressure penetration:To account for the asperities on the contacting surfaces, a critical contact pressure, below whichfluid penetration starts to occur, is introduced. The higher this value, the easier the fluid penetrates.The default value of the critical contact pressure is zero, in which case fluid penetration occurs onlyif contact is lost.

How much is it dependent on following?

pressure and type of fluid,

surface quality and material type of borehole,

type of packer elastomeric material.

2. in hourglass control:

Critical mechanical contact pressure

Amount of stiffness

�

�

�

Hourglassing is essentially a spurious deformation mode of a FE-mesh, resulting from the excitation of zero-energy degrees offreedom. It typically manifests as a patchwork of zig-zag orhourglass like element shapes, where individual elements areseverely deformed, while the overall mesh section is undeformed.This happens on hexahedral 3D solid reduced integration elementsand on the respective tetrahedral 3D shell elements and 2D solidelements.

Assigning stiffness to the finite elements is used to suppress hourglassing. Therefore, the followingquestions arise:

Can we relate this artificial stiffness to the "surface layer effect"?

How much stiffness is right to be assigned to the elements?

How do we measure the stiffness of the surface layer in elasmoters?

Which mechanical tests are needed? Indentation tests?

�

�

�

�

element stiffness critical contact pressure

fluid pressure

how related?

Introduction & Objectives

Swellable elastomeric seal is a type of specifically engineered packer that swell upon contact with wellbore fluids.Such packers have been widely employed in various oil-&-gas and minerals applications including slimming of welldesign, zonal isolation, water shut-off, and multi-stage fracturing. Downhole conditions are difficult to be reproducedusing physical testing environment, but feasible to be simulated in virtual environment using CAE software. A betterunderstanding of packers’ mechanical behaviour in downhole conditions would provide a higher confidence andimprovement of existing engineering design practices for manufacturing of packers. The numerical simulation can beincorporated into optimisation procedure searching for an optimal shape of packers with the goals to minimise the timeto seal the borehole and maximise the contact pressure between the seal and borehole. Such an optimisation wouldfacilitate the development of a packer with various designs optimised for different downhole conditions. The objectiveof this research project is to develop a design tool integrated into a CAE to implement parametric numerical studiesusing FEM simulation. However, development of such a CAE plugin is associated with a number of technicalchallenges specific to this class of multiphysics problems.

Hyperelasticity with swelling

The key component is an advanced material model comprising both hyperelasticity and moisture swelling. It has to consider two-wayinteraction between mechanical properties and swelling capacity. Implementation of such material model requires programming of aFortran subroutine for the user defined material using the Flory-Rehner theoretical background [2].

In polymer science Flory–Rehner equation is an equation that describes the mixing of polymer and liquid molecules as predicted by theequilibrium swelling theory of Flory and Rehner. It describes the equilibrium swelling of a lightly crosslinked polymer in terms ofcrosslink density and the quality of the solvent. The theory considers forces arising from three sources [2]:

The entropy change caused by mixing of polymer and solvent.

The entropy change caused by reduction in numbers of possible chain conformations via swelling.

The heat of mixing of polymer and solvent, which may be positive, negative, or zero.

The equation is written as

where is the volume fraction of polymer in the swollen mass, the molar volume of the solvent, is the number of network chain

segments bounded on both ends by crosslinks, and is the Flory solvent-polymer interaction term.

�

�

�

ν n

χ2 1

1

V

� �1

2 23

2 2 1 2 1 2ln 1

2V n

� �� �� � �� � �

� �

�� � � � �

Adaptive remeshing

withoutadaptive

remeshing

withadaptive

remeshing

Non-uniform swelling can be associated with a localised increase ofmaterial volume. So it may cause a significant distortion of FE meshand result into analysis convergence problems. To overcome this, anadaptive mesh-to-mesh solution mapping (rezoning) may be required.

Fluid pressure penetration

The moisture swelling process isnot uniform and develops fromthe surfaces which are subject tofluid. Adsorption, which governsthe progress of swelling canoccur only at open surfaces.Therefore, the fluid pressurepenetration technique needs tobe involved into simulation. Thisis an automated application offluid pressure dependent onchanges of contact conditions.

3

2

Parametric study assumes going through a bignumber of different geometric configurations, lookingat material properties variation and different downholeconditions. This means a search for an optimalgeometry through a sensitivity study, which wouldresult into specific design recommendations for thegeometry of a packer. It is reasonable to automate theanalysis procedure through a Plugin with a convenientGUI, which provides access to the parameters ofgeometry, material, service conditions, etc.

ABAQUS plugin with GUI

4

Shape optimisation with Tosca Structure

2.0

original

optimised

contact area

R=

3.2

5

*dimensionsare in inches

pipe side

borehole side

0.7

5

0

1

2

3

4

5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Conta

ct pre

ssure

(M

Pa)

Normalised length of contact area

original

optimised

Benchmark problem for leakage and extrusion

FE-simulation of Pressure penetration & leakage in packer

16.0

0

0.25

0.5

0.75

R =

3.0

R = 4

R = 4.5

packer

pipe

rock

endring

Max. Principal Strain

0.0680.1970.3250.4540.5820.7100.8390.9671.0961.2241.3521.4811.609

criticalcontactpressure4 MPa

fluid pressureto cause failure byextrusion ~ 14.2 MPa

*dimensionsare in inches

Strain

Max. Principal

0.0600.1060.1520.1980.2440.2890.3350.3810.4270.4730.5190.5650.611

Strain

Max. Principal

0.0640.1280.1910.2550.3190.3820.4460.5090.5730.6360.7000.7630.827

Strain

Max. Principal

0.0610.1520.2420.3330.4240.5140.6050.6960.7860.8770.9681.0581.149

Strain

Max. Principal

0.0550.1690.2840.3990.5140.6280.7430.8580.9721.0871.2021.3161.431

Strain

Max. Principal

0.0650.1940.3220.4510.5790.7080.8370.9651.0941.2221.3511.4801.608

Strain

Max. Principal

0.0660.2000.3330.4670.6000.7330.8671.0001.1331.2671.4001.5331.667

0 3 6 8 10 10.7

fluid pressure fluid pressure fluid pressure fluid pressure fluid pressure fluid pressure

criticalcontactpressure0.6 MPa

Max.PrincipalStrain

0.050.100.140.190.230.280.320.370.420.460.510.550.60

Max.PrincipalStrain

0.040.110.170.240.310.370.440.510.570.640.700.770.84

Max.PrincipalStrain

0.040.150.260.360.470.580.690.790.901.011.121.231.33

Max.PrincipalStrain

0.040.160.280.390.520.640.760.880.991.111.231.351.47

0 5 14 15 16.2

fluid pressure fluid pressure fluid pressure fluid pressure

Max.PrincipalStrain

0.040.180.330.470.610.760.901.041.191.331.481.621.76

fluid pressure

criticalcontactpressure1.0 MPa