Fluid-structure interaction in flow induced sealing in wellhead isolation tool.

The wellhead isolation tool (WIT) isolates the wellhead from exposure to treating fluids and pressures. The isolation tool (figure 1) contains a seal element and mandrel that are inserted through the existing wellhead bore and tubing hanger into the production tubing. The seal element and mandrel configuration allow treating fluids to be pumped through the WIT directly into the production tubing. Tubing pressure activates the tool by energizing the sealing element. The simple and economical WIT is ideal for breakdown treatments and fracturing jobs. It is also used to protect the wellhead from high pressure in tubing conveyed perforating situations where pressure actuated firing heads are used.

Due to larger variation of casing ID in WIT cup applications than was expected in the design process, the pressure rating of many cups needs to be reevaluated. The performance aspects of the WIT cup of great interest include:

* Whether a cup can be set properly in a given casing ID; and

* once set, what maximum pressure the cup can sustain. Physically testing each cup under various casings would be very time consuming and expensive. Virtual testing (nonlinear FEA simulation) on WIT cups for determination of the operating pressure envelope can significantly reduce the amount of time and money spent on testing, and helps to understand cup operating and failure mechanics.

A virtual test model for two types of WIT cup was developed and successfully validated (ref. 1). During the process, it was found that a cup that was designed for a nominal casing ID did not have interference with the corresponding maximum API casing ID; so the cup did not have an initial seal. As a matter of fact, the cup would not seal under available flow rate in the lab tests. In the lab test, the initial seal between the cup and the maximum API casing ID is artificially introduced. Virtual testing on the cup is conducted under the assumption that the cup will seal. Virtual test results are validated with respect to pressure rating. But the following questions remain:

* Will the cup seal for a given flow rate?

* Under what flow rate will the cup seal?

* How can we model the interaction between the flow of the fluid and the large deformation in the seal during the seal setting process?

To have a high fidelity virtual test on the WIT cup seal, we would need to model fluid-structure interaction in our models. Fluid-structure interaction is a very difficult problem to solve, especially when turbulent flow in the fluid and large deformation in the solid are involved, such as the case for the problem at hand. Simulation of fluid-structure interaction has been a subject of academic research for many years (ref. 2), with limited applications in an industrial environment until recently. Recently, several major computational modeling commercial code developers offered fluid-structure interaction (FSI) capabilities for general-purpose simulation. For example, finite element analysis (FEA) commercial code developer Abaqus offered FSI capability (ref. 3) through a software suite of Abaqus-MpCCI-Fluent; where Fluent is computational fluid dynamics (CFD) software from Fluent Inc., and MpCCI is an inter-process communication software developed and distributed by the research institute Fraunhofer SCAI. This software suite is used in our effort to analyze the multi-physics problem of flow induced initial seal in wellhead isolation tools.

In the following, the FSI approach used in Abaqus-MpCCI-Fluent is first examined and its limitations are identified. The formulation of an FSI model for flow induced sealing is then presented, where a work-around of the major limitation of the FSI approach is proposed. The simulations of the flow induced sealing in a wellhead isolation tool are shown to demonstrate the effect of fluid-structure interaction on the sealing process, and the necessity of the multi-physics approach. The article ends with a summary and discussions on potential improvement of the FSI approach.

Fluid-structure interaction modeling approaches

There are two general approaches for numerical simulation of fluid-structure interaction phenomena. One is the strongly coupled approach, which solves the governing equations for solids and fluids simultaneously. In this approach, the coupling and interaction between solid and fluid can be accurately represented. But the strong coupling also leads to significant

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by Allan Zhong, Halliburton ([e-mail])

numerical difficulties in numerical computation, especially when highly turbulent flow and finite deformation in a nonlinear solid are involved. For these reasons, the strongly coupled approach is typically limited to very specific applications; for a recent example, one can refer to Stein, et al, (ref. 4). Developing an efficient, robust algorithm for strongly coupled fluid-structure interaction problems remains to be a subject of academic research.

The other approach is the so-called weakly coupled approach. In this approach, the governing equations for solids and fluids are solved separately. The interaction between the two solution domains is realized via the interface between the solid and the fluid. The structural solution provides the displacements and/or temperatures at the interface surface; the flow solution provides the pressure/heat flux loading at the interface surface. Due to the nature of the method to couple fluid and solid responses, the approach can only be applied to weakly coupled fluid-structure interaction phenomena. For many industrial applications, such as flow in turbine machinery, motion of valves and flow induced sealing processes, the fluid-structure interaction is weakly coupled. In the weakly coupled approach, one can utilize proven FEA/CFD software for solid/fluid problems. Recently, the weakly coupled fluid-structure interaction simulation has become widely available through commercial software, e.g., the Abaqus-MpCCI-Fluent suite, which makes the approach even more appealing for industrial applications.

The Abaqus-MpCCI-Fluent FSI software suite was used in the current study. Its technical features are recapped here from the user's guide (ref. 3) for discussion. A staggered solution scheme is employed in this suite. The structural and fluid equations are solved independently, i.e., Abaqus solves the structural domain and Fluent solves the fluid domain. Then, loads and boundary conditions are exchanged after a converged increment via the mesh-based parallel code coupling interface (MpCCI). In addition to the limitation to weakly coupled FSI problems, the FSI suite cannot handle a system involving topology change of fluid domain during the fluid-structure interaction process. The limitation is in fact a limitation of current CFD technology. The flow induced sealing process involves a change of topology of the fluid domain during the sealing process. How to work around the limitation on topology change of fluid domain is a major challenge in applying the FSI suite to the flow induced sealing problem.

A fluid-structure interaction model for flow induced sealing

Based upon past FEA-based virtual tests on the flow induced sealing process (ref. 1) via an approximated pressure boundary condition, it is known that a seal may be lifted off the mandrel where the seal has an interference fit. It is also known that, upon sealing, the single fluid domain that existed before sealing is divided into two separated domains. So the topology of the fluid domain changes in the sealing process. This change poses a serious issue for the application of the FSI suite to the flow induced sealing in a cup seal. Strictly speaking, the FSI suite cannot be applied to the flow induced sealing problem. In addition, in reality, a cup seal usually has interference with a mandrel, which leads to a few additional difficulties in the modeling process:

* The fluid domain cannot be determined from part drawings;

* meshing of irregular shapes of the fluid domain; and

* increased difficulty in convergence of CFD computation. As discussed in a previous paper by the author (ref. 1), an axis symmetric model is sufficient to model the cup seal problem. Following the generic procedure for FSI model generation, an axis symmetric FSI model is created in the following way:

* Create an FEA axis symmetric model for the structure with definition of a fluid-structure interface (figure 1). The model has the following features:

--large deformation is considered;

--hyper-elasticity for the elastomeric seal, metal plasticity for steel parts; and

--contact among all components.

* Conduct an interference fit analysis to determine the fluid domain (figure 2);

* Create an axis symmetric turbulent flow model for the fluid domain. To work around the potential fluid domain topology change during the sealing process, a dummy domain is created at the potential new fluid region. Dynamic mesh capability (ref. 5) is invoked. The CFD model has the following features:

--steady state turbulent flow analysis--standard k-[epsilon] method;

--dynamic mesh for the fluid domain, local mesh refinement;

--changing fluid domain during FSI iteration; and

--the fluid is water.

* The coupling between the flow and seal deformation is realized via serial coupling in the following way:

--start FSI simulation at the step after interference fit;

--conduct flow analysis at a given flow rate and determine flow pressure on the fluid--structure interface. Communicate the pressure to FEA model via MpCCI;

--determine structure deformation under flow pressure at the fluid--structure interface. Communicate deformed interface boundary back to CFD model; and

--increase flow rate, repeat steps b) and c) until initial seal is achieved.

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It is noted that how the dummy fluid domain is generated influences the FSI simulation process. An inadequate dummy fluid domain can lead to an inaccurate solution or difficulty in completing the simulation process. Currently, the axis symmetric model is not acceptable to the FSI suite due to different conventions of axis of symmetry between Abaqus and Fluent. This is mainly due to the fact that MpCCI GUI does not sup-port the capability. Axis symmetric FSI analysis involves a manual procedure in model generation, as well as a workaround of the MpCCI GUI limitation.

Flow induced sealing in wellhead isolation tool

When an 88.9 mm (3.5") WIT cup is used to seal a corresponding API maximum casing ID 73.03 mm (2.875"), the cup does not have an initial seal with the casing ID (figure 1). The initial seal of the annular area between cup mandrel and casing ID is flow induced. As pointed out in reference 1, the flow rate in the lab test, which is limited by available lab pump capacity, cannot induce the cup to seal. The cup, however, has no problem sealing in the field when fluid of very high flow rate is pumped through it. So the cup cannot seal when the available flow rate is low, but the cup can seal when the flow rate is high enough. An FSI model has to be applied to analyze the flow induced seal.

To determine if the cup will seal at a given rate is straightforward in the FSI model, i.e., conduct flow analysis, communicate flow pressure to the cup, and then conduct structural analysis and exchange information between CFD/FEA. The iteration between the CFD/FEA is usually needed. It is important to ratchet the flow rate up to the final flow rate; otherwise the flow analysis may fail due to large interface motion induced negative volume in fluid domain.

To determine minimum flow rate for the cup seal requires a bit more work. Start the FSI at low flow rate:

* Conduct flow analysis, communicate flow pressure to structure;

* conduct FEA, exchange information between CFD/FEA;

* keep flow rate constant, iterate on CFD/FEA results a few times, e.g., four times, depending on the change in response; and

* increase flow rate--repeat the last two steps until cup seal.

It is noted that when the sealing flow rate is reached, the seal may experience relatively large deformation. It may take a few more iterations to find the rate at which sealing occurs due to strong fluid-structure interaction.

Simulation of the flow induced sealing of an 88.9 mm cup

First of all, the cup is interference fit on the cup mandrel. The interference fit between cup and mandrel provides additional stiffness to the cup, which helps to resist cup 'push--through' due to setting pressure. Pretension of the cup in the circumferential direction, as shown in figure 3, leads to the stiffening. The flow field is formed after the installation of the cup, as shown in figure 2.

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The FSI analysis starts from 1 kg/s flow rate in the flow analysis, after four iterations between CFD/FEA computation at each flow rate, the flow rate is increased to 2 kg/s, 4 kg/s, 6 kg/s and 8 kg/s recursively. The pressure fields under 1 kg/s, 2 kg/s, 4 kg/s, and 6 kg/s flow rate are shown in figure 4. The corresponding structural responses are shown in figure 5. As is evident from the figures, at low flow rates (1 kg/s, 2 kg/s), despite the increase in differential pressure across the cup, there was little change in cup configuration. When the flow rate was increased to 4 kg/s, visible deformation of the cup, and change of the fluid domain was observed. When the flow rate was increased to 6 kg/s, substantial change in cup configuration, as well as change in fluid domain occurred. It is interesting to see the fluid-structure interaction at fixed flow rate during CFD/FEA iteration.

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Results from different iterations at 6 kg/s are shown in figures 6 and 7. The initial seal occurs at a flow rate larger than 6 kg/s. When the flow rate is increased from 6 kg/s to 8 kg/s, the flow pressure leads to cup seal at first iteration (figures 8 and 9). No additional flow analysis is conducted due to negative volume in the CFD model. This is not a problem, since from this point forward there is no flow of fluid and it becomes a static pressure problem--FEA should suffice.

The trend predicted by the FSI model, i.e., the cup would not seal at low flow rate and would seal at high enough flow rate, agrees with physical observations qualitatively. Due to lack of test data, the FSI model predictions cannot be validated quantitatively at this time.

The pressure rating of this cup is determined from finite element analysis (structural analysis) of the cup deformation by starting the analysis from the end of FSI simulation.

It is noted that the flow field in the system is actually in a transient state during the sealing process. However, steady state fluid dynamics are utilized here, instead of transient fluid dynamics, to avoid two issues. One issue is the large oscillation in numerical results in the transient solution of incompressible fluid (water). The other issue is that transient analysis typically takes longer time due to the small time steps used. One may still use transient fluid dynamics for this problem by introducing small compressibility to the 'incompressible' fluid.

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Effect of interference fit

The amount of interference between the cup and cup mandrel is an important design parameter. The effect of interference fit on the initial sealing is known empirically. A hypothetical cup is used to check the trend the FSI model will predict. The hypothetical cup is the drawing of the cup after interference fit. The difference between the predicted cup configuration and the drawing is shown in figure 10. The red (darker) figure is due to the FEA prediction, and the green (lighter) figure is from a Solid Works drawing. If the Solid Works drawing were used in the FEA model, there would be no interference between mandrel and cup. One would expect that the cup would be sealing at a lower flow rate due to lack of pre-tension.

The flow field at different flow rates with the cup that has no interference with the cup mandrel is shown in figure 11. The FSI model predicted that the initial seal occurs at a flow rate lower than 6 kg/s. One important observation is that the cup is lifted off the mandrel at the seal under 6 kg/s flow rate (figure 12). It was noted that a cup with interference fit on the mandrel was not lifted off at seal at a higher flow rate. The lift-off makes it easier for the cup to be extruded downstream at higher pressure. A proper amount of interference fit should lead to proper cup setting, as well as no difficulty in cup installation. It is noted that the predicted effect of interference agrees with physical observations qualitatively.

FEA vs. FSI

For virtual testing on this cup without FSI (ref. 1), FEA was exclusively used to simulate cup response under a setting condition. The flow pressure on the cup was approximated via pressure boundary conditions. Uniform pressure is assumed on the upstream side of the cup. Cup configuration at initial seal can be approximately determined from the FEA simulation in this way. From flow analysis in this section, we know that the uniform pressure is a gross approximation of flow pressure on the cup. Apparently, the FEA-predicted cup configuration (figure 13) is significantly different from that from the FSI prediction (figure 9). It is noted that FEA simulation (structural analysis) is very sensitive to the pressure boundary condition assumed. FSI is necessary for modeling the flow induced initial sealing process.

Summary and concluding remarks

A work-around that deals with the topology change of the fluid domain during the flow induced sealing process was proposed and successfully applied to a real industrial problem--flow induced initial sealing in a wellhead isolation tool. The FSI model clearly demonstrated the effect of fluid-structure interaction. The general predictions from the FSI model agree with physical observations qualitatively. Due to lack of test data, the FSI model predictions cannot be validated quantitatively at this time.

The Abaqus-MpCCI-Fluent FSI suite is easy to use and works well for this work and a few other cases the author has evaluated. One area for improvement, from a user's point of view, is for the suite to deal with the topology change of fluid domain more accurately and efficiently. The dummy fluid region approach would be more appealing if the flow pressure from a dummy fluid cell was not transmitted to solid until the dummy cell became a real fluid cell. What needs to be done to reach this goal includes:

* identification of fluid cells in the dummy region; and

* determination if/when a dummy cell becomes real fluid cell. Only pressure from dummy-to-real fluid cell is transmitted to solid.

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This can be achieved in Fluent and/or MpCCI. Another area for improvement is to enable the automated coupling between (Abaqus standard) FEA quasi static analysis and (Fluent) CFD

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steady state dynamics, like the case for coupling of FEA explicit dynamics and CFD transient dynamics; this so that users can utilize the advantages provided from quasi static analysis (FEA) and steady state dynamics (CFD).

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With the continuing improvements in FSI technology, it is expected that FSI will have wider applications in real industrial settings and lead to high fidelity virtual tests on many tools used in the oil/gas industry and other industries.

This article is based on a paper presented at a meeting of the Rubber Division, ACS (www.rubber.org).

References

(1.) A. Zhong and G. Testa, "Virtual testing of the performance of sealing elements in wellhead isolation tools," 168th Technical Meeting of the Rubber Division, ACS, Pittsburgh, PA, November 1-3, 2005.

(2.) T. Belytschko, "Fluid-structure interaction," Journal of Computers and Structures, Vol. 12, pp. 459-469 (1980).

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(3.) Abaqus, Inc., Fluid-Structure Interaction using Abaqus and Fluent, User's Guide, 2005.

(4.) K. Stein, T. Tezduyar and R. Benney, "Computational methods for modeling parachute systems," Computing in Science & Engineering, IEEE, January/February (2003) 39-46.

(5.) Fluent, Inc., Fluent User's Manual, 2005.