CFD Study of Surface Flow and Gas Dispersion From ...

Proceedings of the ASME 2014 33rd International Conference on Ocean, Offshore and Arctic Engineering OMAE2014 June 8-13, 2014, San Francisco, California, USA

OMAE2014-24707

CFD STUDY OF SURFACE FLOW AND GAS DISPERSION FROM A SUBSEA GAS RELEASE Qing Qing Pan Department of Energy and Process Engineering, Norwegian university of Science and Technology, Trondheim, Norway Stein Tore Johansen Department of Flow Technology, SINTEF Materials and Chemistry, Trondheim, Norway

Jan Erik Olsen* Industrial Process Technology, SINTEF Materials and Chemistry, Trondheim, Norway

Mark Reed Department of Marine Environmental Monitoring and Modelling, SINTEF Materials and Chemistry, Trondheim, Norway

ABSTRACT With increasing subsea oil and gas activities, the safety is challenged by accidental gas release. This can be caused by leakage from gas transport pipelines or blowouts from oil and gas wells. Risk assessment of such events is associated to the correct prediction of gas flux and gas distribution through the ocean surface and the resulting surface flows. A quantitative multiphase CFD model can satisfy such needs. Bubbles can be tracked by discrete phase model (DPM), using a parcel-based Lagrangian approach. Capturing the free surface formed by surfacing bubble plumes can be handled by a volume of fluid (VOF) model. This constitutes an Eulerian-Lagrangian model framework combining the DPM and VOF models. The model is presented and validated by experiments of a gas release in 7 m deep test basin. Results from modelling and experiments are consistent. INTRODUCTION Increasing subsea oil and gas activity and critically long operation time on many existing pipe lines necessitates improved methods for risk assessment concerning subsea gas release. A gas release is caused by well blowouts, pipeline failure (rupture or leak) or malfunction of subsea processing equipment. Engebretsen et al. [2] reported several accidental gas releases in the past years. If a release occurs, gas bubbles will travel to the surface due to buoyancy. The transport of gas and gas bubbles in the

Lars Roar Sætran Department of Energy and Process Engineering, Norwegian university of Science and Technology, Trondheim, Norway

water column is illustrated in Figure 1 [1]. Gas degassing into the atmosphere may cause fire or explosion hazards. The resulting surface current and loss of buoyancy may destabilize vessels and platforms operating near the release. Risk assessment is associated to the correct prediction of the resulting surface flows, the degassing flux and gas distribution at the surface. This can be achieved by traditional integral models for bubble plumes, or more recently developed CFD models. Cloete et al. [1] presented a detailed study of gas blowout using an Eulerian-Lagrangian CFD model.

Figure 1: Schematic of sub-sea gas release; from the release point, through the fully developed plume, to the degassing zone with induced surface flow [1].

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NOMENCLATURE CD interphasial drag coefficient C , C1 , C2 constants in the standard k-epsilon model

Eo F FPG FB FD

the Eötvös number total forces on a single bubble (N) pressure gradient force on a single bubble (N) buoyancy force on a single bubble (N)

uf

drag force on a single bubble (N) turbulent dispersion force on a single bubble (N) virtual mass force on a single bubble (N) gravitational constant (ms-2) forces exerted on fluid by bubbles per unit volume (kg m-1s-2) Fc  FDc  FVc source term of turbulent kinetic energy by buoyancy- modified turbulence (kgs-3m-1) 2 -2 turbulent kinetic energy (m s ) single bubble mass (kg) pressure (Nm-2) bubble Reynolds number free surface damping source term of epsilon (kgs-4m-1) flow velocity (ms-1)

Vcell

control volume (m3)

vb

single bubble velocity (ms-1)

xi

coordinate direction

FTD

Fvirtual g

mass

Fc

GB

k mb p Reb

Sdamping

Greek letters



 ij 

 t   k ,  L  Subscripts b f g t

volume fraction kroenecker delta

1. MODEL DESCRIPTION A modelling concept based on Lagrangian tracking of bubble motion and Eulerian equations describing the continuous phases constituted by the ocean and the atmosphere was developed by Cloete et al. [1]. This model has later been improved by implementing a proper interface restriction for turbulence at the ocean surface [3]. The modelling concept is presented in the following chapter. 1.1. DPM Bubbles are tracked using the following force balance equation due to Newton's 2nd law, supplemented by a kinematic relationship which defines the trajectory of bubbles: dv b F   FD  FTD  FB  Fgravity  Fvirtual mass  FPG dt mb b   f  18CD Reb (1) u f  vb  g   2 24 b bdb  f  Du f dv b   f Du f Cv     b  Dt dt   b Dt





dx b  vb (2) dt The terms on the RHS of (1) are bubble drag, turbulent dispersion, buoyancy, gravity, virtual mass and convective contribution to the pressure gradient force per bubble mass respectively. The lift force is assumed insignificant for relatively high flow rates [4]. The Tomiyama bubble drag law for contaminated system (sea water) was used [5]. The virtual mass coefficient Cv is 0.5. The effects of flow turbulence are reflected by the turbulent dispersion forces on the bubbles embedded in the total drag term. u f in the drag term is the instantaneous velocity, where the turbulent fluctuations in the flow field are modeled by a normally distributed random

2 k. 3

dissipation rate of turb. kinetic energy (m2s-3) viscosity (kgm-1s-1)

number and local turbulence parameters, i.e.

turbulent viscosity (kgm-1s-1)

Bubble-bubble interactions are not considered. For shallow plumes, the gas density almost remains constant. However for deeper plumes, the dramatic increase of gas density with depth should be considered. Density increases proportionally with pressure due to the ideal gas law. M b  P b (3) RT where P is pressure; M b is bubble molar mass . R is the gas

density (kgm-3) constants in the standard k-epsilon model Lagrangian integral time scale (s) arbitrary property

bubble water phase atmosphere phase (continuous gas phase) Turbulence

ui'  

constant, which has the value 8.314 J  K 1mol 1 . The bubble size model, accounting for breakup and coalescence mechanisms, was developed by Laux and Johansen [6], where the bubble size is governed by material properties and turbulence parameters. The bubble will achieve an equilibrium diameter given by Calderbank [7] if it resides sufficiently long at the same flow conditions.

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d beq

 C1b0.5

 /  0.6  b 0.25  C

(4)   2  0.4    Here  is the surface tension between bubble and fluid;  is density of water; b is the material viscosity of the gas ; C1 and

C2 are coefficients, here we used C1  4 and C2  200 μm , which is frequently used for gas bubbles. The time evolution of the instantaneous bubble diameter d b is balanced by a source term which account for breakup and coalescence. d  b db  d eq  d b (5)  b b dt  rel Here  b  b b is the bubble bulk density. The relaxation time

 rel is controlled by the speed of the breakup or the coalescence

process, and the dominating process is determined by the comparison between the local diameter and equilibrium diameters.  if d b  d beq (6)  rel   B if d b  d beq  C The relaxation time is restricted by the turbulent microscale given by  k  6 

 , where  is the kinematic viscosity of

fluid. We have  rel   rel ,  k

max

2

which is modeled as  B  db 3

;  B is the breakup time scale

1

and  C is the coalescence db time scale which is modeled as  C  . Details 0.2  6  b k 3

can be found in Laux and Johansen [6]. 1.2. VOF The VOF method which is a single phase Eulerian-Eulerian mixture model, employs an advanced interface tracking scheme known as Youngs’ VOF [8] to track the interface through the Eulerian mesh. If a cell is found to consist of two or more phases, an interface must be interpolated through it. The volume fraction mass equations for water (f) and atmosphere (g) are solved. Note that liquid displacement by bubbles is neglected since coupling to the bubbles is only accounted for in the momentum equations. The transport equation for volume fractions of read:   (7) k  u j  k  0 t x j with the constraint  g   f  1 . This is solved together with a single set of Reynolds averaged Navier- Stokes equations expressing conservation of momentum

  p    u u     ui   (  ui u j )       i  j  t x j xi x j   x j xi      g (8)  Kg xi  c ' '   ui u j   gi  Fi   1 x j  g  l 2 where density and viscosity are volume-averaged properties







  k



and  

k

  k

k



.

The exchange force from the bubble parcels (coupling to the Lagrangian bubbles) is implemented as follows:

F  c

M b mb

n

  F

D

 Fvirtual mass  dtb

k 1 t f

Vcell

Here M b is the total mass flow rate of one parcel trajectory and k represents each trajectory in the control volume. Vcell is the control volume. FD and Fvirtual mass are drag and virtual mass forces on a single bubble. By integrating them with respect to the bubble time step tb within the flow time step t f , F c is obtained. Through the Boussinesq hypothesis, the turbulent stress is represented by:  u u  2  f ui' u'j   f kij  t  i  j   x j xi  3   1.3. Free surface damping There is an increase in turbulent dissipation at the free surface in bubble plumes as reported by Soga and Rehmann [9]. This is the same effect which is observed at walls. Walls and internal interfaces cause damping of turbulence. However, most implementations of the standard k-ε turbulence model only consider walls. Internal interfaces such as a liquid-gas interphase in a VOF-model is normally ignored. Thus the standard implementation of the k-ε model over-predict the TKE at the free surface when compared to experiments as reported by Sheng and Irons [10]. Cloete et al. [1] also pointed out that the standard k-ε model under predicts the surface velocity at higher flow rate. “This is due to a phenomenon of increased turbulence kinetic energy dissipation in the region of the free surface which is not captured by the standard turbulence model. When turbulent eddies approach and locally lift a free surface, there is an increase in the rate of the turbulent energy cascade, which ultimately leads to increased TKE dissipation rates.” Due to this we have to improve the standard implementation of the k-ε model to account for the proximity of a free surface which is seen as an internal interphase in the VOF concept. Being aware that the epsilon transport equation is actually the eddy length scale equation, a model is required to supply the correct characteristic length to treat the near surface

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turbulence, and this model should assure the length scale approaches zero at the free surface. Then a proportional relationship between the length scale and the physical distance to the free surface is proposed by Soga & Rehmann (9). The modeled epsilon  new is designed to override the epsilon value in computational cells near the surface through the source term Sdamping in (10). 1/4

 3  C3/4 k 3/2 C3/4 k 3/2 l0   ls , l0   t   ,  new     new  ls  new  Sdamping  large_number  ( new   )

(9) (10)

where:  =0.4 is the von Karman constant; ls is the physical distance to the free surface; l0 is eddy length scale. One should be careful with the choice of “large_number” in (10), as it should be sufficiently large to enforce  new and at the same time avoid stability issues. Different scenarios of 10, 100, 1000, 10000 were tested and 1000 satisfied the requirements. The model framework is thus closed by an enhanced kepsilon turbulence model: u u j ui k k   u j  t ( i  ) t x j x j xi x j (11) t k          x j   k x j 

    u u j ui   u j  C1  t ( i  )  t x j k  x j xi x j       2   Sdamping   t    C2 x j    x j  k source



where



  k

k

and  

  k

k

(12)

Figure 2: Grids of center plane and bottom plane. Red lines represent 1.75 m, 3.8 m and 5.88m in height.'

Figure 3. Predicted gas density [kg/m3], changing with height, for a gas release of 170 Nl/s.

The source terms in

(12) is implemented through a UDF in FLUENT. 2. RESULTS AND DISCUSSION The model is compared against the experimental data of Engebretsen et al. [2]. They performed a series of experiments in a rectangular basin with depth of 7 m and a surface area of 6 and 9 m, applying gas rates of 83, 170 and 750 Nl/s. The data for 170 Nl/s (0.208 kg/s) is used for validation. Model simulations was performed on a grid with 843528 hexahedral cells, see Figure 2. The computational domain is 6m by 9m as the tank, and in vertical direction, it is extended to 10 m to account for the atmosphere above the water. The cells are refined to 5cm in the plume and free surface regions. Some simulation results are illustrated in Figure 3 and Figure 4. The increase of gas density with depth is shown in Figure 3. Bubble size is seen in Figure 4. The larger bubbles exists in the outer parts of the plume, where coalescence dominates due to low turbulence levels; while smaller bubbles tend to be formed in the center plume, where breakup dominates due to high turbulence levels.

Figure 4. Predicted bubble size [m] distributions for a gas release of 170 Nl/s. The vertical velocity profiles at three heights of 1.75 m, 3.8 m and 5.88m were validated against the experiments as seen in Figure 5. Here the surface damping effect is small, and only modelling results including surface damping is shown. It is observed that the vertical plume velocities predicted by the model at two lower heights match the experiment quite well, however there is an underestimation of plume velocities at 5.88m height. In the experiment, the vertical and horizontal velocities are measured with Höntzsch turbine flow meters [2]. The turbine flow meters works well for mono-directional flows.

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3 exp 1.75m exp 3.8m exp 5.88m model 1.75m model 3.8m model 5.88m

vertical velocity [m/s]

2.5

2

1.5

1

0.5

0 0

0.5

1 radial distance [m]

1.5

2

Figure 5: Comparison of predicted vertical velocities and experiments at 1.75 m, 3.8 m and 5.88m in height for a gas release of 170 Nl/s. However, the flow starts to bend when approaching the surface, which will give an underestimation of the measurement of flow velocities. Thus the inconsistency between model and experiments at the upper level should not be attributed to model shortcomings. Figure 6-Figure 8 compare the standard k-ε implementation and the k-ε implementation with surface damping correction. The surface damping model will produce higher dissipation (Figure 8) that will dampen the turbulent kinetic energy (Figure 7), and produce a faster surface flow (Figure 6). Figure 9 gives a quantitative comparison of the outwelling surface flow between model and experiments. We see that the damping module gives 75% improvement compared to the standard model. Figure 10 compares the gas concentrations leaking into the atmosphere. Most gas reach the surface in the center boil region, also it is shifted away by the surface current. The damping module gives the higher gas concentration.

Figure 7: Comparison of contours of TKE [m2/s2]. Left is the standard k-epsilon model and the right is with damping effects.

Figure 8: Comparison of contours of dissipation [m2/s3]. Left is the standard k-epsilon model and the right is with damping effects. 7 6.8 6.6

Height [m]

6.4 6.2

exp standard damping

6 5.8 5.6 5.4 5.2 5 0

Figure 6: Comparison of contours of velocity magnitude [m/s]. Left is the standard k-epsilon model and the right is with damping effects.

0.2

0.4

0.6 0.8 1 velocity magnitude [m/s]

1.2

1.4

1.6

Figure 9: Comparison between experimental and modeled velocity magnitudes near the top surface, 1.75 m from the plume center. Flows are predominantly in the radial direction. Square symbols represent experimental data. Simulation results from the standard k-epsilon model ("standard") is marked with dashed lines, while simulation results from the enhanced turbulence model that account for damping effects ("damping") is given by solid lines.

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REFERENCES [1]

[2]

[3]

[4]

[5]

[6]

Figure 10: Comparison of predicted contours of bubble mass concentrations [kg/m3] leaking into atmosphere. Above is with the standard k-epsilon model, while below is with the enhanced turbulence model that account for damping effects. 3. CONCLUSIONS A modelling concept for bubble plumes resulting from a subsea gas release has been presented. This includes en enhanced implementation of the k-ε model which accounts for turbulence damping at the ocean surface. The free surface damping model provides more reasonable eddy length scales in vicinity of free surface and thus improve the prediction of the surface velocities of the bubble plumes. When compared to experiments there is good consistency of the results. The modelling concept should thus be applicable to risk assessment of potential incidents with subsea gas release.

[7]

[8]

[9]

[10]

S. Cloete, J.E.Olsen and P.Skjetne, "CFD modeling of plume and free surface behavior resulting from a subsea gas release," Applied Ocean Research, vol. 31, pp. 220-225, 2009. T. Engebretsen, et al., "Surface flow and gas dispersion from a subsea release of natural gas," in The Proceedings of the International Offshore and Polar Engineering Conference, 1997, pp. 566-573. Q. Q. Pan, "Modeling of Turbulent Flows with Strong Dispersed Phase Interactions " Doctoral thesis, NTNU (Norway), 2013. J. E. Olsen and M. Popescu, "On the effect of lift forces in bubble plumes " presented at the proceedings of Ninth International Conference on CFD in the Minerals and Process Industries 2012. A. Tomiyama, "Struggle with computational bubble dynamics," Multiphase Science and Technology, vol. 10, pp. 369-405, 1998. H. Laux and S. T. Johansen, "A CFD analysis of the air entrainment rate due to a plunging steel jet combining mathematical models for dispersed and separated multiphase flows," Fluid Flow Phenomena in Metal Processing, 1999. P. Calderbank, "Physical rate processes in industrial fermentation. Part I: The interfacial area in gas-liquid contacting with mechanical agitation," Trans. Inst. Chem. Eng, vol. 36, pp. 443-463, 1958. D. Youngs, "Time-dependent multi-material flow with large fluid distortion," Numerical methods for fluid dynamics, vol. 24, pp. 273-285, 1982. C. L. Soga and C. R. Rehmann, "Dissipation of turbulent kinetic energy near a bubble plume," Journal of hydraulic engineering, vol. 130, pp. 441-449, 2004. Y. Sheng and G. Irons, "Measurement and modeling of turbulence in the gas/liquid two-phase zone during gas injection," Metallurgical Transactions B, vol. 24, pp. 695-705, 1993.

ACKNOWLEDGMENTS The authors would like to thank the funding from SURE project (Advanced Modeling Tool for Subsea Gas Release) in SINTEF for this research.

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