Numerical models to simulate oil and gas blowout plumes and associated chemical and physical...

E-proceedings of the 36th IAHR World Congress 28 June – 3 July, 2015, The Hague, the Netherlands

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Numerical models to simulate oil and gas blowout plumes and associated chemical and physical processes of hydrocarbons

ANUSHA L. DISSANAYAKE (1), INOK JUN(2) & SCOTT A. SOCOLOFSKY(3)

Texas A&M University, College Station, TX, USA(1),(2),(3) [email protected](1), [email protected](2), [email protected](3)

ABSTRACT

In this paper, we present an integral plume-modeling suite that is developed to simulate multiphase oil and gas blowout plumes and demonstrate the model validations against laboratory and field data. The modeling suite is capable of simulating plumes formed in both stratification-dominant (Stratified Plume Model) and ambient current-dominant (Bent Plume Model) environments, along with hydrodynamic, chemical, and thermodynamic processes of hydrocarbons. The fate of these hydrocarbons released as plumes significantly depends on their rise velocity, mass transfer rates, and induced plume velocities. However, especially in the deep ocean, physical and chemical parameters of the gas bubbles are potentially affected by the formation of clathrate hydrate shells around them, yielding unknown mass transfer effects. Hydrate shells can stop the fluid circulation within a bubble and interfere in the mass transfer between the bubble and ambient. During the model calibration for the bubble dissolution rate, we found that the transition of a bubble status from clean to dirty in the ocean depends on the initial bubble size, and hydrate kinetics could accelerate this transition time at high levels of subcooling. But, hydrate skins generally do not inhibit mass transfer below standard values for contaminated interfaces. The stratified and bent plume models are developed based on the Eulerian double-plume model theory and Lagrangian approach, respectively. The plume models are capable of simulating the size distributions of the dispersed phases and their separation from the main plume in high cross flow conditions. These models can predict the distribution of oil/gas in the water column along with their approximate surfacing volume, time, and location with respect to the plume release point. These parameters are important for contingency planning and response to accidental under water oil/gas spills.

Keywords: plumes, oil and gas, gas hydrates, stratification, cross flow

1. INTRODUCTION

Jets and plumes are a frequent occurrence in our surroundings and are formed due to both manmade and natural reasons. They attract our attention because of their roles in distribution and dispersion patterns of energy and materials that they carry and changes they create in their ambient environments. Oil and gas blowout plumes release hydrocarbons, which pollute the aquatic environments, jeopardizing the health and survival of organisms within them. Moreover, they cause damages to the oil/gas exploration facilities causing financial damages along with human casualties as seen in many past incidents. Numerical models are developed to study these plumes to better prepare and respond to accidental blowout incidents. In this paper we present a model suite, which is capable of simulating the near field of the oil and gas blowout plumes and the subsequent advective transport of bubbles and droplets in the far-field. The full modeling suite is called the Texas A&M Oilspill Calculator (TAMOC). The model has methods to consider the physical, chemical, and thermodynamic properties (i.e. slip velocity, solubility, mass and heat transfer coefficient) of dispersed phases using discrete bubble model that tracks these properties for representative bubbles. A single bubble model inherits the discrete bubble model capabilities to simulate the fate of a bubble or droplet rising in the ambient ocean, outside any induced plume effect. The plume models are developed by integrating the single bubble model and its capabilities to account for the entrainment and induced fluid flow of groups of bubbles. The behavior of blowout plumes depends on both the initial release conditions as well as ambient conditions such as stratification and cross flow. The modeling suite is capable of simulating multiphase plumes in stratification dominated (Stratified Plume Model) and cross-flow dominated (Bent Plume Model) ambient environments. TAMOC is freely available in its-up-to-date version from http://github.com/socolofs/tamoc. Section 2 describes the details of the chemical and physical processes of the dispersed phases in the model. Section 3 discusses the numerical modeling approaches of the stratified plume and the bent plume models. Sections 4 and 5 follow with details on the model verification and application respectively. Finally, section 6 discusses the model results and states the conclusions.

2. CHEMICAL AND PHYSICAL PROCESSES OF THE DISPERSED PHASES

2.1 Bubble Models

Once hydrocarbon gases are released in the water, they undergo physical and chemical processes. A bubble or a droplet is advected by the three-dimensional ambient currents and undergoes dissolution and heat transfer as it rises through the water column. In this study, the single bubble model (similar to McGinnis et al. (2006) is developed to predict the evolving bubble size, gas composition, and rise distance. The model simulates the rising fluid particle by the advection equation for

E-proceedings of the 36th IAHR World Congress, 28 June – 3 July, 2015, The Hague, the Netherlands

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a single particle coupled with the mass transfer equation for each chemical component in a particle and a heat transfer equation for the whole particle. These equations yield a coupled set of nonlinear ODEs. Advection is computed from the slip velocity, or terminal rise velocity in a stagnant ambient and the ambient crossflow. Mass and heat transfer are depend on the mass and heat transfer coefficients and the driving potential, taken as the difference between the ambient value and the value at the particle-water interface. Slip velocity and mass and heat transfer rates are modeled using the formulations given in Clift et al. (1978) for different shaped and sized bubbles in different environment conditions (i.e. spherical, ellipsoidal, clean, dirty, etc.)

2.1.1 Rise Velocity of The Dispersed Phases

The rise velocity of a bubble inherently depends on its size, shape and density. For small bubbles, the rise velocity strongly depends on liquid properties such as surface tension and viscosity. For large bubbles, the rise velocity is insensitive to liquid properties (Fan 1989). The rise velocity of a fluid particle in water strongly depends on water purity, especially in the ellipsoidal range. In this study, we calculated the buoyant velocity based on the correlations presented by Clift et al. (1978), and validated with laboratory measurements from the literature. The non-ideal compressibility behavior of a bubble or droplet is modeled by using the Peng-Robinson equation of state with the modified Henry’s law (McCain 1990).

2.1.2 Mass Transfer of The Dispersed Phases

The mass transfer coefficient of dissolving bubbles depends on its interface mobility (Griffith 1960). If surfactants are added, they reduce the interfacial mobility and make it less sensitive to variations in solute concentration. The mass transfer coefficient is about three to five times greater for the mobile surface (clean) than for the immobile surface (dirty) in case of a typical gas bubble in water. The model computes the mass transfer based on the equations from Clift et al. (1978) and Johnson et al. (1969) which are functions of bubble density, size, and type. The dispersed phases in the model can be in liquid or gas phases under different temperature and pressure conditions.

2.2 Gas Hydrates Effect

Under high pressure and low temperature conditions of the deep ocean, a clathrate hydrate can be formed of gas and water and can remain stable until a critical depth where the hydrate subcooling reaches zero. Gas bubbles released in the deep ocean can get coated with a hydrate skin/film, which may reduce the mass transfer between the bubble and ambient seawater by stopping the fluid circulation within the bubble. In many field experiments, it is observed that methane bubbles released from deep water within the hydrate stability zone (HSZ), as from a natural seep, rose much higher in the water column than predicted by previous bubble models ignoring the effects of hydrate films on mass transfer (McGinnis et al. 2006; Rehder et al. 2009; Zhang 2003). Therefore to estimate the accurate vertical transport of hydrocarbon gases in the oceans, the hydrate effects on bubble mass transfer must be included in the model. Jähne et al. (1987) and Vasconcelos et al. (2002) studied the transition of mass transfer from clean to dirty bubble in water and found the transition time depended on the initial bubble diameter. By analyzing methane gas bubble measurements in Rehder et al. (2009), we found that the transition time for hydrate skin formation also depends on the initial bubble size, and that it could be accelerated for deeper releases with higher initial hydrate subcooling. We found that both the transition time (t*) and the reduction of the transition time () at a certain depth is a function of the temperature difference between the ambient and hydrate formation/dissociation temperature (called the hydrate subcooling). The mass transfer is shown to match the clean bubble mass transfer until the hydrate skin forms, and the mass transfer generally does not go below a standard value for contaminated interfaces, which is equivalent to the behavior of dirty bubbles. Therefore, mass transfer coefficient of dirty bubbles presented in Clift et al. (1978) are used in the model along with prediction of transition time, to simulate the presence of the hydrate.

3. MULTI PHASE INTEGRAL PLUME MODELS

Integral plume models are developed to simulate both single and multiphase plumes. Lee and Cheung (1990) and Jirka (2004) are examples of single-phase models developed for stratified cross flow environments. The ambient water entrainment due to velocity differences between the plume and ambient along the plume axis, and water entered into the plume, perpendicular to its axis due to the forcing of the cross currents, are accounted in these models, to predict their three dimensional trajectories. McDougall (1978), Asaeda and Imberger (1993), Crounse et al. (2007), and Socolofsky et al. (2008) are examples of multiphase integral plume models developed for still and stratified environments using an Eulerian approach. An inner plume with dispersed phases (bubbles/droplets/ particles) and an annular outer plume are common to these models. They have differences in how they handle the entrainment between the inner, outer plumes, and ambient water, and how they predict and initialize the outer plume. Yapa and Zheng (1997), Zheng et al. (2003), and Johansen (2000) developed multiphase integral plume models to simulate oil and gas blowouts using a Lagrangian approach. They have the capability of simulating plumes in stratified and cross flow environments and the dispersed phase separation from the main plume; however, they neglect all interaction between an inner plume containing the dispersed phase and a separated, outer plume forming an intrusion. In general, the double-plume integral models are appropriate in stratification-dominated environments and the single-plume integral models apply in crossflow-dominated environments. A plume in stratification rises in the water column, dragging entrained ambient fluid upward until a terminal level is reached where the upward buoyancy of the dispersed phase cannot overcome the negative buoyancy of the entrained water. At this terminal level, entrained water is arrested and descends to form intrusions at levels where the plume water density equals the ambient water density. This level is identified as the trap height, hT. Multiphase plumes in cross flow environments also have the tendency to separate the dispersed phase from continuous phase when the current speed on the downwind side of the plume exceeds the entrainment velocity into the plume. This height of the plume is identified as the separation height, hs (Socolofsky and Adams 2002). While limited experiments are available with the combined effect

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of stratification and crossflow, Socolofsky and Adams (2002) define plumes as crossflow-dominated when hs << hT and stratification dominated when hs >> hT. The stratified plume model presented here is for stratification-dominant cases and the bent plume model for cross flow-dominant environments. The details of these models are given briefly in the following sections.

3.1 Stratified plume model

The stratified plume model is an integral multiphase plume model, which is developed based on the double plume model using an Eulerian approach presented in Socolofsky et al. (2008). It is designed to simulate plumes in still or near still environments. A double plume model consists of an inner plume with dispersed phases and entrained ambient continuous phase rising in the water column and an annular, outer plume, which contains detrained, heavy continuous phase fluid. The outer plume forms when the inner plume fluid detrains and tracks the detrained fluid until it reaches an intrusion level. The entrainment and detrainment of the plumes continues between the inner and outer plumes, creating several outer plumes, until the plume reaches the water surface or the dispersed phase completely dissolves. The stratified plume model includes multi component and mixed fluid approaches, discrete and continuous peeling, and two different entrainment models, which are dependent either only on the inner plume velocity or on the relative velocities of the inner and outer plume (Socolofsky et al. 2008). The version distributed in TAMOC is extended from the Socolofsky et al. (2008) model by providing a non-ideal equation of state in the discrete bubble model and by allowing multiple bubble and/or droplets to be present in the inner plume. When multiple bubble or droplet sizes are simulated, the buoyant force of the dispersed phase is computed by summing over the contribution from each individual dispersed phase particle.

3.2 Bent plume model

The bent plume model is developed based on the Lagrangian model formulation presented in Lee and Cheung (1990), and Lee and Chu (2003) for buoyant single phase jets in stratified, shearing environments. The model includes the full single-phase capability of the Lee and Cheung-type model and is extended to simulate multi-phase plumes by introducing the dispersed phases (added buoyancy), and by tracking the mean path of the dispersed-phase particles within the plume. Because dispersed phases travel vertically faster within the plume due to their slip velocities, they get separated from the bent entrained ambient water plume (Chen and Yapa 2004; Johansen 2003; Socolofsky and Adams 2002). Dispersed phase separation causes loss of buoyancy and affects the behavior of the plume. In the bent plume model, when dispersed phases cross the plume edge, their effects on the plume are removed. Paths of the separated dispersed phases are tracked in the far field as individual particles travelling under the influence of slip and ambient cross flow velocities (e.g., using the single bubble model).

3.2.1 Entrainment formulation

Ambient water entrained into the plume is taken as forced and shear entrainment (Lee and Cheung (1990). The entrainment due to cross flow is the forced entrainment and is calculated based on the total area of the plume element, which intercepts the ambient uni-directional cross flow on the plume’s windward side. The shear entrainment is a function of relative velocity between the plume and ambient currents, and the entrainment coefficient is taken to be dependent on the local densimetric Froude number. In this model, the shear entrainment coefficient defined in Lee and Chu (2003) is modified based on Jirka (2004) to accommodate the transition range of local negative and positive buoyancy effects on the plumes in the stratified environments. In stratified environments local densimetric Froude number of a plume has an asymptotic value (Flp) of 4.67, when the ratio of concentration to velocity profile widths and asymptotic plume entrainment coefficient are taken as 1.2 and 0.083, respectively (Jirka (2004). Plumes can reach the asymptotic values by accelerating or decelerating depending on their release conditions (Figure 13 in Jirka (2004). In the present model the shear entrainment coefficient, α in the transition region from accelerating to decelerating plume or vice versa is taken to be linearly varying with the local densimetric Froude number of the plume as in Eq. [1].

(p j )

Fl2

Flp2 sin()

[1]

where, p 0.083, j 0.057, Fl local densimetric Froude number, vertical angle of the plume axis with the horizontal plane.

3.2.2 Initial conditions and Numerical solution

The initial conditions used in the bent plume model is the same as for the inner plume of stratified plume model, and is given by Socolofsky et al. (2008), which follows a method presented by Wuest et al. (1992). They calculate the initial velocity of the multiphase plume using the densimetric Froude number at the level of the plume release. The initial half width of the plume is taken as the radius of the release orifice. Model equations are numerically solved using 'vode' ordinary differential equation integrators in scipy. Vode uses an adaptive step sizes for the integration with implicit Adams method and a method based on a backward differentiation formula.

4. VALIDATION OF THE MODEL

4.1 Validation of bubble models

The model for mass transfer and slip velocity are validated with available laboratory experimental data and shown in Figures 1 and 2, respectively. Curves are calculated by the discrete bubble model for clean and dirty bubbles, respectively, and symbols are laboratory measurements from the literature. Circles represent data for a clean (circulating) bubble, and crosses denote data for a dirty (rigid) bubble. In Figure 2, the mass transfer is plotted on the y-axis by its non-dimensional form of the Sherwood number, given by Sh = βde/D, where β is the mass transfer coefficient, de is the equivalent spherical diameter of the particle, and D is the molecular diffusivity.


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Figure 1. Rise velocity of air bubbles in clean/dirty water at 20 deg C.

Figure 2. Mass transfer factor (Sh) for gas bubbles (O2 & CO2) in clean/dirty condition.

The single bubble model is validated using data for natural gas seeps from McGinnis et al. (2006) and Römer et al. (2012). The transition time in the model is calibrated by matching the data in Rehder et al. (2009). Figure 3 shows the comparison of total rise height predicted by the model for different initial bubble sizes using ambient conditions for the Black Sea. The bubble rise height in Black Sea observed by McGinnis et al. (2006) was 1300 m and is well predicted by the model, when the transition time model is used (red line) for bubble sizes between 14 to 20 mm. These bubble sizes are within the range reported in McGinnis et al. (2006) paper. Figure 4 shows the model predicted bubble mass reduction due to the dissolution in the water column, as a function of depth for different bubble flares from natural gas seeps observed by Römer et al. (2012). For all the flares, the model prediction considering the transition time (green line) compares well with the observed flare height (black line). For these simulations, 1000 bubbles are simulated using the measured bubble size distribution in the Römer et al. (2012) paper to predict the flare fate. In the single bubble model, it is assumed a bubble is totally dissolved when its mass is reduced below 0.01 % of the initial mass. These simulations validate the correct prediction of mass transfer in the model using the transition time prediction for the hydrate formation and the clean (no hydrate) and dirty (hydrate coated) mass transfer rates in Clift et al. (1978) and Johnson et al. (1969).



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Figure 3. Predicted flare height for each initial bubble size with different mass transfer coefficients for natural gas seep site in Black Sea

(McGinnis et al. 2006).

Figure 4. Predicted bubble mass reduction as a function of depth for each flare site in offshore Pakistan (Römer et al. 2012).

4.2 Validation of stratified and bent plume models

The stratified plume model is validated in Socolofsky et al. (2008). The single and multiphase versions of the bent plume model are validated here based on laboratory and field experimental data. Figures 5 and 6 show model comparisons with experimental data for a non-buoyant plume in crossflow by Chu and Goldberg (1974) and for horizontal single-phase plumes in cross flow (Cheung 1991), respectively. Figure 7 shows how model results compared with the data for a plume in a stratified cross flow environment (Hirst 1972).

The multiphase bent plume model comparisons with laboratory (Socolofsky and Adams 2002) and field data from Deepspill experiments (Johansen et al. 2003) are shown in Figures 8 and 9, respectively. For all the validation cases the model results are in similar agreement with the experimental data to validations of single-phase models.


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Figure 5. Model results comparison with laboratory experimental data (Chu and Goldberg 1974) or Non buoyant plumes in cross flow.

lm = Momentum length scale, X and Z = Horizontal and vertical coordinates, respectively.

Figure 6. Model results comparison with laboratory experimental data from Cheung (1991) for a horizontal jet in cross flow.

C/C0 = Ratio of plume concentration to its initial value, X = Horizontal coordinate and D = Orifice diameter.

Figure 7. Model results comparison with laboratory experimental data (Hirst 1972) for plume in stratified and cross-flow environment.

b = Orifice radius, X and Z = Horizontal and vertical coordinates, respectively.



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Figure 8. Model results comparison with laboratory experimental data (Socolofsky and Adams 2002) for a multiphase plume in cross flow.

Figure 9. Model results comparison with Deepspill experiment data (Johansen et al. 2003) for diesel release (dashed blue lines show

bubble/droplet path, continuous blue lines show the plume edges and centerline); orange color shows the acoustic measurement of oil droplets and gas bubbles in the water column during the experiments.

5. APPLICATION: MODEL SIMULATIONS

Stratified and bent plume models are simulated for the scenarios shown in Table 1, which are taken from the test matrix proposed by the American Petroleum Institute (API) Model Inter-comparison Workshop on Blowout Models. The plume release diameter and temperature are taken as 0.3 m and 150 ˚C, respectively. Composition of gas is taken to be 80% - Methane, 15% - Ethane and 5% - Propane. Ambient salinity, temperature and dissolved oxygen properties are given in Figure 10. Ambient velocity is taken as 0.05 m/s uniformly distributed over the depth for bent plume model simulations. Droplet and bubble size distributions are assumed to follow Rosin-rammler distribution. Model results from the stratified and bent plume models are given in Tables 2 and 3, respectively.


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Table 1. Input parameters for the model simulations Parameter Case 1 Case 2 Case 3 Case 4

Release depth (m) 2000 2000 200 200 Oil mass flow rate (kg/s) 34.5 34.5 29.2 29.2 Gas mass flow rate (kg/s) 7.4 7.4 12.7 12.7 Dispersant to oil ratio (%) 0 2 0 2 Density of oil (kg/m3) 599.3 599.3 718.5 718.5 Mean bubble diameter (mm) 10 10 10 10 Mean droplet diameter (mm) 3.8 0.2 3.9 0.41

Figure 10. Profiles of ambient ocean properties (Sarmiento and Gruber 2006)

Table 2. Simulation results from the stratified plume model

Parameter Case 1 Case 2 Case 3 Case 4 Oil mass flow rate to the surface (kg/s) 34.5 34.5 29.2 29.2 Gas mass flow rate to the surface (kg/s) 0.39 0.27 10.32 10.2 Surfacing time (min) 69 80 2 2 Depth to the first intrusion (m) 1830 1820 84 76

Table 3. Simulation results from the bent plume model

Parameter Case 1 Case 2 Case 3 Case 4 Volume flux of entrained water into the intrusion (m3/s) 7224 6934 1063 1065 Oil mass flow rate to the surface (kg/s) 33.34 0.0 29.2 29.2 Oil surfacing radius (m) 812 - 8 8 Average oil surfacing time (min) 254 - 3 3 Oil mass flow rate into the intrusion (kg/s) 1.16 34.5 - - Gas mass flow rate to the surface (kg/s) 0.0 0.0 4.29 4.29 Gas surfacing radius (m) - - 7.5 7.5 Average gas surfacing time (min) - - 3 3 Gas mass flow rate into the intrusion (kg/s) 0.0 0.0 - - Depth to the first intrusion (m) 1677 1672 Plume surfaces Plume surfaces

6. DISCUSSION AND CONCLUSIONS

Multiphase plume models developed are applied to four different cases with the input given in Tables 1 and the results are shown in Table 2 and 3. Figure 11 shows a sectional view of the plume, and mean paths of bubbles and droplets for the Case 1 from the bent plume model. The near-field plume rises to a maximum height of about 1500 m depth, where the entrained water begins to descend to form an intrusion and larger gas bubbles and oil droplets leave the top of the plume. Smaller gas bubbles and oil droplets follow the plume into the intrusion, which comes to rest at a level of neutral buoyancy around 1680 m depth. Separated larger oil droplets and gas bubbles rise in the water column individually using the single bubble model. There, the particles dissolve and are advected with their buoyant velocities while displacing horizontally due to cross flow, until they reached the surface or completely dissolve, as is the case for the gas bubbles close to the water surface. Case 2 has a similar behavior in the model predictions, while plumes in cases 3 and 4 reach the water surface before reaching a trapping level in the water column since their release locations are relatively shallower with higher gas release rates. Oil and gas surfacing times are shorter in all the cases for the stratified plume model than for the bent plume model. This is because the particles in the stratified plume model remain in the plume all the way to the surface, benefiting from the induced plume rise velocity; whereas, particle separate from the bent plume model at a depth close to 1500 m and rise the remaining distance under their slip velocity alone. For all the cases mass flow rate of gas to the surface is higher in the stratified plume model than the bent plume model, because the former stays as a plume until it reaches the surface,



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bringing gas to the surface fast, with less dissolution due to shorter travel time. In the bent plume model since the particle travel time in the water column is longer, the total dissolution increases thus, reducing the amount of gas reaching the surface. Moreover, a higher percentage of gas released at shallower depths reaches the surface, when compared with the deeper cases, again due to longer travel time of bubbles in the water column for the deeper releases. Total oil flow rates reaching the water surface at steady conditions are same as the release rates for all the cases of the stratified plume model. A part of oil bubbles released get trapped in the intrusion of the bent plume model reducing the surfacing oil flow rates. In the cases 2 with dispersant added to the plume, all of the oil released was trapped in the intrusion cutting off the oil reaching the water surface entirely in the bent plume model simulations. This is because of small droplets formed due to dispersant injection; these do not have high enough buoyant velocities to get separated from the continuous phase intrusion. The reduction in droplet sizes due to the addition of dispersants didn’t have a significant effect on the first intrusion level for both models because it does not have a significant effect on the total buoyancy, which is the main driving force of the plume. The model also predicts the surfacing radius of the dispersed phases compared to their released location for the bent plume model simulations. The downstream distance to surfacing is larger for the deeper cases than shallower releases because of the longer travel time of the dispersed phases that increase the horizontal displacement in deeper releases. The TAMOC modeling suite presented here is capable of simulating oil and gas blowouts in the water under stratification and cross-flow dominated conditions along with the physical, chemical, and thermodynamic processes. Multiphase plume model validations with experimental and field data were presented along with the model application to four different scenarios. The formulations used in the model for mass transfer, slip velocity of hydrocarbons, and effects of hydrates on gases are successfully validated. The model predicts oil and gas surfacing rates, times, and locations; their rates of entering into the intrusions; along with volumes of seawater that is transported along with these plumes to the upper layers in the water column. These are important parameters needed during planning and responding phases of accidental blowout incidents. In the deep cases with mild crossflow, there are significant differences between the stratified plume model (which predicts a plume formation all the way through the water column) and the bent plume model (which stops plume formation at the first peel). The validation data for the DeepSpill experiment shed some light on which model is more appropriate, but that was for a very strong cross flow case. Further validation using data for the Deepwater Horizon, where multiple intrusions were observed, is expected to help converge these two models toward a unified prediction, and is the topic of on-going application of the TAMOC modeling suite.

Figure 11. Sectional view of the plume and the particle paths for the Case 1 simulation

ACKNOWLEDGMENTS

This research was funded by the grant from the BP/The Gulf of Mexico Research Initiative through the Center for Integrated Modeling and Assessment of the Gulf Ecosystem (C-IMAGE) Consortium. REFERENCES

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