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Energy Procedia

Energy Procedia 1 (2009) 4969-4976

www.elsevier.com/locate/procedia

GHGT-9

The fate of CO2 bubble leaked from seabed

Baixin Chena *, Masahirc Nishic b, Ycngehen Scng e, and Makctc Akai

aHeriot-Watt University, Edinburgh, EH14 4AS, United Kingdom b National Institute of Advanced Industrial Science and Technology, AIST, 1-2 Namiki, Tsukuba, 305-8564, Japan c Dalian University of Technology, Dalina 116024, China

Abstract

A numerical model of an individual CO2 bubble dissolution and ascent in shallow seawater was developed to simulate the fate of CO2 leaked from seabed naturally or artificially. The model consists of a solubility sub-model of CO2 gas in seawater, a CO2 bubble mass transfer sub-model, and a CO2 bubble momentum transfer sub-model. The model is applied to predict the dynamics of leaked CO2 in seawater at various depths from 0-150m (temperature from 10 oC to 25 oC) and for initial bubble sizes from 3.0 to 40.0mm in diameter. A diagram of CO2 ascending distance vs dissolution time is obtained from model simulations. It is found that CO2 bubbles ascend at a mean speed of 16 cm/sec and a mean shrinking rate of 30x10-3 mm/s in diameter approximately if leaked from a shallow ocean (<150m) seabed. A parameter, named as critical depth, is defined and suggested as a parameter to indicate if the CO2 leaked from seabed can return to atmosphere. This critical depth is approximately linearly related to the initial bobble size with a gradient of - 0.68 m/mm under seawater conditions in the simulation ocean.

© 2009 Elsevier Ltd. All rights reserved.

"Keywords: CO2; Droplet/Bubble; Dissolusion; Momentum changes; Modeling"

1. Introduction

It has been recognized that Carbon Capture and Storage (CCS) has grown, over the last decade, from a concept and then a research topic to a potential engineering solution to mitigate greenhouse gas [1]. Among the proposed storage options in CCS, CO2 sub-seabed storage recently draws particular attention of which has been operating in two projects, the Sleipner project (Norway) and the K12-B project (Netherlands), both located in the North Sea [2]. In these two projects, the CO2 is separated from the supply gas stream with naturally high CO2 contents and then injected into sub-seabed geological formations. An additional benefit from this option is that there is the possibility of combining CO2 storage with offshore Enhanced Oil or Gas Recovery (EOR or EGR). Some power companies have also started to investigate offshore CCS as a mitigation option of relevance to their industry [2].

As same as other options, the safety and efficiency are two major concerns, in addition to the technologies and cost, for implementing CO2 under-seabed storage in an engineering scale. From point of view of storage efficiency,

* Corresponding author. Tel.: +44 131 451 4305. Fax: ++44 131 451 3129 E-mail address: b.chen@hw.ac.uk.

doi:10.1016/j.egypro.2009.02.329

the seawater plays an additional role to isolate the injected CO2 from returning to atmosphere, in comparison with onshore geological CO2 storage. This is one of aspects. In the other aspect, however, leaked CO2 is soluble in seawater leading to an increase of pCO2 and then may disturbs the local marine environments. Therefore, for safely employment of this technology in practice, it is necessary to understand the mechanism and reasonably estimate the physicochemical and biological impacts of leaked CO2 on the marine environments.

The changes in pCO2 of seawater due to CO2 dissolution are, in principle, governed by the dynamics of interactions of CO2 droplets/bubbles with seawater and the dilution of CO2 solution in a turbulent ocean, of which can be modeled and simulated by a so-called two-phase/fluid turbulent ocean model[3,4,5]. In such a model, CO2 droplet/bubble dynamic sub-model is one of the key sub-models that describes the momentum and mass transfer mechanism of CO2 droplet/bubble in seawater. CO2 droplet dynamics, which is covered with a solid hydrate film, had been extensively studied within last decade as one of the interested research topics of CO2 ocean sequestration [6, 7]. The major parameters that effect mass and momentum transfer of CO2 droplet with hydrate layer into seawater, such as CO2 solubility in hydrate formable region and the drag coefficient, have been modeled and validated by Lab. [8] and field observation data[9]. Since the injection depth suggested for CO2 ocean sequestration is deeper than 1000m [10], less attention, however, has been draw to the dynamics of liquid CO2 droplets in hydrate free zone and gas bubbles, of which are the major concerns in CO2 sub-seabed storage with seawater shallower than 500m. At this range of depths, CO2 can be liquid droplets or gas bubbles when leaked from seabed according to the phase diagram.

The objective of this study is to construct a numerical model of CO2 bubble in seawater and predict the fate of an individual CO2 bubble leaked from seabed. In section 2, the physical characteristics of an individual CO2 bubble interacting with seawater are discussed as the basis of the physical model. Then, the mathematical model is developed from the physical concepts and models. The preliminary application of the developed model to the simulation of the fate of leaked CO2 bubble as a case study is introduced in section 4. The results are discussed in section 5, of which finally leads to the conclusions and the suggestions for the further studies.

2. Physical Models

Field observations [11] and laboratory experiments [7] both provide the evidence that the leaked CO2 from seabed, depending on the depth, are in the form of droplets or bubbles because of the instability at the interface between CO2 and seawater. Whether they are the droplets or the bubble is in turn according to the phase diagram. In general, in the ocean at depth deeper than 550m CO2 is in liquid state and turns to gas state at depth shallower than 400m. The size of droplet/bubble would vary, which should be determined by the local geological structure of sediments formations. The mechanism investigation and the model of initial bubble formation are not the subject discussed in this study. Therefore, the initial size of the bubble emerged from seabed is considered as a given parameter for the modelling of the fate of CO2 bubbles in seawater, which is at a range of 0.3mm to 40.0mm. Because of the relative smaller in size of CO2 bubbles to the surrounding seawater, it is assumed that CO2 bubble and seawater reaches thermodynamic equilibrium as soon as the bubble emerged from seabed. Consequently, the dynamics of CO2 bubble in seawater are governed by conservations of momentum and mass.

2.1. Momentum exchange between CO2 bubble and seawater

The schematics of an individual CO2 droplet/bubble in seawater is that the buoyancy force driving the droplet/bubble rising is against by the drag produced by shear stress at interface boundary. These two major forces are the forces governing the movement of an individual bubble in seawater, in addition to the additional mass force, of which is at least one order smaller in magnitude in comparison with the two forces mentioned above. Bubble buoyancy is proportional to the volume of the bubble and the density difference between CO2 and seawater. Lower buoyancy at deep seawater shifts bubble to more spherical shapes. Larger bubbles and those leaked at shallower seabed have greater buoyancy and consequently are deformed towards ellipsoidal shapes.

The major difficulty to predict the drag is due to the complex of boundary layer dynamics at the interface. At a larger Reynolds number Re, which is defined by a ratio of relative velocity (uc, m s-1 ) and bubble diameter (de, m) to the kinematic viscosity of the seawater (v, m2 s-1) as Re=uc de/v, a turbulent boundary layer will significantly enhance the drag force, which is presented by drag coefficient, Cd. The Stokes's law is no longer available for a

bubble with a turbulent boundary layer. In such a case, the drag coefficient has to be determined in general by laboratory experiments. Additionally, another parameter that makes significant contribution to the Cd is the deformation of the bubble. Bubble shapes vary with respective to relevant Eotvos number which is proportional to the ratio of buoyancy and interfacial tension, Eo = g Apd2 la , g is the gravity acceleration (m s-2), Ap the density difference between CO2 and seawater (kg m-3 ), a the interface tension (dyn). In the range of pressure and temperature of shallower water, the shape or the deformation of a bubble can be characterized by the Eotvos number alone. At a middle Eotvos number (10 < Eo <100), the large bubble attempts to deform to an ellipsoidal bubble. At very large Eotvos number (Eo > 100) the CO2 bubble becomes a bubble in a shape of ellipsoidal cup or even the spherical cup.

2.2. Mass transfer from CO2 bubble to seawater

As discussed above, CO2 is a kind of fluid that is soluble in seawater. The solubility of CO2 gas is smaller than that of liquid and decrease as temperature increase. A mass boundary layer associated with the momentum boundary layer forms as bubble rising up. The turbulent flow at interface enhances the mass transportation from bubble to seawater. The effective mass transfer is measured by an effective mass transfer coefficient k (m s-1) and defined by Sherwood number, Sh = k dJDf , which is a ratio of production of effective mass transfer coefficient and bubble size to the molecular diffusivity of CO2 in seawater (Df m2 s-1). In general, Sh is function of Reynolds number and has to be obtained by laboratory experiments for bubbles with variable shapes.

3. Mathematical models

The mathematical description of interaction between an individual CO2 bubble and seawater can be derived by application of conservation laws of momentum and mass according to the physical models discussed in last section. The governing equations of CO2 bubble is given first and then the sub-models of CO2 solubility, effective drag coefficient (relative velocity) and effective mass transfer coefficient are discussed subsequently.

3.1. Governing Equations of a free rising CO2 bubble in seawater

With above descriptions, the dynamics of free-rising CO2 bubbles leaked from seabed, including dissolution and buoyant ascending, can be simulated by the dynamics of an individual bubble when a further assumption made that the collision and collection among bubbles could occur negligibly. The mass and momentum conservative equations of an individual bubble are:

d d) = -_L(i p + ISf-C)) (1)

dt pc 3 dc

±(uc) = £±«1.0-P)g - 4fcd ) - uA (2)

dt Pc Ps 4dc mc

where uc is bubble velocity relative to seawater (m/sec), m represents mass of bubble (kg), C is the CO2 concentration (kg m-3). The subscripts of 'c', 'cs' and 's' indicate CO2, CO2 bubble surface, and seawater, respectively.

In Eq. (1), the first term is the contribution due to the CO2 expansion (positive) or compression (negative), while the second is the dissolution which always makes the bubble shrinking. It is not difficult to find that the first term in Eq. (2) is the buoyancy term that is against by the drag, the second term. The last term is the additional mass force due to the mass changes. To solve numerically this set of governing equations, sub-models are required, such as submodels of physical properties of CO2/seawater system, the effective drag coefficient, and effective mass transfer coefficient.

3.2. Sub-models

3.2.1. Sub-model of physical properties of CO2/seawater system

In this sub-model, the physical properties, such as densities of CO2 and seawater, CO2 diffusivity in seawater, and interface tension, are formulated based on experimental data. They are the data independent with flow characteristics. CO2 density data are collected from Chemical handbook [12] at temperature range from 273.15 K to 330.15 K and pressure from atmosphere pressure (0.101325 MPa) to 30 MPa. A fourth order polynomial interpolating method is employed to calculate CO2 density at a given state (P & T). The international standard state equation of seawater [13] is used in this study to predict seawater density, which is a function of pressure, temperature, and salinity.

The shape of a bubble can be sufficiently characterized by the Eotvos number. The interface tensor is a property parameter to calculate the Eotvos number. There seems to be no systematic investigation of the interfacial tension of CO2 bubbles in seawater at P-/T-conditions in the range of interest found from the literature. Ohmura et al. [14] estimate CO2/seawater at a seawater depth of 3300 m to be 24 g/s2 while Gangst0 et al. [15] considered the interface tension at CO2/seawater to be a constant value of 23 g/s2 for the range of seawater depths from 496.8m to 804.5m. The data from Uchida et al. [16] is used in this study, which is the function of temperature.

CO2 solubility in seawater is one of key parameter in mass transfer simulation. An experimental data based submodel [5] is extended to cover the range of gas bubble. The formulation model can well predict the experimental data at three regions, hydrate formation, liquid CO2 and gas CO2. The details of the numerical method applied in developing the model can be found from reference [5].

3.2.2. Sub-model of relative velocity of a CO2 bubble in seawater

Literature review found that there exist few studies on CO2 bubble movement in seawater at pressure ranging from atmosphere to 4.0 MPa. One experiment carried by Johnson et al [17] offer a set of the data of CO2 bubble rising velocity at atmosphere pressure and temperature of 295.15 K in tap water. Regarding to the modeling, the bubble dynamics in general had been well studied, a set of equations describing the bubble movement in liquids can be found from a text book [18]. The velocity is expressed in term of Morton number (M) and Eotvos to handle the effects from bubble deformation. It is simple for a spherical bubble that can be treated as a spherical solid and a standard equation of drag coefficient can be directly applied. To an ellipsoidal bubble (M< 103; Eo< 40), the bubble velocity can be estimated by

u = M J0149(/ - 0.857) P,d.

J = alH" (2 < H < 59.3) H = 4EoM-0149^/ )-0-14

3 /(3)

M = gft4 AP -3

0.94 2 < H < 59.3 [0.757 2 < H < 59.3

1 = i a, = i

1 [3.42 H > 59.3 2 [0.441 H > 59.3

For larger deformed bubbles (Spherical-cup bubble, Eo > 40), a simple equation with a constant Cd is suggested, which means that buoyancy and bubble size play a key role and leads a velocity [18]:

u = 0 . 7 1 1 (gdeAp / ps )0'5 (4)

For an ellipsoidal bubble and a Spherical-cup bubble Eq. (3) and (4) are used in this study, while the standard Stokers equation is applied for spherical bubble with standard drag coefficient. The model is validated by the experimental data [17] and found the molding results predict the data very well.

3.2.3. Sub-model of effective mass transfer coefficient

As same as the mechanism of bubble movement in liquid, the effective mass transfer varies with the shapes of bubble of which produces a different turbulent boundary layer. According to Clift et al.[18], three regions are castellated depending on the bubble side. The effective mass transfer coefficients at each region are suggested as:

0 . 0 1 13(-^-) 05 d < . 5 (5)

V 0 . 45 + 0 .2de ' (5)

Ke = 0.065Df05 .5 < de < 1.3

0.0694d_1'4Df05 1.3 < de

This set of equations was tested by Zheng & Yapa [19] for CO2 bubble in fresh water and in 96% aqueous solution, respectively under atmosphere pressure and room temperature. The model predicts experimental data very well, as can be found from the Fig. 4 and Fig 5 in reference article [19]. It should be noted that the effects from high pressure at depth about 100m (P= 1.0 MPa) has not yet been investigated especially from experimental observations.

4. Model application and case set up

The mathematical models as a set of no-linear ordinary different equations described in last section are numerical solved by using 4th order Runge-Kutta method. The model and computer code are used to simulate the fate of CO2 bubble leaked from seabed at Target Ocean in Southern China Sea.

The field observation data from target ocean in Southern China Sea are reconstructed for the modelling simulations. The data of temperature distributions are interpolated to the data at depth where the CO2 bubble reached in the simulation. Because the distributions of temperature at each season are differ, the simulations are set for seasons of winter, summer, and spring, while autumn season seems to be covered at deep water by spring and at shallower water by winter and summer. The temperature from observation and those interpolated are shown in Fig. 1. The observation data of background CO2 concentration and salinity are used in the simulation. Because the data are only available till to depth of 100m, the background CO2 concentration and salinity at depth deeper than 100m are set to be the data at 100m.

To estimate the fate of leaked CO2 from seabed a case study is carried out by means of application of the model developed to the target ocean. Having analyzed the observation data from target field, the three seasons, winter, summer, and spring, are selected as a season cases, as discussed above. The leakage depth is another parameter listed for the case study. From Fig. 1, it is found that there exits a temperature jump at depth about 60m in both seasons of winter and summer. In order to count the role of this temperature jump layer, the leakage depths at 150m, 75m, 40m and 25m are determined as the case studies. The initial bubble sizes are suggested to be 40mm, 30mm, 20mm, 10mm, 5mm and 3mm, respectively. The simulation results are discussed in the next section.

5. Simulation results and discussion

20 22 24 26 28 30 32 Temperature ( C )

Fig.1. Temperature distribution at target ocean in each seasons

The fate of an individual CO2 bubble leaked from seabed in seawater column is simulated at variant conditions listed in the last section. Among the results predicted from the model, the bubble shrinking as rising up is selected as one of parameter to present bubble behaviors in seawater, which is shown as the bubble size against the depth. Bubble rising velocity is also examined as the function of bubble size leaked from variant depths. This is aimed to check the role of buoyancy on bubble dynamics. Finally, the results from each case run are summarized. The analysis on the simulation data leads to define a parameter named as critical leakage depth for assessing possibility of a CO2 bubble return to atmosphere. It is discussed that the relations between terminal distances, which are the distance of a CO2 bubble could rise up before completely dissolving up, and terminal time, which is the time associated with terminal distance.

5.1. the effects of leakage depth and initial bubble size

At each leakage depth for seasons of winter, summer, and spring, the dissolution and rising dynamics of leaked CO2 bubble are predicted in term of bubble size against the depth. Fig. 2 shows the results. It is found that the rising distance of leaked bubble are significantly sensitive to the bubble size, while seems to be insensitive to the leakage depth. The larger the bubble, the longer the distance can rise up. This is due to the large velocity of a large bubble and the longer time required to be dissolved up. For large bubbles, the bubbles in size larger than 30 mm, the rising distance is approximately proposed linearly to the initial size for each leakage depth and seasons; say the bubble with initial size of 40mm could rise up about 40m from leaked depth. At leakage depth shallower than 40m some bubbles are remaining when reached to the ocean surface. This means that these bubbles return partially to the atmosphere where they had been sequestrated from. From the numerical simulations, it is found that at leakage depth of 25 m, approximately 33% of a bubble in volume with initial leakage size of 40mm could return to atmosphere at spring season, while about 12.5% in winter season. The shallower the bubble leaked the more CO2 remains unsolved and return to atmosphere, as indicated in Fig.2.

Fig. 2. CO2 bubble dissolution and rising from variant leakage depth of 10m (left top), 25m (right top), 40m (down left), and 150m (down right)

Concerned with the risks estimation and monitoring system design, the possibility of leaked CO2 return to atmosphere is one of the key parameter for assessing CO2 under seabed storage technologies. To give a simple and useful parameter, a critical depth for bubbles with initial size is defined, of which is the depth at where leaked CO2 bubble at a given initial size could possibly return to the atmosphere. A best fitted function of critical depth against the initial bubble size is well expressed by a second order polynomial function, as shown in Fig. 3. The data used for data fitting are the data with 1.15 times the data from numerical simulations for the safety, of which is shown as yellow triangle samples shown in the Fig 3. It has to be noted that the critical depth equation from this study is available at temperature ranging from 23 oC to 28 oC at depth down to 150m. It also has to be mentioned that the effects from ocean current and ocean turbulent mixing on this critical depth were not taken into account in this

study. Therefore, a modified parameter which should be larger than 1.3~1.5 times the critical depth obtained from this study is strongly suggested when uses this equation in engineering practices.

5.2. Terminal distance and time

The bubble rising distance and time when has been completely dissolved up are the useful data to estimate the bubble dynamics in seawater. These sets of data from simulations in winter and spring seasons (the data in summer season are indistinguishable from those in winter season) at leakage depths of 150m, 75m and 40m are collected and shown in Fig. 4. From this Fig. the mean rising velocity of bubbles leaked can be estimated by the gradient with respect to the time. Approximately a data of 14 cm/s can be the mean velocity at all seasons, bubble size and leakage depths.

Difference from seasons

The variation of bubble rising distance in seasons is due to the difference of temperature. It is found that at each leakage depth, the bubbles leaked in spring season can rise to a large distance than those in both summer and winter seasons. In the summer and winter seasons, it seems hardly to distinguish the difference as the temperature differs not too much, especially at depth deeper than 40m. As discussed in the above sections, the dynamics of bubble in seawater is governed by momentum and mass exchanges between CO2 bubble and seawater. They couples with each other, for instance, the larger relative velocity will enhance the mass transfer and lead to a quick shrinking. This quick shrinking rate leads a smaller bubble size that is feedback to reduce the relative velocity because the relative velocity is the function of bubble size as predicted in Eq. 5. To investigate the reason for which dynamics play the role, the velocities data of bubble leaked from depth of 150m from winter and spring are compared. The difference in temperature distribution for two seasons seems making little contribution to producing a difference in velocity. This means that the buoyancy due to density difference is insensitive to this temperature difference, of which are about 4 degrees. This result indicates that the large distance the bubble can rise up in spring season is majorly due to the slower dissolution rate, actually the smaller solubility at higher temperature (27 oC in spring season and 23 oC in winter season).

£ -20 a

• Winter Season ■ Spring Season

V _ x 1.15 ■Best fitted

y = -0 0121x2 - 0 6361x

0 10 20 3D 40

C02 bubble Initial size (mm) Fig 3. Critical depth vs initial bubble size

Terminal Time (min)

; 4. Bobble terminal distance vs terminal time

6. Conclusions

a). A mathematic model of an individual CO2 bubble dissolution and rising a an quiescent seawater is constructed to simulate the dynamics of interaction between CO2 bubble and seawater. Model consists of sub-models of physicochemical properties of CO2-seawater system, including densities, diffusivity of CO2 into seawater, CO2 solubility; effective mass transfer, and effective drag coefficient (relative velocity).

b). Model is applied to simulate the fate of an individual CO2 bubble leaked from seabed in target ocean at regions at 150 km North-east from Malaysia in South China Sea. Following results are obtained from the case simulations:

A parameter, named as critical depth, is defined and suggested as an over-all assessment parameter to assess the fate of CO2 bubble in the shallower ocean in engineering applications. This critical depth is defined as a depth from where a leaked CO2 bubble might be able to return to atmosphere. It was found from simulations that this critical depth is linearly related to the bubble initial size leaked from seabed. For example, a CO2 bubble with initial diameter of 40 mm leaked from 40 m depth might be critically, if rather than hardly, dissolved completely before reach to sea surface, while a bubble with size smaller than 40mm leaked from seabed at the same depth is found to be unable to return to atmosphere.

The seasonal effects on CO2 bubble dynamics in the target ocean are also investigated by using the temperature data observed in seasons of winter, summer, and spring. It is indicated from the simulations results that during spring season leaked CO2 bubble could move up to much shallower depth because of a relative higher temperature at depth deeper than 60m in caparison with those in winter and summer seasons. About 33% of a bubble with leaked size of 40mm at depth of 25m would return to atmosphere at spring season, while only 12.5% in winter season.

Acknowledgement

This study is part work of the project of Confidential Construction of Carbon Dioxide Capture and Storage funded by NETO, Japan. The research was carried out in Heriot-Watt University, UK.

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