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Detailed experimental study on the dissolution of CO2 and air bubbles rising in water
Chemical Engineering Science 158 (2017) 552–560
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Detailed experimental study on the dissolution of CO2 and air bubbles rising in water ⁎
Daniel Legendre , Ron Zevenhoven Thermal and Flow Engineering Laboratory, Åbo Akademi University, FI-20500 Turku, Finland
A R T I C L E I N F O
A BS T RAC T
Keywords: CO2 Air Bubble dissolution Bubble path tracking Bubble tower
An experimental investigation of single bubbles rising in water in a confined cylindrical geometry is performed as means of obtaining further understanding on the CO2 dissolution and chemical conversion in multi-phase bubble towers. Single isolated bubbles (D~ 4,5– 5,5 mm) and individual bubble tracking in small bubble swarms at low gas volume fraction is evaluated using a high-speed camera. Comparison with dissolution rate of air and CO2 bubbles reveals hardly a diameter change for air bubbles, in contrast with near-total dissolution of CO2 bubbles within the 2 m column height. Comparison with 1D numerical analysis on single rising bubbles and previous 3D CFD simulations of small bubble swarms show a fair agreement although certain deviations are encountered. Only CO2 bubbles decrease their aspect ratio from wobbling ellipsoidal bubbles to spherical bubbles depending on their vertical location in the tower, i.e. their size. The amplitude of oscillation is decreased while bubbles dissolve.
1. Introduction Mass transfer and chemical reaction effects between a gas phase dispersed in an aqueous solution is still a design challenge to be addressed, modelled and validated in the area of bubble reactors. Although is estimated that 25% of all reactions in chemical industry take place in multiphase liquid-gas flows (Martín et al., 2011), bubble reactor engineering design is closer to an art than a science because low-accuracy algorithms may disrupt the physics reflected by the models implemented (Jakobsen, 2001). Therefore experimental comparison is necessary to modify and improve these models. One of such liquid-gas flows is the bubble reactor of the so-called Slag2PCC process (Mattila and Zevenhoven, 2014) designed and being scaled-up at Aalto university in cooperation with Åbo Akademi in Finland (Fig. 1). This is one of a portfolio of efforts in the field of carbon capture and storage (CCS), aiming at valorization of calcium-based industrial wastes (here: steelmaking slag) using carbon dioxide, producing precipitated calcium carbonate (PCC) with significant market-value. While the process operates, in a continuous mode, at near-ambient temperatures and pressures, the rate of the carbonation step is determined by the dissolution of CO2 bubbles. Therefore, while the quality (purity, particle size, crystal shape) of the PCC is crucial for the economic viability of the process, it is considered to be a CCS method for which it is essential that CO2 is effectively and efficiently bound into PCC product, with negligible amounts leaving the process with exhaust
⁎
gases. Thus, an assessment is being made of dissolution process for CO2 bubbles as used in the Slag2PCC process, tracking bubble size and velocity while rising in aqueous solutions, comparing visual observations with a deterministic model recently presented elsewhere (Legendre and Zevenhoven, 2016). Since mixers are used in the carbonator reactor (as well as in the upstream reactor for calcium extraction, using ammonium salt solvent) to further improve solution mixing, these can be put into the here used bubble tower reactor as well, similar to the reactor shown in Fig. 1 and the eight times larger demonstration-size test set-up at Aalto University (Said et al., 2016). The current paper, however, gives a detailed assessment of air versus CO2 bubble dissolution leaving the impact of the mixers, as well as the presence of dissolved calcium that with CO2 gives PCC particles for a future reporting. An experimental assessment of the bubble size and position using a high speed camera can be used to the further calculation of a bubble or bubble cluster local velocity, shape and dissolution rate (Aoki et al., 2015; Colombet et al., 2014; Nock et al., 2016). Bubble size and shape can be directly determined by means of integral shadowgraphy (Böhm et al., 2014). These variables can be used to provide a detailed description of bubble size decrease during dissolution processes in terms of bubble shape, size, velocity, acceleration regime and dissolution dynamics which can be translated into mass transfer from the gas phase towards the liquid phase (Maldonado et al., 2013). The present
Corresponding author. E-mail address: daniel.legendre@abo.fi (D. Legendre).
http://dx.doi.org/10.1016/j.ces.2016.11.004 Received 23 August 2016; Received in revised form 31 October 2016; Accepted 2 November 2016 Available online 05 November 2016 0009-2509/ © 2016 Elsevier Ltd. All rights reserved.
Chemical Engineering Science 158 (2017) 552–560
D. Legendre, R. Zevenhoven
effect of the thin vessel polycarbonate walls of refractive index 1.60) and values of ≈1 for the vertical direction. In the current research, however, only uncorrected measured values without the use of a magnification factor are presented. The radius of the circular tank is much larger than the radius of the measured bubbles, which are also near the center line of the pipe. Therefore magnification (correction) factors will not be notably larger than 1, as the effective magnification effect must be between the values estimated for horizontal and vertical factors. For bubbles further from the center line of the vessel the magnification correction calculated experimentally with a reference measurement tape inside the vessel immersed in water would be < 1,245…1,5 in the horizontal direction and < 0,965…1,05 in the vertical direction. The current work uses a cylindrical section tank, as this set up would be extended in future research to become a mixed tank, as an important part of the Slag2PCC process equipment. Finally, pH measurements in the water column are recorded to verify that the liquid phase is far from CO2 saturation during the tests. As the bubble tower is a slender structure (vertical length » other dimensions), extra fastening points are needed. These fastening points are represented by fastening bands on the pipe. These bands interfere with the image processing; as a bubble passing behind one of them implies that the image tracking algorithm cannot successfully lock on to the same bubble once appears again after passing these fastening points. An algorithm to overcome this issue is described in Appendix A. Furthermore, after the video recordings the gas flow was increased to verify the pH behavior towards a fully saturated solution in which a CO2 bubble does not dissolve. Experiments were performed in steady state of approx. 1 bubble per second with bubbles feed through a single perforated central flange hole Ø 0,5 mm. Bubble flow is controlled by a needle valve at the lowest point of the experimental set up, set to a flow rate of ~0.1 l/min (STP). The experimental set up can be appreciated in Fig. 3.
Fig. 1. Slag2PCC experimental set up (left) and calcium carbonate bubble reactor graphical representation (right) (Mattila and Zevenhoven, 2014).
paper provides a detailed specification of such parameters for air and CO2 bubbles streams that are necessary to compare models on CO2 bubble dissolution and develop these towards the modelling of industrial carbonation processes.
2. Experimental set up and instrumentation Previous estimations on CFD Euler-Lagrange one-way coupling calculations by Legendre and Zevenhoven (2016) on CO2 bubble swarm dissolution (with initial bubble diameter DBubble=5 mm) at low gas volume fraction gave approximately 1.95 m height in the vessel as an estimate to be sufficient to reach total bubble (swarm) dissolution in water at ambient conditions. These numerical estimations raise the need to modify the original design of the Slag2PCC carbonation method, suggesting a new reactor tank of a similar height is required (depending on the intensity of mixing used). A circular pipe made of clear polycarbonate of diameter D =133 mm (3 mm wall thickness) and height, H =2 m acts as the center of the experimental observations for bubble tracking; further expansion with impellers is addressed in ongoing and future research. A double centered flange arrangement in Fig. 2, with an inside perforated cap (d =0,5 mm) is used as gas inlet while an external surrounding flange couples it to the outer vertical polycarbonate pipe. Several authors have defined different configurations and geometry cross-section tanks for the characterization of rising bubbles. It is acknowledged that most authors prefer a rectangular cross section to avoid image distortion (Böhm et al., 2014). Nevertheless there are authors that use circular sections and claim to have an optical distortion negligibly small as a result of the similar refractive indexes for tank walls and containing liquid (Aoki et al., 2015). Theoretical approximations on the magnification index in a refractive circular convex surface (Young and Freedman, 2012) with a refractive index of water (1.333) and the geometrical specifications of the circular vessel presented in this work, give a maximum magnification of the image recorded by the camera of a factor 1.32 with respect to the actual size of the bubble in the horizontal direction with respect to center of the vessel. Furthermore, in the vertical direction theoretically this magnification factor is equal to 1 because in this direction the refractive surface is planar for which the image produced would always retain the same lateral size as the original object (Young and Freedman, 2012). Experimentally, using a reference measurement tape immersed in water, the magnification factor on the center of the pipe gives maximum values of ≈1.37 in the horizontal dimension (small discrepancies with the theoretical value due to the extra magnification
2.1. High speed camera tracking The most important characteristic of a multiphase flow is the existence of an interface separating the phases and associated discontinuities of properties across the phase interface (Joshi, 2001). This phase separation can be achieved with image analysis, as bubbles present a clear interface that contrast with the surrounding liquid phase. The image recording set-up consisted of a high-speed Photrom camera SA3 Model 120K-M3 equipped with a 52 mm Nikon 200773 lense and a distance of 1-1,5 m to visualize a window of 45 cm (for larger bubbles) to 20 cm (for smaller bubbles) located at different heights of the bubble tower. The special resolution of the system is 2,4 4,45 pixel/mm at a frame rate of 1000 images per second with a constant exposure of 1/2000. The lighting is supplied by a set of 8 parallel arrangement of fluorescence tubes T5 39 W. 2.2. Size and shape estimation The recorded images are processed using the Matlab® image processing toolbox. Several authors had used this shadowgraphy technique (Nock et al., 2016; Colombet et al., 2011,2014) with acceptable results, the technique is generally standard and for the present paper this routine is based on i) the removal of the background detail, ii) threshold iteration for B & W conversion, iii) size position filtering, iv) edge detection and filling of structures, v) size, shape and position estimation in base of a reference point and finally vi) ellipse fit. Image discarding may be needed as an intermittent step. The overall procedure can be grouped as three steps as shown in Fig. 4. A literature review of different experimental approaches based on different techniques on different tank cross sections (cylindrical and rectangular) was recently given by Böhm et al. (2014). From the authors’ perspective perhaps the use of a second shadowsgraphy camera for reconstruction of 3D bubbles by image integration as by 553
Chemical Engineering Science 158 (2017) 552–560
D. Legendre, R. Zevenhoven
Fig. 2. Cross section of the bubble column and high speed camera placement.
(pfluid) and the pressure jump (pJump) at the bubble surface due superficial tension forces according to the Laplace equation for bubbles (Gong et al., 2007); (pJump=2σ/rBubble), with surface tension σ and bubble radius rBubble. In a still water column the local pressure of the fluid can be estimated as the sum of the atmospheric pressure (patm) and the static pressure of the water at a determinate height. Therefore the bubble internal pressure (pBubble) can be calculated as:
pBubble =patm +
(2)
3. CFD simulation of bubble reactors
Fujiwara et al. (2004) might be the best approach as it is known that a bubble shows a spiral rising path, that especially for the case of wobbly regime bubbles might not be axi-symmetric. In terms of the use of one camera the assumption of axi-symmetry is generally made. In terms of a specific cross-section a correction factor must be estimated, as the image might be disturbed by the refraction of light on the liquid and on the walls of the tank. All bubbles are here assumed to be oblate spheroids with a minor semi-axis a and a major semi -axis b, which are measured from the two dimensional parameters of the ellipse fit, similar to Colombet et al. (2014) using the bubble aspect ratio χ = b / a . The estimated bubble diameter is then estimated from the volume of this spheroid as: 1
ρg (Hcolumn−ZBubble )
with water density ρ , gravity constant g, column of water/ height of the reactor Hcolumn and vertical position of the bubble ZBubble measured upwards. Furthermore the bubble mass mBubble can be estimated based on the spheroid volume and the bubble internal pressure using the ideal gas equation. Bubble velocities in the x (horizontal) and z (vertical) directions were estimated as the simple derivatives of the centroid positions with time between images. The reference point was taken using the measuring tape positioned on the wall next to the bubble tower (Fig. 3).
Fig. 3. Experimental set up.
d =(8b 2a ) 3
2σ + rBubble
Dissolution of a gas stream into fluid phase is one of the most recurrent phenomena in multiphase reactors, which may be driven by pure diffusion, convection or chemical reaction effects. Diverse stateof-the-art models can aim to predict a certain dissolution rate, but still validation of numerical models is needed (Joshi, 2001). We recently (Legendre and Zevenhoven, 2016) presented a 3D oneway coupling method to simulate the dissolution of small CO2 bubble swarms in a bubble reactor with mixers. For this 3D model a variable time step is used in the Lagrangian tracking of the bubble swarm using a Generalized Alpha Method with a free sizing of the time step used by the solver. Furthermore a linear predictor and a backward Euler consistent initialization (fraction of the initial step for backward Euler =0.001) with and absolute tolerance of 1·10−5 is used. The experimental results presented in this paper will be used as a
(1)
Bubble internal pressure is the sum of the fluid local pressure 554
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Fig. 4. Image processing. (a) Original image, (b) step i, (c) steps ii-vi..
Fujiwara et al., 2004; Maldonado et al., 2013; Nock et al., 2016) that experimentally a bubble rise in a helicoidally trajectory, the 1D dissolution model can be used as comparison only for the dissolution rate of bubbles in terms of vertical displacement.
comparison point to improve such numerical models. 1D estimation model estimation of bubble dissolution is also presented below in this paper. This model is the result of a simplification of the 3D model previously presented by the authors. Although it has been extensible studied in literature (Böhm et al., 2014; Colombet et al., 2011;
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4. Numerical 1D simulation of rising bubbles dissolution and tracking This model is a simplification from a 3 dimensional bubble dissolution model to a 1 dimension model of the previous work presented by the authors (Legendre and Zevenhoven, 2016). In this 1D model the bubble can only ascend in a vertical straight line. Although a straight line ascend of a bubble is something far from reality, this model can be used to estimate the height of dissolution of certain bubble/solution combination. 4.1. Model state of the art As a first step to model a large-scale bubble reactor a single bubble while rising and dissolving can be modelled as a spherical body submitted to point forces. Combined with a description for the decreasing mass and size of a dissolving bubble in an aqueous solution this will be the basis for bubble swarm modelling. A link between mass transfer boundary layer and bubble force is established through the mass time derivative of the dissolving bubble, as function of the local Reynolds, Schmidt and Sherwood numbers, furthermore by chemical conversion defined by mass transfer theory via the boundary layer thickness δ for a first order chemical reaction with dissolved calcium (not yet presented here). A free body diagram of the model can be observed in Fig. 5. For any instant the force balance for a moving bubble can be written, with FDrag, FLift and Fi forces in generic directions, as Eq. (1):
→ ⎯ ⎯ d (m. VBubble ) → =FBuoyancy+ dt
n
→ ⎯ → ⎯ → ⎯ → ⎯ FGravity+FDrag+FLift + ∑ Fi i
(3)
Finally this 1D model is an application of free body diagram, represented by Eq. (3) projected on the Z vertical direction, with a fluid velocity equal to zero, as its represents a better estimation for stagnant water in a tank. The exact equation set can be found in (Legendre and Zevenhoven, 2016).
Fig. 6. Bubble dissolution, diameter reduction. (a) Air, (b) CO2.
over time with adequate time step and initial conditions. The bubble mass time derivative necessarily implies abrupt changes in the immersed body velocity, mass and path unless an adequate integration step size is used. In order to integrate this equation a variable step size method is used where the error is estimated as the difference between the fifth- and fourth-order estimates of the Runge-Kutta Felhberg method (Chapra and Canale, 2010). In practice for this model the time step oscillates between a max step size 3.914·10−4 s and a minimum of
4.2. Numerical integration scheme Eq. (3) gives a first order non-linear differential equation in the → ⎯ variable velocity (VBubble ). In order to solve this equation and obtain the velocity profile of the rising object is necessary to integrate the solution
Fig. 5. Free body diagram and mass transfer boundary (Legendre and Zevenhoven, 2016).
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Fig. 7. Comparison of the path of two bubbles rising under different dissolution regimens. (a) Air, (b) CO2. Note the different axis.
Fig. 8. Vertical velocity comparison with previous simulations CO2.
Fig. 9. Vertical displacement comparison with previous simulations CO2.
1.298·10–19 s (mean value of the time step 3.722·10−5 s). As it is desired to obtain the size change in time of the rising bubble we can establish a link between the mass transfer, the bubble radius and bubble internal pressure (Eq. (2)) through the ideal gas equation. The pressure inside the bubble is calculated using the Laplace equation according to (Gong et al., 2007) and thermal effects are neglected.
Therefore if an integration time step (h) is defined then the bubble mass (mbubble) for the next iteration (i+1) is defined as:
m bubble
(i +1)=m bubble(i )+
dm h (i ) dt (i )
(4)
and the concentration increase (CBulk) in the reactor can be computed 557
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5. Results The experiments started by a flow of CO2 bubbles through the water as to remove dissolved air. After several minutes a short steady state was reached as indicated by pH and the size of the CO2 bubbles leaving the vessel via the top. After this point the data given here was collected while level saturation of water with CO2 staid below a few % as indicated by the pH meter. Image recording of rising bubbles in a water column was performed and analyzed. With CO2, footage only up to a height of 1,2 m due to the small size of the bubble could be successfully produced by the highspeed camera. For air footage could be obtained up to 1,80 m. A first comparison could be made for the dissolution rate of CO2 bubbles and air bubbles. As depicted in Fig. 6 CO2 bubbles decrease their diameter by more than 60% from an initial size ~4,5–5 mm to 1,5 mm at 1,2 m of height. In contrast, air bubbles do not dissolve and maintain at a constant diameter (Fig. 6a). In Fig. 7a clear reduction on CO2 bubble oscillation amplitude compared to air bubbles can be appreciated, especially towards the top of the reactor where the CO2 bubbles are almost completely dissolved. In terms of velocity profiles we recently reported (Legendre and Zevenhoven, 2016), a fair agreement for simulated bubbles of initial DBubble =5 mm is found as shown in Fig. 8. The earlier predicted linear ascension path as function of time for several simulated bubbles could be verified for heights H < 1,20 (the maximum recorded height beyond which the bubble size gave insufficient visual resolution) as shown in (Fig. 9). Bubble Reynolds numbers experimentally present a more scattered behavior for initially big wobbly bubbles, but as the bubbles dissolve a clear tendency of decrease can be appreciated. Even when both models seem to have certain divergence, it can be observed that both of them follow the clear decrease of bubble Reynolds number (Fig. 10). Finally in terms of dissolution rate, bubbles show a clear asymptotically decreasing mass (Fig. 11). The 1D model seems to be a better estimation for bubble dissolution, nevertheless the 3D model presents a quite close behavior as well. Possibly the discrepancies of the Comsol 3D model arise from the local turbulent flow field where the simulation was performed i.e. a stirred bubble tower (Legendre and Zevenhoven, 2016). In terms of bubble shape air bubbles show a wobbling behavior during their total trajectory. On the contrary as CO2 bubbles rise a transition from an oscillating wobbling bubble behavior to a fairly linear spherical bubble behavior can be observed. In Fig. 12 the evolution of the bubble aspect ratio (χ = b / a ) in terms of the vertical position is presented. Three major regions can be observed i) the wobbling area (from height 0 to ~50 cm) in which the bubble ellipsoidals show a scattered behavior and χ > 1, ii) the ellipsoidal area (from ~50 to ~90 cm) where the ellipse image approximation is better, giving a more dense set and χ > 1 and finally iii) the spherical area (from ~90 cm upwards) where the aspect ratio χ ≈ 1 and the ellipse fit reduces to a circular fit. Further comparison with the bubble shape diagram (Amaya-bower and Lee, 2010) is presented in Fig. 13. It can be appreciated how the recorded bubbles progress from the wobbling region with high Reynolds numbers (Re=1200 ~ 1500) towards the spherical shape region as the Reynolds number decreases. Furthermore a remark must be made in terms of bubble internal pressure. An initial difference of mass is found; as according to the ideal gas equation the mass of the bubble is proportional to its internal pressure which is correlated to the local pressure of the surrounding liquid (most significant term defining bubble internal pressure). This liquid local pressure value corresponds to the pressure of the static water column in still water (1D model and experiments) and to the local pressure in a stirred environment (3D model with mixers). In the scenario of stirred water, the pressure presents lower local values due to the stirred velocity of the continuously moving liquid phase as higher
Fig. 10. Reynolds number comparison with previous simulations CO2.
Fig. 11. Bubble mass comparison with previous simulations CO2.
Fig. 12. Bubble aspect ratio vs. vertical bubble position.
with a known reactor volume (VReactor) as:
CBulk(i +1)=CBulk(i)+
dm ⎛ h(i ) ⎞ ⎜ ⎟ dt (i ) ⎝ VReactor ⎠
(5)
The model expressions used for calculating dm/dt and bubble size change via the mass transfer coefficient of a moving bubble, including the effects of chemical reaction in the water and considering both drag and lift forces and (initial) non-sphericity of the bubbles were recently presented elsewhere (Legendre and Zevenhoven, 2016).
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Fig. 13. Shape regime map (Amaya-bower and Lee, 2010) (left), simulated and experimental results (right).
Fig. A1. Bubble tracking scheme.
was found. Furthermore, comparison with previous simulations is presented, thus showing a good agreement with experimental data. Model estimations seem to match the dissolution phenomena of bubbles rising in water. A 1D model is a good estimation for bubble dissolution design purposes, furthermore the extension of the equations in a full bubble tower reactor with stirred impellers was presented as well for comparison. Results although similar do show deviations, as a result of the mixing characteristics of the fluid surrounding the bubbles. Current experimenting includes the effect of (four) mixers present in the vessel at 50 cm intermediate space. The dissolution, i.e. change in size of (so far) up to 120 bubbles simultaneously is analyzed by comparing 20 cm height sections above and below the mixer, again as 5 s recordings á 1000 images/s. Measurements are made around the mixers at different heights and up to 200 rpm rotation speed. Visual interpretation of results is ongoing. This will be reported in a future
velocities zones normally imply pressure drops. This difference in local pressure results in a difference in mass between identical size bubbles: for a 5 mm bubble it gives approx. 17% more mass in still water compared to water mixed at (here) 100 rpm in the 3D model. This is translated in bubbles with velocities slightly slower in the vertical direction for the 3D case with a lower dissolution rate as results to less initial massive bubbles. The faster bubbles in the 1D case with still water present a higher dissolution rate that presents a good agreement with experiments on still water conditions. 6. Conclusions Bubble dissolution in a bubble tower was experimentally studied using high speed camera recording and image processing. Results show a clear tendency of bubble dissolution in water and moreover a clear distinction of CO2 dissolving bubbles vs. air non-dissolving bubbles 559
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paper, including also the formation of precipitated calcium carbonate (PCC) after adding a calcium salt and additional chemicals to the water.
radius of the targeting circle is smaller than the distance between two bubbles.
Acknowledgements
References
This work was funded by the Doctoral Program in Energy Efficiency and Systems (EES) of Finland (2012–2015) and the CLIC Oy Carbon Capture and Storage Program CCSP (2011–2016). The authors acknowledge the help with the experimental set up design and mounting of Alf Hermanson and the use of the high speed camera of Debanga Mondal from our laboratory.
Amaya-bower, L., Lee, T., 2010. Computers & fluids single bubble rising dynamics for moderate reynolds number using lattice Boltzmann method. Comput. Fluids 39, 1191–1207. Aoki, J., Hayashi, K., Tomiyama, A., 2015. Mass transfer from single carbon dioxide bubbles in contaminated water in a vertical pipe. Int. J. Heat. Mass Transf. 83, 652–658. Böhm, L., Kurita, T., Kimura, K., Kraume, M., 2014. Rising behaviour of single bubbles in narrow rectangular channels in newtonian and non-newtonian liquids. Int. J. Multiph. Flow. 65, 11–23. Chapra, S.C., Canale, R.P., 2010. Numerical Methods for Engineers Sixth ed.. McGrawHill, New York. Colombet, D., Legendre, D., Cockx, A., Guiraud, P., Risso, F., Daniel, C., Galinat, S., 2011. Experimental study of mass transfer in a dense bubble swarm. Chem. Eng. Sci. 66, 3432–3440. Colombet, D., Legendre, D., Risso, F., Cockx, A., Guiraud, P., 2014. Dynamics and mass transfer of rising bubbles in a homogenous swarm at large gas volume fraction. J. Fluid Mech. 763, 254–285. Fujiwara, A., Danmoto, Y., Hishida, K., Maeda, M., 2004. Bubble deformation and flow structure measured by double shadow images and PIV/LIF. Exp. Fluids 36, 157–165. Gong, X., Takagi, S., Huang, H., Matsumoto, Y., 2007. A numerical study of mass transfer of ozone dissolution in bubble plumes with an Euler – Lagrange method. Chem. Eng. Sci. 62, 1081–1093. Jakobsen, H.A., 2001. Phase distribution phenomena in two-Phase bubble column reactors. Chem. Eng. Sci. 56, 1049–1056. Joshi, J.B., 2001. Computational flow modelling and design of bubble column reactors. Chem. Eng. Sci. 56, 5893–5933. Legendre, D., Zevenhoven, R., 2016. A numerical Euler – Lagrange method for bubble tower CO2 dissolution modeling. Chem. Eng. Res. Des. 111, 49–62. Maldonado, M., Quinn, J.J., Gomez, C.O., Finch, J.A., 2013. An experimental study examining the relationship between bubble shape and rise velocity. Chem. Eng. Sci. 98, 7–11. Martín, M., Galán, M. a., Cerro, R.L., Montes, F.J., 2011. Shape oscillating bubbles: hydrodynamics and mass transfer - a review. Bubble Sci. Eng. Technol. 3, 48–63. Mattila, H.-P., Zevenhoven, R., 2014. Design of a continuous process setup for precipitated calcium carbonate production from steel converter slag. ChemSusChem (3), 903–913. Nock, W.J., Heaven, S., Banks, C.J., 2016. Mass transfer and gas – liquid interface properties of single CO2 bubbles rising in tap water. Chem. Eng. Sci. 140, 171–178. Said, A., Laukkanen, T., Järvinen, M., 2016. Pilot-scale experimental work on carbon dioxide sequestration using steelmaking slag. Appl. Energy 177, 602–611. Young, H.D., Freedman, R.A., 2012. Sears and Zemansky's university physics: with modern physics (94111 USA). Pearson Education, San Francisco, CA.
Apendix A: Bubble tracking algorithm to lock on to one single bubble Earlier experiments revealed that a perforated flange with a hole diameter of ~0,5 mm produced a stable and easily controllable flow of single bubbles with spacing determined by the flow rate (here ~0.1 l/ min). Nevertheless due to different values of surface tension forces in CO2 bubbles, bubble flow with one bubble in the field of vision was not always possible, giving a swarm of small scattered bubbles instead. Added to this phenomena the bubble tower has fastening points, as mentioned, where a rising bubble is invisible to the camera, passing behind an obstacle. As the main goal of the current research is to follow a single bubble and compare its qualities and behavior with a simulated bubble, a lock-on targeting algorithm was used to isolate the information of a particular desired entity. This tracking concept can be observed in Fig A1. A targeting moving circle is defined, with an initial radius previously defined (large enough to overcome the dimensions of the obstacle). This targeting center will be continuously updated to follow the center of the locked on bubble. When this bubble passed behind an obstacle, the targeting center will remain in the last position known of the bubble centroid. A try/catch statement allows the video tracking program to continue processing video frames when the bubble is not visible. This circle will wait until the lock bubble overcomes the obstacle and can be visible again in camera recordings. Finally the targeting center is updated to follow the centroid of the locked-on bubble. This targeting method is effective as long the bubble swarm is sufficiently scattered, and for low gas volume fractions in which the
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Contents lists available at ScienceDirect
Chemical Engineering Science journal homepage: www.elsevier.com/locate/ces
crossmark
Detailed experimental study on the dissolution of CO2 and air bubbles rising in water ⁎
Daniel Legendre , Ron Zevenhoven Thermal and Flow Engineering Laboratory, Åbo Akademi University, FI-20500 Turku, Finland
A R T I C L E I N F O
A BS T RAC T
Keywords: CO2 Air Bubble dissolution Bubble path tracking Bubble tower
An experimental investigation of single bubbles rising in water in a confined cylindrical geometry is performed as means of obtaining further understanding on the CO2 dissolution and chemical conversion in multi-phase bubble towers. Single isolated bubbles (D~ 4,5– 5,5 mm) and individual bubble tracking in small bubble swarms at low gas volume fraction is evaluated using a high-speed camera. Comparison with dissolution rate of air and CO2 bubbles reveals hardly a diameter change for air bubbles, in contrast with near-total dissolution of CO2 bubbles within the 2 m column height. Comparison with 1D numerical analysis on single rising bubbles and previous 3D CFD simulations of small bubble swarms show a fair agreement although certain deviations are encountered. Only CO2 bubbles decrease their aspect ratio from wobbling ellipsoidal bubbles to spherical bubbles depending on their vertical location in the tower, i.e. their size. The amplitude of oscillation is decreased while bubbles dissolve.
1. Introduction Mass transfer and chemical reaction effects between a gas phase dispersed in an aqueous solution is still a design challenge to be addressed, modelled and validated in the area of bubble reactors. Although is estimated that 25% of all reactions in chemical industry take place in multiphase liquid-gas flows (Martín et al., 2011), bubble reactor engineering design is closer to an art than a science because low-accuracy algorithms may disrupt the physics reflected by the models implemented (Jakobsen, 2001). Therefore experimental comparison is necessary to modify and improve these models. One of such liquid-gas flows is the bubble reactor of the so-called Slag2PCC process (Mattila and Zevenhoven, 2014) designed and being scaled-up at Aalto university in cooperation with Åbo Akademi in Finland (Fig. 1). This is one of a portfolio of efforts in the field of carbon capture and storage (CCS), aiming at valorization of calcium-based industrial wastes (here: steelmaking slag) using carbon dioxide, producing precipitated calcium carbonate (PCC) with significant market-value. While the process operates, in a continuous mode, at near-ambient temperatures and pressures, the rate of the carbonation step is determined by the dissolution of CO2 bubbles. Therefore, while the quality (purity, particle size, crystal shape) of the PCC is crucial for the economic viability of the process, it is considered to be a CCS method for which it is essential that CO2 is effectively and efficiently bound into PCC product, with negligible amounts leaving the process with exhaust
⁎
gases. Thus, an assessment is being made of dissolution process for CO2 bubbles as used in the Slag2PCC process, tracking bubble size and velocity while rising in aqueous solutions, comparing visual observations with a deterministic model recently presented elsewhere (Legendre and Zevenhoven, 2016). Since mixers are used in the carbonator reactor (as well as in the upstream reactor for calcium extraction, using ammonium salt solvent) to further improve solution mixing, these can be put into the here used bubble tower reactor as well, similar to the reactor shown in Fig. 1 and the eight times larger demonstration-size test set-up at Aalto University (Said et al., 2016). The current paper, however, gives a detailed assessment of air versus CO2 bubble dissolution leaving the impact of the mixers, as well as the presence of dissolved calcium that with CO2 gives PCC particles for a future reporting. An experimental assessment of the bubble size and position using a high speed camera can be used to the further calculation of a bubble or bubble cluster local velocity, shape and dissolution rate (Aoki et al., 2015; Colombet et al., 2014; Nock et al., 2016). Bubble size and shape can be directly determined by means of integral shadowgraphy (Böhm et al., 2014). These variables can be used to provide a detailed description of bubble size decrease during dissolution processes in terms of bubble shape, size, velocity, acceleration regime and dissolution dynamics which can be translated into mass transfer from the gas phase towards the liquid phase (Maldonado et al., 2013). The present
Corresponding author. E-mail address: daniel.legendre@abo.fi (D. Legendre).
http://dx.doi.org/10.1016/j.ces.2016.11.004 Received 23 August 2016; Received in revised form 31 October 2016; Accepted 2 November 2016 Available online 05 November 2016 0009-2509/ © 2016 Elsevier Ltd. All rights reserved.
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effect of the thin vessel polycarbonate walls of refractive index 1.60) and values of ≈1 for the vertical direction. In the current research, however, only uncorrected measured values without the use of a magnification factor are presented. The radius of the circular tank is much larger than the radius of the measured bubbles, which are also near the center line of the pipe. Therefore magnification (correction) factors will not be notably larger than 1, as the effective magnification effect must be between the values estimated for horizontal and vertical factors. For bubbles further from the center line of the vessel the magnification correction calculated experimentally with a reference measurement tape inside the vessel immersed in water would be < 1,245…1,5 in the horizontal direction and < 0,965…1,05 in the vertical direction. The current work uses a cylindrical section tank, as this set up would be extended in future research to become a mixed tank, as an important part of the Slag2PCC process equipment. Finally, pH measurements in the water column are recorded to verify that the liquid phase is far from CO2 saturation during the tests. As the bubble tower is a slender structure (vertical length » other dimensions), extra fastening points are needed. These fastening points are represented by fastening bands on the pipe. These bands interfere with the image processing; as a bubble passing behind one of them implies that the image tracking algorithm cannot successfully lock on to the same bubble once appears again after passing these fastening points. An algorithm to overcome this issue is described in Appendix A. Furthermore, after the video recordings the gas flow was increased to verify the pH behavior towards a fully saturated solution in which a CO2 bubble does not dissolve. Experiments were performed in steady state of approx. 1 bubble per second with bubbles feed through a single perforated central flange hole Ø 0,5 mm. Bubble flow is controlled by a needle valve at the lowest point of the experimental set up, set to a flow rate of ~0.1 l/min (STP). The experimental set up can be appreciated in Fig. 3.
Fig. 1. Slag2PCC experimental set up (left) and calcium carbonate bubble reactor graphical representation (right) (Mattila and Zevenhoven, 2014).
paper provides a detailed specification of such parameters for air and CO2 bubbles streams that are necessary to compare models on CO2 bubble dissolution and develop these towards the modelling of industrial carbonation processes.
2. Experimental set up and instrumentation Previous estimations on CFD Euler-Lagrange one-way coupling calculations by Legendre and Zevenhoven (2016) on CO2 bubble swarm dissolution (with initial bubble diameter DBubble=5 mm) at low gas volume fraction gave approximately 1.95 m height in the vessel as an estimate to be sufficient to reach total bubble (swarm) dissolution in water at ambient conditions. These numerical estimations raise the need to modify the original design of the Slag2PCC carbonation method, suggesting a new reactor tank of a similar height is required (depending on the intensity of mixing used). A circular pipe made of clear polycarbonate of diameter D =133 mm (3 mm wall thickness) and height, H =2 m acts as the center of the experimental observations for bubble tracking; further expansion with impellers is addressed in ongoing and future research. A double centered flange arrangement in Fig. 2, with an inside perforated cap (d =0,5 mm) is used as gas inlet while an external surrounding flange couples it to the outer vertical polycarbonate pipe. Several authors have defined different configurations and geometry cross-section tanks for the characterization of rising bubbles. It is acknowledged that most authors prefer a rectangular cross section to avoid image distortion (Böhm et al., 2014). Nevertheless there are authors that use circular sections and claim to have an optical distortion negligibly small as a result of the similar refractive indexes for tank walls and containing liquid (Aoki et al., 2015). Theoretical approximations on the magnification index in a refractive circular convex surface (Young and Freedman, 2012) with a refractive index of water (1.333) and the geometrical specifications of the circular vessel presented in this work, give a maximum magnification of the image recorded by the camera of a factor 1.32 with respect to the actual size of the bubble in the horizontal direction with respect to center of the vessel. Furthermore, in the vertical direction theoretically this magnification factor is equal to 1 because in this direction the refractive surface is planar for which the image produced would always retain the same lateral size as the original object (Young and Freedman, 2012). Experimentally, using a reference measurement tape immersed in water, the magnification factor on the center of the pipe gives maximum values of ≈1.37 in the horizontal dimension (small discrepancies with the theoretical value due to the extra magnification
2.1. High speed camera tracking The most important characteristic of a multiphase flow is the existence of an interface separating the phases and associated discontinuities of properties across the phase interface (Joshi, 2001). This phase separation can be achieved with image analysis, as bubbles present a clear interface that contrast with the surrounding liquid phase. The image recording set-up consisted of a high-speed Photrom camera SA3 Model 120K-M3 equipped with a 52 mm Nikon 200773 lense and a distance of 1-1,5 m to visualize a window of 45 cm (for larger bubbles) to 20 cm (for smaller bubbles) located at different heights of the bubble tower. The special resolution of the system is 2,4 4,45 pixel/mm at a frame rate of 1000 images per second with a constant exposure of 1/2000. The lighting is supplied by a set of 8 parallel arrangement of fluorescence tubes T5 39 W. 2.2. Size and shape estimation The recorded images are processed using the Matlab® image processing toolbox. Several authors had used this shadowgraphy technique (Nock et al., 2016; Colombet et al., 2011,2014) with acceptable results, the technique is generally standard and for the present paper this routine is based on i) the removal of the background detail, ii) threshold iteration for B & W conversion, iii) size position filtering, iv) edge detection and filling of structures, v) size, shape and position estimation in base of a reference point and finally vi) ellipse fit. Image discarding may be needed as an intermittent step. The overall procedure can be grouped as three steps as shown in Fig. 4. A literature review of different experimental approaches based on different techniques on different tank cross sections (cylindrical and rectangular) was recently given by Böhm et al. (2014). From the authors’ perspective perhaps the use of a second shadowsgraphy camera for reconstruction of 3D bubbles by image integration as by 553
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Fig. 2. Cross section of the bubble column and high speed camera placement.
(pfluid) and the pressure jump (pJump) at the bubble surface due superficial tension forces according to the Laplace equation for bubbles (Gong et al., 2007); (pJump=2σ/rBubble), with surface tension σ and bubble radius rBubble. In a still water column the local pressure of the fluid can be estimated as the sum of the atmospheric pressure (patm) and the static pressure of the water at a determinate height. Therefore the bubble internal pressure (pBubble) can be calculated as:
pBubble =patm +
(2)
3. CFD simulation of bubble reactors
Fujiwara et al. (2004) might be the best approach as it is known that a bubble shows a spiral rising path, that especially for the case of wobbly regime bubbles might not be axi-symmetric. In terms of the use of one camera the assumption of axi-symmetry is generally made. In terms of a specific cross-section a correction factor must be estimated, as the image might be disturbed by the refraction of light on the liquid and on the walls of the tank. All bubbles are here assumed to be oblate spheroids with a minor semi-axis a and a major semi -axis b, which are measured from the two dimensional parameters of the ellipse fit, similar to Colombet et al. (2014) using the bubble aspect ratio χ = b / a . The estimated bubble diameter is then estimated from the volume of this spheroid as: 1
ρg (Hcolumn−ZBubble )
with water density ρ , gravity constant g, column of water/ height of the reactor Hcolumn and vertical position of the bubble ZBubble measured upwards. Furthermore the bubble mass mBubble can be estimated based on the spheroid volume and the bubble internal pressure using the ideal gas equation. Bubble velocities in the x (horizontal) and z (vertical) directions were estimated as the simple derivatives of the centroid positions with time between images. The reference point was taken using the measuring tape positioned on the wall next to the bubble tower (Fig. 3).
Fig. 3. Experimental set up.
d =(8b 2a ) 3
2σ + rBubble
Dissolution of a gas stream into fluid phase is one of the most recurrent phenomena in multiphase reactors, which may be driven by pure diffusion, convection or chemical reaction effects. Diverse stateof-the-art models can aim to predict a certain dissolution rate, but still validation of numerical models is needed (Joshi, 2001). We recently (Legendre and Zevenhoven, 2016) presented a 3D oneway coupling method to simulate the dissolution of small CO2 bubble swarms in a bubble reactor with mixers. For this 3D model a variable time step is used in the Lagrangian tracking of the bubble swarm using a Generalized Alpha Method with a free sizing of the time step used by the solver. Furthermore a linear predictor and a backward Euler consistent initialization (fraction of the initial step for backward Euler =0.001) with and absolute tolerance of 1·10−5 is used. The experimental results presented in this paper will be used as a
(1)
Bubble internal pressure is the sum of the fluid local pressure 554
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Fig. 4. Image processing. (a) Original image, (b) step i, (c) steps ii-vi..
Fujiwara et al., 2004; Maldonado et al., 2013; Nock et al., 2016) that experimentally a bubble rise in a helicoidally trajectory, the 1D dissolution model can be used as comparison only for the dissolution rate of bubbles in terms of vertical displacement.
comparison point to improve such numerical models. 1D estimation model estimation of bubble dissolution is also presented below in this paper. This model is the result of a simplification of the 3D model previously presented by the authors. Although it has been extensible studied in literature (Böhm et al., 2014; Colombet et al., 2011;
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4. Numerical 1D simulation of rising bubbles dissolution and tracking This model is a simplification from a 3 dimensional bubble dissolution model to a 1 dimension model of the previous work presented by the authors (Legendre and Zevenhoven, 2016). In this 1D model the bubble can only ascend in a vertical straight line. Although a straight line ascend of a bubble is something far from reality, this model can be used to estimate the height of dissolution of certain bubble/solution combination. 4.1. Model state of the art As a first step to model a large-scale bubble reactor a single bubble while rising and dissolving can be modelled as a spherical body submitted to point forces. Combined with a description for the decreasing mass and size of a dissolving bubble in an aqueous solution this will be the basis for bubble swarm modelling. A link between mass transfer boundary layer and bubble force is established through the mass time derivative of the dissolving bubble, as function of the local Reynolds, Schmidt and Sherwood numbers, furthermore by chemical conversion defined by mass transfer theory via the boundary layer thickness δ for a first order chemical reaction with dissolved calcium (not yet presented here). A free body diagram of the model can be observed in Fig. 5. For any instant the force balance for a moving bubble can be written, with FDrag, FLift and Fi forces in generic directions, as Eq. (1):
→ ⎯ ⎯ d (m. VBubble ) → =FBuoyancy+ dt
n
→ ⎯ → ⎯ → ⎯ → ⎯ FGravity+FDrag+FLift + ∑ Fi i
(3)
Finally this 1D model is an application of free body diagram, represented by Eq. (3) projected on the Z vertical direction, with a fluid velocity equal to zero, as its represents a better estimation for stagnant water in a tank. The exact equation set can be found in (Legendre and Zevenhoven, 2016).
Fig. 6. Bubble dissolution, diameter reduction. (a) Air, (b) CO2.
over time with adequate time step and initial conditions. The bubble mass time derivative necessarily implies abrupt changes in the immersed body velocity, mass and path unless an adequate integration step size is used. In order to integrate this equation a variable step size method is used where the error is estimated as the difference between the fifth- and fourth-order estimates of the Runge-Kutta Felhberg method (Chapra and Canale, 2010). In practice for this model the time step oscillates between a max step size 3.914·10−4 s and a minimum of
4.2. Numerical integration scheme Eq. (3) gives a first order non-linear differential equation in the → ⎯ variable velocity (VBubble ). In order to solve this equation and obtain the velocity profile of the rising object is necessary to integrate the solution
Fig. 5. Free body diagram and mass transfer boundary (Legendre and Zevenhoven, 2016).
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Fig. 7. Comparison of the path of two bubbles rising under different dissolution regimens. (a) Air, (b) CO2. Note the different axis.
Fig. 8. Vertical velocity comparison with previous simulations CO2.
Fig. 9. Vertical displacement comparison with previous simulations CO2.
1.298·10–19 s (mean value of the time step 3.722·10−5 s). As it is desired to obtain the size change in time of the rising bubble we can establish a link between the mass transfer, the bubble radius and bubble internal pressure (Eq. (2)) through the ideal gas equation. The pressure inside the bubble is calculated using the Laplace equation according to (Gong et al., 2007) and thermal effects are neglected.
Therefore if an integration time step (h) is defined then the bubble mass (mbubble) for the next iteration (i+1) is defined as:
m bubble
(i +1)=m bubble(i )+
dm h (i ) dt (i )
(4)
and the concentration increase (CBulk) in the reactor can be computed 557
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5. Results The experiments started by a flow of CO2 bubbles through the water as to remove dissolved air. After several minutes a short steady state was reached as indicated by pH and the size of the CO2 bubbles leaving the vessel via the top. After this point the data given here was collected while level saturation of water with CO2 staid below a few % as indicated by the pH meter. Image recording of rising bubbles in a water column was performed and analyzed. With CO2, footage only up to a height of 1,2 m due to the small size of the bubble could be successfully produced by the highspeed camera. For air footage could be obtained up to 1,80 m. A first comparison could be made for the dissolution rate of CO2 bubbles and air bubbles. As depicted in Fig. 6 CO2 bubbles decrease their diameter by more than 60% from an initial size ~4,5–5 mm to 1,5 mm at 1,2 m of height. In contrast, air bubbles do not dissolve and maintain at a constant diameter (Fig. 6a). In Fig. 7a clear reduction on CO2 bubble oscillation amplitude compared to air bubbles can be appreciated, especially towards the top of the reactor where the CO2 bubbles are almost completely dissolved. In terms of velocity profiles we recently reported (Legendre and Zevenhoven, 2016), a fair agreement for simulated bubbles of initial DBubble =5 mm is found as shown in Fig. 8. The earlier predicted linear ascension path as function of time for several simulated bubbles could be verified for heights H < 1,20 (the maximum recorded height beyond which the bubble size gave insufficient visual resolution) as shown in (Fig. 9). Bubble Reynolds numbers experimentally present a more scattered behavior for initially big wobbly bubbles, but as the bubbles dissolve a clear tendency of decrease can be appreciated. Even when both models seem to have certain divergence, it can be observed that both of them follow the clear decrease of bubble Reynolds number (Fig. 10). Finally in terms of dissolution rate, bubbles show a clear asymptotically decreasing mass (Fig. 11). The 1D model seems to be a better estimation for bubble dissolution, nevertheless the 3D model presents a quite close behavior as well. Possibly the discrepancies of the Comsol 3D model arise from the local turbulent flow field where the simulation was performed i.e. a stirred bubble tower (Legendre and Zevenhoven, 2016). In terms of bubble shape air bubbles show a wobbling behavior during their total trajectory. On the contrary as CO2 bubbles rise a transition from an oscillating wobbling bubble behavior to a fairly linear spherical bubble behavior can be observed. In Fig. 12 the evolution of the bubble aspect ratio (χ = b / a ) in terms of the vertical position is presented. Three major regions can be observed i) the wobbling area (from height 0 to ~50 cm) in which the bubble ellipsoidals show a scattered behavior and χ > 1, ii) the ellipsoidal area (from ~50 to ~90 cm) where the ellipse image approximation is better, giving a more dense set and χ > 1 and finally iii) the spherical area (from ~90 cm upwards) where the aspect ratio χ ≈ 1 and the ellipse fit reduces to a circular fit. Further comparison with the bubble shape diagram (Amaya-bower and Lee, 2010) is presented in Fig. 13. It can be appreciated how the recorded bubbles progress from the wobbling region with high Reynolds numbers (Re=1200 ~ 1500) towards the spherical shape region as the Reynolds number decreases. Furthermore a remark must be made in terms of bubble internal pressure. An initial difference of mass is found; as according to the ideal gas equation the mass of the bubble is proportional to its internal pressure which is correlated to the local pressure of the surrounding liquid (most significant term defining bubble internal pressure). This liquid local pressure value corresponds to the pressure of the static water column in still water (1D model and experiments) and to the local pressure in a stirred environment (3D model with mixers). In the scenario of stirred water, the pressure presents lower local values due to the stirred velocity of the continuously moving liquid phase as higher
Fig. 10. Reynolds number comparison with previous simulations CO2.
Fig. 11. Bubble mass comparison with previous simulations CO2.
Fig. 12. Bubble aspect ratio vs. vertical bubble position.
with a known reactor volume (VReactor) as:
CBulk(i +1)=CBulk(i)+
dm ⎛ h(i ) ⎞ ⎜ ⎟ dt (i ) ⎝ VReactor ⎠
(5)
The model expressions used for calculating dm/dt and bubble size change via the mass transfer coefficient of a moving bubble, including the effects of chemical reaction in the water and considering both drag and lift forces and (initial) non-sphericity of the bubbles were recently presented elsewhere (Legendre and Zevenhoven, 2016).
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Fig. 13. Shape regime map (Amaya-bower and Lee, 2010) (left), simulated and experimental results (right).
Fig. A1. Bubble tracking scheme.
was found. Furthermore, comparison with previous simulations is presented, thus showing a good agreement with experimental data. Model estimations seem to match the dissolution phenomena of bubbles rising in water. A 1D model is a good estimation for bubble dissolution design purposes, furthermore the extension of the equations in a full bubble tower reactor with stirred impellers was presented as well for comparison. Results although similar do show deviations, as a result of the mixing characteristics of the fluid surrounding the bubbles. Current experimenting includes the effect of (four) mixers present in the vessel at 50 cm intermediate space. The dissolution, i.e. change in size of (so far) up to 120 bubbles simultaneously is analyzed by comparing 20 cm height sections above and below the mixer, again as 5 s recordings á 1000 images/s. Measurements are made around the mixers at different heights and up to 200 rpm rotation speed. Visual interpretation of results is ongoing. This will be reported in a future
velocities zones normally imply pressure drops. This difference in local pressure results in a difference in mass between identical size bubbles: for a 5 mm bubble it gives approx. 17% more mass in still water compared to water mixed at (here) 100 rpm in the 3D model. This is translated in bubbles with velocities slightly slower in the vertical direction for the 3D case with a lower dissolution rate as results to less initial massive bubbles. The faster bubbles in the 1D case with still water present a higher dissolution rate that presents a good agreement with experiments on still water conditions. 6. Conclusions Bubble dissolution in a bubble tower was experimentally studied using high speed camera recording and image processing. Results show a clear tendency of bubble dissolution in water and moreover a clear distinction of CO2 dissolving bubbles vs. air non-dissolving bubbles 559
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paper, including also the formation of precipitated calcium carbonate (PCC) after adding a calcium salt and additional chemicals to the water.
radius of the targeting circle is smaller than the distance between two bubbles.
Acknowledgements
References
This work was funded by the Doctoral Program in Energy Efficiency and Systems (EES) of Finland (2012–2015) and the CLIC Oy Carbon Capture and Storage Program CCSP (2011–2016). The authors acknowledge the help with the experimental set up design and mounting of Alf Hermanson and the use of the high speed camera of Debanga Mondal from our laboratory.
Amaya-bower, L., Lee, T., 2010. Computers & fluids single bubble rising dynamics for moderate reynolds number using lattice Boltzmann method. Comput. Fluids 39, 1191–1207. Aoki, J., Hayashi, K., Tomiyama, A., 2015. Mass transfer from single carbon dioxide bubbles in contaminated water in a vertical pipe. Int. J. Heat. Mass Transf. 83, 652–658. Böhm, L., Kurita, T., Kimura, K., Kraume, M., 2014. Rising behaviour of single bubbles in narrow rectangular channels in newtonian and non-newtonian liquids. Int. J. Multiph. Flow. 65, 11–23. Chapra, S.C., Canale, R.P., 2010. Numerical Methods for Engineers Sixth ed.. McGrawHill, New York. Colombet, D., Legendre, D., Cockx, A., Guiraud, P., Risso, F., Daniel, C., Galinat, S., 2011. Experimental study of mass transfer in a dense bubble swarm. Chem. Eng. Sci. 66, 3432–3440. Colombet, D., Legendre, D., Risso, F., Cockx, A., Guiraud, P., 2014. Dynamics and mass transfer of rising bubbles in a homogenous swarm at large gas volume fraction. J. Fluid Mech. 763, 254–285. Fujiwara, A., Danmoto, Y., Hishida, K., Maeda, M., 2004. Bubble deformation and flow structure measured by double shadow images and PIV/LIF. Exp. Fluids 36, 157–165. Gong, X., Takagi, S., Huang, H., Matsumoto, Y., 2007. A numerical study of mass transfer of ozone dissolution in bubble plumes with an Euler – Lagrange method. Chem. Eng. Sci. 62, 1081–1093. Jakobsen, H.A., 2001. Phase distribution phenomena in two-Phase bubble column reactors. Chem. Eng. Sci. 56, 1049–1056. Joshi, J.B., 2001. Computational flow modelling and design of bubble column reactors. Chem. Eng. Sci. 56, 5893–5933. Legendre, D., Zevenhoven, R., 2016. A numerical Euler – Lagrange method for bubble tower CO2 dissolution modeling. Chem. Eng. Res. Des. 111, 49–62. Maldonado, M., Quinn, J.J., Gomez, C.O., Finch, J.A., 2013. An experimental study examining the relationship between bubble shape and rise velocity. Chem. Eng. Sci. 98, 7–11. Martín, M., Galán, M. a., Cerro, R.L., Montes, F.J., 2011. Shape oscillating bubbles: hydrodynamics and mass transfer - a review. Bubble Sci. Eng. Technol. 3, 48–63. Mattila, H.-P., Zevenhoven, R., 2014. Design of a continuous process setup for precipitated calcium carbonate production from steel converter slag. ChemSusChem (3), 903–913. Nock, W.J., Heaven, S., Banks, C.J., 2016. Mass transfer and gas – liquid interface properties of single CO2 bubbles rising in tap water. Chem. Eng. Sci. 140, 171–178. Said, A., Laukkanen, T., Järvinen, M., 2016. Pilot-scale experimental work on carbon dioxide sequestration using steelmaking slag. Appl. Energy 177, 602–611. Young, H.D., Freedman, R.A., 2012. Sears and Zemansky's university physics: with modern physics (94111 USA). Pearson Education, San Francisco, CA.
Apendix A: Bubble tracking algorithm to lock on to one single bubble Earlier experiments revealed that a perforated flange with a hole diameter of ~0,5 mm produced a stable and easily controllable flow of single bubbles with spacing determined by the flow rate (here ~0.1 l/ min). Nevertheless due to different values of surface tension forces in CO2 bubbles, bubble flow with one bubble in the field of vision was not always possible, giving a swarm of small scattered bubbles instead. Added to this phenomena the bubble tower has fastening points, as mentioned, where a rising bubble is invisible to the camera, passing behind an obstacle. As the main goal of the current research is to follow a single bubble and compare its qualities and behavior with a simulated bubble, a lock-on targeting algorithm was used to isolate the information of a particular desired entity. This tracking concept can be observed in Fig A1. A targeting moving circle is defined, with an initial radius previously defined (large enough to overcome the dimensions of the obstacle). This targeting center will be continuously updated to follow the center of the locked on bubble. When this bubble passed behind an obstacle, the targeting center will remain in the last position known of the bubble centroid. A try/catch statement allows the video tracking program to continue processing video frames when the bubble is not visible. This circle will wait until the lock bubble overcomes the obstacle and can be visible again in camera recordings. Finally the targeting center is updated to follow the centroid of the locked-on bubble. This targeting method is effective as long the bubble swarm is sufficiently scattered, and for low gas volume fractions in which the
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