Numerical simulation of a high viscosity bubble column

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1 20th Internationa Congress on Modeing and Simuation, Adeaide, Austraia, 1 6 December Numerica simuation of a high viscosity bubbe coumn Danio Carvajaa, Victor Meendez-Vejara, Maik Irrázabaa and Caros Caresi-Jaraa a Pontificia Universidad Catóica de Vaparaíso, Escuea de Ingeniería Química, Av. Brasi 2950, Vaparaíso , Chie Emai: danio.carvaja@ucv.c. Abstract: The objective of this work is to deveop fuid dynamic mode to simuate a high viscosity bubbe coumn for CO2 absorption in Ionic Liquids (ILs). A very promising sovent for CO2 capture and conversion are ionic iquids (ILs); ILs consist of a wide group of sats, which are iquids at room temperature, have ow vapor pressure, high ionic conductivity and therma stabiity. However, the use of ILs for industria CO2 depetion has a series of technica and economic issues that must be soved if this strategy is to be impemented. A very important drawback of ILs used for gas remova is its high viscosity, reaching vaues above Pa s which resuts in a decrease of the overa mass transfer rate and an increase in the power required for pumping and mixing. In order to eucidate the hydrodynamic behavior in a bubbe coumn for CO2 absorption with one gas feed inet, a Computationa Fuid Dynamic (CFD) mode was deveoped, which was experimentay vaidated through a aboratory scae bubbe coumn. To simpify the cacuations and increase the accuracy of the resuts, the system was modeed as a singe rising bubbe which permits the estimation of the bubbe rising veocity and the change of the bubbe shape and size during its dispacement. The mode approach consists in a simpified two-dimensiona mutiphase fow mode which considers the iquid sovent as a Newtonian fuid. The aminar, isotherma, and non-stationary hypotheses for both phases is appied. To mode the dispacement of the gas-iquid interface, the Leve Set method was used. The aboratory tests were carried out using water-gycero mixtures (58 %, 78 %, 84 % and 88 % by weight) and two Imidazoium type ionic iquids (pure [bmim]bf4 and [bmim]pf6). To compare the resuts obtained from the aboratory and the simuations, the drag coefficient for gas bubbes in iquids was used which correates the fuid physica properties of fuids and the bubbe equivaent diameter and termina veocity. The resuts were aso compared with predicted vaues obtained through a new correation for the drag coefficient of singe rising bubbes in ILs proposed by Dong et a. (2010). The resuts indicated that the CFD mode is in good agreement with the experimenta resuts, particuary for bubbe Reynods numbers beow 5. Above this vaue, the mode tends to underestimate the bubbe termina veocity which can be expained by the effect of the high veocity gradients cose to the gas-iquid interface. Future steps wi invove improving of the computationa mesh, a parametric anaysis of the reintiaization parameter and the parameter controing the thickness at the interface transition zone. Acknowedgments. This work was supported by FONDECYT postdoc N from CONICYT (Chie). Keywords: Computationa Fuid Dynamic, Bubbe Coumn, Ionic Liquid. 719

2 1. INTRODUCTION The continuous increase in CO 2 atmospheric concentration has caused a great concern in the scientific community because of its environmenta hazard and its socia impications. The European Union has set a target of 20% reduction of CO 2 emission by the year 2020; to meet this goa, a significant reduction in the CO 2 reeases from fossi fue wi be required during the next years. This can be achieved by adopting an effective strategy for carbon capture, such as the use of iquids sovents for CO 2 capture. The ionic iquids present severa characteristics which make them very interesting for CO 2 capture appications. However, when a gas is absorbed into an ionic iquid, typicay the viscosity suffers an increase which has severa negative impacts incuding the reduction of the species transport rate across the sovent and the increase the energy required for pumping and mixing. The physica properties of ILs may be modified by changing the substitute group in the cations and anions (Gaán Sánchez et a., 2007). During the gas absorption process, the increasing viscosity process may be controed by a continuous remova of the sovent before the viscosity increases in a decontroed way. There are very few theoretica and experimenta investigations focusing on bubbe coumns using ILs as sovent one being the work by Dong et a. (2010), who conducted experiments using the ionic iquids [bmim]bf 4, [omim]bf 4 and [bmim]pf 6 at different operating conditions (i.e. temperature, gas fow rate and gas inet diameter) in a bubbe coumn fed with pure nitrogen. From the experimenta resuts, they proposed a new correation for the estimation of the drag coefficient as a function of Reynods number and bubbe aspect ratio as a function of a new dimensioness parameter; both correations are particuary appicabe to gas bubbe formation in ionic iquids and demonstrated to be in good agreement with experimenta resuts. Dong et a. (2010) then deveoped a couped Computationa Fuid Dynamic and Popuation Baance Mode to study the mass transfer during CO 2 absorption in ILs (Wang et a., 2010). However, there has been not undertaking as yet into investigation of bubbe coumns with ILs focused at the micro-scae eve. An in-depth knowedge of the interface shape and dispacement is important particuary of the mass transfer at a oca scae. 2. EXPERIMENTAL SECTION 2.1. Test fuids and physica properties Four water-gycero mixtures (58 %, 78 %, 84 % and 88 % by weight) were prepared by stirring distied water with the appropriate mass of gycero for 60 min. Ionic iquids [bmim]bf 4 and [bmim]pf 6 were purchased from Ioitec GmbH (Denzingen, Germany) with a purity of above 98 %. A the fuids were anayzed to determine density, viscosity and surface tension. A the measurements were carried out at 20ºC to match the conditions of aboratory bubbe coumn procedures. The density was measured using a pycnometer, the viscosity was obtained with an Ostwad viscometer (and compared with a rotationa Fungiab viscometer) and the surface tension was measured with a staagmometer. The physica properties of the tested fuids are isted in Tabe 1. Tabe 1. Physica properties of the test fuids Fuid Description Density, kg/m 3 Viscosity, Pa.s Surface tension, N/m A1 Gycero 58 % A2 Gycero 78 % A3 Gycero 84 % A4 Gycero 88 % A5 BmimBF A6 BmimPF Experimenta setup A schematic diagram of the experimenta setup is depicted in Figure 1. The bubbe coumn was made of transparent acryic (Fig. 2) with a square base of 5 cm each side and 12 cm height (tota voume of 300 m). The coumn was tighty seaed to prevent eakage of both iquid and gas phases, and to avoid contamination with ambient air. The coumn has a therma jacket (fuid: water) to maintain the temperature fixed at 20 ºC. Pure nitrogen gas is injected through a singe orifice in the bottom of the coumn.the gas fow rate is controed by a mass fow controer, and, the gas fow rate constanty checked with a soap fim meter. To produce different sizes of bubbes for each fuid tested; two diameters of orifice (0.8 mm and 1.25 mm) and two gas fow rates (7 m/min and 20 m/min) were appied. The size and shape of the bubbes were recorded with a digita camcorder (Panasonic HC V500M) set with a resoution of 1080 x 1920 pixes, frames 720

3 per second (progressive) and 1/2000 s of shooter speed. To propery iuminate the coumn and avoid heating the coumn during the tests; a 30 W ed amp (equivaent to a 200 W haogen amp) was used. To obtain good image quaity (brightness and contrast) a semitransparent (white) acryic pane was paced between the coumn and the video camera, which acted as a ight diffusion fiter. The image anaysis was carried out through a MATLAB script deveoped by our workgroup. The script determine of the position and shape of the bubbe in each frame of the recorded video fie Testing procedure Before starting the testing procedure, the coumn is washed and dried to eiminate a residues from previous tests, and then the testing fuid is injected inside the coumn from the top side unti reaching a iquid eve of 60 mm above the gas inet orifice. The iquid is sowy injected to avoid the formation of bubbes which may hinder the recording process. By controing the gas fow rate and stabiizing the frequency of formation of bubbes, the bubbe motion is then recorded during 30s to obtain a wide sampe of bubbes to anayse. Before and after each test, measurements of temperature and gas fow rate are performed. Figure 1. Fow diagram of the experimenta set up. 3. CFD MODEL 3.1. Basic equations The genera assumptions for the mode used are the aminar, incompressibe and isotherma fows. The governing continuity and momentum equations for the two-phase fow are as foows: u = 0, (1) 2 u 1 μ ρ + u u = p + u + F v, t ρ ρ Figure 2. Photography of the aboratory scae bubbe coumn. (2) respectivey, where ρ is the fuid density (kg/m 3 ), μ the dynamic viscosity (Pa s), u is the veocity vector (m/s), t is time (s) and p the tota pressure (Pa). The source term F v (kg/m 2 s), incudes the voumetric forces, such as the gravity force appied to the fuid over the whoe domain and the surface tension to the gas-iquid interface Interface tracking mode To mode the dispacement of the gas-iquid interface, the Leve Set method was used, which was introduced by Osher and Sethian (1988), for incompressibe two phase fow. The motion of the interface is characterized through the scaar function φ, which is a smoothing function where φ = 0.5 defines the position of the interface (COMSOL, 2012). For our mode, φ = 0 defines the gas phase, meanwhie φ = 1 defines the iquid phase. The advection equation which defines the transport and reinitiaization of Φ through the entire domain is defined as foows: φ + u φ = γ ε φ φ t ( 1 φ) φ φ, (3) where the veocity vector (u) is obtained from the numerica soution of the Navier-Stokes equations (equations 1 and 2). The reintiaization parameter γ determines the thickness of the interface transition zone 721

4 where 0 < φ < 1. When stabiization techniques for the eve set equation are used, it is recommended using a vaue of ε = h/2, where h is the typica size (m) of the mesh eements in the vicinity of the interface (Osher and Sethian, 1988). The γ parameter can be initiay approximated by the maximum veocity magnitude of the system. The physica properties such as viscosity and density are estimated from a heaviside function which uses the properties of pure phases: ( ρ ρ ) φ ρ = ρ + g, (4) for the density and simiary for the viscosity: ( μ μ ) φ μ = μ + g, (5) where ρ g, ρ, μ g and μ, are the density of the gas and the iquid, and viscosities of the gas and the iquid respectivey. For the eve set method, the surface tension and the gravity force are incorporated into the Navier-Stokes equations as voume forces in the source term of the momentum conservation equation (Eq. 2), which are defined as foows: F v T [ σ{ I + ( n n )} δ] = ρ g +, (6) where the first term on the right side defines the gravity force and the second the surface tension, σ is the surface tension (N/m), I is the identity matrix and n is a unitary norma vector to the interface with direction from the disperse phase to the continuous phase and is defined as foows (Deshpande, 2006): φ n = (7) φ The eve set parameter φ, is used to approximate the deta function δ through the foowing expression: ( φ) φ δ = 6 φ 1 (8) 3.3. Drag coefficient In order to vaidate the resuts obtained from the CFD predictions, the drag coefficient obtained from the data produced during the aboratory tests are used. To compare de resuts with the iterature, the drag coefficient correation proposed by Dong et a. (2010) for bubby fow using ionic iquids was used. The correation was deveoped from experimenta data using [bmim]bf 4, [omim]bf 4 and [bmim]pf 6 at different temperatures (37-82 ºC, gas fow rate (0.1 5 m/min) and gas inet diameter (0.17, 0.47, 0.8 and 1.4 mm). The empirica expression for the drag coefficient (C d ) is based on two dimensioness numbers (i.e. Reynods and Morton) and is defined as foows (Dong et a., 2010): C d b c = a Re Mo, (9) where a, b and c are defined as foowing: For 0.5 Re 5: a = 22.73, b = , c = 0.020, and for 5 < Re 50: a = 20.08, b = , c = The use of these vaues wi be termed Cd H.Dong (Tabe 2). The drag coefficient for spherica bubbes is defined as foowing: C d 4 de = 3 ρ ( ρ ρ ) v g 2 t g, (10) where d e is the bubbe equivaent diameter (m), and v t is the termina rising veocity of bubbe (m/s). Termina veocity is reached when there is a baance between buoyancy and drag forces. The Reynods number defined for a singe rising bubbe and Morton number are defined as: ρ vt de Re =, (11) μ 4 3 ( ρ ρ ) g μ g Mo =, (12) σ ρ 2 722

5 respectivey, where d e is cacuated as foows: d e = d (13) 3 2 dx y where d x and d y are the horizonta and vertica diameters (m) of the bubbe, respectivey Geometry and boundary conditions The numerica domain has a height of 60 mm and a width of 40 mm. The size and aspect ratio of the initia condition of the interface gas-iquid is fixed according to the video recording from the experimenta procedure (the first frame after the bubbe detachment is used). The upper side of the fuid domain is defined as a zero pressure outet. A non-sip condition is used for the was. A representation of the geometry and boundary conditions are depicted in Figure Numerica detais The CFD software COMSOL 4.2 was used for a the simuations. COMSOL uses the finite eement method to discretize the partia differentia equations defining the mathematica mode. Both the geometry and the computationa mesh were created in COMSOL. Different two-dimensiona grids were tested and a fina mesh of trianguar ces was used. The mesh was refined to resove regions of high gradients efficienty. The fina minimum eement size was approximatey 0.09 mm in the interface dispacement zone. The fina eement size Figure 4. Computationa mesh. ranges between 0.09 and 1.43 mm. A representation of the computationa mesh is depicted in Figure 4. The system was defined as non-stationary and the tota time needed for each simuation was 27.6 hours per second of simuation. The direct PARDISO sover was used for a simuations. Convergence was achieved when a normaized residuas of veocity and concentration reached vaues smaer than The simuations were performed on a HP Workstation with four 2.26 GHz Inte cores and 8 GB RAM. In order to ensure stabiity, the time step was fixed to s. The maximum number of iterations is reached when the reative toerance exceeds with respect of a variabes. 4. RESULTS Figure 3. Geometry detais and boundary conditions Bubbe rising veocity After detachment, bubbes rise and suffering deceeration reaching a constant termina veocity when a baance between buoyancy and drag forces is reached. From the experimenta data and the simuations it is confirmed that a high viscosity Figure 5. Bubbe rising veocity evoution for 4 testing conditions using [bmim]bf 4 as iquid phase (3.1 < Re < 8). The trianges represent the CFD cacuations and the circes the aboratory experiments. 723

6 eads to a decrease in rising veocity of bubbes. The CFD cacuations for the bubbe raising veocity presented good agreement with the experimenta tests for severa appied conditions, particuary for ow Reynods number, beow 5. Most experimenta fuids had viscosities above 0.1 Pa.s incuding the gycero 84 % and 88 % w/w, the [bmim]bf 4 and [bmim]pf 6. Experimenta and simuated bubbe rising veocities for [bmim]bf 4 and [bmim]pf 6 sampes are shown in Figure 5 and Figure 6 respectivey. The figures show the high accuracy of the simuations for severa conditions. However, when the Reynods number exceeds a vaue of 5, the accuracy of the method decreases and the bubbe termina veocities are underestimated. The ow accuracy of the CFD cacuations at ow viscosities can be expained from the effect of the high veocity gradients cose to the interface gas-iquid. This probem was partiay overcome by performing a finer computationa mesh in the vicinity of the interface; however a further improvement of the mode is necessary. Improvements woud incude a parametric anaysis of the reintiaization parameter and the parameter controing the thickness at the interface transition zone Mode vaidation: Drag coefficient The Drag coefficients and its associated Reynods numbers cacuated from the aboratory tests and the CFD simuations are graphicay depicted in the Figure 7. As can be seen in the graph, experimenta resuts ceary present a power aw pattern between Re and Cd. Incuded in this reationship is the Morton number with which it is possibe to estimate the coefficients of equation 9 using the east squares method giving the foowing parameters: for Re 5 : a = 58.66, b = , c = 0.185, and for Re > 5 : a = 4.601, b = , c = The use of these vaues in equation (9) wi be termed Cd fit (Tabe 2). These parameters can be used to compare experimenta resuts via eqn (9) with CFD simuations. The CFD Figure 6. Bubbe rising veocity evoution for 4 testing conditions using [bmim]pf 6 as iquid phase (1.8 < Re < 3.0). The trianges represent the CFD cacuations and the circes the aboratory experiments. predictions are consistent with the experimenta resuts for Reynods numbers beow 5. A high deviation between the experiments and CFD predictions were obtained for bubbe Reynods numbers above 20 (Figure 7). The comparison between the Drag coefficients cacuated from the CFD mode, experimenta resuts using Tabe 2. Drag coefficients for the tested ionic iquids with different conditions, using three different approaches: experimenta, CFD and H.Dong correation. Fuid V t mm/s d eq, mm Re Mo C d CFD C d fit experim C d H.Dong bmim[bf 4 ] E bmim[bf 4 ] E bmim[bf 4 ] E bmim[bf 4 ] E bmim[pf 6 ] E bmim[pf 6 ] E bmim[pf 6 ] E bmim[pf 6 ] E

7 the equation 9 and the Dong s correation using equation is shown in Tabe 2. As can be seen in the tabe, at very ow Reynods number there is no a cear reationship between the deviation of the CFD resuts in respect to the experimenta resuts. Given the imited amount of data avaiabe for this Reynods number range, further testing is necessary, incuding ower gas fow rates and higher viscosity 5. DISCUSSION AND CONCLUSIONS The CFD cacuations for the bubbe raising veocity presented good agreement in respect to the experimenta tests for severa appied conditions. In particuar, this occurred for instances of Reynods number beow 5, most of experimenta fuids had viscosities above 0.1 Pa.s, incuding, gycero 84 % and 88 % w/w, the [bmim]bf 4 and [bmim]pf 6. When the Reynods number exceeds a vaue of 5, the accuracy of the method decreases and the bubbe termina veocities are underestimated. The ow accuracy of the CFD cacuations at ow viscosities can be expained from the effect of the high veocity gradients cose to the gas-iquid interface which is reated to deformation of the interface, which in turn affects the bubbe rising veocity. Future experimentation and modeing wi invove improvements in the computationa mesh and a parametric anaysis of the reintiaization parameter and the parameter controing the thickness at the interface transition zone. Figure 7. Drag coefficient vs. Reynods number for severa testing conditions (each point represent one test). The trianges represent the CFD cacuations and the circes the aboratory experiments. ACKNOWLEDGMENTS This work was supported by FONDECYT N project and FONDECYT post-doc N , both from CONICYT (Chie). REFERENCES COMSOL (2012). Product information COMSOL Mutiphysics 4.2, Stockhom. Deshpande, K. B., Zimmerman, W. B. (2006) Simuation of interfacia mass transfer by dropet dynamics using the eve set method. Chemica Engineering Science 61(19): Dong, H., Wang, X., Liu, L., Zhang, X., Zhang S. (2010). The rise and deformation of a singe bubbe in ionic iquids. Chemica Engineering Science 65 (10): Gaán Sánchez, L. M., Meindersma, G. W. & de Haan A.B. (2007). Sovent properties of functionaized ionic iquids for CO 2 absorption, Chemica Engineering Research and Design, 85 (1): Osher, S., Sethian J.(1988). Fronts propagating with curvature-dependent speed: Agorithms based on Hamiton-Jacobi formuations, Journa of Computationa Physics, 79: Wang, X., Dong, H., Zhang, X., Xu, Y., Zhang, S. (2010). Numerica simuation of absorbing CO 2 with ionic iquids. Chemica Engineering Technoogy, 33(10):