Student Number: 200338840Student Name: Osiki Izijesu. OCourse Name: Advanced Mass TransferDepartment: Process Systems Engineering

Number 1A-1TITLE: Determination of Gas diffusion coefficients in saturated porous media: Helium, He and Methane, CH4 diffusion in Boom clay

BRIEF INTRODUCTIONBoom Clay is presently a potential host rock mainly as a medium of disposal of high level and long lived radioactive waste in Belgium, and also because production of gas is ineluctable in geological depository (Yongfeng Deng et al., 2011). Today, gas is produced by a number of different mechanisms including radiolysis of water and organic materials, microbial debasement of organic wastes as well as anaerobic corrosion of metals in waste materials (Elke Jacops et al., 2013). Rodwell et al., 1999 and Yu and Weetjens, 2009 for instance write that, hydrogen gas is produced from corrosion and radiolysis and conversely methane and carbon dioxide are products of microbial debasement. Diffusion is the main transport phenomenon in the boom clay since dissolved gases diffuse from the repository as dissolved species. Importantly, good estimates for gas diffusion coefficient is necessary in order to estimate and understand the diffusion process such as gas generation and dissipation through barriers (Elke Jacops et al., 2013).Literature provides limited information as to the determination of diffusion coefficients of gases in saturated porous media and available information and data is difficult to analyze or understand (Elke Jacops et al., 2013). However, there are generally three types of methods that have been adopted as possible methods to analyze and estimate diffusion coefficients of gases regardless of individual methods limitations. In the first method already used by Bigler et al. (2005) and Gomes-Hernandez (2000), the diffusion coefficient of gases is determined using gas concentrations from outgassing of the clay samples stored in a vacuum container and measurement of the concentration of gas released by the clay samples. In fact, Bigler et al. (2005) estimated the diffusion coefficient of Helium using a spherical sample of the callovo-oxfordian shale with an uncertainty of 20%. He explains that calculated uncertainty might have been due to imperfection of the sphere and errors in cutting of the sample.The second method determines diffusion coefficient based on the concentration profiles of gases as natural tracers. Rubel et al. (2002) used this technique and computed the apparent diffusivity for helium in opalinus clay based on heliums natural profile obtained at Mount Terri. Bensenonic et al. (2011) using this technique obtained a helium profile for samples that were collected from vertical drilled boreholes in the Toarcian shale in France for which the diffusion coefficients was obtained from outgassing of the water in high vacuum containers. This is an interesting technique but like the previous method it is only applicable for gases present naturally in clay and limited to He, Ar and CH4. Of note is what Mazurek et al. (2011) wrote that, the core outgassing of noble gases requires advanced equipment and that there is apparent possibility of leakage at several stages.The third method for determination of the diffusion coefficient for gases is based on the in or through diffusion technique. This method has been used by Rebour et al. (1997). Although reported error on the diffusion coefficient of Helium on callovo-oxfordian clay was 20%, this method has been found to be more versatile as it can be used to compute the diffusion coefficients for different gases. However, Bigler et al. (2005) argue that interpretation of data with this method suffered from complications such as anisotropy effects which was not taken into account and that measured porosity (23%) did not correspond to the porosity value needed to obtain a good fit (16%). Therefore, a more versatile and simple method that allows for a better assessment of the diffusivity and suitable for several gases was developed to determine the gas diffusion coefficient (Elke Jacops et al., 2013).In this study, the authors developed a method to ascertain the gas diffusion coefficient for dissolved gases in boom clay and gases, where Helium (He) and Methane (CH4) served as reference gases. They write that, their adopted diffusion methodology allows two gases to diffuse through a clay sample at the same time.

METHODOLOGYPrincipleThe experimental work was based on a thorough diffusion test where two dissolved gases were placed on opposite sides of the Boom clay test core as shown in figure 1 (Shackelford, 1991; Van Loon et al., 2003). In this method, the porous media is placed between two vessels one of which contains a known concentration of the diffusant and is the high concentration compartment while the other known as the low concentration compartment is free of the diffusant. This method used two diffusants, He and CH4 where the gases are initially concentrated at one side and expectedly diffuse in different directions afterwards. Importantly, the clay core was sealed in a stainless steel diffusion cell and connection was via stainless steel plate at both sides to water vessels that were pressurized with two different gases at the same pressure, shown also in figure 1. Data is reported in the study only for Helium, He and Methane, CH4.

Experimental Set-upSince helium diffuses easily through many materials such as polymers used often as seals, Elke Jacops et al., 2013, emphasize the importance of gas tightness of the entire set up. Thus to avoid gas leakages, components used are selected based on their gas tightness. For instance, Jacops et al., 2013 used metal contacts for valves, sensors and couplings as opposed to polymers. Constant volume was obtained by sealing the diffusion cell properly and the hydraulic press was used to press the clay core, having a diameter of 80mm and height of 30mm in the diffusion cell. They also write that perfect sealing between the clay and the diffusion cell was due mainly to the high plasticity of the clay (Van Geet et al., 2008). Furthermore, contact between the gas saturated water and the clay was achieved by placing a porous stainless steel filter plate of diameter 80mm, thickness 2mm and porosity 40% on both sides of the clay core, where the cover as well as the connections for the water inlet and outlet were welded onto the body of the container. Gas tightness was ensured by connecting a pressure sensor, PTX 600 to the two vessels that monitored pressure evolution.The water with dissolved gas was then circulated over the filters using a magnetically coupled gear pump, REGLO-Z (ISMTEC, Glattbrugg, Switzerland) calibrated for a flow rate of 3 0.1 ml/min while still ensuring gas tightness and low flow.

Fig 1: Schema of the experimental set-up (vessels and diffusion cell not at scale). Dimensions clay core: diameter 80 mm, length 30 mm. Volume vessels: 1 l, lled with 500 ml water and500 ml gas (at 10 bar). (Elke Jacops et al., 2013)ProcedureThe clay sample used was taken perpendicular to the bedding plane based on the mineralogical and physical properties of Boom clay reported by Maes et al (2008). As stated previously, care was taken to ensure gas tightness prior to the diffusion experiment by pressurizing the set-up with 10 bar Helium for a 68 day period. Furthermore, gas migration properties had to be established prior also to the diffusion experiment, by determining the hydraulic conductivity, K of the clay core. This was done by injecting demineralized water at 0.55MPa, and water flowing out of the diffusion cell was collected, placed on a precision balance until a stable value was obtained for five successive intervals. The obtained precision was 8%, with Yu et al. (2013) reporting that, values for hydraulic conductivity of Boom clay are usually around 1.5 and 8 10-12m/s. Measurement of the hydraulic conductivity was then followed by the preparation of a solution of oxygen-free water that was 0.014 mol/l NaHCO3. The water used for preparation of the solution was stored in an anaerobic compartment and then made to come to equilibrium with the test gas for a few days to remove N2. After 500ml of the solution was transferred to each vessel of the set-up, a gas buffer was placed into the headspace and a sample was then taken to determine the initial gas composition of both vessels. Once, the diffusion experiment started, sampling was done regularly in a temperature controlled room (21 2oC) until about 10 data points were obtained and to avoid pressure drops sample volume was kept strictly at 6ml. Gas composition was analyzed with a CP4900 micro GC

Transport ModelTest results obtained from experiment were interpreted with a diffusive model that represents the transport equation in 1 dimensional geometry and this model is founded on both the first and second law of Fick for diffusive transport in porous media as represented in equations 1 and 2.

F = - Dp (1)

= Dapp (2)

Where F is flux, Dapp is the apparent diffusion coefficient, Dp is the pore diffusion coefficient, denotes porosity; c denotes concentration in the porous medium, t denotes time (s) and x denotes length (m).

Furthermore, the diffusion coefficients can be correlated by equation 3.

Dapp = (3)

Of importance, is the decrease of the concentration at the inlet at sampling that could hamper correct experimental determination of the apparent diffusivity and based on this the model was implemented numerically. Figure 2 shows the clay core being represented by 30 elements. Henrys law (R. Sander, 1999) was applied at one end of figure 2, where the amount of the dissolving gas is proportional to the partial pressure of the gas in the vessel, while at the other end the amount of the gas was assumed to be zero. Again, the diffusion accessible porosity set at 0.37 was derived from migration experiments done by Maes et al, (2008) and since assumption was that there was no adsorption, R is set as 1.At regular time intervals and concentration in selected elements (grey shades in figure 2), Ficks law was applied to determine the fluxes at both faces. Further calculations were performed using COMSOL multi physics version 3.5a, Earth Science module. Finally, detailed information provided by Glaus et al, (2008) was used to establish the possible (if any) influence of the filters on the transport process.

Figure 2: Geometry used in the diffusive transport model. Grey cells indicate where the evolution of the dissolved gas concentrations is recorded. (Elke Jacops et al., 2013)

Results and Discussion

As highlighted in the procedure section, the hydraulic conductivity of the clay core was pre-determined as 2.5 10 -12 m/s which is a distinctive value for Boom clay (Yu et al., 2013). To optimize and modify experimental conditions, the sampling volume, frequency and measuring methodology for the entire experiment, Helium, He and Argon, Ar were used initially even though both experimental and practical problems resulted in unsatisfactory data. Accordingly, a second experiment fully described previously and using Helium, He and Methane, CH4 was carried out and figures 3 and 4 show graphic representation of results. Furthermore, using the diffusion model and implementing it in COSMOL, yielded the diffusion coefficients of He and CH4 as 12.2 10 -10 m2/s and 2.42 10 -10 m2/s respectively as shown in table 1.

Figure 3: CH4 concentration profile in the opposite vessel, showing the experimental vs. fitted curve. The dotted lines are calculated results for Dapp (upper line: 3.03 10 -10 m2/s; lower line: 1.82 10-10 m2/s) and the thick line is value obtained as best fit, 2.42 10 -10 m2/s (Elke Jacops et al., 2013)

From figures 3 and 4, one can observe that not only is the best fit for Dapp plotted but also for Dapp 25%, which indicates the sensitivity of the method as well as the possibility of obtaining precise measurements for Dapp and this result is in line with work done by Aertsens, 2009.

Again, to estimate diffusion coefficient for other gases, the experimentally obtained diffusion coefficient is used to compute values for the tortuosity/constrictivity ratio as shown in equation 4.2 / (4)Where R is the retardation factor and is the constrictivity (Put and Henrion, 1988).

Figure 4: He concentration profile in the opposite vessel, showing the experimental vs. fitted curve. The dotted lines are calculated results for Dapp (upper line: 15.3 10 -10 m2/s; lower line: 9.15 10-10 m2/s) and the thick line is value obtained as best fit, 12.2 10 -10 m2/s (Elke Jacops et al., 2013)

The tortuosity, is known as the ratio of the effective travelled distance vs the start and end point distances while constrictivity accounts for the widening and narrowing of clay pore (Collin and Rasmuson, 1988). Again, since there is no adsorption of gases and pore size distribution of the boom clay is between 6 and 30 000nm (Hemes et al, 2012), both constrictivity, and retardation, R factor are equal to one.

Table 1: Overview of the tted diffusion parameters for He and CH4 in Boom Clay

a Jaehne et al. (1987)b Boudreau (1996)

The tortuosity/constrictivity ratio determine for both CH4 and He as shown in table 1, can be used to predict the Dapp ranges for other gases. This is calculated by rearranging equation 4 and substituting already known Do value and average value of as computed in table 2.

Dapp = () () (5)

Table 2:

a Boudreau (1996)

Gas diffusion in other clay formations was compared with those of the Boom clay and although direct comparism cannot be made due to differences in physical and mineralogical properties, it provides estimates as to whether obtained values are in line with already conducted research work. For instance, calculated values for 2/ in opalinus clay, 3.5 and Oxfordian clay, 3.8 (Gomez-Hernandez, 2000; Bigler et al, 2005)proved to be in line with those determined experimentally considering factors such as higher densities and lower porosity in these formations.

In Conclusion, the authors have been able to use a simple method that is both precise and sensitive in determining the diffusion coefficients of gases in porous media and this method shows prospects for use in a number of industries and not just for geological disposals.

References

Aertsens, M., 2009. Re-Evaluation of the Experimental Data of the MEGAS Experiment onGas Migration Through Boom Clay. SCKCEN-ER-100. SCKCEN, Mol, Belgium. (http://hdl.handle.net/10038/1182).

Bensenouci, F., Michelot, J., Matray, J., Savoye, S., Lavielle, B., Thomas, B., Dick, P., 2011. Aprole of helium-4 concentration in porewater for assessing the transport phenomenathrough an argillaceous formation (Tournemire, France). Phys. Chem. Earth. 36,15211530.

Bigler, T., Ihly, B., Lehmann, B., Waber, H., 2005. Helium Production and Transport in theLow Permeability CallovoOxfordian Shale at the Site Meuse/Haute Marne, France.Nagra Arbeitsbericht NAB 05-07, Switzerland.

Boudreau, P., 1996. Diagenic Models and Their Interpretation Modelling Transport andReactions in Aquatic Sediments. Springer, Berlin.

Collin, M., Rasmuson, A., 1988. A comparison of gas diffusivity models for unsaturatedporous media. Soil Sci. Soc. Am. J. 52, 15591565.

Elke. J, G. Volckaert, N. Maes, E. Weetjens, and J. Govaerts. Determination of gas diffusion coefficients in saturated porous media: He and CH4 diffusion in Boom Clay. Applied Clay Science 83-84 (2013) 217-223

Glaus, M., Ross, R., Van Loon, L., Yaroshchuk, A., 2008. Tracer diffusion in sintered stainlesssteel lters: measurement of effective diffusion coefcients and implications fordiffusion studies with compacted clays. Clay Clay Miner. 56, 667685.Gomez-Hernandez, J.J., 2000. FM-C Experiment: Part A) Effective Diffusivity and AccessiblePorosity Derived Fromin-situ He-4 Tests. Part B) Prediction of He-3 Concentrationin a Cross-Hole Experiment. Mont Terri Project Technical Note TN 2000-40.Switzerland.

Grathwohl, P., 1998. Diffusion in Natural Porous Media: Contaminant Transport, Sorption/Desorption and Dissolution Kinetics. Kluwer Academic Publishers.

Hemes, S., Desbois, G., Urai, J., De Craen, M., Honty, M., 2012. Variability of the Morphologyof the Pore Space in Boom Clay From BIB-SEM, FIB and MIP Investigations onRepresentative Samples. 2nd Project Report. SCKCEN-ER-208. SCKCEN, Mol,Belgium (http://hdl.handle.net/10038/7752).

Jaehne, B., Heinz, G., Dietrich, W., 1987. Measurement of the diffusion coefcients of sparinglysoluble gases in water. J. Geophys. Res. 92, 1076710776.

Kroos, B., Schaefer, R., 1987. Experimental measurements of the diffusion parameters oflight hydrocarbons in water-saturated sedimentary rocks I. A new experimentalprocedure. Org. Geochem. 11, 193199.

Maes, N., Salah, S., Jacques, D., Aertsens, M., Van Gompel, M., De Cannire, P., Velitchkova,N., 2008. Retention of Cs in Boom Clay: comparison of data from batch sorption testsand diffusion experiments on intact clay cores. Phys. Chem. Earth. 33, S149S155.

Mazurek, M., Alt-Epping, P., Bath, A., Gimmi, T., Waber, N., Buschaert, S., De Cannire, P.,De Craen, M., Gautschi, A., Savoye, S., Vinsot, A., Wemaere, I., Wouters, L., 2011. Naturaltracer proles across argillaceous formations. Appl. Geochem. 26, 10351064.

Put, M., Henrion, P., 1988. An improved method to evaluate radionuclide migration modelparameter from ow-through diffusion tests in reconsolidated clay plugs. Radiochim.Acta 44 (45), 343347.

Rebour, V., Billiotte, J., Deveughele, M., Jambon, A., le Guen, C., 1997. Molecular diffusionin water-saturated rocks: a new experimental method. J. Contam. Hydrol. 28, 7193.2

Rodwell, W., Harris, W., Horseman, S., Lalieux, P., Mller, W., Ortiz, L., Pruess, K., 1999. GasMigration and Two-Phase Flow Through Engineered And Geological Barriers for aDeep Repository for Radioactive Waste. EUR19122 EN. Luxembourg. (http://bookshop.europa.eu/en/gas-migration-and-two-phase-ow-through-engineered-and-geologicalbarriers-for-a-deep-repository-for-radioactive-waste-pbCGNA19122/).

Rbel, A., Sonntag, C., Jippmann, J., Pearson, F., Gautschi, A., 2002. Solute transport informations of very low permeability: prole of stable isotope and dissolved noblegas contents of pore water in the Opalinus Clay; Mont Terri, Switzerland. Geochim.Cosmochim. Acta 66, 13111321.

Sandler, R., 1999. Compilation of Henrys Law Constants for Inorganic andOrganic Species of Potential Importance in Environmental Contents Chemistry (http://www.mpch-mainz.mpg.de/~sander/res/henry.html)

Shackelford, C., 1991. Laboratory diffusion testing for waste disposal a review. J. Contam. Hydrol. 7, 177217.

Van Geet, M., Bastiaens, W., Ortiz, L., 2008. Self-sealing capacity of argillaceous rocks: review of laboratory results obtained from SELFRAC project. Phys. Chem. Earth. 33, S396S406.

Van Loon, L., Soler, J., Bradbury, M., 2003. Diffusion of HTO, Cl-36(-) and I-125(-) in Opalinus Clay samples from Mont Terri effect of conning pressure. J. Contam. Hydrol. 61, 7383.

Yongfeng Deng, Anh Minh Tang, Yu-Jun Cui, Xuan-Phu Nguyen, Xiang-Ling Li, Laurent Wouters. Laboratory Hydro-mechanical Characterisation of Boom Clay at Essen and Mol. Physics and Chemistry of The Earth, Elsevier, 2011, 36 (17-18), pp.1878-1890. Yu, L., Weetjens, E., 2009. Summary of Gas Generation and Migration Current State-of the Art. SCKCEN-ER-108. SCKCEN, Mol, Belgium. (http://hdl.handle.net/10038/1209).

Yu, L., Rogiers, B., Gedeon, M., Marivoet, J., De Craen, M., Mallants, D., 2013. A critical review of laboratory and in-situ hydraulic conductivity measurements of the Boom Clay in Belgium. Appl. Clay Sci. 75 (76), 112.

Number 1A-2Some other models for estimating Diffusivity include the following;

1. Wilke-Chang model for estimating diffusivity in liquid phasesA number of research work both completed and ongoing have proposed a number of methods for estimating diffusivity in liquid phase systems. However, the Wilke-Chang model is the most widely used and diffusion coefficient is given as (Reid R. C. et al, 1977);Dm = . (1)Where T is the absolute temperature, M is the molecular weight, is the viscosity, Vb the molar volume at the normal boiling point, the subscripts a and sv denote the solute and solvent respectively.If the aggregation of solute molecules is accounted for, then the Wilke-Chang equation is modified as follows (Kanji M. and R. Isogai, 2011);Dm = = . (2)Where a is the association coefficient of the solute

2. Maxwell-Stefan Diffusivity model for Binary Liquid systemsThis model is based on Eryings absolute reaction rate theory and an extension of the Vignes model (Glasstone et al, 1941; Vignes. A, 1966). For a non-ideal concentrated binary mixture, the diffusion coefficient can be expressed as;D = Did (1)Where, is the thermodynamic correction factor, Did is diffusion coefficient for an ideal system and is equal to the Maxwell-Stefan diffusivity, D12 thus;Did = D12 (2)Again, Did is directly proportional to the distance between two successive equilibrium positions, , that is;Did = 2k (3) k is the rate constant and is computed from the change in Gibbs energy, thus;k = exp() (4)gi is the net activation energy for the diffusion process, and combining equation 2 to 4 gives;D12 = exp() (4)For the Vignes model, a linear dependence of gi on the composition is assumed (Vignes. A, 1966), thus;g12 = x2 + x1 (5)And the diffusion coefficient is deduced as;D12 = ()x2 ()x1 (6)For non-ideal systems,g12 = 2 + 1 (7)Where Vi is the partial molar volume of component i, V is the molar volume of the system and i is volume fraction of component i.Replacing i by ii the local volume fraction we obtain,g12 = 22 + 11 (8)We can then obtain a new form of the Vignes model for the Maxwell-Stefan diffusivity as;D12 = = ()V22/V2 ()V11/V1 (9)

3. Fuller, Schettler, and Giddings Correlation prediction for Binary Gas DiffusivitiesFuller et al, 1966 used 308 experimental values of the diffusivities of various gases to determine the coefficients a, b, c, d, g, and f equation using a nonlinear least- squares analysis, thus;DAB = (1)The emperical equation that gives the smallest standard deviation is,DAB = (2)Where p is the total pressure (atm), Mi is the molecular weight, DAB is the diffusivity (cm2/s), T is the temperature and Vi is the diffusion volume for component i.

REFERENCESFuller E. N, P. D. Schettler, and J. C. Giddings,Ind. Eng. Chem.58(5), 19 (1966).

Glasstone. S, Laidler K. J. and H. Eyring. The Theory of Rate Processes: the Kinetics of Chemical Reactions, Viscosity, Diusion and Electrochemical Phenomena; McGraw-Hill: New York, 1941.

Kanji M, and R. Isogai, Estimation of Molecular Diffusivity in Liquid Phase Systems by the Wilke-Chang equation, Journal of Chromatography A 1218 (2011) 6639 6645

Reid R. C, J.M. Prausnitz and T.K. Sherwood, The Properties of Gases and Liquids, McGraw-Hill, New York, 1977.

Vignes, A. Diffusion in Binary Solutions. Variation of Diffusion Coefficient with Composition. Ind. Eng. Chem. Fundamentals. 1966, 5, 189-199.

QUESTION 1B

TITLE: On the Modelling of Gas-phase Mass-transfer in Metal sheet Structured packings

Introduction

The efficiency of mass transfer in gas-liquid reactors is expressed using the volumetric mass transfer coefficient, KGa. To better understand mas transfer it is imperative that the film coefficient, KG and the effective interfacial area, a be separated and determined from the volumetric mass transfer coefficient (Alves S.S et al, 2004). Early works of Chilton and Colburn, 1934 state that, gas-phase mass transfer correlations are often based on fundamental models such as turbulent flow models, and boundary layer models.

In this article, modelling of gas-phase mass transfer in metal sheet structured packings (M250Y, M350Y, M500Y, M452Y) was carried out under absorption systems of SO2 chemisorption into NaOH aqueous solution and CO2 chemisorption into the NaOH aqueous solution. The determination of the gas-phase mass transfer coefficient for all reviewed packings were correlated to the dimensionless equationShG = 0.409 (1)

ExperimentalThe experiments were carried out using a column of inner diameter, 0.29m and bed height of 0.84m. For the withdrawal of gas samples by aid of a sampling device (of diameter 30mm), each packing element was drilled horizontally using an electrical discharge machinery (Valenz et al, 2011). Again, liquid distribution was carried out using a pipe liquid distributor having a drip point density of 630 dp/m2, while gas entered the column through a large drum. As mentioned earlier, the aqueous solution of NaOH having a concentration of 1kmol/m3 served as the absorption liquid. The batch was replaced when the hydroxyl concentration began to drop, 0.5kmol/m3 for the interfacial area measurement and 0.1kmol/m3 for the volumetric mass transfer measurements. Furthermore, the temperature of the gas and liquid entering the column was kept at 20oC and atmospheric pressure. The velocities of the liquid used were 4, 10, 20, 40, 60, 80, 100 m3/(m2 h) and that of the gas superficial velocities were 0.5, 1.0, 1.5, 2.0, 2.5, 3.0 m/s.Importantly, introduction of the tracer gas into the gas phase was done before its entry into the column to ensure proper mix and its concentration maintained at the lowest sampling point of at least 1000 ppm. Continuous measurement of the concentration of CO2 and SO2 in the gaseous samples was done using IR analyzer S710, prior to which the gas was dried by passing it through a cartridge containing crushed CaCl2 (CO2 analysis) or Mg(ClO4)2 (SO2 analysis).

Determination of Volumetric Mass Transfer Coefficient, KGaTo determine the volumetric mass transfer coefficient (KGa), measurements should be carried out by experiments where the mass transfer resistance is limited to the gas-phase and where evaporation of the gaseous solute is used (Danckwerts, 1970; Rejl et al, 2009). In this work, absorption of SO2 into the NaOH solution was used and the volumetric mass transfer coefficient, KGa determined with the relation;

KGa = ln (2)An independence of volumetric mass transfer coefficient, KGa on hydroxyl concentration in the NaOH concentration range of 0.1M to 1.0M has been shown by the authors.

Effective area, a determinationDetermination included the absorption of diluted CO2 from the air into the lye where the mass transfer resistance in the gas phase is low and increased reaction of CO2 with the hydroxyl takes up more CO2 within the liquid film. This leads to determination of the mass transfer rate by the reaction transport phenomena in the liquid film correlated to the physical quantities of the system. Determining the effective interfacial area is by correlation of the CO2 local mass transfer rate with its balance along the packing height (Linek et al, 1984) as shown in equation 3. = (3)and substituting value for the volumetric mass transfer as shown in equation 2 gives; = . . ln (4)Also, effective area data was correlated to the gas phase mass transfer resistance as shown in equation 5 (Hoffmann et al, 2007);a = (5)where RG is the relative mass transfer resistance which the authors defined as;RG = . (6)

Mass transfer coefficient determinationThe absorption experiments for the volumetric mass transfer coefficient determination and the effective interfacial area was performed using the aqueous NaOH as the liquid phase and air as the gas phase. Thus, considering the same liquid and gas flow rate, interfacial area was considered as equal, as shown in equation 7;

KG = (7)

Results

Using the power law, experimental results of volumetric mas transfer coefficient and interfacial area were correlated as show in equation 8 and 9 and table 1 shows the constants for individual packings; Figures 1a to d also shows a plot of experimental data for which the correlations are valid.KGa = C1 . (8)a = C2 . (9)

(Rejl F. J. et al, 2014)

Experimental data collected for the volumetric mass transfer coefficient was compared to those obtained for Mellpak 250Y and SO2-air-lye system by Klement. M (2002) as shown in figure 1a. Results further reveal that, the mass transfer coefficient is dependent on the superficial gas phase velocity, while its dependence on the liquid flow rate is quite weak. Also, since the geometry of the studied packing were similar, it became imperative to correlate the resulting values of the mass transfer coefficient as shown in equation 1, for the range of ReG = 240-2500 and ReL = 10-300.

Figure 1(a) M 250Y: volumetric mass-transfer coefcients kGa data used for construction of the correlation Eq. (24). The lines represent the correlation. Comparison with the data of Klement (2002). (b) M350Y: volumetric mass-transfer coefcients kGa data used for construction of the correlation Eq. (24). The lines represent the correlation. (c) M452Y: volumetric mass-transfer coefcients kGa data used for construction of the correlation Eq. (24). The lines represent the correlation. (d) M500Y: volumetric mass-transfer coefcients kGa data used for construction of the correlation Eq. (24). The lines represent the correlation. (Rejl F. J. et al, 2014)

Figure 2: Comparism of experimental and correlated volumetric mass transfer coefficient.(Rejl F. J. et al, 2014)

Again, mass transfer coefficient for M250Y were correlated in two different ways, effective phase velocity (UE) or superficial velocity (UG). This further indicated that effective phase velocity improved fit of the mass transfer coefficient data as seen from the comparative standard deviation (2.85%) of the correlation, thus;KG = 0.0308 . rel.st.dev = 3.16% (10)KG = 0.0209 . rel.st.dev = 2.85% (11)

Finally, mass transfer data obtained for all packing types under present study was successfully correlated by the dimensionless form as in equation 1 which shows how the phase velocity and packing geometry affect the mass transfer (Rejl F. J. et al, 2014).

ReferencesAlves S.S, C. I. Maia, J. M. T. Vasconcelos. Gas-Liquid Mass Transfer Coefficient in Stirred tanks interpreted through bubble contamination Kinetics. Chemical Engineering and Processing 43 (2004) 823 830.

Chilton, T.H., Colburn, A.P., 1934. Mass transfer (absorption) coefcients. Prediction from data on heat transfer and uid friction. Ind. Eng. Chem 26, 11831187

Danckwerts, P. V., 1970. GasLiquid Reactions. McGraw-Hill Book Company, New York.

Hoffmann, A., Mackowiak, J.F., Gorak, A., Haase, M., Loning, J.-M., Runiwski, T., Hallenberger, K., 2007. Standardization of mass transfer measurements. Basis for the description of absorption processes. Chem. Eng. Res. Des. 85 (A1), 4049.

Klement, M., (Diploma thesis) 2002. Studium transportnch charakteristik vypln Mellapak (Study of the transport characteristics of the Mellapak packings). ICT, Prague.

Linek, V., Petrcek, P., Benes, P., Braun, R., 1984. Effective interfacial area and liquid side mass transfer coefcients in absorption columns packed with hydrophilised and untreated plastic packing. Chem. Eng. Res.Des. 62, 1321.

Rejl, F. J . , Linek, V., Moucha, T., Valenz, L., 2009. Methods standardization in the measurement of mass-transfer characteristics in packed absorption columns. Chem. Eng. Res. Des. 87, 695704.

Rejl F. J, L. Valenz, J. Haidl, M. Kordac, and T. Moucha. On the modelling of gas phase mass transfer in metal sheet structured packings. Chemical Engineering Research and Design 93 (2015) 194-202.

Valenz, L., Rejl, F. J . , Linek, V., 2011. Effect of gas- and liquid-phase axial mixing on the rate of mass transfer in a pilot-scale distillation column packed with Mellapak 250Y. Ind. Eng. Chem. Res. 50 (4), 22622271.

Question 1B-2

Other Models to predict the volumetric mass transfer coefficient include the following

1. Model for rising Taylor bubble in circular capillaries developed by Van Baten and Krishna (2004)This model considers two contributions to mass transfer, one of which is the caps at either end of the bubble while the other is the liquid film that seemingly surrounds the bubble (Madhvanand N. K. et al, 2011). The following correlation was developed by the aforementioned authors for the overall volumetric mass transfer coefficient, KLa (liquid volume);

KLa = KL, cap acap + KL, filmafilm (1)Furthermore, the mass transfer coefficients KL, cap and KL, film was derived from the penetration mass transfer model and is as shown in equations 2 and 3, thus;KL, cap = (2)KL, film = (3)Then substituting the value of the specific interfacial area of the two caps (acap) and the film specific interfacial area (afilm), the volumetric mass transfer coefficient, KLa (liquid volume) becomes;KLa = + (4)Where Luc is unit cell length, is gas hold up, ub is bubble rise velocity

2. Dynamic TechniqueThis technique was proposed by Taguchi and Humphrey, 1966. With this technique, the volumetric mass transfer coefficient for oxygen transfer in a fermentation process can be estimated (Atiya, Z. Y, 2012) and is based on oxygen material balance. Thus, = KLa(C* - CL) Cx (1)Where is cell respiration rateAgain, if KLa is equal to zero, the slope of a plot of CL versus t will give an estimate of Cx. rearranging equation 1 to give a linear relationship we obtain; CL = CL* - (2)

And a graphical plot will give a slope of from which the volumetric mass transfer coefficient can be estimated.

3. Billet and Schultes (1999) gas-phase mass transfer model

KGa = Cv (3)

Where Cv is the packing specific constants, a is the area, and the hydraulic dimension of the packing, dp

References

Atiya Z. Y. Estimation of Volumetric Mass Transfer Coefficient in Bioreactor. Al-Khwarizmi Engineering Journal, Vol. 8, No.3, (2012) 75-80

Billet, R., Schultes, M., 1999. Prediction of mass transfer columns with dumped and arranged packings. Updates summary of the calculation method of Billet and Schultes. Trans IChemE 77 (Part A), 498504.

Madhvanand N. K, A. Renken, and L. Kiwi-Minsker. Gas-liquid and Liquid-Liquid mass transfer in microstructured reactors. Chemical Engineering Science 66 (2011) 3876 3897

Taguchi, H., Humphrey, A.E., 1966. Dynamic measurement of the volumetric oxygen transfer coefficient in fermentation systems. J. Ferment. Technol. 44, 881889.

Van Baten, J.M., Krishna, R., 2004. CFD simulations of mass transfer from Taylor bubbles rising in circular capillaries. Chemical Engineering Science 59,25352545