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Hydrodynamics and mass transfer phenomena in counter-current packed column at elevated pressures
Chemical Engineering Science 55 (2000) 6251}6257
Hydrodynamics and mass transfer phenomena in counter-current packed column at elevated pressures B. Benadda, K. Kafou", P. Monkam, M. Otterbein* LAEPSI, INSA, Bat. 404, 20 avenue A. EnL nstein 69621, Villeurbanne Cedex, France Received 21 December 1999; received in revised form 4 July 2000; accepted 13 July 2000
Abstract The aim of this study is to determine mass transfer parameters such as interfacial area a and volumetric liquid side mass transfer coe$cient k a during gas}liquid absorption in a packed column according to pressure within the range 0.1}1.3 MPa. A preliminary * hydrodynamic study was carried out in order to characterize gas and liquid #ows according to the operating pressure. The residence time distribution method shows that #uids #ows can be modeled as plug #ow with axial dispersion. In contrast to the liquid #ow, an e!ect of pressure on the gas #ow has been observed. The axial dispersion coe$cient of the gas increases with pressure. These results allow modeling of the gas}liquid absorption in a packed column with or without chemical reaction and at elevated pressures. The basic equations de"ning the hydrodynamic pro"le of the gas and liquid "lms are completed by the terms describing mass transfer coupled with an irreversible chemical reaction in the liquid phase. The numerical resolution of the system of equations obtained has allowed the study of the in#uence of pressure on the interfacial area a. This parameter increases with pressure. The same result has been observed with the volumetric liquid side mass transfer coe$cient k a. The coe$cient k is independent of pressure. 2000 * * Elsevier Science Ltd. All rights reserved. Keywords: Hydrodynamics; Mass transfer; Pressure; Packed column; Gas absorption; Axial dispersion
1. Introduction Understanding processes concerning gas}liquid absorption with chemical reaction requires good knowledge of the mass transfer parameters, i.e. the interfacial area a and the mass transfer coe$cient k a. These para* meters are useful both for dimensioning and calculating the e$ciency of gas}liquid contactors. Many research workers have measured their values at atmospheric pressure using many di!erent types of apparatus. However, the evolution of these parameters with pressure has not been studied to the same extent; few studies carried out in this "eld are questionable and often show a signi"cant e!ect of pressure on mass transfer parameters. The information obtained at atmospheric pressure cannot simply be extrapolated to describe the same phenomena at elevated pressures. In a recently published study (Benadda, Otterbein, Kafou" & Prost, 1996b), we have reported that the mass transfer parameters, in particular the interfacial area, * Corresponding author. Tel.: #33-04-72-43-84-30; fax: #33-0472-43-87-17.
depend on the operating pressure within the range 0.1}1.2 MPa. This study was carried out in a countercurrent packed column with constant gas and liquid mass #ow rates. The chemical system used to study mass transfer is CO (Na CO }NaHCO ), catalyzed by NaClO. The interfacial area and the liquid side mass transfer coe$cient k a were obtained using the so-called * Danckwerts straight-line method with an intermediate chemical regime. The representation of the square of the absorbed #ux (this #ux being determined experimentally) versus catalyst concentration [ClO\] is a straight-line whose slope and original ordinate give access to the interfacial area a and the mass transfer coe$cient k a. * The interest of this study (Benadda, et al., 1996b), is not only to have shown the unexpected in#uence of pressure on the interfacial area, a parameter which in general only depends on the liquid properties, but also to have revealed the application limits of Danckwerts straightline method at elevated pressures. An in#ection in the straight lines representing absorbed #ux variations versus catalyst concentration was observed above the atmospheric pressure. In fact, at an operating pressure above 0.1 MPa, the increase in catalyst concentration leads to
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the observation of an in#ection point implying a limit to catalyst concentration above which no evolution in the reaction is observed. The determination of mass transfer coe$cients under these conditions was carried out according to the hypothesis of plug #ow in both #uid phases and a linear variation in gaseous reactant concentration according to the height of the packing. The appearance of these limits for interpreting the experimental results at elevated pressure has led us to study the hydrodynamics of the column in order to characterize the gas and liquid #ows at di!erent pressures, and also to use a rapid reaction regime in order to avoid using Danckwerts straight-line method. Finally, the experiments were carried out at constant gas velocity and therefore with a variable gas mass #ow rate. This study "rst aims to identify the #ows of the two #uid phases in a packed column at elevated pressure. Second, modeling of the column to determine the in#uence of pressure on mass transfer parameters will be carried out using the adequate hydrodynamic hypotheses. The operating ranges were as follows: at atmospheric pressure: 0(J (8 kg/ms, * 0(; (0.14 m/s, E under elevated pressure: 0.1(P(1.3 MPa, ; "0.037 m/s, E 0(; (4.63;10\ m/s. * 2. Experimental set-up The experimental set-up has already been described in detail elsewhere (Kafou", 1997). It is mainly composed of a cylindrical column (1), the inner diameter and height of which are 0.062 and 1 m, respectively. This column is packed with Berl saddles (6.4 mm) and operates with a counter-current at a pressure up to 1.3 MPa. The water or aqueous solution is fed into the column from a tank (2) maintained at a higher pressure than that operating pressure. Gas is fed into the bottom of the column from a gas cylinder (10). The pressurization of the installation is controlled by means of both inlet and outlet pressure regulators (11,6). A schematic #ow sheet of the experimental is presented in Fig. 1. 3. Flow characterization 3.1. Method In order to establish mass balance equations and thereby quantify the mass transfer phenomena, we considered it is necessary to characterize the #ow of both phases using the same experimental conditions as for the mass transfer study.
Fig. 1. Flowsheet of the experimental apparatus. 1-packed column, 2-liquid feed tank, 3-gas #owmeter, 4-liquid #owmeter, 5-gas analyser, 6-outlet pressure regulator, 7-safety valve, 8-manometer, 9-recorder, 10-gas cylinder and 6-inlet pressure regulator.
Whether in liquid or gas phase, the classical residence time distribution method was used. It consists of a Dirac injection of a known quantity of tracer at the column input which is monitored at the output. This method was relatively simple for the liquid phase, where the tracer used was KCl. It was not so simple for the gas phase as this technique takes place at elevated pressure, and the choice of tracer gas satisfying certain quality criteria was not obvious. We chose oxygen as tracer gas. It was measured at the column output by an analyzer using the paramagnetic detection principle. The liquid phase was saturated in oxygen before entering the column to avoid absorption of the tracer gas. For each experiment, and before injection of the tracer, a test experiment analyzing the gas at the column input and output was carried out. No di!erence in oxygen concentration was observed even under extreme conditions, i.e. high throughputs and elevated pressure. Interpretation of the response curves from the residence time distribution (RTD) showed plug #ow with axial dispersion of the two #uids. Application of this model gives access to the Peclet number Pe and consequently the axial dispersion coe$cient D according to the following de"nition: Pe";H/D.
(1)
In the case of a non-porous packing, the response curve of the RTD gave access to the total holdup which was related to residence time by the following equation (Fahim & Wakawo, 1992; Hofmann, 1977; Ramachandran,
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Dudukovic & Mills, 1987): ;q b" . R H
(2)
3.2. Results of the liquid phase According to our results obtained up to 1.3 MPa (Benadda, Kafou" & Otterbein, 1996a), no e!ect of pressure on the Peclet number was observed. The axial dispersion coe$cient D , depends only on the liquid #ow * rate for a given gas #ow rate. For our works concerning the mass transfer we use the value of D (D "3.36; * * 10\ m/s) obtained at ; "1.48;10\ and ; "0.037 m/s, irrespective of the pressure used. E Another series of experiments allowed us to study the variation in total liquid hold-ups according to the liquid and gas #ow rates within the range 0.1}1.3 MPa. Our results show that the operating pressure has no e!ect on hold-up. In fact, for ; "1.48;10\ and ; " * E 0.037 m/s, liquid hold-up is 0.21 for pressure ranging between 0.1 and 1.3 MPa. These results seem obvious if we consider that the physical properties of the liquid are independent of the pressure in this range. 3.3. Results of the gas phase To avoid errors in extrapolating results from the RTD of the gas phase, it was necessary to study the RTD of the monitoring system consisting of the oxygen analyzer and a series of protection accessories. The response to a Dirac injection at the column output allowed us to model the response curve of the analytical system. The experimental curve was modeled by a plug #ow with low axial dispersion, the Peclet number being 135. This result showed that the analytical system acted like a plug #ow reactor, introducing a simple pure delay equal to the mean residence time, i.e. 10 s. From the results obtained, the modeling of gas #ow in a column by plug #ow with axial dispersion was quite satisfactory within the ranges of pressure and #uid #ow rates studied. At atmospheric pressure, the axial dispersion coe$cient D increased from 0.5;10\ to 9.5;10\ m/s E when the gas #ow velocity increased from 0.021 to 0.133 m/s. Concerning the in#uence of pressure, we observed an e!ect of this parameter on gas #ow via the axial dispersion coe$cient. In fact, the gas #ow tended to depart from plug #ow when the pressure increased. For a couple such as gas}liquid velocity maintained constant, the axial dispersion coe$cient increased signi"cantly when the operating pressure increased from 0.1 to 1.3 MPa as shown in Fig. 2 for gas #ow alone and for counter-current #ow (; "1.48;10\ * and 4.6;10\ m/s.). The gas velocity was maintained constant at 0.037 m/s.
Fig. 2. In#uence of pressure on axial dispersion coe$cient of the gas phase.
These results could be interpreted by the fact that at constant gas #ow rate, the increase in pressure led to an increase in the Reynolds number via the gas density. Assuming the hypothesis that the relationship between Bodenstein's number and the Reynolds number (Sater & Levenspeil, 1966) remains valid at elevated pressure, we can explain the evolution of the axial dispersion coe$cient with pressure by the increase in Reynolds number via the gas density. It can be thought that these variations were subjected to the phenomenon of molecular di!usion. However, molecular di!usion governs axial dispersion of the gas only at low gas #ow rates. Westerterp, Dil'man, Kronberg and Benneker (1995) propose values of Re (1 for gas dispersion to be determined E by molecular di!usion. Furthermore, the pressure gave rise to a viscous dissipation of the gas. Taking into account the low range of pressure variation, this hypothesis was not su$cient to explain such high variations in the axial dispersion coe$cient. Westerterp, Wijngaarden and Nijhuis (1996) and Westerterp and Wijngaarden (1990) have proposed an interpretation concerning the increase in axial dispersion coe$cients observed according to pressure within the range 0.1}2 MPa, in a packed column with gas #ow alone. These authors have identi"ed the elasticity of the gas as being the factor responsible for the variation in axial dispersion coe$cient according to pressure. A correlation between the dispersion coe$cient and the elasticity would therefore explain the phenomenon. Concerning hold-up results, at zero liquid #ow rate, the gas hold-up was 0.58. This value corresponds to the porosity of the packing determined by weighing to 10% accuracy. For a constant gas velocity of 0.037 m/s, the total hold-up in the gas phase showed that pressure had no e!ect on this hydrodynamic parameter within the range 0.1}1.3 MPa. This result allowed extrapolation of the values of gas hold-ups obtained at atmospheric pressure to elevated pressures as proposed by Larachi,
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Laurent, Midoux and Wild (1991) for the co-current down#ow. After this hydrodynamic study, it would seem logical for further studies to maintain the hypothesis of plug #ow with axial dispersion within the column irrespective of the phase considered.
4. Modeling the column In order to simplify the structure of the model and the calculations, we assumed a negligible resistance in the gas phase, a permanent #ow regime, an isothermal process and "nally all the physical properties of the gas and liquid were considered as constant throughout the column and in time. Assuming these conditions, the equations of the model were limited to partial mass balances in each phase to which the conditions at the limits were added. The basic equations describing the hydrodynamic pro"le of the gas and liquid "lms, established and validated during the hydrodynamic study, were completed by the terms translating mass transfer coupled with an irreversible chemical reaction of the (n, m)th order in the liquidphase such as l A#l BPProducts, where A is the gas solute and B the reactant in the liquid phase. The transfer of the gas solute took place from the gas phase towards the liquid phase. The respective concentrations of the transferred constituent were denoted c and c : Indices g and ¸ represent the gas and liquid E * phases, respectively. By carrying out a balance in solute on each phase for an elementary part of height dz (Fig. 3) we obtained the following equations for the gas and liquid phases,
respectively: dc dc E #; E #U"0, !D e E E dz E dz
(3)
dc dc * !l k cL cK#U"0. * #; !D e * * dz * dz L K
(4)
In these equations, U represents the #ux expressing mass transfer which depends on the mass transfer parameter to be determined and the chemical reaction regime. The conditions at the limits were obtained from Fig. 3:
D e dc "cC , (5) c ! E E E E E ; dz X E dc * "0, (6) dz X D e dc c ! * * * "cC , (7) * * ; dz * X* dc E "0. (8) dz X* This model of the column allowed us to determine the mass transfer parameters, i.e. the interfacial area a and the liquid side mass transfer coe$cient k a. *
4.1. Interfacial area In the case of a pseudo-"rst-order chemical reaction and a rapid reaction regime U is expressed as (Danckwerts, 1970) U"a((D k )C . (9) G If physical equilibrium is established at the interface for low concentrations of solute, it is expressed by a straight line such as c "mC . E G Eqs. (3) and (4) become dc dc E #; E #a((D k )c /m"0, !D e E E dz E dz E
(10)
(11)
dc dc * #; * !k c #a((D k )c /m"0. !D e * * dz * dz * E (12) Resolution of the system of equations consisting of Eqs. (11), (12), (5)}(8) allows the determination of a. 4.2. The volumetric coezcient k a *
Fig. 3. Mass balance of an elementary part of column and the conditions at the limits.
The product k a or volumetric liquid side mass trans* fer coe$cient was determined by physical absorption of an only slightly soluble solute in the liquid which therefore had a low resistance to transfer in the gas phase. The
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transfer #ux can be expressed as follows (Danckwerts, 1970): U"k a(c /m!c ). (13) * E As the term due to chemical reaction is equal to zero, Eqs. (3) and (4) become dc dc E #; E #k a(c /m!c )"0, !D e E E dz E dz * E
(14)
dc dc * #k a(c /m!c )"0. * #; !D e * * dz * dz * E
(15)
Resolution of the system of equations consisting of Eqs. (14), (15), (5)}(8) allowed determination of k a. * After discreting the two systems of equations, an algorithm for their resolution was developed and a program written in turbo Pascal (Kafou", 1997). This calculation code provided us with a pro"le of the gas solute concentrations in the two phases throughout the column. The gas concentration at the column output, determined by infra red analysis of the gas phase, was the resolution criterion. The value of the interfacial area a or the coe$cient k a fed into the calculation code at the beginning * was readjusted until it corresponded to the minimum di!erence between the calculated concentration (z"¸) and the concentration measured experimentally at the same point. This di!erence was "xed at a maximum value of 10\.
5. Determination of mass transfer parameters 5.1. Interfacial area The interfacial area a, was determined for a rapid reaction regime using CO absorption from a mix ture of CO /N at 12% CO by volume in a solution of NaOH. The reaction takes place near the interface in the liquid "lm and is written as
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The NaOH concentration was chosen so that the rapid reaction regime conditions were veri"ed, i.e. a Hatta number Ha'5 and an acceleration factor E equal to Ha. These conditions have been veri"ed at atmospheric pressure whatever the mass #ow rates used, and at elevated pressure. The di!usivity of CO in NaOH was estimated from the literature according to the works of Nijsing and Kramers (1959). At elevated pressure, it is important to ensure that only the pressure varies, otherwise it would be impossible to speak of a study of the in#uence of pressure on a. However, if the gas mass #ow rate was maintained constant, the gas #ow rate ; varied. The experiments were therefore E carried out with constant gas and liquid velocities maintained at ; "0.037 and ; "1.48;10\ m/s, respectiveE * ly, for an operating pressure between 0.1 and 1.3 MPa. As shown in Fig. 4, for constant gas #ow rate, we observed an increase in interfacial area a with increased pressure: a increased from 60 to more than 200/m for a pressure which increased from 0.1 to 1.3 MPa, i.e. a multiplication of a by a factor between 3 and 4. The geometrical area of the bed of Berl Saddles is 360 m/m. As shown in the hydrodynamic study, an increase in pressure led to an increase in the axial dispersion coe$cient D and consequently gave rise to a dispersion of the E gas phase as bubbles. The increase of the interfacial area can be interpreted by the interpenetrating of this new formation of bubbles in the liquid "lm, the latter not being a!ected by pressure. These results do not contradict our previous studies (Benadda et al., 1996b) even if the pressure in#uences the interfacial area in the opposite way. This is due to the fact that in our previous studies, the experiments were carried out with a constant gas mass #ow rate and therefore a decreasing gas velocity with increasing pressure. As studies on packed columns under pressure are very scarce, it was di$cult to compare our results with the literature.
I PHCO\#Na> CO #NaOHP According to Pohorecki and Moniuk (1988), the reaction kinetics is as follows: . (16) r "k;C ;C , -& J !Here NaOH concentration only varies slightly between the input and output and we can consider that C is , -& constant and that the reaction is of a pseudo-"rst order. This criterion is veri"ed by the experiment. Therefore, r "k C with k "kC . (17) , -& J !The value of the kinetic constant k was determined from the literature according to the correlation of Pohorecki and Moniuk (1988).
Fig. 4. In#uence of pressure on interfacial area * CO absorption in NaOH.
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Fig. 5. In#uence of pressure on volumetric liquid side mass transfer coe$cient * CO /water system.
Fig. 6. In#uence of pressure on liquid side mass transfer coe$cient k } CO /water system. *
In a packed glass cylinder column, Oyevaar, Zijl and Westerterp (1988) found that the interfacial area remained constant with increased pressure. The interfacial area was determined by Danckwerts method concerning chemical absorption of CO by DEA. The authors prob ably underestimated the interfacial area by neglecting the axial dispersion of the gas "lm according to the plug #ow hypothesis. However, Badssi, Bugarel, Blanc, Peytavy and Laurent (1988) observed a decrease in interfacial area when the pressure increased up to 5 MPa, working on a co-current column with perforated plates. In a publication concerning a state of the art of mass transfer phenomena at elevated pressure, Oyevaar and Westerterp (1989) as well as Larachi, Cassanello and Laurent (1998) underlined how few studies existed on the subject and the di!erences which were found in the results from one gas}liquid contactor to another. Benadda (1994) came to the same conclusion after a literature survey on this question.
This study, which contributes towards understanding of the mass transfer and hydrodynamic behavior of gas}liquid reactors at elevated pressure, has shown an important e!ect of pressure up to 1.3 MPa on gas #ow and mass transfer parameters. It is therefore not wise to consider the same hypothesis obtained at atmospheric pressure, such as plug #ow, valuable at elevated pressure. No in#uence of pressure was found on liquid #ow. Concerning the mass transfer study, our results showed the increase of interfacial area with increasing pressure up to 1.3 MPa. The coe$cient k remained constant in this * range of pressure. It should be important to notice that the literature review showed that most other seem to agree on the independence of k towards pressure; in * contrast the results obtained for interfacial area, are di!erent and sometimes contradictory.
5.2. Volumetric coezcient k a: *
Notation
The coe$cient k a was determined by physical ab* sorption of CO in water. The gas used was a mixture of CO /N with 3.8% CO by volume. The in#uence of pressure on this parameter is presented in Fig. 5 which shows an increase in the coe$cient k a with pressure * varying from 0.1 to 1.3 MPa with gas and liquid #ow rates of 0.037 and 1.48;10\ m/s, respectively. This effect of pressure on k a was probably due to the in#uence * of pressure on the interfacial area. In fact, the mass transfer coe$cient k is independent of pressure as * shown in Fig. 6. This parameter was determined from the ratio k a/a. Though the two chemical systems are di!er* ent, the solute and also the operational conditions remain unchanged. Then we consider that the above ratio can be used all the more since the solvents used, water and dilute sodium hydroxide, have very similar physicochemical properties.
6. Conclusion
a A B Bo C C G C
c E c * D D E D * d N
interfacial area, m/m gaseous solute liquid reactant Bodenstein's number solute concentration A within the liquid, kmol/m solute concentration A at gas}liquid interface, kmol/m concentration of reactant B far from the interface, kmol/m solute concentration within the gas, kmol/m solute concentration within the liquid, kmol/m di!usivity of gas A in the solution, m/s gas side axial dispersion coe$cient, m/s liquid side axial dispersion coe$cient, m/s characteristic dimension of packing, m
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E H Ha He I J k k k a * m P Pe Re r T t Q ; ; E ; * z z G
acceleration factor height of packed column, m Hatta number Henry's constant, kPa m/kmol ionic strength, kmol/m mass #ow rate, kg/m/s pseudo-"rst-order kinetic constant, s\ second-order kinetic constant, m/kmol/s liquid side volumetric mass transfer coe$cient, s\ straight line slope of physical equilibrium between phases operating pressure, Pa Peclet number Reynolds number reaction velocity per unit volume, kmol/s/m residence time, s #ow velocity, m/s super"cial gas velocity, m/s super"cial liquid velocity, m/s axis according to height valency of species i
Greek letters e q k U o
hold-up mean residence time, s dynamic viscosity, kg/m/s #ux absorbed per unit volume, kmol/m/s density, kg/m.
Superscripts and subscripts g ¸ t
gas phase liquid phase total
References Badssi, A., Bugarel, R., Blanc, C., Peytavy, J. L., & Laurent, A. (1988). In#uence of pressure on the gas-liquid interfacial area and the gas-side mass transfer coe$cient of a laboratory column equipped with cross-#ow sieve trays. Chemical Engineering Process, 23, 89. Benadda, B. (1994). Contribution a% l+e& tude du transfert de matie% re dans une colonne a% garnissage. Inyuence de la pression. UniversiteH Claude Bernard-Lyon I France (164p.).
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Benadda, B., Otterbein, M., Kafou", K., & Prost, M. (1996b). In#uence of pressure on the gas/liquid interfacial area a and the coe$cient k a in a counter-current packed column. Chemical Engineering * Process, 35, 247. Benadda, B., Kafou", K., & Otterbein, M. (1996a). Hydrodynamic behaviour of column under high pressure. In ph. Rudolf von Rohr & Ch. Trepp (Eds.), High pressure chemical engineering (v. 12, 679). Amsterdam: Elsevier. Danckwerts, P. V. (1970). Gas-liquid reactions (270p.). New York, USA: McGraw-Hill. Fahim, M. A., & Wakawo, N. (1992). Parameter estimation from tracer response measurements. Chemical Engineering Journal, 25, 1. Hofmann, H. (1977). Hydrodynamics transport phenomena and mathematical models in trickel-bed reactors. International Chemical Engineering, 17, 19. Kafou", K. (1997). Determination des parame% tres de transfert de matie% re dans une colonne a% garnissage fonctionnant sous pression e& leve& e. UniversiteH Claude Bernard, Lyon I France (133p.). Larachi, F., Cassanello, M., & Laurent, A. (1998). Gas-liquid interfacial mass transfer in trickle-bed reactors at elevated pressure. Industrial and Engineering Chemistry Research, 37, 718. Larachi, F., Laurent, A., Midoux, N., & Wild, G. (1991). Experimental study of a trickle-bed reactor operating at high pressure: Two-phase pressure drop and liquid saturation. Chemical Engineering Science, 46, 1233. Nijsing, R. A. T. O., & Kramers, H. (1959). Absorption of CO in jets and falling "lms of electrolyte solutions, with and without chemical reaction. Chemical Engineering Science, 10, 88. Oyevaar, M. H., & Westerterp, K. R. (1989). Mass transfer phenomena and hydrodynamics in agitated gas-liquid reactors and bubble columns at elevated pressures: State of the art. Chemical Engineering Process, 25, 85. Oyevaar, M. H., Zijl, Ad., & Westerterp, K. R. (1988). Interfacial areas and gas hold-ups in gas-liquid contactors at elevated pressures in a mechanically agitated gas-liquid reactor. Chemical Engineering Technology, 11, 1. Pohorecki, R., & Moniuk, W. (1988). Kinetics of Reaction between Carbon Dioxyde and Hydroxyl Ions in Aqueous Electrolyte Solutions. Chemical Engineering Science, 43, 7, 1677. Ramachandran, P. A., Dudukovic, M. P., & Mills, P. L. (1987). Recent advances in the analysis and design of trickle-bed reactors. Sadhna, 10, 269. Sater, V. E., & Levenspeil, O. (1966). Two-phase #ow in packed beds. Industrial and Engineering Chemistry, Fundamentals, 5,1, 86. Westerterp, K. R., Dil'man, V. V., Kronberg, A. E., & Benneker, A. H. (1995). Wave model for longitudinal dispersion: Analysis and applications. A.I.Ch.E. Journal, 41, 2029. Westerterp, K. R., & Wijngaarden, R. J. (1990). Dispersion in packed beds: Does the #uid elasticity play a ro( le? Developments in Chemical Engineering, 41, 117. Westerterp, K. R., Wijngaarden, R. J., & Nijhuis, N. B. J. (1996). Does the #uid elasticity in#uence the dispersion in packed beds? Chemical Engineering Technology, 19, 291.
Hydrodynamics and mass transfer phenomena in counter-current packed column at elevated pressures B. Benadda, K. Kafou", P. Monkam, M. Otterbein* LAEPSI, INSA, Bat. 404, 20 avenue A. EnL nstein 69621, Villeurbanne Cedex, France Received 21 December 1999; received in revised form 4 July 2000; accepted 13 July 2000
Abstract The aim of this study is to determine mass transfer parameters such as interfacial area a and volumetric liquid side mass transfer coe$cient k a during gas}liquid absorption in a packed column according to pressure within the range 0.1}1.3 MPa. A preliminary * hydrodynamic study was carried out in order to characterize gas and liquid #ows according to the operating pressure. The residence time distribution method shows that #uids #ows can be modeled as plug #ow with axial dispersion. In contrast to the liquid #ow, an e!ect of pressure on the gas #ow has been observed. The axial dispersion coe$cient of the gas increases with pressure. These results allow modeling of the gas}liquid absorption in a packed column with or without chemical reaction and at elevated pressures. The basic equations de"ning the hydrodynamic pro"le of the gas and liquid "lms are completed by the terms describing mass transfer coupled with an irreversible chemical reaction in the liquid phase. The numerical resolution of the system of equations obtained has allowed the study of the in#uence of pressure on the interfacial area a. This parameter increases with pressure. The same result has been observed with the volumetric liquid side mass transfer coe$cient k a. The coe$cient k is independent of pressure. 2000 * * Elsevier Science Ltd. All rights reserved. Keywords: Hydrodynamics; Mass transfer; Pressure; Packed column; Gas absorption; Axial dispersion
1. Introduction Understanding processes concerning gas}liquid absorption with chemical reaction requires good knowledge of the mass transfer parameters, i.e. the interfacial area a and the mass transfer coe$cient k a. These para* meters are useful both for dimensioning and calculating the e$ciency of gas}liquid contactors. Many research workers have measured their values at atmospheric pressure using many di!erent types of apparatus. However, the evolution of these parameters with pressure has not been studied to the same extent; few studies carried out in this "eld are questionable and often show a signi"cant e!ect of pressure on mass transfer parameters. The information obtained at atmospheric pressure cannot simply be extrapolated to describe the same phenomena at elevated pressures. In a recently published study (Benadda, Otterbein, Kafou" & Prost, 1996b), we have reported that the mass transfer parameters, in particular the interfacial area, * Corresponding author. Tel.: #33-04-72-43-84-30; fax: #33-0472-43-87-17.
depend on the operating pressure within the range 0.1}1.2 MPa. This study was carried out in a countercurrent packed column with constant gas and liquid mass #ow rates. The chemical system used to study mass transfer is CO (Na CO }NaHCO ), catalyzed by NaClO. The interfacial area and the liquid side mass transfer coe$cient k a were obtained using the so-called * Danckwerts straight-line method with an intermediate chemical regime. The representation of the square of the absorbed #ux (this #ux being determined experimentally) versus catalyst concentration [ClO\] is a straight-line whose slope and original ordinate give access to the interfacial area a and the mass transfer coe$cient k a. * The interest of this study (Benadda, et al., 1996b), is not only to have shown the unexpected in#uence of pressure on the interfacial area, a parameter which in general only depends on the liquid properties, but also to have revealed the application limits of Danckwerts straightline method at elevated pressures. An in#ection in the straight lines representing absorbed #ux variations versus catalyst concentration was observed above the atmospheric pressure. In fact, at an operating pressure above 0.1 MPa, the increase in catalyst concentration leads to
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the observation of an in#ection point implying a limit to catalyst concentration above which no evolution in the reaction is observed. The determination of mass transfer coe$cients under these conditions was carried out according to the hypothesis of plug #ow in both #uid phases and a linear variation in gaseous reactant concentration according to the height of the packing. The appearance of these limits for interpreting the experimental results at elevated pressure has led us to study the hydrodynamics of the column in order to characterize the gas and liquid #ows at di!erent pressures, and also to use a rapid reaction regime in order to avoid using Danckwerts straight-line method. Finally, the experiments were carried out at constant gas velocity and therefore with a variable gas mass #ow rate. This study "rst aims to identify the #ows of the two #uid phases in a packed column at elevated pressure. Second, modeling of the column to determine the in#uence of pressure on mass transfer parameters will be carried out using the adequate hydrodynamic hypotheses. The operating ranges were as follows: at atmospheric pressure: 0(J (8 kg/ms, * 0(; (0.14 m/s, E under elevated pressure: 0.1(P(1.3 MPa, ; "0.037 m/s, E 0(; (4.63;10\ m/s. * 2. Experimental set-up The experimental set-up has already been described in detail elsewhere (Kafou", 1997). It is mainly composed of a cylindrical column (1), the inner diameter and height of which are 0.062 and 1 m, respectively. This column is packed with Berl saddles (6.4 mm) and operates with a counter-current at a pressure up to 1.3 MPa. The water or aqueous solution is fed into the column from a tank (2) maintained at a higher pressure than that operating pressure. Gas is fed into the bottom of the column from a gas cylinder (10). The pressurization of the installation is controlled by means of both inlet and outlet pressure regulators (11,6). A schematic #ow sheet of the experimental is presented in Fig. 1. 3. Flow characterization 3.1. Method In order to establish mass balance equations and thereby quantify the mass transfer phenomena, we considered it is necessary to characterize the #ow of both phases using the same experimental conditions as for the mass transfer study.
Fig. 1. Flowsheet of the experimental apparatus. 1-packed column, 2-liquid feed tank, 3-gas #owmeter, 4-liquid #owmeter, 5-gas analyser, 6-outlet pressure regulator, 7-safety valve, 8-manometer, 9-recorder, 10-gas cylinder and 6-inlet pressure regulator.
Whether in liquid or gas phase, the classical residence time distribution method was used. It consists of a Dirac injection of a known quantity of tracer at the column input which is monitored at the output. This method was relatively simple for the liquid phase, where the tracer used was KCl. It was not so simple for the gas phase as this technique takes place at elevated pressure, and the choice of tracer gas satisfying certain quality criteria was not obvious. We chose oxygen as tracer gas. It was measured at the column output by an analyzer using the paramagnetic detection principle. The liquid phase was saturated in oxygen before entering the column to avoid absorption of the tracer gas. For each experiment, and before injection of the tracer, a test experiment analyzing the gas at the column input and output was carried out. No di!erence in oxygen concentration was observed even under extreme conditions, i.e. high throughputs and elevated pressure. Interpretation of the response curves from the residence time distribution (RTD) showed plug #ow with axial dispersion of the two #uids. Application of this model gives access to the Peclet number Pe and consequently the axial dispersion coe$cient D according to the following de"nition: Pe";H/D.
(1)
In the case of a non-porous packing, the response curve of the RTD gave access to the total holdup which was related to residence time by the following equation (Fahim & Wakawo, 1992; Hofmann, 1977; Ramachandran,
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Dudukovic & Mills, 1987): ;q b" . R H
(2)
3.2. Results of the liquid phase According to our results obtained up to 1.3 MPa (Benadda, Kafou" & Otterbein, 1996a), no e!ect of pressure on the Peclet number was observed. The axial dispersion coe$cient D , depends only on the liquid #ow * rate for a given gas #ow rate. For our works concerning the mass transfer we use the value of D (D "3.36; * * 10\ m/s) obtained at ; "1.48;10\ and ; "0.037 m/s, irrespective of the pressure used. E Another series of experiments allowed us to study the variation in total liquid hold-ups according to the liquid and gas #ow rates within the range 0.1}1.3 MPa. Our results show that the operating pressure has no e!ect on hold-up. In fact, for ; "1.48;10\ and ; " * E 0.037 m/s, liquid hold-up is 0.21 for pressure ranging between 0.1 and 1.3 MPa. These results seem obvious if we consider that the physical properties of the liquid are independent of the pressure in this range. 3.3. Results of the gas phase To avoid errors in extrapolating results from the RTD of the gas phase, it was necessary to study the RTD of the monitoring system consisting of the oxygen analyzer and a series of protection accessories. The response to a Dirac injection at the column output allowed us to model the response curve of the analytical system. The experimental curve was modeled by a plug #ow with low axial dispersion, the Peclet number being 135. This result showed that the analytical system acted like a plug #ow reactor, introducing a simple pure delay equal to the mean residence time, i.e. 10 s. From the results obtained, the modeling of gas #ow in a column by plug #ow with axial dispersion was quite satisfactory within the ranges of pressure and #uid #ow rates studied. At atmospheric pressure, the axial dispersion coe$cient D increased from 0.5;10\ to 9.5;10\ m/s E when the gas #ow velocity increased from 0.021 to 0.133 m/s. Concerning the in#uence of pressure, we observed an e!ect of this parameter on gas #ow via the axial dispersion coe$cient. In fact, the gas #ow tended to depart from plug #ow when the pressure increased. For a couple such as gas}liquid velocity maintained constant, the axial dispersion coe$cient increased signi"cantly when the operating pressure increased from 0.1 to 1.3 MPa as shown in Fig. 2 for gas #ow alone and for counter-current #ow (; "1.48;10\ * and 4.6;10\ m/s.). The gas velocity was maintained constant at 0.037 m/s.
Fig. 2. In#uence of pressure on axial dispersion coe$cient of the gas phase.
These results could be interpreted by the fact that at constant gas #ow rate, the increase in pressure led to an increase in the Reynolds number via the gas density. Assuming the hypothesis that the relationship between Bodenstein's number and the Reynolds number (Sater & Levenspeil, 1966) remains valid at elevated pressure, we can explain the evolution of the axial dispersion coe$cient with pressure by the increase in Reynolds number via the gas density. It can be thought that these variations were subjected to the phenomenon of molecular di!usion. However, molecular di!usion governs axial dispersion of the gas only at low gas #ow rates. Westerterp, Dil'man, Kronberg and Benneker (1995) propose values of Re (1 for gas dispersion to be determined E by molecular di!usion. Furthermore, the pressure gave rise to a viscous dissipation of the gas. Taking into account the low range of pressure variation, this hypothesis was not su$cient to explain such high variations in the axial dispersion coe$cient. Westerterp, Wijngaarden and Nijhuis (1996) and Westerterp and Wijngaarden (1990) have proposed an interpretation concerning the increase in axial dispersion coe$cients observed according to pressure within the range 0.1}2 MPa, in a packed column with gas #ow alone. These authors have identi"ed the elasticity of the gas as being the factor responsible for the variation in axial dispersion coe$cient according to pressure. A correlation between the dispersion coe$cient and the elasticity would therefore explain the phenomenon. Concerning hold-up results, at zero liquid #ow rate, the gas hold-up was 0.58. This value corresponds to the porosity of the packing determined by weighing to 10% accuracy. For a constant gas velocity of 0.037 m/s, the total hold-up in the gas phase showed that pressure had no e!ect on this hydrodynamic parameter within the range 0.1}1.3 MPa. This result allowed extrapolation of the values of gas hold-ups obtained at atmospheric pressure to elevated pressures as proposed by Larachi,
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Laurent, Midoux and Wild (1991) for the co-current down#ow. After this hydrodynamic study, it would seem logical for further studies to maintain the hypothesis of plug #ow with axial dispersion within the column irrespective of the phase considered.
4. Modeling the column In order to simplify the structure of the model and the calculations, we assumed a negligible resistance in the gas phase, a permanent #ow regime, an isothermal process and "nally all the physical properties of the gas and liquid were considered as constant throughout the column and in time. Assuming these conditions, the equations of the model were limited to partial mass balances in each phase to which the conditions at the limits were added. The basic equations describing the hydrodynamic pro"le of the gas and liquid "lms, established and validated during the hydrodynamic study, were completed by the terms translating mass transfer coupled with an irreversible chemical reaction of the (n, m)th order in the liquidphase such as l A#l BPProducts, where A is the gas solute and B the reactant in the liquid phase. The transfer of the gas solute took place from the gas phase towards the liquid phase. The respective concentrations of the transferred constituent were denoted c and c : Indices g and ¸ represent the gas and liquid E * phases, respectively. By carrying out a balance in solute on each phase for an elementary part of height dz (Fig. 3) we obtained the following equations for the gas and liquid phases,
respectively: dc dc E #; E #U"0, !D e E E dz E dz
(3)
dc dc * !l k cL cK#U"0. * #; !D e * * dz * dz L K
(4)
In these equations, U represents the #ux expressing mass transfer which depends on the mass transfer parameter to be determined and the chemical reaction regime. The conditions at the limits were obtained from Fig. 3:
D e dc "cC , (5) c ! E E E E E ; dz X E dc * "0, (6) dz X D e dc c ! * * * "cC , (7) * * ; dz * X* dc E "0. (8) dz X* This model of the column allowed us to determine the mass transfer parameters, i.e. the interfacial area a and the liquid side mass transfer coe$cient k a. *
4.1. Interfacial area In the case of a pseudo-"rst-order chemical reaction and a rapid reaction regime U is expressed as (Danckwerts, 1970) U"a((D k )C . (9) G If physical equilibrium is established at the interface for low concentrations of solute, it is expressed by a straight line such as c "mC . E G Eqs. (3) and (4) become dc dc E #; E #a((D k )c /m"0, !D e E E dz E dz E
(10)
(11)
dc dc * #; * !k c #a((D k )c /m"0. !D e * * dz * dz * E (12) Resolution of the system of equations consisting of Eqs. (11), (12), (5)}(8) allows the determination of a. 4.2. The volumetric coezcient k a *
Fig. 3. Mass balance of an elementary part of column and the conditions at the limits.
The product k a or volumetric liquid side mass trans* fer coe$cient was determined by physical absorption of an only slightly soluble solute in the liquid which therefore had a low resistance to transfer in the gas phase. The
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transfer #ux can be expressed as follows (Danckwerts, 1970): U"k a(c /m!c ). (13) * E As the term due to chemical reaction is equal to zero, Eqs. (3) and (4) become dc dc E #; E #k a(c /m!c )"0, !D e E E dz E dz * E
(14)
dc dc * #k a(c /m!c )"0. * #; !D e * * dz * dz * E
(15)
Resolution of the system of equations consisting of Eqs. (14), (15), (5)}(8) allowed determination of k a. * After discreting the two systems of equations, an algorithm for their resolution was developed and a program written in turbo Pascal (Kafou", 1997). This calculation code provided us with a pro"le of the gas solute concentrations in the two phases throughout the column. The gas concentration at the column output, determined by infra red analysis of the gas phase, was the resolution criterion. The value of the interfacial area a or the coe$cient k a fed into the calculation code at the beginning * was readjusted until it corresponded to the minimum di!erence between the calculated concentration (z"¸) and the concentration measured experimentally at the same point. This di!erence was "xed at a maximum value of 10\.
5. Determination of mass transfer parameters 5.1. Interfacial area The interfacial area a, was determined for a rapid reaction regime using CO absorption from a mix ture of CO /N at 12% CO by volume in a solution of NaOH. The reaction takes place near the interface in the liquid "lm and is written as
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The NaOH concentration was chosen so that the rapid reaction regime conditions were veri"ed, i.e. a Hatta number Ha'5 and an acceleration factor E equal to Ha. These conditions have been veri"ed at atmospheric pressure whatever the mass #ow rates used, and at elevated pressure. The di!usivity of CO in NaOH was estimated from the literature according to the works of Nijsing and Kramers (1959). At elevated pressure, it is important to ensure that only the pressure varies, otherwise it would be impossible to speak of a study of the in#uence of pressure on a. However, if the gas mass #ow rate was maintained constant, the gas #ow rate ; varied. The experiments were therefore E carried out with constant gas and liquid velocities maintained at ; "0.037 and ; "1.48;10\ m/s, respectiveE * ly, for an operating pressure between 0.1 and 1.3 MPa. As shown in Fig. 4, for constant gas #ow rate, we observed an increase in interfacial area a with increased pressure: a increased from 60 to more than 200/m for a pressure which increased from 0.1 to 1.3 MPa, i.e. a multiplication of a by a factor between 3 and 4. The geometrical area of the bed of Berl Saddles is 360 m/m. As shown in the hydrodynamic study, an increase in pressure led to an increase in the axial dispersion coe$cient D and consequently gave rise to a dispersion of the E gas phase as bubbles. The increase of the interfacial area can be interpreted by the interpenetrating of this new formation of bubbles in the liquid "lm, the latter not being a!ected by pressure. These results do not contradict our previous studies (Benadda et al., 1996b) even if the pressure in#uences the interfacial area in the opposite way. This is due to the fact that in our previous studies, the experiments were carried out with a constant gas mass #ow rate and therefore a decreasing gas velocity with increasing pressure. As studies on packed columns under pressure are very scarce, it was di$cult to compare our results with the literature.
I PHCO\#Na> CO #NaOHP According to Pohorecki and Moniuk (1988), the reaction kinetics is as follows: . (16) r "k;C ;C , -& J !Here NaOH concentration only varies slightly between the input and output and we can consider that C is , -& constant and that the reaction is of a pseudo-"rst order. This criterion is veri"ed by the experiment. Therefore, r "k C with k "kC . (17) , -& J !The value of the kinetic constant k was determined from the literature according to the correlation of Pohorecki and Moniuk (1988).
Fig. 4. In#uence of pressure on interfacial area * CO absorption in NaOH.
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Fig. 5. In#uence of pressure on volumetric liquid side mass transfer coe$cient * CO /water system.
Fig. 6. In#uence of pressure on liquid side mass transfer coe$cient k } CO /water system. *
In a packed glass cylinder column, Oyevaar, Zijl and Westerterp (1988) found that the interfacial area remained constant with increased pressure. The interfacial area was determined by Danckwerts method concerning chemical absorption of CO by DEA. The authors prob ably underestimated the interfacial area by neglecting the axial dispersion of the gas "lm according to the plug #ow hypothesis. However, Badssi, Bugarel, Blanc, Peytavy and Laurent (1988) observed a decrease in interfacial area when the pressure increased up to 5 MPa, working on a co-current column with perforated plates. In a publication concerning a state of the art of mass transfer phenomena at elevated pressure, Oyevaar and Westerterp (1989) as well as Larachi, Cassanello and Laurent (1998) underlined how few studies existed on the subject and the di!erences which were found in the results from one gas}liquid contactor to another. Benadda (1994) came to the same conclusion after a literature survey on this question.
This study, which contributes towards understanding of the mass transfer and hydrodynamic behavior of gas}liquid reactors at elevated pressure, has shown an important e!ect of pressure up to 1.3 MPa on gas #ow and mass transfer parameters. It is therefore not wise to consider the same hypothesis obtained at atmospheric pressure, such as plug #ow, valuable at elevated pressure. No in#uence of pressure was found on liquid #ow. Concerning the mass transfer study, our results showed the increase of interfacial area with increasing pressure up to 1.3 MPa. The coe$cient k remained constant in this * range of pressure. It should be important to notice that the literature review showed that most other seem to agree on the independence of k towards pressure; in * contrast the results obtained for interfacial area, are di!erent and sometimes contradictory.
5.2. Volumetric coezcient k a: *
Notation
The coe$cient k a was determined by physical ab* sorption of CO in water. The gas used was a mixture of CO /N with 3.8% CO by volume. The in#uence of pressure on this parameter is presented in Fig. 5 which shows an increase in the coe$cient k a with pressure * varying from 0.1 to 1.3 MPa with gas and liquid #ow rates of 0.037 and 1.48;10\ m/s, respectively. This effect of pressure on k a was probably due to the in#uence * of pressure on the interfacial area. In fact, the mass transfer coe$cient k is independent of pressure as * shown in Fig. 6. This parameter was determined from the ratio k a/a. Though the two chemical systems are di!er* ent, the solute and also the operational conditions remain unchanged. Then we consider that the above ratio can be used all the more since the solvents used, water and dilute sodium hydroxide, have very similar physicochemical properties.
6. Conclusion
a A B Bo C C G C
c E c * D D E D * d N
interfacial area, m/m gaseous solute liquid reactant Bodenstein's number solute concentration A within the liquid, kmol/m solute concentration A at gas}liquid interface, kmol/m concentration of reactant B far from the interface, kmol/m solute concentration within the gas, kmol/m solute concentration within the liquid, kmol/m di!usivity of gas A in the solution, m/s gas side axial dispersion coe$cient, m/s liquid side axial dispersion coe$cient, m/s characteristic dimension of packing, m
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E H Ha He I J k k k a * m P Pe Re r T t Q ; ; E ; * z z G
acceleration factor height of packed column, m Hatta number Henry's constant, kPa m/kmol ionic strength, kmol/m mass #ow rate, kg/m/s pseudo-"rst-order kinetic constant, s\ second-order kinetic constant, m/kmol/s liquid side volumetric mass transfer coe$cient, s\ straight line slope of physical equilibrium between phases operating pressure, Pa Peclet number Reynolds number reaction velocity per unit volume, kmol/s/m residence time, s #ow velocity, m/s super"cial gas velocity, m/s super"cial liquid velocity, m/s axis according to height valency of species i
Greek letters e q k U o
hold-up mean residence time, s dynamic viscosity, kg/m/s #ux absorbed per unit volume, kmol/m/s density, kg/m.
Superscripts and subscripts g ¸ t
gas phase liquid phase total
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Benadda, B., Otterbein, M., Kafou", K., & Prost, M. (1996b). In#uence of pressure on the gas/liquid interfacial area a and the coe$cient k a in a counter-current packed column. Chemical Engineering * Process, 35, 247. Benadda, B., Kafou", K., & Otterbein, M. (1996a). Hydrodynamic behaviour of column under high pressure. In ph. Rudolf von Rohr & Ch. Trepp (Eds.), High pressure chemical engineering (v. 12, 679). Amsterdam: Elsevier. Danckwerts, P. V. (1970). Gas-liquid reactions (270p.). New York, USA: McGraw-Hill. Fahim, M. A., & Wakawo, N. (1992). Parameter estimation from tracer response measurements. Chemical Engineering Journal, 25, 1. Hofmann, H. (1977). Hydrodynamics transport phenomena and mathematical models in trickel-bed reactors. International Chemical Engineering, 17, 19. Kafou", K. (1997). Determination des parame% tres de transfert de matie% re dans une colonne a% garnissage fonctionnant sous pression e& leve& e. UniversiteH Claude Bernard, Lyon I France (133p.). Larachi, F., Cassanello, M., & Laurent, A. (1998). Gas-liquid interfacial mass transfer in trickle-bed reactors at elevated pressure. Industrial and Engineering Chemistry Research, 37, 718. Larachi, F., Laurent, A., Midoux, N., & Wild, G. (1991). Experimental study of a trickle-bed reactor operating at high pressure: Two-phase pressure drop and liquid saturation. Chemical Engineering Science, 46, 1233. Nijsing, R. A. T. O., & Kramers, H. (1959). Absorption of CO in jets and falling "lms of electrolyte solutions, with and without chemical reaction. Chemical Engineering Science, 10, 88. Oyevaar, M. H., & Westerterp, K. R. (1989). Mass transfer phenomena and hydrodynamics in agitated gas-liquid reactors and bubble columns at elevated pressures: State of the art. Chemical Engineering Process, 25, 85. Oyevaar, M. H., Zijl, Ad., & Westerterp, K. R. (1988). Interfacial areas and gas hold-ups in gas-liquid contactors at elevated pressures in a mechanically agitated gas-liquid reactor. Chemical Engineering Technology, 11, 1. Pohorecki, R., & Moniuk, W. (1988). Kinetics of Reaction between Carbon Dioxyde and Hydroxyl Ions in Aqueous Electrolyte Solutions. Chemical Engineering Science, 43, 7, 1677. Ramachandran, P. A., Dudukovic, M. P., & Mills, P. L. (1987). Recent advances in the analysis and design of trickle-bed reactors. Sadhna, 10, 269. Sater, V. E., & Levenspeil, O. (1966). Two-phase #ow in packed beds. Industrial and Engineering Chemistry, Fundamentals, 5,1, 86. Westerterp, K. R., Dil'man, V. V., Kronberg, A. E., & Benneker, A. H. (1995). Wave model for longitudinal dispersion: Analysis and applications. A.I.Ch.E. Journal, 41, 2029. Westerterp, K. R., & Wijngaarden, R. J. (1990). Dispersion in packed beds: Does the #uid elasticity play a ro( le? Developments in Chemical Engineering, 41, 117. Westerterp, K. R., Wijngaarden, R. J., & Nijhuis, N. B. J. (1996). Does the #uid elasticity in#uence the dispersion in packed beds? Chemical Engineering Technology, 19, 291.