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Hydrodynamic and gas phase axial dispersion in an air-molten salt two-phase system (molten salt oxidation reactor)
Chemical Engineering and Processing 44 (2005) 1054–1062
Hydrodynamic and gas phase axial dispersion in an air-molten salt two-phase system (molten salt oxidation reactor) Yong-Jun Cho a,∗ , Hee-Chul Yang a , Hee-Chul Eun b , Jae-Hyung Yoo a , Joon-Hyung Kim a b
a Nuclear Fuel Cycle R&D Group, Korea Atomic Energy Research Institute, P.O. Box 105, Yuseong, Daejeon 305-600, South Korea Quantum Energy Chemical Engineering, University of Science and Technology, P.O. Box 52, Yuseong, Daejeon 305-333, South Korea
Received 13 July 2004; received in revised form 17 September 2004; accepted 11 January 2005 Available online 25 April 2005
Abstract The effects of the gas velocity (0.05–0.22 m/s) and temperature (870–970 ◦ C) on the gas holdup and the gas phase axial dispersion coefficient have been studied in a molten salt oxidation reactor (0.076 m i.d. × 0.653 m H., air-molten sodium carbonate salt two-phase system). The gas phase holdup and the amount of the axial gas phase dispersion coefficient were experimentally evaluated by means of the pressure drop measurement and residence time distribution (RTD) experiments using inert tracer gas (CO), respectively. Results indicated that the gas holdup increases with an increasing temperature, but the increasing rate of the gas holdup decreases with an increasing gas velocity. The gas phase axial dispersion coefficients show an asymptotic value with an increasing gas velocity due to the plug-flow like behavior at a higher gas velocity. Temperature has positive effects on the gas phase axial dispersion. To detect the regime characteristics, a spectral method based on the differential pressure fluctuation has been applied, which enables us to obtain the flow characteristics in the MSO reactor. © 2005 Elsevier B.V. All rights reserved. Keywords: Molten salt oxidation reactor; Gas phase holdup; Flow regime characteristics; Gas phase axial dispersion; Spectral analysis
1. Introduction Gas–liquid bubble columns have been widely used in the chemical, biochemical and environmental processes as a absorber, contactor or reactor due to their simplicity of construction, low maintenance cost, excellent transfer ability, no mechanical moving parts and high transfer phenomena [1–3]. In recent years, as a kind of bubble column, molten salt oxidation (MSO, air-molten salt two-phase system) regarded as one of the most attractive alternatives to, and offers several advantages over, incineration is studied for the destruction (or oxidation) of mixed wastes, chemical warfare agents, medical wastes and energetic materials such as explosives and propellants [4–6]. In this MSO process, combustible wastes together with oxidant air are introduced into the molten salt (ordinary alkali metal carbonate) reactor in which air (gas phase) is dispersed in the molten salt (liquid phase) via a waste/gas ∗
Corresponding author. Tel.: +82 42 868 8631; fax: +82 42 868 8667. E-mail address: [email protected] (Y.-J. Cho).
0255-2701/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.cep.2005.01.006
injector and rises in the form of bubbles. By a flameless oxidation, in the MSO reactor, the organic compounds react with the oxygen, then they are converted into carbon dioxide, nitrogen and water. The inorganic compounds in the wastes form residue retained in the molten salt bed. For the proper design, scale-up and operation of the MSO reactor, knowledge on the hydrodynamics is essential because the hydrodynamics strongly affect the reaction (oxidation) efficiency of the reactor. It has been generally accepted that phase holdup and phase mixing are the most important governing factors for reactor performance [7–17]. The effects of operating variables such as the temperature, pressure, gas and liquid phase properties on the phase holdup have been studied by many researchers. But, there is no hydrodynamic study on the air-molten salt two-phase system. The extent of an axial dispersion in an individual phase can affect the reaction rates and product selectivity [14–18]. While the liquid phase dispersion in a two-phase system has been studied widely, relatively little studies have been carried out on the gas phase axial dispersion. Moreover, most of the studies on the gas
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phase dispersion have been done in the air–water system. Variation in the system properties is responsible for the bubbling phenomena, and thus alters the gas holdup structure, which directly affects the gas phase dispersion. Hydrodynamics, the phase mixing and transfer phenomena strongly depend on the flow regime. So, the elucidation of the flow characteristics is very important to properly design and model a reactor. Numerous studies have been made to describe the prevailing flow characteristics, and the flow characteristics in a multi-phase flow system have been successfully interpreted by means of the pressure fluctuation signals [19–21]. Thus, in this present study, the effects of the gas velocity and the temperature on the gas phase holdup and the gas phase axial dispersion coefficient have been investigated in the MSO reactor. In addition, the differential pressure fluctuations have been measured and analyzed by means of a spectral analysis to describe the flow regime characteristics in the MSO reactor with a variation of the operating conditions.
2. Experimental Experiments were carried out in a cylindrical column of 0.076 m in diameter and 0.653 m in height as shown in Fig. 1. The column is fabricated from Inconnel 600 materials. Corrosion tests have shown that Inconnel 600 has an acceptable corrosion rate in sodium carbonate at operating conditions [5]. Sodium carbonate (melting point: 850 ◦ C) and air were used as the liquid and gas phase, respectively. Oxidizing air is fed into the molten carbonate salts bed through a 0.013 m i.d. vertical single-tube. The column is heated by the surrounding ceramic three-zone heaters. The superficial gas velocity of the gas phase varied from 0.05 to 0.23 m/s, and the tem-
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Table 1 Physical properties of the molten sodium carbonate with the temperature Temperature (◦ C)
Density (kg/m3 )
Viscosity (Pa s)
Surface tension (dyne/cm)
870 900 930 970
2476.62 2476.54 2476.46 2476.35
4.1 × 10−3 3.0 × l0−3 2.2 × 10−3 1.6 × l0−3
211 210 208 206
perature of molten salt bed ranged from 870 to 970 ◦ C. The physical properties of the molten sodium carbonate with the temperature are given in Table 1. The gas holdup was evaluated from the pressure drop measurement method using differential pressure transducer [1]. To measure the differential pressure drop, P, two stainless steel tube tubes (SUS 316) were installed vertically in the molten salt bed. The vertical distance between the pressure measuring points, L, was 0.3 m. The output voltage–time signals form the differential pressure transducer, corresponding to the pressure–time signal, were processed with the aid of a data acquisition system. The differential pressure signals were sampled at a rate of 200 Hz for 20 s yielding the 4000 data points. The gas phase holdup was calculated from the following equation: εG =
P Lg
− ρL
ρG − ρ L
(1)
A tracer gas sampling technology has been used to evaluate the axial gas phase dispersion coefficient. A pulse input of the CO gas as a tracer gas was introduced into the molten carbonate salt bed with air using a switching magnetic valve. The CO concentration leaving the reactor was continuously recorded by a sensitive CO concentration transducer. The output voltage–time data were converted to concentration–time data using data acquisition system. From the effluent concentration–time curve, C(t), the residence time (or the exit-age of distribution) for a pulse input, E(t), is induced [22]: C(t) E(t) = ∞ 0 C(t) dt
(2)
where the denominator of Eq. (2) means the area under the C(t). The gas phase axial dispersion coefficient, DZ,G , could be induced from the momentum analysis. The first momentum of RTD is the mean residence time, tm , and the second momentum means the variance, σ 2 , which means the distribution about the mean. Assuming that the reactor is a closed–closed system, the relationship between the momentum parameters and the Peclet number of the gas is given by Eq. (3) based on a simple one-dimensional axial dispersion model [23]. Fig. 1. Schematic diagram of molten salt oxidation system: (1) Molten salt vessel; (2) gas/waste injector; (3) electric heater; (4) thermocouple; (5) T. indicator; (6) T. controller; (7) magnetic valve; (8) CO gas reservoir; (9) pressure transducer; (10) data acquisition system; (11) computer; (12) CO gas detector; (13) heat exchanger; (14) cold-water bath; (15) HEPA filter; (16) silica bed; (17) i.d. fan.
σ2 2 2 = − 2 (1 − e−Pe ) 2 tm Pe Pe
(3)
where Pe = UG H/εG DZ,G . Pe is experimentally obtained by tm and σ 2 from the RTD data and then solving Eq. (3) for Pe.
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Fig. 2. Effects of gas velocity on the gas phase holdup with the variation of the molten slat temperature.
The procedure for the RTD evolution is presented in detail elsewhere [14,22,23].
al. [10] and Pohorecki et al. [12] found that the gas holdup always increased with the increase of the temperature. Lin et al. [3] noted that the increasing trend of the gas holdup with the temperature is due to the dominant rule of the associated reduction in the liquid viscosity and the surface tension, which leads to a smaller average bubble size and a narrower bubble size distribution and also noted that the associated decrease in the gas density plays a secondary role. Pohorecki et al. [12] suggested that the influence on the surface tension on the gas holdup is greater than that of the liquid viscosity. The surface tension and viscosity of the molten sodium carbonate salt decreased with an increasing temperature in the MSO reactor (Table 1). So, it is anticipated that the increasing trend of the gas holdup with the temperature is due to the decreasing tendency of the surface tension and the viscosity of the molten sodium carbonate salt with the temperature in the MSO reactor. The temperature effects on the gas holdup could be conveniently interpreted by the temperature effect on the bubble characteristics such as the bubble formation and bubble breakup since the gas holdup is directly influenced by the bubble characteristics. The initial bubble size formed from a single-hole or a nozzle gas injector, db,0 can be calculated by the following equation [24]:
db,0 3. Results and discussion 3.1. Gas holdup Effects of the superficial gas velocity on the gas holdup can be seen in Fig. 2, with the variation of the molten sodium carbonate salt temperature. In this figure, the gas holdup increases with an increasing of the gas velocity, showing a change of the increasing trend of the gas holdup with the gas velocity. The change of the increasing trend with the gas velocity may be due to the flow regime transition [1,2,7–9]. In the air–water vertical up-flow two-phase system, the flow regime with a gas velocity gradually develops to a homogeneous bubble, bubble-slug, churn-turbulent or slug flow [11–13]. The prevailing regime mainly depends on the gas velocity, liquid properties and gas distributor. In the case of a MSO reactor, the density and the surface tension of the liquid phase are relatively high and the air is dispersed into the molten slat bed through a single-point sparging tube, which produces a non-uniform gas distribution. Therefore, it is estimated that the homogeneous bubble flow regime is not present in the flow regime of the MSO reactor. Instead, a flow regime, with a gas velocity, develops from a bubble-slug to a slug flow in the MSO system. It can also be noted in Fig. 2 that the gas holdup increases with an increasing molten sodium carbonate salt temperature. The increasing trend of the gas holdup with the temperature in a MSO reactor is in agreement with the observation of the several researchers in a bubble column [3,10,12]. Renjun et
6D0 σL = g(ρL − ρG )
1/3 (4)
As is well known, the maximum stable bubble size is a primary parameter characterizing the bubble breakup process. Based on the Rayleigh–Taylor instability, Bellman and Pennington [25] proposed that the instability of a bubble with a diameter larger than a critical wavelength, λc , or maximum stable bubble size, db,max , will grow exponentially and eventually breakup. The critical wavelength or maximum stable bubble size can be derived from the equation below: σL (5) λc (= db,max ) = 2π g(ρL − ρG ) But Eq. (5) is only useful in the case where there is no relative velocity between the gas and liquid phase. To overcome the limitation of Eq. (5), Wilkinson and Dierndonck [26] suggested an equation, which accounts for the relative velocity between the two-phases: L 2π g(ρLσ−ρ G) db,max =
2 0.5 ρL ρL +ρG
√
ρG
Ur2 2
σL g(ρL −ρG )
+ 1 +
ρL ρ G
Ur2 2
(ρL +ρG )2 σL g(ρL −ρG )
(6) where Ur is the relative velocity between the gas and liquid phase at the gas–liquid interface. In the case of the liquidbatch system, Ur could be inferred from the slip velocity. To calculate the maximum stable bubble size, Walter and Blanch
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temperature by those at 870 ◦ C. The effect of the temperature on the initial bubble size is negligible. But the maximum stable bubble size is decreased with the temperature. So, it is anticipated that an increase in the gas holdup with an increase in the temperature is may be due to a decrease in the maximum stable bubble size in the MSO reactor. Experimentally obtained gas holdup data have been compared with the literature correlation equations listed in Table 2 (Fig. 4). The gas holdup data of this study show the lowest values among the gas holdup values calculated by the correlation equations. This may be due to the high liquid density and non-uniform gas phase distribution. 3.2. Flow regime
Fig. 3. Effects of the molten salt temperature on the normalized initial and maximum stable bubble size.
[27] also proposed a correlation equation as shown in Eq. (7): µL 0.1 σ 0.6 (7) db,max = 1.12 0.6 L 0.4 µG ρL (gUG ) Fig. 3 shows the effects of the temperature on the normalized initial and maximum stable bubble size obtained by dividing the initial and maximum stable bubble size at a given
The flow regime characteristics of the multi-phase flow could be obtained from a spectral analysis of the pressure fluctuations using a power spectrum density function (PSDF) [19–21]. PSDF of the time series, x(t), can be obtained from the following relation [20]: PSDF(x) = F (Rxx )
(8)
where F and Rxx mean the Fourier transform and autocorrelation function (ACF) of x(t), respectively, defined as below [19]: F (x) =
+∞
−∞
x(t) exp(−j2πft) dt
(9)
Table 2 Correlation equations for the gas holdup in a bubble column Investigator
Correlation equation
System
Conditions
Kumar et al. [32]
εG (U = UG [ρL 2 /σ L (ρL − ρG )g]0.25 )
D = 0.05–0.6 m single-/multi-nozzle (d0 = 0.87–2.65 mm) air–water, kerosene, glycerol solution
0.0014 ≤ UG ≤ 0.14 m/s 31.2 ≤ σ L ≤ 74.5 mN/m 790 ≤ ρL ≤ 1100 kg/m3 0.063 ≤ µL ≤ 0.320 Pa s
Shumpe and Deckwer [9]
εG = 0.0404(100UG )0.627 (in the slug flow regime)
D = 0.1 m sintered plate, air–CMC solution
0.005 < UG ≤ 0.17 m/s UL = 0.006 m/s
Zahradnik et al. [8]
εG = UG /(2.02UG + 0.257)
D = 0.14, 0.15, 0.29 m perforated plate (d0 = 0.5, 1.6 mm) air–water, ethanol solution
0.02 ≤ UG ≤ 0.13 m/s 3 ≤ µL ≤ 110 mPa s
Pohorecki et al. [12]
εG = 0.383 UG0.65 σL−0.52
D = 0.3 m sparger (d0 = 1–5 mm), nitrogen-cyclohexane
0.002 ≤ UG ≤ 0.055 m/s UL = 0.0014 m/s 0.2 ≤ P ≤ 1.1 MPa 30 ≤ T ≤ 160 ◦ C
Akita and Yoshida [7]
εG /(1 − εG )4 = 0.2(D3 ρL g/σL ) 0.083 (D3 ρL2 g/µ2L ) (UG /(gD)0.5 )
D = 0.152 m single-nozzle (d0 = 5 mm) air, O2 , CO2 , He-water, glycol solution, methanol solution
0.005 ≤ UG ≤ 0.149 m/s 22.3 ≤ σ L ≤ 74.2 mN/m 790 ≤ ρL ≤ 1590 kg/m3 0.58 ≤ µL ≤ 21.2 mPa s
Shawaqfeh [2]
εG = (0.775 ± 0.040)UG (0.657 ± 0.03)
D = 0.074 m concentric distributor, air–water
0.094 ≤ UG ≤ 0.41 m/s 0 ≤ UL ≤ 0.0116 m/s
Anabtawi et al. [11]
εG = 0.362 UG0.60 µ−0.24 H −0.38 L static bed height)
D = 0.074 m single-nozzle sprayer (d0 = 10 mm) air–oil
0.0018 ≤ UG ≤ 0.28 m/s 0.0248 ≤ σ L ≤ 0.035 N/m 906 ≤ ρL ≤ 928 kg/m3 0.063 ≤ µL ≤ 0.320 Pa s
= 0.728U − 0.458U2
+ 0.0975U3
0.125
(H:
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Fig. 4. Comparison between the experimental and calculated values of the gas holdup.
1 Rxx (τ) = lim T →∞ T
T
x(t)x(t + τ) dt
(10)
0
where T and τ are the whole time length of the time series and time lag, respectively. Drahos et al. [28] have shown that the interesting frequencies of the PSDF spectrum range from 0 to 20 Hz for bubble columns. Fig. 5 shows the PSDF of the differential pressure at two different gas velocities, UG = 0.07 and 0.18 m/s. The PSDFs show a different trend for the each gas velocity. When the gas velocity is 0.07 m/s, there is a relatively weak contribution to the power spectrum of the frequencies between 2 and 6 Hz compared to those when the gas velocity is 0.18 m/s. The PSDF, at a lower frequency, is
Fig. 5. PSDF of the differential pressure fluctuations at two different gas velocities.
Fig. 6. Typical example of ACF curves with the gas velocity.
much larger for the slug flow regime than for the bubbleslug flow regime. Vial et al. [19] noted that the PSDF, in the heterogeneous flow regime, exhibits a broader peak in the range 3–5 Hz. These results suggest a potential method for determining a regime’s transition. The ACF of the pressure fluctuation signals is one of the useful tools for a spectral analysis and can provide quantitative information on the pressure fluctuations [19–21]. The typical ACF curves with the gas velocity are shown in Fig. 6. As can be seen in this figure, the ACF shows a more gradual and oscillatory decrease tendency with an increasing time lag when the gas velocity is 0.07 m/s compared to those of 0.18 and 0.22 m/s. Whereas, in the case of 0.18 and 0.22 m/s, they have a similar changing trend with the time lag, which means they are involved in the same flow regime. As a consequence, it is anticipated that the flow regime transition can be detected by the ACF curve. Vial et al. [19,20] have shown that the ACF shape reflects the classical random process in the homogeneous regime, but in the heterogeneous flow regimes, it is characterized by a quasi-periodic component superimposed on random processes. The decreasing trend of the magnitude of the ACF can be represented by the expression [21] Rxx (τ) τ R xx (τ) = = exp − cos(2πf0 τ) (11) Rxx (0) τ0 In Eq. (11), τ 0 and f0 are the characteristic time of the flow structure and the characteristic frequency, which corresponds to the frequency of the peak observation in the PSDF, respectively. Fig. 7 shows that Eq. (11) is in good agreement with the ACF evaluated from the experimental data. The optimum values of τ 0 and f0 are evaluated through the Levenberg–Marquardt method [29]. The Levenberg–Marquardt method is one of the most widely used non-linear curve fitting methods, which is very useful for
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Fig. 7. Comparison of the ACF based on the model with those obtained experimentally.
Fig. 9. Effects of the gas velocity on the gas phase axial dispersion coefficient with the variation of the molten salt temperature.
finding solutions to complex fitting problems. The characteristic time, τ 0 , has been used for the flow regime identification [19–21]. The changing tendency of the characteristic time with the gas velocity is presented in Fig. 8 together with the result of the model calculation proposed by Vial et al. [19] using the dimension structure and liquid circulation velocity. In this figure, the characteristic time at 870 ◦ C shows a decreasing trend then is nearly constant when the gas velocity is greater than 0.15 m/s in the MSO reactor. This trend is similar to that of the gas holdup (Fig. 2). Vial et al. [19] observed that the characteristic time, in a heteroge-
neous flow regime, tends to decrease as the flow becomes more chaotic, which accords well with the finding of Fan et al. [21] in a liquid–solid fluidized bed. The difference of the values of the characteristic time between this study and the model calculation may be attributed to the sharp difference of the liquid phase properties, density, surface tension, viscosity.
Fig. 8. Changing tendency of the characteristic time with the gas velocity.
3.3. Axial gas phase dispersion The gas phase dispersion coefficients were plotted as a function of the gas velocity in Fig. 9. The dispersion coefficient increases gradually at low gas velocities and then reaches an asymptotic value with a further increase of the gas velocity. The effect of the gas velocity on the gas phase axial dispersion is similar to that on the gas holdup (Fig. 2) and on the characteristic time (Fig. 8). Increase in the gas velocity leads to an increase in the turbulence in the molten sodium carbonate salt bed and a consequent increase in the gas phase mixing in both the axial and radial directions. However, a further increase of the gas velocity above 0.15 m/s makes the flow produce a plug-flow like behavior, which reduces the formation frequency of the micro-scale eddies in the bed resulting in a weak axial dispersion phenomena. Micro-eddies can increase the contacting frequencies between the fluid elements and consequently increase the phase mixing in the multi-phase flow systems [18]. It seems that at a higher gas velocity condition (above 0.15 m/s), the gas phase dispersion coefficients do not increase with a further increase of the gas velocity due to the plug-flow like behavior in the MSO reactor. Fig. 9 also illustrates the effects of the temperature on the gas phase dispersion coefficient. As can be noted from this
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3.4. Correlation The drift-flux model has been frequently used for the fitting of the gas holdup data [2,8]. Based on the drift-flux model, the gas holdup, in a liquid-batch system, is fitted in the form of Eq. (12) [8,19,20]. εG =
UG C 0 UG + C 1
(12)
where C0 is a constant measure of the interaction of the void and velocity distribution and C1 is the weighted average drift velocity accounting for the local slip. C1 is often taken as the rise velocity of a bubble in an infinite medium. Another method to fit the gas holdup data has been provided by several researchers as below [2,9]. εG = aUGb
Fig. 10. Comparison between the experimental and calculated values of the gas phase axial dispersion coefficients.
figure, the gas phase axial dispersion coefficient increases with the temperature. As we have seen, the elevated temperature increases the gas holdup in the MSO reactor (Fig. 2), and this result induces the increase of the gas phase axial dispersion phenomena. A comparison of the present data with the literature correlation data is shown in Fig. 10. The gas phase dispersion coefficients obtained in this research are smaller than those obtained by Joshi [30], Mangartz and Pilhofer [31] and Field and Davidson [22], but higher than that by Deckwer et al. [33]. The gas phase dispersion strongly depends on the liquid properties, especially the liquid density. An increase of the liquid density results in an enhancement of the buoyancy forces acting on the gas bubbles, which makes the flow pattern a plug-flow like flow, which induces a mixing intensity in both the axial and radial directions. It is suspected that the radial gas holdup variation is less prominent in the MSO reactor when compared to the water system due to the large density difference of the phases. Therefore, lower gas phase dispersion values are observed in the molten salt system when compared to the water system. The correlation proposed by Deckwer et al. [33] has been used to determine the dispersion coefficient of a homogeneous bubble flow regime. The gas phase dispersion in a homogeneous regime differs from that in a heterogeneous flow regime. In the homogeneous flow regime, smaller bubbles, which have a narrow size distribution, arise without hindering each other [16–18]. So a very weak liquid circulation takes place in the bed. The dispersion coefficient of the small bubbles is taken equal to the liquid phase dispersion coefficient. Therefore, correlation by Deckwer et al. [33] is same to that of the liquid phase. It has been generally understood that the gas phase dispersion coefficients are roughly 2–10 times greater than the liquid phase dispersion coefficients [17].
(13)
Fig. 11(a) shows a typical example of a fitting result of the model equations, and the comparison between the experimental and correlated value of the gas holdup is shown in Fig. 11(b). The resulting values for the best fit of Eqs. (12) and (13) are listed in Table 3 with the temperature. As can be seen in Fig. 11(b), the best correlation of the gas holdup is accomplished by the drift-flux model (Eq. (12)) in the MSO reactor.
Fig. 11. Typical example of a fitting result of the model equations (a) and the comparison between the experimental and correlated value of the gas holdup (b).
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Table 3 Resulting values for the best fit of Eqs. (12) and (13)
Appendix A: Nomenclature
T (◦ C)
C0 , C1 drift flux parameters in Eq. (12) C(t) tracer gas concentration at exit of reactor at time t (ppm) Do orifice diameter (m) DZ,G axial gas phase dispersion coefficient (m2 /s) db,0 initial bubble diameter (m) db,max maximum stable bubble diameter (m) E(t) exit-age distribution function (s−1 ) g gravity acceleration (m/s2 ) H reactor height (m) Pe Peclet number (=UG H/εG DZ,G ) mean residence time (s) tm UG superficial gas velocity (m/s) Ur relative velocity between the gas and liquid phase (m/s)
870 900 930 970
Parameters UG /εG = C1 + Co UG
y = aXb
C1
Co
a
0.393 0.381 0.370 0.363
3.060 2.850 2.703 2.591
0.468 0.501 0.527 0.548
b ± ± ± ±
0.04 0.04 0.06 0.06
0.525 0.533 0.539 0.543
± ± ± ±
0.08 0.04 0.06 0.06
The present data of the axial gas phase dispersion coefficients in terms of the Peclet number in the MSO reactor were correlated with the dimensionless experimental variables as [10]: −0.0070 UG H UG µL 0.3594 µ4L g Pe= = 418.87 (14) εG DZ,G ρL ρL σL3 with the correlation coefficient of 0.94. Eq. (14) covers the following range of variables: 4.37 ≤ Pe ≤ 8.89, 3.04 × 10−12 ≤ µ4L g/ρL σL3 ≤ 1.18 × 10−10 , 3.91 × 10−4 ≤ UG µL /ρL ≤ 4.26 × 10−3 .
4. Conclusion In the MSO reactor, the gas phase holdup increases with an increase of the molten sodium carbonate salt temperature, but shows a different increasing trend at gas velocities above 0.15 m/s under all the experimental temperature condition. It is found that the gas phase axial dispersion coefficient in the MSO reactor is smaller than that in the air–water bubble column due to the higher liquid density. The dispersion coefficient increases gradually at low gas velocities and then reaches an asymptotic value with a further increase of the gas velocity. The effects of the operating variables on the flow regime characteristics have been successfully interpreted by means of a spectral analysis of the differential pressure fluctuations. The experimentally obtained gas phase holdup is best fitted via the drift-flux model, and the gas phase axial dispersion coefficient has been correlated in terms of the Peclet number in the MSO reactor conditions with the dimensionless experimental variables. These results may be useful for the design and operation of the MSO system.
Acknowledgement This study has been carried out under the Nuclear R&D Program by the Korean Ministry of Science and Technology.
Greek letters εG gas phase holdup µL liquid viscosity (Pa s) ρL liquid density (kg/m3 ) σL liquid surface tension (dyne/cm) σ2 variance of the residence time distribution (s2 )
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Y.-J. Cho et al. / Chemical Engineering and Processing 44 (2005) 1054–1062 bubble columns with a single sparger, Chem. Eng. Proc. 42 (2003) 403–408. R. Pohorecki, W. Moniuk, A. Zdrojkowski, P. Bielski, Hydrodynamics of a pilot plant bubble column under elevated temperature and pressure, Chem. Eng. Sci. 56 (2001) 1167–1174. X. Luo, D.J. Lee, R. Lau, G. Yang, L.S. Fan, Maximum stable bubble size and gas holdup in high-pressure slurry bubble columns, AIChE J. 45 (1999) 665–680. J. Zahradnik, M. Fialova, The effect of bubble regime in gas and liquid phase mixing in bubble column reactors, Chem. Eng. Sci. 51 (1996) 2491–2500. S. Wachi, Y. Nojima, Gas-phase dispersion in bubble columns, Chem. Eng. Sci. 45 (1990) 901–905. S.A. Shetty, M.V. Kantak, B.G. Kelkar, Gas-phase backing in bubblecolumn reactors, AIChE J. 38 (1992) 1013–1026. M.V. Kantak, R.P. Hesketh, B.G. Kelkar, Effect of gas and liquid properties in gas phase dispersion in bubble columns, Chem. Eng. J. 59 (1995) 91–100. Y. Kang, S.D. Kim, Radial dispersion characteristics of two- and three-phase fluidized beds, Ind. Eng. Chem. Des. Dev. 25 (1986) 717–722. C. Vial, E. Camarasa, S. Poncin, G. Wild, N. Midoux, J. Bouillard, Study of hydrodynamic behavior in bubble columns and external loop airlift reactors through analysis of pressure fluctuations, Chem. Eng. Sci. 55 (2000) 2957–2973. C. Vial, S. Poncin, G. wild, N. Midoux, A simple method for identification and flow characteristics in bubble columns and airlift reactors, Chem. Eng. Proc. 40 (2001) 135–151. L.T. Fan, Y. Kang, M. Yashima, D. Neogi, Stochastic behavior of fluidised particles in a liquid–solid fluidized bed, Chem. Eng. Commun. 135 (1995) 147–160.
[22] R.W. Field, J.F. Davidson, Axial dispersion in bubble columns, Trans. Inst. Chem. Eng. 58 (1980) 228–236. [23] H.S. Fogler, Elements of Chemical Reaction Engineering, second ed., Prentice Hall, New Jersey, 1992, pp. 765–769. [24] J.S. Davidson, B.O.G. Schuler, Bubble coalescence in viscous liquids, Trans. Inst. Chem. Eng. 38 (1960) 335–341. [25] R. Bellman, R.H. Pennington, Effects of surface tension and viscosity on taylor instability, Q. J. Appl. Math. 12 (1953) 151–162. [26] P.M. Wilkinson, L.L.V. Dierendonck, Pressure and gas density effects on bubble break-up and gas hold-up in bubble columns, Chem. Eng. Sci. 45 (1990) 2309–2315. [27] J.F. Walter, H.W. Blanch, Bubble break-up in gas–liquid bioreactor break-up in turbulent flows, Chem. Eng. J. 32 (1986) B7– B17. [28] J. Drahos, J. Zahradnik, M. Puncocha, M. Fialova, F. Bradka, Effects of operating condition on the characteristics of pressure fluctuations in a bubble column, Chem. Eng. Proc. 29 (1991) 107– 115. [29] S.C. Chapra, R.P. Canale, Numerical Methods for Engineers, second ed., McGraw-Hill, New York, 1988, p. 245. [30] J.B. Joshi, Gas-phase dispersion in bubble column, Chem. Eng. J. 24 (1982) 213–216. [31] K.H. Mangartz, Th. Pilhofer, Interpretation of mass transfer measurement in bubble columns considering dispersion of both phases, Chem. Eng. Sci. 36 (1981) 1069–1077. [32] A. Kumar, T.E. Degaleesan, G.S. Laddha, H.E. Hoelscher, Bubble swarm characteristics in bubble columns, Can. J. Chem. Eng. 54 (1976) 503–508. [33] W.D. Deckwer, R. Burckhart, G. Zoll, Mixing and mass transfer in tall bubble column, Chem. Eng. Sci. 29 (1974) 2177–2188.
Hydrodynamic and gas phase axial dispersion in an air-molten salt two-phase system (molten salt oxidation reactor) Yong-Jun Cho a,∗ , Hee-Chul Yang a , Hee-Chul Eun b , Jae-Hyung Yoo a , Joon-Hyung Kim a b
a Nuclear Fuel Cycle R&D Group, Korea Atomic Energy Research Institute, P.O. Box 105, Yuseong, Daejeon 305-600, South Korea Quantum Energy Chemical Engineering, University of Science and Technology, P.O. Box 52, Yuseong, Daejeon 305-333, South Korea
Received 13 July 2004; received in revised form 17 September 2004; accepted 11 January 2005 Available online 25 April 2005
Abstract The effects of the gas velocity (0.05–0.22 m/s) and temperature (870–970 ◦ C) on the gas holdup and the gas phase axial dispersion coefficient have been studied in a molten salt oxidation reactor (0.076 m i.d. × 0.653 m H., air-molten sodium carbonate salt two-phase system). The gas phase holdup and the amount of the axial gas phase dispersion coefficient were experimentally evaluated by means of the pressure drop measurement and residence time distribution (RTD) experiments using inert tracer gas (CO), respectively. Results indicated that the gas holdup increases with an increasing temperature, but the increasing rate of the gas holdup decreases with an increasing gas velocity. The gas phase axial dispersion coefficients show an asymptotic value with an increasing gas velocity due to the plug-flow like behavior at a higher gas velocity. Temperature has positive effects on the gas phase axial dispersion. To detect the regime characteristics, a spectral method based on the differential pressure fluctuation has been applied, which enables us to obtain the flow characteristics in the MSO reactor. © 2005 Elsevier B.V. All rights reserved. Keywords: Molten salt oxidation reactor; Gas phase holdup; Flow regime characteristics; Gas phase axial dispersion; Spectral analysis
1. Introduction Gas–liquid bubble columns have been widely used in the chemical, biochemical and environmental processes as a absorber, contactor or reactor due to their simplicity of construction, low maintenance cost, excellent transfer ability, no mechanical moving parts and high transfer phenomena [1–3]. In recent years, as a kind of bubble column, molten salt oxidation (MSO, air-molten salt two-phase system) regarded as one of the most attractive alternatives to, and offers several advantages over, incineration is studied for the destruction (or oxidation) of mixed wastes, chemical warfare agents, medical wastes and energetic materials such as explosives and propellants [4–6]. In this MSO process, combustible wastes together with oxidant air are introduced into the molten salt (ordinary alkali metal carbonate) reactor in which air (gas phase) is dispersed in the molten salt (liquid phase) via a waste/gas ∗
Corresponding author. Tel.: +82 42 868 8631; fax: +82 42 868 8667. E-mail address: [email protected] (Y.-J. Cho).
0255-2701/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.cep.2005.01.006
injector and rises in the form of bubbles. By a flameless oxidation, in the MSO reactor, the organic compounds react with the oxygen, then they are converted into carbon dioxide, nitrogen and water. The inorganic compounds in the wastes form residue retained in the molten salt bed. For the proper design, scale-up and operation of the MSO reactor, knowledge on the hydrodynamics is essential because the hydrodynamics strongly affect the reaction (oxidation) efficiency of the reactor. It has been generally accepted that phase holdup and phase mixing are the most important governing factors for reactor performance [7–17]. The effects of operating variables such as the temperature, pressure, gas and liquid phase properties on the phase holdup have been studied by many researchers. But, there is no hydrodynamic study on the air-molten salt two-phase system. The extent of an axial dispersion in an individual phase can affect the reaction rates and product selectivity [14–18]. While the liquid phase dispersion in a two-phase system has been studied widely, relatively little studies have been carried out on the gas phase axial dispersion. Moreover, most of the studies on the gas
Y.-J. Cho et al. / Chemical Engineering and Processing 44 (2005) 1054–1062
phase dispersion have been done in the air–water system. Variation in the system properties is responsible for the bubbling phenomena, and thus alters the gas holdup structure, which directly affects the gas phase dispersion. Hydrodynamics, the phase mixing and transfer phenomena strongly depend on the flow regime. So, the elucidation of the flow characteristics is very important to properly design and model a reactor. Numerous studies have been made to describe the prevailing flow characteristics, and the flow characteristics in a multi-phase flow system have been successfully interpreted by means of the pressure fluctuation signals [19–21]. Thus, in this present study, the effects of the gas velocity and the temperature on the gas phase holdup and the gas phase axial dispersion coefficient have been investigated in the MSO reactor. In addition, the differential pressure fluctuations have been measured and analyzed by means of a spectral analysis to describe the flow regime characteristics in the MSO reactor with a variation of the operating conditions.
2. Experimental Experiments were carried out in a cylindrical column of 0.076 m in diameter and 0.653 m in height as shown in Fig. 1. The column is fabricated from Inconnel 600 materials. Corrosion tests have shown that Inconnel 600 has an acceptable corrosion rate in sodium carbonate at operating conditions [5]. Sodium carbonate (melting point: 850 ◦ C) and air were used as the liquid and gas phase, respectively. Oxidizing air is fed into the molten carbonate salts bed through a 0.013 m i.d. vertical single-tube. The column is heated by the surrounding ceramic three-zone heaters. The superficial gas velocity of the gas phase varied from 0.05 to 0.23 m/s, and the tem-
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Table 1 Physical properties of the molten sodium carbonate with the temperature Temperature (◦ C)
Density (kg/m3 )
Viscosity (Pa s)
Surface tension (dyne/cm)
870 900 930 970
2476.62 2476.54 2476.46 2476.35
4.1 × 10−3 3.0 × l0−3 2.2 × 10−3 1.6 × l0−3
211 210 208 206
perature of molten salt bed ranged from 870 to 970 ◦ C. The physical properties of the molten sodium carbonate with the temperature are given in Table 1. The gas holdup was evaluated from the pressure drop measurement method using differential pressure transducer [1]. To measure the differential pressure drop, P, two stainless steel tube tubes (SUS 316) were installed vertically in the molten salt bed. The vertical distance between the pressure measuring points, L, was 0.3 m. The output voltage–time signals form the differential pressure transducer, corresponding to the pressure–time signal, were processed with the aid of a data acquisition system. The differential pressure signals were sampled at a rate of 200 Hz for 20 s yielding the 4000 data points. The gas phase holdup was calculated from the following equation: εG =
P Lg
− ρL
ρG − ρ L
(1)
A tracer gas sampling technology has been used to evaluate the axial gas phase dispersion coefficient. A pulse input of the CO gas as a tracer gas was introduced into the molten carbonate salt bed with air using a switching magnetic valve. The CO concentration leaving the reactor was continuously recorded by a sensitive CO concentration transducer. The output voltage–time data were converted to concentration–time data using data acquisition system. From the effluent concentration–time curve, C(t), the residence time (or the exit-age of distribution) for a pulse input, E(t), is induced [22]: C(t) E(t) = ∞ 0 C(t) dt
(2)
where the denominator of Eq. (2) means the area under the C(t). The gas phase axial dispersion coefficient, DZ,G , could be induced from the momentum analysis. The first momentum of RTD is the mean residence time, tm , and the second momentum means the variance, σ 2 , which means the distribution about the mean. Assuming that the reactor is a closed–closed system, the relationship between the momentum parameters and the Peclet number of the gas is given by Eq. (3) based on a simple one-dimensional axial dispersion model [23]. Fig. 1. Schematic diagram of molten salt oxidation system: (1) Molten salt vessel; (2) gas/waste injector; (3) electric heater; (4) thermocouple; (5) T. indicator; (6) T. controller; (7) magnetic valve; (8) CO gas reservoir; (9) pressure transducer; (10) data acquisition system; (11) computer; (12) CO gas detector; (13) heat exchanger; (14) cold-water bath; (15) HEPA filter; (16) silica bed; (17) i.d. fan.
σ2 2 2 = − 2 (1 − e−Pe ) 2 tm Pe Pe
(3)
where Pe = UG H/εG DZ,G . Pe is experimentally obtained by tm and σ 2 from the RTD data and then solving Eq. (3) for Pe.
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Fig. 2. Effects of gas velocity on the gas phase holdup with the variation of the molten slat temperature.
The procedure for the RTD evolution is presented in detail elsewhere [14,22,23].
al. [10] and Pohorecki et al. [12] found that the gas holdup always increased with the increase of the temperature. Lin et al. [3] noted that the increasing trend of the gas holdup with the temperature is due to the dominant rule of the associated reduction in the liquid viscosity and the surface tension, which leads to a smaller average bubble size and a narrower bubble size distribution and also noted that the associated decrease in the gas density plays a secondary role. Pohorecki et al. [12] suggested that the influence on the surface tension on the gas holdup is greater than that of the liquid viscosity. The surface tension and viscosity of the molten sodium carbonate salt decreased with an increasing temperature in the MSO reactor (Table 1). So, it is anticipated that the increasing trend of the gas holdup with the temperature is due to the decreasing tendency of the surface tension and the viscosity of the molten sodium carbonate salt with the temperature in the MSO reactor. The temperature effects on the gas holdup could be conveniently interpreted by the temperature effect on the bubble characteristics such as the bubble formation and bubble breakup since the gas holdup is directly influenced by the bubble characteristics. The initial bubble size formed from a single-hole or a nozzle gas injector, db,0 can be calculated by the following equation [24]:
db,0 3. Results and discussion 3.1. Gas holdup Effects of the superficial gas velocity on the gas holdup can be seen in Fig. 2, with the variation of the molten sodium carbonate salt temperature. In this figure, the gas holdup increases with an increasing of the gas velocity, showing a change of the increasing trend of the gas holdup with the gas velocity. The change of the increasing trend with the gas velocity may be due to the flow regime transition [1,2,7–9]. In the air–water vertical up-flow two-phase system, the flow regime with a gas velocity gradually develops to a homogeneous bubble, bubble-slug, churn-turbulent or slug flow [11–13]. The prevailing regime mainly depends on the gas velocity, liquid properties and gas distributor. In the case of a MSO reactor, the density and the surface tension of the liquid phase are relatively high and the air is dispersed into the molten slat bed through a single-point sparging tube, which produces a non-uniform gas distribution. Therefore, it is estimated that the homogeneous bubble flow regime is not present in the flow regime of the MSO reactor. Instead, a flow regime, with a gas velocity, develops from a bubble-slug to a slug flow in the MSO system. It can also be noted in Fig. 2 that the gas holdup increases with an increasing molten sodium carbonate salt temperature. The increasing trend of the gas holdup with the temperature in a MSO reactor is in agreement with the observation of the several researchers in a bubble column [3,10,12]. Renjun et
6D0 σL = g(ρL − ρG )
1/3 (4)
As is well known, the maximum stable bubble size is a primary parameter characterizing the bubble breakup process. Based on the Rayleigh–Taylor instability, Bellman and Pennington [25] proposed that the instability of a bubble with a diameter larger than a critical wavelength, λc , or maximum stable bubble size, db,max , will grow exponentially and eventually breakup. The critical wavelength or maximum stable bubble size can be derived from the equation below: σL (5) λc (= db,max ) = 2π g(ρL − ρG ) But Eq. (5) is only useful in the case where there is no relative velocity between the gas and liquid phase. To overcome the limitation of Eq. (5), Wilkinson and Dierndonck [26] suggested an equation, which accounts for the relative velocity between the two-phases: L 2π g(ρLσ−ρ G) db,max =
2 0.5 ρL ρL +ρG
√
ρG
Ur2 2
σL g(ρL −ρG )
+ 1 +
ρL ρ G
Ur2 2
(ρL +ρG )2 σL g(ρL −ρG )
(6) where Ur is the relative velocity between the gas and liquid phase at the gas–liquid interface. In the case of the liquidbatch system, Ur could be inferred from the slip velocity. To calculate the maximum stable bubble size, Walter and Blanch
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temperature by those at 870 ◦ C. The effect of the temperature on the initial bubble size is negligible. But the maximum stable bubble size is decreased with the temperature. So, it is anticipated that an increase in the gas holdup with an increase in the temperature is may be due to a decrease in the maximum stable bubble size in the MSO reactor. Experimentally obtained gas holdup data have been compared with the literature correlation equations listed in Table 2 (Fig. 4). The gas holdup data of this study show the lowest values among the gas holdup values calculated by the correlation equations. This may be due to the high liquid density and non-uniform gas phase distribution. 3.2. Flow regime
Fig. 3. Effects of the molten salt temperature on the normalized initial and maximum stable bubble size.
[27] also proposed a correlation equation as shown in Eq. (7): µL 0.1 σ 0.6 (7) db,max = 1.12 0.6 L 0.4 µG ρL (gUG ) Fig. 3 shows the effects of the temperature on the normalized initial and maximum stable bubble size obtained by dividing the initial and maximum stable bubble size at a given
The flow regime characteristics of the multi-phase flow could be obtained from a spectral analysis of the pressure fluctuations using a power spectrum density function (PSDF) [19–21]. PSDF of the time series, x(t), can be obtained from the following relation [20]: PSDF(x) = F (Rxx )
(8)
where F and Rxx mean the Fourier transform and autocorrelation function (ACF) of x(t), respectively, defined as below [19]: F (x) =
+∞
−∞
x(t) exp(−j2πft) dt
(9)
Table 2 Correlation equations for the gas holdup in a bubble column Investigator
Correlation equation
System
Conditions
Kumar et al. [32]
εG (U = UG [ρL 2 /σ L (ρL − ρG )g]0.25 )
D = 0.05–0.6 m single-/multi-nozzle (d0 = 0.87–2.65 mm) air–water, kerosene, glycerol solution
0.0014 ≤ UG ≤ 0.14 m/s 31.2 ≤ σ L ≤ 74.5 mN/m 790 ≤ ρL ≤ 1100 kg/m3 0.063 ≤ µL ≤ 0.320 Pa s
Shumpe and Deckwer [9]
εG = 0.0404(100UG )0.627 (in the slug flow regime)
D = 0.1 m sintered plate, air–CMC solution
0.005 < UG ≤ 0.17 m/s UL = 0.006 m/s
Zahradnik et al. [8]
εG = UG /(2.02UG + 0.257)
D = 0.14, 0.15, 0.29 m perforated plate (d0 = 0.5, 1.6 mm) air–water, ethanol solution
0.02 ≤ UG ≤ 0.13 m/s 3 ≤ µL ≤ 110 mPa s
Pohorecki et al. [12]
εG = 0.383 UG0.65 σL−0.52
D = 0.3 m sparger (d0 = 1–5 mm), nitrogen-cyclohexane
0.002 ≤ UG ≤ 0.055 m/s UL = 0.0014 m/s 0.2 ≤ P ≤ 1.1 MPa 30 ≤ T ≤ 160 ◦ C
Akita and Yoshida [7]
εG /(1 − εG )4 = 0.2(D3 ρL g/σL ) 0.083 (D3 ρL2 g/µ2L ) (UG /(gD)0.5 )
D = 0.152 m single-nozzle (d0 = 5 mm) air, O2 , CO2 , He-water, glycol solution, methanol solution
0.005 ≤ UG ≤ 0.149 m/s 22.3 ≤ σ L ≤ 74.2 mN/m 790 ≤ ρL ≤ 1590 kg/m3 0.58 ≤ µL ≤ 21.2 mPa s
Shawaqfeh [2]
εG = (0.775 ± 0.040)UG (0.657 ± 0.03)
D = 0.074 m concentric distributor, air–water
0.094 ≤ UG ≤ 0.41 m/s 0 ≤ UL ≤ 0.0116 m/s
Anabtawi et al. [11]
εG = 0.362 UG0.60 µ−0.24 H −0.38 L static bed height)
D = 0.074 m single-nozzle sprayer (d0 = 10 mm) air–oil
0.0018 ≤ UG ≤ 0.28 m/s 0.0248 ≤ σ L ≤ 0.035 N/m 906 ≤ ρL ≤ 928 kg/m3 0.063 ≤ µL ≤ 0.320 Pa s
= 0.728U − 0.458U2
+ 0.0975U3
0.125
(H:
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Fig. 4. Comparison between the experimental and calculated values of the gas holdup.
1 Rxx (τ) = lim T →∞ T
T
x(t)x(t + τ) dt
(10)
0
where T and τ are the whole time length of the time series and time lag, respectively. Drahos et al. [28] have shown that the interesting frequencies of the PSDF spectrum range from 0 to 20 Hz for bubble columns. Fig. 5 shows the PSDF of the differential pressure at two different gas velocities, UG = 0.07 and 0.18 m/s. The PSDFs show a different trend for the each gas velocity. When the gas velocity is 0.07 m/s, there is a relatively weak contribution to the power spectrum of the frequencies between 2 and 6 Hz compared to those when the gas velocity is 0.18 m/s. The PSDF, at a lower frequency, is
Fig. 5. PSDF of the differential pressure fluctuations at two different gas velocities.
Fig. 6. Typical example of ACF curves with the gas velocity.
much larger for the slug flow regime than for the bubbleslug flow regime. Vial et al. [19] noted that the PSDF, in the heterogeneous flow regime, exhibits a broader peak in the range 3–5 Hz. These results suggest a potential method for determining a regime’s transition. The ACF of the pressure fluctuation signals is one of the useful tools for a spectral analysis and can provide quantitative information on the pressure fluctuations [19–21]. The typical ACF curves with the gas velocity are shown in Fig. 6. As can be seen in this figure, the ACF shows a more gradual and oscillatory decrease tendency with an increasing time lag when the gas velocity is 0.07 m/s compared to those of 0.18 and 0.22 m/s. Whereas, in the case of 0.18 and 0.22 m/s, they have a similar changing trend with the time lag, which means they are involved in the same flow regime. As a consequence, it is anticipated that the flow regime transition can be detected by the ACF curve. Vial et al. [19,20] have shown that the ACF shape reflects the classical random process in the homogeneous regime, but in the heterogeneous flow regimes, it is characterized by a quasi-periodic component superimposed on random processes. The decreasing trend of the magnitude of the ACF can be represented by the expression [21] Rxx (τ) τ R xx (τ) = = exp − cos(2πf0 τ) (11) Rxx (0) τ0 In Eq. (11), τ 0 and f0 are the characteristic time of the flow structure and the characteristic frequency, which corresponds to the frequency of the peak observation in the PSDF, respectively. Fig. 7 shows that Eq. (11) is in good agreement with the ACF evaluated from the experimental data. The optimum values of τ 0 and f0 are evaluated through the Levenberg–Marquardt method [29]. The Levenberg–Marquardt method is one of the most widely used non-linear curve fitting methods, which is very useful for
Y.-J. Cho et al. / Chemical Engineering and Processing 44 (2005) 1054–1062
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Fig. 7. Comparison of the ACF based on the model with those obtained experimentally.
Fig. 9. Effects of the gas velocity on the gas phase axial dispersion coefficient with the variation of the molten salt temperature.
finding solutions to complex fitting problems. The characteristic time, τ 0 , has been used for the flow regime identification [19–21]. The changing tendency of the characteristic time with the gas velocity is presented in Fig. 8 together with the result of the model calculation proposed by Vial et al. [19] using the dimension structure and liquid circulation velocity. In this figure, the characteristic time at 870 ◦ C shows a decreasing trend then is nearly constant when the gas velocity is greater than 0.15 m/s in the MSO reactor. This trend is similar to that of the gas holdup (Fig. 2). Vial et al. [19] observed that the characteristic time, in a heteroge-
neous flow regime, tends to decrease as the flow becomes more chaotic, which accords well with the finding of Fan et al. [21] in a liquid–solid fluidized bed. The difference of the values of the characteristic time between this study and the model calculation may be attributed to the sharp difference of the liquid phase properties, density, surface tension, viscosity.
Fig. 8. Changing tendency of the characteristic time with the gas velocity.
3.3. Axial gas phase dispersion The gas phase dispersion coefficients were plotted as a function of the gas velocity in Fig. 9. The dispersion coefficient increases gradually at low gas velocities and then reaches an asymptotic value with a further increase of the gas velocity. The effect of the gas velocity on the gas phase axial dispersion is similar to that on the gas holdup (Fig. 2) and on the characteristic time (Fig. 8). Increase in the gas velocity leads to an increase in the turbulence in the molten sodium carbonate salt bed and a consequent increase in the gas phase mixing in both the axial and radial directions. However, a further increase of the gas velocity above 0.15 m/s makes the flow produce a plug-flow like behavior, which reduces the formation frequency of the micro-scale eddies in the bed resulting in a weak axial dispersion phenomena. Micro-eddies can increase the contacting frequencies between the fluid elements and consequently increase the phase mixing in the multi-phase flow systems [18]. It seems that at a higher gas velocity condition (above 0.15 m/s), the gas phase dispersion coefficients do not increase with a further increase of the gas velocity due to the plug-flow like behavior in the MSO reactor. Fig. 9 also illustrates the effects of the temperature on the gas phase dispersion coefficient. As can be noted from this
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3.4. Correlation The drift-flux model has been frequently used for the fitting of the gas holdup data [2,8]. Based on the drift-flux model, the gas holdup, in a liquid-batch system, is fitted in the form of Eq. (12) [8,19,20]. εG =
UG C 0 UG + C 1
(12)
where C0 is a constant measure of the interaction of the void and velocity distribution and C1 is the weighted average drift velocity accounting for the local slip. C1 is often taken as the rise velocity of a bubble in an infinite medium. Another method to fit the gas holdup data has been provided by several researchers as below [2,9]. εG = aUGb
Fig. 10. Comparison between the experimental and calculated values of the gas phase axial dispersion coefficients.
figure, the gas phase axial dispersion coefficient increases with the temperature. As we have seen, the elevated temperature increases the gas holdup in the MSO reactor (Fig. 2), and this result induces the increase of the gas phase axial dispersion phenomena. A comparison of the present data with the literature correlation data is shown in Fig. 10. The gas phase dispersion coefficients obtained in this research are smaller than those obtained by Joshi [30], Mangartz and Pilhofer [31] and Field and Davidson [22], but higher than that by Deckwer et al. [33]. The gas phase dispersion strongly depends on the liquid properties, especially the liquid density. An increase of the liquid density results in an enhancement of the buoyancy forces acting on the gas bubbles, which makes the flow pattern a plug-flow like flow, which induces a mixing intensity in both the axial and radial directions. It is suspected that the radial gas holdup variation is less prominent in the MSO reactor when compared to the water system due to the large density difference of the phases. Therefore, lower gas phase dispersion values are observed in the molten salt system when compared to the water system. The correlation proposed by Deckwer et al. [33] has been used to determine the dispersion coefficient of a homogeneous bubble flow regime. The gas phase dispersion in a homogeneous regime differs from that in a heterogeneous flow regime. In the homogeneous flow regime, smaller bubbles, which have a narrow size distribution, arise without hindering each other [16–18]. So a very weak liquid circulation takes place in the bed. The dispersion coefficient of the small bubbles is taken equal to the liquid phase dispersion coefficient. Therefore, correlation by Deckwer et al. [33] is same to that of the liquid phase. It has been generally understood that the gas phase dispersion coefficients are roughly 2–10 times greater than the liquid phase dispersion coefficients [17].
(13)
Fig. 11(a) shows a typical example of a fitting result of the model equations, and the comparison between the experimental and correlated value of the gas holdup is shown in Fig. 11(b). The resulting values for the best fit of Eqs. (12) and (13) are listed in Table 3 with the temperature. As can be seen in Fig. 11(b), the best correlation of the gas holdup is accomplished by the drift-flux model (Eq. (12)) in the MSO reactor.
Fig. 11. Typical example of a fitting result of the model equations (a) and the comparison between the experimental and correlated value of the gas holdup (b).
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Table 3 Resulting values for the best fit of Eqs. (12) and (13)
Appendix A: Nomenclature
T (◦ C)
C0 , C1 drift flux parameters in Eq. (12) C(t) tracer gas concentration at exit of reactor at time t (ppm) Do orifice diameter (m) DZ,G axial gas phase dispersion coefficient (m2 /s) db,0 initial bubble diameter (m) db,max maximum stable bubble diameter (m) E(t) exit-age distribution function (s−1 ) g gravity acceleration (m/s2 ) H reactor height (m) Pe Peclet number (=UG H/εG DZ,G ) mean residence time (s) tm UG superficial gas velocity (m/s) Ur relative velocity between the gas and liquid phase (m/s)
870 900 930 970
Parameters UG /εG = C1 + Co UG
y = aXb
C1
Co
a
0.393 0.381 0.370 0.363
3.060 2.850 2.703 2.591
0.468 0.501 0.527 0.548
b ± ± ± ±
0.04 0.04 0.06 0.06
0.525 0.533 0.539 0.543
± ± ± ±
0.08 0.04 0.06 0.06
The present data of the axial gas phase dispersion coefficients in terms of the Peclet number in the MSO reactor were correlated with the dimensionless experimental variables as [10]: −0.0070 UG H UG µL 0.3594 µ4L g Pe= = 418.87 (14) εG DZ,G ρL ρL σL3 with the correlation coefficient of 0.94. Eq. (14) covers the following range of variables: 4.37 ≤ Pe ≤ 8.89, 3.04 × 10−12 ≤ µ4L g/ρL σL3 ≤ 1.18 × 10−10 , 3.91 × 10−4 ≤ UG µL /ρL ≤ 4.26 × 10−3 .
4. Conclusion In the MSO reactor, the gas phase holdup increases with an increase of the molten sodium carbonate salt temperature, but shows a different increasing trend at gas velocities above 0.15 m/s under all the experimental temperature condition. It is found that the gas phase axial dispersion coefficient in the MSO reactor is smaller than that in the air–water bubble column due to the higher liquid density. The dispersion coefficient increases gradually at low gas velocities and then reaches an asymptotic value with a further increase of the gas velocity. The effects of the operating variables on the flow regime characteristics have been successfully interpreted by means of a spectral analysis of the differential pressure fluctuations. The experimentally obtained gas phase holdup is best fitted via the drift-flux model, and the gas phase axial dispersion coefficient has been correlated in terms of the Peclet number in the MSO reactor conditions with the dimensionless experimental variables. These results may be useful for the design and operation of the MSO system.
Acknowledgement This study has been carried out under the Nuclear R&D Program by the Korean Ministry of Science and Technology.
Greek letters εG gas phase holdup µL liquid viscosity (Pa s) ρL liquid density (kg/m3 ) σL liquid surface tension (dyne/cm) σ2 variance of the residence time distribution (s2 )
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