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Minimum fluidization velocities for supercritical water fluidized bed within the range of 633–693 K and 23–27 MPa
International Journal of Multiphase Flow 49 (2013) 78–82
Contents lists available at SciVerse ScienceDirect
International Journal of Multiphase Flow j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / i j m u l fl o w
Minimum fluidization velocities for supercritical water fluidized bed within the range of 633–693 K and 23–27 MPa Youjun Lu ⇑, Liang Zhao, Qiang Han, Liping Wei, Ximin Zhang, Liejin Guo, Jinjia Wei State Key Laboratory of Multiphase Flow in Power Engineering (SKLMF), Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China
a r t i c l e
i n f o
Article history: Received 11 March 2012 Received in revised form 8 October 2012 Accepted 9 October 2012 Available online 18 October 2012 Keywords: Supercritical water Fluidized bed Frictional pressure drop Minimum fluidization velocity
a b s t r a c t Supercritical water fluidized bed is a new reactor concept for biomass gasification. In this paper, an experimental study on the hydrodynamics of a supercritical water fluidized bed was conducted. The frictional pressure drops of a fixed bed and a fluidized bed were measured for a temperature ranging from 633 to 693 K and pressure ranging from 23 to 27 MPa. The results show that the Ergun formula for calculating the frictional pressure drop of a fixed bed can still be applied in supercritical water conditions. The average deviation between Ergun formula and experiment results is 13.3%. A predicting correlation for the minimum fluidization velocity in a supercritical water fluidized bed was obtained based on the experimental results of a fixed bed and the fluidized bed pressure drop. The average error between the correlation and experiment results was about 3.1%. The results in this paper are useful for the design of SCW fluidized bed. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Supercritical water gasification is a promising technology for wet biomass utilization (Hao et al., 2003). The fluidized bed reactor concept was proposed by Matsumura and Minowa (2004) to gasify wet biomass in supercritical water (SCW). After that, Lu et al. (2008) successfully developed a SCW fluidized bed to avoid reactor plugging which often takes place in the tubular reactor. However, some problems, such as instability in the composition of the product gas, nonuniform fluidized bed temperature and particles overflowing from the reactor, existed because the design of the SCW fluidized bed was based on the theory of classical fluidized bed. It is necessary to study the hydrodynamics of a SCW fluidized bed for the design of a SCW fluidized bed. A lot of studies on hydrodynamics in classical fluidized bed have been conducted (Gamwo et al., 1999; Shuyan et al., 2009; Hosseini et al., 2010). Some researchers also studied the hydrodynamics in different kinds of fluidized beds operating at high temperature and pressure, but those reports are mainly about supercritical CO2 fluidized beds. Few experimental studies on the hydrodynamics in SCW fluidized beds were reported in the literature. Tarmy et al. (1984) studied the three-phase flow characteristics of fluidized beds under a pressure of 17 MPa and temperature of 723 K. Liu et al. (1996) studied liquid–solid fluidized bed, in which solid particles (Geldart Groups A, B and D) were fluidized by supercritical CO2 fluid. A criterion was also proposed to determine the fluid⇑ Corresponding author. Tel.: +86 29 8266 4345; fax: +86 29 8266 9033. E-mail address: [email protected] (Y. Lu). 0301-9322/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijmultiphaseflow.2012.10.005
ized regime. Jiang et al. (1997) investigated the bed contraction and expansion in a high pressure and high temperature gas–liquid–solid fluidized bed. The bed was operated at pressures ranging from 0.1 to 17.4 MPa and temperatures from 293 to 367 K. The bubble dynamic behavior in the bed was visualized through transparent windows. The effect of pressure and temperature on the bed expansion and contraction is mainly due to the variation of the bubbles behavior and the changes of liquid properties. Marzocchella and Salatino (2000) studied the fluidized characteristics of two granular materials belonging to Geldart Groups A–B powders in CO2 at 308 K and at 0.1–8 MPa. Vogt et al. (2005) carried out a comprehensive experimental study to investigate the fluidization behavior with supercritical carbon dioxide at pressures up to 30 MPa for various solids which behave as Geldart A and B powders, respectively, under ambient conditions. From pressure drop measurements, minimum fluidizing velocities and bed voidages were determined. Potic et al. (2005) introduced the concept of a micro-fluidized bed, which was a cylindrical quartz reactor with an internal diameter of only 1 mm used for process conditions up to 773 K and 244 bar. Properties of the micro-fluidized bed such as the minimum fluidization velocity, the minimum bubbling velocity, bed expansion, and identification of the fluidization regime were investigated by visual inspection. However, the wall effects of micro-fluidized bed made the application of research results more difficult. In this paper, the hydrodynamics of a SCW fluidized bed was studied. The frictional pressure drop of fixed beds and fluidized beds were measured with temperature ranging from 633 to 693 K and pressure ranges from 23 to 27 MPa. An experimental
79
Y. Lu et al. / International Journal of Multiphase Flow 49 (2013) 78–82
10
700 ρ
23MPa
ρ /kg.m-3
2. Experimental apparatus and procedure Fig. 1 presents the schematic diagram of the setup for studying the hydrodynamics of the SCW fluidized bed. The setup consists of a SCW fluidized bed test section and other additional elements including a tank, high-pressure pump, heat exchanger, pre-heater, cooler, back pressure regulator and so on. The SCW fluidized bed test section is constructed of stainless steel with a bed internal diameter of 35 mm and length of 600 mm. It was designed for temperatures up to 823 K and pressures up to 30 MPa. A porous metal foam with bore diameter of 30 lm was used as the distributor of the SCW fluidized bed test section, and a metal foam filter is installed in the exit of the fluidized bed to avoid the escape of the bed materials. The flow rate of the pumps is measured by a mass flow meter (RHOENIK, Germany). The superficial velocity can be determined by the mass flow rate, water density and geometry of the test section. The water density and viscosity of supercritical water using in this paper are calculated by IAPWS-IF97 (Wagner et al., 2000), and Fig. 2 shows the variations of water density and viscosity with temperature and pressure. The temperature of SCW fluidized bed is measured by two type K thermocouples in good thermal contact with the inlet and outlet of the SCW fluidized bed. The temperature difference between inlet and outlet can be less than 1 K because of good thermal insulation of the test section. Therefore, the average of the two measured temperatures is used as the bed temperature. The pressure in the fluidized bed is measured by a pressure transducer (PA23/8465, Keller) located at the upper part of the test section. The frictional pressure drop of the fluidized bed is measured by four differential pressure sensors (Foxboro, USA). Fig. 3 shows the position of the four sensors in the test section. The measured pressure difference between the pressure ports includes two parts: the frictional pressure drop and supercritical water’s gravity pressure drop. The bed frictional pressure drop should equal the mea-
8
25MPa
μ
500
27MPa
400 6 300 200
23MPa 25MPa 27MPa
-5
600
μ / 10 pa.s
correlation for calculating minimum fluidization velocities of a SCW fluidized bed were obtained, which is useful for design of a SCW fluidized bed.
4
100 0
2 620
640
660
680
700
T/K Fig. 2. The variations of water density and viscosity with temperature and pressure.
sured differential pressure minus the fluid gravitational pressure drop. The bed height for the fluidized bed is determined by measuring the differential pressures by four differential pressure sensors, as shown in Fig. 3. Ideally, the lines connecting the measurement ports and pressure probes are filled with supercritical water of the same temperature. The pressure difference between the pressure ports is equal to the measured pressure difference minus the hydrostatic pressure of water in the lines. If the resulting pressure is compared to a reference pressure like the pressure at the surface of the fluidized bed, the resulting plot can be used to determine the height of the fluidized bed surface (Vogt et al., 2005). Quartz sand particles are used as bed material in the experiments for its stable physicochemical property at high temperature. Its real density is measured as 2620 kg/m3 by a dripping water method. And the bulk density is 1467 kg/m3 measured using a metering tank and electronic balance. A digital microscope (VHX600E, KEYENCE) was used to determine particle size distribution. Fig. 4 displays the results of the particle size distribution. As shown in Fig. 4, the quartz sand particles used in this paper have different sizes and the diameters are in the range of 0.16–0.32 mm. For the
Fig. 1. Schematic diagram of experimental setup.
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Y. Lu et al. / International Journal of Multiphase Flow 49 (2013) 78–82
standing the hydrodynamics of a fixed bed. Fig. 5 displays the bed pressure drop versus superficial velocity (u) at 633–699 K and 23– 27 MPa. The bed pressure drop increases with increasing superficial velocity until the superficial velocity exceeds the minimum fluidization velocity, which has been proven to be a universal phenomenon in fluidization engineering. It can be seen from Fig. 5 that the same phenomenon can be observed in a SCW fluidized bed. The fixed bed pressure drop dramatically decreases with increasing temperature at a fixed superficial velocity as shown in Fig. 5, which can be interpreted as that the fixed bed pressure drop is in proportion to the density and viscosity which decrease with increasing temperature. The bed pressure drop can be expressed by a function of fluid flow rate, geometrical constraints of the bed and physical proper-
a
2400
Fig. 3. The distribution of differential pressure transducers in the SCW fluidized bed.
Pressure drop / Pa
2000 1600 633 K 643 K 653 K 663 K 673 K 683 K 693 K
1200 800 400
40
0 0.0
0.5
x /%
30
1.0 -2
1.5
u / 10 m⋅s
b
20
2.0
-1
2000
Pressure drop / Pa
1600 10
0 80
120
160
200
240
280
320
360
dp /μm
633 K 643 K 653 K 663 K 673 K 683 K 693 K
800
400
Fig. 4. Particle size distribution of quartz sand particles.
mixed particles, the frictional pressure drop of fixed beds and the minimum fluidization velocity can be calculated approximately using the equations for single size of particles, but with the single size particle diameter dp replaced by a mean diameter dp . The mean diameter dp is
0 0.0
0.4
0.8
1.2 -2
u / 10 m⋅s
c
1.6
2.0
-1
1600
ð1Þ
where x is the fraction of particles in size inter i. The calculated average diameter of the particles used in this paper is 213 lm. The uncertainty of experimental data is analyzed. The uncertainty of absolute pressure, differential pressure, temperature and flow rate are less than 2.17%, 0.94%, 1.02% and 2.0% respectively. 3. Results and discussion 3.1. Pressure drop in fixed bed The description of the fixed bed pressure drop is a key parameter for determining the minimum fluidization velocity and under-
Pressure drop / Pa
1 dp ¼ P ðx=d p Þi i
1200
1200 633 K 643 K 653 K 663 K 673 K 683 K 693 K
800
400
0 0.0
0.4
0.8
1.2 -2
u / 10 m⋅s
1.6
2.0
-1
Fig. 5. Bed pressure drop versus superficial velocity: (a) 23 MPa, (b) 25 MPa, (c) 27 MPa.
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Y. Lu et al. / International Journal of Multiphase Flow 49 (2013) 78–82
2400 1.2
23MPa 25MPa 27MPa
2000
1.0 -2
umf /10 m/s
1600
ΔpEr / Pa
23MPa 25Mpa 27Mpa
1200 800
0.8
0.6
400 0.4 0 0
400
800
1200
1600
2000
2400
630
640
650
ΔpEx / Pa
660
670
680
690
700
T/K
Fig. 6. Comparison of calculated bed pressure drop using Ergun equation with the experimental data at 633–693 K and 23–27 MPa. The subscript Er refers to Ergun equation, and Ex refers to experimental data.
ties of the particles. The well-known equation used for predicting the pressure drop in a fixed bed was proposed by Ergun (1952) as follows:
Dp ð1 eÞ2 lu 1 e qf u 2 ¼ 150 þ 1:75 3 2 3 L e up dp e ðup dp Þ
ð2Þ
where Dp is the pressure drop of the fixed bed. l is the fluid viscosity. qf is the fluid density. e is the voidage that can calculated from the real and bulk densities of the particles. up is the particle sphericity that is 0.67 recommended for sharp sand in literature (Masuda et al., 2006). dp is the particle diameter that is replaced here by a mean diameter dp for the mixed particles. u refers to the fluid superficial velocity. Fig. 6 compares the pressure drop calculated by the Ergun equation against the experimental measuring values. In the range of pressure from 23 to 27 MPa and temperature from 633 to 693 K, the average error between the experimental data and calculated values of Ergun formula was 13.3%. Therefore, the Ergun equation is reasonable for predicating the pressure drop in a SCW fixed bed. Vogt et al. (2005) also concluded that Ergun’s equation is suitable for supercritical carbon dioxide fixed bed. 3.2. Minimum fluidization velocity The minimum fluidization velocity (umf) serves as a critical parameter for design and operation of a fluidized bed. The determination of the minimum fluidization velocity is conventionally based on experimental testing (Rao et al., 2001; Ramos Caicedo et al., 2002). It can be seen from Fig. 5 that the pressure drop increases from zero to umf. When the superficial velocity (u) increases successively beyond umf, the pressure drop remains almost constant and equals to the effective weight of fluidized bed. Table 1 displays the effective weight of fluidized bed at different experimental pressures and temperatures. Thus, in the plot of bed pressure drop versus u, there are two linear sections, one for u < umf and another for u > umf. The interception of these two lines is de-
Fig. 7. Effects of temperature and pressure on minimum fluidization velocity.
fined as the minimum fluidization velocity. Fig. 7 displays the effects of temperature and pressure on the minimum fluidization velocity. It can be seen from this figure that umf increases with increasing temperature, but decreases with increasing pressure. In the pressure range of 23–27 MPa, water properties show dramatic changes in density, viscosity as temperature increases from 643–673 K (As shown in Fig. 2), therefore, the minimum fluidization velocity increases sharply in this temperature range. In this paper, a minimum fluidization velocity correlation for SCW fluidized beds is proposed according to experimental data in terms of the Reynolds and Archimedes numbers. The relationship between the Reynolds and Archimedes numbers can be given by,
Remf ¼ ðC 21 þ C 2 ArÞ0:5 C 1
ð3Þ
where C1 and C2 are the constant that can be fitted from experimental data. Remf is the Reynolds number at minimum fluidization velocity (umf). Ar is the Archimedes number that is expressed as: 3
Ar ¼
dp qf ðqp qf Þg
ð4Þ
l2
where qp is particle density and g is the acceleration due to gravity. The Ar and Remf number can be calculated from the experimental umf, water and particle properties. By the least squares fitting, the constant C1 and C2 contained in Eq. (3) are estimated to be 27.3 and 0.0434 respectively. Therefore, Eq. (3) can be expressed as:
Remf ¼ ð27:32 þ 0:0434 ArÞ0:5 27:3
ð5Þ
3.3. Comparison of different correlations for minimum fluidization velocity Fig. 8 compares the calculated minimum fluidization velocity using different experimental correlations proposed by Wen and Yu (1966), Babu et al. (1978), Grace (1982), Chitester et al. (1984), Thonglimp et al. (1984) and this work, with the experimental data. It can be seen from Fig. 8 that the average error of the min-
Table 1 Effective weight of fluidized bed at different pressures and temperatures.a
23 MPa 25 MPa 27 MPa a
633 K
643 K
653 K
663 K
673 K
683 K
693 K
1698.4 Pa 1469.6 Pa 1227.1 Pa
1751.1 Pa 1505.1 Pa 1252.2 Pa
1924.1 Pa 1574.4 Pa 1256.1 Pa
1991.2 Pa 1685.6 Pa 1394.5 Pa
2084.0 Pa 1736.8 Pa 1352.5 Pa
2100.1 Pa 1759.9 Pa 1387.7 Pa
2111.8 Pa 1774.6 Pa 1406.2 Pa
Effective weight = (weight of bed materials buoyancy of bed materials)/cross-sectional area of fluidized bed.
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Y. Lu et al. / International Journal of Multiphase Flow 49 (2013) 78–82
Acknowledgements
2.0
-2
umf-Cal / 10 m⋅s
-1
1.6
1.2
Correlation in this paper Wen & Yu Babu Chitester Thonglimp +20% Grace
This work is currently supported by the National Natural Science Foundation of China through contract No. 50906069 and the National Key Project for Basic Research of China (973 program) through contract No. 2009CB220000.
-20%
References
0.8
0.4
0.0 0.0
0.4
0.8
1.2 -2
umf-Exp / 10 m ⋅s
1.6
2.0
-1
Fig. 8. Comparison of experimental data with correlation prediction of minimum fluidization velocity.
imum fluidization velocity predicted by Chitester, Thonglimp and Grace’s correlations is about 10%. Babu’s correlation deviated from the experimental values too far and the average error is running to 52.5%. Rodriguez-Rojo and Cocero (2009) used the Wen and Yu (1966) correlation to predict the minimum fluidization velocity of a supercritical CO2 fluidized bed. For SCW fluidized bed, however, minimum fluidization velocities calculated by the Wen and Yu correlation are lower than the experiment value and the average error is nearly 20%, which is not so accurate but can be accepted in engineering application. The average error of the correlation presented in the present work is 3.1%. The new correlation proposed in this paper can be used for the design of SCW fluidized bed. 4. Conclusions The hydrodynamics of a SCW fluidized bed were studied by experimental methods. The work in this paper is very important for the design of SCW fluidized bed. The conclusions of this work can be summarized as follows: (1) The Ergun equation is reasonable for predicating the pressure drop in a SCW fixed bed. In the range of pressures from 23 to 27 MPa and temperatures from 633 to 693 K, the average error between experimental results and Ergun formula was 13.3%. (2) A new correlation for minimum fluidization velocity was obtained through a series of experiments on a SCW fluidized bed. This experimental correlation can be used to predict minimum fluidization velocity of SCW fluidized bed. The Wen and Yu equation for minimum fluidization velocity calculation can be also accepted in engineering application. Our future work will focus on bed expansion, solid distribution, heat transfer and modeling of SCW fluidized bed.
Babu, S., Shah, B., Talwalkar, A., 1978. Fluidization correlations for coal gasification materials – minimum fluidization velocity and fluidized bed expansion ratio. AIChE J. Sympos. Ser. 74, 176–186. Chitester, D.C., Kornosky, R.M., Fan, L.S., Danko, J.P., 1984. Characteristics of fluidization at high pressure. Chem. Eng. Sci. 39, 253–261. Ergun, S., 1952. Fluid flow through packed columns. Chem. Eng. Prog. 48, 89–94. Gamwo, I.K., Soong, Y., Lyczkowski, R.W., 1999. Numerical simulation and experimental validation of solids flows in a bubbling fluidized bed. Powder Technol. 103, 117–129. Grace, J.R., 1982. Handbook of Multiphase Systems. Hemisphere Publ. Corp, Washington. Hao, X.H., Guo, L.J., Mao, X., Zhang, X.M., Chen, X.J., et al., 2003. Hydrogen production from glucose used as a model compound of biomass gasified in supercritical water. Int. J. Hydrogen Energy 28, 55–64. Hosseini, S.H., Ahmadi, G., Rahimi, R., Zivdar, M., Esfahany, M.N., 2010. CFD studies of solids hold-up distribution and circulation patterns in gas–solid fluidized beds. Powder Technol. 200, 202–215. Jiang, P., Luo, X., Lin, T.J., Fan, L.S., 1997. High temperature and high pressure threephase fluidization-bed expansion phenomena 1. Powder Technol. 90, 103–113. Liu, D., Kwauk, M., Li, H., 1996. Aggregative and particulate fluidization – the two extremes of a continuous spectrum. Chem. Eng. Sci. 51, 4045–4063. Lu, Y., Jin, H., Guo, L., Zhang, X., Cao, C., Guo, X., 2008. Hydrogen production by biomass gasification in supercritical water with a fluidized bed reactor. Int. J. Hydrogen Energy 33, 6066–6075. Marzocchella, A., Salatino, P., 2000. Fluidization of solids with CO2 at pressures from ambient to supercritical. AIChE J. 46, 901–910. Masuda, H., Higashitani, K., Yoshida, H., 2006. Powder Technology Handbook. CRC Press. Matsumura, Y., Minowa, T., 2004. Fundamental design of a continuous biomass gasification process using supercritical water fluidized bed. Int. J. Hydrogen Energ. 29, 701–707. Potic, B., Kersten, S., Ye, M., Van der Hoef, M., Kuipers, J., Van Swaaij, W., 2005. Fluidization with hot compressed water in micro-reactors. Chem. Eng. Sci. 60, 5982–5990. Ramos Caicedo, G., Garcia Ruiz, M., Prieto Marques, J.J., Guardiola Soler, J., 2002. Minimum fluidization velocities for gas–solid 2D beds. Chem. Eng. Process. 41, 761–764. Rao, R., Ram, T., Bheemarasetti, J., 2001. Minimum fluidization velocities of mixtures of biomass and sands. Energy 26, 633–644. Rodriguez-Rojo, S., Cocero, M., 2009. Supercritical fluidized bed modeling. J. Supercrit. Fluid. 50, 54–60. Shuyan, W., Xiang, L., Huilin, L., Long, Y., Dan, S., Yurong, H., Yonglong, D., 2009. Numerical simulations of flow behavior of gas and particles in spouted beds using frictional-kinetic stresses model. Powder Technol. 196, 184–193. Tarmy, B., MIN, C., Coulaloglou, C., Ponzi, P., 1984. Hydrodynamic characteristics of three phase reactors. Chem. Eng., 18–23. Thonglimp, V., Hiquily, N., Laguerie, C., 1984. Vitesse minimale de fluidisation et expansion des couches fluidisées par un gaz. Powder Technol. 38, 233–253. Vogt, C., Schreiber, R., Brunner, G., Werther, J., 2005. Fluid dynamics of the supercritical fluidized bed. Powder Technol. 158, 102–114. Wagner, W., Cooper, J.R., Dittmann, A., Kijima, J., Kretzschmar, H.-J., Kruse, A., et al., 2000. The IAPWS Industrial formulation 1997 for the thermodynamic properties of water and steam. J. Eng. Gas Turb Power 122, 150–182. Wen, C.Y., Yu, Y.H., 1966. Mechanics of Fluidization. Chem. Eng. Prog. Symp. 62, 100–111.
Contents lists available at SciVerse ScienceDirect
International Journal of Multiphase Flow j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / i j m u l fl o w
Minimum fluidization velocities for supercritical water fluidized bed within the range of 633–693 K and 23–27 MPa Youjun Lu ⇑, Liang Zhao, Qiang Han, Liping Wei, Ximin Zhang, Liejin Guo, Jinjia Wei State Key Laboratory of Multiphase Flow in Power Engineering (SKLMF), Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China
a r t i c l e
i n f o
Article history: Received 11 March 2012 Received in revised form 8 October 2012 Accepted 9 October 2012 Available online 18 October 2012 Keywords: Supercritical water Fluidized bed Frictional pressure drop Minimum fluidization velocity
a b s t r a c t Supercritical water fluidized bed is a new reactor concept for biomass gasification. In this paper, an experimental study on the hydrodynamics of a supercritical water fluidized bed was conducted. The frictional pressure drops of a fixed bed and a fluidized bed were measured for a temperature ranging from 633 to 693 K and pressure ranging from 23 to 27 MPa. The results show that the Ergun formula for calculating the frictional pressure drop of a fixed bed can still be applied in supercritical water conditions. The average deviation between Ergun formula and experiment results is 13.3%. A predicting correlation for the minimum fluidization velocity in a supercritical water fluidized bed was obtained based on the experimental results of a fixed bed and the fluidized bed pressure drop. The average error between the correlation and experiment results was about 3.1%. The results in this paper are useful for the design of SCW fluidized bed. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Supercritical water gasification is a promising technology for wet biomass utilization (Hao et al., 2003). The fluidized bed reactor concept was proposed by Matsumura and Minowa (2004) to gasify wet biomass in supercritical water (SCW). After that, Lu et al. (2008) successfully developed a SCW fluidized bed to avoid reactor plugging which often takes place in the tubular reactor. However, some problems, such as instability in the composition of the product gas, nonuniform fluidized bed temperature and particles overflowing from the reactor, existed because the design of the SCW fluidized bed was based on the theory of classical fluidized bed. It is necessary to study the hydrodynamics of a SCW fluidized bed for the design of a SCW fluidized bed. A lot of studies on hydrodynamics in classical fluidized bed have been conducted (Gamwo et al., 1999; Shuyan et al., 2009; Hosseini et al., 2010). Some researchers also studied the hydrodynamics in different kinds of fluidized beds operating at high temperature and pressure, but those reports are mainly about supercritical CO2 fluidized beds. Few experimental studies on the hydrodynamics in SCW fluidized beds were reported in the literature. Tarmy et al. (1984) studied the three-phase flow characteristics of fluidized beds under a pressure of 17 MPa and temperature of 723 K. Liu et al. (1996) studied liquid–solid fluidized bed, in which solid particles (Geldart Groups A, B and D) were fluidized by supercritical CO2 fluid. A criterion was also proposed to determine the fluid⇑ Corresponding author. Tel.: +86 29 8266 4345; fax: +86 29 8266 9033. E-mail address: [email protected] (Y. Lu). 0301-9322/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijmultiphaseflow.2012.10.005
ized regime. Jiang et al. (1997) investigated the bed contraction and expansion in a high pressure and high temperature gas–liquid–solid fluidized bed. The bed was operated at pressures ranging from 0.1 to 17.4 MPa and temperatures from 293 to 367 K. The bubble dynamic behavior in the bed was visualized through transparent windows. The effect of pressure and temperature on the bed expansion and contraction is mainly due to the variation of the bubbles behavior and the changes of liquid properties. Marzocchella and Salatino (2000) studied the fluidized characteristics of two granular materials belonging to Geldart Groups A–B powders in CO2 at 308 K and at 0.1–8 MPa. Vogt et al. (2005) carried out a comprehensive experimental study to investigate the fluidization behavior with supercritical carbon dioxide at pressures up to 30 MPa for various solids which behave as Geldart A and B powders, respectively, under ambient conditions. From pressure drop measurements, minimum fluidizing velocities and bed voidages were determined. Potic et al. (2005) introduced the concept of a micro-fluidized bed, which was a cylindrical quartz reactor with an internal diameter of only 1 mm used for process conditions up to 773 K and 244 bar. Properties of the micro-fluidized bed such as the minimum fluidization velocity, the minimum bubbling velocity, bed expansion, and identification of the fluidization regime were investigated by visual inspection. However, the wall effects of micro-fluidized bed made the application of research results more difficult. In this paper, the hydrodynamics of a SCW fluidized bed was studied. The frictional pressure drop of fixed beds and fluidized beds were measured with temperature ranging from 633 to 693 K and pressure ranges from 23 to 27 MPa. An experimental
79
Y. Lu et al. / International Journal of Multiphase Flow 49 (2013) 78–82
10
700 ρ
23MPa
ρ /kg.m-3
2. Experimental apparatus and procedure Fig. 1 presents the schematic diagram of the setup for studying the hydrodynamics of the SCW fluidized bed. The setup consists of a SCW fluidized bed test section and other additional elements including a tank, high-pressure pump, heat exchanger, pre-heater, cooler, back pressure regulator and so on. The SCW fluidized bed test section is constructed of stainless steel with a bed internal diameter of 35 mm and length of 600 mm. It was designed for temperatures up to 823 K and pressures up to 30 MPa. A porous metal foam with bore diameter of 30 lm was used as the distributor of the SCW fluidized bed test section, and a metal foam filter is installed in the exit of the fluidized bed to avoid the escape of the bed materials. The flow rate of the pumps is measured by a mass flow meter (RHOENIK, Germany). The superficial velocity can be determined by the mass flow rate, water density and geometry of the test section. The water density and viscosity of supercritical water using in this paper are calculated by IAPWS-IF97 (Wagner et al., 2000), and Fig. 2 shows the variations of water density and viscosity with temperature and pressure. The temperature of SCW fluidized bed is measured by two type K thermocouples in good thermal contact with the inlet and outlet of the SCW fluidized bed. The temperature difference between inlet and outlet can be less than 1 K because of good thermal insulation of the test section. Therefore, the average of the two measured temperatures is used as the bed temperature. The pressure in the fluidized bed is measured by a pressure transducer (PA23/8465, Keller) located at the upper part of the test section. The frictional pressure drop of the fluidized bed is measured by four differential pressure sensors (Foxboro, USA). Fig. 3 shows the position of the four sensors in the test section. The measured pressure difference between the pressure ports includes two parts: the frictional pressure drop and supercritical water’s gravity pressure drop. The bed frictional pressure drop should equal the mea-
8
25MPa
μ
500
27MPa
400 6 300 200
23MPa 25MPa 27MPa
-5
600
μ / 10 pa.s
correlation for calculating minimum fluidization velocities of a SCW fluidized bed were obtained, which is useful for design of a SCW fluidized bed.
4
100 0
2 620
640
660
680
700
T/K Fig. 2. The variations of water density and viscosity with temperature and pressure.
sured differential pressure minus the fluid gravitational pressure drop. The bed height for the fluidized bed is determined by measuring the differential pressures by four differential pressure sensors, as shown in Fig. 3. Ideally, the lines connecting the measurement ports and pressure probes are filled with supercritical water of the same temperature. The pressure difference between the pressure ports is equal to the measured pressure difference minus the hydrostatic pressure of water in the lines. If the resulting pressure is compared to a reference pressure like the pressure at the surface of the fluidized bed, the resulting plot can be used to determine the height of the fluidized bed surface (Vogt et al., 2005). Quartz sand particles are used as bed material in the experiments for its stable physicochemical property at high temperature. Its real density is measured as 2620 kg/m3 by a dripping water method. And the bulk density is 1467 kg/m3 measured using a metering tank and electronic balance. A digital microscope (VHX600E, KEYENCE) was used to determine particle size distribution. Fig. 4 displays the results of the particle size distribution. As shown in Fig. 4, the quartz sand particles used in this paper have different sizes and the diameters are in the range of 0.16–0.32 mm. For the
Fig. 1. Schematic diagram of experimental setup.
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Y. Lu et al. / International Journal of Multiphase Flow 49 (2013) 78–82
standing the hydrodynamics of a fixed bed. Fig. 5 displays the bed pressure drop versus superficial velocity (u) at 633–699 K and 23– 27 MPa. The bed pressure drop increases with increasing superficial velocity until the superficial velocity exceeds the minimum fluidization velocity, which has been proven to be a universal phenomenon in fluidization engineering. It can be seen from Fig. 5 that the same phenomenon can be observed in a SCW fluidized bed. The fixed bed pressure drop dramatically decreases with increasing temperature at a fixed superficial velocity as shown in Fig. 5, which can be interpreted as that the fixed bed pressure drop is in proportion to the density and viscosity which decrease with increasing temperature. The bed pressure drop can be expressed by a function of fluid flow rate, geometrical constraints of the bed and physical proper-
a
2400
Fig. 3. The distribution of differential pressure transducers in the SCW fluidized bed.
Pressure drop / Pa
2000 1600 633 K 643 K 653 K 663 K 673 K 683 K 693 K
1200 800 400
40
0 0.0
0.5
x /%
30
1.0 -2
1.5
u / 10 m⋅s
b
20
2.0
-1
2000
Pressure drop / Pa
1600 10
0 80
120
160
200
240
280
320
360
dp /μm
633 K 643 K 653 K 663 K 673 K 683 K 693 K
800
400
Fig. 4. Particle size distribution of quartz sand particles.
mixed particles, the frictional pressure drop of fixed beds and the minimum fluidization velocity can be calculated approximately using the equations for single size of particles, but with the single size particle diameter dp replaced by a mean diameter dp . The mean diameter dp is
0 0.0
0.4
0.8
1.2 -2
u / 10 m⋅s
c
1.6
2.0
-1
1600
ð1Þ
where x is the fraction of particles in size inter i. The calculated average diameter of the particles used in this paper is 213 lm. The uncertainty of experimental data is analyzed. The uncertainty of absolute pressure, differential pressure, temperature and flow rate are less than 2.17%, 0.94%, 1.02% and 2.0% respectively. 3. Results and discussion 3.1. Pressure drop in fixed bed The description of the fixed bed pressure drop is a key parameter for determining the minimum fluidization velocity and under-
Pressure drop / Pa
1 dp ¼ P ðx=d p Þi i
1200
1200 633 K 643 K 653 K 663 K 673 K 683 K 693 K
800
400
0 0.0
0.4
0.8
1.2 -2
u / 10 m⋅s
1.6
2.0
-1
Fig. 5. Bed pressure drop versus superficial velocity: (a) 23 MPa, (b) 25 MPa, (c) 27 MPa.
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Y. Lu et al. / International Journal of Multiphase Flow 49 (2013) 78–82
2400 1.2
23MPa 25MPa 27MPa
2000
1.0 -2
umf /10 m/s
1600
ΔpEr / Pa
23MPa 25Mpa 27Mpa
1200 800
0.8
0.6
400 0.4 0 0
400
800
1200
1600
2000
2400
630
640
650
ΔpEx / Pa
660
670
680
690
700
T/K
Fig. 6. Comparison of calculated bed pressure drop using Ergun equation with the experimental data at 633–693 K and 23–27 MPa. The subscript Er refers to Ergun equation, and Ex refers to experimental data.
ties of the particles. The well-known equation used for predicting the pressure drop in a fixed bed was proposed by Ergun (1952) as follows:
Dp ð1 eÞ2 lu 1 e qf u 2 ¼ 150 þ 1:75 3 2 3 L e up dp e ðup dp Þ
ð2Þ
where Dp is the pressure drop of the fixed bed. l is the fluid viscosity. qf is the fluid density. e is the voidage that can calculated from the real and bulk densities of the particles. up is the particle sphericity that is 0.67 recommended for sharp sand in literature (Masuda et al., 2006). dp is the particle diameter that is replaced here by a mean diameter dp for the mixed particles. u refers to the fluid superficial velocity. Fig. 6 compares the pressure drop calculated by the Ergun equation against the experimental measuring values. In the range of pressure from 23 to 27 MPa and temperature from 633 to 693 K, the average error between the experimental data and calculated values of Ergun formula was 13.3%. Therefore, the Ergun equation is reasonable for predicating the pressure drop in a SCW fixed bed. Vogt et al. (2005) also concluded that Ergun’s equation is suitable for supercritical carbon dioxide fixed bed. 3.2. Minimum fluidization velocity The minimum fluidization velocity (umf) serves as a critical parameter for design and operation of a fluidized bed. The determination of the minimum fluidization velocity is conventionally based on experimental testing (Rao et al., 2001; Ramos Caicedo et al., 2002). It can be seen from Fig. 5 that the pressure drop increases from zero to umf. When the superficial velocity (u) increases successively beyond umf, the pressure drop remains almost constant and equals to the effective weight of fluidized bed. Table 1 displays the effective weight of fluidized bed at different experimental pressures and temperatures. Thus, in the plot of bed pressure drop versus u, there are two linear sections, one for u < umf and another for u > umf. The interception of these two lines is de-
Fig. 7. Effects of temperature and pressure on minimum fluidization velocity.
fined as the minimum fluidization velocity. Fig. 7 displays the effects of temperature and pressure on the minimum fluidization velocity. It can be seen from this figure that umf increases with increasing temperature, but decreases with increasing pressure. In the pressure range of 23–27 MPa, water properties show dramatic changes in density, viscosity as temperature increases from 643–673 K (As shown in Fig. 2), therefore, the minimum fluidization velocity increases sharply in this temperature range. In this paper, a minimum fluidization velocity correlation for SCW fluidized beds is proposed according to experimental data in terms of the Reynolds and Archimedes numbers. The relationship between the Reynolds and Archimedes numbers can be given by,
Remf ¼ ðC 21 þ C 2 ArÞ0:5 C 1
ð3Þ
where C1 and C2 are the constant that can be fitted from experimental data. Remf is the Reynolds number at minimum fluidization velocity (umf). Ar is the Archimedes number that is expressed as: 3
Ar ¼
dp qf ðqp qf Þg
ð4Þ
l2
where qp is particle density and g is the acceleration due to gravity. The Ar and Remf number can be calculated from the experimental umf, water and particle properties. By the least squares fitting, the constant C1 and C2 contained in Eq. (3) are estimated to be 27.3 and 0.0434 respectively. Therefore, Eq. (3) can be expressed as:
Remf ¼ ð27:32 þ 0:0434 ArÞ0:5 27:3
ð5Þ
3.3. Comparison of different correlations for minimum fluidization velocity Fig. 8 compares the calculated minimum fluidization velocity using different experimental correlations proposed by Wen and Yu (1966), Babu et al. (1978), Grace (1982), Chitester et al. (1984), Thonglimp et al. (1984) and this work, with the experimental data. It can be seen from Fig. 8 that the average error of the min-
Table 1 Effective weight of fluidized bed at different pressures and temperatures.a
23 MPa 25 MPa 27 MPa a
633 K
643 K
653 K
663 K
673 K
683 K
693 K
1698.4 Pa 1469.6 Pa 1227.1 Pa
1751.1 Pa 1505.1 Pa 1252.2 Pa
1924.1 Pa 1574.4 Pa 1256.1 Pa
1991.2 Pa 1685.6 Pa 1394.5 Pa
2084.0 Pa 1736.8 Pa 1352.5 Pa
2100.1 Pa 1759.9 Pa 1387.7 Pa
2111.8 Pa 1774.6 Pa 1406.2 Pa
Effective weight = (weight of bed materials buoyancy of bed materials)/cross-sectional area of fluidized bed.
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Acknowledgements
2.0
-2
umf-Cal / 10 m⋅s
-1
1.6
1.2
Correlation in this paper Wen & Yu Babu Chitester Thonglimp +20% Grace
This work is currently supported by the National Natural Science Foundation of China through contract No. 50906069 and the National Key Project for Basic Research of China (973 program) through contract No. 2009CB220000.
-20%
References
0.8
0.4
0.0 0.0
0.4
0.8
1.2 -2
umf-Exp / 10 m ⋅s
1.6
2.0
-1
Fig. 8. Comparison of experimental data with correlation prediction of minimum fluidization velocity.
imum fluidization velocity predicted by Chitester, Thonglimp and Grace’s correlations is about 10%. Babu’s correlation deviated from the experimental values too far and the average error is running to 52.5%. Rodriguez-Rojo and Cocero (2009) used the Wen and Yu (1966) correlation to predict the minimum fluidization velocity of a supercritical CO2 fluidized bed. For SCW fluidized bed, however, minimum fluidization velocities calculated by the Wen and Yu correlation are lower than the experiment value and the average error is nearly 20%, which is not so accurate but can be accepted in engineering application. The average error of the correlation presented in the present work is 3.1%. The new correlation proposed in this paper can be used for the design of SCW fluidized bed. 4. Conclusions The hydrodynamics of a SCW fluidized bed were studied by experimental methods. The work in this paper is very important for the design of SCW fluidized bed. The conclusions of this work can be summarized as follows: (1) The Ergun equation is reasonable for predicating the pressure drop in a SCW fixed bed. In the range of pressures from 23 to 27 MPa and temperatures from 633 to 693 K, the average error between experimental results and Ergun formula was 13.3%. (2) A new correlation for minimum fluidization velocity was obtained through a series of experiments on a SCW fluidized bed. This experimental correlation can be used to predict minimum fluidization velocity of SCW fluidized bed. The Wen and Yu equation for minimum fluidization velocity calculation can be also accepted in engineering application. Our future work will focus on bed expansion, solid distribution, heat transfer and modeling of SCW fluidized bed.
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