Ind. Eng. Chem. Res. 1987,26, 967-972
967
Hydrodynamics of Turbulent Bed Contactors. 2. Pressure Drop, Bed Expansion, and Minimum Fluidizing Velocity G. V. Vunjak-Novakovii! and D. V. Vukovi6 Faculty of Technology and Metallurgy, Department of Chemical Engineering, Belgrade University, 11001 Belgrade, Yugoslavia
H. Littman* Rensselaer Polytechnic Institute, Troy, New York 12180-3590
Correlations for pressure drop, bed expansion, and minimum fluidization velocity in turbulent bed contactors are presented. They show the importance of the flow regime in which the bed is operated. The characteristics of each operating regime are discussed and compared with the characteristics of packed-bed columns. The first paper in this series dealt with operating regimes and liquid holdup in three-phase fluidized and packed-bed contactors. Two regimes of fluidized-bed operation were identified, and criteria for specifying each of them are given. Correlations for the liquid holdup in each fluidizing regime and for packed beds were presented. In this paper, we address the remaining hydrodynamic properties: pressure drop, bed expansion, minimum fluidizing velocity, and the maximum capacity of the contactor.
Literature Review Muroyama and Fan (1985) have recently published an excellent review of three-phase fluidized beds which includes tabulations of correlations for the pressure drop, bed expansion, and minimum fluidizing velocity. In our review, we will focus only on those aspects of the literature that are relevant to this paper. (a) Bed Pressure Drop. The overall pressure drop in the gas phase of a turbulent bed contactor (TBC) is the sum of losses in the bed, across the supporting grid, in the mist eliminator, and in the spray sections above and below the bed. Losses in the bed account for about half of the overall drop. Two basic approaches have been used to describe bed pressure drop. The first is based on trying to modify the two-phase theory and applying it to three-phase beds. This approach, first tried by Tichy et al. (1972), has proved to be unsuccessful. The other approach is based on the assumption that the pressure drop is the sum of contributions due to the weight of the dry packing and the operational liquid holdup, as expressed by AP = K1 - d
~
+phLoPLIgHo
(1)
Prediction of the pressure drop depends, therefore, on the availability of a reliable equation for calculating the liquid holdup. Correlations for this quantity have been presented in part 1of this series (Vunjak-Novakovieet al., 1987). We emphasize that only the operational liquid holdup contributes to the pressure drop. Levsh et al. (1968) and Balabekov et al. (1969a,b, 1971) were the first to recognize the existence of two regions on the curve relating pressure drop to gas velocity. However, the range of their proposed correlations for partially and fully developed fluidized beds is limited due to the specific particles and the low open areas of the supporting grids 0888-5885/87/2626-0967$01.50/0
they used in their experiments. It is generally known that the bed pressure drop increases when the static bed height, liquid flow rate, and particle density are increased and when the particle diameter is decreased. The reliability with which particular effects of these variables can be predicted in the various operating ranges is closely related to the evaluation of the liquid holdup data. (b) Bed Expansion. Many bed expansion data are available in the literature due to the importance of this design parameter and to the relative ease of measuring it. Three measurement techniques have been used to obtain the data necessary to develop bed height vs. gas velocity curves: (1)visual observation of the expansion, (2) estimation from the breakpoint in the static pressure profile, and (3) analysis of photographs taken with a high-speed camera. The expanded bed height increases with gas and liquid flow rates after the minimum fluidization velocity is reached (Handl, 1976; Zhivaikin et al., 1967), and the existence of two regions of bed expansion (Balabekov, 1969a, 1971; Gelperin and Kruglyakov, 1979; Handl, 1976; Tichy and Douglas, 1972) have also been reported. Theory concerning bed expansion is very limited so that data are correlated in terms of simple empirical correlations (Muroyama and Fan, 1985). Three models for bed expansion in fluidized beds have been proposed in the literature (Levsh et al., 1970; O’Neill et al., 1973; Tichy and Douglas, 1972). The model of Levsh et al. (1970) is incomplete because it included the gas fraction in the bed, for which no correlation was given. O’Neill et al. (1973) based their analysis on a hydrodynamic model which includes two regimes of fluidization. However, their model does not agree with experimental data due to the assumption that conditions of incipient flooding, if present in the bed at umF,are maintained throughout the whole range of fluidization flow rates. Tichy and Douglas (1972) have used an equation for flow through porous media to analyze bed expansion. The shortcomings of this approach are the use of an equivalent diameter of gas channels, somewhat fictitious for fluidized beds, and the use of correlations valid for the fully fluidized beds at all gas velocities. The mechanics of bed expansion is not well understood at present as we have mentioned, and the empirical correlations that are available do not give reliable predictions because they are limited to specific experimental conditions. As shown in Table I, the importance of the various 0 1987 American Chemical Society
968 Ind. Eng. Chem. Res., Vol. 26, No. 5, 1987 Table I. Effect of ODeratinct Variables on Bed E x ~ a n s i o n predicted exDonent variable min max references U 0.48 2.1 Gelperin et al., 1976; Kuroda and Tabei, 1981; Vunjak-NovakoviE, 1980 L 0.30 0.75 Akselrod and Yakovenko, 1969; Blvakher et al., 1967; Burkat et al., 1977: Ivaniukov et al.. 1968 Koch and Kubisa. 1973; Strumilo et al., 1976; Tarat et al., 1974; Tichy and Douglas, 1972; Zhivaikin et al.; 1967‘ d, -0.50 -2.14 Balabekov et al., 1969a,b; Gelperin et al., 1973; Handl, 1976; Koch and Kubisa, 1973; Strumilo et al., 1976; Tichy and Douglas, 1972; Ushida et al., 1977 -1 0.18 Balabekov et al., 1969a,b, 1971; Gelperin et al., 1976; Handl, 1976; Ushida et al., 1977 -0.2 -0.5 Akselrod and Yakovenko, 1969; Balabekov et al., 1969a,b, 1971; Gelperin et al., 1976; Ivaniukov et al., 1968; Koch and Kubisa, 1973; Strumilo et al., 1976; Volak and Palaty, 1978 D, 0.81 0.81 Strumilo et al., 1976 4 -0.14 -0.84 Balabekov et al., 1969a,b, 1971; Gelperin et al., 1976; Koch and Kubisa, 1973; Strumilo et al., 1976; Volak and Palaty, 1978 ~~
2o
operating variables varies considerably from one correlation to another. Some are conflicting as, for instance, the effect of particle density. (c) Minimum Fluidizing Velocity. Most of the available equations are purely empirical, and there are substantial differences in the predictions of those equations. I t is generally found that umFdecreases when the liquid flow rate and the particle diameter are increased (Chen and Douglas, 1968; Kit0 et al., 1976; VunjakNovakoviE et al., 1980a,b; Kuroda and Tabei, 1981). It has also been reported that the static bed height does not affect the minimum fluidizing velocity (Kito et al., 1976). However, the significance of the liquid flow rate and particle diameter varies from equation to equation, and the predicted effect of particle density and free crosssectional area of the supporting grid are conflicting (Muroyama and Fan, 1985). The confusion in the literature is attributable primarily to the essential differences in the hydrodynamic behavior of type-I and type-I1 fluidized beds and to some extent to the different methods of measuring umF.As shown in part 1 of this series (Vunjak-NovakoviE et al., 1987), u,F increases with particle density in type-I fluidized beds but no effect of particle density is observed in type-I1 fluidized beds.
Experimental Section Two methods were used to measure the bed height. They gave essentially the same results. The first involved obtaining an average of the low-amplitude fluctuations in bed height; the second makes use of the fact that the axial pressure, plotted as b(0) - p ( z ) ]vs. z, levels off at the top of the bed. At high gas velocities when the bed is slugging, the upper and lower limits of the bed height are estimated visually and averaged. The mean of the extremes is taken as the bed height. The most reliable method of obtaining umFis to observe changes in bed height with gas velocity. A plot of H / H o vs. u gives a horizontal line for velocities below u,F and a linear increase above u,F. The point of intersection of the two lines is taken as umF.This is the velocity at which fluidization is observed at the top of the bed. Measurements of the pressure drop and liquid holdup have been described in part 1 of this series (VunjakNovakoviE et al., 1987). Results (a) Pressure Drop. The pressure drop at minimum fluidization is equal to
01
02
1
03 0 4 05
2
3
4
5
u (mls)
10
Figure 1. Bed expansion as a function of gas velocity: effect of liquid mass flow rate. 101
02
I
0.3 0 4 0.5
1
2
3
4
5
u(m/s)
Figure 2. Bed expansion as a function of gas velocity: effect of particle density.
and our liquid holdup correlations (Vunjak-NovakoviE et al., 1987) are hL = 6.49Ro,-”(3gFrLo~42g( -0.567 0.02 (3)
2)
+
for type-I operation and h, = 7.33ReL-0.059Fr L0.435 (4) for type-I1 operation. We have confirmed experimentally that it is hh, the operating liquid holdup, and not hL, the total liquid holdup, that contributes to the pressure drop. Thus, to calculate the pressure drop in eq 2, use hLo = hL - 0.02 (5) (b) Bed Expansion. Basic Equations. The experimental results presented in Figures 1and 2 show that there are three regions on the bed expansion curve. The operating bed height increases when the liquid flow rate is
Ind. Eng. Chem. Res., Vol. 26, No. 5, 1987 969 increased and the particle density is decreased. Other variables, such as particle diameter, initial bed height, and the free cross-sectional area of the supporting grid also affect the bed expansion. The basic equation for the operating bed height is simple to derive. The volume of the fluidized bed is the sum of volumes occupied by the particles, the gas, and the liquid phases. Thus, = v p + VG + VL (6)
v
In terms of the fractions of each phase, eq 6 becomes tp EG EL = 1 (7)
+ +
The material balance for the same particles in the packed and in the fluidized beds gives AHo(1 - €0) = AH(l - 6 ) (8) where = 6G + EL Combining eq 7 and 8, we obtain for cp H O €, = 1 - t = -(1 - €0) H The fraction of the liquid phase, q,,is related to the liquid holdup, hL, by
By use of eq 10 and 11,the relative bed expansion becomes H _ - 1-eP+hL (12) Ho 1- E G Equation 1 2 satisfies the boundary condition, H = Ho, when u < umFand can be used to predict the operating bed height correlations for liquid holdup, hL, when the gasphase fraction, E ~ is, available. Since the liquid holdup correlations are given in eq 3 and 4, only a correlation for tG is needed to evaluate H/H,,. Interstitial Gas Velocity in the Bed. The gas-phase fraction was calculated from eq 2 using experimental data for H, hL, and E@ An attempt to correlate EG over the whole range of gas velocities with a single equation was not successful since it varied from regime to regime and also within each regime. It was then decided to relate the interstitial and superficial gas velocities in the hope of finding a simple relationship for tG. In this way, the interstitial gas velocity was chosen as the indicator of flow conditions. Defining u ’ = U / Q , we obtained an equation for calculating u’from experimental data, using eq 12 to obtain tG. Thus, u’ =
U
Figure 3. Variation of the interstitial gas velocity with superficial gas velocity in packed and fluidized beds.
If we use our correlation for the liquid holdup in packed beds, which is the same as eq 3, and rearrange,
2)
-0.567
tG
=
€0
-
2.48 x
io-3(
dp-0~56sL0~719 - 0.02
(15)
The liquid holdup increases above the loading point, causing a faster decrease in EG than expected from eq 15. The liquid holdup at the flooding point can be predicted by using eq 4 and the limiting particle density for type-I1 operation, corresponding to fluidization at the flooding point (Vunjak-NovakoviEet al., 1987). Since u’does not vary widely between loading and flooding, we recommend a linear relationship for u’ between those points. Since eG is constant in the packed bed region, U ’= U / C G
= ku
(16)
showing, as seen in Figure 3, that the interstitial gas velocity increases linearly with the superficial gas velocity below the loading point. Equation for t G in Partially Fluidized Beds. The initial gas velocity remains constant in the region of partial fluidization, as seen in Figure 3, and u’is equal to its value at minimum fluidization. After all the particles have been fluidized, beginning in the region of fully developed fluidization, u’ starts to increase linearly with u. In the type-I operating regime (see the data for pp = 156 kg/m3 in Figure 3), u’is constant and equal to 2L’
=
(13)
1 - (1 ;;iohL) u’ was then calculated from our data for u, to, hL,H, and Ho and was plotted as a function of gas velocity. The results, shown in Figure 3 for the two operating regimes, type I ( p , = 156 kg/m3) and type I1 (p, = 379 and 683 kg/m3), give insight into the hydrodynamics of the TBC. For each operating regime, there are three regions on the u’-vs.-u curve: (a) packed bed (below point P), (b) partially fluidized bed (region PR), (c) fully developed fluidized bed (above point R). Equations for Gas-Phase Fraction in Packed Beds. In packed beds, the bed voidage and liquid holdup are constant, so tG is constant. By use of eq 12 with H = Ho and the definition of t (eq 91, tG = to - hL (14)
For the type-I1 operating regime (cf. data for pp = 379 and 683 kg/m3 in Figure 31, the interstitial gas velocity is equal to u’at the flooding point of the packed bed and can be predicted by using
where u,F = U F and pp represents the minimum particle density for type-I1 operation (Vunjak-NovakoviE et al., 1987).
970 Ind. Eng. Chem. Res., Vol. 26, No. 5, 1987
Equation for CG in Fully Fluidized Beds. The interstitial gas velocity follows the simple relationship (Figure 3) u' = 1.59~0.763 (19) The corresponding equation for gas voidage is EG = 0 . 6 2 8 ~ O . ~ ~ ~ (20) Equation 20 fits the data at all liquid flow rates as well as data for two-phase, gas-fluidized beds. It seems that an increased liquid flow rate causes a corresponding increase in liquid holdup but does not affect u' and tG. Correlations for the Operating Bed Height. The operating bed height is calculated from eq 12 by inserting the appropriate correlations for hL and tG. In the region of partial fluidization for type-I operation, the gas-phase voidage using eq 16 and 17 is
Table 11. Range of Experimental Data Used for the Correlation of Type-I Fluidized Beds. Data for umF d,, mm on. ka/m3 L, kg/(m2 8 ) reference 195
