Phase Holdups in Three-Phase Semifluidized Beds and the

Special attention was paid to the parameters of the generalized bubble wake model and their predictability with an artificial neural network. Phenomen...
0 downloads 0 Views 2MB Size
Download PDF
Ind. Eng. Chem. Res. 2009, 48, 8393–8401

8393

Phase Holdups in Three-Phase Semifluidized Beds and the Generalized Bubble Wake Model Markus Schubert† and Faı¨c¸al Larachi* Department of Chemical Engineering, LaVal UniVersity, Que´bec, Canada, G1V 0A6

A new experimental measurement methodology was proposed to characterize the hydrodynamics in gas-liquid-solid semifluidized beds. Using pressure drop measurements in the lower fluidized bed section and a tracer response technique in the upper fixed bed portion, the six phase holdup components of the reactor were determined simultaneously. Available models for macroscopic predictions of holdups, initially proposed for three-phase fluidization, were extended, and their applicability was discussed concerning semifluidized beds. Special attention was paid to the parameters of the generalized bubble wake model and their predictability with an artificial neural network. Phenomenological observations identified an additional interface region between both beds, which, viewed as an inchoate freeboard region determines the mechanisms of attachment and release of particles from the fluidized bed to the fixed bed portion. 1. Introduction Three-phase fluidized beds are widely encountered in the chemical, petrochemical, and biochemical industry. Traditionally, they have been employed for hydrogenation and hydrodesulfurization of heavy oil and petroleum residuum in hydrotreating and upgrading processes,1 for the Fischer-Tropsch synthesis,2 for coal liquefaction and gasification,3,4 but also for bio-oxidation processes for wastewater treatment5 and for the production of pharmaceuticals.6,7 However, the field of application is widespread, including also physical processing such as filtration, particle collection, air cooling, and (de)humidification, as well as three-phase transport, and was summarized comprehensively in the book of L.S. Fan.8 Fluidized beds can be operated in different modes; however, the most common one is the cocurrent gas and liquid upflow fluidized bed system with liquid as the continuous phase. The semifluidization phenomenon is characterized by a combination of a fluidized bed and a fixed bed in series in a single containing column. Such a bed is built by expansion of the fluidized bed and then compressing the solid particles against a porous retaining grid at the top that constrains the bed. A semifluidized bed is claimed to overcome some inherent drawbacks of fluidized beds such as solids backmixing, attrition of particles, and erosion of surfaces, and is characterized by uniform bed temperature profiles and flow distribution which may not be as easily achievable as in the case of fixed beds.9 Investigations in semifluidization have been mainly attributed to gas-solid systems (e.g., Roy and Gupta,9 Wen et al.,10 Ho et al.11) and, to a lesser extent, to liquid-solid operation (e.g., Roy and Sarma,12 Roy and Chandra13). Some of the early semifluidized bed applications concerned biological systems14 in which the fluidized layer, exhibiting the highest backmixing, carries the main load of biological reaction, whereas the top packed bed acts as a polishing section. Recently, Dehkissia et al.15 studied the filtration behavior in an alternating bed, switching between semifluidization and fluidization for oil sand application. * To whom correspondence should be addressed. E-mail: [email protected]. Tel.: 1-418-656-3566. Fax: 1-418-6565993. † Current address: Forschungszentrum Dresden-Rossendorf, P.O. Box 51 05 19, 01314 Dresden, Germany.

Contrary to these above studies regarding two-phase applications, only two references can be traced back in the open literature where gas-liquid-solid semifluidization has been studied. The semifluidization behavior was investigated in the countercurrent mode and in the cocurrent upflow mode, respectively.16,17 For the cocurrent upflow mode in an air-water system, Chern et al.17 applied two types of nonporous model particles, that is, glass beads and PVC packing. Based on a phenomenological description of the semifluidized bed, the hydrodynamics for both sections were characterized separately. The total pressure drop of the semifluidized bed was reasonably well predicted by ad hoc model equations proposed for each section. However, the individual holdups were not directly measured for the fixed bed section. The gas holdup in the upper fixed bed section was calculated on the basis of the pressure drop measurements and on using separate flow model equations.18 Knowledge about the porosity is required which was proposed to take a constant value. While this assumption is valid for isolated packed beds, it is not evident that it holds in a semifluidized system, especially for industrial porous catalyst particles. To overcome these interrogations in the hydrodynamic description of the fixed bed in a semifluidized bed, a conductivity measurement method was developed in this work that provides access to the individual phase holdups during semifluidization. Furthermore, Chern et al.17 applied a simplified solids-free generalized bubble wake model to account for the expansion of the fluidized bed. For large and heavy particles this assumption was already verified by Dhanuka and Stephanek.19 However, for a system with a smaller difference between solid and liquid density (porous alumina packings in a sucrose solution) and a higher liquid viscosity, the applicability of a solid-free or solid-containing wake model and the artifical neural network of Larachi et al.20 for the prediction of the fluidized region in a semifluidized bed will be discussed. 2. Experimental Setup and Procedure The experimental setup used in this study is shown in Figure 1. Eighteen pressure taps, arranged equispaced 50 mm apart from each other enabled us to measure pressure gradients across the semifluidized bed in the acrylic column (dC ) 57 mm I.D., HC ) 105 cm).

10.1021/ie900426f CCC: $40.75  2009 American Chemical Society Published on Web 08/17/2009

8394

Ind. Eng. Chem. Res., Vol. 48, No. 18, 2009

Figure 1. Experimental setup and electrical conductivity probe. Table 2. Liquid Properties

Table 1. Catalyst Properties property

value

material internal particle porosity, εP (-) dry particle density, FS,dry (kg/m3) average particle diameter, dP (mm) total solid mass, mS (kg)

Al2O3 0.53 857 2.655 0.942

sucrose weight dynamic kinematic surface fraction, density, viscosity, viscosity, tension, liquid χ (w/w%) FL (kg/m3) ηL (mPa · s)a υL (m2/s) σL (dyn/cm)b L-I L-II L-III a

The gas-liquid distributor is a perforated plate consisting of 225 holes (diameter 1.6 mm) arranged in seven equidistant concentric circles resulting in an open area of approximately 18%. The quality of the distribution was visually proved to be uniform for the flow rates applied. Below the distributor, a funnel-shaped chamber was packed with 6 mm glass beads for initial gas-liquid mixing. Gas-liquid separation was realized in a disengagement section at the top of the column. Liquid phase was operated in the recirculation mode. The semifluidized bed height was fixed at 100.4 cm by an adjustable restraining grid installed at the top. The grid opening had a quadratic shape (1 mm) to retain the packing from crossing over. The column was filled with polydisperse commercial catalyst particles (2.1 to 3.3 mm diameter) with an average diameter of 2.655 mm. The height of the resting packing was approximately 68.5 ( 4.5 cm corresponding to a porosity of 0.35 ( 0.05 depending on the settling conditions (sudden or slow decrease of gas and/or liquid flow after fluidization). The catalyst properties are summarized in Table 1. The catalyst was immersed beforehand in the liquid for 12 h to ensure liquid had filled all the intraparticle porosity. Air and water with different concentrations of sucrose are used in the experiments. The experiments were performed at room temperature and atmospheric pressure. The liquid properties are summarized in Table 2. Gas and liquid were fed cocurrently upward through the column from the compressed air supply and via positive displacement pump from the stirred liquid storage tank, respectively. The fluidization was initiated with liquid flow only. Subsequently, the gas flow was adjusted to the desired value and the

0.24 0.33 0.39

1096 1137 1167

1.92 2.72 4.53

1.75 2.39 3.88

60.1 64.4 66.6

ARES Rheometric Scientific. b Tensiometer Kru¨ss14.

liquid velocity increased to build a fixed bed below the restraining grid. Liquid velocities were chosen to establish fixed bed heights of 40 cm (height 1, H1) and 45 cm (height 2, H2), respectively. The gas and liquid superficial velocities were in the range from 0 to 0.016 m/s and from 0.023 to 0.043 m/s, respectively. For every operating condition, the experiment was started from the resting bed. To determine the phase holdups in the fixed bed section of the semifluidized bed, liquid residence time distribution (RTD) measurements in the fixed bed were performed via conductivity tracer response. The aqueous sodium chloride solution tracer (cNaCl ) 0.43 mol/L) was injected upstream in the liquid feeding line by a syringe connection port. Two integrated conductivity sensors were installed 5 cm (C2) and 34.2 cm (C1) below the restraining grid. During semifluidization the sensors are embedded in the fixed bed. It was verified visually that the thin wires did not alter the flow significantly. The flange design and the dimensions of the developed electrical conductivity probes are shown in Figure 1. The analytical transfer equation which relates the response concentration curve to the imperfect pulse21-23 in the time-domain for the axial dispersion model with open-open boundary conditions was used.24 The space time, τ, and the axial dispersion Pecle´t number (based on the bed height), PeL, were determined using a nonlinear least-squares fitting of the tracer response functions. Figure 2 shows an example of the match between measured and predicted curves. By utilizing the delayed bed collapse after closing the gas line, RTD experiments enabled access to the liquid holdup at single phase liquid flow, which is, at the same time, the volumeaveraged porosity of the fixed bed.

Ind. Eng. Chem. Res., Vol. 48, No. 18, 2009

8395

Figure 3. Effect of the fixed bed height, liquid properties, and gas velocity on the superficial velocity at semifluidization. Figure 2. Example of the experimental conductance tracer response curves at H1 and H2 along with the fit of the response at H2 using the axial dispersion model (uL ) 0.0300 m/s, uG ) 0.0033 m/s, L-II)

Furthermore, separate liquid-solid fluidization experiments were performed with a lower initial packing height of 27.5 cm to cover a broader range of porosities. At this height the packing porosity was estimated to be 0.382. 3. Governing Equations for Holdups in the Semifluidized Bed The fixed bed of the semifluidized bed configuration is characterized by the gas, liquid, and solid phase volume fraction conservation (eq 1). Solid and liquid holdups are determined from the RTD experiments using eqs 2 and 3. εL,fixed + εG,fixed + εS,fixed ) 1 εL,fixed )

uLτ ∆L

εS,fixed ) 1 -

(from RTD at gas-liquid flow) uLτ ∆L

(from RTD at liquid flow)

(1) (2)

(3)

uL represents the superficial liquid velocity, τ is the space time and ∆L is the distance between both conductivity sensors which was 29.2 cm. For the fluidized bed section the following equations can be applied:25 εL,fluid + εG,fluid + εS,fluid ) 1

(4)

Hfluidg(FLεL,fluid + FGεG,fluid + FSεS,fluid) ) -∆pfluid

(5)

It is assumed that the acceleration and wall friction terms can be neglected. Hfluid and -∆pfluid can be determined experimentally. εS,fluid can be calculated from the solid phase balance (eq 6).

εS,fluid

mS π - dC2εS,fixedHfixed FS,dry 4 ) π 2 d H 4 C fluid

(6)

The semifluidized bed requires six closing relations to determine the six phase volume fractions. Hence, applying eqs 1-6 is sufficient to determine the phase fractions in both sections of the semifluidized bed. 4. Results and Discussion The characterization was performed experimentally for three different sucrose concentrations, resulting in different liquid properties. For all the gas superficial velocities applied in this study, the liquid velocity was adjusted to fixed bed heights of approximately 40 cm (H1) and 45 cm (H2) representing fixedto-fluidized bed height ratios (R ) Hfixed/Hfluid) of 0.67 and 0.82, respectively. 4.1. Flow Pattern. Similar to a typical flow regime map, Figure 3 summarizes the superficial gas and liquid velocities that are necessary to achieve specific fixed bed heights or fixedto-fluidized bed height ratios, respectively. The line which is the closest to each measurement point indicates the height of the fixed bed for this experiment (H1 or H2). For all liquids applied in this study a higher gas superficial velocity results in lower liquid superficial velocities needed. As expected, at constant gas flow rates, a higher fixed bed height requires at the same time higher liquid velocities. Furthermore, increasing the liquid viscosity and density shifts the line toward lower superficial velocities. Zhang et al.26 proposed an empirical correlation for the prediction of the regime transition from dispersed bubble flow to the coalesced bubble flow regime in three-phase fluidization.

()

uG FS ) 0.721FrG0.339ArL0.0746 uL FL

-0.667

(7)

On the basis of eq 7 it can be concluded that most of the gas-liquid-solid fluidization experiments (except uL ) 0.0415 m/s, uG ) 0.0032 m/s, H2, L-I) fall into the coalesced bubble flow regime (see gray lines in Figure 3). However, experimental results and valid correlations specifically tailored for viscous systems involving small gaps between liquid and solid densities are rare. Furthermore, the effect of the column diameter is a crucial parameter, especially for labscale columns. The black symbols in Figure 3 show the required liquid superficial velocities to ensure the desired fixed bed heights

8396

Ind. Eng. Chem. Res., Vol. 48, No. 18, 2009

at liquid-solid semifluidization. Except for L-I (encircled symbols), the liquid superficial velocities at liquid flow only (i.e., no gas) are lower than the corresponding values for gas-liquid flow at the lowest superficial gas velocity. This phenomenon can be explained by the presence of solidsstarved wakes which allow some liquid flow to bypass the liquid-solid fluidized region at higher velocity. This bypass of liquid thus reduces the liquid velocity in the liquid-solid fluidized region, and hence the bed contracts.27 Mathematical descriptions based on the generalized bubble wake model were presented to identify conditions for fluidized bed contraction.28 It was concluded that, for example, high-liquid viscosities favor bed contraction which is in agreement with our experimental results. The same findings were shown by Kim et al.29 4.2. Gas-Liquid-Solid Semifluidization. For all the gas-liquid superficial velocity pairs shown in Figure 3, the phase holdups and the porosity of the fixed bed and of the fluidized bed section were determined. The porosity of the fixed bed (ε ) 1 - εS) was estimated from the RTD measurements at single phase liquid flow to be in a wide range between 0.34 and 0.42. No trends depending on liquid properties and adjusted gas and liquid superficial velocities were observed. This confirms that the buildup of the fixed bed layer is not reproducible even if the general procedure is adhered to tightly. Already slight differences in the slope of the manually increased superficial velocities effect the mixing behavior in the fluidization along with inception of some segregation of the slightly polydisperse character of the catalyst particles which in turn gives rise to different porosities. The obtained porosities are approximately overlapping with the porosity range of the resting bed which indicates that the attachment of the fluidized particles to the fixed bed layer is strongly affected by the bed-expanding mechanism, too. For the ease of comparison, the fluid phase holdups are considered with respect to the void space, that is, using a fluid saturation scale common in treating immiscible fluids in porous media (eq 8). βj,i )

εj,i , εL,i + εG,i

j ) G, L;

i ) fluidized, fixed

Figure 4. Liquid saturation in the fixed-bed section of the semifluidized bed.

(8)

Figure 4 shows the liquid saturation in the fixed-bed section. The line which is the closest to each measurement point indicates the liquid phase used for this experiment (L-I to L-III). At constant gas flow rates for constant liquid properties, the liquid saturation increases with superficial liquid velocities (compare H1 and H2). The effect of the superficial liquid velocity on the liquid saturation is more pronounced at higher sucrose concentration (L-III). Considering for the purpose of illustration the encircled area in the figure, the effect of the sucrose concentration and thus the effect of viscosity is obvious. The superficial gas and liquid velocities for both experiments are nearly the same. However, the higher sucrose content clearly results in higher liquid saturation values, in agreement with discussion of the viscosity effect in packed beds operated in cocurrent up-flow mode.30 The gas phase fraction is not discussed separately as it takes the remaining part of the void space. Based on eq 8, Figure 5 shows the determined gas saturation in the fluidized section of the semifluidized bed.

Figure 5. Gas saturation in the fluidized bed section of the semifluidized bed.

Again, the line which is the closest to each measurement point indicates the liquid phase used for this experiment (L-I to L-III). At constant gas flow rates for constant liquid properties, the gas saturation decreases with superficial liquid velocities as the ratio of the liquid-to-gas flow rate increases for the longer fixed bed (H2). The effect of the superficial liquid velocity on the gas saturation exhibits the same slope and trend for all sucrose concentrations. Comparison of the gas saturation at the same gas and liquid superficial velocities (see for instance the encircled area) indicates that a higher viscosity results in lower gas saturation values. The effects of superficial liquid velocity and viscosity show the expected trends, which was reported at numerous occasions in the literature too.31-33 However, the quantitative behavior of the gas holdup varies significantly with flow regime and unified correlations are difficult to establish.8

Ind. Eng. Chem. Res., Vol. 48, No. 18, 2009

8397

Table 3. Comparison of Richardson-Zaki Relation with Experimental Data

Figure 6. Liquid-solid fluidization and derivation of the Richardson-Zaki parameters.

4.3. Applicability of the Generalized Bubble Wake Model for Semifluidized Beds. The voidage in fluidized beds can be expressed by the generalized bubble wake model proposed by Bhatia and Epstein.34 The model postulates that the bed can be subdivided into a gas bubble region, an associated bubble wake region, and a liquid-solid fluidized region. It is assumed that the solid content in the wake can be different from that in the liquid-solid fluidized region and that the bubble wake and bubble velocity are identical. The final basic equation of the model in eq 9 describes the bed porosity of the fluidized bed and has been proved to be widely applicable for design purposes.8 εfluid ) 1 - εS,fluid ) εG,fluid + εL,fluid 1/n uL - uG(1 - x) ) [1 - εG,fluid(1 + k ui(1 - εG,fluid + kεG,fluid) (9) kx)] + εG,fluid(1 + k - kx)

[

]

Hfix

liquid

εS.fluid (-) [exp]

εS.fluid (-) [eq 10]

H1 H2 H1 H2 H1 H2

L-I L-I L-II L-II L-III L-III

0.31 0.30 0.29 0.27 0.30 0.29

0.33 0.29 0.33 0.29 0.33 0.28

Equation 10 was applied to the fluidized bed section of the liquid-solid semifluidized bed. Table 3 shows that experimentally determined solids holdup in this section is in fair agreement with the one computed using eq 10. It can be concluded that the experimentally determined parameters in eq 10 can be used subsequently in the generalized bubble wake model for the prediction of the holdups in the gas-liquid-solid semifluidized bed. The applicability of the generalized bubble wake model for the prediction of the solid and liquid holdup in a semifluidized bed was verified with empirical correlations for k and x originally developed for mere three-phase fluidization setups. For closure of the system, the gas holdup was calculated with an empirical correlation and with our own experimental data, respectively. As the correlations for cases number 2 and 3 (Table 4) require liquid and solid holdup, together with the generalized bubble wake model (eq 9), they were solved iteratively. Furthermore, the multilayer perceptron artificial neural network and dimensional analysis approach (ANN-DA) developed by Larachi et al.20 was used to derive the phase holdups. This approach is based on 23000 experiments on bed porosity and liquid, gas, and solid holdups. The tested correlations are summarized in Table 4. Figure 7 shows the quality of the predictions of the individual phase holdups based on the generalized bubble wake model and on the artificial neural network correlations. The deviation of the predictions of k using eqs 13 and 15 from Table 4 are up to 25%. However, the calculated holdups for cases 2 and 3 (Table 4 and Figure 7) give the same value. For drawing quantitative conclusions regarding the applicability of the generalized bubble wake model to gas-liquid-solid semifluidized beds, using the k and x

In eq 9, x represents the ratio of the solids holdup in the bubble wake region to that in the liquid-solid fluidized region, and k is the ratio of the bubble wake volume to the bubble volume. Both parameters have to be evaluated empirically. However, few correlations are available in the literature to access them as presented below. The solid holdup in the liquid-solid fluidized region is described by eq 10 which is the well-known Richardson-Zaki correlation35 that appears from eq 9 as the gas velocity approaches zero. εfluid )

() uL ui

1/n

(10)

ui is the extrapolated superficial liquid velocity as the bed voidage approaches zero, that is, the particle terminal velocity, and n is the Richardson-Zaki index. To apply the generalized bubble wake model, both parameters were determined using separate liquid-solid fluidization experiments. The results are shown in Figure 6.

Figure 7. Parity plot of experimental and predicted holdup data.

8398

Ind. Eng. Chem. Res., Vol. 48, No. 18, 2009

Table 4. Correlations for Prediction of Phase Holdups Using the GBWM and ANN-DA nr.

k

x

k ) 0.398uL0.246uG-0.646

1

Chern et al.

εG,fluid ) 0.098uL-0.98uG0.70

0

17

Chern et al.

(

k ) (1 - εS)3 0.61 +

2

(11)

closure

0.037 εG + 0.013

)

ui uG uL εG εL x ) 1 - a for a < 1 x ) 0 for a > 1

(13)

a ) 0.877

Bhatia and Epstein34

(12)

17

εG,fluid (exp), (eq 4)

(14)

El-Temtamy and Epstein36 k ) (1 - εS)3(e-1.2εG + 2.5e-32.8εG)

3

Khang et al.

(eq 14) El-Temtamy and Epstein36

(15)

εG,fluid(exp), (eq 4)

37

ANN-DA approach, Larachi et al.20

4

literature correlations and artificial neural network correlations, the average absolute relative error (eq 16) was calculated for all four cases (Table 5). errorεj )

1 N

∑|

|

εj,pred - εj,exp , εj,exp

j ) G, L, S

(16)

For the generalized bubble wake models (cases 1 to 3) the liquid holdups are predicted quite well and the average absolute relative errors for the solids holdup are in a similar range. However, although in cases 2 and 3 the experimental gas holdup values were directly used instead of estimating them through a correlation, the liquid holdup data show slightly larger errors. It can be concluded that correlations for k that consider the gas superficial velocity instead of the gas holdup are more reliable. Furthermore, the effect of the parameter k is more pronounced than the effect of the gas holdup. By applying empirical correlations it is difficult to draw conclusions regarding applicability of the generalized bubble wake model to the behavior of a semifluidized bed. Therefore, the experimental data were compared to the artificial neural network predictions (case 4) using Larachi et al.20 ANN correlations. It was proved that all experimental conditions fell into the validity ranges of these correlations. Even if the solids holdup estimation shows a large error, the gas and liquid holdup predictions were found to be superior to those estimated from the generalized bubble wake model. Furthermore, for all experimental conditions, k- and x-correlations based on artificial neural networks have also been derived by Larachi et al.20 which can also be used to Table 5. Average Absolute Relative Error of the Predictions nr.

liquid

errorεG,fluid

errorεS,fluid

errorεL,fluid

1

L-I L-II L-III ∑

65.1 61.3 56.7 59.9

20.7 20.9 6.2 16.9

5.7 3.8 4.0 4.7

2, 3

L-I L-II L-III ∑

26.2 20.8 8.1 19.6

13.5 9.1 3.9 9.3

4

L-I L-II L-III ∑

45.1 57.9 32.0 46.3

3.4 3.8 3.5 3.6

32.6 17.1 41.5 29.0

generate other estimations for x and k in our semifluidization conditions. Note that these ANNs were developed on the basis of a huge (pseudo)experimental database that was created with an inverse version of the generalized bubble wake model formulation (eqs 17-21 and eq 4) which is different from other authors with respect to the definition of the relative bubble rise velocity, VGL (eq 21). εL,fluid ) εG,fluidk(1 - x) + εLF(1 - εG,fluid - kεG,fluid + kxεG,fluid) uG ) VGεG,fluid εLF ) VG )

(

uL - uGk(1 - x) ui(1 - εG,fluid - kεG,fluid)

(17) (18)

)

1/n

(19)

uL + uG + VGLεLF(1 - εG,fluid - kεG,fluid) 1 - εS,fluid

(20)

uG εG,fluid(1 - εG,fluid)

(21)

VGL )

Both artificial neural network (ANN) predictions and iteratively determined values for k and x from the generalized bubble wake model (GBWM) are shown in Figure 8 panels a and b, respectively. The physical sense dictates that only positive values of k and x must be taken into consideration. When, because of experimental inaccuracies, these constraints were not fulfilled with the generalized bubble wake model, the data were discarded from the figures. Nevertheless, the trends are obvious and give additional insights about the predictive quality of the artificial neural network and show how semifluidization operation affects these values. The fixed bed height and the liquid properties are not explicitly indicated as their effect on the values of k and x cannot be extracted clearly. On the contrary, a clear-cut influence of the superficial velocities was observed. The predictions of the artificial neural network show a linear dependency of x and k on the superficial liquid velocity (emphasized by trend lines). While k roughly halves in value by doubling the superficial gas velocity, the decreasing effect is just slight for x. Despite the slightly scattered data plot, the values for k obtained from the generalized bubble wake model are in fair agreement with the predictions of the artificial neural network.

Ind. Eng. Chem. Res., Vol. 48, No. 18, 2009

8399

Figure 9. Interface region of the fluidized and the fixed bed at uG ) 0.0065 m/s, height 1 (H1).

Figure 8. Comparison of values for (a) k and (b) x from the artificial neural network (ANN) and from the generalized bubble wake model (GBWM).

Furthermore, the quasi-experimental data for k follow the common trend proposed in the fluidization literature even if the magnitude is different due to different formulations of the relative bubble rise velocity.17,38,39 The values of x determined with the generalized bubble wake model increase as the superficial liquid velocity decreases and as the superficial gas velocity increases. This behavior is in agreement with the observations from El-Temtamy and Epstein.36 The x values predicted with the artificial neural network show an opposite trend while the dependency of x on the superficial velocities is only weakly manifested. However, the analysis of the x values reveals that for an industrial porous catalyst (e.g., alumina or activated carbon) with small density differences between solid and liquid (FS - FL) and using viscous liquids, the ratio of the solids holdup in the bubble wake region to that in the liquid-solid fluidized region cannot be neglected as it can be for example for glass particles larger than 2 mm using water-based systems.19 4.4. Phenomenological Aspects During Semifluidization. Even if the predictions with the generalized bubble wake model and with the artificial neural network are tolerable compared to the experimental data, some phenomenological

observations during semifluidizations especially with typical industrial catalysts should not be concealed and require additional effort for deeper investigation. The fundamental mechanism for the particle entrainment and de-entrainment in the disengagement zone of a fluidized bed was proposed by Page and Harrison.40 Particles enter such a freeboard zone from the upper surface of the fluidized bed in the wake behind bubbles. In the freeboard, vortices with solids are shed from the wake and the solids settle back to the bed when the liquid velocity in the freeboard is less than the particle terminal velocity. At first glance, in the semifluidized bed such a freeboard zone is not expected because of the fixed bed prevailing atop of the fluidization section. Figure 9 shows the interface region of the fluidized bed and the fixed bed for different experimental conditions of the semifluidized bed. Some of the particles being trailed in the wake past a bubble which bursts right beneath the bottom layer of the fixed bed can lodge and attach therein. Provided the local fluid velocities are in excess of the particle terminal velocity, these cannot return to the bulk fluidized region due to the lack of a solid disengagement zone as it may have encountered in conventional fluidized beds. The necessary fluid velocity to promote the particles to settle down into the fluidized bed is clearly lower than that required for the fixed bed buildup. Due to this hysteretic behavior, at steady state operating conditions a zone with low solid holdup between the fluidized bed and the fixed bed occur. This zone is characterized by an axial solid holdup profile. Theoretically, this solids-depleted region connecting between both beds represents a disengagement-like zone as in the wellknown freeboard region. In fluidized beds the demarcation between the freeboard region and the bulk fluidized bed region is much more distinct for large and heavy particles than for small and light particles. Furthermore, the particle entrainment decreases with an increase in liquid velocity and particle size.40 For the semifluidized bed experiments, although the liquid velocity decreases, an increasing solid disengagement zone was visually observed for increasing kinematic viscosities (see Figure 9). Especially for small density differences between solid and liquid (FS - FL), the effect of the liquid viscosity superimposes with that of the liquid velocity. The solid disengagement zone has a minor importance for tall columns; however, in shallow semifluidized beds this zone has to be considered for balancing of the individual holdups. 5. Conclusion The phase fractions in the fluidized region and in the fixed bed were simultaneously determined during semifluidization

8400

Ind. Eng. Chem. Res., Vol. 48, No. 18, 2009

operation for an industrial catalyst. A new experimental measurement methodology is proposed that gives access to the phase holdups in the fixed bed by a tracer response technique. The fluidized part was characterized by pressure drop measurements considering the total solid mass balance. A flow pattern map identified the effect of the fixed bed height and of the liquid properties on the superficial gas and liquid velocities as well as bed expansion and extraction behavior in the coalesced bubble flow regime. The liquid saturation in the fixed bed increases with superficial liquid velocity. For the same gas and superficial liquid velocities, the liquid saturation decreases with decreasing liquid kinematic viscosities. Opposite trends were observed for the gas saturation in the subjacent fluidized bed. Furthermore, the generalized (solid-free and solid-containing) bubble wake model was applied, considering experimentally determined Richardson-Zaki parameters and correlations proposed in the literature. The predictions are in fair agreement. The gas holdup in the fluidized bed was identified to be the most crucial parameter. For the fluid phase holdup predictions, the macroscopic hydrodynamic artificial neural network of Larachi et al. (2001) is recommended to apply for three-phase semifluidized beds too. However, the analysis of the bubble wake model parameters obtained from the model formulation equations based on experimental holdup data and from the neural network revealed a discrepant trend for x. From a phenomenological point of view, semifluidized beds with liquids and solids with small density gaps and viscous liquids develop an interface region between both sections which represent a solid-disengagement-like zone as known for conventional fluidized beds, which could become important especially in shallow semifluidized beds. The results encourage advancing semifluidization studies with respect to more generalized flow maps that consider reactor dimensions, fluid properties, and fixed-to-fluidized bed height ratios using dimensionless numbers. Furthermore, the mechanisms of attachment and release of particles from the fluidized bed to the fixed bed portion are not investigated so far. Future work would also demand studies with foaming and nonNewtonian liquids as the liquid properties in both of the sections are different because of the effect of the shear stress on the viscosity. Acknowledgment M.S. gratefully acknowledges the Government of Canada for their financial support during the postdoctoral fellowship period. Financial support from the Natural Sciences and Engineering Research Council of Canada and Natural Resources Canada is also gratefully acknowledged. Profs. D. Rodrigue (Department of Chemical Engineering) and B. Riedl (Department of Soil and Forest Sciences) are also acknowledged for their help in accessing their analytical laboratory facilities. Nomenclature ArL ) liquid Archimedes number, gdP3FL(FS - FL)/ηL2 c ) tracer concentration (mol/L) CN ) normalized tracer concentration d ) diameter (m) D ) axial dispersion coefficient (m2/s) error ) average absolute relative error (%) FrG ) gas Froude number, uG/(gdP) g ) gravitational acceleration (m/s2) H ) height (m)

k ) ratio of the wake volume to bubble volume ∆L ) measurement distance (m) m ) mass (kg) n ) Richardson-Zaki parameter ∆P ) pressure drop (Pa) Pe ) axial dispersion Pe´clet number, uL∆L/D R ) fixed-to-fluidized bed height ratio t ) time (s) ui ) extrapolated superficial liquid velocity (m/s) uG ) superficial gas velocity (m/s) uL ) superficial liquid velocity (m/s) VG ) wake velocity (m/s) VGL ) relative bubble rise velocity (m/s) x ) ratio of the solid holdup in the wake to that in the liquid-solid fluidized region Greek Letters β ) saturation χ ) weight fraction (w/w%) ε ) bed porosity εG ) gas holdup εL ) liquid holdup εLF ) liquid holdup in the liquid-solid fluidized region εS ) solid holdup η ) dynamic viscosity (Pa/s) F ) density (kg/m3) σ ) surface tension (dyn/cm) τ ) space time (s) υ ) kinematic viscosity (m2/s) Subscripts C ) column dry ) dry porous material exp ) experimental fixed ) fixed bed fluid ) fluidized bed G ) gas L ) liquid P ) particle pred ) prediction S ) solid AbbreViations RTD ) residence time distribution ANN ) artificial neural network GBWM ) generalized bubble wake model

Literature Cited (1) Bridge, A. G. Hydrogen Processing. In Handbook of Petroleum Refining Processes, 2nd ed.; Meyers, R. A., Ed.; McGraw-Hill: New York, 1996; Chapter 14, pp 14.3-14.68. (2) Satterfield, C. N.; Huff, G. A., Jr. Effects of Mass Transfer on Fischer-Tropsch Synthesis in Slurry Reactors. Chem. Eng. Sci. 1980, 35, 195. (3) Ashland Synthetic Fuels Inc., Final Report to U.S. Department of Energy, Contract No. DE-AC05-76ET10143, 1984. (4) Cover, A. E.; Schreiner, W. C.; Skaperdas, G. T. Kellogg Coal Gasification Process. Chem. Eng. Prog. 1973, 69, 31. (5) Donaldson, T. L.; Strandberg, G. W.; Hewitt, J. D.; Shields, G. S. Biooxidation of Coal Gasification Wastewaters. EnViron. Prog. 1984, 3, 248. (6) Schu¨gerl, K. Three-Phase Bio-FluidizationssApplication of ThreePhase Fluidization in the BiotechnologysA Review. Chem. Eng. Sci. 1997, 52, 3661. (7) Godia, F.; Sola, C. Fluidized-Bed Bioreactors. Biotechnol. Prog. 1995, 11, 479. (8) Fan, L.-S. Gas-Liquid-Solid Fluidization Engineering; Butterworth Series in Chemical Engineering; Butterworth: Stoneham, MA, 1989.

Ind. Eng. Chem. Res., Vol. 48, No. 18, 2009 (9) Roy, G. K.; Gupta, P. S. Prediction of the Packed Bed Height in a Gas-Solid Semifluidization. Ind. Eng. Chem. Process Des. DeV. 1974, 13, 219. (10) Wen, C. Y.; Wang, S. C.; Fan, L. T. Semifluidization in SolidGas Systems. AIChE J. 1963, 9, 316. (11) Ho, T. C.; Yau, S. J.; Hopper, J. R. Hydrodynamics of Semifluidization in Gas-Solid Systems. Powder Technol. 1987, 50, 25. (12) Roy, G. K.; Sarma, K. J. R. Dynamics of Liquid-Solid Semifluidization. III. Relation between Onset of Semifluidization and Minimum Fluidization Velocity. Chem. Eng. J. 1972, 4 (3), 294. (13) Roy, G. K.; Chandra, H. N. S. Liquid-Solid Semi-Fluidization of Heterogeneous Mixtures. II: Prediction of the Minimum Semi-Fluidization Velocity. Chem. Eng. J. 1976, 12, 77. (14) Fan, L. T.; Wen, C. Y. Method of Wastewater Treatment in Fluidized Bed Biological Reactors. U.S. Patent 4,253,047, 1981. (15) Dehkissia, S.; Bacaoui, A.; Iliuta, I.; Larachi, F. Dynamics of Fines Deposition in an Alternating Semifluidized Bed. AIChE J. 2008, 54, 2120. (16) Chern, S.-H.; Muroyama, K.; Fan, L.-S. Hydrodynamics of Constrained Inverse Fluidization and Semifluidization in a Gas-LiquidSolid System. Chem. Eng. Sci. 1983, 38, 1167. (17) Chern, S.-H.; Fan, L.-S.; Muroyama, K. Hydrodynamics of Cocurrent Gas-Liquid-Solid Semifluidization with a Liquid as the Continuous Phase. AIChE J. 1984, 30, 288. (18) Wallis, G. B. One-Dimensional Two-Phase Flow; McGraw-Hill. Inc.: New York, 1969. (19) Dhanuka, V. R.; Stephanek, J. B. Gas and Liquid Hold-up and Pressure Drop Measurements in a Three-Phase Fluidized Bed. In Fluidization; Davidson, J. F., Keairns, D. L., Ed.; Cambridge University Press: New York, 1978; pp 179-183. (20) Larachi, F.; Belfares, L.; Iliuta, I.; Grandjean, B. P. A. Three-Phase Fluidization Macroscopic Hydrodynamics Revisited. Ind. Eng. Chem. Res. 2001, 40, 993. (21) Van der Laan, E. T. Notes on Diffusion-Type Model for the Longitude Mixing of Fluids in Flow. Chem. Eng. Sci. 1958, 7, 187. (22) Aris, R. Notes on Diffusion-Type Model for the Longitude Mixing of Fluids in Flow. Chem. Eng. Sci. 1959, 9, 266. (23) Bischoff, K. B.; Levenspiel, O. Fluid Dispersion-Generalization and Comparison of Mathematical Models. I. Generalization of Models. Chem. Eng. Sci. 1962, 17, 245. (24) Chrittenden, B. D.; Lau, A.; Brinkmann, T.; Field, R. W. Oscillatory Flow and Axial Dispersion in Packed Beds of Spheres. Chem. Eng. Sci. 2005, 60, 111. (25) Ostergaard, K. Studies of Gas-Liquid Fluidization; Danish Technical Press: Copenhagen, Denmark, 1969. (26) Zhang, J.-P.; Grace, J. R.; Epstein, N.; Lim, K. S. Flow Regime Identification in Gas-Liquid Flow and Three-Phase Fluidized Beds. Chem. Eng. Sci. 1997, 52, 3979.

8401

(27) Stewart, P. S. B.; Davidson, J. F. Three-Phase Fluidization: Water, Particles, and Air. Chem. Eng. Sci. 1964, 19, 319. (28) Jean, R. H.; Fan, L.-S. On the Particle Terminal Velocity in a GasLiquid Medium with Liquid as the Continuous Phase. Can. J. Chem. Eng. 1987, 65, 351. (29) Kim, S. D.; Baker, C. G.; Bergougnou, M. A. Phase Hold-up Characteristics of Three-Phase Fluidized Beds. Can. J. Chem. Eng. 1975, 53, 134. (30) Bensetiti, Z.; Larachi, F.; Grandjean, B. P. A.; Wild, G. Liquid Saturation in Cocurrent Upflow Fixed-Bed Reactors: A State-of-the-Art Correlation. Chem. Eng. Sci. 1997, 52, 4239. (31) Jena, H. M.; Roy, G. K.; Meikap, B. C. Prediction of Gas Holdup in a Three-Phase Fluidized Bed from Bed Pressure Drop Measurement. Chem. Eng. Res. Des. 2008, 86, 1301. (32) Chen, J.; Gupta, P.; Degaleesan, S.; Al-Dahhan, M. H.; Dudukovic, M. P.; Toseland, B. A. Gas Holdup Distributions in Large-Diameter Bubble Columns Measured by Computed Tomography. Flow Meas. Instr. 1998, 9, 1998–91. (33) Han, J. H.; Wild, G.; Kim, S. D. Phase Holdup Characteristics in Three Phase Fluidized Beds. Chem. Eng. J. 1990, 43, 67. (34) Bhatia, V. K.; Epstein, N. Three-Phase Fluidization: A Generalized Wake Model. In Fluidization and Its Application; Angelino, H., Couderc, J. P., Gibert, H., Laguerie, C., Ed.; Cepadues-Editions: Toulouse, France, 1974, pp 380. (35) Richardson, J. F.; Zaki, W. N. Sedimentation and Fluidization: Part I. Trans. Inst. Chem. Eng. 1954, 32, 35. (36) El-Temtamy, S. A.; Epstein, N. Bubble Wake Solids Content in Three-phase Fluidized Beds. Int. J. Multiphase Flow 1978, 4, 19. (37) Khang, S. J.; Schwartz, J. G.; Buttke, R. D. A Practical Wake Model for Estimating Bed Expansion and Holdup in Three-Phase Fluidized Systems. AIChE Symp. Ser. 1983, 79, 247. (38) Baker, C. G. J.; Kim, S. D.; Bergougnou, M. A. Wake Characteristics of Three-Phase Fluidized Beds. Powder Technol. 1977, 18, 201. (39) Darton, R. C.; Harrison, D. Gas and Liquid Hold-up in Three-Phase Fluidization. Chem. Eng. Sci. 1975, 30, 581. (40) Page, R. E.; Harrison, D. Particle Entrainment from a Three-Phase Fluidized Bed. In Fluidization and Its Application, Angelino, H., Couderc, J. P., Gibert, H., Laguerie, C., Ed.; Cepadues-Editions: Toulouse, France, 1974.

ReceiVed for reView March 15, 2009 ReVised manuscript receiVed July 28, 2009 Accepted August 1, 2009 IE900426F