Ind. Eng. Chem. Res. 2010, 49, 1105–1112
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Hydrodynamic Simulation of Pulsing-Flow Regime in High-Pressure Trickle-Bed Reactors Rodrigo J. G. Lopes* and Rosa M. Quinta-Ferreira Group on EnVironmental, Reaction and Separation Engineering (GERSE), Department of Chemical Engineering, UniVersity of Coimbra, Rua Sı´lVio Lima, Polo II - Pinhal de Marrocos, 3030-790 Coimbra, Portugal
In the present study, attention is focused on the CFD simulation of trickle-bed reactors when the tricklingflow regime changes into the pulsing-flow regime, along with the parameters that characterize this latter regime. These parameters include the velocity at which the pulse front travels along the bed, the frequency of pulsations, and the structure of pulses being formed (i.e., the sizes of the liquid-rich and gas-rich zones). Results are presented for a three-phase reactor operating at an elevated pressure in the pulsing-flow regime. Several parameters that characterize the pulsing flow, namely, the velocity of pulses traveling along the bed, the frequency of pulsations and their structure, the length of the pulses, and the length of the liquid-rich zone, were examined at high pressure by means of an Eulerian CFD model. 1. Introduction Trickle-bed reactors (TBRs) find widespread applications in industrial three-phase reaction systems of the type gas-liquid-solid. TBRs are packed with a solid catalyst over which the streams of gas and liquid flow cocurrently downward. Similar behavior of plug flow can ensure a high degree of conversion of the liquid reactants, which is one of the advantages of trickle-bed reactors over three-phase reactors, where the catalyst is introduced as either a suspension or a fluidized bed. TBRs can also operate with high flow rates of both phases without flooding, which is of great importance in processes in which large amounts of gas or liquid are purified. TBRs have traditionally been employed in refineries and in the chemical and petrochemical industries. In the petrochemical industry, the annual throughput of threephase solid-bed reactors (in the processes of hydrotreating various petroleum fractions, including hydrodesulfurization, hydrodemetallization, hydrodenitrification, hydrorefining, and hydrocracking) is estimated at 1.6 billion tons.1 Therefore, any improvement in the operation of three-phase reactors used in these processes would lead to measurable economic results. Meanwhile, the large and increasing number of publications devoted to both biochemical processes and advanced oxidation processes shows that TBRs are envisaged for the purification of wastewaters and gases polluted with toxic organic compounds using a bed of immobilized bacteria or chemical catalyst, respectively.2 The hydrodynamic operation of trickle beds can be affected by changing the multiphase flow regime from the trickleflow regime (or gas-continuous flow, which is the most frequently used in practice) to the pulsing-flow regime. According to several experiments, pulsing flow has received a growing interest because of its excellent properties for carrying out processes in which mass transfer is a ratelimiting step (e.g., hydropurification). This is true because, in this regime, the mass-transfer coefficients are several times higher than in the trickle-flow regime and the packing surface is comprehensively wetted by the liquid, which is crucial when the rate-limiting step is diffusion of the reactants in * Author to whom correspondence should be addressed. Tel.: +351239798723. Fax: +351-239798703. E-mail:
[email protected].
the liquid phase. In the trickle-flow regime, spreading of the liquid over the catalyst surface is controlled by the nature of the solid surface and its dry or wetted condition. Trickleand pulse-flow characteristics are extremely complex and associated with the strong interactions of the fluids in the bed. 2. Previous Work Most experimental studies on trickle-bed hydrodynamics have been restricted to the trickle- and pulse-flow regimes. Several techniques have been used to identify the flow-regime transition from trickle to pulse flow. Latifi et al.3 used a microelectrode technique to determine the flow-regime transition in trickle-bed reactors. However, detailed information on the frequency distribution in the pulse-flow regime was not reported. Nonlinear time series analysis has been extensively used to characterize flow-regime transitions in bubble columns and fluidized-bed reactors.4-6 Relatively few attempts have been made to use these techniques to identify flow-regime transitions in trickle-bed reactors. Krieg et al.7 studied flow regimes in trickle beds with wall pressure fluctuations and power spectral density. Their study indicated that visual techniques are not able to capture regime transitions accurately. They used variations in pressure fluctuations and conductance values to identify regime transitions. Horowitz et al.8 used nonlinear time series analysis tools such as rescaled range analysis and correlation dimension to find the flow-regime transition. Urseanu et al.9 identified flow-regime transition based on standard deviations in the pressure drop. However, this technique could not give sharp boundary at which the transition occurs. It is therefore essential to develop easy-to-use techniques to identify flowregime transitions in trickle-bed reactors. The benefits of trickle-bed reactor operation under the induced pulsing-flow regime were investigated using experiments and modeling by Wilhite et al.10 The trickling- and pulsing-flow regimes were achieved by cycling the liquid feed under time-averaged conditions and extended the experimental results on the hydrogenation of phenylacetylene over Pt/ γ-Al2O3 catalyst, showing that, in a laboratory-scale reactor, operating under mild gas-limiting conditions provides better
10.1021/ie900767q 2010 American Chemical Society Published on Web 12/22/2009
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performance for steady flow, as opposed to induced pulsing flow. Burghardt et al.11 characterized the hydrodynamics of pulsing flow in a trickle-bed reactor operating at elevated pressures. Comprehensive investigations of the hydrodynamics were performed for the transition line between the gascontinuous-flow and pulsing-flow regimes, the liquid holdup, and the pressure drop in the bed, as well as the pulse velocity and the frequency of pulsations. They also proposed mathematical models describing the reactor hydrodynamics and verified the models through the application of their own base of experimental data in which the measured values of the pulse velocity and frequency of pulsation were expressed in the form of correlation equations. Advanced experimental characterization techniques such as magnetic resonance imaging have recently been used to image local pulsing events that are associated with the transition from trickle to pulsing flow in trickle-bed reactors. Gladden et al.12 reported magnetic resonance imaging measurements of the liquid distribution in two and three dimensions within a 43-mm-internal-diameter column packed with cylindrical porous pellets of 3 mm length and diameter, operating under conditions of cocurrent air-water downflow. The three-dimensional data allowed the spatial extent and number of local pulsing events to be quantified as a function of the bed operating conditions. Local temporal correlations in the liquid content were observed in the trickle-flow regime, suggesting that the local pulses originate from instabilities in liquid films present on the surface of the catalyst pellets. These data provide strong evidence in support of earlier theoretical studies proposing that the trickle-to-pulse transition originates from film instabilities on the surface of catalyst pellets comprising the bed and, hence, that the transition itself is best modeled by considering the pore-scale characteristics of the trickle-bed reactor. More recently, Wilhite et al.13 studied experimentally the mechanism for the formation of cocurrent downflow pulse flow. Those authors pointed out that pulses form from trickling flow as a result of a global convective instability. Existing global instability models based on averaged (dispersed-flow) momentum equations were modified to explain the experimental results. A similar dispersed-flow model was used to explain the bubbling-topulsing flow transition. Although the predictions agree with the experimental data for part of the range, the model accuracy is limited by the accuracy of the constitutive expressions for the interaction forces between phases. Recently, models based on computational fluid dynamics (CFD) are showing promising results for the treatment of a variety of complex reactors. Several efforts have been made to develop computational flow models for trickle-bed reactors. Attou and Ferschneider14 developed a one-dimensional flow model for the prediction of global hydrodynamic parameters. Because it is one-dimensional, their model cannot take account of radial variations in bed porosity. Jiang et al.15 developed a two-dimensional CFD model including variations in bed porosity. This model was able to capture some of the key features of hydrodynamics of trickle beds. Iliuta et al.16 and Souadnia and Latafi17 used CFD models for predicting hydrodynamic characteristics over a wide range of operating parameters. Gunjal et al.18 used a similar CFD model for studying liquid-phase mixing and liquid distributions. However, all of these studies were restricted to trickle-flow regime. None of the CFD models published so far have been used to simulate spray or pulse regimes or to simulate multiphase reacting flows.
With the aid of modern CFD codes, this work encompasses the identification of different flow regimes and knowledge of their flow characteristics, because they are essential to other transport processes such as heat- and mass-transfer rates that are dependent on flow regimes and the extent of interactions among gas, liquid, and solid phases. To gain insight into the hydrodynamic operation of TBRs at pulsing-flow conditions, an Eulerian CFD framework was developed to identify the relevant parameters that can affect the hydrodynamic transition from the gas-continuous-flow regime to the pulsing-flow regime. In the pulse-flow regime, model parameters including pulse formation, pulse frequency, and holdup are evaluated in terms of their effects on TBR hydrodynamic characteristics. In addition, the velocity of pulses traveling along the bed, the frequency of pulsations, and their structure (i.e., the length of the pulses and the length of the liquid-rich zone) are compared to experimental data on liquid saturation and two-phase pressure drop. 3. CFD Methodology Taking into account the numerical power available today to address complex chemical process operating and design issues, our case study outlines an alternative CFD modeling method for investigating the hydrodynamic behavior of a trickle-bed reactor at elevated pressure operating in the pulsing-flow regime. Transport phenomena such as interfacial momentum transfer are integrated into an Eulerian k-fluid model, resulting from the volume averaging of the continuity and momentum equations, and the model is solved for a 3D representation of the bed at unsteady state. In the Euler-Euler mathematical approach, both continuous and dispersed phases are considered as interpenetrating continuous media.19 This model incorporates two-way coupling, and interfacial momentum transfer between the liquid and the gas comprises the individual force contributions for each phase, including also the mass force as an inertial force caused by relative acceleration, the effect of turbulent fluctuations on the effective momentum transfer, and the velocity gradients. The CFD model equations were implemented in the commercial software FLUENT using user-defined routines. Only the main conservation equations are presented. The continuity and momentum balances for phase q are given by eqs 1 and 2, respectively n
∑ (m˙
∂ (R F ) + ∇ · (RqFqb V q) ) ∂t q q
pq
-m ˙ qp) + Sq
(1)
p)1
∂ (R F b u ) + ∇ · (RqFqb u qb u q) ) -Rq∇p + ∇ · cτq + RqFqb g + ∂t q q q n
∑ (Rb
pq
+m ˙ pqb u pq - m ˙ qpb u qp)
(2)
p)1
b Rpq represents the interphase force and depends on the friction, pressure, cohesion, and other effects. It is subject to the bqp and b Rqq ) 0. The momentum balance conditions that b Rpq ) -R equation is closed, with interphase exchange terms assuming individually the form of a simple phase interaction term given by the equation n
∑ bR
pq
p)1
n
)
∑K
bp pq(u
-b u q)
(3)
p)1
where Kpq ) Kqp is the interphase momentum exchange coefficient, which is expressed based on the model developed by Attou and Ferschneider.20 The interphase coupling terms are
Ind. Eng. Chem. Res., Vol. 49, No. 3, 2010
written in terms of interstitial velocities and phase volume fractions for gas-liquid, gas-solid, and liquid-solid momentum exchange forms, as expressed in the equations
[
KGL ) RG
[
KGS ) RG
E1µG(1 - RG)2 RG2dp2
(
RS 1 - RG
)
2/3
RG2dp2
KLS ) RL 11
(
(
RS 1 - RG
)
RL2dp2
+
)] 1/3
F5 )
(
E2FLuGRS RLdp
)
)] 1/3
(5)
(6)
Burghardt et al. reviewed both the experimental data and mathematical criteria concerning the transition of the gascontinuous-flow regime to the pulsing-flow regime in reactors operating at atmospheric pressure, whereas Al-Dahhan et al.1 presented empirical correlations and theoretical models that were developed or tested using experimental data obtained at elevated pressures in a trickle-bed reactor. In this area, two hydrodynamic models were developed for the comparison between the transition lines obtained experimentally and the mathematical criteria available in the literature that are the models of Grosser et al.21 and Attou and Ferschneider.20 The criterion investigated was derived based on the linear stability analysis of the equations describing the multiphase flow in trickle beds. In the present work, we used the polynomial form of the criterion presented by Attou and Ferschneider.20 It is worth mentioning that eqs 1 and 2 describe the flow of interspersed fluid phases, and with proper closures expressed in eqs 4-6 by Kpq, they can give accurate description of flow in trickle-bed reactors as reported by Gunjal et al.18 and Lopes and Quinta-Ferreira.19 The most extensive use of such equations has been for predicting the onset of instabilities in the local void fraction for solid-gas and gas-liquid flows.22 The continuity and momentum equations (eqs 1 and 2) are functionally equivalent to the set of equations employed by Grosser et al.,21 which were implemented in C language in the Eulerian CFD framework for the trickle-to-pulse transition. The two momentum and mass balance equations can be converted into a single wave equation with spatial derivatives as shown by Wilhite et al.13 The neutral stability condition is established through the substitution of a small perturbation in the volume fraction term, where s is a complex frequency and ω is a real wavenumber in the vertical flow direction. Equations of this type have been used extensively in hydrodynamic analysis, including those of falling films23,24 and sheared liquid layers.25,26 Using this methodology, the analysis of Grosser et al.21 and Attou and Ferschneider20 yielded the expressions in eqs 9-13 for the Fi coefficients corresponding to the trickling-flow regime. To establish the stability condition, the real part of the attenuation factor or the pulsation of the harmonic perturbation (s) must be less or equal to zero, which gives the inequality Ω ≡ F1F52 + 2F2F3F5 + F22F4 e 0
(7)
F1s + (F2 + 2jωF3)s - (ω F4 + jωF5) ) 0
(8)
2
2
where the coefficients Fi are given by F1 )
FG FL + RG (1 - RG)
F4 )
(4)
+
RS E2FGuG(1 - RG) RGdp 1 - RG E1µLRS2
RG
2
-
F3 )
(
2/3
λG,uG
+
RS E2FG(uG - uL)(1 - RG) RGdp 1 - RG E1µG(1 - RG)2
F2 ) -
(9)
uL
[
λL,uL + πL,uL
λL,uG + λG,uL
+
(1 - RG)
2
(1 - RG)2 λL,uL + πL,uL (1 - RG)2
+ -
fint,G
(10)
RG(1 - RG)
FGuG F L uL + RG (1 - RG)
(11)
[
]
FGuG2 FLuL2 ∂ + (p - pL) RG (1 - RG) ∂RG G
fint,L + fw,L
[
+ uG
RG2 λG,uL
λG,uG
RG(1 - RG)
RG2
]
+
-
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λL,uG RG(1 - RG) λL,RG
(1 - RG)
-
]
(12) +
λG,RG RG
(13)
and λq,uq and πL,uL are derivative quantities defined by λq,uq ) ∇fint,q
πL,uL )
∂fw,L ∂uL
(14)
Turbulent flows are characterized by fluctuating velocity fields mixing transported quantities such as momentum, energy, and species concentrations and cause the transported quantities to fluctuate as well. We used the k-ε mixture model, which is a semiempirical model based on model transport equations for the turbulence kinetic energy (k) and its dissipation rate (ε) as described for the liquid phase in eqs 15 and 16
(
)
(
)
µt,L ∂ (FLRLkL) + ∇ · (FLRLb u LkL) ) ∇ · RL ∇kL + RLGk,L ∂t σk RLFLεL + RLFLΠkL (15) µt,L ∂ (F R ε ) + ∇ · (FLRLb u LεL) ) ∇ · RL ∇εL + ∂t L L L σε εL RL (C1εGk,L - C2εFLεL) + RLFLΠεL kL
(16)
The representative computational grid for the experimental system investigated in this work is described elsewhere.27 It consists of a cylindrical vessel with a 5-cm internal diameter and a 1-m bed height packed with spherical, 2-mm-diameter catalyst particles. The catalytic bed was meshed in tetrahedral cells by means of the FLUENT preprocessor GAMBIT 2. The mesh quality was analyzed using the skewness criteria, and the results were made to be grid-independent. Numerical simulations were previously compared to experimental data in order to validate the predicted hydrodynamic parameters pressure drop and liquid holdup.28 The simulated operating conditions were 10-30 bar pressure and temperatures from 290 to 500 K. Gas and liquid mass flow rates were in the range 0.10-0.70 and 0.05-15 kg/(m2 s), respectively. The system domain was discretized by an unstructured finitevolume method using the CFD solver FLUENT 6. The gas flow rate at the distributor was defined by inlet-velocity-type boundary conditions with the gas volume fraction changing according to the specifications made in the simulations. The flow model was based on solving Navier-Stokes equations for the Eulerian-Eulerian multiphase model along with a multiphase k-ε turbulence model. The governing differential equations were solved using an iterative solution to the discrete form of the mathematical model using a PISO algorithm for pressurevelocity coupling with an implicit formulation for unsteady integration and second-order upwind scheme discretization for spatial derivatives. The gas and liquid were described as interpenetrating continua, and equations for the conservation
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Figure 1. Effect of gas flow rate on liquid holdup versus liquid flow rate (P ) 30 bar, d ) 2 mm, experimental data from ref 25).
of mass and momentum were solved for each phase. The transient calculations were made for two-phase flow starting with different time steps, and the converged solution was assumed to be found when the scaled residuals of all variables were smaller than 10-6. 4. Results and Discussion The Eulerian CFD simulation of the pulse-flow regime requires a detailed understanding of the complex interactions of a liquid spreading on a solid surface, capillary forces, and gas flow. Although the underlying physics of such complex flows is not completely understood, computational models can shed some light on such complex flows. In the present work, CFD modeling of the periodic operation of trickle beds was carried out to identify differences and similarities between periodic operation (liquid-rich-gas-rich feed) and the pulseflow regime observed experimentally. In Figure 1, the liquid holdup predictions are plotted as a function of liquid flow rate at different gas flow rates in the range 0.1-0.7 kg/(m2 s) for 2.0-mm spheres as the packing material. The liquid holdup increases with increasing liquid flow rate and decreases with increasing gas flow rate. A comparison of the measured liquid holdup29 versus a number of literature correlations was found to be in good agreement.30 When the liquid flow rate was increased, the transition boundary from trickling to pulsing flow remained practically constant for different packing surface areas. However, when the gas flow rate was increased, the point of pulse inception began to move to the top of the trickle-bed reactor. This fact can be explained by the higher volumetric gas flow rate with increasing distance from the top of the column due to the pressure drop over the bed. Therefore, a relatively large increase in gas flow rate will be necessary to shift the point of pulse inception upward when compared to pressure drop. The effect of cycling the liquid feed on the liquid holdup at gas flow rates just before pulse initiation is shown in Figure 2. According to Figure 2, the introduction of the additional liquid feed results in an instantaneous increase in liquid holdup. The back of the liquid-rich region is characterized by a more gradual decrease in liquid holdup. A well-defined high liquid holdup is reached as a result of the additional liquid feed. This high liquid holdup is probably identical to the liquid holdup during steadystate operation at a steady liquid flow rate, equivalent to the high liquid feed rate. Because of cycling of the liquid feed, the
Figure 2. Liquid holdup profile during cycling of liquid feed from L ) 5 f {6, 7, 8} f 5 kg/(m2 s) [P ) 30 bar, d ) 2 mm, G ) 0.7 kg/(m2 s)].
liquid holdup varies between two values resembling the liquid holdups obtained during steady-state operation at comparable liquid feed rates. It is worth mentioning that the formation of continuity shock waves resulting from a step change in the liquid flow rate can also be identified by means of CFD codes. Continuity waves occur whenever the flow rate of a substance depends on the amount of that substance present. The accuracy of the calculated values increases with increasing difference between high and low liquid holdups. Mainly because of the step change in the liquid feed rate, continuity shock waves are initiated in the column. As a result, the column can be split into two regions of different liquid holdups, both corresponding to steady-state conditions in the pulsing-flow regime. At the same time, two different steady-state conditions are present in the column. These steady-state conditions are separated by a moving boundary whose velocity can be calculated using accurate liquid holdup data obtained during steady-state operation at equivalent liquid feed rates. During liquid-induced pulsing-flow simulations, it is possible to induce pulses at average liquid flow rates, generally associated with trickle flow during steady-state operation. Although throughputs of liquid are equal under the two sets of conditions, the prevailing flow regime is pulsing instead of trickle flow. The advantages associated with pulsing flow can be utilized to enhance the mass- and heat-transfer rates, resulting in improved reactor performance. Moreover, with liquid-induced pulsing flow, longer contact times can be achieved compared to self-generated pulsing flow, whereas average liquid flow rates are reduced. This fact is commonly reported in the literature as the enlargement of the pulsing-flow regime by cycling of the liquid feed. The appearance and downward movement of a liquid-rich region in the process of liquid-induced pulsing flow results from the step change in the liquid feed rate that is responsible for the initiation of continuity shock waves. The effect of superficial liquid velocity on liquid holdup at different superficial gas velocities and at P ) 9 bar is plotted in Figure 3, whereas Figure 4 shows the similar influence at an increased operating pressure of 12 bar. According to these computational runs, one can observe two branches in the rising liquid holdup that can certainly be separated by the dotted vertical transition line between the gas-continuous and pulsingflow regimes computed by the stability criterion of eqs 7 and 8. As the superficial gas velocity increased, the liquid holdup became smaller due to the high interaction regime. The Eulerian CFD model slightly underpredicted the liquid fraction in the
Ind. Eng. Chem. Res., Vol. 49, No. 3, 2010
Figure 3. Effect of superficial liquid velocity on liquid holdup for different gas velocities at P ) 9 bar (experimental data from ref 11).
Figure 4. Effect of superficial liquid velocity on liquid holdup for different gas velocities at P ) 12 bar (experimental data from ref 11).
whole simulated flow regime at P ) 9 bar (Figure 3), as well as at P ) 12 bar (Figure 4). Nevertheless, it should be pointed out that the lower deviations between the computed results and the experimental data were attained at the highest operating pressure. Moreover, the CFD framework handled the computation of liquid holdup properly at moderated pulsing-flow conditions at different gas-liquid interaction velocities. The velocity of the pulses is plotted in Figure 5 as a function of superficial gas velocity at different superficial liquid velocities at P ) 9 bar. According to Figure 5, the pulse velocity increases with the gas velocity, and the higher the liquid velocity is, the quicker the pulse travels through the catalytic bed, as one should expect. The CFD profiles attained for the pulse velocity systematically underpredicted the experimental data.31 The computed pulse velocities for different superficial liquid velocities exhibited two branches that can be differentiated at uG ) 0.25 m/s. This fact can be explained by the effect of gas velocity on the pulse formation, so that, once the pulse is generated, the pulse velocity does not depend as significantly for the higher gas velocities as for the lower ones. This behavior is supported also by the experimental data, as the value of the pulse velocity increases with both the liquid and the gas velocities; however, at high gas velocities, the pulse velocity stabilizes. Bartelmus et al.32 observed this propensity for different pressures, and their findings agree especially with the variation of the pulse velocity in reactors operating at atmospheric pressure.
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Figure 5. Effect of superficial gas velocity on pulse velocity for different liquid velocities at P ) 9 bar (experimental data from ref 31).
Figure 6. Effect of superficial gas velocity on pulse velocity for different reactor pressures (experimental data from ref 31).
The computed pulse velocity as a function of superficial gas velocity for different pressures is plotted in Figure 6. The CFD profiles for the pulse velocity agree reasonably well with the experimental data.31 In the whole range of superficial gas velocities simulated, the Euler-Euler model indicated that, for operation at isobaric conditions, the pulse velocity increases with increasing gas velocity and the higher the operating pressure is, the slower the pulse moves along the trickle-bed reactor. Moreover, at the highest pressure (P ) 12 bar), the pulse velocity becomes practically independent of the gas velocity. Therefore, the operating pressure can be regarded as having an opposite effect when compared to the influence of the superficial liquid velocity; for example, at the same velocities of the two phases, an increase in the pressure leads to a drop in the pulse velocity, as shown in Figure 6. According to the Eulerian simulations carried out so far on the pulse-flow regime, the velocity of the initiated pulses was not too different from the shock-wave velocity. This fact is not in accordance with the experimental observations reported in the literature that pulses will eventually move out of the liquidrich region and, under these circumstances, the pulse velocity would be much higher than the shock-wave velocity. The pulse frequency is another feature of liquid-induced pulsing flow related to the tuning of the pulse dynamics or the time constant of the pulses. In this regard, the number of pulses generated during one liquid feed cycle was investigated with the present
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Figure 7. Effect of superficial liquid velocity on pulse frequency for different gas velocities at P ) 9 bar (experimental data from ref 31).
Figure 9. Effect of superficial liquid velocity on pulse frequency for different reactor pressures at uG ) 0.26 m/s (experimental data from ref 31).
Figure 8. Effect of superficial liquid velocity on pulse frequency for different reactor pressures at uG ) 0.16 m/s (experimental data from ref 31).
Figure 10. Effect of superficial liquid velocity on pulse length for different gas velocities at P ) 9 bar (experimental data from ref 31).
CFD model to evaluate both the critical length of the liquidrich region and the effects of different packing materials. Trivizadakis et al.33 showed that the values of pulse velocity and frequency, as well as the length of the pulse, should be correlated as functions of the actual velocities of the gas and liquid phases. Hence, the actual velocity for a single phase is given by the ratio between the superficial phase velocity and the respective phase holdup. Figure 7 shows the computed pulse frequencies as a function of superficial liquid velocity for different superficial gas velocities at P ) 9 bar. The qualitative behavior observed in Figure 7 is in agreement with that shown in Figure 5 for the pulse velocity. However, slight differences can be observed regarding the two branches previously identified. The pulse frequency has an inflection point at uL ) 0.21 m/s, so that, until this point, the pulse frequency is increasing rapidly and then it decelerates from that value of superficial liquid velocity onward. Once more, the Eulerian model slightly underpredicted the experimental data23 for different superficial gas velocities. The effect of operating pressure on the pulse frequency as a function of superficial liquid velocity is shown in Figure 8 at uG ) 0.16 m/s. As one should expect, the increasing of reactor pressure led to lower pulse frequencies. The computed pulse frequency as a function of superficial liquid velocity at uG ) 0.26 m/s is plotted in Figure 9. According to Figures 8 and 9, the same qualitative behavior was identified for both superficial
gas velocities, and the CFD profiles for the pulse frequency were stretched out for the higher one. Therefore, for all of the pressures investigated, the frequency of pulsations noticeably increased with increasing liquid flow rate and, to a lesser extent, with increasing gas velocity; at higher pressures, the effect of the gas velocity on the frequency of pulsations became more prominent. As one can conclude, an increase in the operating pressure at constant phase velocities leads to a recognizable increase in the frequency of pulsations. Regarding the structure of the pulses, based on the experimental values of the pulse velocity and the frequency of pulsations, the length of the pulses formed in the reactor can be calculated as the ratio between the pulse velocity and the respective frequency. Figure 10 shows a plot of the computed length of pulses as a function of superficial liquid velocity for different gas velocities at P ) 9 bar. As can be seen from this figure, the pulse length decreases with increasing superficial liquid velocity, and the higher the superficial gas velocity, the shorter the pulse attained at constant liquid velocity. The Eulerian profiles followed the experimental data, but one should not that the higher differences were achieved at lower liquid velocities. The effect of operating pressure on the pulse length as a function of superficial liquid velocity is plotted in Figure 11 for uG ) 0.16 m/s, whereas Figure 12 shows a plot of the influence of the reactor pressure at uG ) 0.26 m/s. The pulse
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operation. Finally, the pulse frequency and the number of pulses generated during one liquid feed cycle were examined to gain further insight into features of the pulse-flow regime. Acknowledgment The authors gratefully acknowledge financial support from REMOVALS (6th Framework Program for Research and Technological Development) FP06 Project 018525 and Fundac¸a˜o para a Cieˆncia e Tecnologia, Portugal. Nomenclature
Figure 11. Effect of superficial liquid velocity on pulse length for different reactor pressures at uG ) 0.16 m/s (experimental data from ref 31) .
C1ε, C2ε ) k-ε model parameters: 1.44 and 1.92, respectively d ) particle nominal diameter, m E1, E2 ) Ergun’s constants b g ) gravitational acceleration, 9.81 m/s2 G ) gas mass flux, kg/(m2 s) k ) k-ε model kinetic energy Kqp ) interphase momentum exchange coefficient for phases p and q L ) liquid mass flux, kg/(m2 s) p ) pressure, bar b Rpq ) interaction force between phases p and q s ) complex frequency of the wave equation b u ) superficial velocity vector, m/s Greek Symbols Rq ) volume fraction of the qth phase ∆p ) total pressure drop, bar ε ) k-ε model dissipation energy µq ) viscosity of the qth phase, Pa s Fq ) density of the qth phase, kg/m3 σk, σε ) k-ε model parameters: 1.2 and 1.0, respectively τq ) shear stress tensor of the qth phase, bar ω ) real wavenumber
Figure 12. Effect of superficial liquid velocity on pulse length for different reactor pressures at uG ) 0.26 m/s (experimental data from ref 31).
structures attained for different gas velocities are qualitatively similar; however, it is worth mentioning that the sharper profile was achieved at the highest gas velocity (uG ) 0.26 m/s) because of the strong interaction of the gas-phase velocity with the pulse length regardless of the reactor pressure. 5. Conclusions For the purposes of TBR industrial applications, liquidinduced periodic operations are preferable because reactor operation with natural pulsing is difficult for large reactors. Therefore, it is worthwhile to apply state-of-the-art CFD modeling to simulate the periodic operation of a trickle bed. In the natural pulse-flow regime, liquid-enriched pulses form after some distance from the inlet, and they accelerate while moving downward. Formation of the pulses is associated with complex interactions among capillary forces, wall adhesion, and convective forces. To gain insight into pulse flow in trickle beds, this work focused on the CFD simulation of periodic operation in trickle beds with induced pulses by manipulating the inlet liquid velocity. First, the steady- and unsteady-state hydrodynamics of pulsing flow were examined in terms of liquid holdup. Second, the enlargement of the pulsing-flow regime in liquid-induced operation and the necessary gas flow rate and available column length for pulse formation were investigated under high-pressure
Subscripts G ) gas phase L ) liquid phase q ) qth phase S ) solid phase
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ReceiVed for reView May 12, 2009 ReVised manuscript receiVed November 19, 2009 Accepted November 30, 2009 IE900767Q
