Transient Behavior and Stability in Miniaturized Multiphase Packed

Ind. Eng. Chem. Res. 2010, 49, 1033–1040

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Transient Behavior and Stability in Miniaturized Multiphase Packed Bed Reactors Nathalie Ma´rquez,† Pedro Castanõ,† Jacob A. Moulijn,† Michiel Makkee,† and Michiel T. Kreutzer*,‡ Catalysis Engineering and Product and Process Engineering, Delft UniVersity of Technology, DelftChemTech, Julianalaan 136, NL 2628 BL Delft, The Netherlands

The step response, including various startup procedures, in a three-phase microreactor of 2 mm internal diameter packed with nonporous particles of 100 µm is reported. We demonstrate that the bed behaves reproducibly through many cycles of operating conditions. Interestingly, we find that the different startup procedures have little effect on the steady state that is achieved. In other words, minimal hysteresis was observed, in sharp contrast to larger-scale reactors with larger particles where prewetting has a remarkable impact on the hydrodynamic behavior. The powder-packed beds have very high liquid saturation values, and prewetting is not needed. At least four liquid-residence times were needed to achieve stable pressure drop and dispersion values over the bed. This indicates that the hydrodynamic response into a stable operation may well be the limiting factor that determines the rate at which kinetic experiments can be performed in high-throughput equipment. 1. Introduction High-throughput catalyst testing has gained increasing popularity, not only for stage I testing (testing qualitatively many new catalyst formulations) but also for stage II (measuring quantitatively performance, kinetics, and deactivation).1-7 The reactors used are significantly smaller than the conventional packed beds, and design rules and operating procedures for these smaller-scale systems are very limited. In this paper we address one important aspect of operation: the transient behavior. The time required to achieve steady state, of limited relevance in industrial units, is crucial in high-throughput testing, and we are motivated to understand how fast we can switch from one experimental condition to another. There are important differences in flow behavior upon downscaling. In industrial and laboratory trickle bed reactors, gravity and inertia are important: the relative importance of gravity with respect to surface tension is given by the Bond number Bo, in large scale systems, 0.1 < Bo < 10. This indicates that gravity is neither dominant nor unimportant, leading to the well-known hard-to-quantify difference between upflow and downflow and strong hysteresis effects in wetting. The importance of inertia, relative to viscous stresses, is given by the Reynolds number Re, 0.1 < Re < 100 for trickle beds. In miniaturized packed beds, Bond numbers Bo and Reynolds numbers Re are of the order 10-2-10-3. This has the pleasant consequence that we can ignore the gravity and inertial terms in the Navier-Stokes equations: upflow and downflow are identical. Rather, the dominant forces are viscous and interfacial forces in microfluidic devices. The dimensionless capillary Ca number is the ratio between these two forces. Miniaturized packed beds with dp ∼ 100 µm have capillary Ca numbers on the order of 10-4-10-1 which lead to flow patterns completely different to those observed in larger-scale, three-phase systems. The flow is dominated by viscous stresses and the interfacial tension at the gas-liquid boundary. As in large-scale systems, * To whom correspondence should be addressed. Tel.: +31 15 278 9084. Fax: +31 15 278 5006. E-mail address: [email protected]. † Catalysis Engineering. ‡ Product and Process Engineering.

flow maps have been constructed for microreactors that map flow patterns on a 2D domain of liquid and gas velocities.8 Low Ca values indicate that interfacial forces are dominant, inducing the area minimization of gas-liquid interfaces into long thin threads that meander through the packed bed. It seems that droplets flows are more prevalent in this regime. High Ca values indicate higher viscous forces, and stratified flows are more dominant at high Ca number. The capillary number and gas/ liquid ratio are, however, not enough to characterize the flow pattern; the actual flow pattern, that can be present in a micropacked bed, depends on how the fluids are introduced into the bed.9 Figure 1 shows that the hydrodynamic behavior of multiphase flow in micropacked beds has more in common with flow in porous media than with flow in industrial packed beds. In the porous-media literature, the main interest is in the displacement of one phase by another at constant or variable saturation values for imbibition and drainage applications.11,12 Considerable effort

Figure 1. Typical ranges of force ratios (Bo ≡ [(FL - FG)gl2]/σ is the gravity/surface tension ratio and Ca ≡ ηLuL/σ is the viscous force/surface tension ratio) in multiphase flow for packed beds, micropacked beds, and fine porous media. The term u is the superficial velocity, F is the density, l is the characteristic hydrodynamic length, i.e. wetted area over wetted perimeter (pore diameter dpore for the petroleum recovery application and particle diameter dp for the packed bed applications), g is gravity, η is the viscosity, and σ is the surface tension. The subscripts L and G refer to liquid and gas, respectively. This is based on ranges in the work of de Santos.10

10.1021/ie900694r  2010 American Chemical Society Published on Web 08/05/2009

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Ind. Eng. Chem. Res., Vol. 49, No. 3, 2010

has been invested in extending Darcy’s law to multiphase flow in porous media by adapting the permeability coefficient. Even though this gives simple equations, several authors13,14 have argued that the different nature of forces that act in a multiphase system invalidate this approach. Another approach is to resolve each pore of the network, including Laplace pressures over interfaces.11,12,14,15 Such analyses give insight into fingering patterns that develop when a liquid penetrates into another stagnant liquid. The case of two conflowing fluids, which resembles multiphase reactors more, has not received the same level of attention. Large-scale reactors exhibit either trickling or pulsing flow. Numerous studies have reported multiple hydrodynamic states, or hysteresis, in the trickling flow regime, depending on the flow history of the bed.16-20 A plot of the pressure drop per unit of reactor length versus the liquid superficial velocity at constant gas velocity can have the shape of a closed loop with two branches: the lower branch corresponds to an increase in liquid-flow rate from a dry initial condition and the upper branch corresponds to the subsequent decrease of liquid-flow rate from a fully wetted condition. For liquid superficial velocities between 1 to 10 mm/s and a gas superficial velocity of the order of 100 mm/s, the pressure drop per unit of reactor length is in the range of 1-20 kPa/m and the pressure drop in the two branches can differ by a factor of 2 for the same gas and liquid velocities. The hysteresis effect increases as the particle size decreases for a particle diameter (dp) range between 0.5 and 8 mm.21,22 In fact, the hysteresis phenomenon is only observed in the trickling flow regime and will disappear when particles are fully wetted by a change in flow pattern, e.g. by short-lived full wetting in a pulsing flow regime. In contrast to the well-studied hysteresis phenemoma, there are few reports of the time required to reach a hydrodynamic steady state in multiphase reactors. According to the work of Ravindra et al.,23 after startup the pressure drop in the bed increases with time and it attains a steady-state value in a period that can vary between 600 and 20 000 s, depending on the type of packing, the prewetting procedure, and the inlet liquid distribution. Van der Merwe et al.24 show, using X-ray radiography, that the liquid saturation inside the bed stabilizes between 50 and 150 s after startup when the bed is prewetted following different protocols. The nonprewetted bed did not reach steady state after 10 000 s of continuous operation. Stanek et al.25 reported pressure and liquid holdup overshoots at startup and after a step change of the liquid-flow rate for a countercurrent gas-liquid packed bed column. For their transient experiments, the new steady state was reached within 20 s. As pointed out by Tabeling,26 viscous effects can make the pressure and flow densities vary over substantial time scales in a microsystem. There is an important analogy to chromatography here, where the “bottleneck effect”, related to the compressibility of liquid or gas, explains the long time required to achieve steady flow, even when pulse-free syringe pumps are used.27 In such cases, that are also encountered in microreactors, it is important to consider both volume and resistance in the bed itself and in the connected feed and outflow tubing. A large volume in the feed section gives a large capacity that can delay a new steadystate: in order to achieve a stable flow, it is necessary first to compress the flow in the large feed chamber and the compressibility of the fluid will enlarge the time to achieve the necessary pressure, which can be minutes or even longer, depending on the fluid properties (viscosity and compressibility), the channel

Figure 2. Micropacked bed for stability and transient times studies. (A) 10 µL tracer injection loop. (B) Zoom showing the way that gas and liquid are introduced in the bed. (C) Differential pressure transmitter. (D) Gas-liquid separator. (E) Refractive-index cell.

or column characteristics (dimensions and porosity), the feedsection volume, the flow rate, and the elasticity of the materials.28 The objective of this work is to define operating procedures and develop design rules for small-scale catalyst testing equipment. We analyze the dynamic behavior for multiphase flow in a miniaturized packed bed of 2 mm internal diameter filled with glass (nonporous) particles of 100 µm. As the short description of relevant literature shows, experimental data on the response of reactors with such small particles (dp ∼ 100 µm) is still unavailable at present, whether it concerns hysteresis or the response to a step change. The paper is organized as follows. We begin by describing our experiments, in which we study the dynamics of the fluid flow by monitoring the pressure drop and hydrodynamic dispersion of a tracer in the liquid phase over time. Next, we report and analyze the data in terms of hydrodynamic stability and response to step changes in flow and startup procedure. Later, we discuss the different factors that influence the characteristic time of response to a step change in both gas and liquid flow. 2. Experimental Section 2.1. Experimental Setup. The experimental apparatus (Figure 2) is a packed bed glass column consisting of (i) liquid inlet, (ii) gas inlet, (iii) the packed bed, (iv) separation of phases, and (v) analysis. Tetradecane (liquid) is delivered to the column by a syringe pump (ISCO, model 500D) with a flow rate between 0.01 and 0.10 mL/min. The pump was connected to an HPLC injection valve (Rheodyne, model 7725) with a sample volume of 10 µL (section A). The gas feed line was connected to the bed in a T-junction. The liquid feed tubing passed through this T-junction, such that the gas flowed through the annular area between the liquid feed line and the outer tubing (zoom B). N2 gas was fed at flow rates between 0.05 and 1.0 mL/min at normal conditions with a mass-flow controller (El-flow; Bronkhorst). The differential pressure drop over the system was measured with a differential pressure transducer (Deltabar PMD


Figure 3. Hydrodynamic reproducibility for dry startup at varying liquidflow rate. The gas-flow rate φG ) 0.50 mL/min (interstitial gas velocity uiG ) 5.15 mm/s). (a) Pressure drop. (b) Liquid saturation. The data points are at steady-state conditions. The characteristic times of response to a step change depend on the flow rates and vary between 1800 and 7200 s.

130) located between the gas-feed tubing at the inlet section and the gas-exit tubing at the separation section, as indicated by the letter C. All experiments were performed at room temperature. The packed bed consisted of a glass tube of 2.0 mm inner diameter. Two columns of different lengths, 7 and 97 cm, were used. Both columns were filled with monodisperse glass spherical spheres (GP0116, sieve fraction 106-125 µm; Whitehouse Scientific) under regular tapping. We have found that this packing procedure is reproducible in the sense that we obtain the same pressure drop and residence time characteristics in repacked columns. Still, all experiments were carried out with one set of columns, so no experimental variations are introduced by differences in packing. The porosity of the beds was determined by weight as 0.43. The gas was separated from the effluent of the column with a gas-liquid separator based on the capillary pressure of a metal filter with 10 µm pores (10SR4-10, VICI AG), as depicted in section D of Figure 2. After separation, the liquid phase runs into the refractive-index cell (R401, Waters Associates) as can be seen in section E. The gas phase (N2) is vented to the atmosphere. 2.2. Data Processing. The hydrodynamic state of the system was determined by monitoring the pressure drop over the bed. To compensate for inlet and outlet effects, the steady-state pressure drop in a 90 cm bed was determined as the difference in the differential pressure value obtained with the 97 cm column and the 7 cm column. Depending on the flows, the pressure drop over 90 cm of the bed amounted to 55-90% of the total pressure drop. Residence time distribution curves were obtained by injecting, at 10 min intervals, pulses of a diluted solution of cumene in tetradecane (mole fraction less than 5%) into the liquid phase and determining the spread of the solute pulse leaving the packed bed with the refractive index detector. The mean residence time τ is used to calculate the liquid saturation L, defined as the fraction of the space between the particles that is, on average, filled with liquid. The volume occupied by the liquid, for liquid-flow rate φL, is obtained from the distribution as VL ) τφL. The volume, that is available for liquid flow, depends on the bed porosity that was 0.43. Then, the liquid saturation is calculated as L )

τφL ) Vpore

(τ97 - τ7)φL π (L97 - L7) dcol2 4

(1)

in which dcol is the diameter of the empty column and Vpore refers to the interparticle space.

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Figure 4. Hydrodynamic reproducibility for wet startup. The liquid-flow rate φL ) 0.02 mL/min (interstitial liquid velocity uiL ) 0.21 mm/s). (a) Pressure drop results. (b) Liquid saturation results. The data points are at steady-state conditions. The characteristic times of response to a step change depend on the flow rates and vary between 1800 and 3600 s.

The switching time is defined as the time required to achieve a stable value of the monitored variable (differential pressure or residence time) after a step change in the flow rate. We considered the monitored variable is at steady state when its value is constant within 3% for at least 1 h. The interstitial velocity is defined as the flow of the phase divided by the available area for that phase: uiL )

uiG )

φL π 2 d εε 4 col L φG

π 2 d ε(1 - εL) 4 col

(2)

(3)

3. Results and Discussion 3.1. Effect of Startup Procedure in Bed Stability-Reproducibility. To check the presence of multiple hydrodynamic states for the flows of gas and liquid relevant to gas-liquid-solid reactions in miniaturized packed beds, several startup procedures were selected that mimic startup procedures in larger-scale systems. Furthermore, we investigated if the steady-state liquid saturation is affected by the startup procedure. It should be noted that all liquid saturation is static, i.e. we do not have dynamic zones.29 Representative experiments were repeated several times, and the reproducibility is within 3%. Dry Startup. The bed was flushed with N2 at 0.95 mL/min for 12 h. Later on, the gas-flow rate was set to the desired value (0.50 mL/min), and the liquid-flow rate was first increased and subsequently decreased. After each change, we waited until the system was stable. This could take hours, as we discuss later. As can be observed in Figure 3, the largest deviation in the pressure drop is 25% and the largest deviation in the liquid saturation is 7%. The data on liquid saturation in Figure 3b shows that the liquid saturation is a function of flow rate alone, irrespective of the flow history. In other words, an increase of the liquid-flow rate does not remove pockets of gas from the packed bed. When reducing the liquid flow, the liquid saturation values obtained are comparable to the increasing flow section. Wet Startup. The system was running with a low liquidflow rate (0.02 mL/min) and a low gas-flow rate (0.05 mL/ min) for 24 h. Then, the gas-flow rate was increased and subsequently decreased. The results are presented in Figure 4.

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Figure 5. Liquid saturation (all dynamic) for different startup procedures. The table indicates the liquid- and gas-flow rates that are sequentially set and kept until steady state. For example, in cycle A there is first only gas flow (0.95 mL/min) for 12 h, then 0.1 mL/min liquid and 0.5 mL/min gas until steady state, then the gas-flow rate is reduced to 0.1 mL/min and kept until a new steady state, etc.

Figure 6. Conceptualized flow structure evolution in trickle beds (top section) and miniaturized multiphase packed beds (lower section). Adapted from the work of Wang et al.18

The largest deviation in pressure drop is 13%, and that in the liquid saturation is 3%. Complex Cycles of Conditions. The flow of gas and liquid were changed using different sequences and startup procedures as depicted in Figure 5. This figure shows the overall results in terms of the liquid saturation values for a 90 cm packed bed. The data reproducibility is within 2.5%, and the largest deviation in the liquid saturation value is 6.4%. Our results contrast with those of Kan and Greenfield16 who found pressure drop deviations as high as 97% for a column of 25 mm inside diameter packed with 0.5 mm glass particles. Interestingly, it was this paper by Kan and Greenfield that first

reported more pronounced hysteresis with small particles, but their smallest particles were still five times as large as ours. Clearly, the monotonic trend toward stronger hysteresis with decreasing particle size breaks down in the 0.1 mm range. For different startup procedures, we found that the pressure drop in the increasing flow branch is actually higher than that in the decreasing branch, which is the opposite trend compared to trickle bed reactors. The difference between the branches (up to 25%) is larger than the experimental error but considerably smaller than those reported for larger particles. We understand that the hysteresis is much less pronounced, since in our system we do not have a flow-regime transition such as pulsing-to-


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Figure 7. (a) Schematic representation of the step changes in gas and liquid flow. (b) Dimensionless stabilization times, as multiples of the liquid-residence time in the column, for various step changes. The change in pressure is normalized on a scale [0, 1] using the old and the new steady state. (c) Variation of the pressure in time. These data are recorded for the 97 cm column. The lines between the data points are provided to guide the eye.

trickling but only a slight change in liquid saturation. An explanation for the opposite trend, however, is still lacking. In large-scale trickle bed reactors, the prewetting of the system determines the liquid-phase distribution in the reactor and the possible formation of liquid bridges between the packing particles due to capillary forces. According to the parallel zone model developed by Wang et al.,18 the existence of multiple hydrodynamic states or hysteresis in trickle bed reactors corresponds to varying degrees of nonuniformity of the gas and liquid distribution inside the packed bed, as the liquid-flow rate increases from zero while maintaining a constant gas-flow rate, it is difficult for the gas and liquid to spread evenly over the packings. As depicted in the top section of Figure 6, at low liquid-flow rates the gas and liquid phases present some segregation inside the packed bed with part of the bed void volume only gas-filled, another zone only liquid-filled, and a multiphase zone. Under this condition, the pressure drop per unit of reactor length is low due to ineffective contact between the gas, liquid, and solid phases corresponding to the lower branch of the hysteresis loop. When the flows are increased and the pulsing regime is reached, the single phase zones disappear and a uniform distribution of gas-liquid flows results in larger pressure drop values, corresponding to the upper branch of the hysteresis loop because the uniform gas-liquid distribution persists when the flow rates are reduced. For miniaturized packed bed reactors, the capillary forces are so strong that the packed bed is almost completely saturated with liquid at all gas- and liquid-flow rates of practical interest, as depicted in the lower section of Figure 6. Our experimental results show that at all conditions of gas- and liquid-flow rates, the liquid saturation is very high (L∼ 0.7) with a weak dependency on the gas and liquid flows. Flow-visualization experiments performed in microfabricated packed beds at similar flow conditions30 show a stratified flow pattern with high local

liquid saturation values that corresponds with the liquid saturation values of the 2 mm diameter micropacked bed. We are currently studying the factors that determine the percentage of the liquid-filled zone that is dynamic. Our residence time distribution studies in the same micropacked bed29 show that under the same conditions the liquid phase has near plug flow behavior, implying that there are no significant wall effects. 3.2. Characteristic Time of Response to a Step Change in Flow Rate. We measure the time necessary to achieve steady state at startup or when one of the flow rates is changed. The experiment was started by flushing the 97 cm packed bed with N2 at 0.95 mL/min for 12 h. Then the gas- and liquid-flow rates were set to 0.10 mL/min for tetradecane and 0.50 mL/min for N2. Subsequent changes to the flow rates are indicated in Figure 7a. We recorded the evolution of pressure drop. A dimensionless change in pressure drop P* is defined as P* )

P - P0 P∞ - P0

(4)

where P is the pressure drop, P0 is the initial pressure drop, and P∞ is the pressure drop at the new steady state. Similarly, a dimensionless time θL is defined as θL )

t - t0 τ97

(5)

where t0 is the initial time at the new condition and τ97 is the mean residence time of a tracer pulse injected in the liquid at the new steady state. Figure 7b and c shows the transient behavior of P* vs θL and ∆P vs time after step changes in liquid- or gas-flow rates. As seen in Figure 7b, the time required to reach 98% of the

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Figure 8. Variation of the pressure drop over the 97 cm column after a step change of liquid flow for three different gas-feed section volumes. The lines between the data points are provided to guide the eye. In the inset, the dimensionless pressure drop P* is represented against the dimensionless time with respect to the residence time of the gas in the feed section θG,feed.

total pressure drop change at startup is at least 3000 s (4.1 times the liquid-residence time). Figure 7c shows the dependency of the absolute multiphase pressure drop with the flow rates. The pressure drop in the system correlates strongly with the liquidflow rate: for φL) 0.02 mL/min, ∆P ∼ 50 kPa, and for φL) 0.10 mL/min, ∆P ∼ 250 kPa regardless the gas-flow rate. As expected, the switching times depend on the absolute pressure drop in the system and it can take up to 2400 s (3.2 times the liquid-residence time) to reach the steady value of pressure. After several alternating changes of gas or liquid flow, the absolute pressure drop and the liquid-residence time values return to the initial value, within experimental error (240 kPa at 22.8 °C vs 220 kPa at 23.2 °C; 709 vs 734 s, 3.5% deviation). We observed that the characteristic time to reach the new pressure drop and the new residence time are the same, indicating that the pressure drop is a good variable to monitor the stability of the system. The absolute characteristic times of response to a step change for our experimental setup are 1 order of magnitude higher than those reported by Van der Merwe et al.24 and Stanek et al.25 This suggests that the feed section volume may have a dominant effect in the transient behavior. It is worthwhile to mention that for these experiments the volume of the gas-feed section is 3.50 mL; this volume corresponds to the tubing and connections from the mass-flow controller exit until the annular volume at the top of the bed plus the necessary connections to one entry of the differential pressure transducer (Figure 2). This volume is roughly 9 times larger than that of the gas-filled volume inside the bed (∼0.40 mL). The bed volume that is occupied by gas is calculated according to Vgas_inside_the_bed

π ) dcol2L97ε(1 - εL) 4

(6)

3.3. Influence of the Feed Section Volume in the Transient Response. To analyze further the impact of the gas-feed section volume in the characteristic time of response to a step change

in flow rate, the same step change in liquid flow was made for three different gas-feed section volumes (3.26, 6.65, and 9.05 mL). After the micropacked bed was stable at a liquid-flow rate of 0.02 mL/min and a gas-flow rate of 0.5 mL/min, the liquidflow rate was changed to 0.1 mL/min and the pressure drop values along the column were recorded until the new steady state was achieved. The gas-flow rate remained constant at 0.5 mL/min. As observed in Figure 8, the time to achieve steady state increases, with an increase in the gas-feed section volume. It was observed experimentally that after increasing the liquid flow, no gas bubbles exit the packed bed until the pressure drop reaches at least 70% of the new steady state value. The dimensionless stabilization times, as multiples of the gasresidence time in the gas-feed section, were calculated as θG,feed ) t/τG,feed, where τG,feed ) Vgas-feed/φG. In the inset of Figure 8, it is shown that the characteristic time of the initial rapid response correlates with the gas-feed volume. After 1.5 units of the gas-residence time in the feed section, the system reaches 75% of the new pressure drop value. This initial rapid response is followed by a very slow process, in which the bed adapts to the new feed pressure. This process can take up to 12 h. On the basis of these results, we continued with the smallest volume of the feed section and we tried to identify the controlling phenomena of the transient behavior. Table 1 summarizes the time to reach steady state at each combination of gas- and liquid-flows and compares those with several characteristic times. Roughly, for ∆P ∼ 250 kPa, the system needs 2400 s, and for ∆P ∼ 50 kPa, the system stabilizes in 600 s. The times to reach steady state do not correspond with the experimentally measured liquid-residence times indicating that the transient behavior is not controlled by liquid convection. We tried to interpret these results using the bottleneck phenomena26 from chromatography, describing the characteristic times of response to a step change with the compressibility of the gas-feed section, treating the packed bed as a hydrodynamic resistance with instantaneous response. This model was composed of the macroscopic mass balance in the gas-feed section (eq 7), the ideal gas law, and an empirical correlation to relate the pressure drop in the packed bed with the gas and liquid flows (eq 8). MWV dP )m ˙1 - m ˙2 RT dt

(7)

m ˙ 2 ) f(∆Pcol)

(8)

Combining these equations, we get a first order ordinary differential equation that allows us to calculate the variation of pressure with time. Such a model could only describe the initial rapid change as shown in Figure 8. The gas-feed section was constructed from Teflon tubing (PTFE). The Young modulus of PTFE, 5.171 × 105 kPa, is high enough to rule out any contribution of the PTFE elasticity in the transients.

Table 1. Time to Reach Steady State tSS after a Step Change in One of the Flows and Estimated Transient Timesa φL, mL/min

φG, mL/min

∆P, kPa

tSS experimental, s

τL, s

tSS for compression-decompression gas-feed section, s

τG, s

0.1 0.1 0.02 0.02

0.5 0.1 0.1 0.5

240.67 221.67 55.00 75.00

2400 2400 600 600

709.7 757.3 3472.3 3281.0

355 378 347 328

467 2336 2336 467

a These results correspond with the data shown in Figure 7. Volume gas-feed section ) 3.50 mL. The first two columns correspond to the liquid- and gas-flow rates at the new steady state; the third and fourth columns correspond to the experimentally measured pressure drop and time. The last three columns correspond to the liquid-residence time, the bottleneck time needed to compress or decompress the gas-feed section volume, and the gas-residence time in the system (feed section and bed).


The residence times for the gas phase τG were estimated considering the volume of the gas-feed section (3.50 mL) and the gas-filled volume inside the bed (∼0.40 mL). Even though some characteristic times of response to a step change are equivalent to certain gas-residence times, there is not a reproducible trend between the experimental results and the estimated gas-residence times as depicted in Table 1. These results concerning the gas-phase behavior (residence times and compression-decompression effect) indicate that the transients in the system cannot be attributed solely to the gas phase. Clearly, the multiphase, micropacked bed does not act as an instantaneously responding resistance for the gas, but in fact, it has an important contribution on the transient times due to the redistribution of the gas and liquid flows inside the bed. The characteristic times of momentum diffusion inside the packed bed were calculated as tmomentum_diffusion_R-phase )

L2 νR-phase

(9)

where L represents the characteristic length (packed bed length) and ν is the kinematic viscosity of the R-phase (gas or liquid); with a kinematic viscosity of 2.8 × 10-6 m2/s for the liquid and 1.2 × 10-5 m2/s for the gas, the momentum diffusion times are 3.5 × 105 and 8.3 × 104 s for the liquid and gas phases, respectively. These characteristic times are at least 1 order of magnitude larger than the experimental results; therefore, the controlling mechanism is not axial momentum diffusion. It is possible that the liquid saturation evolution inside the packed bed is very slow due to the dominant effect of the capillary forces. When a step change is made in one of the flows (gas or liquid), a pore of a channel filled with one phase has to be replaced by another, to accomplish that the capillary pressure value should be exceeded. Unfortunately, we do not have the axial profile of liquid saturation over the packed bed length to prove or disprove this hypothesis. Still, the hypothesis, that the slow pressure drop variation is due to slow liquid saturation variations, is a reasonable one because this work shows that both pressure drop and liquid saturation evolve on the same time scale. Nevertheless, the main point of this work is to demonstrate the significant hydrodynamic transients in micropacked beds. Our system is an idealized one; for instance, we have used nonporous spherical monodisperse particles, but the observed behavior is to the greatest extent due to the different ranges of Bo and Ca numbers and as a consequence to a minor degree dependent on local packing morphology. 4. Conclusions • In a reactor that was packed with 0.1 mm particles, wet or dry startup procedures resulted in the same hydrodynamic state after stabilization. • Due to very strong capillary forces, miniaturized multiphase packed bed reactors have very high liquid saturation values and, therefore, more stable hydrodynamic conditions when compared with trickle bed reactors. The little hysteresis, that we found, had a higher pressure drop in the branch of increasing flow of both gas and liquid. • We found startup times of the magnitude of four liquidresidence times and switching times as long as three liquidresidence times. These times are much longer than the time required to flush out the bed. • The long characteristic time of response to a step change encountered in micropacked beds can be attributed to a

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combined effect of compressibility in the gas-feed section and flow resistance in the packed bed itself. A large volume in the feed section gives a large capacity that delays the new steady state. The contribution of the packed bed to the switching times is largely due to the slow rearrangement of gas- and liquidflows inside the packed bed to the adjusted flow rates. • During this slow response toward a new steady state, the pressure (i.e., the dissolved gas concentration) and the residence time of liquid-phase components are not constant and kinetic data obtained during this slow response, which can take up to 12 h, cannot reliably be used in the evaluation of kinetic parameters. Acknowledgment The authors thank Shell Global Solutions International B.V. and Albemarle Catalysts Company B.V. for financial support. This research was also supported by the Programme Alβan, the European Union Programme of High Level Scholarships for Latin America, scholarship No. E04D028997 VE. Note Added after ASAP Publication: Changes involving selected text in section 3.1 have been made to the version of this paper that was published online August 5, 2009. The corrected version of this paper was reposted to the Web on September 1, 2009. Notation A ) cross-sectional area (m2) d ) diameter (m) dp ) particle diameter (µm) g ) gravity (m/s2) L ) bed length (m) m ) mass of gas (kg) MW ) molecular weight (g/mol) P ) pressure (kPa) R ) universal gas constant (R ) 8.314472 J/(K · mol)) T ) temperature (K) t ) time (s or h) u ) superficial velocity (mm/s) ui ) interstitial velocity (mm/s) V ) volume (m3) V ) kinematic viscosity (m2/ s) Greek Letters ) bed porosity (-) L ) liquid saturation (AL/(AL + AG)) η ) viscosity (Pa · s) θ ) dimensionless time (s/s) F ) density (kg/m3) σ ) surface tension (N/m) τ ) mean residence time (s) φ ) volumetric flow rate (mL/min) Dimensionless Numbers Bo ) Bond number ([(FL - FG)gl2]/σ) Ca ) Capillary number (ηLuL/σ) Re ) Reynolds number (FLuLdp/ηL) Sub- and Superscripts · (overhead dot) ) flow * ) dimensionless 0 ) initial ∞ ) final col ) column feed ) feed section

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G ) gas L ) liquid iG ) attached to u for interstitial gas velocity iL ) attached to u for interstitial liquid velocity por ) epore SS ) steady state 1 ) entrance to gas-feed section 2 ) exit of gas-feed section 7 ) 7 cm bed 90 ) 90 cm bed 97 ) 97 cm bed

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ReceiVed for reView April 30, 2009 ReVised manuscript receiVed June 8, 2009 Accepted June 30, 2009 IE900694R

Transient Behavior and Stability in Miniaturized Multiphase Packed

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