Elsevier

Chemical Engineering Journal

Volume 250, 15 August 2014, Pages 99-111
Chemical Engineering Journal

Residence time and axial dispersion of liquids in Trickle Bed Reactors at laboratory scale

https://doi.org/10.1016/j.cej.2014.03.062Get rights and content

Highlights

  • Mean residence time was inversely proportional to liquid flowrate.

  • Mean residence time was not dependent of the gas flowrate.

  • Axial dispersion + 1-tank model gave average absolute deviations, AAD < 3%.

  • Higher gas and liquid velocities decrease the axial dispersion in the trickle bed.

  • Péclet number correlated with Pe = (a + b · ReGp) · ReLp0.571/Ga with less than AAD = 16%.

Abstract

Hydrodynamic behavior in a lab-scale Trickle Bed Reactor (I.D. 1.15 cm, L = 30 cm, filled with silica particles of 0.2–0.8 mm) has been investigated. Residence time distribution curves were determined using a step transient response via conductivity measurement varying gas flowrate (0–12 mL/min CO2–H2–O2 at 78–4.0–18 mol.%) and liquid flowrates (methanol 0.5–2.0 mL/min) at −10 °C and atmospheric pressure. We demonstrate that this reactor can be accurately modelled using a combined model of axial dispersion followed by one mixed tank reactor with absolute average deviations lower than 2.6% (maximum deviation of 6.50%). The best results were obtained for a model combining 1-tank reactor with 1.20–6.15 min of residence time in series with a plug flow with residence times from 8.1 to 38.1 min. These values highlight the prevalence of the axial dispersion over the backmixing (exemplified by the mixed tank reactor) with a contribution between 80.3% and 90.1% of the total residence time. The Péclet numbers determined were in the interval of 248.3–699.3, the highest values of Pe were obtained at the highest liquid flowrate indicating the lowest axial dispersion. Correlations with the fraction of liquid flow, gas and liquid Reynolds numbers and the Galilei number are given.

Introduction

Trickle Bed Reactors (TBRs) are extensively used in the oil industry for hydrodesulphurization processes (HDS) and also in the chemical industry for hydrogenations and oxidations. We are focused in the study of the direct synthesis of H2O2 at mild pressures and low temperatures [1], [2], [3]. ‘A major difference with HDS is that the gas phase contains only 4% H2 as this is the lower flammability limit of H2 (and O2 is present), which limits the yield per pass. Multi-injection is an option, but is not considered at lab scale commonly.

The operation of TBRs is not trivial, and operation of laboratory-scale TBRs relies on the knowledge of several factors that highly influence the final results, such as the wettability of the bed, liquid maldistribution, liquid and gas hold-up and residence time [4]. On laboratory scale, the behavior of a TBR is different from that at pilot, demonstration or industrial scale, due to wall effects, pumping or compression pulsation and other effects related to mini and microscales. It is difficult to find the correct ratio of sizes between bed length and diameter (L/D) and between bed and particle diameters (D/dp) to avoid radial effects. Furthermore, the different behavior in TBRs at industrial scale and laboratory scale might even cause the absence of the trickle flow at lab scale [5]. Considering the phenomena in the TBR there are four main forces governing, characterized by physical properties or parameters related, i.e. inertial (velocity-direction), gravitational (density-direction), viscous (viscosity) and capillary forces (surface tension) [6].

One of the common problems in laboratory scale using TBRs is the difficulty in the extrapolation to large scale and vice versa. In many cases, the industrial TBR process is working and it is necessary to downscale the process to study kinetic parameters or to improve the large scale process. Van Herk et al. studied the downscaling of hydrodesulphurization processes (HDS) in oil industry. These processes normally operate in a downflow TBR at temperatures between 300 and 400 °C and pressures ranging from 20.0 MPa to 40.0 MPa, depending on the fuel targeted, i.e. gasoline or diesel. In industrial scale the reactor is designed for a Linear Hourly Spatial Velocity (LSHV) between 0.5 and 4 h−1, that, for a normal capacity of 100 m3/h, means reactor volumes between 25 and 200 m3 and column diameters between 1.0 and 3.0 m at L/D between 8 and 12 [7]. In their work the authors studied a 6-manifold TBR with 2 mm diameter packed beds with particles of approximately 0.1 mm (i.e. a downscaling factor ca. 107–108). In that scale the authors found a plug flow behavior for the liquid and only at high gas flowrates a maldistribution appeared.

Residence time distribution (RTD) is a simple and effective method to describe deviations from the ideal flow pattern, especially relevant in complex flow dynamic systems as Trickle Bed Reactors. By definition, the residence time of an element or volume element is the fraction of time that the element spends inside the reactor. According to the type of design, the distribution of the times (or ages) for the different elements entering and exiting the system can be narrow or wide. The two limiting cases are represented by plug flow reactor (PFR) and continuous stirred tank reactor with complete backmixing (CSTR). In an ideal PFR, all the elements in the same cross-section have the same age or residence time. Therefore, there is no distribution of residence times in such system. On the other hand, in CSTRs exists the largest distribution possible, covering from zero to infinity. The residence time distribution in packed bed reactors (and in TBRs) is often comparable to PFR systems due to the fact that only radial backmixing is remarkable while axial backmixing is limited [8].

The simplest method to determine RTD is based on the monitoring a tracer substance in its way through the system. This is usually realized by detecting the tracer (concentration) at the inlet, which will correspond to time zero, and at the outlet. Common analytical methods to monitor the tracer are conductometry, photometry, mass spectroscopy, paramagnetic analysis, radioactivity, and gas or liquid chromatography. Depending on how the tracer is introduced in the reactor, tracer experiments are divided in three types: pulse or impulse, step, and periodic input. In pulse experiments, the tracer is introduced in a very short time (infinitesimally short time in impulse method) in the system; in the step response method, the flow rate of fluid is substituted with an equal flow rate containing the tracer till new steady state is achieved; while in periodic measurements the tracer is introduced in a periodic changing input.

The use of RTD curves has been extensively discussed in literature; probably the first reference was done by Danckwerts [9]. After that Levenspiel explained in detail in an academic style in the first edition of his book [10]. It is worth citing the work of Marcandeli et al. in liquid distribution in TBR, as they identified the best techniques to detect maldistribution problems [11]. The authors conclude that, for an industrial reactor, the best option is always to measure the RTD, it is quantitative and reliable. The use of pressure drop (−ΔP) can insinuate maldistribution but, it is not quantitative and other factors e.g. bed attrition, coking can interfere. The use of thermal sensors is an option for certain critical regions, but not the solution for the whole reactor. Other options, such as liquid collectors or tomography are unrealistic from the operational point of view.

The determination of RTD is frequently combined with the modelling of the system using one, two or three-parameter models, either based in mass balance or in statistical analysis.

As explained above, to accomplish the determination of flow behavior via RTD, it is common to use conductivity measurements determining the transient tracer response at the reactor outlet. Instead of conductivity, Nigam et al. determined the RTD in a TBR using a radioisotope method. They used the axial dispersion model to simulate the experimental data and estimate mixing index, i.e. Peclet number, comparing it to the experimental mean residence time (t¯) by the moment method [12]. The system behaved like an axial dispersed system matching the results of both experimental and simulated residence time. They studied three different packaging, concluding that the Peclet number increases with increasing liquid flow rate (lower axial dispersion) for glass beads and tablets, while for extrudates it is almost constant. This clearly indicated that that axial dispersion depends on the shape and size of the packing.

Another option for short residence times was the one used by Wibel et al., measuring precisely the RTD in microreactors using thermal conductivity detectors (TCD) before and after the reactor [13]. They confirmed that the dispersion model was valid for describing the gas flow in the microchannels. Nevertheless, they modelled the system using the proprietary software FLUENT and they found that there were mixing regions at the inlet and outlet due to the reduction fittings that restricted the flow. Within the group of Garcia-Serna et al. it was found a similar behavior for a mini tubular reactor with CO2 under supercritical conditions [14], [15]. The two mixing zones at the entrance and outlet caused a long tail in the residence time curve. We have detected this behavior in our TBR system too, as will be explained in the results section.

In terms of design parameters, Wanchoo et al. carried out an experimental RTD study using the two-parameter dispersed flow model obtaining bad correlation results [16]. The authors used a glass column (D = 40 mm) filled with nonporous dp = 3.38 mm spherical glass beads. The problem could be that the ratio between the column diameter and the particle diameter was D/dp = 11.8, and that is often not enough to avoid radial effects and liquid maldistribution. To avoid this inconvenience, Saroha et al. used a system with D/dp > 75, indicating that with this ratio the radial effects were negligible [17]. They used air and water with 3.76 < ReL < 9.3 and 0 < ReG < 2.92 for a TBR diameter of 15.2 cm (10-fold our reactor). They estimated the liquid hold-up using the average residence time (statistical residence time). They used the simplified Levenspiel model for Péclet number (Pe). They calculated the liquid axial dispersion terms of Bodenstein number (Bo). The total liquid holdup was found to increase with increasing the liquid flow rate and decrease with increasing the gas flow rate.

The behavior of Trickle Bed Reactors behavior in terms of liquid hold-up is difficult to determine in advance, as many factors interact [4]. Stegeman et al. measured precisely the different hold-up contributions [18]. They indicated that, although the liquid holdup can be divided into a dynamic and a stagnant holdup, as many authors have stated, also another subdivision could be made. When operating unsteady (to improve the efficiency by improving wetness [19]), if both liquid and gas supply are stopped suddenly, a part of the liquid holdup will trickle out of the reactor (free-draining holdup), while another part will stay in the column because of capillary forces (residual holdup). The authors emphasized that residual holdup and the so-called “stagnant holdup” are not the same concept. While the stagnant fraction is affected by the process conditions, the residual fraction is a function of the liquid and packing properties. Furthermore, the stagnant holdup is always smaller than the residual holdup when operating at steady conditions because of eddies formed in and around the dead regions between particles.

It is not very common that the solid phase moves. Normally the solid phase is static and the liquid trickles and the gas flows. Nevertheless, Roes et al. operated a packed bed in a countercurrent mode and used RTD for its characterization [20]. The system was somewhat special, as the solid moved. They used the one dimensional dispersed plug-flow model, since the tracers were present in one phase only. The authors found that the Bo number was similar to 2.0 when the solid was static and increased up to 20 when the solid phase moved.

Michell et al., as in the 1970s, already determined that the dispersion model is one of the best options to model the trickle flow in packed beds [21]. However, they found that it describes the RTD up to twice the mean residence time (accounting for ca. 90% of the flow elements). Furthermore, they encountered that it also underestimates the tailing response beyond twice the mean residence time.

The models based in axial dispersion normally used the dimensionless Bodenstein number, although Pe is also commonly used.

The estimation of the values of the Bodenstein number in TBRs has been studied extensively since the 1950s. Piché, Larachi et al. collected 973 values of axial dispersion coefficient from 1958 to 2001 and evaluated a number of correlations in the literature, proposing one correlation trained with a neural network that has an average error of 24% for the whole database [22]. The correlation is remarkable and can be used easily through the free-software that they offer in Larachi’s webpage at Laval University (Quebec, Canada). Piche et al. also improved the correlation of liquid hold-up correlating more than 1500 experiments on liquid hold-up below the flooding point from the literature. They used several dimensionless groups, i.e. liquid and gas Reynolds, liquid and gas Froude, liquid Ohnesorge (Oh) and gas Stoke’s numbers (Stk) obtaining a noteworthy correlation absolute average relative error of ca. 14% for the whole database [23].

Valderrama et al. a modelled the TBR considering an effectiveness factor within the n-tanks in series model for RTD [24]. Using this factor they managed to model the long-tail shape of the curves.

Rangaiah et al. evaluated four different models, i.e. CFM (cross flow model), DCM (dispersion model with close-close boundaries), GDTDM (gamma distributed time delay model) [25] and METDM (modified exponentially distributed time delay model), trying to methods of fitting [26]. Mainly, the authors determined the average residence time via experimental conditions (using the moment method) or including it in the fitting. The results were quite similar in both cases with only 6% difference between them in all cases. The match of the four models to the experimental data was good.

Saravanathamizhan et al. measured and modeled RTD curves for a stirred tank used for an electrochemical reaction [27]. They utilized a three parameter model considering perfect backmixing, a bypass and a dead volume to simulate a color removal reaction. However the number of experimental RTD curves were few compared to the three parameters fit.

Erdogan et al. accomplished the modelling of the Taylor flow in square mini-channels by using a compartment model consisting of a plug flow reactor in series with two parallel continuous-stirred-tank reactors [28]. The experimental data had a long tail which was conveniently represented by the two CSTRs, in combination with the delay coming from the dispersion model.

In this work, we determined the RTD behavior of a laboratory scale TBR used for the direct synthesis of H2O2 by measuring an ionic-tracer conductivity response. The predictions using an axial dispersion model (ADM) were not enough accurate to model the behavior [29]. The difference between the predicted and experimental RTD was the long tail in the real reactor. For the direct synthesis of H2O2 the catalyst particles used are powdery microparticles (100 μm or less) with active metal as nanoparticles. The SiO2 particles are added as an inert surface that decreases catalyst concentration and increases transfer area. We modeled the system using a combination of the axial dispersion model and one perfectly backmixed tank reactor in series to predict the long-tail (or slug) behavior. The experimental average residence time and standard deviation were determined using the moment method. Most important, we correlated all the statistical parameters and the Péclet number from the combined model using dimensionless numbers and the relationships proposed by Van Herk et al. [7] and by Khanna [30].

Section snippets

Materials

Methanol was used as the reaction medium (J.T. Baker 99.99%). Hydrochloric acid (J.T. Baker 36–38%) was used in solution 0.125 M in methanol as an inert tracer. Quartz sand (Merck Millipore, 107536 quartz fine granular, washed and calcined for analysis, particle size 0.2–0.8 mm) and quartz wool (Carl Roth, 9208.2 quartz wool chemically pure fiber size 5–30 μm) were used for filling the reactor. Inert fraction particles were obtained from crushing pellets of compressed silica gel (Merck Millipore,

Mathematical model of the RTD

The curves which results from the RTD tracer experiments are denoted as distribution function E(t) (impulse) and F(t) (step response). The exit age distribution curve or density function E(t) is the distribution of times of the elements leaving the reactor. It is obtained changing the concentration scale of the response curve from pulse experiments so that the area under the curve is unity. The portion of incoming volume which leaves the system within the time interval t to t + dt is expressed as

Modeling results and discussion

In this paper we explored the influence of liquid flowrate (0.5, 1.0 and 2.0 mL/min) and gas flowrate (0.0, 1.0, 2.7, 6.0 and 12.0 mL/min) in the RTD curves for two different fixed bed configurations (A and B). As explained in Section 2.3 (Fig. 2), configuration A refers to the reactor where a sub-bed of catalyst pellets was inserted, while configuration B denotes to the fixed bed full of silica particles.

We followed a factorial design criteria (3 × 5 × 2) carrying out a total of 30 experiments.

The

Conclusions

Laboratory scale Trickle Bed Reactors are very useful for the research of three phase reactions at high pressures. Unfortunately, their operation at particularly low liquid and gas Reynolds numbers, compared to the industrial scale, require for specific correlations to determine the residence time.

In this study, we have determined the residence time distribution curves using a tracer in step response (obtaining F(t) curve) for a lab scale Trickle Bed Reactor (I.D. 1.15 cm, L = 30 cm, filled with

Acknowledgements

This work is part of the activities Process Chemistry Centre (PCC) financed by the Åbo Akademi University. Dr. Juan Garcia Serna acknowledges the Spanish Economy and Competitiveness Ministry, Project Reference: ENE2012-33613 for funding and “Programa Salvador Madariaga 2012” for mobility scholarship. Financial support from Academy of Finland to Academy Professor Tapio Salmi is gratefully acknowledged.

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