Axial Dispersion Based on the Residence Time ... - ACS Publications

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Axial Dispersion Based on the Residence Time Distribution Curves in a Millireactor Filled with β‑SiC Foam Catalyst Meryem Saber, Cuong Pham-Huu, and David Edouard* Laboratoire des Matériaux, Surfaces et Procédés pour la Catalyse (LMSPC), UMR 7515 CNRSECPM, Université de Strasbourg, 25 rue Becquerel, 67087 Strasbourg, France ABSTRACT: The hydrodynamics of the platelet millireactor filled with different morphologies of the commercial open cell β-SiC foams (0.8 < porosity (ε) < 0.95 and 890 μm < cell size (Φ) < 2700 μm) has been investigated. The axial dispersion profile of an inert tracer in a gas flow (superficial velocity from 0.01 to 0.3 m/s) is estimated by a robust deconvolution procedure. The axial Peclet number based on Φ is found to be on the order of 1. The results are in agreement with the literature data and can be compared with the available results for the standard fixed bed.

1. INTRODUCTION The emergence of microreactors and process miniaturization over the past decade has provided a potentially new platform for accelerating the development of next-generation catalysts and multiphase catalytic process technologies. Due to increased process intensification offered by the microreactors, more traditional pilot-scale reactor systems and pilot plant systems can be replaced by smaller, faster responding, and more flexible miniplants with reduced operating costs and a reduced environmental impact.1−3 The microreactors generally consist of submillimeter channels which exhibit several advantages such as a high surface-to-volume ratio (4−5 orders of magnitude greater than in a “conventional” batch reactor), high heat and mass transfer rates, high controllability of the reaction conditions due to the small holdup, laminar flow behavior, compactness, and parallel possibility.4−7 However, today the microreactors present again the following different gaps: − the machining of these submillimeter channels is not straightforward, and generally, lithography or other hightech technologies are needed to ensure their realization. Moreover, in the channel, the problem of plugging during manufacturing exists. − from a catalytic point of view, the immobilization of the catalysts in such small channels and a strong anchorage of the catalytic layer on the reactor wall are still difficult to achieve.8−11 Consequently, it is of interest to develop new structured reactors in which the channel is filled with host structures such as metallic or ceramic foams, pure or covered with a network of nanostructured carbon.12,13 In this context, a new multiscale structured technology based on platelet millireactor filled with a microcellular matrix (β-SiC foam with or without addition of nanofibers) has recently14−18 been developed. The macroscopic dimension of the channel allowed it to be shaped by a traditional mechanical device without any need for high-tech technology as encountered with the microstructured reactors with submillimeter dimension. In addition, the catalyst, in a macroscopic shape, can be easily prepared and characterized before loading into the reactor unlike traditional microreactors where the deposition of catalyst inside the microchannel is not straightforward. These new © 2012 American Chemical Society

reactors allow the coupling, in the same tool, of the advantages of millimeter reactor technologies with the transport properties of the open cell β-SiC foam. The tunable morphology of the solid foam (cell size, macroscopic porosity, strut diameter) allows an adjustment of both axial and radial flow patterns in the reactor and ensures local fluid recirculation, which are favorable to heat and mass transfer.19−21 The other advantages of open cell foam are the high specific surface area and the low pressure drop along the catalyst bed.22 Finally, the solid ligaments (or struts) in foam material allow the continuous connection of the structure and thus increase the solid effective thermal conductivity on the entire system, without thermal breaking points as encountered with the “conventional” packed bed.23,24 The major objective of this work is to characterize and compare the phenomena of dispersion of the different β-SiC foams in a platelet millireactor. Dispersion plays an important role in chemical engineering and petroleum engineering. There are several variables that must be considered in the analysis of dispersion in packed beds, like the length of the packed bed, viscosity and density of the fluid, particle shape, porosity of bed, etc. In this work, we focus only on the effect of fluid velocity and the characteristic length of the sample open cell foam (i.e., Reynolds number) for the prediction of the axial dispersion. So far, and to the best of our knowledge, relatively few publications exist characterizing the axial dispersion through solid foams with a single flow. The main works are reported by Hutter et al.25 However, to illustrate this, we can cite a nonexhaustive list of these main studies: For single flow conventional reactor, Zuercher et al.26 investigate axial dispersion for open cell foam with different morphologies (45, 30, 20 ppi). They found that gas dispersion increases by increasing the number of pores per inch and is generally higher than in glass bead packings. Montillet et al.27 characterized the axial dispersion in liquid flow through packed reticulated metallic foams and compared it to fixed beds of Received: Revised: Accepted: Published: 15011

July 5, 2012 October 9, 2012 October 11, 2012 October 11, 2012 dx.doi.org/10.1021/ie3017829 | Ind. Eng. Chem. Res. 2012, 51, 15011−15017

Industrial & Engineering Chemistry Research

Article

Figure 1. Platelet millireactor filled with open cell foam.

different structures. They found a very low axial dispersion for flow through the investigated nickel foam of 45, 60, and 100 ppi. The data is obtained for very low superficial flow velocities (U < 0.001 m/s). In the case of foam in millimetric reactors, Hutter et al.25 characterize commercial foams with different ppi (20 and 30 ppi) and found that the dispersion coefficient increases with increasing pore size. The authors show a high potential of foam bed for catalyst reactions. In the most common case, axial dispersion is studied by injecting a tracer, as a single pulse on the whole cross section (or upstream) of the packed bed, and then measuring the outlet response. Furthermore, this technique allows the detecting of any anomalies related to the reactor design like dead volume or fluid bypass between the wall and foam and inappropriate fluid dispersion, which can be translated into a direct effect on mass and heat transfer performance. Using this pulse tracing technique, the present work focuses on the hydrodynamic investigation of the platelet millireactor filled with different morphologies of the commercial open cell β-SiC foams. The results, in terms of axial dispersion, are compared with some reported data of the open literature.

Figure 2. Foam microscopic 2D images.

2.2. Foam’s Characteristics. Silicon carbide foam (β-SiC, Figure 2), which has recently been reported to be an efficient support in several exothermic and endothermic reactions, has been chosen as a catalyst support.28,29 Silicon carbide foam with an average surface area ranging between 10 and 60 m2 g−1 is used for this investigation. It possesses high porosity, high thermal stability, good thermal conductivities, and mechanical strength. In addition, silicon carbide foam is covered by a layer consisting of a mixture of SiO2 and SiOxCy, which allows a strong anchorage of the deposited active phase without a need for a wash-coat deposition as generally encountered with metallic or ceramic foams.28 The open cell β-SiC foam (Figure 2) used in this work has the same macroscopic dimensions as those of the platelet reactor channel and is supplied by SICAT.30 Finally, the different morphological characteristics of foams investigated in this work are given in Table 1 and compared to some reported data. The cell diameter is given directly by the manufacturer or calculated from the relation (eq 12) given by Truong et al.31 2.3. Tracer Experiment Procedure. The flow behavior through open cell foams has been characterized by the wellknown tracer technique. Tracer injection reproducibility is very important, so in our work the injection system is controlled by an electronic box to ensure tracer pulse injection reproducibility. Following the schematic Figure 1, argon intensity was determined by quadripolar mass spectroscopy with a temporal

2. EXPERIMENTAL SETUP AND TRACER INJECTIONS 2.1. Setup. The assembly of the open cell foams and the platelet reactor is displayed in Figure 1. In Figure 1, we can see that the platelet reactor was made from a stainless steel plate with a single central channel (5 (depth) × 18 (width) × 120 mm) with a large radial gas entrance and exit via the 1/4 in. stainless steel tube connection. The plate reactor was assembled from each other via a Teflon O-ring allowing it to be operated at a reaction temperature of up to 280 °C. The macroscopic dimension of the channel allows it to be shaped by a traditional mechanical device without any need for high-tech technology as encountered with the microreactors with submillimeter dimension. Nitrogen and argon (tracer) gases were supplied through mass flow controllers (Brooks Instrument Model 5850TR) and controlled by a Brooks Microprocessor box. The investigated gas flow rates ranged between 0.88 × 10−6 and 25 × 10−6 m3/s. Prior to each experiment, the setup was prepared to ensure the appropriate mixing of tracer in the gas vector (argon 2.8 vol % in nitrogen). The injection system contains three electrovalves (Brukert Model 00126149) that ensure the periodic injection during a time interval of 500 ms. Argon intensity was determined by quadripolar mass spectroscopy at the inlet and outlet reactor, respectively. 15012

dx.doi.org/10.1021/ie3017829 | Ind. Eng. Chem. Res. 2012, 51, 15011−15017


Article

Because the evaluation of E(t) from eq 1 is not trivial, according to Hutter et al.,25 a transformation from the time domain to frequency domain is implemented:

Table 1. Support Characteristics for the Different Foams Investigated in This Work and the Reported Literature Data author

pore diameter (or window) a (μm)

cell diameter Φ (μm)

strut diameter ds (μm)

ppi

porosity ε (−)

480 700 850 140 1500 1100 1187 930 1187

890 1330 1900 2700 3445a 2620a 2730a 2139a 2730a

80 130 230 300 − − − − −

− − − − 20 30 20 30 20

0.8 0.9 0.92 0.95 0.83 0.86 0.75 0.75 0.75

this work

Hutter et al. (2010) Zuercher et al. (2009)

E(jw) =

Cout(jw) C in(jw)

(2)

The inverse transformation of E(jw) results in the residence time distribution E(t). The transformation of the signals and inverse transformation are directly obtained from the fast Fourier transform algorithm (Matlab). When the noise is not negligible, an additional filter function in the frequency domain, as recommended by Andrews,33 can be used. In this work, the Nahman− Guillaume optimum filter, also used by Hutter et al.,25 is tested with success

a

The cell diameter is calculated from the relation (eq 12) given by Truong et al.31

E(jw) =

resolution of 25 ms at the inlet and outlet, respectively. The injection system ensures the periodic injection during a time interval of 500 ms. Figure 3 shows an example of typical experimental results of single tracer pulse experiments.

Cout(jw) F(jw) C in(jw)

(3)

where F(jw) = 1/(1 + ((λw4)/(|Cin/(jw)|2))) is a low-pass filter taking into account the spectral variations of the inlet signal (see Bennia and Nahman34 and Hutter et al.25). In this work, the following well-known axial dispersion model is used in order to describe the tracer transport in the open cell foam ∂ 2C(z , t ) ∂C(z , t ) ∂C(z , t ) −u = Dax 2 ∂z ∂t ∂z

(4)

with the typical boundary and initial conditions for a pulse injection ⎧ ∂C = 0; ⎪ ⎪ ∂z z = L ⎪ ⎨C|t = 0 = 0 (initial condition) ⎪ Dax ∂C ⎪ ⎪C|z = 0− = C|z = 0+ − u ∂z ⎩ z=0

where z is the axial coordinate, Dax is the axial dispersion coefficient, u is the interstitial fluid velocity, and L the porous media length. According to Hill,35 the solution of eq 4 is given below

Figure 3. Normalized inlet and outlet tracer concentration at u = 0.065 m/s for open cell foam 1330.

We can observe that there are no significant tailing effects or bypass related to the reactor behavior under the operating conditions. From these normalized signals, it seems possible to directly use the moment method described by Levenspiel.32 However, it appears that the tracer signal is not a perfect Dirac, and inlet effects increase the broadness of the tracer pulse. These effects are directly translated in the outlet tracer signal. Consequently, the deconvolution method (described next in the section 3) is recommended in order to estimate the real dispersion caused by the foam reactor.

2τ

∫0

t

C in(t ′)E(t − t ′) dt

t πD τ

t

2

e(1 − τ )

/4D τt

(5)

where D = Dax/uL is the vessel dispersion number and τ is the mean residence time Finally, from the E(t) curve (directly given by the inverse transformation of eq 3) and eq 5, a classical Levenberg− Marquardt algorithm is implemented to estimate the free parameters Dax and τ. Initial values for these free parameters were varied over a wide range, and the same couple of optimal parameters were finally obtained for each operating condition. The exemplarily experimental RTD curves obtained for different foam morphologies with different fluid velocities are reported in Figure 4. The dots correspond to the experimental data and the dashed lines to the fitted curves obtained with the dispersion model. For all cases, the peaks are uniformly distributed over time and the difference in the peaks’ width is due to the fluid velocity and the foam’s morphology. An increased dispersion phenomenon and, therefore, broader peaks are observed when the cell size (Φ)

3. RESIDENCE TIME DISTRIBUTION MODEL AND PARAMETERS ESTIMATION STRATEGY In this paragraph the adopted deconvolution method is described. In our experimental conditions, the evaluation of E(t) can be obtained from the normalized signals Cin(t) and Cout(t) by Cout(t ) =

1

E (t ) =

(1)

where Cout(t) is the convolution of E(t) and Cin(t). 15013



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Figure 5. Theoretical residence time versus the experimental residence time.

low velocities near the wall which is well-known to broaden the E(t) curves. 4.2. Axial Dispersion Coefficients and Proposed Correlation. The axial dispersion coefficients are obtained from the estimation procedure described in section 3. The experimental (or estimated) results of this study are summarized in Figure 6. This graphical method is used to give a direct

Figure 4. Experimental and theoretical RTD curves: (A) for the different foams with U = 0.065 m/s and (B) for the Foam 1330 with different fluid velocities.

decreases. Finally, Figure.4 shows the accuracy of the estimation strategy proposed in section 3.

4. RESULTS AND DISCUSSION 4.1. Mean Residence Time Values. The residence time (τ) is a very important parameter for the characterization of the millireactor. In case of dead volume, the experimental (or estimated) residence time is clearly decreased compared to the theoretical value given by: τth = (εV/Q). Conversely, in the presence of short-circuit (or bypass), it is increased. In this work, the experimental residence time (τexp) is estimated by fitting the axial dispersion model to the E(t) curves (see section 3). In order to obtain the standard deviation, all series of measure are reproduced several times. Figure 5 presents the theoretical residence time versus that of the experimental one. With knowledge that the calculated mean maximum deviation is 0.9 s for the very low velocities (τexp = 10.9 s), for the foam890, it can be considered that no significant anomalies in flow (dead volume or bypass) are recorded. According to Mendez-Portillo et al.,36 the probable cause of this deviation for the low velocities can be attributed essentially to the tailing effect produced by the tracer flowing at sufficiently

Figure 6. Axial dispersion coefficient for different foam morphologies versus the fluid superficial velocity.

comparison of the general nature of these results with those reported by other authors. For all foam samples, and in accordance with the general results of the literature, it easy to see that the axial dispersion coefficient (Dax) continuously increases by increasing the fluid velocity. According to Montillet et al.,27 it can be represented by a linear function of the superficial velocity (Dax = αU). However, it is clear (Figure 6) that the correlation proposed by Montillet et al.27 underestimates the axial dispersion coefficients. Effectively, because this correlation is obtained for the foams with high porosity (ε > 0.97) and with a low flow velocity (U < 1·10−2 m/s), it is only valid for foam1900 and foam2700 (see Table 1), also with low fluid velocity. 15014



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fixed bed filled with open cell foam or “conventional” packings. The main results can be summarized as the following: − Radial Peclet

The accuracy of this correlation is directly given by the authors through the α values (i.e., 0.9·10−3 < α < 1.26·10−3) In this work, the best fit (except for foam890) is given by Dax = 2.4·10−3U

(6)

Standard fixed bed: Pe = (ud p/Dr ) = 10 − 12

(Gunn and Pryce,39 Gunn,40 Delgado41,42)

This exception for foam890 can be related to the clogging cells which are very important for this foam (see Figure 2). Effectively, it is well-known that during the impregnation phase, the added matter is preferentially deposited onto the nodes of cell (Lacroix et al.22 and Truong et al.31) due to capillary force and consequently the accumulate matter can clogged the cell (especially for the foams with high ppi (or small porosity)). Generally, a large amount of data and empirical correlations concerning the dispersion phenomenon in fixed beds is given in the following form

Dax Re = i ScDm Pe

Open cell foam bed: Pe = (uΦ/Dr ) = 13 − 15

(Truong et al,37 Edouard et al24) − Axial Peclet Standard fixed bed: Pe = (ud p/Dax ) = 1.5 − 2

(Gunn and Pryce,39 Gunn,40 Delgado41,42) Open cell foam bed: Pe = (uΦ/ Dax ) = 0.8 − 1.2

(this work) (7)

5. CONCLUSION The millireactor filled with open cell foam is characterized by the well-known tracing method. The usual dispersive model can be used to fit the residence time distribution curves which are obtained with robust deconvolution procedure. The free parameters, namely, axial dispersion coefficient and mean residence time, are correctly estimated for different morphologies of the foams. No significant anomalies in flow (dead volume or bypass) are recorded. From these results, and others mentioned in previous studies, a correlation based on the Peclet number is established. According to the previous works, this study seems to conform that cell size (Φ) is a judicious characteristic length and avoids some possible pitfalls in the characteristic length chosen for calculating the transport properties in open cell foam. The axial Peclet number based on Φ is found to be on the order of 1. This result is in agreement with the literature data and was compared with the available results for the standard fixed bed. Although further experimental data (with foam of smaller porosities) would be welcome to give better support or to relax the proposed approximation, these correlations could be used for planning and designing chemical engineering processes. Finally, based on the work of Ahmed et al.43 on estimation of the foam’s tortuosity, it should be possible to investigate the influence of the latter on the Peclet number41,42 and will be the subject of the future works.

where Pe represents the Peclet number Consequently, in order to compare our results with the available literature and according to refs 23, 24, 31, 37, and 38, the axial dispersion coefficient is related to the Peclet number on the basis of cell diameter (Φ):

Pe =

uΦ Dax

(8)

Figure 7 shows the dimensionless dispersion number versus interstitial Reynolds number.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: + 33 368 852 633. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors thank the ANR 2010 JCJC 904 01 SIMI9 “Millimatrix” and University of Strasbourg for financial support during this work. Drs. Bernardht, Vignerons, and Schwartz are gratefully acknowledged for their help and advice.

Figure 7. Dimensionaless dispersion number versus Reynolds number.

We can see that the best fit is obtained with Pe = 1 ± 0.25. Indeed, the majority of the values (i.e., 31 experimental values for a total of 41 data) lie in the 25% region. This result can be compared at the Peclet value for a standard fixed bed (ε ≅ 0.4). Gunn and Pryce39,40 and more recently Delgado41,42 gave asymptotic (high Rei) Pe of the order to 2. Thus, it can only be said that the order of magnitude seems to be satisfactory and that using the cell size (Φ) in Pe would lead to a correct asymptotic value. Finally, from this work, it is now possible to compare the global phenomenon of dispersion (axial and radial Peclet) in a

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NOTATIONS USED a Window size or pore diameter, m ds Strut side, m dp Particle diameter, m Dm Molecular diffusion coefficient, m2·s−1 D Vessel dispersion number, − Dax Axial dispersion coefficient m2·s−1 15015


Industrial & Engineering Chemistry Research u U Pe Rei Sc

Article

Interstitial fluid velocity, m·s−1 Superficial fluid velocity, m·s−1 Peclet number, − Interstitial Reynolds number (Rei = ρuΦ/μ), − Schmidt number (Sc = μ/ρDm), −

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Greek Symbols

ε μ ρ Φ τ

Porosity of the cellular material, − Fluid viscosity, Pa·s Fluid volumetric mass, kg·m−3 Cell diameter or cell size, m Mean residence time, s

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