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A hydrodynamic study of cylindrical metal foam packings: Residence time distribution and two phase pressure drop
Accepted Manuscript Title: A hydrodynamic study of cylindrical metal foam packings: residence time distribution and two phase pressure drop Author: Farzad Lali PII: DOI: Reference:
S0255-2701(17)30186-1 http://dx.doi.org/doi:10.1016/j.cep.2017.02.010 CEP 6930
To appear in:
Chemical Engineering and Processing
Received date: Revised date: Accepted date:
12-4-2016 30-1-2017 24-2-2017
Please cite this article as: Farzad Lali, A hydrodynamic study of cylindrical metal foam packings: residence time distribution and two phase pressure drop, Chemical Engineering and Processing http://dx.doi.org/10.1016/j.cep.2017.02.010 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
A hydrodynamic study of cylindrical metal foam packings: residence time distribution and two phase pressure drop Farzad Lalia,b a Institute of chemical process fundamentals of the Czech academy of sciences, Rozvojova 2/135, 165 02 Prague, Czech Republic, phone: +420 220 390 233, fax:220920661,220920649, E-Mail: [email protected] b Technische Universität Dresden, Münchner Platz 3, 01062 Dresden, Germany
Graphical abstract
Research highlights: - Liquid downward flow through foam packing showed poor spreading - Measurement of the axial residence time distribution in upward flow through foams - two phase pressure drop through foams in an upward flow
Nomenclature
Bo
[uz lR Dax-1]
Bodenstein number
Cj
[kmol m-3]
molar concentration of species j
Cj0
[kmol m-3]
molar concentration of species j before inlet
Cjin
[kmol m-3]
molar concentration of species j at inlet
Cjout
[kmol m-3]
molar concentration of species j at outlet
CT
[kmol m-3]
tracer concentration
Dax
[m2 s-1]
axial dispersion coefficient
dR
[m]
reactor diameter
E(t)
probability density function of residence times
PeL
[uL dR Dax-1]
Peclet number
lR
[m]
characteristic bed length variance of E(t)
Sc
[-]
Schmidt number
t
[s]
time
tm
[s]
mean residence time
uj
[m s-1]
velocity of the phase j
uz
[m s-1]
liquid axial velocity
VR
[m3]
reactor volume
[m3 s-1]
inlet volumetric flow rate
[m s-1]
velocity in z direction
θ
[-]
normalized time
υ
[m² s-1]
kinematic viscosity
σ
[kg s-2]
surface tension
τ
[s]
residence time
w
Greek letters
Abstract The present study deals with hydrodynamic characterization of a cylindrical metal foam packings in terms of wetting efficiency, residence time distribution and pressure drop. It was shown that the operation of foam packings in liquid downward flow does not lead to an optimal wetting efficiency according to very high void volume and is very sensitive to the wall issues i.e. fabrication tolerances in the range of 100 µm, Therefore, the study was performed for an upward flow operation mode. The RTD measurements in liquid upward flow and gas/liquid co-current upward flow revealed that the axial backmixing in the foam packing was less than in a vertical pipe with the same diameter. Furthermore, it was shown that the two phase pressure drop for 30 PPI and 45 PPI pore densities were below 250 Pa m -1 and 350 Pa m-1 respectively. The energy dissipation of 30 and 45 PPI foam packings were below 1 W m-3 indicating a very energy efficient type of packing. Keywords: metal foam, hydrodynamics, residence time distribution, two phase flow, two phase pressure drop 1.1 Introduction A previous study [1] published by the author has revealed the advantages of the utilization of foam packings in a tubular reactor in the example of a hydrogenation reaction compared to conventional trickle bed reactors.
The present study gives more insight about the
hydrodynamic characteristics of the metal foam packings such as wetting efficiency in downward flow, residence time distribution and two phase pressure drop in upward flow configuration. The ultimate aim of developing of innovative reactor technologies should certainly involve a significant improvement in the productivity of the chemical reactor at a lower energy consumption. Therefore, in order to fully exploit the potential of metal foams as packing for chemical reactor, the methods which focus on fulfilling the above mentioned aims are favored. Several studies concerning the hydrodynamic characterization of foam structures are published in the previous decade that attempted to encompass a larger operation area of the flow rates in order to derive correlations and rarely focused flow rate ranges which are relevant for an improvement of productivity in case of a catalytically active packing. In light of this background, the present study tries to identify operation modes which lead especially to an improved wetting efficiency and avoid flow regimes of intensified annular flow and extremely low liquid holdups that bring about a low productivity consequently. Furthermore, the application of metal foam packings for multiphase flow reactors was mainly discussed in
this work in order to support reaction studies using catalytically active foams. Moreover, the importance of residence time distribution to attain an improved productivity was taken into consideration for the choice of flow rate ranges for liquid and gas.
Several studies concerning single or multiphase flow through foam packings are published in the last decade. Topin et al. [2] investigated multiphase flow of water-air or water-vapor through a horizontal channel packed with 10, 40, 60, 100 PPI metallic foams (nickel and copper) and gives a Darcy’s law correlation for the two phase pressure drop. Stemmet et al. [3-5] studied the rectangular foam packings for vertical co-current downward, upward and counter-current flows. They investigated the gas liquid mass transfer coefficient and axial dispersion for rectangular foam packings with a pore densities of 10 and 40 PPI for gas velocities ranging from 0.02 to 0.1 m s-1 and liquid velocities ranging from 0.1 to 1 m s-1. In the above mentioned study, an overall mass transfer of 1.3 s-1 obtained that was not influenced by pore density. Furthermore, the effect of viscosity and surface tension and other hydrodynamic parameters such as liquid holdup and frictional pressure drop were studied. Edouard et al. [6] studied the multiphase flow through a 90 cm tubular SiC foam packing with a diameter of 37 mm inner diameter. They investigated the residence time distribution by applying a pulse injection of tracer and they also proposed a model for two phase pressure drop using the relative permeability model of Saez and Carbonell [7] as well as the slit model of Holub et al.[8] and Iliuta et al.[9]. In another study, Edouard et al. [10] published a review of morphological parameters as well as Ergun type correlations for single phase flow through foams. Calvo et al.[11] used X-ray radiography and micro-tomography to reveal the phase distribution as well as hydrodynamic parameters for liquid downward flow and countercurrent flow of gas and liquid through a rectangular foam packing with a height of 40 cm. Lévêque et al.[12] characterized ceramic foam packings for distillation, thereby determining the pressure drop, dynamic liquid holdup, flooding behavior for a mixture of n-heptane and cyclohexane at atmospheric pressure. They revealed the potential of foam packings for reactive distillation. Wenmakers et al.[13, 14] investigated the liquid solid mass transfer for co-current gas flow through a 5% Pd on –alumina washcoated rectangular aluminum foam packing with pore densities of 10, 20 and 40 PPI. Based on the literature data, the potential for increasing the performance of gas-liquid-solid reactions in tubular reactors was revealed. As the application of tubular reactors is very common for gas liquid solid reactions particularly for the reactions at elevated pressures Mohammed et al.[15-17] focused their studies on the gas-liquid downward flow through cylindrical foam packings, thereby investigating the
hydrodynamic multiplicity for two types of prewetting (LEVEC and KAN-Liquid), static and dynamic liquid holdup, residence time distribution as well as liquid-solid mass transfer by applying an electrochemical measurement method. It was shown by Tourvielle et al. [18] that the application of catalytically active foams as packing in minichannels for a hydrogenation reaction enhance the external mass transfer significantly. In order to apply the minichannel technology in the industry, the minichannels should be numbered up. But for the industrial application a lower pressure drop and a uniform distribution of gas and liquid are crucial, which are both challenging for a bundle of packed minichannels. Therefore, the application of foam packings as tubular reactor packing was favored in this study, which focuses on some of hydrodynamic properties of gas-liquid upward flow through a cylindrical aluminum foam packing i.e. the backmixing behavior of the liquid upward flow and two phase pressure drop were investigated. Furthermore, the wetting efficiency in downward was evaluated compared to the upward flow. 1.2 Design of liquid and gas distributors
The gas and liquid distributors play a significant role in gas-liquid-solid reactions. The key requirement for the liquid distributors was, that a symmetrical liquid distribution over the whole cross sectional area of the reactor could be obtained. Moreover, a less complicated construction of the liquid and gas distributors was favored. The liquid and gas distributors were constructed for two reactor inner diameters of 17 and 38 mm. It is also crucial to guarantee a good liquid distribution in different flow directions i.e. liquid downward or upward flow. In case of liquid downward flow, which is characteristic for the co-current downward flow or the countercurrent flow, the wetting efficiency of the foam packing is important to maximize the liquid-gas contact area. In contrast, a good distribution of the gas bubbles plays the key role in the co-current upward flow, because the bubble size is a major factor in the gas liquid mass transfer in the foam packing. Due to this background, four distributors were constructed i.e. two distributors for each reactor inner diameter appropriate to the flow direction. The uniform distribution of the liquid over the cross sectional area in the downward flow was a challenging issue. For a uniform liquid distribution, different parameters such as fluid properties i.e. surface tension and viscosity, liquid flow rate and pressure should be taken into consideration.
In order to obtain a uniform distribution, the liquid passages, which were in form of nozzles, should not be compatible with lower flow rates. At lower flow rates for instance below 10 mL min-1, if the diameter of the inner liquid passages is large enough, the outer passage will not be flowed through. Therefore, a viable design strategy would be varying the nozzle diameter sizes from smaller to larger, from the distributor center to the edge. But there is a risk that at higher flow rates for instance above 100 mL min-1, the liquid would only flow through the outer nozzles thereby flowing further to the packing edges and reactor wall. In order to keep a balance between the higher and lower liquid flow rates, it is crucial to obtain more or less equal flow through probability for all liquid passages. In addition, the expansion chamber above the fluid passages facilitates the distribution of the liquid through passages. The advantage of using nozzles as fluid passages is, that the probability of coalescence of liquid droplets with the droplets from the adjacent passages can be minimized.
The design of the liquid distributor was done using Solidworks student kit. One of the features of the software was the limited possibility of a CFD simulation of water and/or air flow through the designed components. Using this tool, the compatibility of a distributer design could be tested. Fig. 1 shows that all nozzles of the liquid distributor for a tubular reactors with diameters of 17 mm and 38 mm, were uniformly flowed through by a liquid flow 5 mL min-1. The simulation with water/air indicates that the stream lines spread first and then flow through the nozzles uniformly. Moreover, the colors in the simulation indicate the velocities at any passage, which are equal for the liquid passing through the nozzles. According to the continuity equation, the highest liquid velocity was reached in the inlet pipe while the velocity in the expansion chamber decreased. The 17 mm liquid distributor had 22 and the 38 mm distributor had 71 nozzles of uniformly positioned liquid passages and three and eight gas passages respectively. Thus, gas and liquid were introduced separately in the reactor. The results of the steady state CFD simulation with water show uniformly distributed liquid flowing through all liquid passages. The outlet velocity for flow rate of 5 mL min-1 was 0.012 m s-1. In the operation mode of co-current upward flow, it is of crucial importance to disperse the gas bubbles uniformly. Smaller and fine dispersed bubbles enhance the gas liquid mass transfer due to the larger gas liquid contact area. In this operation mode, it was assumed that
the foam packing was first flooded with liquid and subsequently, gas was introduced into the reactor.
1.3 Characterization of liquid distribution in downward flow in tubular columns Trickle bed reactors are widely used in chemical, pharmaceutical and petrochemical industries. It is typical for the trickle bed reactors that gas and liquid are introduced cocurrently downward into the reactor.
Moreover, it is characteristic for the trickle bed reactors compared to the trickle bed absorbers that the gas liquid flow rates in trickle bed reactors are low. Firstly, the application of open cell foam as fixed bed packing for trickle bed reactors was investigated
In hydrodynamic experiments with a foam packing with pore densities of 20 and 30 PPI in an acrylic glass column. An overview of the foams, which are used in this study is given in table [1]. The foam packings have different geometrical surface areas and strut thicknesses but they have the same porosity (void volume).
It was observed after several variations of liquid flow rates with distilled water, that starting from a flow rate of 5 mL min-1and a bed length of 2 cm, the liquid flowed through a unique preferred path in the center of the packing (Fig. 2).
Moreover, any slight distance (~100 µm) from the edge of packing at the column wall would lead to a drastic channeling effect as shown in Fig. 3. The right hand side image depicts the wetted foam pieces that were lying upon another as packing. The major part of the packing remained non-wetted. Furthermore, the preferred paths did not change over time like in a random bed of pellets. The poor spreading of the liquid in the downward flow through the foam packing indicates a major drawback in the operation of catalytically active foams in trickle regime. To visualize
the preferred liquid paths, sodium fluorescein was added to pure water as tracer. The wetted areas of a liquid downward flow of 20 mL min-1 through a 30 PPI foam packing with a length of 15 cm, were made visible by irradiation of UV light. It can be seen in Fig. 3, that the wetted areas are mainly in the packing edges and the areas in the middle of the foam samples were not wetted. This effect can be explained by the very high void volume in the foam packing, which is above 90 %. The liquid flow stream tends to decrease its cross sectional surface area with increasing velocity according to the continuity equation. The narrow stream of water at the column outlet in Fig. 2, can be explained this way. The wall effects were strongly related to the construction tolerances of the foam samples. It is known that a weak wetting efficiency leads to a poor catalytic performance in trickle bed operation mode.
The effect of distributor was ruled out by utilizing appropriate liquid distributors and also by placing an inert layer of glass pearls on the foam packing with a thickness of 1 and 2 cm to enhance the liquid distribution. Despite a uniform distribution by the distributor or a combination of distributor and inert layer, a poor spreading of liquid in the foam packing was observed. Various pore densities of 20, 30 and 45 PPI were compared in terms of liquid spreading in the packing. In case of 45 PPI, the liquid spreading was rather better than 30 and 20 PPI foams due to very high geometric surface area but still not satisfactory. To rule out that the weak liquid spreading do not exclusively takes place for water due to high surface tension, other liquids with various surface tensions and viscosities such as isopropanol and glycerin were investigated. Isopropanol was taken because of lower surface tension and glycerin because of higher viscosity. It was observed that the lower surface tension of isopropanol enhanced the spreading to a very limited extent. But the higher viscosity of glycerin did not influence the liquid spreading. Reducing the reactor or packing diameter suppresses the weak spreading of the liquid due to smaller size a relatively larger area can be wetted. This is a major design limitation that limits the diameter to packing length ratio. A practical solution to overcome the limitations imposed by the weak liquid spreading in the foam packing, was to carry out the multiphase reaction in catalytically active foams by applying a cocurrently upward flow.
It should be noted that the obtained data is gathered by investigation of metallic open cell foams. In case of ceramic foams, the spreading behavior could be different due to irregularities in the ceramic foam structure which are caused by clogging of the ceramic material as depicted in Fig. 4. In fact, the clogged cells enhance the liquid spreading in a ceramic foam packing in downward flow by acting like ceramic pellets. It was also shown by Mohammed et al. [15, 17, 19] the insufficient spreading of the liquid in co-current downward flow through cylindrical ceramic foam packings.
1.4 Residence time distribution (RTD) measurements
theoretical background The simple definition of the residence time (Eq. 1) as the ratio of reactor volume to the volumetric flow rate is a simplified definition that describes the average residence time in a reactor regardless of its design specifications. Eq. 1
But it should be noted that the Eq. 1 does not represent the flow of all liquid elements through a reactor, which is in fact strongly dependent upon the reactor type, design and flow characteristics. It is therefore also relevant for the selectivity of a chemical reaction that takes place in a continuous reactor, how the residence times of fluid elements are distributed. In order to investigate the RTD in a continuous tubular reactor with a foam packing in a co-current upward flow operation mode, the dispersion model is proposed in the literature [20] to evaluate the RTD curves. The RTD measurements were carried out for steady state condition using a tracer impulse. The probability density function of the residence times in the apparatus is expressed by E(t), also called the age distribution in the apparatus (Eq. 2).
Eq. 2
The Eq. 2 gives information about a fluid element marked by tracer, that entered the apparatus at the time of t = 0 and left the apparatus at the time of t+dt. After a certain time (infinite time) all of the marked elements leave the apparatus and therefore the time integral of the age distribution is equal to unity. The unit of E(t) is usually given as s-1.
In order to obtain an impulse at the inlet, the tracer should be introduced as fast as possible to approach a Dirac-impulse. The indicator material that the tracer is consisted of should fulfill various requirements. The tracer should not undergo a chemical reaction with the apparatus content. It should also not remain permanently in the system by a physical or chemical absorption or adsorption. The key parameter to evaluate the RTD in the variance of the E(t) curve because a relationship between the variance and the Bodenstein number (Bo). A dimensionless number that describes
Probability density
Eq. 3
function
Average residence time
Variance of E(t)
Eq. 4
Eq. 5
the ratio of convective flow to axial diffusion flow, whereas characteristic length in the Bo is the bed length. The Bo number gives insight about the axial dispersion viz. backmixing in a chemical reactor (Eq. 8). In order to compare different apparatuses in terms of size and space time, a normalized time was introduced. Eq. 6
The tracer mass balance can be expressed as follows by applying the dispersion model
Eq. 7 Eq. 8 Eq. 9 Eq. 10
By introducing the normalized time , dimensionless length as well as the Bodenstein number the following differential equation for the tracer mass balance in the system can be derived.
Eq. 11
The Bodenstein number is a measure for the backmixing in the reactor according to its definition. An infinite Bodenstein number means no axial dispersion and a Bodenstein number equal to zero means an axially thoroughly mixed system. A Bodenstein number equal to 7 is the threshold value between the backmixing in a stirred tank and in a tubular apparatus. For the values above 7, a plug flow can be approximately assumed [21]. The differential equation above demands boundary conditions to be solved. A closed-closed system boundary was chosen to solve the differential equation. The boundary conditions were set on the basis of the Danckwert’s boundary conditions [22]. Assuming a closed-closed system, boundary conditions for the mass balances in the liquid phase result in Eq. 12 for the inlet: Eq. 12
For the outlet, the equation for system boundaries is: Eq. 13
By applying the mentioned conditions for solution of the differential equation of the tracer concentration distribution, the following equation can be derived to calculate the Bodenstein number from the variance of E(t) as given by Reschetilowski [20]. The definitions of the probability density function E(t), the variance of the probability density function st, average residence time tm and the normalized time θ are given in equation [3-6].
Eq. 12
In addition to the Bodenstein number, Peclét number is also often adopted to describe backmixing. Eq. 13
The Peclét number is also defined as the ratio of the convective to diffusive flows with one difference. The characteristic length in Pe number is the apparatus diameter (Eq. 13).
1.5 Experimental section The measurement of the RTD was carried out in a stainless steel tubular reactor, which was used later to support the reaction studies, with an inner diameter of 17 mm and a length of 50 cm. A structured packing of uncoated 30 PPI aluminum substrates with a diameter of 17 mm, each one with a length of 2 cm were placed in the tubular reactor to obtain a total bed length of 50 cm. The stationary phase was deionized water and the gas phase was consisting of pressurized air. A 1mL (0.0022 mol) injection of pure Ethanol was adopted as tracer for all RTD measurements. The tracer concentration at the reactor outlet was analyzed using a flow through refractometer (Rudolf J357). The refractometer had a measurement frequency of 0.5 Hz. Firstly, a dilution series for various concentrations of pure ethanol subject to their refractive index in deionized water was determined. By applying the resulting calibration line shown in Fig. 5 , the time dependent concentration of the tracer at the reactor outlet can be determined resulting in E(t) curves. Subsequently, 50 measured values for deionized water were taken as baseline for E(t) curves.
After reaching the steady state conditions, while keeping the temperature constant at 25±0.2 °C a tracer impulse of pure ethanol was introduced into the reactor. The measurements were continued until the outlet concentration reached the aforementioned baseline concentration. The RTD experiments were carried out for single and multiphase systems. The examined liquid (pure water) flow rates were ranging between 10-140 mL min-1. The RTD two phase flow was investigated using a distilled water/N2 system for a single liquid flow rate of 50 mL min-1 and gas flow rates ranging from 0.2 to 0.4 L min-1. The solution of the integrals was calculated numerically by applying trapezoidal solution method.
Baseline alignment During the experiments, the baseline with a refractive index of 1.3352 (refractive index of pure water at 25 °C) was not always reached (Fig. 6). The reason for this deviation is mainly the temperature sensitivity of refractive index.
In order to compare different baselines, the baselines were shifted to the baseline corresponding to the pure water at 25 °C. For this purpose, an average of the first 50 measured values for every data series was calculated. After that, the difference between the calculated average and the baseline of 1.33252 was added to all measured values to shift the curve to a common baseline.
Shifting the baselines to a common baseline reduced the deviation of RTD curves to about 1%.
The study of residence time distribution elucidates the influence of the foam packing on the residence time and backmixing in single or two phase flow through foam packing. The experimentally measured axial dispersion coefficients are also crucial for the mathematical modeling of reactors. Firstly, the RTD of a single phase liquid upward flow of pure water through a cylindrical foam packing with a pore density of 30 PPI and a packing length of 50 cm was studied. In Fig. 7, the density probability of a cylindrical 30 PPI packing with a diameter of 17 mm, was compared with a single phase flow through a pipe with the same diameter. The foam packing narrows the probability density of residence times by increasing the velocity according to the continuity equation.
The effect of liquid velocity on the RTD in a 30 PPI packing is also illustrated in Fig. 8 for different superficial velocities. The narrowing effect was strengthened with increasing superficial velocities. The average residence time decreases with increasing liquid velocity. Fig. 9 depicts the average residence times versus the liquid velocity, thereby comparing the residence time in a 30 PPI packing with a non-packed tubular reactor. The Fig. 9 shows that the average residence times of the cylindrical foam packing are slightly higher than the residence times in the unpacked column, whereas the difference between packed and unpacked columns decreases with increasing liquid velocity.
The calculated Bodenstein numbers based on the RTD experiments in the cylindrical foam packing was always higher than the unpacked column (Fig. 10). Thus the axial dispersion of the packed column was less than the unpacked column.
1.6 Residence time distribution in two phase flow The influence of gas velocity on the RTD was studied for a liquid velocity of 3.3 mm s-1 (50 mL min-1). The two phase flow leaving the column was visible through the flexible PFA pipe before entering the online refractometer. The resulting refractive index was often out of the calibration range of the tracer in distilled 1.33252
A value below 1.33252 indicated a two phase flow of gas (N2) and liquid (water+tracer) in the measuring chamber. A maximum measurement frequency of 0.5 Hz could be achieved. This frequency was not enough to detect the passing liquid and gas slugs with a high resolution. The noises in the RTD curve caused by large gas bubbles made the interpretation of the curves difficult. Therefore, the values out of calibration range were filtered, thereby replacing the out of range value with the average of two preceding values.
Fig. 11 presents the influence of the gas velocity on the RTD. It can be seen, that the RTD curves shift from the vicinity
to coordinate origin, thereby the RTD curves for
gas/liquid ratios of 3 and 4 were in a similar position. A shift of RTD curves in the direction of origin can be interpreted as a decrease of Bodenstein number and therefore an increase of the backmixing. Fig. 12 depicts the influence of the gas velocity on the Bodenstein number. Three measurements were performed for each gas velocity. The measurements for the two lower gas velocities scatter but with increasing gas velocity the Bodenstein numbers converge and reach a plateau. 1.7 Multiphase pressure drop
in the preliminary experiments the dynamic pressure drop signals from a 50 cm foam packing of two different pore densities with a diameter of 1.8 cm were investigated. The pressure drop signals were measured by difference pressure transducer (Huba control 692). The two phase pressure drop signals involved the dynamic and frictional pressure drop. The transducer was connected with the packed column using two flexible PFA tubes, which were mounted before
and after the foam packing. In order to increase the precision of the measurement, the appearance of any gas bubbles in the PFA flexible tubes was avoided by using extra valves. In order to attain an optimal wetting efficiency, the flow regimes should change from bubbly flow to slug flow and finally churn flow with increasing gas flow rate respectively. But if the gas flow rate is further increased the liquid holdup decreases drastically and presumably an annular flow regime emerges. The annular flow regime is logically counterproductive due to very poor wetting of the foam structure and wetting the non-active wall.
Four liquid flow rates from 10 mL min-1 to 40 mL min-1 were investigated. The gas flow rates were increased with a step size, at which a change in pressure difference was still measureable, until the pressure difference signals approached zero. The gas flow rates were varied from 50 to 350 mL/min. The preliminary experiments were carried out with pure distilled water and nitrogen. In order to convey the investigated flow rates to the Hydrogen and AMS/Cumene system a few extra gas flow rates were added. Based on the dynamic pressure drop values a parameter window for the continuous tubular reactor experiments were determined in order to avoid annular flow that leads to a very poor wetting efficiency. A comparison between figures 13 and 14 shows clearly that the two phase pressure drop in a 45 PPI foam packing was around 30 % higher than the 30 PPI due to a higher geometrical surface area of the 45 PPI foams. It can be observed in both measurement series that the two phase pressure drop declines with increasing gas flow rate. The decline of pressure drop by increasing the gas flow rate was accompanied by a decreasing liquid holdup. The most probable reason for this effect can be an increase of the entrainment of liquid droplet with an increasing gas flow rate. Several correlations from the literature were tested in order to evaluate the experimental results. The majority of the two phase pressure drop models in the literature are developed for liquid-vapor flow in heat exchangers or similar units. The Lockhart-Martinelli or Chisholm [23] correlations are basically developed for two phase pressure drop through horizontal pipes and therefore, the calculated pressure drop using this model showed a large deviation. The two phase pressure drop model proposed by Saez and Carbonell [7] is a relative permeability model, which is developed for liquid downward flow, which seem to be inappropriate to model the two phase pressure drop of an upward flow through foam packings. Friedel [24]
proposed a two phase pressure drop correlation for vertical upflow. But the application of Friedel correlation did not result in satisfactory results for the values presented in Fig. 13 and Fig. 14.
Conclusions The present study revealed that the liquid downward flow is subject to poor spreading and a preferred wall pathway although a well-designed liquid distributor was applied. Therefore, the upward flow was favored for this study. For the later studies, it will be reasonable to apply technologies such as laser sintering and 3D printing in order fabricate the foam structure together with shell as one piece and control the pore size and strut thickness at the same time. Using this technology, it would be possible to overcome the problem with the gaps to the wall. The study of the residence time distribution for the liquid phase in upward flow direction through a foam packing showed clearly that the local turbulences caused by interconnected network of struts, reduced the backmixing so that the Bo number was smaller than in an unpacked tube. The RTD measurement for the gas liquid upward flow showed that an increase of gas velocity increases the backmixing which is shown by a declining Bo number by increasing gas velocity that reached a plateau after a gas velocity of 1.5 cm s-1. Thus, as a future perspective, studying the bubble size evolution in an upward gas/liquid flow through a foam packing using imaging methods is highly encouraged. the two phase pressure drop for the 45 PPI foam was around 30% more than the 30 PPI due to the higher specific surface area. But in both measurement series the two phase pressure drop was very low and the energy dissipation in the 30 PPI and 45 PPI packings were less than 1 W m-3.
Acknowledgement The Author gratefully acknowledges Prof. Dr.-Ing. habil. Rüdiger Lange for giving me the opportunity to accomplish the present study and the TU Dresden, Institute of chemical engineering for enabling me to perform the experiments for this work. References
1. 2.
3. 4.
5. 6. 7. 8.
9.
10. 11.
12.
13. 14.
15. 16. 17. 18.
19.
20. 21.
Lali, F., Characterization of foam catalysts as packing for tubular reactors. Chemical Engineering and Processing, 2016.105, 1-9. Topin, F., et al., Experimental Analysis of Multiphase Flow in Metallic foam: Flow Laws, Heat Transfer and Convective Boiling. Advanced Engineering Materials, 2006. 8(9): p. 890-899. Stemmet, C.P., et al., Solid Foam Packings for Multiphase Reactors. Chemical Engineering Research and Design, 2006. 84(12): p. 1134-1141. Stemmet, C.P., et al., Influence of liquid viscosity and surface tension on the gas– liquid mass transfer coefficient for solid foam packings in co-current two-phase flow. Chemical Engineering Research and Design, 2008. 86(10): p. 1094-1106. Stemmet, C.P., Gas-liquid Solid Foam Reactors: Hydrodynamics and Mass Transfer. 2008, Technische Universiteit Eindhoven. Edouard, D., et al., Experimental Measurements and Multiphase Flow Models in Solid SiC Foam Beds. AIChE Journal, 2008. 54(11): p. 2823-2832. Sáez, A.E. and R.G. Carbonell, Hydrodynamic Parameters for Gas-Liquid Cocurrent Flow in Packed Beds. AIChE Journal, 1985. 31(1): p. 52-62. Holub, R.A., Dudukovic, M. P. and P.A. Ramachandran, A Phenomenological Model for Pressure Drop, Liquid Holdup and Flow Regime Transition in Gas-Liquid Trickle Flow. Chem. Eng. Sci.,, 1992. 47: p. 2343-2348. Iliuta, I., C. Petre, and F. Larachi, Hydrodynamic continuum model for two-phase flow structured-packing-containing columns. Chemical Engineering Science, 2004. 59(4): p. 879-888. Edouard, D., et al., Pressure drop modeling on SOLID foam: State-of-the art correlation. Chemical Engineering Journal, 2008. 144(2): p. 299-311. Calvo, S., et al., Phase distribution measurements in metallic foam packing using Xray radiography and micro-tomography. Chemical Engineering and Processing, 2009. 48(5): p. 1030-1039. Leveque, J., Rouzineau, D., Prevost, M., Meyer,M., Hydrodynamic and mass transfer efficiency of ceramic foam packing applied to distillation. Chemical Engineering Science, 2009. 64: p. 2607-2616. Wenmakers, P.W.A.M., et al., Liquid-Solid Mass Transfer for Cocurrent Gas-Liquid Upflow Through Solid Foam Packings. Aiche Journal, 2010. 56(11): p. 2923-2933. Wenmakers, P.W.A.M., et al., Enhanced liquid–solid mass transfer by carbon nanofibers on solid foam as catalyst support. Chemical Engineering Science, 2010. 65(1): p. 247-254. Mohammed, I., et al., Hydrodynamic multiplicity in a tubular reactor with solid foam packings. Chemical Engineering Journal, 2013. 231: p. 334-344. Mohammed, I., et al., Liquid-solid mass transfer in a tubular reactor with solid foam packings. Chemical Engineering Science, 2014. 108: p. 223-232. Mohammed, I., et al., Gas-liquid distribution in tubular reactors with solid foam packings. Chemical Engineering and Processing, 2015. 88: p. 10-18. Tourvieille, J.N., R. Philippe, and C. de Bellefon, Milli-channel with metal foams under an applied gas-liquid periodic flow: External mass transfer performance and pressure drop. Chemical Engineering Journal, 2015. 267: p. 332-346. Mohammed, I.H.M., et al., Investigation of hydrodynamics and mass transfer of solid foam packings for gas-liquid applications. Abstracts of Papers of the American Chemical Society, 2014. 248. Reschetilowski, W., Technisch-Chemisches Praktikum. Vol. 1. 2002: WILEY-VCH. Hagen, J., Chemiereaktoren: Auslegung und Simulation. 2004, Weinheim: WileyVCH.
22. 23. 24.
Fogler, H.S., Elements of chemical reaction engineering. 4. ed. ed. 2005, Englewood Cliffs, NJ: Prentice-Hall. Chisholm, D., A theoretical basis for the Lockhart-Martinelli correlation for two phase flow. International Journal of Heat and Mass Transfer, 1967. 10: p. 1767-1778. Friedel, L., Pressure drop during gas vapor liquid flow in pipes. Chemie Ingenieur Technik, 1978. 50(3): p. 167-180.
A
B
C
Fig. 1: CFD simulation of water flow for a liquid distributor with a diameter of A:38 mm and B: 17 mm at T= 293.15 K and P= 101.33 kPa. mL min-1 C: CAD drawing of liquid distributor 38 mm
Fig. 2: narrow water stream at the outlet of 30 PPI foam packing
cross section
Fig. 3: visualization of wetted areas in a 15 cm foam packing with UV-light
Fig. 4: clogged cells in a ceramic foam sample
Fig. 5: calibration line for different concentration of the tracer, Ethanol
Fig. 6: Baselines for the RTD curves for a flow rate of 60 mL min-1
Fig. 7: comparison between a with 30 PPI foams packed column with an unpacked column UL,s=1.175 mm s-1
Fig. 8: Influence of the liquid superficial velocity on the RTD curves
30 PPI non-packed
Fig. 9: Influence of liquid flow rate on the average residence time
30 PPI non-packed
Fig. 10: Bodenstein numbers for 30 PPI foam packing compared with a non-packed tube for various liquid flow rates
Fig. 11: RTD curves for a multiphase flow of water/air with various flow ratios
Fig. 12: Influence of gas velocity on Bodenstein number for 30 PPI and unpacked column
Fig. 13: Average dynamic two phase pressure drop for 45 PPI foam packing
Fig. 14: Average dynamic two phase pressure drop for 30 PPI foam packing
Table 1. Specification of the used foams Material
Pore density
Surface area
Strut thickness
Porosity or void volume
(PPI)
(m²/m³)
(mm)
(%)
Al-Si-Mg
20
855
0.37
93
Al-Si-Mg
30
1617
0.25
94
Al-Si-Mg
45
2330
0.2
92
S0255-2701(17)30186-1 http://dx.doi.org/doi:10.1016/j.cep.2017.02.010 CEP 6930
To appear in:
Chemical Engineering and Processing
Received date: Revised date: Accepted date:
12-4-2016 30-1-2017 24-2-2017
Please cite this article as: Farzad Lali, A hydrodynamic study of cylindrical metal foam packings: residence time distribution and two phase pressure drop, Chemical Engineering and Processing http://dx.doi.org/10.1016/j.cep.2017.02.010 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
A hydrodynamic study of cylindrical metal foam packings: residence time distribution and two phase pressure drop Farzad Lalia,b a Institute of chemical process fundamentals of the Czech academy of sciences, Rozvojova 2/135, 165 02 Prague, Czech Republic, phone: +420 220 390 233, fax:220920661,220920649, E-Mail: [email protected] b Technische Universität Dresden, Münchner Platz 3, 01062 Dresden, Germany
Graphical abstract
Research highlights: - Liquid downward flow through foam packing showed poor spreading - Measurement of the axial residence time distribution in upward flow through foams - two phase pressure drop through foams in an upward flow
Nomenclature
Bo
[uz lR Dax-1]
Bodenstein number
Cj
[kmol m-3]
molar concentration of species j
Cj0
[kmol m-3]
molar concentration of species j before inlet
Cjin
[kmol m-3]
molar concentration of species j at inlet
Cjout
[kmol m-3]
molar concentration of species j at outlet
CT
[kmol m-3]
tracer concentration
Dax
[m2 s-1]
axial dispersion coefficient
dR
[m]
reactor diameter
E(t)
probability density function of residence times
PeL
[uL dR Dax-1]
Peclet number
lR
[m]
characteristic bed length variance of E(t)
Sc
[-]
Schmidt number
t
[s]
time
tm
[s]
mean residence time
uj
[m s-1]
velocity of the phase j
uz
[m s-1]
liquid axial velocity
VR
[m3]
reactor volume
[m3 s-1]
inlet volumetric flow rate
[m s-1]
velocity in z direction
θ
[-]
normalized time
υ
[m² s-1]
kinematic viscosity
σ
[kg s-2]
surface tension
τ
[s]
residence time
w
Greek letters
Abstract The present study deals with hydrodynamic characterization of a cylindrical metal foam packings in terms of wetting efficiency, residence time distribution and pressure drop. It was shown that the operation of foam packings in liquid downward flow does not lead to an optimal wetting efficiency according to very high void volume and is very sensitive to the wall issues i.e. fabrication tolerances in the range of 100 µm, Therefore, the study was performed for an upward flow operation mode. The RTD measurements in liquid upward flow and gas/liquid co-current upward flow revealed that the axial backmixing in the foam packing was less than in a vertical pipe with the same diameter. Furthermore, it was shown that the two phase pressure drop for 30 PPI and 45 PPI pore densities were below 250 Pa m -1 and 350 Pa m-1 respectively. The energy dissipation of 30 and 45 PPI foam packings were below 1 W m-3 indicating a very energy efficient type of packing. Keywords: metal foam, hydrodynamics, residence time distribution, two phase flow, two phase pressure drop 1.1 Introduction A previous study [1] published by the author has revealed the advantages of the utilization of foam packings in a tubular reactor in the example of a hydrogenation reaction compared to conventional trickle bed reactors.
The present study gives more insight about the
hydrodynamic characteristics of the metal foam packings such as wetting efficiency in downward flow, residence time distribution and two phase pressure drop in upward flow configuration. The ultimate aim of developing of innovative reactor technologies should certainly involve a significant improvement in the productivity of the chemical reactor at a lower energy consumption. Therefore, in order to fully exploit the potential of metal foams as packing for chemical reactor, the methods which focus on fulfilling the above mentioned aims are favored. Several studies concerning the hydrodynamic characterization of foam structures are published in the previous decade that attempted to encompass a larger operation area of the flow rates in order to derive correlations and rarely focused flow rate ranges which are relevant for an improvement of productivity in case of a catalytically active packing. In light of this background, the present study tries to identify operation modes which lead especially to an improved wetting efficiency and avoid flow regimes of intensified annular flow and extremely low liquid holdups that bring about a low productivity consequently. Furthermore, the application of metal foam packings for multiphase flow reactors was mainly discussed in
this work in order to support reaction studies using catalytically active foams. Moreover, the importance of residence time distribution to attain an improved productivity was taken into consideration for the choice of flow rate ranges for liquid and gas.
Several studies concerning single or multiphase flow through foam packings are published in the last decade. Topin et al. [2] investigated multiphase flow of water-air or water-vapor through a horizontal channel packed with 10, 40, 60, 100 PPI metallic foams (nickel and copper) and gives a Darcy’s law correlation for the two phase pressure drop. Stemmet et al. [3-5] studied the rectangular foam packings for vertical co-current downward, upward and counter-current flows. They investigated the gas liquid mass transfer coefficient and axial dispersion for rectangular foam packings with a pore densities of 10 and 40 PPI for gas velocities ranging from 0.02 to 0.1 m s-1 and liquid velocities ranging from 0.1 to 1 m s-1. In the above mentioned study, an overall mass transfer of 1.3 s-1 obtained that was not influenced by pore density. Furthermore, the effect of viscosity and surface tension and other hydrodynamic parameters such as liquid holdup and frictional pressure drop were studied. Edouard et al. [6] studied the multiphase flow through a 90 cm tubular SiC foam packing with a diameter of 37 mm inner diameter. They investigated the residence time distribution by applying a pulse injection of tracer and they also proposed a model for two phase pressure drop using the relative permeability model of Saez and Carbonell [7] as well as the slit model of Holub et al.[8] and Iliuta et al.[9]. In another study, Edouard et al. [10] published a review of morphological parameters as well as Ergun type correlations for single phase flow through foams. Calvo et al.[11] used X-ray radiography and micro-tomography to reveal the phase distribution as well as hydrodynamic parameters for liquid downward flow and countercurrent flow of gas and liquid through a rectangular foam packing with a height of 40 cm. Lévêque et al.[12] characterized ceramic foam packings for distillation, thereby determining the pressure drop, dynamic liquid holdup, flooding behavior for a mixture of n-heptane and cyclohexane at atmospheric pressure. They revealed the potential of foam packings for reactive distillation. Wenmakers et al.[13, 14] investigated the liquid solid mass transfer for co-current gas flow through a 5% Pd on –alumina washcoated rectangular aluminum foam packing with pore densities of 10, 20 and 40 PPI. Based on the literature data, the potential for increasing the performance of gas-liquid-solid reactions in tubular reactors was revealed. As the application of tubular reactors is very common for gas liquid solid reactions particularly for the reactions at elevated pressures Mohammed et al.[15-17] focused their studies on the gas-liquid downward flow through cylindrical foam packings, thereby investigating the
hydrodynamic multiplicity for two types of prewetting (LEVEC and KAN-Liquid), static and dynamic liquid holdup, residence time distribution as well as liquid-solid mass transfer by applying an electrochemical measurement method. It was shown by Tourvielle et al. [18] that the application of catalytically active foams as packing in minichannels for a hydrogenation reaction enhance the external mass transfer significantly. In order to apply the minichannel technology in the industry, the minichannels should be numbered up. But for the industrial application a lower pressure drop and a uniform distribution of gas and liquid are crucial, which are both challenging for a bundle of packed minichannels. Therefore, the application of foam packings as tubular reactor packing was favored in this study, which focuses on some of hydrodynamic properties of gas-liquid upward flow through a cylindrical aluminum foam packing i.e. the backmixing behavior of the liquid upward flow and two phase pressure drop were investigated. Furthermore, the wetting efficiency in downward was evaluated compared to the upward flow. 1.2 Design of liquid and gas distributors
The gas and liquid distributors play a significant role in gas-liquid-solid reactions. The key requirement for the liquid distributors was, that a symmetrical liquid distribution over the whole cross sectional area of the reactor could be obtained. Moreover, a less complicated construction of the liquid and gas distributors was favored. The liquid and gas distributors were constructed for two reactor inner diameters of 17 and 38 mm. It is also crucial to guarantee a good liquid distribution in different flow directions i.e. liquid downward or upward flow. In case of liquid downward flow, which is characteristic for the co-current downward flow or the countercurrent flow, the wetting efficiency of the foam packing is important to maximize the liquid-gas contact area. In contrast, a good distribution of the gas bubbles plays the key role in the co-current upward flow, because the bubble size is a major factor in the gas liquid mass transfer in the foam packing. Due to this background, four distributors were constructed i.e. two distributors for each reactor inner diameter appropriate to the flow direction. The uniform distribution of the liquid over the cross sectional area in the downward flow was a challenging issue. For a uniform liquid distribution, different parameters such as fluid properties i.e. surface tension and viscosity, liquid flow rate and pressure should be taken into consideration.
In order to obtain a uniform distribution, the liquid passages, which were in form of nozzles, should not be compatible with lower flow rates. At lower flow rates for instance below 10 mL min-1, if the diameter of the inner liquid passages is large enough, the outer passage will not be flowed through. Therefore, a viable design strategy would be varying the nozzle diameter sizes from smaller to larger, from the distributor center to the edge. But there is a risk that at higher flow rates for instance above 100 mL min-1, the liquid would only flow through the outer nozzles thereby flowing further to the packing edges and reactor wall. In order to keep a balance between the higher and lower liquid flow rates, it is crucial to obtain more or less equal flow through probability for all liquid passages. In addition, the expansion chamber above the fluid passages facilitates the distribution of the liquid through passages. The advantage of using nozzles as fluid passages is, that the probability of coalescence of liquid droplets with the droplets from the adjacent passages can be minimized.
The design of the liquid distributor was done using Solidworks student kit. One of the features of the software was the limited possibility of a CFD simulation of water and/or air flow through the designed components. Using this tool, the compatibility of a distributer design could be tested. Fig. 1 shows that all nozzles of the liquid distributor for a tubular reactors with diameters of 17 mm and 38 mm, were uniformly flowed through by a liquid flow 5 mL min-1. The simulation with water/air indicates that the stream lines spread first and then flow through the nozzles uniformly. Moreover, the colors in the simulation indicate the velocities at any passage, which are equal for the liquid passing through the nozzles. According to the continuity equation, the highest liquid velocity was reached in the inlet pipe while the velocity in the expansion chamber decreased. The 17 mm liquid distributor had 22 and the 38 mm distributor had 71 nozzles of uniformly positioned liquid passages and three and eight gas passages respectively. Thus, gas and liquid were introduced separately in the reactor. The results of the steady state CFD simulation with water show uniformly distributed liquid flowing through all liquid passages. The outlet velocity for flow rate of 5 mL min-1 was 0.012 m s-1. In the operation mode of co-current upward flow, it is of crucial importance to disperse the gas bubbles uniformly. Smaller and fine dispersed bubbles enhance the gas liquid mass transfer due to the larger gas liquid contact area. In this operation mode, it was assumed that
the foam packing was first flooded with liquid and subsequently, gas was introduced into the reactor.
1.3 Characterization of liquid distribution in downward flow in tubular columns Trickle bed reactors are widely used in chemical, pharmaceutical and petrochemical industries. It is typical for the trickle bed reactors that gas and liquid are introduced cocurrently downward into the reactor.
Moreover, it is characteristic for the trickle bed reactors compared to the trickle bed absorbers that the gas liquid flow rates in trickle bed reactors are low. Firstly, the application of open cell foam as fixed bed packing for trickle bed reactors was investigated
In hydrodynamic experiments with a foam packing with pore densities of 20 and 30 PPI in an acrylic glass column. An overview of the foams, which are used in this study is given in table [1]. The foam packings have different geometrical surface areas and strut thicknesses but they have the same porosity (void volume).
It was observed after several variations of liquid flow rates with distilled water, that starting from a flow rate of 5 mL min-1and a bed length of 2 cm, the liquid flowed through a unique preferred path in the center of the packing (Fig. 2).
Moreover, any slight distance (~100 µm) from the edge of packing at the column wall would lead to a drastic channeling effect as shown in Fig. 3. The right hand side image depicts the wetted foam pieces that were lying upon another as packing. The major part of the packing remained non-wetted. Furthermore, the preferred paths did not change over time like in a random bed of pellets. The poor spreading of the liquid in the downward flow through the foam packing indicates a major drawback in the operation of catalytically active foams in trickle regime. To visualize
the preferred liquid paths, sodium fluorescein was added to pure water as tracer. The wetted areas of a liquid downward flow of 20 mL min-1 through a 30 PPI foam packing with a length of 15 cm, were made visible by irradiation of UV light. It can be seen in Fig. 3, that the wetted areas are mainly in the packing edges and the areas in the middle of the foam samples were not wetted. This effect can be explained by the very high void volume in the foam packing, which is above 90 %. The liquid flow stream tends to decrease its cross sectional surface area with increasing velocity according to the continuity equation. The narrow stream of water at the column outlet in Fig. 2, can be explained this way. The wall effects were strongly related to the construction tolerances of the foam samples. It is known that a weak wetting efficiency leads to a poor catalytic performance in trickle bed operation mode.
The effect of distributor was ruled out by utilizing appropriate liquid distributors and also by placing an inert layer of glass pearls on the foam packing with a thickness of 1 and 2 cm to enhance the liquid distribution. Despite a uniform distribution by the distributor or a combination of distributor and inert layer, a poor spreading of liquid in the foam packing was observed. Various pore densities of 20, 30 and 45 PPI were compared in terms of liquid spreading in the packing. In case of 45 PPI, the liquid spreading was rather better than 30 and 20 PPI foams due to very high geometric surface area but still not satisfactory. To rule out that the weak liquid spreading do not exclusively takes place for water due to high surface tension, other liquids with various surface tensions and viscosities such as isopropanol and glycerin were investigated. Isopropanol was taken because of lower surface tension and glycerin because of higher viscosity. It was observed that the lower surface tension of isopropanol enhanced the spreading to a very limited extent. But the higher viscosity of glycerin did not influence the liquid spreading. Reducing the reactor or packing diameter suppresses the weak spreading of the liquid due to smaller size a relatively larger area can be wetted. This is a major design limitation that limits the diameter to packing length ratio. A practical solution to overcome the limitations imposed by the weak liquid spreading in the foam packing, was to carry out the multiphase reaction in catalytically active foams by applying a cocurrently upward flow.
It should be noted that the obtained data is gathered by investigation of metallic open cell foams. In case of ceramic foams, the spreading behavior could be different due to irregularities in the ceramic foam structure which are caused by clogging of the ceramic material as depicted in Fig. 4. In fact, the clogged cells enhance the liquid spreading in a ceramic foam packing in downward flow by acting like ceramic pellets. It was also shown by Mohammed et al. [15, 17, 19] the insufficient spreading of the liquid in co-current downward flow through cylindrical ceramic foam packings.
1.4 Residence time distribution (RTD) measurements
theoretical background The simple definition of the residence time (Eq. 1) as the ratio of reactor volume to the volumetric flow rate is a simplified definition that describes the average residence time in a reactor regardless of its design specifications. Eq. 1
But it should be noted that the Eq. 1 does not represent the flow of all liquid elements through a reactor, which is in fact strongly dependent upon the reactor type, design and flow characteristics. It is therefore also relevant for the selectivity of a chemical reaction that takes place in a continuous reactor, how the residence times of fluid elements are distributed. In order to investigate the RTD in a continuous tubular reactor with a foam packing in a co-current upward flow operation mode, the dispersion model is proposed in the literature [20] to evaluate the RTD curves. The RTD measurements were carried out for steady state condition using a tracer impulse. The probability density function of the residence times in the apparatus is expressed by E(t), also called the age distribution in the apparatus (Eq. 2).
Eq. 2
The Eq. 2 gives information about a fluid element marked by tracer, that entered the apparatus at the time of t = 0 and left the apparatus at the time of t+dt. After a certain time (infinite time) all of the marked elements leave the apparatus and therefore the time integral of the age distribution is equal to unity. The unit of E(t) is usually given as s-1.
In order to obtain an impulse at the inlet, the tracer should be introduced as fast as possible to approach a Dirac-impulse. The indicator material that the tracer is consisted of should fulfill various requirements. The tracer should not undergo a chemical reaction with the apparatus content. It should also not remain permanently in the system by a physical or chemical absorption or adsorption. The key parameter to evaluate the RTD in the variance of the E(t) curve because a relationship between the variance and the Bodenstein number (Bo). A dimensionless number that describes
Probability density
Eq. 3
function
Average residence time
Variance of E(t)
Eq. 4
Eq. 5
the ratio of convective flow to axial diffusion flow, whereas characteristic length in the Bo is the bed length. The Bo number gives insight about the axial dispersion viz. backmixing in a chemical reactor (Eq. 8). In order to compare different apparatuses in terms of size and space time, a normalized time was introduced. Eq. 6
The tracer mass balance can be expressed as follows by applying the dispersion model
Eq. 7 Eq. 8 Eq. 9 Eq. 10
By introducing the normalized time , dimensionless length as well as the Bodenstein number the following differential equation for the tracer mass balance in the system can be derived.
Eq. 11
The Bodenstein number is a measure for the backmixing in the reactor according to its definition. An infinite Bodenstein number means no axial dispersion and a Bodenstein number equal to zero means an axially thoroughly mixed system. A Bodenstein number equal to 7 is the threshold value between the backmixing in a stirred tank and in a tubular apparatus. For the values above 7, a plug flow can be approximately assumed [21]. The differential equation above demands boundary conditions to be solved. A closed-closed system boundary was chosen to solve the differential equation. The boundary conditions were set on the basis of the Danckwert’s boundary conditions [22]. Assuming a closed-closed system, boundary conditions for the mass balances in the liquid phase result in Eq. 12 for the inlet: Eq. 12
For the outlet, the equation for system boundaries is: Eq. 13
By applying the mentioned conditions for solution of the differential equation of the tracer concentration distribution, the following equation can be derived to calculate the Bodenstein number from the variance of E(t) as given by Reschetilowski [20]. The definitions of the probability density function E(t), the variance of the probability density function st, average residence time tm and the normalized time θ are given in equation [3-6].
Eq. 12
In addition to the Bodenstein number, Peclét number is also often adopted to describe backmixing. Eq. 13
The Peclét number is also defined as the ratio of the convective to diffusive flows with one difference. The characteristic length in Pe number is the apparatus diameter (Eq. 13).
1.5 Experimental section The measurement of the RTD was carried out in a stainless steel tubular reactor, which was used later to support the reaction studies, with an inner diameter of 17 mm and a length of 50 cm. A structured packing of uncoated 30 PPI aluminum substrates with a diameter of 17 mm, each one with a length of 2 cm were placed in the tubular reactor to obtain a total bed length of 50 cm. The stationary phase was deionized water and the gas phase was consisting of pressurized air. A 1mL (0.0022 mol) injection of pure Ethanol was adopted as tracer for all RTD measurements. The tracer concentration at the reactor outlet was analyzed using a flow through refractometer (Rudolf J357). The refractometer had a measurement frequency of 0.5 Hz. Firstly, a dilution series for various concentrations of pure ethanol subject to their refractive index in deionized water was determined. By applying the resulting calibration line shown in Fig. 5 , the time dependent concentration of the tracer at the reactor outlet can be determined resulting in E(t) curves. Subsequently, 50 measured values for deionized water were taken as baseline for E(t) curves.
After reaching the steady state conditions, while keeping the temperature constant at 25±0.2 °C a tracer impulse of pure ethanol was introduced into the reactor. The measurements were continued until the outlet concentration reached the aforementioned baseline concentration. The RTD experiments were carried out for single and multiphase systems. The examined liquid (pure water) flow rates were ranging between 10-140 mL min-1. The RTD two phase flow was investigated using a distilled water/N2 system for a single liquid flow rate of 50 mL min-1 and gas flow rates ranging from 0.2 to 0.4 L min-1. The solution of the integrals was calculated numerically by applying trapezoidal solution method.
Baseline alignment During the experiments, the baseline with a refractive index of 1.3352 (refractive index of pure water at 25 °C) was not always reached (Fig. 6). The reason for this deviation is mainly the temperature sensitivity of refractive index.
In order to compare different baselines, the baselines were shifted to the baseline corresponding to the pure water at 25 °C. For this purpose, an average of the first 50 measured values for every data series was calculated. After that, the difference between the calculated average and the baseline of 1.33252 was added to all measured values to shift the curve to a common baseline.
Shifting the baselines to a common baseline reduced the deviation of RTD curves to about 1%.
The study of residence time distribution elucidates the influence of the foam packing on the residence time and backmixing in single or two phase flow through foam packing. The experimentally measured axial dispersion coefficients are also crucial for the mathematical modeling of reactors. Firstly, the RTD of a single phase liquid upward flow of pure water through a cylindrical foam packing with a pore density of 30 PPI and a packing length of 50 cm was studied. In Fig. 7, the density probability of a cylindrical 30 PPI packing with a diameter of 17 mm, was compared with a single phase flow through a pipe with the same diameter. The foam packing narrows the probability density of residence times by increasing the velocity according to the continuity equation.
The effect of liquid velocity on the RTD in a 30 PPI packing is also illustrated in Fig. 8 for different superficial velocities. The narrowing effect was strengthened with increasing superficial velocities. The average residence time decreases with increasing liquid velocity. Fig. 9 depicts the average residence times versus the liquid velocity, thereby comparing the residence time in a 30 PPI packing with a non-packed tubular reactor. The Fig. 9 shows that the average residence times of the cylindrical foam packing are slightly higher than the residence times in the unpacked column, whereas the difference between packed and unpacked columns decreases with increasing liquid velocity.
The calculated Bodenstein numbers based on the RTD experiments in the cylindrical foam packing was always higher than the unpacked column (Fig. 10). Thus the axial dispersion of the packed column was less than the unpacked column.
1.6 Residence time distribution in two phase flow The influence of gas velocity on the RTD was studied for a liquid velocity of 3.3 mm s-1 (50 mL min-1). The two phase flow leaving the column was visible through the flexible PFA pipe before entering the online refractometer. The resulting refractive index was often out of the calibration range of the tracer in distilled 1.33252
A value below 1.33252 indicated a two phase flow of gas (N2) and liquid (water+tracer) in the measuring chamber. A maximum measurement frequency of 0.5 Hz could be achieved. This frequency was not enough to detect the passing liquid and gas slugs with a high resolution. The noises in the RTD curve caused by large gas bubbles made the interpretation of the curves difficult. Therefore, the values out of calibration range were filtered, thereby replacing the out of range value with the average of two preceding values.
Fig. 11 presents the influence of the gas velocity on the RTD. It can be seen, that the RTD curves shift from the vicinity
to coordinate origin, thereby the RTD curves for
gas/liquid ratios of 3 and 4 were in a similar position. A shift of RTD curves in the direction of origin can be interpreted as a decrease of Bodenstein number and therefore an increase of the backmixing. Fig. 12 depicts the influence of the gas velocity on the Bodenstein number. Three measurements were performed for each gas velocity. The measurements for the two lower gas velocities scatter but with increasing gas velocity the Bodenstein numbers converge and reach a plateau. 1.7 Multiphase pressure drop
in the preliminary experiments the dynamic pressure drop signals from a 50 cm foam packing of two different pore densities with a diameter of 1.8 cm were investigated. The pressure drop signals were measured by difference pressure transducer (Huba control 692). The two phase pressure drop signals involved the dynamic and frictional pressure drop. The transducer was connected with the packed column using two flexible PFA tubes, which were mounted before
and after the foam packing. In order to increase the precision of the measurement, the appearance of any gas bubbles in the PFA flexible tubes was avoided by using extra valves. In order to attain an optimal wetting efficiency, the flow regimes should change from bubbly flow to slug flow and finally churn flow with increasing gas flow rate respectively. But if the gas flow rate is further increased the liquid holdup decreases drastically and presumably an annular flow regime emerges. The annular flow regime is logically counterproductive due to very poor wetting of the foam structure and wetting the non-active wall.
Four liquid flow rates from 10 mL min-1 to 40 mL min-1 were investigated. The gas flow rates were increased with a step size, at which a change in pressure difference was still measureable, until the pressure difference signals approached zero. The gas flow rates were varied from 50 to 350 mL/min. The preliminary experiments were carried out with pure distilled water and nitrogen. In order to convey the investigated flow rates to the Hydrogen and AMS/Cumene system a few extra gas flow rates were added. Based on the dynamic pressure drop values a parameter window for the continuous tubular reactor experiments were determined in order to avoid annular flow that leads to a very poor wetting efficiency. A comparison between figures 13 and 14 shows clearly that the two phase pressure drop in a 45 PPI foam packing was around 30 % higher than the 30 PPI due to a higher geometrical surface area of the 45 PPI foams. It can be observed in both measurement series that the two phase pressure drop declines with increasing gas flow rate. The decline of pressure drop by increasing the gas flow rate was accompanied by a decreasing liquid holdup. The most probable reason for this effect can be an increase of the entrainment of liquid droplet with an increasing gas flow rate. Several correlations from the literature were tested in order to evaluate the experimental results. The majority of the two phase pressure drop models in the literature are developed for liquid-vapor flow in heat exchangers or similar units. The Lockhart-Martinelli or Chisholm [23] correlations are basically developed for two phase pressure drop through horizontal pipes and therefore, the calculated pressure drop using this model showed a large deviation. The two phase pressure drop model proposed by Saez and Carbonell [7] is a relative permeability model, which is developed for liquid downward flow, which seem to be inappropriate to model the two phase pressure drop of an upward flow through foam packings. Friedel [24]
proposed a two phase pressure drop correlation for vertical upflow. But the application of Friedel correlation did not result in satisfactory results for the values presented in Fig. 13 and Fig. 14.
Conclusions The present study revealed that the liquid downward flow is subject to poor spreading and a preferred wall pathway although a well-designed liquid distributor was applied. Therefore, the upward flow was favored for this study. For the later studies, it will be reasonable to apply technologies such as laser sintering and 3D printing in order fabricate the foam structure together with shell as one piece and control the pore size and strut thickness at the same time. Using this technology, it would be possible to overcome the problem with the gaps to the wall. The study of the residence time distribution for the liquid phase in upward flow direction through a foam packing showed clearly that the local turbulences caused by interconnected network of struts, reduced the backmixing so that the Bo number was smaller than in an unpacked tube. The RTD measurement for the gas liquid upward flow showed that an increase of gas velocity increases the backmixing which is shown by a declining Bo number by increasing gas velocity that reached a plateau after a gas velocity of 1.5 cm s-1. Thus, as a future perspective, studying the bubble size evolution in an upward gas/liquid flow through a foam packing using imaging methods is highly encouraged. the two phase pressure drop for the 45 PPI foam was around 30% more than the 30 PPI due to the higher specific surface area. But in both measurement series the two phase pressure drop was very low and the energy dissipation in the 30 PPI and 45 PPI packings were less than 1 W m-3.
Acknowledgement The Author gratefully acknowledges Prof. Dr.-Ing. habil. Rüdiger Lange for giving me the opportunity to accomplish the present study and the TU Dresden, Institute of chemical engineering for enabling me to perform the experiments for this work. References
1. 2.
3. 4.
5. 6. 7. 8.
9.
10. 11.
12.
13. 14.
15. 16. 17. 18.
19.
20. 21.
Lali, F., Characterization of foam catalysts as packing for tubular reactors. Chemical Engineering and Processing, 2016.105, 1-9. Topin, F., et al., Experimental Analysis of Multiphase Flow in Metallic foam: Flow Laws, Heat Transfer and Convective Boiling. Advanced Engineering Materials, 2006. 8(9): p. 890-899. Stemmet, C.P., et al., Solid Foam Packings for Multiphase Reactors. Chemical Engineering Research and Design, 2006. 84(12): p. 1134-1141. Stemmet, C.P., et al., Influence of liquid viscosity and surface tension on the gas– liquid mass transfer coefficient for solid foam packings in co-current two-phase flow. Chemical Engineering Research and Design, 2008. 86(10): p. 1094-1106. Stemmet, C.P., Gas-liquid Solid Foam Reactors: Hydrodynamics and Mass Transfer. 2008, Technische Universiteit Eindhoven. Edouard, D., et al., Experimental Measurements and Multiphase Flow Models in Solid SiC Foam Beds. AIChE Journal, 2008. 54(11): p. 2823-2832. Sáez, A.E. and R.G. Carbonell, Hydrodynamic Parameters for Gas-Liquid Cocurrent Flow in Packed Beds. AIChE Journal, 1985. 31(1): p. 52-62. Holub, R.A., Dudukovic, M. P. and P.A. Ramachandran, A Phenomenological Model for Pressure Drop, Liquid Holdup and Flow Regime Transition in Gas-Liquid Trickle Flow. Chem. Eng. Sci.,, 1992. 47: p. 2343-2348. Iliuta, I., C. Petre, and F. Larachi, Hydrodynamic continuum model for two-phase flow structured-packing-containing columns. Chemical Engineering Science, 2004. 59(4): p. 879-888. Edouard, D., et al., Pressure drop modeling on SOLID foam: State-of-the art correlation. Chemical Engineering Journal, 2008. 144(2): p. 299-311. Calvo, S., et al., Phase distribution measurements in metallic foam packing using Xray radiography and micro-tomography. Chemical Engineering and Processing, 2009. 48(5): p. 1030-1039. Leveque, J., Rouzineau, D., Prevost, M., Meyer,M., Hydrodynamic and mass transfer efficiency of ceramic foam packing applied to distillation. Chemical Engineering Science, 2009. 64: p. 2607-2616. Wenmakers, P.W.A.M., et al., Liquid-Solid Mass Transfer for Cocurrent Gas-Liquid Upflow Through Solid Foam Packings. Aiche Journal, 2010. 56(11): p. 2923-2933. Wenmakers, P.W.A.M., et al., Enhanced liquid–solid mass transfer by carbon nanofibers on solid foam as catalyst support. Chemical Engineering Science, 2010. 65(1): p. 247-254. Mohammed, I., et al., Hydrodynamic multiplicity in a tubular reactor with solid foam packings. Chemical Engineering Journal, 2013. 231: p. 334-344. Mohammed, I., et al., Liquid-solid mass transfer in a tubular reactor with solid foam packings. Chemical Engineering Science, 2014. 108: p. 223-232. Mohammed, I., et al., Gas-liquid distribution in tubular reactors with solid foam packings. Chemical Engineering and Processing, 2015. 88: p. 10-18. Tourvieille, J.N., R. Philippe, and C. de Bellefon, Milli-channel with metal foams under an applied gas-liquid periodic flow: External mass transfer performance and pressure drop. Chemical Engineering Journal, 2015. 267: p. 332-346. Mohammed, I.H.M., et al., Investigation of hydrodynamics and mass transfer of solid foam packings for gas-liquid applications. Abstracts of Papers of the American Chemical Society, 2014. 248. Reschetilowski, W., Technisch-Chemisches Praktikum. Vol. 1. 2002: WILEY-VCH. Hagen, J., Chemiereaktoren: Auslegung und Simulation. 2004, Weinheim: WileyVCH.
22. 23. 24.
Fogler, H.S., Elements of chemical reaction engineering. 4. ed. ed. 2005, Englewood Cliffs, NJ: Prentice-Hall. Chisholm, D., A theoretical basis for the Lockhart-Martinelli correlation for two phase flow. International Journal of Heat and Mass Transfer, 1967. 10: p. 1767-1778. Friedel, L., Pressure drop during gas vapor liquid flow in pipes. Chemie Ingenieur Technik, 1978. 50(3): p. 167-180.
A
B
C
Fig. 1: CFD simulation of water flow for a liquid distributor with a diameter of A:38 mm and B: 17 mm at T= 293.15 K and P= 101.33 kPa. mL min-1 C: CAD drawing of liquid distributor 38 mm
Fig. 2: narrow water stream at the outlet of 30 PPI foam packing
cross section
Fig. 3: visualization of wetted areas in a 15 cm foam packing with UV-light
Fig. 4: clogged cells in a ceramic foam sample
Fig. 5: calibration line for different concentration of the tracer, Ethanol
Fig. 6: Baselines for the RTD curves for a flow rate of 60 mL min-1
Fig. 7: comparison between a with 30 PPI foams packed column with an unpacked column UL,s=1.175 mm s-1
Fig. 8: Influence of the liquid superficial velocity on the RTD curves
30 PPI non-packed
Fig. 9: Influence of liquid flow rate on the average residence time
30 PPI non-packed
Fig. 10: Bodenstein numbers for 30 PPI foam packing compared with a non-packed tube for various liquid flow rates
Fig. 11: RTD curves for a multiphase flow of water/air with various flow ratios
Fig. 12: Influence of gas velocity on Bodenstein number for 30 PPI and unpacked column
Fig. 13: Average dynamic two phase pressure drop for 45 PPI foam packing
Fig. 14: Average dynamic two phase pressure drop for 30 PPI foam packing
Table 1. Specification of the used foams Material
Pore density
Surface area
Strut thickness
Porosity or void volume
(PPI)
(m²/m³)
(mm)
(%)
Al-Si-Mg
20
855
0.37
93
Al-Si-Mg
30
1617
0.25
94
Al-Si-Mg
45
2330
0.2
92