Modeling Mass Transfer in a Three-Phase Minireactor Filled with

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Modeling Mass Transfer in a Three-Phase Minireactor Filled with Trilobe Catalytic Extrudates in Series Chrysovalantis C. Templis and Nikos G. Papayannakos* School of Chemical Engineering, National Technical University of Athens, 9, Heroon Polytechniou Street, Gr-15780 Zografos, Athens, Greece ABSTRACT: The internal and external gas−liquid mass transfer limitations in a three-phase spiral string bed minireactor are estimated, using as a model reaction the benzene hydrogenation over a commercial trilobe Ni/γ-Al2O3 catalyst at elevated pressures and temperatures. A detailed two-phase flow model incorporating liquid volatility, intrinsic catalytic reaction rates, gas−liquid mass transfer effects, liquid−solid mass transfer effects, internal mass transfer effects, and wetting of the catalytic particles, was used for the simulation of the spiral string bed reactor performance. The benzene intrinsic reaction kinetics was estimated conducting benzene hydrogenation experiments over crushed catalyst particles. The gas−liquid mass transfer coefficient was estimated from the data of this study, and the liquid−solid mass transfer effects were estimated from data of a previous communication. The proposed correlation for the prediction of gas−liquid mass transfer coefficients can describe the gas−liquid mass transfer limitations in the spiral string bed reactor at various operating conditions.

1. INTRODUCTION In three-phase fixed bed reactors the intraparticle diffusion, the external mass transfer limitations, and fluid dynamic characteristics are of major importance affecting the reactor performance. In scaling down applications, reducing the reactor scale and operating with small scale laboratory reactors, the impact of hydrodynamics on reactor performance increases due to reduction of gas and liquid superficial velocities and reactor diameter-to-particle diameter ratio. Wall effects, channeling, and catalyst bypassing could greatly affect the small-scale reactor performance. A string-bed reactor1 is an alternative configuration that has been proposed for tests with industrial size catalysts in miniscale units as an attempt to avoid the main drawbacks from the use of small scale three-phase fixed bed reactors. The reactor’s internal diameter is controlled by the particle’s diameter so as a “string bed” of catalyst particles to be created. The typical catalyst particles’ diameter varies from 1.1 up to 1.6 mm, and for these dimensions the typical reactor’s internal diameter can vary between 1.8 to 2.4 mm. The string bed reactor can operate either in vertical and horizontal position or in spiral form. For the case of the spiral form typical small furnaces can be used. Miniscale string bed reactors are characterized by certain advantages. The small amounts of the catalyst used result in small experimental units with improved safety and minimization of operating cost and time. The construction is very easy. The loading is repeatable allowing the formation of structured beds. Radial isothermal conditions are achieved because of the small tube diameter and the highest possible ratio of external reactor surface to catalyst mass which results in the avoidance © XXXX American Chemical Society

of hot spots when highly exothermic reactions are performed. Gas and liquid superficial velocities are high, and both gas and liquid are forced to flow over all the catalyst particles, avoiding bypassing, channeling, and poor gas distribution at any flow rate while the operation of the unit is very stable.2−4 However, as in any type of small-scale three-phase reactor, particle partial wetting and inter- and intraparticle mass transfer limitations are unavoidably present and affect the reactor operation, their impact effects must be understood and quantitatively described for an efficient use of the data collected from such systems. Partial wetting of the catalyst particles in three-phase systems has a direct effect on the catalyst effectiveness factor. The concentration of the reactants at the catalyst surface is not uniform due to the different mass transfer rates to the catalyst surface in the wetted and nonwetted parts. The models proposed for determining the effectiveness factor in the case of reactions limited by the gaseous reactant, consider full internal wetting of the catalyst due to capillary forces and negligible mass transfer effects on the nonwetted surface.5−8 The determination of the individual gas−solid, liquid−solid, and gas−liquid mass transfer limitations is very crucial for the system’s characterization, and for the reliable interpretation of the data derived from such systems and the derivation of the pertinent reaction kinetics. Special Issue: Tapio Salmi Festschrift Received: Revised: Accepted: Published: A

May 2, 2017 September 11, 2017 September 12, 2017 September 12, 2017 DOI: 10.1021/acs.iecr.7b01813 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research

communication,13 a more rigorous analysis is necessary with a model taking into account the process characteristics and the catalyst shape. In this way, the liquid−solid and the gas−liquid mass transfer effects as well as the internal diffusional effects would be separately determined allowing the estimation of the importance of each of them in the performance of the stringbed reactor loaded with small amounts of real size extrudates. The main objective of this work is the study and modeling of the inter- and intraparticle mass transfer limitations in a spiral string-bed minireactor loaded with real size trilobe catalytic extrudates, using as model reaction the benzene hydrogenation to cyclohexane over a commercial Ni/γ-Al2O3 catalyst. The liquid solid mass transfer effects studied in nonreacting systems and presented in a recent communication33 are integrated in the three-phase model for the reacting system of this work. The modeling of the three-phase string bed reactors’ performance under reaction conditions taking into account the flow characteristics, particle wetting, and intra- and interparticle mass transfer effects, is important for the reliable interpretation of the experimental data derived from such small-scale systems aiming at kinetic studies and scale up purposes.

In literature, a number of gas−liquid mass transfer investigations have been referred for large-scale packed beds, while little information is published for mini-packed-bed reactors. The most widely used techniques for the investigation of the gas−liquid mass transfer effects include either the physical adsorption/desorption or the chemical absorption of a gas in a liquid phase. The latter includes the transport of a gaseous reagent to the liquid phase and its reaction with a reagent in the liquid phase while the system is operated in the gas−liquid mass transfer controlled regime. In the physical adsorption technique usually O29−13 and CO214−17 are used as the gas phase. Concerning the chemical absorption technique, the absorption of CO2 in amine solutions18−20 and the O2 absorption into sulphite (Na2SO3) solutions19 and into aqueous hydrazine (N2H4)21 were used. Mass transfer effects in three-phase reactors have also been investigated with fast catalytic reactions such as benzene hydrogenation,13,22,23 toluene hydrogenation,24 α-methylstyrene hydrogenation,25−29 cyclohexene hydrogenation,30 as well as 1,5,9-cyclo-dodecatriene, cyclo-dodecane,31 and o-nitroanisole hydrogenation.32 Many of the researchers that conducted experiments with fast catalytic reactions determined overall mass transfer coefficients which include the gas−liquid and liquid−solid mass transfer effects.26,27,29,30 Some researchers attributed the observed limitations only to the gas−liquid mass transfer effects considering or proving small to negligible liquid−solid transfer resistances,22,32 while others calculated individual mass transfer coefficients for gas−liquid and liquid− solid using the experimental data.28,31 Mass transfer effects under reaction conditions in three-phase mini-string-reactors loaded with catalyst extrudates are limited. Liquid−solid mass transfer effects have been recently reported33 while overall mass transfer coefficients have been published in another communication13 using overall reaction rates of the catalyst particles. In a horizontal square-shaped single-pellet string reactor with channel size 4 × 4 mm Hipolito27 conducted α-methylstyrene hydrogenation experiments for the determination of the overall mass transfer effects. Langsch et al.29 estimated the overall mass transfer coefficients conducting α-methylstyrene hydrogenation experiments over spherical Pd/Al2O3 catalyst with 0.8 mm diameter. The experiments were performed in a packed bed minireactor with an internal diameter of 2 mm. The packing was dense but the spherical catalyst particles were not in a string along the axis. Haase et al.28 conducted α-methylstyrene hydrogenation experiments on spherical Pd/Al2O3 catalyst of 0.8 mm diameter, in a rectangular cordierite channel with 1 mm hydraulic diameter for the study of the mass transfer effects. Mass transfer studies in miniscale reactors loaded with packed beds of crushed particles and having tube-to-particle diameter ratios from 5 to 10 have also been reported. Losey et al.30 conducted cyclohexene hydrogenation experiments in a microfabricated packed bed filled with crushed catalyst Pt/γAl2O3. Tadepalli et al.32 conducted o-nitroanisole hydrogenation experiments in a miniscale packed-bed reactor with 0.775 mm internal diameter over Pd/zeolite catalyst particles with a mean size in the range of 75−150 μm. In all the cases of the miniscale reactors with spherical particles, the gas and liquid superficial velocities were above the upper limit of the velocities used in the experimentation with the string bed configuration in this work. Although first indicative values of the overall mass transfer coefficient in a string-bed reactor were presented in a previous

2. EXPERIMENTAL SECTION The experimental investigation of the internal and external mass transfer effects was conducted using as model reaction the benzene hydrogenation over a commercial trilobe Ni/γ-Al2O3 catalyst with a mean trilobe width of 1.57 mm, a mean lobe diameter of 0.84 mm, and a mean particle length of 4−6 mm. For the determination of the benzene hydrogenation intrinsic kinetics, experiments were performed using crushed catalyst particles (0.200 mm < dp 420 NLH2 Lliquid−1) were proven to be marginally affected by the external mass transfer effects and were used for the intrinsic kinetic determination. In all experiments the liquid and gas were introduced cocurrently in upflow mode. The upflow mode was applied because it has been demonstrated that the operation of an upflow string-bed reactor was excellent at hydrotreatment conditions,3 while Bellos et al.1 mention that the direction of the fluid flow has no effect on the string reactor performance at similar conditions. Moreover, the necessary data for the modeling exist in literature in a number of studies mostly in the upflow mode.1,3,4,13,33 The liquid product of the reaction was collected, and benzene conversion to cyclohexane for each experimental run at steady state conditions was determined by gas chromatography. Standard experiments at high G/L flow rate ratios were repeated at regular time intervals to determine the catalyst deactivation for the determination of the activity level (a) for each experimental run and at any time of operation. Before starting the experiments, the catalyst was reduced in situ at 10 bar, with a hydrogen flow rate of 10 NLH2 h−1. The thermoprogram that was followed is presented in Figure 1. Two temperature plateaus at 150 and 200 οC were included.

RB =

kKBC BKH2C H2 (1 + KBC B)(1 + KH2C H2)

(1)

⎛ Ea ⎞ ⎟ k = k 0 exp⎜ − ⎝ R′T ⎠

(2)

⎛ ΔHB ⎞ ⎟ KB = K 0,B exp⎜ ⎝ R′T ⎠

(3)

⎛ ΔHH2 ⎞ ⎟ KH2 = K 0,H2 exp⎜ ⎝ R′T ⎠

(4)

The interparticle mass transfer effects on reactor performance have been investigated by performing experiments at various gas-to-liquid flow rate ratios (G/L), as presented in Figure 2. In

Figure 2. Benzene conversion against the gas-to-liquid flow rate ratio at different temperatures. Benzene hydrogenation kinetic experiments over crushed Ni/γ-Al2O3 catalyst. Liquid mass flow rate, 10.5 gLh−1. Pressure, 31 bar.

this figure it is observed that for gas-to-liquid flow rate ratios greater than 400 NLH2 Lliquid−1 the conversion measured reaches a plateau indicating that at these conditions the interparticle mass transfer effects are negligible. The experimental data of the three groups in Figure 2 correspond to different levels of catalyst activity due to catalyst deactivation during operation. However, the experiments of each group were performed consecutively and the effects of the catalyst activity decline for each group were insignificant. For the treatment of the experimental results and the estimation of the kinetic parameters a plug flow model that incorporates the liquid volatility (modified EOS Soave− Redlich−Kwong44) and the reaction kinetics in the liquid phase was developed. The effect of the axial dispersion was neglected due to the high ratio of the reactor length to catalyst particles size (400).34 The differential mass balance equations derived for benzene (B), hydrogen (H2), and cyclohexane (C) in the liquid phase (L) are given below:

Figure 1. Thermoprogram for catalyst reduction.

3. BENZENE HYDROGENATION INTRINSIC KINETIC MODEL For the determination of the intrinsic kinetics of benzene hydrogenation over the crushed Ni/γ-Al2O3 catalyst, the reaction rate expression proposed by Metaxas and Papayannakos22 was used (eqs 1−4). The reaction was considered to be of first order with respect to benzene and first order with respect to H2, while the reaction rate expression involves benzene and hydrogen inhibition terms.

dFL,H2 dz

dFL,B dz C

=−

=−

mcat 3RB L BED

mcat RB L BED

(5)

(6) DOI: 10.1021/acs.iecr.7b01813 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research dFL,C dz

=

mcat RB L BED

reactors, the catalytic particles touch the lower internal wall of the reactor tube with two lobes, while the liquid phase is continuously flowing through the lower part of the reactor tube and wetting permanently the low part of the catalytic particles. In the whole range of the tested operating conditions the general flow regime does not change. The gas phase flow is not continuous, since small pulses of liquid are periodically created in the upper part of the reactor due to the higher gas phase velocity. As a consequence of the two-phase flow the lower part of the catalytic particle is always wetted by the liquid phase, while the upper part of the particle is surrounded by the flowing gas and periodically covered by the fast passing liquid pulses. The length, the velocity and the frequency of the pulses are depended on the gas and liquid superficial velocity. The periodic operation of the two phase flow in the reactor tube is simulated by a pseudo-steady-state approach in which the two lobes of the catalytic particle touch the lower reactor internal wall, the liquid continuously flows through the lower part of the reactor wetting the lower part of the catalytic particle, while the gas phase flows continuously in the upper part of the reactor. Adopting this assumption the reactor is divided in two regions: the liquid−solid (LS) region and the gas−solid (GS) region as shown in Figure 4. The GS region

(7)

The differential mass balances were solved using the Runge− Kutta method of fourth order. The kinetic parameters were estimated implementing the optimization technique Nelder− Mead Simplex,35 and using as the optimization function the sum of the percent absolute relative differences of the calculated values from the corresponding experimental ones. Because the experimental data had been derived over a long operation time, catalyst deactivation was followed by performing standard experiments and it was taken into account for the treatment and interpretation of the experimental results. In Table 1, the kinetic parameters corresponding to initial activity (a = 1) and estimated from the optimization of the model fitting to the experimental results are presented. Table 1. Kinetic Parameters of Benzene Hydrogenation Intrinsic Kinetics over the Crushed Catalyst Ni/γ-Al2O3 ko Ea K0,B ΔHB K0,H2 ΔHH2

9.4 × 1007 83403.0 3.76 × 10−07 33514.5 2.60 × 10−09 42580.7

molB gcat−1 s−1 J mol−1 m3 mol−1 J mol−1 m3 mol−1 J mol−1

The estimated values for the adsorption enthalpies are close to the values that have been reported in the literature. For the adsorption enthalpies of benzene and hydrogen, values of 5.7− 80 kJ mol−1 and 30−77 kJ mol−1, respectively, have been reported.22,36−40 The fitting of the model to the experimental data is presented in Figure 3. It is shown that most of the calculated values diverge less than ±15% from the experimental values.

Figure 4. Schematic representation of the reactor cross section according to the model’s assumptions.

includes the gas phase and the fraction of the particle surface that is not wetted by the liquid phase. The LS region includes the liquid phase and the fraction of the particle surface that is surrounded by the liquid phase. In the LS region where the liquid wets a big part of the catalyst particle, there is formed a region with stagnant liquid located at the lower part of the reactor between the two particle’s lobes and under the two contacts points of the particle with the reactor wall. Thus, the LS region can be further divided in two regions; the LSW region which involves the moving liquid phase and the particle surface fraction that is free for the liquid−solid mass transfer and the LSNW that includes the stagnant liquid with the particle surface fraction which is not effectively wetted by moving and renewed liquid and therefore not used for liquid−solid mass transfer. The fraction of the particle mass and surface that is surrounded by the liquid phase in the LS region can be geometrically calculated using data of liquid holdup,4,41 and for the conditions tested in this work the liquid holdup is estimated to be in the range 0.21−0.29. The dependence of the surface fraction (w) and the corresponding mass fraction (mfL) of the particle that is covered by the liquid phase in the LS region on

Figure 3. Parity plot of the experimental and the calculated from the kinetic model benzene conversions within the range of the conditions tested. Benzene hydrogenation over the crushed catalyst Ni/γ-Al2O3.

4. EXTERNAL AND INTERNAL MASS TRANSFER EFFECTS 4.1. Model. 4.1.1. Gas−Liquid Flow Model. The coils of the spiral reactor are horizontal with a small inclination (3 deg) and thus the gas and liquid phase flow in a slightly inclined tube filled with solid particles. According to our optical observations during the mock up experiments with transparent spiral D

DOI: 10.1021/acs.iecr.7b01813 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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is rich in H2. For the same reason, the gas side mass transfer resistances in the GS region are negligible. Because of the capillary forces, the pores of the catalyst are filled by liquid6−8,42,43 and thus the liquid at the pore mouths on the particle external surface is in equilibrium with the gas phase, as it is schematically represented in Figure 6. Because of the different mass transfer resistances on the two regions, LS and GS, the concentration of the components on the surface of the catalyst particles is not uniform and thus the effectiveness factor must be calculated separately for the two parts of the catalyst particle. The intrinsic reaction rate is different for the two particle parts, the LS and the GS region, due to the different surface concentration on those parts. In the GS region the intrinsic reaction rate per unit mass of catalyst fraction surrounded by gas (eq 10) is expressed using species concentration calculated C from the gas−liquid equilibrium (CS,i = C*L,i = G,i ).

the liquid hold up is given by eqs 8 and 9 and presented in Figure 5.

w = 0.590hL + 0.531

(8)

mfL = 0.542hL + 0.57

(9)

Hi

R int,GS,i = vi

akKBC*L,B KH2C*L,H2 (1 + KBC*L,B )(1 + KH2C*L,H2 )

(10)

In the LS region, the intrinsic reaction rate per unit mass of catalyst fraction that is surrounded by the liquid phase (eq 11) is expressed using the species concentrations on the wetted by the moving liquid particle surface (LSW region).

Figure 5. Surface fraction of the particle surrounded by liquid and the corresponding mass fraction against liquid hold up.

The fraction of the particle external surface that is surrounded by stagnant liquid corresponds to 32% of the total surface and therefore the particle surface fraction that is effectively wetted by the moving liquid phase is wfL = w − 0.32. 4.1.2. Mathematical Model. A detailed two phase plug flow model has been developed incorporating intrinsic catalytic reaction rates, internal mass transfer effects, external gas−liquid and liquid−solid mass transfer effects, liquid volatility, and wetting of the catalytic particles in order to describe a reactor’s performance. The mass transfer effects were expressed on the basis of the thin-film theory using mass transfer coefficients. Using experimental data of liquid axial dispersion in stringbed spiral reactors,4,41 it was calculated that the axial dispersion affects less than 1% the final conversion at the tested conditions and thus the liquid flow through the string bed is well approximated by plug flow. In the LSNW region the stagnant liquid and particle surface included are not effective for gas−liquid and liquid−solid mass transfer. In the LSW region, where the catalyst particles are surrounded by moving liquid, the reactor performance can be limited by liquid−solid and gas−liquid mass transfer effects (Figure 6). The mass transfer limitations from the gas phase to the gas−liquid interfacial area are negligible since the gas phase

R int,LS,i = vi

akKBCS,BKH2CS,H2 (1 + KBCS,B)(1 + KH2CS,H2)

(11)

For the calculation of the overall observed reaction rate expressed per total catalyst mass, the individual intrinsic reaction rates, the particle mass fractions, and the effectiveness factor values of the individual particle fractions in the two regions GS and LS have to be taken into account. The overall observed reaction rate expressed per total catalyst mass is R tot,i = mfLηLR int,LS,i + (1 − mfL)ηGR int,GS,i

(12)

where ηL denotes the effectiveness factor of particle fraction that is surrounded by liquid in the LS region and ηG denotes the effectiveness factor of the particle fraction covered by gas in the GS region. Since in the conditions tested, H2 is the limiting reactant and at the same time the reactant that controls the reactor performance as it will be discussed below, the calculation of the effectiveness factor is based on H2 diffusion in the catalyst pores. The characteristic length in Thiele modulus of the wetted particle fraction in the LS region is calculated using the effective for liquid−solid mass transfer particle surface i.e the part of the external surface surrounded by moving liquid in LSW region and the mass fraction of the particle that is surrounded by liquid phase, Lc,LS = (mfLVp)/(wfLSp). For the nonwetted surface fraction by the liquid, the corresponding characteristic length was calculated as Lc,GS= ((1 − mfL)Vp)/((1 − w)Sp). The mathematical model includes eight differential equations of mass balances for the four components: H2, benzene, cyclohexane, and n-hexane, for both the liquid and the gas phases. The differential mass balance for the reactants and products in the gas phase (eq 13) involves the gas−liquid mass transfer rate from or to the moving liquid phase in the LS region, and the reaction rate on the particle surface in the GS region. The mass balance for hexane does not involve the reaction rate term.

Figure 6. Resistances for the H2 mass transport in the GS and LSW region. E


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Industrial & Engineering Chemistry Research dFG, i dz

=

mcat (1 − mfL)ηGR int,GS, i L BED ⎞ ⎛ CG, i − k GL,iαGLAR ⎜ − C L, i⎟ ⎠ ⎝ Hi

calculations were based on the equivalent diameter of the cylindrical particle as characteristic length (dp,eq= 1.42 × 10−3 m). (k GL, iαGL)

(13)

DL, i

The vapor−liquid equilibrium constants Hi for the calculation of the driving force for the gas−liquid mass transport of each component were calculated using the modified Soave− Redlich−Kwong equation of state.44 The differential mass balance for the reactants and products in the liquid phase (eq 14) involves the liquid−solid and gas− liquid mass transfer effects in the LS region. The mass balance for the diluent hexane does not involve the reaction rate term. dFL, i dz

=

(17)

The only parameter required to estimate the gas−liquid mass transfer coefficient for all the components is the ratio of the volumetric specific area of the gas−liquid interface to the thickness of the liquid thin film for one component (αGL/lL). The Leffler and Cullinan mixing rule45 for multicomponent nonpolar liquid systems was used for the estimation of the diffusivity of each component in the liquid phase mixture. The binary infinite dilution diffusivities of H2 in nonpolar organic compounds were estimated using the Wilke and Chang method.46 For the calculation of the binary infinite dilution diffusivities of the organic compounds, a modified form of the Tyn and Calus method46 was used. The liquid viscosity of the liquid phase mixture was determined using the mixing rule developed by Kendall and Monroe45 depending only on the pure component viscosities at the given temperature and the mixture composition. 4.1.3. Solution of the Mathematical Model. The system of the differential mass balances for all components in the liquid and the gas phase was solved using the Runge−Kutta method of fourth order. At each discretization node the modified SRK equation of state44 was solved for the calculation of the Henry’s constants and the liquid and gas phase densities. The algebraic equations are solved at each discretization node resulting in the surface concentration of the components on the individual parts of the catalyst particle and the respective effectiveness factor. Catalyst deactivation was taken into account for the treatment of the experimental results by including the catalyst activity factor for each experiment in the respective reaction rates. At the reactor inlet the gas and liquid phases were considered to be at equilibrium, and the initial values for the molar flow rates of the components at the reactor inlet were calculated using the modified SRK equation of state.44 The optimization parameters are the effective diffusivity of H2 in the catalyst, and the three coefficients in the correlation (eq 17) of the gas−liquid mass transfer coefficient. The optimization method Nelder−Mead−Simplex35 was employed for the fittings in this study using as the optimization function the sum of the percent absolute relative differences of the calculated values from the corresponding experimental ones. The calculation of the effective diffusivity of H2 inside the catalyst at each temperature was initially attempted using experimental data at high gas to liquid flow rate ratios. At such conditions the assumption of negligible gas−liquid mass transfer effects is very close to reality. The first estimates of the effective diffusivity which resulted from the best fitting to the experimental data at high G/L ratios were used to derive first estimates for the parameters of the gas−liquid mass transfer correlation. Using the first estimates for the diffusivity and mass transfer correlation, the global optimization was performed and the optimum values for all the parameters were derived. 4.2. Results. The fitting of the model to the experimental data obtained with the trilobe extrudate catalyst is presented in

⎛ CG, i ⎞ mcat − C L, i⎟ mfLηLR int,LS, i + k GL, iαGLAR ⎜ L BED ⎝ Hi ⎠ (14)

In the LS region, the liquid−solid mass transfer flux toward the effectively wetted part of the particles by the moving liquid (LSW region) is equal to the reaction rate in the catalytic particle mass fraction that is totally surrounded by liquid (LS). The system of algebraic eqs (eq 15) is solved for H2 and benzene, the surface concentrations of those components are calculated, and both the liquid−solid mass transfer rate and the surface reaction rate can be determined. RLS, i = mfLηLvi =

akKBCS,BKH2CS,H2 (1 + KBCS,B)(1 + KH2CS,H2)

VR kLS, iαLS(C L, i − CS, i) mcat

⎛α ⎞ d p,eq 2 = ⎜ GL ⎟ d p,eq 2 = c1ReL c2ReG c3Sc L, i c4 ⎝ 1L ⎠i

(15)

33

In a previous publication the liquid−solid mass transfer coefficient per external geometric surface area for the spiral reactor was determined conducting mock up experiments and applying the diffusion controlled dissolution of cylindrical copper particles from acidified dichromate ion aqueous solution within the range of gas and liquid superficial velocities tested in this work. For the demands of this study and for the calculation of the liquid−solid mass transfer coefficients expressed per effective for liquid solid mass transfer surface area, the proposed liquid−solid correlation of Sh with Re was appropriately modified taking into account the particle wetting within the conditions tested in mock up experiments. The particle wetting for the O2 adsorption mock up experiments was also calculated geometrically using liquid hold up data derived from residence time distribution experiments.4 The volumetric liquid−solid mass transfer coefficients were estimated using the modified correlation taking into account the effective particle surface fraction for liquid−solid mass transfer for the calculation of the volumetric interfacial area for liquid−solid mass transfer αLS. According to the thin film theory, the gas−liquid mass transfer coefficient for each component is related to the liquid diffusivity of this component and to the liquid film thickness according to eq 16. α k GL,iαGL = DL,i GL 1L (16) The mass transfer coefficients of each component in dimensionless form were correlated with the Reynolds number of the liquid and gas phase and the Schmidt number of each component in the liquid phase according to eq 17. Re F


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Industrial & Engineering Chemistry Research Figure 7, and from this data it is calculated that the experimental benzene conversion is predicted with an average error of 6%.

Figure 9. Effectiveness factors of the wetted and nonwetted particle fractions within the range of the tested conditions.

Figure 7. Parity plot of experimental and calculated benzene conversion, over trilobe Ni/γ-Al2O3 catalyst.

the greater characteristic length of the wetted particle fraction and second because of the higher surface concentration of the reactants on the nonwetted surface due to the absence of external mass transfer resistances. The effectiveness factor decreases with temperature especially due to the intrinsic rate increase and at high temperature, 110 °C, it lies within the range of 0.12−0.19 for the wetted particle fraction and 0.23−0.35 for the nonwetted part indicating strong diffusional effects. Since the benzene hydrogenation is a strongly exothermic reaction, the effect of the thermal phenomena inside the catalytic particles was estimated. Using the estimated values of the effective diffusivity, the maximum temperature increase inside the catalyst particle was calculated less than 2.3 °C for both the wetted and nonwetted parts of the particles, for the whole range of the experimental conditions of this work, and thus the thermal effects inside the catalyst particle have been neglected. 4.2.2. Gas−Liquid Mass Transfer Coefficient. Within the range of the conditions tested for the catalytic experiments, the physical properties of the liquid phase do not significantly change. For inclusion in the mass transfer correlation of the liquid properties effects, the mock up experimental data of O2 absorption from an aqueous phase in a spiral string bed reactor13 were also used. The O2 absorption experiments were conducted within the gas and liquid superficial velocity range of this study, and the string bed spiral reactor was loaded with cylindrical particles of 1.4 mm in diameter which is equal to the equivalent diameter of the trilobe particles used in this study. The correlation of the ratio of the volumetric specific area of interface for gas−liquid mass transfer to the liquid film thickness obtained from the fitting and optimization is the following:

A second catalyst bed was tested at similar conditions as those of the first bed, and the results are presented in Figure 8.

Figure 8. Parity plot of experimental and calculated from the model benzene conversion, over trilobe Ni/γ-Al2O3 catalyst. The second catalyst bed was tested for model verification.

The purpose of the tests with the second catalyst bed was to check the model predictions and system reproducibility. The comparison between the calculated values by the model and the experimental conversions indicate that the reproducibility of the experimental values is very good and the model predictions are in a very good agreement with the experimental results, giving the same error of prediction achieved with the first catalyst bed. 4.2.1. Intraparticle Mass Transfer Limitations. The effective diffusivity values estimated from the global optimization are in the range (1.4−5.5) × 10−8 m2/s for the experiments carried out in the temperature range 70−110 °C. In Figure 9, the effectiveness factors of the wetted and nonwetted particle fractions in the LS and GS regions, respectively, for the limiting reactant H2 are presented. Within the range of the experimental conditions studied, the effectiveness factor ηG of the nonwetted catalyst particle fraction is about 50−100% higher than the effectiveness factor ηL of the wetted catalyst particle fraction. This is mainly due to

⎛ αGL ⎞ ⎜ ⎟ d p,eq 2 = 1.085ReL 0.7ReG 0.7Sc L,i 0.3 ⎝ 1L ⎠i

(18)

This correlation indicates that the ratio of the gas−liquid volumetric interfacial area to the liquid film thickness for gas− liquid mass transfer αGL/lL, and thereby the volumetric gas− liquid mass transfer coefficient, increases with both the liquid and gas superficial velocity. In Figure 10 the gas−liquid volumetric interfacial area to liquid film thickness ratio αGL/lL calculated by eq 18 is compared with the values calculated from O2 absorption G


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Figure 10. Comparison of the volumetric gas−liquid interfacial area to liquid film thickness ratio αGL/lL predicted by the proposed relation (eq 18) with the values derived from mass transfer coefficients data of oxygen absorption experiments.13

experiments using data presented in a previous publication of Kallinikos and Papayannakos.13 The differences between the predictions and the experimental values in Figure 10 appear generally satisfactory while only for the high liquid velocities and ugs/uls values the difference is close to 50%. This discrepancy can be attributed to the expected higher experimental error at high gas flow rates due to small differences between the inlet and outlet O2 concentration. However, the deviations cannot be considered as significant given that the mean experimental error of the estimated mass transfer coefficient for such stochastic threephase systems is close to 25% and the methods of obtaining the data are different: one includes a chemically reacting system while the other one operates by physical gas absorption. Besides, the high aGL/lL values at high ugs/uls ratios have a minor effect on the reactor performance. 4.2.3. Gas−Liquid versus Liquid−Solid Mass Transfer. As indicated from the mass transfer correlations, the effect of gas and liquid superficial velocity is more pronounced for the volumetric gas−liquid mass transfer coefficient in comparison to the liquid−solid mass transfer coefficient. In Figure 11 the volumetric liquid−solid mass transfer coefficient kLS,H2αLS and the volumetric gas−liquid mass transfer coefficient kGL,H2αGL for H2 derived from the proposed correlations are presented against the gas to liquid superficial velocity ratio. The values were calculated at typical conditions 31 bar, liquid mass flow rate 10 gL h−1 and temperatures 70 and 90 °C. As also shown in Figure 11 the effect of the gas velocity is more pronounced for the gas−liquid mass transfer coefficients kGL,H2αGL. The volumetric liquid−solid mass transfer coefficient does not change significantly with the gas superficial velocity and its small decrease with the gas velocity is due to the reduction of liquid velocity caused by higher evaporation as well as the reduction of the effective wetting leading to a decrease of the interface surface for effective liquid−solid mass transfer. It is easily observed that the volumetric gas−liquid mass transfer coefficients for H2, kGL,H2αGL, are higher than the liquid−solid coefficient kLSH2αLS within the whole range of the conditions tested, and the difference between the gas−liquid and the liquid−solid mass transfer coefficient increases with the ratio of the gas to liquid superficial velocity ratio reaching 1 order of magnitude at high ugs/uls ratios. The increase of the volumetric gas−liquid mass transfer coefficient with the gas superficial velocity can be attributed to the decrease of the

Figure 11. Volumetric liquid−solid and gas−liquid mass transfer coefficients for H2 versus the gas to liquid superficial velocity ratio. Liquid mass flow rate, 10 gL h−1; pressure, 31 bar; temperature, (a) 70 °C, (b) 110 °C. Results from proposed correlations.

liquid film thickness for gas−liquid mass transfer and at the same time the increase of the gas−liquid interface area. Analogous results with the same trend were obtained for the benzene mass transfer coefficients, but due to its bigger size, the corresponding values are 40−50% lower than those of hydrogen. 4.2.4. Mass Transfer Rate Controlling Reactant. The impact of the individual components mass transfer limitations on the reactor performance is examined at three different temperatures and at a typical liquid feed flow rate of 10 gL h−1. Three different possibilities were considered, and the predictions were obtained by appropriately modifying the model. In the first possibility, the estimated external mass transfer limitations were considered only for benzene while the resistances to H2 transport were assumed negligible, in the second the estimated external mass transfer limitations were considered only for H2 while for benzene transport no resistances were taken into account. These two possibilities are compared to the case that the estimated external mass transfer limitations were considered for all the components. In Figure 12 the predicted benzene conversion against the gas-toliquid superficial velocity ratio is presented for the three different cases examined. As shown in Figure 12, the influence of benzene external mass transfer resistance seems to hardly affect the reactor performance even for low ugs/uls. The effect of the gas flow on benzene conversion is minor for the case that external mass transfer limitations were considered negligible for H2. The H


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Figure 12. Study of the mass transfer effects on the reactor performance. Pressure, 31 bar; liquid feed, 4 wt % benzene in n-hexane; liquid mass flow rate,10 gLh−1; temperatures, (a) 70 °C, (b) 90 °C, (c) 110 °C.

assumption of the existence of mass transfer limitations only for H2 results in conversions close to those for the case that mass transfer limitations were considered for all the components. Mass transfer limitations for H2 reduce the reactor efficiency and appear to control the process although the diffusivity of hydrogen in the liquid phase is higher than that of benzene. This is attributed to the low solubility of H2 in the liquid phase which results in a low hydrogen concentration in this phase and also to the reaction stoichiometry demanding 3 mol of H2 for the hydrogenation of 1 mol of benzene. 4.2.5. Reaction Rates on the Wetted and Nonwetted Catalytic Surface. As mentioned above, the catalyst particle wetting is not complete, while the effective wetting is even less than the particle wetting due to the stagnant liquid zone in the lower part of the reactor near the contact points of the particles with the reactor tube. In the stagnant liquid, mass diffusion takes place and the particles’ surface in contact with moving liquid for fast liquid−solid mass transport is reduced. The surface concentration and the intrinsic reaction rate Rint,GS in the nonwetted fraction of the catalyst particle that is surrounded by gas in the GS region are greater than those in the wetted fraction of the catalyst particle in the LS region Rint,LS because of the negligible H2 external mass transfer limitation in the GS region. The overall intrinsic reaction rate is calculated as R int,tot = mfLR int,LS + (1 − mfL)R int,GS

(19)

and is a measure of the conversion rate of the catalyst particle in the absence of diffusional limitations. In Figure 13, the intrinsic reaction rates ratio Rint,GS/Rint,LS and the contribution of the reaction rate Rint,GS in the nonwetted particle fraction to the overall intrinsic reaction rate against temperature are presented for the whole range of ugs/uls ratios tested. The pertinent results for the observed rates are also shown in this figure. These results correspond to the conditions at the inlet of the catalytic bed, at a typical liquid feed flow rate of 10 gL h−1. The ratio Rint,GS/Rint,LS lies within the narrow range 1.2−1.4 and increases slightly with the temperature increase. The contribution of the reaction rate Rint,GS to the overall intrinsic reaction rate for the conditions tested varies from 0.3 up to 0.4. This relatively low contribution in comparison to the ratios Rint,GS/Rint,LS and its small change with the operating conditions is attributed to the high particle wetting which changes very little within the tested conditions. As also shown in Figure 13, the ratio of the observed reaction rates RGS/RLS lies within the range 2−3 and is higher than the respective ratio of intrinsic reaction rates due to the smaller

Figure 13. (a) Ratio of intrinsic Rint,GS/Rint,LS and observed RGS/RLS reaction rates, (b) contribution of the reaction rate Rint,GS and RGS to the overall intrinsic and observed, respectively, reaction rate for the whole range of ugs/uls ratios tested. Liquid flow rate, 10 gLh−1; P = 31 bar; liquid feed, 4 wt % benzene in n-hexane; catalytic bed inlet. Model results.

effectiveness factor of the wetted fraction of the particle. The contribution of the observed reaction rate RGS to the overall observed reaction rate varied from 0.4 up to 0.55 within the entire range of the conditions tested.

5. CONCLUSIONS Intraparticle diffusional limitations and gas−liquid mass transfer limitations in a ministring-bed reactor loaded with trilobe extrudates were studied with a reacting system using as a model reaction the benzene hydrogenation over Ni/γ-Al2O3 catalyst. The extent of the liquid−solid mass transfer resistances was estimated from recently published data33 and was taken into account in the simulation of the system. I


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AR = reactor tube cross section area [m2] Ci = concentration of component i [mol m−3] CG,i = concentration of component i in gas phase [mol m−3] CL,i = concentration of component i in liquid phase [mol m−3] CS,i = concentration of component i on external particle surface [mol m−3] C*L,i = equilibrium concentration of component i in liquid phase [mol m−3] DL,i = diffusivity of the component i in the liquid phase mixture [m2 s−1] dp = particle diameter [m] dp,eq = diameter equivalent to cylindrical particle [m] Ea = activation energy [J mol−1] FL,i = molar flow rate of the component i in the liquid phase [moli s−1] FG,i = molar flow rate of the component i in the gas phase [moli s−1] G/L = gas to liquid flow rate ratio [NLH2 Lliquid−1] Hi = Henry’s constant of component i [-] hL = liquid hold up [mL3 mvoid −3] Ki = adsorption constant of component i [m3 mol−1] k0 = reaction specific constant [molB gcat−1 s−1] K0,i = preexponential factor of the adsorption constant of component i [m3 mol−1] kGL,i αGL = gas−liquid mass transfer coefficient of the component i [mL3 mR−3 s−1] kLS,i αLS = liquid−solid mass transfer coefficient of the component i [mL3 mR−3 s−1] LBED = length of the catalyst bed [m] Lc = characteristic length [m3 m−2] lL = liquid film thickness for the gas−liquid mass transport [m] mcat = catalyst mass [g] mfL = particle mass fraction surrounded by liquid [gwetted‑cat gcat−1] P = pressure [Pa] R′ = universal constant of gases [J mol−1 K−1] Ri = reaction rate of component i [moli gcat−1 s−1] Rint,GS,i = intrinsic reaction rate of component i in the nonwetted particle fraction, [moli gnonwetted‑cat−1 s−1] Rint,LS,i = intrinsic reaction rate of component i in the wetted particle fraction, [moli gwetted‑cat−1 s−1] Rint,tot.i = overall intrinsic reaction rate of component i in the particle [moli gcat−1 s−1] RGS,i = observed reaction rate of component i in the nonwetted particle fraction, [moli gnonwetted‑cat−1 s−1] RLS,i = observed reaction rate of component i in the wetted particle fraction, [moli gwetted‑cat−1 s−1] Rtot.i = overall observed reaction rate of component i in the particle [moli gcat−1 s−1] ReL = Reynolds number of liquid phase ReL=ρlulsdp,eq/μl [-] ReG = Reynolds number of gas phase ReG=ρgugsdp,eq/μg [-] Sp = particle external surface [m2] ScL,i = Schmidt number of component i in the liquid phase, Sc = μl/ρl/DL,i [-] T = temperature [K] ugs = gas superficial velocity [m s−1] uls = liquid superficial velocity [m s−1] Vp = particle volume [m3] VR = catalyst bed volume [m3] w = total particle wetting [mwetted2 mtotal −2] WHSV = weight hourly space velocity [gL gcat−1 h−1]

The operation of the catalytic system was simulated by considering three ways of gas and liquid contacting with the catalyst. One way is the contact of the flowing gas with the upper part of the particles, a second way is the contact of the flowing liquid with another part of the particle while a third way concerns the contact of a stagnant liquid with the lower part of the particles. Experiments with crushed catalyst were conducted for the benzene hydrogenation intrinsic kinetic determination and revelation of the intraparticle mass transfer limitations in the catalytic particles of commercial size. A detailed simulation model incorporating liquid volatility, intrinsic reaction rates, internal and external gas−liquid and liquid−solid mass transfer effects and catalyst wetting was developed combining data from cold flow mock up experiments4,13,33,41 and experiments at reaction conditions. The model predicts satisfactorily the performance of the string bed reactor at conditions of fast hydrogenation reaction. The effectiveness factor of the particle fraction that is covered by gas but not wetted by liquid is about 50−100% higher than the effectiveness factor of the wetted fraction of the catalyst particle. This is attributed to the bigger characteristic length of the wetted catalyst part and to the higher reactant concentrations on the nonwetted surface due to the absence of external mass transfer resistances in the gas phase. A correlation for the prediction of the gas−liquid mass transfer in string-bed three-phase reactors has been obtained by coupling benzene hydrogenation data and oxygen adsorption data. That correlation predicts well the oxygen absorption mass transfer rates. It is revealed that gas−liquid volumetric mass transfer coefficients are higher than the liquid−solid ones indicating that mass transfer through the wetted part of the particle that is covered by the flowing liquid has the highest contribution to the mass transfer resistances. The difference between the gas−liquid and the liquid−solid mass transfer coefficient increases with the ratio of the gas-to-liquid superficial velocity, and the gas−liquid mass transfer coefficient reaches values up to 10 times higher than the liquid−solid ones for the highest gas to liquid superficial velocity ratio (50) tested in this work. The presence of a stagnant region filled with liquid at the lower part of the reactor tube near the contact points of the particles with the reactor wall result in a decreased wetted interfacial area for mass transfer and inadequate liquid mixing. At the tested experimental conditions the low solubility of hydrogen in the organic phase and the stoichiometry of the reaction make hydrogen the limiting reactant that controls the mass transfer rates, while the benzene external mass transfer resistance was calculated to hardly affect the reactor performance.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: (+30) 210 7723239. Fax: +30 210 772 3155. E-mail: [email protected]. ORCID

Nikos G. Papayannakos: 0000-0002-6941-7520 Notes

The authors declare no competing financial interest.

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NOMENCLATURE a = activity of the catalyst [-] J


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wfL = surface particle fraction wetted by moving liquid [mwetted,eff2 mtotal−2] Xcalc = calculated benzene conversion [-] Xexp = experimental benzene conversion [-] z = length ordinate [m] Greek Letters

αGL = volumetric interfacial area for gas liquid mass transfer [minterf,GL2 mR−3] αLS = volumetric interfacial area for liquid solid mass transfer [minterf,LS2 mR−3] ΔHi = adsorption enthalpy of component i [J mol−1] η = effectiveness factor [-] ηG = effectiveness factor of the non wetted particle fraction [-] ηL = effectiveness factor of the wetted particle fraction [-] μg = viscosity of gas phase [Pa s] μl = viscosity of liquid phase [Pa s] νi = Stoichiometric coefficient of component i [-] ρl = density of liquid phase [kg m−3] ρg = density of gas phase [kg m−3] Abbreviations

B = benzene C = cyclohexane Cat = catalyst G = gas GL = gas−liquid GS = gas−solid int = intrinsic interf = interface L = liquid LS = liquid−solid LSW = liquid solid region which include the moving liquid LSNW = liquid solid region which include the stagnant liquid R = reactor S = solid surface

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Modeling Mass Transfer in a Three-Phase Minireactor Filled with

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