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Experimental and Modeling Study of Catalytic Hydrogenation of Glucose to Sorbitol in a Continuously Operating Packed Bed Reactor Teuvo Tapani Kilpiö, Atte Aho, Dmitry Yu Murzin, and Tapio Olavi Salmi Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/ie4009265 • Publication Date (Web): 20 May 2013 Downloaded from http://pubs.acs.org on May 20, 2013

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Industrial & Engineering Chemistry Research

1 Abstract Experimental and Modeling Study of Catalytic Hydrogenation of Glucose to Sorbitol in a Continuously Operating Packed Bed Reactor Teuvo Kilpiö*, Atte Aho, Dmitry Murzin, Tapio Salmi Åbo Akademi, Department of Chemical Engineering, Laboratory of Industrial Chemistry and Reaction Engineering, Piispankatu 8, Turku/Åbo, FI-20500, Finland, e-mail: [email protected], Phone: +358 2 215 4983, Fax: +358 2 215 4479 Sorbitol is an alternative sweetener and a platform chemical for a wide variety of compounds. Selective hydrogenation of glucose to sorbitol over a commercial Ru/C catalyst was studied both experimentally and with the aid of detailed mathematical modeling. The experiments were conducted in a laboratory scale trickle bed and in a semi-batch stirred tank reactor. Sorbitol was obtained from the packed bed reactor as the main product typically with roughly 90% selectivity within the studied temperature range (90-130 ºC) while the side product was mannitol. The factors of interest were: the temperature and concentration dependent reaction kinetics, deactivation, internal diffusion and heat conduction within particles, radial heat conduction and mass dispersion in the selected reactor section, liquid hold-up, gas-liquid mass transfer, pressure drop and axial dispersion. A mass balance based axial dispersion model (using temperature dependent kinetics and deactivation modeled using the final activity concept) was capable to explain the observed continuous packed bed behavior rather well. The stirred tank reactor behavior could be described by a mass balance based model. Parameter estimation revealed that the main difference between semi-batch and continuous operations arouse from the more severe deactivation in the packed bed. Simultaneous solution of heat and mass transfer for the top most reactor section and for a catalyst particle revealed that heat transfer limitations were not severe.

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2 1. Introduction One way to produce sorbitol is by catalytic hydrogenation of glucose1. Sorbitol is an alternative sweetener and also a platform chemical for a wide variety of compounds of interest, such as polyols. Heterogeneous catalysis in a continuously operated packed bed reactor could be one of the most desirable ways to produce it. In order to be successful in this, however, a highly active and selective catalyst is needed. Pursuits for progressing in the search for the best catalyst for this purpose have been reported in open literature1-7. Also recently, catalyst development studies conducted using either Ru or Ni based catalysts have been reported4-7.Large scale production of sugar alcohols is carried out mainly with Raney-type Ni catalyst in slurry reactors. Slurry reactors use catalyst effectively, but separation of the catalyst is required and abrasion of the catalyst is a problem. For Ni as the catalyst, new kinds of catalyst supports have been tested for reducing the leaching in laboratory scale slurry reactor4. Also for Ru, new kinds of catalyst supports have been tested in a laboratory scale semi-batch reactors5,6. An experimental study, using self prepared Ruthenium catalyst supported on active charcoal pellets in a continuous reactor has also been reported7. Ruthenium on carbon support has been found to be considerably active and selective and is regarded as one of the most promising catalysts tested so far5-7. Quantitative kinetic modeling studies for this specific reaction system have so far been done utilizing the experimental data from semi-batch experiments.1 This study is based on experimental data obtained from continuous down-flow packed bed and a semi-batch reactor. Studies for finding out the most probable reaction mechanism, and consequently, the most accurate kinetic expression based on experimental batch and semi-batch data have been conducted for some catalysts1-3. The reaction has been observed to follow the first order kinetics in terms of hydrogen at reasonable pressure (20 bar) and temperature (130°C), but in terms of glucose, the reaction order has been observed to change gradually from first to zero order as the concentration is increased well above 0.3 mol/l. The exact reaction mechanism is still an open issue, but kinetic expressions for describing the experimental behavior well over the studied concentration range have been given in literature for some catalysts1. Expressions originating from Langmuir-Hinshelwood Hougen-Watson approach have been able to describe this kind of kinetics for one kind of commercial Ru/C catalyst pretty well. The expressions have a power law in the numerator and the adsorption terms in the denominator, which makes them able to describe the changing reaction order for glucose. The packed bed reactor experiments in this study were carried out using various superficial velocities of liquid at various temperatures. The aim was to find out which combinations of flow velocities and temperatures produced the highest productivity and selectivity. The productivity was enhanced by elevating the temperature. Slow flows provided more residence time which increased the glucose conversion. Although some initial deactivation of the catalyst was observed, the activity later on reached a constant level, which was maintained. The selectivity for sorbitol was around 90 % for all the conducted experiments and the side product was mannitol. The aim of the modeling effort was to find out quantitatively how much each phenomenon influenced the productivity. The factors of interest were: the temperature and concentration dependent reaction kinetics, the roles of liquid hold-up, gas-liquid mass transfer, pressure drop and axial dispersion, radial heat conduction and mass dispersion in the selected reactor section and internal diffusion and heat conduction within particles.


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3 2. Features of modeling work The central features of the modeling work are presented in Table 1. Table 1 Description of packed bed models Experimental Data and Models for Glucose H ydrogenation Data • Temperatures (T= 90-130ºC) • Commercial Ru/C catalyst (0.5 g, 0.7% Ru) • Liquid velocities (Vl= 1.5-4 ml/min) • Particles 0.125-0.25 mm 0.33-0.5 mm • Reactor set-up: (d = 1.15 cm, l= 7 cm) • Catalyst diluted by fine sand

Models for the glucose hydrogenation studies 1. Reactor model • Mass balance based (Temperature dependent kinetics)

2. Particle model 3. Reactor section model • Mass and heat balance based • Based on radial heat and mass balances

Model used for: • Evaluating T and C profiles within particles • Evaluating effectiveness

• Sensitivity study • Parameter estimation

• Studing radial T and C profiles at entrance section

Phenomena included in the model: • Kinetics (T dependent) • Deactivation • Mass transfer • Axial dispersion • Hold-up • Pressure drop

• Kinetics (T dependent) • Internal diffusion • Heat conduction • Spherical geometry

• Radial heat conduction • Radial dispersion • Kinetics (T dependent) • Cylindrical geometry

3. Experimental data One idea was to reveal how the reaction and deactivation kinetics of semi-batch and continuous experiments deviated from each other. Therefore, both semi-batch and continuous experiments were conducted. Semi-batch experiments were carried out in a reactor of 120 ml. The used catalyst amount was the smaller, the higher the temperature was and, therefore, the conversion results are presented as a function of time multiplied by the mass of catalyst, Fig. 1. The catalyst particles that were used in these experiments were small, less than 0.125 mm. The catalyst contained 0.7% ruthenium on carbon support. The selectivity was high, well over 90-% in all the experiments. The experimental data from batch experiments are given in Figures 1 and 2. They present how the glucose conversion and selectivity changed during the experiments.



4

0.10 0.08

T=90°C, mcat=0.50 g

1

T=110°C, mcat=0.30 g

0.9

T=110°C, mcat=0.10 g

0.8

T=120°C, mcat=0.20 g

0.7

T=130°C, mcat=0.05 g 0.06 0.04

Selectivity

Glucose concentration [mol/l]

0.12

0.6

T=90°C, mcat=0.5 g

0.5

T=110°C, mcat=0.3 g

0.4 T=110°C, mcat=0.1 g

0.3

T=120°C, mcat=0.2 g

0.2

0.02

T=130°C, mcat= 0.05 g

0.1

0.00

0

0

50

100

150

0

50

100

Time*mcat [min*g]

150

200

250

Time [min]

Figure 1 Glucose concentration, batch experiments

Figure 2 Sorbitol selectivity, batch experiments

The experimental results from the continuous fixed bed are presented in Figures 3-5. 0.5 g of 0.7 % Ru on carbon support was used in these experiments. The catalyst bed was diluted by quartz sand. Reactor diameter was 1 cm and length 7 cm. Figure 3 shows how the reaction rates which initially were high eventually level down because of the deactivation. Figure 3 presents the glucose conversion as a function of temperature and volumetric liquid feed flow. The low feed flows provide more liquid residence time, which is the main reason for higher yields with lower flows. Increase of temperature speeds up reactions, and therefore, higher yields were obtained at higher temperatures. The sorbitol selectivity is presented in Figure 4. With lower feed flows, somewhat higher selectivities were obtained, although the differences were small. Selectivity exceeded 90% for all the experiments except the one with the highest liquid feed flow rate. Elevated temperatures did not change the selectivity at the studied range of temperatures which implies that the activation energies of sorbitol and mannitol formation are very similar. 90°C, Vl = 1 ml/min

0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0

90°C, Vl = 2 ml/min 90°C, Vl = 4 ml/min 110°C,Vl = 2 ml/min

0

50

100

150

200

Selectivity

Product concentration [mol/l]

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1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

90°C, Vl = 1 ml/min 90°C, Vl = 2 ml/min 90°C, Vl = 4 ml/min 110°C,Vl = 2 ml/min

0

50

Figure 3 Product concentration, continuous experiments

100

150

200

Time [min]

Time [min]

Figure 4 Sorbitol selectivity, continuous experiments


250

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5

Concentration [mol/l]

Figure 5 presents the concentrations of the by-product, mannitol. Using a longer residence time and higher temperature increased the outlet concentration of mannitol, although the trends were not as clearly visible as in case of sorbitol due to the very low concentrations. 0.01 0.009 0.008

90°C, Vl=1 ml/min 90°C Vl=2 ml/min 90°C, Vl=4 ml/min 110°C, Vl=2 ml/min

0.007 0.006 0.005 0.004 0.003 0.002 0.001 0 0

50

100

150

200

Time [min]

Figure 5 Mannitol, continuous experiments The effect of catalyst particle size on the performance was investigated, too. The experiments gave evidence that with the smaller particle sizes (0.125-0.250 mm) a larger glucose conversion was achieved than with the larger ones (0.33-0.50 mm). Figure 6 illustrates the difference. This is an evidence of the internal diffusion resistance. 0.8 Particle size effect T=90°C, p=20 bar, Vl=1.0 ml/min

0.7 Glucose conversion[mol/l]

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0.6 0.5 0.4 0.3 0.2

Particle size 0.35-0.50 mm

0.1

Particle size 0.125-0.25 mm

0 0

50

100 150 Time [min]

200

Figure 6 Glucose conversion for different catalyst particle sizes



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6 4 Presentation of equations 4.1 Reaction kinetics Concentration and temperature dependent reaction rates were used for modeling. The mathematical form of the reaction rate expression originated from the literature1. For ruthenium catalyst on carbon support, the equations were rare. The forms of kinetic expressions of hydrogenation of other sugars of similar nature might also have been applied. The kinetic equations found for Ru/C were from the experiments carried out in a semi-batch mode under powerful agitation and utilizing small catalyst particles, to eliminate all mass transfer restrictions1. These experiments have been carried out using one type of commercial Ru/C catalyst. In the continuous and semi-batch experiments in our laboratory, sieve fractions of a commercial Ru/C catalyst were used. The literature experiments were conducted at 100-130 K and 40-75 bar using the feed solution concentration between 0.56-1.39 mol/l and vigorous stirring. These results could, therefore, be regarded, to represent intrinsic kinetics. A similar temperature range was covered in our continuous experiments, although the hydrogen pressure in our experiments was lower, 20 bar, and concentration of feed solution was 0.1 mol/l. A lower concentration was used mainly because the reactor was a short one. In the literature study, the dependence of the reaction rate on the hydrogen partial pressure was observed to be linear and the dependence on glucose concentration was observed to start deviate from a linear behavior as glucose concentration exceeded 0.3 mol/l. In our continuous experiments, the catalyst particles originated from sieving and particle size ranges were either 0.1-0.25 mm or 0.33-0.5 mm. The properties of our catalysts were different from the ones in the literature and, therefore, although the reaction mechanism might be the same, also the parameters of kinetic expression had to be re-evaluated. For the kinetic expression1, the temperature dependency was given for both the reaction rate constant and the adsorption terms. However, in our case of low concentrations, only the reaction rate constant counted and a single Arrhenius expression was used to express this temperature effect. This reduced the number of parameters to be estimated. The expression corresponding to competitive adsorption of H 2 and organic compounds is given in Eq. 1. The original equation used partial pressure for H 2 , which is a proper selection for the case in which mass transfer was not rate limiting at all. In our case, the extents of internal and gas liquid mass transfer resistances were expected to be somewhat greater due to gravity driven, slow liquid flow. Therefore, it was necessary to use hydrogen concentration instead of partial pressure, since saturation was not straight assumed to prevail everywhere and local deviations from it were allowed. r1 =

v1aρ Cat k main exp(− E A1 / Rg (T + 273.15))CGlu , L C H 2 , L (1 + ∑ K i exp(−∆H ads ,i / Rg (T + 273.15)Ci , L ) 2

(1)

i = Glucose, sorbitol, hydrogen and mannitol.

In the long-term experiments performed in this work, the decline of the catalyst activity was the most prominent at the lowest experimental temperatures. It was the most profound during the initial period of the experiments but later on, after the initial loss, the rate of the main reaction became stable. At higher temperatures, the decline was considerably smaller. The final activity concept was applied for modeling the decline in the catalyst activity.


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7 4.2 Mass balances for the reactor model having temperature dependent kinetics The results of the long-term experiments showed time dependent behavior since a gradual catalyst deactivation to a steady state took place. Dynamic mass balances were, therefore, used to describe this system. The mass balances were written for the liquid-phase components (glucose, sorbitol, mannitol and dissolved H 2 ). The liquid-phase mass balances for the quantitatively identified components (glucose, hydrogen, sorbitol and mannitol) are given in expressions8, Eq. 2-5, together with the applied boundary conditions, Eq. 6-7. This conservation law includes the terms counting for accumulation, material transport via convection, axial mixing by dispersion and mass transfer from the gas-phase to the liquid phase according to the film theory (only for H 2 ) and finally a temperature and concentration and activity dependent term for the reaction. Concentrations became dependent on both axial location and time. ∂CGlu , L (l , t ) ∂t ∂C Sor , L (l , t ) ∂t ∂C H 2, L (l , t ) ∂t

= =

∂t

Ci , L = Ci , F

εL 1

εL 1

=

∂C Man, L (l , t )

1

εL

=

,

1

εL

( − wL ( − wL

(− wL (− wL

l=0

∂CGlu , L (l , t ) ∂l ∂C Sor , L (l , t ) ∂l

∂C H 2 , L (l , t ) ∂l

∂ 2Ci , L ∂l 2

+ ε L Da , L

+ ε L Da , L

∂C Man, L (l , t ) ∂l

+ ε L Da , L

∂ 2 CGlu , L (l , t ) ∂l 2

∂ 2 C Sor , L (l , t ) ∂l 2

∂ 2 C H 2 , L (l , t )

+ ε L Da , L

∂l 2

+ ε L r1 (l , t )))

+ k gl a H 2 (C H 2 , L * −C H 2 , L (l , t )) − ε L (r1 (l , t ) + r2 (l , t )))

∂ 2 C Man, L (l , t ) ∂l 2

− ε L (r1 (l , t ) + r2 (l , t )))

+ ε L r2 (l , t )))

= 0, l = L

(2) (3)

(4) (5) (6)-(7)

For gas-phase, the mass balance could have been formulated in an analogous manner, except by taking into account the flow velocity change due to gas consumption and pressure drop. However, in a short reactor used in this work, in the initial checking phase, the consumption of H 2 was observed to be low. When having also almost negligible pressure drop, the superficial gas velocity remained practically constant. 4.3 Liquid hold-up The liquid hold-up (volume fraction of liquid in the reactor) is well known to depend on the fluid dynamics of the system, which is based on the conservation laws of mass, energy and momentum. It depends also on the detailed system geometry. Power law expressions are the engineering way to describe liquid hold-up in simple terms. Each dimensionless number originates either from specified force- or geometric ratios. Thus, these equations do have a theoretical background. The key parameters in the dimensionless numbers representing the various force and geometric ratios are superficial fluid velocities and physical properties of the fluids and the catalyst bed. In the current case, experimental data were generated for various superficial velocities of the liquid and for various temperatures. Physical properties of fluids depend on temperature. The cross effect of temperature on the hold-up can in the simplest way be modeled as an additional temperature term in the hold-up expression, Eq. 8. This is the case, especially, for a rather narrow temperature range in the experiments. The constant, and the



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8 exponents for liquid and gas velocities and temperature were then to be estimated. An order of magnitude estimate for the temperature exponent can be obtained from literature correlations.

ε L = kε wL aε wG bε (T + 273.15)cε

(8)

A specific expression for very low superficial velocities was given in literature9. In our case, the superficial velocities were very low. For such a case, the liquid hold-up has been observed to be a very weak function of the liquid Reynolds number only. In such a case, the external liquid holdup becomes practically constant.

4.4 Gas-liquid mass transfer In a packed bed reactor with a gravity-driven liquid flow, it is more difficult to avoid gas-liquid mass transfer limitation than in a slurry reactor in which a high degree of turbulence can be generated by vigorous stirring. In the current case, in each individual experiment, the temperature was kept constant, while it was changed in between the separate experiments. A power law which expresses the united mass transfer coefficient as a function of fluid velocities was initially selected to be used10. To a limited extent, the physical properties of the solution varied between the experiments due to temperature variations. A simple temperature correction to the power law can be used to take the cross effect of temperature variations into account. An order of magnitude estimate for the exponent of the temperature can be obtained from an existing mass transfer correlations by studying the cross effect that the temperature had due to changing physical properties. This kind of reasoning is acceptable when relatively narrow temperature range is considered. In literature, k gl a is treated either as a single variable or separated into two individual components of the mass transfer coefficient and the specific surface area. In this study, the option of using the merged mass transfer coefficient was selected. With both approaches, one would eventually end up expressing the mass transfer coefficient as a function of fluid velocities and temperature. This approach has the advantage of having fewer parameters and simple predictable function behavior. The separate values for the specific surface area and gas-liquid mass transfer coefficient (on a randomly packed bed having particles of various sizes and shapes and liquid flowing as a continuous phase along the free surfaces of particles) are really difficult to evaluate, and it was the main reason for favoring the simpler form of equation. The equation became: k gl a H 2 = k mt w L

a mt

wG

bmt

(T + 273.15) cmt

(9)

4.5 Catalyst deactivation The catalyst deactivation was modeled with simple terms using the final activity concept11 and an assumption that the deactivation is raw material dependent, Eq. 10.


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9 −

da(l , t ) = (a(l , t ) − a f )k dea exp(− E A, dea /( Rg (T + 273.15)))CGlu , L (l , t ) dt

(10)

The equation can be motivated physically by the hypothesis that adsorbed glucose forms stable surface intermediates, which block the active catalyst sites. 4.6 Pressure drop The pressure drop10, according to Eq. 11, with the largest flows was only a small fraction of the operation pressure. 2 dp 2 f f ρG wG = dl dK

(11)

Pressure drop was checked for the reactor using a friction factor from literature10 and it was observed to be only 1.5% of total pressure and it was treated as negligible.

4.7 Temperature The temperature profiles were checked both for catalyst particles and the radial feed entrance section of the reactor using simultaneous solutions of energy and mass balances for the highest temperature, 130°C. Since the temperature rise as a consequence of reaction enthalpy turned out to be only moderate, an isothermal model equipped with temperature dependent kinetics was expected to be sufficient to describe the packed bed reactor behavior.

4.8 Radial temperature and concentration profiles inside the reactor Radial temperature and, consequently, concentration profiles may be generated when using the most typical construction of a continuous reactor, a cooling or heating jacket. Especially this is true when the specific reactions are highly exothermic or endothermic. If the radial temperatures are not constant, the local reaction rates will become different, the more so, the stronger the temperature dependence of the reaction rates are. To reveal how severe temperature and concentration profiles emerge, a simultaneous mass and energy balance solution to the radial direction is required12-13. The governing equations for this task are presented here: Energy balance for a radial section, Eq. 12, is: 1 ∂ 2T (r , t ) 1 ∂T (r , t ) ∂T (r , t ) ∂T (r , t ) (−C p , L ρ L wL ) + rGlu (r , t )∆H r ) + λB ( + = r ∂r C p, B ρ B ∂l ∂t ∂ 2r

(12)

This energy balance includes the accumulation term, the convection term to the axial direction, conduction term to radial direction (radial convection is included by a proper adjustment of the effective conductivity of the reactor bed) and the reaction enthalpy term. The reaction enthalpy can be calculated from the enthalpies of formation. The axial convection term will not dominate



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10 in a case where a heat jacket is used to sustain the constant axial temperature. The net heat flux in such a case takes place towards the radial direction. The system approaches a transient effective radial heat conduction case in the presence of the chemical reaction. In case of excellent heat transfer to the wall and a symmetric temperature profile in the reactor centre, the boundary conditions become, Eq 13.-14. ∂T (0, t ) (13)-(14) =0. ∂r The effective heat conductivity of the bed in the presence of three phases (gas, liquid, solid) and porous catalyst particles is the most challenging parameter to estimate. The equation proposed for solid liquid case, Eq. 15, expresses the bed conductivity as a function of the fluid conductivity, the solid conductivity and the bed void fraction.

T ( R, t ) = Tw and

λB = λF (λS / λF )(1−ε B )

(15)

In a reported study15, the heat conductivity of a packed bed was investigated as a function of liquid and gas velocities, since the effective thermal conductivity of a packed bed has been observed to depend on both liquid and gas velocities. However, when comparing the flows used in that study to the ones in our current study, it became evident that practically no promotion of effective conductivity was to be expected by flows in our system. The estimates for the effective radial conductivity of our reactor system based on wide application of Eq. 15 can be found in the Supporting Materials. The energy balance is to be solved together with the associated mass balance, Eq. 16. The mass balance of glucose takes the following form: ∂ 2CGlu (r , t ) 1 ∂CGlu (r , t ) ∂CGlu (r , t ) ∂C (r , t ) ∂ 2CGlu (r , t ) ( ) + rGlu (r , t ) D + + = − wL Glu + Da , L r,L r ∂r ∂t ∂l ∂r 2 ∂l 2

(16)

The balance includes the axial convection term, the axial dispersion term, the radial dispersion terms and the reaction term. In case of having a packed bed operating within the trickling flow regime, the liquid flow is not exactly directed straightly downward as a plug flow, since some back-mixing also takes place. This implies that even if the net mass flow to the radial direction were zero, some local radial flow components could be present. This is especially the case, if the particle-to-reactor diameter ratio is not sufficiently small, which favors the development of wall flow. Fortunately, in our case, the catalyst and the sand particles for bed dilution were small enough to avoid extensive wall flow. The radial dispersion can be regarded as a net term consisting of the possible radial convective flow and flow due to molecular diffusion to radial direction. The radial dispersion coefficient should be larger than the molecular diffusion coefficient. The most interesting case is the situation close to the feed entrance, since the reactant concentrations there are as highest and reaction rates are also high. This location was selected to be on the focus of our example case.


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11 4.9 Heat and mass transfer within a particle The main purposes for the internal heat and mass transfer study was to find out whether the assumption of isothermal behavior within the catalyst particles was well justified and to figure out how severe internal concentration profiles can emerge under the most demanding conditions (with the topmost temperature and concentrations of reactants). Since the temperature rise becomes the higher, the lower the thermal conductivity is, conservative low conductivity case was included. In practice this meant, that we had then a safety marginal in our study. Internal heat and mass transfer was evaluated in two ways. The first one was a simplified engineering approach. There the basic assumption was that the temperature gradients are not severe and, consequently, the heat and mass transfer could be treated separately. Then, for the concentration profile within a spherical particle, an analytical calculation equation was readily available and concentration profile could be calculated with the correlations: Ci = Cs

sinh(Φx) , x sinh(Φ )

Φ2 =

ki R 2 De, i

(17)-(18)

The temperature gradient equation generalized by Prater (and used by Weisz and Hicks15) could be applied when concentration profile was known. This equation states that the temperature profile within a particle can be calculated directly from the concentration profile, if the heat of reaction, the effective diffusivity and the thermal conductivity are known, Eq. 19. Equation is simply: ∆H r De,i (19) (Ci ,S − C ( x)) T ( x) − Ts = λp

As the other option, a more rigorous method based on simultaneous numeric solution of energy and mass balances was applied. This method was originally proposed by Hoyos et.al.16. The equations for this step-by-step calculation of the concentration and temperature profiles are given in the Supporting Materials. The simultaneous calculation of steady-state concentration and temperature profiles inside the catalyst particles16 demanded a solution for the mass and the energy balances. This was done separately using an Excel spreadsheet program. Excel solver was used for the computation. Since the reaction rate was both concentration and temperature dependent, temperature gradients within particle change concentration gradients and vice versa. The equations for this modeling approach are given in “Supporting Materials”. Effectiveness factor was calculated from the concentration profiles within the particle, Eq. 20: M

ηe,i =

∑ (ri , x )Vx

x =1

(20)

ri , SV p

where ri , x denote the local rate inside the particle and ri , S is the rate which would be achieved in the absence of diffusion limitation.



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12 4.10 Equations for improving the identification of parameters in the reactor simulations The following modified reaction rate expressions, Eq 21-25, were used in the parameter estimation stage for improving the identification of the rate constant and the activation energy: rGlu = −r1 − r2 rSor = r1 rMan = r2 r1 = k1 exp(−

(21) (22) (23)

Ea1 1 1 ( − ))CGlu , LC H 2 , L ρ cat a Rg (T + 273.15) (Tref + 273.15)

(24)-(25)

E 1 1 − r2 = k 2 exp(− a 2 ( ))CGlu , LC H 2 , L ρ cat a Rg (T + 273.15) (Tref + 273.15)

Same form of the rate expressions were used in the simulation study. A similar expression was applied for the deactivation since it was regarded as a reaction. Temperature dependence was included in both in the reaction and deactivation rate constants as an Arrhenius law. 5. Solution method: The numerical method of lines The partial differential equations for the continuous reactor models were solved simultaneously using finite difference approximations for the axial derivatives17. This implied that instead of a few partial differential equations, a large group of ordinary differential equations for each and every length step was solved. Discretization schemes of various kinds originate from Taylor series approximations of derivatives, where only the first terms are counted for. This inevitably means that truncation errors exist and their significance can be minimized only by increasing the number of length steps. As a reasonable compromise between the accuracy and the computational speed, 50 length steps were used in this study.

6. Results and discussion 6.1 Single parameter simulation study The aim of this simulation study was simply to figure out how strongly the product concentrations depend on the key parameters of the system. Table 2 shows the inputs used for the study. The sensitivity analysis was made for the reaction temperature of 90ºC, because this temperature was studied experimentally in full detail. Table 2. Variable values used for the sensitivity study Generic parameters: Volumetric flow of liquid Volumetric flow of gas Temperature Pressure

1-4 58 90 20


[ml/min] [ml/min] [°C] [bara]

Page 13 of 30

13 Reactor diameter Reactor length External liquid hold-up Reactions specific parameters: Glucose concentration in feed Mass of catalyst Metal content of the catalyst (Ru) Range and set-point for reaction rate constant Range and set-point for activation energy Range and set-point for deactivation rate constant Range and set-point for deactivation energy Range and set-point for Peclet number Range and set-point for final activity Solubility of hydrogen [90°C] Range and set point for gas-liquid mass transfer coefficient

1.25 7 0.3

[cm] [cm] [ ]

0.1 0.5 0.7 0.1-0.5, 0.3 10-60, 40 0.3-1, 1 10-60, 40 0.3-10, 10 0.1-0.9, 0.2 0.0141 0.01-1, off

[mol/l] [g] [%] [ 1/(min(mol/l)*(g/l))] [kJ/mol] [1/(min(mol/l))] [kJ/mol] [ ] [ ] [mol/l] [1/s]

Figure 7 shows how changes in the reaction rate constant reflect on the product concentration. The reaction rate constant affects both how fast the steady-state is reached and at which level the steady-state settles. As complete conversion is approached, the sensitivity of the reaction rate on the value of the constant decreases. Since the liquid hold-up under low interaction regime depends only weakly on liquid Re number, the volumetric liquid flow directly determines the mean residence time. Therefore, the strong effect the liquid feed has on product concentration is clearly visible. The effect of reaction rate constant is most clearly visible in the achieved steadystate concentration. It influences only slightly the speed at which the final steady-state is reached. The mean residence time is short (0.6-2.5 min) compared to the time taken by deactivation down to the steady-state to occur and due to this, the changes during induction period are fast compared to deactivation. 0.1 0.09


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.08

EA1= 40000 EA,dea= 40000 kdea=1

k1=0.5

0.07 0.06 0.05 0.03

k1=0.1

0.02 0.01

af=0.2 Pe=10

k1=0.5

0.04

k1=0.5 k1=0.1

Vl=1 ml/min

0 0

100

Vl=2 ml/min

k1=0.1 Vl=4 ml/min

200

400

300

500

Time [min]

Figure 7 Sensitive analysis: reaction rate constant


600


14


The sensitivity of the product concentration on changes in the activation energy of the main reaction is illustrated in the Figure 8. The effect becomes more pronounced at high temperature because this is an exponent in the Arrhenius equation describing the temperature dependency. Here for a constant temperature 90 °C, the effects were similar using various feed flow rates for the glucose solution. 0.1 E =60000 a,1 k1 = 0.3 0.09 EA,dea = 40000 0.08 kdea = 1 Ea,1=60000 af = 0.2 0.07 Pe=10 0.06 0.05 Ea,1=60000 0.04 E =10000 0.03 a,1 Ea,1=10000 0.02 Ea,1=10000 0.01 Vl=1ml/min Vl=2 ml/min Vl=4 ml/min 0 0 100 200 300 400 500 600 Time [min]

Figure 8 Sensitivity analysis for the effect of the activation energy. The sensitivity of the product concentration on the final activity, a f , is presented in Figure 9. A broad range was used for this parameter. Final activity is one of those parameters that directly influence the final steady-state concentration.


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Page 14 of 30

0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0

0

af = 0.9 af = 0.9

k1 = 0.3 EA,1 = 40000 EA,dea = 40000 Pe=10 kdea = 1 af = 0.9

af = 0.1 Vl= 1 ml/min

100



200 300 400 Time [min]

500

600

Figure 9 Sensitivity analysis for the effect of the final activity. The effect of Pe number on the product concentration is shown in Figure 10. The range of the Pe number was selected in such a way that it is between completely back-mixed reactor and ideal


Page 15 of 30

15


plug flow reactor. The idea of this analysis was to obtain the value for the Pe number from the separate experiments, since the value of Pe influences the product concentration in a similar way as most of the other system parameters, making its’ identification thereby difficult when all the other phenomena are present. For our system, the expected Pe number was around 10 according to our former experience in modeling tracer tests using similar kinds of packed bed reactors. 0.1 0.09 0.08 0.07 Pe = 10 0.06 0.05 0.04 Pe = 0.3 0.03 0.02 Vl=1 ml/min 0.01 0 0 100

k1=0.3 EA1= 40000 EA,dea= 40000 kdea=1 af=0.2 Pe=10 Pe=0.3 Vl= 2 ml/min 200

300

Pe=10

Pe = 0.3 Vl= 4 ml/min 400 500 600

Time [min]

Figure 10 Sensitivity analysis: Peclet number. The effect of the gas-liquid mass transfer coefficient is illustrated in Figure 11. If this coefficient is small enough it starts to reduce the overall reaction rate. The mass transfer coefficient depends on the flow rate. However, the mean residence time is another clearly flow dependent variable which changes as the liquid feed flow is adjusted and can be the major reason of flow dependent productivity. External liquid hold-up could be treated as constant when having very low superficial velocities7. Generally speaking, the effect of the mass transfer becomes more prominent as the temperature is increased. This arises from the fact that temperature increases exponentially the reaction rate, whereas mass transfer is not so strongly increased by temperature rise. Figure 11 shows only the sensitivity of reactant concentration as a function of feed flow and gas-liquid mass transfer coefficient at 90°C. 0.1

k1 = 0.3 EA,1 = 40000 EA,dea = 40000 Pe=10 kdea = 1 af = 0.2

0.09


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.08 0.07 0.06

kla=1

0.05 0.04 0.03 0.02

kla=1 kla=0.01

0.01 V =1ml/min l 0 0 100

kla=1 kla=0.01 k a=0.01 Vl=2 ml/min Vl=4l ml/min 200 300 400 500

600

Time [min]

Figure 11 Sensitivity analysis: mass transfer coefficient.



16


Figures 12 and 13 reveal the effects of deactivation rate constant and activation energy of the deactivation on glucose consumption. An increase of the deactivation rate constant makes the response faster. Change of the deactivation activation energy at constant temperature has a similar effect. Neither of these parameters alters the final steady-state, which is determined by final activity and kinetic parameters.

0.1 0.09 0.08 kdea=0.3 0.07 0.06 0.05 kdea=0.3 kdea=1 0.04 0.03 kdea=1 0.02 Vl =1 Vl = 2 0.01 ml/min ml/min 0 0 100 200 300

k1=0.3 EA1= 40000 EA,dea=40000

Pe=10 af=0.2

kdea=0.3 kdea=1 Vl = 4 ml/min 400

500

600

Time [min]

Figure 12 Sensitivity analysis: deactivation rate constant.


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Page 16 of 30

0.1 k1 = 0.3 0.09 Ea,dea=60000 EA,1 = 40000 0.08 kdea = 1 af = 0.2 0.07 Pe =10 0.06 Ea,dea=60000 0.05 =10000 E 0.04 a,dea 0.03 Ea,dea=60000 Ea,dea=10000 0.02 Ea,dea=10000 0.01 Vl=1ml/min V =2 ml/min l Vl=4 ml/min 0 0 100 200 300 400 500 600 Time [min]

Figure 13 Sensitivity analysis: deactivation activation energy.

6.2 General conclusions from sensitivity analysis The sensitivity of the product concentration trends on changes in the reaction rate constant, the activation energy, the deactivation rate constant, the deactivation activation energy, the final activity, the gas-liquid mass transfer and the Peclet number were tested. Rather wide ranges for these values were used in numerical simulations. The aim was to give insight in the effects of each parameter. Our reaction experiments were conducted using low concentrations. It was the main reason why the gas-liquid mass transfer did not play a significant role. The gas liquid mass


Page 17 of 30

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17 transfer was set off in the sensitivity studies, except in the particular case where its’ effect was demonstrated, Figure 11. It is well known, how the identification of the reaction rate constant from the activation energy can be improved when data from multiple temperatures are available. Here the sensitivity simulations were made only at one temperature and the effect of these two variables looks, therefore, qualitatively very similar. For the deactivation rate and the activation energy of the deactivation parameter, the situation is the same. These two variables determine how fast the deactivation takes place, while the final activity is the variable which influences mainly the final concentration level. If gas-liquid mass transfer co-efficient is low enough, it starts to determine the reaction rate. The effect of Pe number on the product concentration under studied range could clearly be seen. Probable order of magnitude estimate for the Peclet number is around 10 according to our previous experience. When it is around 10, it is not in a strongly sensitive zone. 6.3 Parameter estimation results Parameters were estimated for both semi-batch and continuous experiments. The parameter estimation was first carried out for the semi-batch data. The activation energy from the semibatch estimation was kept same also for the packed bed. Figures 14-18 reveal the results which were obtained for the semi-batch data. The obtained results were in accordance with the experimentally observed ones. The optimized values of the parameters are given in Table 3. The identification of deactivation kinetics from batch experiments is a tough task, especially when high yield systems are in question, like in this case. The results here were based on the assumption of the known dependences of the reaction rate on glucose and hydrogen concentration. The combination of reaction and deactivation kinetics presented here was able to explain the observed concentration trends with the accuracy illustrated by Figures 14-18 for the semi-batch reactor. In the semi-batch experiments, deactivation was expected to be less severe than it was in the continuous experiments for the following reasons: 1) The catalyst particle sizes there were smaller. 2) The stirring there was vigorous. 3) Catalyst loading ((catalyst mass)/(reactor liquid volume)) there was much smaller. In a well mixed semi-batch reactor, the glucose concentration is location independent. It gradually decreases evenly as time goes by and the reactions progress. In a continuous reactor the situation is different, since the maximum concentration is prevailing near the feed entrance all the time and, consequently, deactivation is local and strongest there. The first order dependence of deactivation on glucose concentration was checked by testing how accurately the calculated concentration trends followed the experimental ones and whether this accuracy could be improved by replacing the first order dependency with a power law dependency on glucose concentration where the exponent was then freely floated. The used Levenberg-Marquardt parameter estimation algorithm ended up giving the exponent the value 1.01 , which in practice meant that with the used data (and covered concentration ranges) the first order dependency gave the best fit. The deactivation in glucose hydrogenation was assumed to originate from the organic reactant since the used solvent was inert (water). The reason why the deactivation order could be evaluated using the semi-batch data was that the dominating main reaction was known in prior to follow the first order dependency on glucose concentration at the studied concentration range.



18

Glucose

Sorbitol Mannitol 0

50

100

150

200

250

0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 0

T = 110°C mcat = 0.1 g Glucose

Sorbitol Mannitol 50

Sorbitol

T = 120°C mcat = 0.2 g

Glucose Mannitol 0

50

100

150

Time [min]

100

150

200

250

Time [min]

Time [min] 0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0


T = 90°C mcat = 0.5 g


0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0



The initial glucose concentration in semi-batch experiments and also the feed concentration of glucose in continuous experiments was in each individual experiment the same. However, as the reaction progressed, a concentration range was covered and the models explain the behavior in that range. Different amounts of catalyst were used in the semi-batch experiments, because the sensitivity on temperature was not exactly known in prior. At higher temperatures generally less catalyst was used.


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Page 18 of 30

200

250

0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0

0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0

T = 110°C mcat = 0.3 g

Sorbitol

Glucose Mannitol 0

50

100

150

200

250

Time [min]

T = 130°C mcat = 0.05 g Glucose

Sorbitol Mannitol 0

50

100

150

200

250

Time [min]

Figures 14-18 Results after parameter estimation for semi-batch experiments (solid lines = model results, dots = experimental results)

The optimum values of the parameters were observed to differ in the semi-batch and packed bed mode of operation, Table 3. The reaction rate constant, activation energy of the main reaction, deactivation rate constant and final activity differed only slightly. The major difference took place in the values of the activation energy of deactivation. The main reason for the deviation is that deactivation in a packed bed is location dependent being strongest at feed entrance where the concentration of reactants are highest. In a vigorously stirred tank, the deactivation is uniform. The results for the packed bed are given in Figure 19 for three cases at 90°C and a single case at 110°C. In parameter estimation for the temperature dependence of the rate constant, the data from the packed bed was limited, but with the aid of semi-batch results serving as support, the difference in the deactivation behavior could be detected. The degree of explanation for the parameter estimation of continuous experiments was 97.9%, whereas for the batch runs it was 82%. For batch runs, the value could have been improved by excluding the data of the experiment at 110°C with 0.3 g catalyst, since this result was not consistent with the other data.


Page 19 of 30

19

0.1 0.09


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.08 0.07 Sorbitol Closed= =Sorbitol Black Glucose White == Glucose Open • o ==90°C, 90°C, 1 ml/min = 90°C, 2 ml/min =90°C, 4 ml/min =110°C, 2 ml/min

0.06 0.05 0.04 0.03 0.02 0.01 0

0

50

100

150

200

250

Time [min] Figure 19 Experimental (marked with symbols) and modeling results (lines) for hydrogenation of glucose over Ru/C at 90°C and 110°C and different flow rates.

Table 3 The values of estimated parameters for a batch and a continuous case

k1 E A1 kdea

Batch 0.24 40.0 1.0

Continuous 0.3 40.0 1.29

Units [1/((mol/l)s)] [kJ/mol] [1/((mol/l)s)]

E A, dea

1.2

41.3

[kJ/mol]

af

0.3

0.20

[-]

T ref

80 80 *based on Pe=10 and CH 2 , L = CH* 2 , L .

[ºC]

The parameter estimation of the continuous experiments set the gas-liquid mass transfer coefficient to the upper limit and, consequently, made the saturation concentration of H 2 to prevail. The main reason for this was regarded to be the low glucose concentration in the feed stream. Saturation can prevail because of the considerably low reaction rate. Hydrogen was abundantly available, since the gas feed was pure hydrogen and it was used in excess. Catalyst loading was much higher in the trickle bed compared to the stirred tank. For the four trickle bed experiments, the model gave an adequate reproduction of primary data. Small deviations in the final steady states were observed. The possible reason for the deviation was that the used simple Arrhenius temperature dependences and constant hold-up assumption



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Page 20 of 30

20 alone could not perfectly describe the complicated system. Liquid hold-up was kept at 30% based on the fact that at very low flows, it depends only very weakly on liquid Reynolds number.

6.4 Simulation of radial dispersion and heat transfer at the reactor entrance The main purpose of the heat and mass transfer study of the radial reactor section, was to verify that the assumption of isothermal reactor behavior was well justified. Simultaneous heat and mass transfer was modeled for the entrance section of the reactor. This first section is the one where the concentration of reactants is as their highest and, therefore, there the highest temperature gradients are expected. The highest feed temperature, 130ºC was used for this simulation. In our packed bed, active metal was present in the catalyst in small proportion (0.7%) as finely distributed nano-particles. The catalyst was diluted to roughly one eight of its volume by fine sand. Liquid volume fraction was around 30%. Gas phase corresponded roughly 10% of reactor volume. Table 4 gives the volume fractions and conductivities of the components. Table 4 Volume fractions, densities and thermal conductivities Component

Quarz sand Water Catalyst

Volume fraction in reactor [%] 53 30 7

Hydrogen

10

Density [kg/m3]

Conductivity [W/(mºC)]

2.6 0.95 2

0.15-1 0.65 Metal: 120 Active carbon: 0.15-0.6 0.2

Sensitivity of temperature profiles to the variations in the effective radial thermal conductivity was studied. The profiles were calculated for three values of conductivity. Only rough value ranges were available for the radial conductivities of dry beds of active carbon and fine sand. In the Supporting Materials, detailed calculations of the wet bed conductivities based on the conductivities and volume fractions of each constituent are given. Figures 20-22 illustrate how large temperature gradients were obtained using various radial wet bed conductivities. With the lowest conductivity values for the sand and active carbon bed, the corresponding effective radial wet bed thermal conductivity became 0.25 W/(mºC), the lowest value used in the sensitivity study. It gave roughly 0.4°C temperature rise in the middle of the reactor while 0.5 W/(mºC) produced only roughly 0.2°C, and 1.0 W/(mºC) only 0.1°C rise, respectively. In practice this meant that isothermal assumption for the case was well justified.


Page 21 of 30

21

130.40

λB=0.25 0.25W/(mK) W/(mK)

130.25

λB= 0.5 W(mK)

130.30

130.20

130.25

Temperature [°C]

Temperature [°C]

130.35

130.20 130.15 130.10 130.05 130.00 0

130.15 130.10 130.05

50

100 Time [s]

150

200

250

130.00

0

50

100 150 Time [s]

200

250

130.14 130.12 Temperature [°C]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


λB= 1.0 W(mK) 1 W/(mK) k=1 W/(mK)

130.10 130.08 130.06 130.04 130.02 130.00 0

50

100 150 Time [s]

200

250

Figures 20-22 The effect of effective radial thermal conductivity on the severity of temperature profiles at feed entrance section Thermal conductivity is known to depend on superficial velocities of gas and liquid14, the flows improving the effective conductivity of the bed. However, the superficial velocities in our case were so low that practically no benefit for conductivity due to flows could be expected. Since the reactor was equipped with a cooling jacked aimed at keeping the axial temperature constant, the axial convective term in the heat balance was set to zero while still having convection term in the mass balance present. The used variable values are collected in Table 5 and the temperature and concentration profiles are given in Figures 23 and 24 for the conservative experimental case of 0.25 W/(m°C) conductivity. The radial temperature profile for the example case is presented in the Figure 23 for the very first axial section, i.e. the feed entrance section. Even there, the radial temperature rise was limited to less than 0.4ºC at the highest operation temperature. As a consequence, the concentration profiles generated by the temperature difference were negligible. The reason for this was the dilute system, the small size of reactor, the fairly conductive liquid and catalyst dilution material, the moderate heat of reaction and the moderate temperature dependency of the reaction rate.



22

Table 5

Inputs for the radial profiles simulation

Generic parameters Feed flow of liquid [ml/min] Temperature [ºC] Pressure [bar] Conductivity of the section [W/(m°C)] Diameter of reactor [m] Length of the first section [m ] Specific heat, section [kJ/(kgK)] Area shape factor [ ] Density of the bed [kg/m3] Peclet number [ ]

1 130 20 0.25 0.01 0.07/50 2 1 800 10

Reaction specific parameters Hydrogen concentration [mol/l] Glucose concentration [mol/l] Heat of reaction [kJ/mol] Reaction rate constant, k 1 Activation energy [kJ/mol] Deactivation rate constant Effective radial diffusivity [m2/s] Deactivation energy [kJ/mol] Final activity, t = ∞ [ ] Gas-liquid mass transfer

Dimensionless radial position

130.4 Temperature [°C]

Centre 130.3

0.25

130.2

0.5

130.1

0.75

Wall 100 150 200 250 Time [min] Figure 23 Radial temperatures after the first step (totally 50 steps) 130

0

Sorbitol concentration [mol/l]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 30

50

0.035 0.03

Centre

0.025

Wall

0.02 0.015 0.01 0.005 00

50

100

150

200

250

Time [min] ACS Paragon Plus Environment

0.015 0.1 83.4 0.3 40.0 1.29 1*10-9 41.0 0.20 saturation

Page 23 of 30

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23

Figure 24 Radial concentrations after the first radial step (totally 50 steps) 6.5. Simulation study of internal diffusion and heat conduction within a catalyst particle A simulation study was conducted for heat conduction and internal mass transfer. The study aimed at figuring out how severe temperature and concentration profiles emerged inside the catalyst particles under the actual conditions. Table 6 Glucose conversion ratio as a function of reaction time (conversion with big particles)/(conversion with small ones)*100 Time [min] 15 30 45 60 75

Conversion ratio 74.1 92.3 96.1 88.6 86.5

Table 6 shows how much smaller the glucose conversion was when the larger particle fraction was used. In the beginning, reaction rate was highest, the difference was greatest and 26% loss in effectiveness was experimentally noticed. 6.6 Simulation of internal diffusion and heat conduction The aim for this study was on one hand to reveal whether the isothermal reactor behavior was really prevailing during our continuous experiments, on the other hand to find out how severe the internal concentration profiles were under the most demanding process conditions. The highest experimental temperature of 130°C was, selected for modeling. Concentrations which were used in this study corresponded to the feed concentration of glucose and the solubility of hydrogen. The parameter values are given below in Table 7. Table 7 Parameters for particle simulations Generic parameters Reactor length, L/ [m] Reactor diameter, d rea /[m] m cat /[g] catalyst in reactor T/[°C] R/[mm] Area shape factor CGlu , L /[mol/l]

0.07 0.0125 0.5 130 0.244 2 0.1

Reaction specific parameters - ∆H r /[kJ/mol] Reaction rate constant E A,1 /[kJ/mol] D Glu,L /[m2/s] D H2,L /[m2/s] D e,H2 /[m2/s] D e,Glu /[m2/s]


83.4 0.23 40.0 4.5•10-9 2.3•10-8 5.75•10-9 1.13•10-9


24 C H2,L /[mol/l]

0.014 0.6

εp

T ref /ºC Tortuosity

80 0.4

The case was modeled both using a simple approach treating the mass and energy balances separately and with a more rigorous simultaneous solution of associated heat and mass balances. The obtained glucose, sorbitol and hydrogen concentration profiles with simple approach were as shown in the Figure 25.

1.6 1.4 Dim.less Concentration

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Page 24 of 30

1.2 1 0.8 0.6 0.4

Glucose Sorbitol Hydrogen

0.2 0 0

0.25

0.5

0.75

1

Dimensionless distance

Figure 25 Glucose concentration within the particle The concentration profile gave the value for the concentration at the particle centre 0.062 mol/l. This was not far from the value 0.065 mol/l obtained by the numeric computation. So both methods gave almost similar concentration profiles and yielded the same effectiveness factor at the most severe process conditions. In the simple approach, after the concentration profiles were calculated, the equation generalized by Prater1 was used to calculate the temperature profiles directly from the concentration profiles. This equation gave the temperature profile as shown in Figure 26 below.


Page 25 of 30

25

130.04 130.03

Temperature [°C]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


130.02 130.01 130.00 129.99 0

0.25 0.5 0.75 Dimensionless distance

1

Figure 26 Temperature profile according to Prater equation, 0.5 mm particle diameter Temperature based on this equation was in the particle centre 130.03 K, while with the numeric method (where both mass and heat balances were solved simultaneously) the obtained result was slightly higher, 130.2 K. Both methods led to the same final conclusions: the internal temperature effect was so small that it may be treated as negligible in the continuous reactor model. Particle diffusion is present to a limited extent at the topmost temperature. The two methods were based on different assumptions and the deviation can at least partly be explained by that. The simulation of internal diffusion and reaction showed that internal diffusion limited the productivity at the most demanding conditions. The effectiveness factor for glucose was 0.71. 7. Conclusions Selective glucose hydrogenation to sorbitol was studied both experimentally and with the aid of detailed mathematical modeling. Sieve fractions of a commercial Ru/C catalyst were used in the experiments that were conducted in a laboratory scale packed bed reactor operating at the trickling flow regime. Sorbitol was obtained as the main product typically with roughly 90% selectivity. The side product was mannitol. The experimental results gave evidence that the rate of glucose hydrogenation depended moderately on temperature. However, the obtained selectivity did not suffer from the temperature increase within the studied range (90-130 ºC). The increase in the liquid feed flow reduced the mean residence time and led the way to lower conversion. A mass balance based axial dispersion model (using temperature dependent kinetics and deactivation modeled using the final activity concept) was capable to explain the observed reaction behavior rather well. Internal diffusion in the catalyst pores was observed to reduce the reaction rate with larger particles. Under the studied conditions (the highest temperature and the highest concentrations), the effectiveness went down to 70 % with biggest particles in the beginning of the reactor. The effectiveness factor was evaluated by solving simultaneously the energy and mass balances for the particle. According to the model, temperature increase within a particle was very limited (below 0.2 ºC) under studied conditions. This was true also for the temperature effect at the feed entrance section of the reactor at 130ºC (rise below 0.4 ºC). Main reason was that the catalyst dilution material and liquid were heat conductive. The operation of the whole reactor could be described rather precisely with a simplified mass balance based model due to low concentrations and minor temperature effects. In the semi-batch experiments,



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Page 26 of 30

26 deactivation was less severe than it was in the continuous experiments for the following reasons: 1) The catalyst particle sizes there were smaller. 2) The stirring there was vigorous. 3) Catalyst loading ((catalyst mass)/(reactor liquid volume)) there was much smaller. In a well mixed semibatch reactor, the glucose concentration was independent of location. In a continuous reactor the situation was different, since the maximum concentration was prevailing near the feed entrance all the time and, consequently, deactivation was local and strongest there. Supporting Information Available: Additional information can be found in the Supporting Materials. This material is available free of charge via the Internet at http://pubs.acs.org.

Symbols A Ap

Parameter, [W/(m3K)] Surface area of the particle, [m2]

a a, a f

Specific surface area, [m2/m3] Activity, final activity, [ ]

aε amt B bε Ap

Parameter in liquid hold-up equation, [ ] Parameter in gas liquid mass transfer expression, [ ] Parameter, [W/(m3K)] Parameter in liquid hold-up expression, [ ] Particle external surface area, [m2]

bmt bε C1 Ci C H 2, L *

Parameter in gas liquid mass transfer expression, [ ] Parameter in liquid hold-up expression, [ ] Parameter, [W/(m3K)] Local concentration of component i in liquid, i = Glu, H 2 , Sor, Man [mol/l] Solubility of component H 2 in liquid, [mol/l]

Ci , L

Concentration of component i in liquid, i = Glu, H 2 , Sor, Man[mol/l]

Ci , F

Concentration of component i in liquid feed, i = Glu, H 2 , Sor, Man [mol/l]

Ci , S

Concentration of component i at surface, i = Glu, H 2 , Sor, Man [mol/l]

cmt CP ,bed

Parameter in gas liquid mass transfer expression, [ ] Specific heat of the bed, [J/(kgK)]

CP, L

Specific heat of liquid, [J/(kgK)]

cε D Da , L

Parameter in liquid hold-up equation [ ] Parameter, [W/(m3K)] Axial dispersion coefficient in liquid, [m2/s]

De,i

Effective diffusivity of the compound i, i = Glu, Sor, H 2 [m2/s]


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27 Di , L

Diffusivity of component i in liquid, [m2/s]

d rea

Diameter of the reactor, [m]

dK E E A , E A,1

Krischer-Kast hydraulic diameter, [m], d p 3 (16ε p3 ) (9π (1 − ε p ) ) Parameter, [W/(m3K)] , E A, dea Activation energy, of the main reaction, of the deactivation, [J/mol]

ff

Two phase friction factor, [ ]

fGlu ,i −1 , fGlu ,i , fGlu ,i +1 Dimensionless concentration for glucose before, at and after step i, [ ] f H 2 ,i −1 f H 2 ,i f H 2,i +1 Dimensionless concentration for hydrogen before, at and after step i, [ ]

HH2 k k1 , k2 kε k dea ki

kl a , k gl aH 2

Henrys law constant for H 2 , [Pa] Reaction rate constant, units to produce rate as [mol/(ls)] Modified reaction rate constant for main and side reaction, units to produce rate as [mol/(ls)] Parameter in liquid hold-up expression, [ ] Deactivation rate constant units to produce activation change as [1/s] Reaction rate constant for component i (including the concentration of other reactant and based on the reaction taking place evenly within the total catalyst particle volume) [1/s] United gas-liquid mass transfer coefficient, for hydrogen, [1/s]

Mass transfer coefficient for component i ,[m/s] kmt K Glu , K H2 , K Sor Adsorption parameters for glucose, hydrogen and sorbitol, [l/mol] Location, [m] l L Reactor length, [m] Mass of catalyst, [kg] mcat M Total number of volume elements, [ ] Pressure, [Pa] p Partial pressure of H 2 , [Pa] pH 2 Pe Peclet number, [ ] Radial location, in particle, in catalyst bed [m] r , rp , r

ri , S

Reaction rate for component i, at surface, i = Glu, Sor, H 2 , Man, [mol/(ls)] Reaction rate of the main and side reaction, [mol/(ls)] Reaction rate of glucose: In mass balances [mol/(ls)] and in energy balance [mol/(m3s)] Reaction rate at the surface of the particle, [mol/(ls)]

ri , x

Reaction rate at location x, [mol/(ls)]

rP R Rg s

Radial location, [m] Particle radius, [m] General gas constant, [J/(molK)] Surface shape factor, [ ]

ri r1 , r2 rGlu



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Page 28 of 30

28 T ,T i-1 , T i ,,T i+1 Temperature, before, at and after step i, [°C] T 1 ,T 2 ,T N Temperature in the first, second and last step, [°C] Temperature of the bed, [°C] Tb Reference temperature, [°C] Tref

TS Tw t v1 Vl V p , Vx

Temperature at the surface, [°C] Temperature of the wall [°C] Time, [s] Stoichiometric coefficient for main reaction, [ ] Volumetric flow rate of liquid, [ml/min] Volume of the particle and volume element x, [m3]

wG

Superficial gas velocity, [m/s] Superficial liquid velocity, [m/s] Location [m] or dimensionless location, [ ] Dimensionless distance from particle centre [ ] Parameter in particle diffusion equation, [ ] Parameter in particle diffusion equation, [ ] Parameter in particle diffusion equation, [l/(mols)] Dimensionless step length, [ ] Adsorption energies for component i , i =Glu, Sor,H 2 and Man, [J/mol]

wL x x X Y Z Glu ∆x ∆H ads ,i − ∆H r

ε

εL εB η e,i λ λp

ρ L ρG , ρ p ρB µl ρcat Φ

Reaction enthalpy, [J/mol] Volume fraction , Met,Cat = metal in catalyst, G, F = gas in fluid, Cat, B= catalyst in bed, B= Fluid in reactor Liquid hold-up, [ ] Porosity of the catalyst bed, [ ] Effectiveness factor for component i, [ ] Effective conductivity, Cat = catalyst, AC = active carbon, Met = metal, F = fluid, L = liquid, G = gas, S = dry bed (metal+active carbon+sand), SB= sand bed, B= wet bed, [W/(m°C)] Conductivity of solid, bed, particles and fluid, [W/(m°C)] Density of liquid, gas and particles, [kg/m3] Density of bed section, [kg/m3] Viscosity of liquid, [kg/(ms)] Catalyst mass concentration, [kg cat /m3] Thiele modulus, [ ]

Literature cited


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29 (1) Crezee, E.; Hoffer, B.; Berger, R.; Makkee, M.; Kapteijn, F.; Moulijn, J.; Three-phase Hydrogenation of D-glucose over a Carbon Supported Ruthenium Catalyst- Mass Transfer and Kinetics, Applied Catalysis A: General 2003, 251, 1. (2) Brahme, P.; Doraiswamy, L. Modeling of a Slurry Reaction. Hydrogenation of Glucose on Raney Nickel, Ind. Eng. Chem. Process Des. Dev., 1976, 15, 130. (3) Kusserow, B.; Schimpf, S.; Claus P. Hydrogenation of Glucose to Sorbitol over Nickel and Ruthenium Catalysts, Adv. Synth. Catal. 2003, 345, 289. (4) Geyer, R.; Kraak, P.; Pachulski, A.; Schödel, R., New Catalysts for the Hydrogenation of Glucose to Sorbitol, Chemie Ingenieur Technik, 2012, 84, 513. (5) Zhang, J.; Lin, L.; Zhang, J.; Shi J., Efficient Conversion of D-Glucose into D-sorbitol over MCM-41 Supported Catalyst Prepared by a Formaldehyde Reduction Process, Carbohydrate Research, 2011, 346,1327. (6) Mishra, D.; Lee, J.; Chang, J.; Hwang, J. Liquid phase hydrogenation of d-glucose to dsorbitol over the catalyst (Ru/NiO–TiO2) of ruthenium on a NiO-modified TiO2 support, Catalysis Today, 2012,185,104. (7) Gallezot, P.; Nicolaus, N.; Fleche G. Fuertes P. Perrard A. Glucose Hydrogenation on Ruthenium Catalysts in a Trickle-Bed Reactor, Journal of Catalysis, 1998,180, 51. (8) Rönnholm M. Thesis: Kinetics and Reactor Design for Oxidation of Ferrous Sulfate with Molecular Oxygen in Sulfuric Acid Milieu Using an Active Carbon Catalyst, Åbo Akademi University, Faculty of Chemical Engineering: Åbo 2001.

(9) Lange, R.; Schubert, M.; Bauer, T. Liquid Holdup in Trickle-Bed Reactors at Very Low Liquid Reynolds Numbers, Ind. Eng. Chem. Res. 2005, 44, 6504. (10) Al-Dahhan, M. ; Larachi, F.; Dudukovic, M. ; Laurent, A. High-Pressure Trickle-Bed Reactors: A Review, Ind. Eng. Chem. Res. 1997, 36, 3292. (11) Salmi, T.; Mikkola, J.,P.; Wärnå J., Chemical Reaction Engineering and Reactor Technology, CRC Press: New York, 2009. (12) Doraiswamy, L.; Sharma, M.; Heterogeneous Reactions: Analysis, Examples, and Reactor Design., John. Wiley and Sons: New York, 1984. (13) Koning, B.; Thesis: Heat and Mass Transport in Tubular Packed Bed Reactors at Reacting and Non-Reacting Conditions, University of Twente: Twente, 2002.



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30 (14) Mousazadeh, F.; van den Akker, H.; Mudde, R. Eulerian Simulation of Heat Transfer in a Trickle Bed Reactor with Constant Wall Temperature, Chemical Engineering Journal, 2012, 207-208, 675. (15) Weisz, P.; Hicks, J. The behaviour of Porous Catalyst Particles in View of Internal Mass and Heat Diffusion Effects, Chemical Engineering Science, 1962, 17, 265. (16) Hoyos, B.; Cadavid, J.; and Rangel, H. Formulation and Numeric Calculation of NonIsothermal Effectiveness Factor for Finite Cylindrical Catalysts with Bi-Dimensional Diffusion, Lat. Am. Appl. Res., 2004, 34, 17. (17) Schiesser, W. The Numerical Method of Lines: Integration of Partial Differential Equations; Academic Press: San Diego, California 1991. (18) Wilke, C.; Chang, P.; Correlation of Diffusion Coefficient in Dilute Solutions, AIChE. J. 1955, 1 , 264. (19) Sifontes V., Thesis Hydrogenation of L-arabinose, D-galactose, D-maltose and L-rhamnose, Process Chemistry Centre, Åbo Akademi University: Åbo 2012. (20) Converti, A.; Zilli, M.; Arni, S.; Di Felice, R.; Del Borghi M. Estimation of Viscosity of Highly Viscous Fermentation Media Containing One or More Solutes, Biochemical Engineering Journal 1999, 4, 81. (21) Ziegler G.; Benado A.; Rizvi S. Determination of Mass Diffusivity of Simple Sugars in Water by the Rotating Disk Method, Journal of Food Science, 1987, 52, 501.


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