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10.2478/v10063-009-0014-2 ANNALES UNIVERSITATIS MARIAE CURIE-SKLODOWSKA LUBLIN POLONIA VOL. LXIII, 21 SECTIO AA 2008 T. Salmi, D. Yu. Murzin, P. Mäki-Arvela, J. Wärnå, K. Eränen, J.-P. Mikkola, A. Denecheau and K. Alho Åbo Akademi, Process Chemistry Centre, FI-20500 Turku/Åbo, Finland A semibatch reactor concept was proposed for the determination of the kinetics in complex catalytic liquid and gas-liquid systems with reactions of highly varying rates. The method is based on continuous removal of liquid phase from the reactor, while the catalyst remains inside the reactor. The concept was demonstrated by catalytic hydrogenation of citral on Ni catalyst. The primary product (citronellal) is formed very rapidly, while the secondary (citronellol) and tertiary (3,7-dimethyloctanol) products appear much more slowly. With the proposed semibatch concept, the formation of the ultimate products was considerably accelerated and all of the rate parameters were successfully estimated by nonlinear regression analysis. The proposed approach can be extended to fixed beds with recycling as demonstrated by computer simulations. 1. INTRODUCTION A majority of kinetic studies is carried out in batch reactors. The system is complicated by the presence of heterogeneous catalysts, since external and internal mass transfer resistances easily corrupt experimentally recorded kinetic data. The general recipe is to suppress the reaction rates, use vigorous stirring to remove external mass transfer resistance and to utilize as small as possible catalyst particles to diminish internal mass transfer resistance. These concepts are reasonable, as such, as complex reaction schemes are treated, where consecutive and parallel reactions appear. Invited article The basic dilemma from a kinetic viewpoint is that the first reactions are very rapid, whilst the consecutive steps are slow. If a small amount of catalyst is placed in the reactor, it guarantees that the system operates in the kinetic regime, but the consecutive steps are far too slow to recognize the real kinetic behaviour. On the other hand, if larger catalyst amounts are placed in the reactor, the first reactions become influenced by external mass transfer limitations. A realistic way to surmount the dilemma is to change the catalyst-to-liquid ratio with time. At the initial stage of the reaction, a small amount of catalyst should be used to push the system towards the kinetic regime, while the relative amount of catalyst should be increased, as the reactions progress. It is more reasonable to start with a small catalyst-to-liquid ratio and increase it with time. In fact, a high liquid-tocatalyst ratio can be used in the beginning of the reaction, but it is decreased by feeding out the reaction liquid as the reaction advances. Thus the catalyst bulk density ( = mcat/VL) increases with time. In the sequel, we shall also envisage, how the idea works for a practical case, namely catalytic three-phase hydrogenation of citral on supported Ni catalyst. The products of citral hydrogenation are used for industrial production of fragrances. 2. THEORY 2.1. Mass balances for a semibatch catalytic three-phase reactor The general mass balance for non-volatile components in a semibatch reactor with complete backmixing but with a decreasing liquid phase volume can be written as follows dni = ri mcat - ni ,out & dt (1) where ni is the amount of substance, ni , out the molar flow, ri the generation rate & and mcat. the mass of catalyst. Diffusion resistance inside the catalyst particle and in the surrounding liquid film are assumed to be negligible, as the catalyst particles are small and the reaction rates are low. Thus all the equations presented in the sequel presume the kinetic regime. The mass balance equation can be written with concentrations, since the amount of substance is ni = ci * VL , where both the concentration ci and the liquid volume, VL will be changed with the reaction time. We get from eq. (1), (ciVL ) = r m dt cat & - ci ,out * Vout (2) Recalling that dVL & & = -Vout (a constant volumetric flow out, Vout from the dt reactor) and ci = ci , out because of perfect mixing simplifies the mass balance is thus simplified to dci = B ri dt (3) where the bulk density (B) of the catalyst is defined by B = mcat & V0 L - Vt (4) The generation rate ri is determined by the stoichiometry, i.e. ri = ij rj , where j denotes the reaction step. 2.2 Isothermal consecutive reactions of first order We consider an isothermal case, where a component A reacts in three irreversible first-order reactions and the initial concentrations of the reaction products R, S and T are assumed to be zero. The reaction temperature is constant. For the reaction sequence A R S T the mass balance equation (3) gives dc A dt dcR dt dcS dt dcT dt = -k1c A B = (k1c A - k 2cR ) B k1 k2 k3 (5) (6) = ( k 2 c R - k3 cS ) B = k 3 cS B For a general case of consecutive reactions, it is practical to solve the problem numerically in the Damköhler space. Balance equation system (6) can be rewritten to dc A - cA = dDa 1 - Da dcR c A - cR 1 = Da dDa 1- dcS c -c = R 1 S 2 Da dDa 1- (7) dcT c = S 2 dDa 1 - Da k1 Bt t k t k and i = i +1 B = i+1 in eq. (7). = k1 B 0 0 Da k1 By using eq. (7), the concentration profiles for consecutive reactions for which k1 > k2 > k3 > k4 with and without pumping were investigated. Some results are depicted in Fig. 1 demonstrating the capability of pumping to enhance the formation of secondary and ternary products (S, T). Without pumping, it would be very difficult to obtain reasonable kinetic data for products S and T from a single experiment. It should be noticed that = 3. EXAMPLE: CITRAL HYDROGENATION In the hydrogenation of citral, both parallel and consecutive reactions proceed simultaneously (Fig. 1) (Mäki-Arvela et al. 2002, Mäki-Arvela et al. 2005). Seven different pressure- and temperature levels were investigated. The following products were detected under the reaction conditions: citronellal, citronellol, geraniol, isopulegol, nerol, 3,7-dimethyloctanal and 3,7-dimetkyloctanol. Some of these products were formed in trace quantities and thus the reaction scheme (Fig. 2) was considerably simplified. Two different reaction schemes were compared in kinetic modelling. In the reaction scheme 1 (Fig. 2) only consecutive reactions for citronellal and citronellol are included. In the modelling A denotes citral, B citronellal, C citronellol and D 3,7-dimethyloctanol. Reaction scheme 2 (Fig. 2) includes consecutive reactions with respect of citronellal and citronellol and one parallel reaction with respect of citronellal. Da In the modelling according to this scheme, A denotes citral, B citronellal, C citronellol and D 3,7-dimethyloctanol; 3,7-dimethyloctanal (E) is hydrogenated further to 3,7-dimethyloctanol (D). In the experimental data, the concentration of 3,7-dimethyloctanal did not increase as a function of time and thus the influence of step 5 in the reaction scheme (Fig. 2) was neglected. a) b) Fig. 1. Kinetics for first-order consecutive reaction system A6 R 6 S 6 T with a) and without b) liquid phase pumping. The kinetic parameters were: k1 =0.5 min-1, k2=0.05 min-1, k3 = 0.005 min-1, with liquid phase pumping 0 = [300,], without pumping 0 = . C E Fig. 2. Simplified reaction schemes for citral hydrogenation. 3.1. Experimental procedures Citral (Alfa Aesar, 97%) hydrogenation kinetics was investigated in a semibatch autoclave (Autoclave Engineers) in 2-pentanol (>98%, Merck 807501) as a solvent in the temperature and pressure ranges of 5090°C and 5 21 bar, respectively. The Ni/Al2O3 (20.2 wt.% Ni, BET surface area (nitrogen physisorption) 101 m2/gcat, metal dispersion (hydrogen chemisorption) 15.7%) catalyst with a mean particle size of 13.5 µm (sieved to fractions less than 100 µm) was reduced prior to the experiment in situ at 270°C at 1 bar for 90 min under flowing hydrogen (99.999%, AGA). Typically, the initial citral concentration and the initial liquid phase volume were 0.1 mol/l and 325 ml, respectively. The catalyst mass was kept constant in all of the experiments (500 mg) and the stirring rate was 1500 rpm (Rushton turbine), which facilitated the hydrogenation under kinetic regime. In the experiments with an increasing catalyst bulk density, about 1 g/min liquid was continuously taken out from the reactor by using a needle valve and weighted in situ. The organic components were analysed with a gas chromatograph (Mäki-Arvela et al. 2002). 3.2. Langmuir-Hinshelwood kinetics Langmuir-Hinshelwood mechanism was applied to citral hydrogenation kinetics. The mechanism is based on the assumption that all of the reactants adsorb on the active sites at a catalyst surface. Reactions occur only between the adsorbed reactants, after which they desorb releasing space to other reactant molecules to adsorb. Surface reactions were presumed to be rate determining in these two models. Molecularly adsorbed hydrogen was assumed to be the catalytically active species. 3.2.1. Kinetic model. This model is based on the assumption that hydrogen molecules are much smaller than the organic ones. The larger organic molecules give empty space between themselves during adsorption, while the smaller hydrogen molecules can be adsorbed on the active sites without any essential competition. The reaction steps in this model are described below. Also here the surface reaction steps were assumed to be rate determining, while the adsorption steps were presumed to be in quasi-equilibria. K H 2 + *1 H 2 *1 Pi + *2 K Ai *2 H 2 *1 + Pi *2 k Pi +1 + *1 + *2 where * and *2 denote vacant sites for hydrogen and organic molecules adsorption, respectively. The model gives to the following rate equations: k1c AcH r1 = D1 D2 r2 = r3 = k 2 cR cH D1 D2 k3 cS c H D1D2 (8) where D1 = 1 + K H cH and D2 = 1 + K i ci and i = A, B, C, D. For the ultimate case that the adsorption effects are negligible, D16 1 and D2 61. 3.2.2. Generation rates. The generation rates for the components become according to the reaction scheme (Fig. 2), rA = -r1 rB = r1 - r2 rC = r2 - r3 rD = r3 (9) 3.3. Parameter estimation The mole fraction of hydrogen ( xH ) in 2-pentanol was obtained froim the measurements of (Mäki-Arvela et al. 2002). The temperature dependence of the rate parameters were calculated from the modified Arrhenius equation, - Ea , j 1 1 - R T T k j = k0, j e (11) Eaj where k0,j is the rate constant at the average temperature ( T ): A = k0 j e R T . The average temperature was 70°C. The rate parameters were determined by non-linear regression analysis by minimizing objective function (Q), a difference between the experimental (ci) and estimated concentrations ( ci ), Q = (ci (t ) - ci (t )) 2 ^ (12) 4. ESTIMATION RESULTS 4.1. Hydrogenation of citral on nickel catalyst in semibatch mode The kinetic model for hydrogenation of citral on the dispersed Ni/Al2O3 catalyst was investigated according to the reaction schemes 1 and 2 (Fig. 2). The estimated results from these two models are equally good and can describe the experimental data well. The degree of explanation exceeded 95 % in most cases. The standard errors of the parameters were reasonable. The most accurate estimations were achieved with reaction scheme 1 (Fig. 2), where all of the kinetic experiments were taken into account. The differences between reaction scheme 1 and 2 were, however, relatively small. The model fits are depicted in Fig. 3 and the values of the kinetic parameters are collected in Table 1. As separate adsorption parameters KA (for citral) and KB (for citronellal) were used, the fit of the model to experimental data did not improve much. These two adsorption parameters were considered for in cases, which contained high amounts of citral (A) and citronellal (B) compared to the other components in the reaction mixture. Additionally, it can be mentioned that the numerical values for KAcA and KBcB were small and had just a minimal effect on the reaction kinetics under the prevailing reaction conditions. Modification of the models according to Langmuir-Hinshelwood kinetics impaired the estimation statistics compared to the models excluding adsorption parameters. The simple model (D1=D2=1) was able to describe the experimental data with a good enough accuracy. a) Temperature = 50 C 0.12 b) Temperature = 70o C 0.12 0.1 concentration (mol/l) 0.08 concentration (mol/l) 0 20 40 60 time (min) 80 100 60 80 time (min) c) Temperature = 90o C 0.12 d) 0.12 0.1 concentration (mol/l) 0.08 Temperature = 60 - 90o C 0.1 concentration (mol/l) 0.08 30 40 time (min) 40 50 time (min) Fig. 3. Kinetics in citral hydrogenation at 10 bar hydrogen at a) 60°C, b) 70°C, c) 90°C and in the temperature programmed reaction between 60°C to 90°C, modeling according to model 1 and reaction scheme 1. Symbols: citral ( ), citronellal (o), citronellol () and 3,7-dimethyloctanol (). Tab. 1. Kinetic models and parameter values for citral hydrogenation with pumping according to the reaction scheme 1. Model Parameter* k01 k02 k03 Ea1 Ea2 Ea3 Ea2 Ea3 KA KB k03 Ea1 Ea2 Ea3 Estimated Parameters 0.454101 0.203100 0.43910-1 0.524105 0.673105 0.352105 0.570105 0.290105 0.161102 0.211102 0.44310-2 0.572105 0.635105 0.540105 Estimated Std Error 0.160100 0.77110-2 0.88110-2 0.226104 0.314104 0.178105 0.297104 0.189105 0.995101 0.119102 0.18110-2 0.243104 0.326104 0.255105 Est. Relative Std Error (%) 3.5 3.8 20.1 4.3 4.7 50.6 5.2 65.2 61.7 56.5 40.9 4.2 5.1 47.2 r1 = k1c AcH r2 = k2 cB cH r3 = k3cC cH R2=95.61%. The rate constants values (k1, k2, k3) are reported at average temperature (70 C) 5. FIXED BED WITH RECYCLE The idea of increasing the catalyst mass-to-liquid volume is by no means limited to slurry reactions, but can be expanded to a fixed bed with recycle and a liquid storage tank. A conceptual flowsheet is sketched in Fig. 4. For the fixed bed, a dynamic balance equation for a volume element V can be written as n i ,in + ri B V = n i ,out + dni dt . . (13) By denoting n i ,out - ni ,in by n i , recalling that the amount of substance in the volume element is ni = ci V and letting V 0 , we obtain the differential equation dc dn L i = B ri - i dt dV (13a) c0i . V c0i ci . . c0i, V'= RV ci . V Fig. 4. Circulating fixed bed system conceptual flowsheet. & Since the volumetric flow rate ( V ) for a such liquid-phase system can be & considered to be virtually constant, the derivative becomes dn dV = Vdci / dV . & & By denoting V / V = we get the hyberbolic PDE dci 1 dc = B ri - i dt L d (14) In case of low conversion per one passing cycle, the space derivative of the concentration is approximatively linear, dci / d (ci - c0,i ) and the PDE is converted to an ODE. Average concentrations can be used in the calculation of the generation rates (ri). In the storage tank is complete backmixing prevails, and no reactions take place there. The balance equation can thus be written as dn0 ,i (15) dt & & After introducing the definitions of volumetric flow rate V ' = RV , and tank ci V = c0 ,i V + c0 ,i V '+ volume VT =V 0,T- V ' t and n0 ,i = c0,iVT we obtain Tab. 2. Simulation of recycled fixed bed reactor for the system A R S T . 0T R Kinetic parameters k1B k2B k3B 0.5 1 min 10 min 0...50 1.0 min-1 0.7 min-1 0.5 min-1 Initial conditions cA(t = 0) =1.0 mol/l, other concentrations zero dc0,i 1 = (ci - c0 ,i ) dt T (16) where T = 0,T - Rt . The model consists of coupled eqs (14) and (16), which were solved numerically for the first-order system A R S T with the sets of parameters listed in Table 2. Some sample calculations are displayed in Fig. 5. As the figure reveals, the concept should work in practice, we get a similar enhancement of the secondary and tertiary reactions as was obtained for the slurry reactor concept. For the fixed bed coupled to the storage tank, there is, however, more space for the adjustment of the experimental conditions, since the tank volume and space time () can be varied within very large intervals. 6. CONCLUSIONS A new reactor concept involving a gradual increase of the catalyst bulk density was proposed. The approach was illustrated by a case sutyd, hydrogenation of citral on supported nickel. The results indicated that the reaction rates are enhanced by increasing the catalyst bulk density, which is achieved by pumping out the liquid phase during the experiments. A kinetic model comprising the increase of the catalyst bulk density was used for the quantitative description of the reactor behaviour. 1 0.9 A 0.8 0.7 0.6 c (mol/l) 0.5 0.4 0.3 0.2 0.1 0 R S T 5 time (s) Fig. 5. Simulation of recycled fixed bed reactor for the system A R S T . The parameters are listed in Table 2. The effect of the catalyst bulk density on the hydrogenation kinetics was demonstrated with the aid of kinetic model. The estimated parameters were used in the demonstration of the system behaviour in the Damköhler space. The semibatch concept proved to be useful in enhancing the efficiency for obtaining kinetic information from semibatch experiments, since the rate parameters of consecutive reaction schemes with successively decreasing parameter values can be obtained from a single experiment. With the conventional technology, this is not possible, but several separate experiments with different catalyst bulk densities, and initial concentrations are necessary. The methodology proposed by us contributes the intensification of kinetic studies of two- and three-phase catalytic systems. It is not limited to agitated slurry reactors only, but can be extended to fixed beds with recycle, as demonstrated by simulations. Acknowledgements This work is part of the activities at the Åbo Akademi Process Chemistry Centre within the Finnish Centre of Excellence Programmes (20002011) financed by the Academy of Finland. 7.
Annales UMCS, Chemia – de Gruyter
Published: Jan 1, 2008
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