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Modelling of Consecutive Reactions with a Semibatch Liquid Phase: Enhanced Kinetic Information by a New Experimental Concept Tapio Salmi,* Pa1 ivi Ma1 ki-Arvela, Johan Wa1 rnå, Kari Era1 nen, Arnaud Denecheau, Kasper Alho, and Dmitry Yu. Murzin A° bo Akademi, Process Chemistry Centre, Laboratory of Industrial Chemistry, FI-20500 Turku/A° bo, Finland
A semibatch reactor concept was proposed for the determination of the kinetics in complex catalytic liquid and gas-liquid systems with reactions that have highly varying rates. The method is based on continuous removal of the liquid phase from the reactor, while the catalyst remains inside the reactor. In this way, the catalyst bulk density (mass of catalyst, relative to the liquid volume) continuously increases, which enhances the secondary and tertiary reactions in the system. It becomes possible to determine all of the kinetic parameters from a single experiment. Mathematical models were presented and then solved analytically (first-order reaction systems) and numerically (general kinetics). The concept works in practice, which was demonstrated by an experimental study: the catalytic hydrogenation of citral on a nickel catalyst. The primary product (citronellal) is formed very rapidly, whereas the secondary (citronellol) and tertiary (3,7-dimethyloctanol) products appear much more slowly. A standard isothermal, constant-volume experiment in a slurry reactor cannot provide data from which all of the rate constants could be determined in a reliable way. With the proposed semibatch concept, the formation of the ultimate products was accelerated considerably, and all of the rate parameters were successfully estimated by nonlinear regression analysis. The proposed approach is not limited to semibatch slurry reactors; however, it can be extended to fixed beds with recycling, as demonstrated by computer simulations. 1. Introduction
Scheme 1. Reaction Scheme for a Molecule with Three Functional Groups
The determination of very precise intrinsic kinetics for complex liquid-phase catalytic systems is a challenge. A majority of kinetic studies are performed in batch reactors. If catalysts are used, they are either dissolved (homogeneous catalysts) or dispersed (heterogeneous catalysts) in the liquid phase. The system is complicated by the presence of heterogeneous catalysts, because external and internal mass-transfer resistances easily corrupt experimentally recorded kinetic data. The general recipe is to suppress the reaction rates, then use vigorous stirring to remove external mass-transfer resistance and utilize catalyst particles that are as small as possible (,0.1 mm) to diminish the effect of internal mass-transfer resistance (diffusion resistance inside the catalyst particles). These concepts are reasonable; as such, as complex reaction schemes are treated. Typical examples are parallel and consecutive hydrogenations, which frequently appear in chemical industry, from bulk chemicals (hydrocarbon refining) to fine chemicals (production of pharmaceuticals and fragrances). A typical reaction scheme for a molecule with three functional groups is displayed as shown in Scheme 1 (i.e., the reactant molecule (A) is, in parallel, forming products, which react consecutively). Furthermore, the reaction intermediates can react with each other, and consecutive-competitive reaction schemes appear. This happens particularly in cases for which several functional groups exist in the reactant molecule. A typical example case is a molecule with carbonyl groups and double bonds, such as citral. The molecular structure of a citral molecule is displayed in Figure 1. The basic dilemma from a kinetic viewpoint is that the first reactions are very rapid, while the consecutive steps are slow. The observed rates of the reactions can be regulated by the
amount of the catalyst; however, a constant amount of catalyst dispersed in the liquid phase is not a sufficient concept. 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 behavior. On the other hand, if larger catalyst amounts are placed in the reactor, the first reactions become influenced by external masstransfer limitations in the gas-liquid-solid catalyst system, and the real kinetic information is lost for these steps. Thus, 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 three-phase system toward the kinetic regime, while the relative amount of catalyst should be increased, as the reactions progress. In practice, it is difficult to increase the catalyst amount during the reaction. Pretreatment and introduction of new solid material become a problem. Consequently, it is more reasonable to start with a small catalyst-to-liquid ratio and increase it with time. In fact, a high liquid-to-catalyst ratio can be used in the
* To whom correspondence should be addressed. Fax: +358-2215479. E-mail address:
[email protected].
Figure 1. Citral molecule with consecutive and parallel reactions of three functional groups.
10.1021/ie061078c CCC: $37.00 © 2007 American Chemical Society Published on Web 01/17/2007
Ind. Eng. Chem. Res., Vol. 46, No. 12, 2007 3913
Figure 2. Citral hydrogenation reaction scheme, showing a combination of parallel-consecutive schemes. The main reaction path is displayed with the colored background.
beginning of the reaction; however, it is decreased by feeding out the reaction liquid as the reaction advances. Thus, the characteristic parameter, the ratio of catalyst mass to liquid volume (the catalyst bulk density, FB ) mcat/VL), increases with time. In this way, the first reactions in a consecutive-competitive reaction sequence are retarded, while the consecutive reactions are enhanced. In this paper, the novel concept is illustrated by showing the balance equations for semibatch reactors and deriving the specific solutions for first-order kinetics. We shall also envisage how the idea works for a practical case, namely, catalytic three-phase hydrogenation of citral on a supported nickel catalyst. The products of citral hydrogenation are used for the industrial production of fragrances. The complete reaction scheme is displayed in Figure 2.
from the reactor) and ci ) ci,out, because of perfect mixing, simplifies the mass balance, which is thus simplified to
dci ) FBri dt where the bulk density (FB) of the catalyst is defined by
FB )
mcat V0L - V˙ t
2.1. Mass Balances for a Semibatch Catalytic Three-Phase Reactor. The general mass balance for nonvolatile components in a semibatch reactor with complete backmixing but with a decreasing liquid-phase volume can be written as follows:
dni ) rimcat - n˘ i,out dt
(ciVL) ) rimcat - ci,outV˙ out d dt
(1)
(2)
Recalling that (dVL/dt) ) -V˙ out (a constant volumetric flow out
mcat V0,L
(5)
and FB can be written as a function of the volumetric flow rate V˙ as follows:
FB )
The symbols are defined in the Notation section at the end of this paper. Diffusion resistance inside the catalyst particle and in the surrounding liquid film are assumed to be negligible, because 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, because the amount of substance is given as ni ) ciVL, where both ci and VL will change with the reaction time. We get, from eq 1,
(4)
The generation rate ri is determined by the stoichiometry, i.e., ri ) ∑νijrj, where j denotes the reaction step. Initially, the catalyst bulk density (F0,B) is
F0,B )
2. Theory
(3)
F0,B 1 - (V/V0.L)t
(6)
When a space time τ0 ) V0,L/V˙ is introduced, the bulk density becomes
FB )
F0,B 1 - (t/τ0)
(7)
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 k1
k2
k3
A 98 R 98 S 98 T the mass balance described by eq 3 gives
(8)
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dcA ) -k1cAFB dt
(9a)
dcR ) (k1cA - k2cR)FB dt
(9b)
dcS ) (k2cR - k3cS)FB dt
(9c)
Thus, the concentrations of A and R can be calculated from the simple expressions
dcT ) k3cSFB dt
(9d)
cA Da R ) 1c0,A R
The first equation can be solved by a separation of variables,
dcA ) -F0,Bk1 c0,A c A
∫
cA
∫0
t
dt 1 - (t/τ0)
(10)
yielding finally
cA ) F0,Bk1τ0 ln[1 - (t/τ0)] ln c0,A
(11)
The ratio between the concentration of A at time t to the initial concentration of A is now obtained:
cA ) [1 - (t/τ0)]k1F0,Bτ0 c0,A
(12)
The balance equation for R becomes
A dimensionless quantity, the Damko¨hler number (Da) is introduced (k1F0,Bt ) Da), in which
t)
Da t Da Da , ) ) k1F0,B τ0 k1F0,Bτ0 R
(
)
(19)
cR 1 Da R Da γR ) 1- 1c0,A γ - 1 R R
(for γ * 1) (20)
[(
) (
)]
where R ) k1F0,Bτ0, Da/R ) t/τ0, and γ ) k2/k1. For the special case of equal rate constants (γ ) 1), it can be shown, with the aid of l’Hoˆpitals’ rule, that eq 20 becomes
cR Da R Da -1 )R1ln 1 c0,A R R
(
) (
)
(for γ ) 1) (21)
For the case where the liquid drainage rate is zero, R f ∞ and eqs 20 and 21 approach the classical solution for consecutive reactions in batch reactors (A f R f S). For a general case of consecutive reactions, it is more practical to solve the problem numerically in the Damko¨hler space. The balance equation system (eqs 9) can be rewritten as
-cA dcA ) dDa 1 - (Da/R)
(22a)
dcR cA - cRβ1 ) dDa 1 - (Da/R)
(22b)
(14)
dcS cRβ1 - cSβ2 ) dDa 1 - (Da/R)
(22c)
This differential equation has an analytical solution, which can be obtained by introducing the substitution cR/c0,A ) y:
dcT cSβ2 ) dDa 1 - (Da/R)
(22d)
dcR F0,B(k1cA - k2cR) ) dt 1 - (t/τ0) i.e.,
(13)
[
]
k2F0,B dcR F0,Bk1c0,A ) c [1 - (t/τ0)]k1F0,Bτ0 dt 1 - (t/τ0) 1 - (t/τ0) R
k2F0,B -1 dy y ) k1F0,B[1 - (t/τ0)]k1F0,Bτ0 dt 1 - (t/τ0)
(15)
If we use the notations k1F0,B ) a1, k2F0,B ) a2, and k1F0,Bτ0 1 ) β, eq 15 becomes
a2y dy ) a1[1 - (t/τ0)]β dt 1 - (t/τ0)
(16)
By denoting 1 - (t/τ0) ) x, it follows that t ) τ0(1 - x). By denoting R1 ) a1τ0 and R2 ) a2τ0, we get
()
dy R2 y ) -R1xβ dx x
(17)
This equation is a differential equation of type y′ + f(x)y ) g(x), which has an analytical solution of y ) e-∫f dx[∫ge∫f dxdx + C]. The integration constant C can be solved by taking into account the initial conditions t ) 0, x ) 1, and y ) 0, giving C ) R1/(β - R2 + 1). Finally, the ratio y ) cR/c0,A is determined to be
[( )
k1 cR t ) 1c0,A k2 - k1 τ0
k1F0,Bτ0
( ) ]
- 1-
t τ0
k2F0,Bτ0
(18)
Note that, in eq 22, Da/R ) k1F0Bt/(k1F0Bτ0) ) t/τ0 and βi ) ki+1F0Bt/Da ) ki+1/k1. Using eq 22, the concentration profiles for consecutive reactions for which k1 > k2 > k3 > k4, with and without drainage, were investigated. Some results are depicted in Figure 3, which demonstrates the capability of liquid drainage to enhance the formation of secondary and ternary products (S and T). Without liquid drainage, it would be very difficult to obtain reasonable kinetic data for products S and T from a single experiment. 3. Case Study: Citral Hydrogenation In the hydrogenation of citral, both parallel and consecutive reactions proceed simultaneously (see Figure 1).1,2 Seven different pressure and temperature levels were investigated. The following products were detected under the reaction conditions: citronellal, citronellol, geraniol, isopulegol, nerol, 3,7dimethyloctanal, and 3,7-dimetlyloctanol. Some of these products were formed in trace quantities, and, thus, the reaction scheme (Figure 2) was simplified considerably. Two different reaction schemes were compared in kinetic modeling. In the reaction scheme 1 in Figure 4, only consecutive reactions for citronellal and citronellol are included. In the modeling, A denotes citral, B is citronellal, C is citronellol, and D is 3,7-
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Figure 3. First-order kinetics of the consecutive reaction system A f R f S f T (a) with and (b) without liquid-phase drainage. The kinetic parameters were k1 ) 0.5 min-1, k2 ) 0.05 min-1, and k3 ) 0.005 min-1, with liquid-phase drainage (τ0 ) [300, ∞]) and without drainage (τ0 ) ∞).
catalyst mass was kept constant in all of the experiments (500 mg), and the stirring rate was 1500 rpm (Rushton turbine). The use of small catalyst particles and vigorous stirring facilitated the hydrogenation under kinetic regime, as was discussed for the same chemical system in the paper by Aumo et al.3 In the experiments with an increasing catalyst bulk density, liquid was continuously taken out of the reactor, at a rate of ∼1 g/min, using a needle valve, and weighted in situ. Moreover, in some experiments, the temperature was increased during the hydrogenation at a rate of 0.8 °C/min, from 60 °C to 90 °C. The components in the reaction mixture were analyzed with a gas chromatograph that was equipped with a flame ionization detector (FID) and a capillary column (DB-1, length 30 m, inner diameter of 0.25 mm, film thickness of 0.50 µm). The following temperature program was used: 120 °C (for 1 min)-0.40 °C/ min to 130 °C-15 °C/min to 200 °C. 3.2. Langmuir-Hinshelwood Kinetics. The LangmuirHinshelwood 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. Two kinetic models were developed, depending on the way the organic molecules and hydrogen are assumed to be adsorbed on the catalyst surface. These two models are called the competitive adsorption model and the noncompetitive adsorption model. Surface reactions were presumed to be ratedetermining in these two models. Molecularly adsorbed hydrogen was assumed to be the catalytically active species. 3.2.1. Competitive Adsorption Model. According to this model, all the reactants are assumed to be adsorbed on the same type of active sites and hydrogen is adsorbed in molecular form. Thus, the reaction steps in citral hydrogenation on nickel surface can be written as follows: Ki
Pi + * 798 Pi* KH
H2 + * 798 H2* Figure 4. Diagram depicting the reaction schemes: reaction scheme 1 consists of reactions 1, 2, and 3, whereas reaction scheme 2 consists of all the reactions. Abbreviations A-E correspond to the labeled structures in Figure 2.
dimethyloctanol. Reaction scheme 2 in Figure 4 includes consecutive reactions, with respect to citronellal and citronellol, and one parallel reaction, with respect to citronellal. In the modeling according to this scheme, A denotes citral, B is citronellal, C is citronellol, and D is 3,7-dimethyloctanol; 3,7dimethyloctanal (E) is hydrogenated further to 3,7-dimethyloctanol (D). In practice, the roles of reactions 4 and 5 were very minor. 3.1. Experimental Procedures. Citral (Alfa Aesar, 97%) hydrogenation kinetics was investigated in a semibatch autoclave (Autoclave Engineers) in 2-pentanol (>98%, Merck 807501) (used as a solvent) in the temperature and pressure ranges of 50-90 °C and 5-21 bar, respectively. The Ni/Al2O3 (20.2 wt % Ni) catalyst with a mean particle size of 13.5 µm (sieved to fractions of
