Ind. Eng. Chem. Res. 2010, 49, 8369–8378
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Dynamic Modeling and Optimization of a Batch Reactor for Limonene Epoxidation Rolando Barrera Zapata,† Aı´da Luz Villa,† Consuelo Montes de Correa,† Luis Ricardez-Sandoval,*,‡ and Ali Elkamel‡ Departamento de Ingenierı´a Quı´mica, UniVersidad de Antioquia, Cra. 53 No. 61-30, Medellı´n, Colombia, and Department of Chemical Engineering, UniVersity of Waterloo, Waterloo, Ontario N2L 3G1, Canada
A mathematical model for limonene epoxidation over PW-Amberlite in a batch reactor was developed and used for reactor simulation and optimization. The mathematical model was validated by comparison of predicted and experimentally determined limonene conversion under isothermal and nonisothermal conditions (23-50 °C) and for several limonene/oxidant molar ratios. By a sequential simulation and an optimization approach using genetic algorithms (GA), the temperature profiles minimizing the energy consumption and the variability of limonene conversion were obtained. Simulation of limonene epoxidation using the optimal temperature strategies showed that it is possible to achieve a limonene conversion of 80% in a shorter period of batch time when compared to typical isothermal conditions at 33 °C. The proposed model may also be used to scale up the catalytic system. As an illustrative example, an optimization formulation was proposed to estimate the minimum volume (18 L), the aspect ratio (height/diameter, H/D ) 1.7), and the temperature profile that maximizes limonene conversion and minimizes energy consumption to obtain at least 1000 g of limonene epoxide. 1. Introduction Limonene epoxide is an intermediate used in fragrance, flavor, and agrochemical industries. Its copolymerization with CO2 is also used in the synthesis of biodegradable plastics.1 This product has been traditionally obtained via limonene epoxidation with a considerable amount of side products (peracids). Therefore, there is much interest in developing friendlier environmental alternatives.2-6 Although several experimental studies have been published about this system,2-11 only few studies associated with modeling, simulation, and scale-up of limonene epoxide production have been reported.9,11 Dalaeli et al.9 proposed a large-scale production of limonene epoxide with a previously studied process at a laboratory scale. The system, composed of a solid silica catalyst, tert-butyl hydroperoxide, and acetone was modeled in a steady-state slurry type continuous stirred tank reactor (3000 gal). The model was implemented and simulated in Pro/II 7.0 assuming that conversions similar to those observed at lab scale were obtained on the large-scale reactor. Although that report presents a technical feasibility study for limonene epoxide production at a high scale, it does not show the model used to simulate the dynamic behavior of this system. Also, to the best of our knowledge, the kinetics of the catalytic system has not been made available in the open literature. The catalytic system formed by the catalyst PWAmberlite and hydrogen peroxide as oxidizing agent, eq 1, has also been studied for limonene epoxide production.11 acetonitrile/PW-Amberlite
C10H16 + H2O2 98 C10H16O + H2O
(1) A high limonene conversion (∼80%) and limonene epoxide selectivity (∼90%) at 33 °C after 24 h have been reported.11 * To whom correspondence should be addressed. E-mail:
[email protected]. † Universidad de Antioquia. ‡ University of Waterloo.
Also, the mechanistic pathway and the accuracy of the proposed kinetic expressions for the physical representation of the isothermal reaction at 33 °C were demonstrated by simulating the process using Aspen Plus.11 The kinetics of limonene epoxidation over PW-Amberlite as well as the effect of different reaction conditions on the reaction rate, that is, molar ratio of reactants, catalyst particle size, stirring speed, and amount of catalyst and solvent, have also been reported.7,8,10,11 In addition, the use of hydrogen peroxide reduces the production of side products. Thus, the proposed PW-Amberlite/hydrogen peroxide system is a suitable candidate for the production of limonene epoxide at a large scale because large amounts of limonene epoxide are obtained under mild reaction conditions with the additional advantage of the possibility to reutilize and regenerate the catalyst.7,8,10 Moreover, the effect of temperature on limonene epoxide production was evaluated by performing the isothermal reaction at different temperatures.10 Although laboratory experiments can be carried out to find out a suitable minimal temperature for a desired final conversion, a nonisothermal profile may achieve the same product’s quality in a shorter period of time. Moreover, the implementation of a nonisothermal profile may reduce the costs associated with this process. However, the temperature realizations minimizing the process economics may be difficult to obtain from experimental runs. In this work, a dynamic mathematical model of a batch reactor for limonene epoxidation over PW-Amberlite is presented. The proposed model was validated using isothermal and nonisothermal experimental data. The proposed model was embedded within an optimization formulation to estimate the nonisothermal profiles that reduces the costs of this process. To analyze the sensitivity of the resulting nonisothermal profile on the process economics, the proposed optimization problem was solved using two different cost functions. The first cost function was defined in terms of limonene conversion to limonene epoxide and the energy consumption of the system. Weighting factors were used in this strategy to assign a cost to these terms. The second cost function was stated in terms of minimizing the difference between a rough estimate of profits and costs. The results were
10.1021/ie100737y 2010 American Chemical Society Published on Web 07/30/2010
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Ind. Eng. Chem. Res., Vol. 49, No. 18, 2010
(T ( 1 °C). Nonisothermal experiments were carried out by randomly changing the bath temperature at 1 h intervals in the temperature range 23-50 °C. Liquid samples were analyzed by gas chromatography.10 The uncertainty for limonene conversion measurements was estimated to be within (1.2% of the reported value.11 Equation 2 shows the kinetic expression developed for this catalytic system.11 -rL ) k3KHKLCTCHCL k3KHKL 1 + KHCH + KHKLCHCL + CHCL + KECWCE + KSCS + KWCW k4
(2) Figure 1. Scheme of the batch reactor used for limonene epoxidation over PW-Amberlite at laboratory scale.
compared to the experimental data obtained at 33 °C. Furthermore, as a first step to scale up the proposed catalytic system, an optimization formulation was proposed to estimate the reactor capacity to obtain a larger amount of product, that is, 1000 g of limonene epoxide. An analysis of the results from this formulation is also presented in this work. A key novelty on this work is the mathematical description proposed for this system. To the best of our knowledge, this is the first study where modeling, simulation, and optimization of this reaction system or analogous reaction systems are shown in detail, that is, reaction systems where high added value products are obtained from rating of essential oils. Thus, the results from this work could be useful for designing experiments aiming at efficiency improvement of this system and scaling up the proposed catalytic system. Another novelty on the current study is the fact that nonisothermal profiles were experimentally tested on this system and used to validate the proposed nonisothermal model. As it is shown in section 3, the implementation of an optimal nonisothermal profile on this catalytic system may result in higher profits and lower operating costs when compared to the traditional isothermal profile. Additionally, the optimization formulations proposed here for the dynamic modeling, optimization, and scale-up of the limonene epoxidation can be easily adapted for studies related to analogous catalytic systems where the goal is to search for the optimal operation parameters or design parameters that improve the performance of the studied systems. This paper is organized as follows: Section 2 presents the mathematical model proposed for the production of limonene epoxide. The model validation and the model sensitivity with respect to changes in the values of key model parameters, that is, the heat transfer coefficient, are also presented in this section. Section 3 presents the optimization formulations used to estimate the nonisothermal profiles as well as analysis of the results obtained by the proposed optimization formulations. Section 4 shows the simulation of a higher scale limonene epoxidation. Conclusions are presented in section 5. 2. Reactor Modeling 2.1. Process Description. Figure 1 shows a sketch of the batch reaction system used for limonene epoxidation over PW-Amberlite.10,11 Limonene (0.5 g), 30% aqueous hydrogen peroxide (0.83 g), acetonitrile (3.2 g), and PW-Amberlite catalyst (0.1 g) were added to 7 mL glass flasks. The mixture was magnetically stirred at 1000 rpm for 24 h in an isothermal temperature controlled bath using an IKA-RH KT/C stirring and heating plate with an IKA ETS-D4 Fuzzy temperature controller
where the limonene reaction rate, -rL′, is expressed in mol s-1 g-1, and the concentrations, Ci, are in mol L-1. CT is the total catalytic site concentration. Table 1 shows the description, values, and units of the kinetic parameters of eq 2.11 The pseudo reaction constant, k3, in eq 2 is assumed to be dependent on temperature according to the Arrhenius law: k3 ) k0e-EA/RT
(3)
where k0 is the frequency factor (1008.3 L s-1 g-1), EA is the activation energy (25 kJ mol-1), R is the universal constant (8.3 J mol-1 K-1), and T is the temperature (K).10 For limonene epoxidation over PW-Amberlite, the temperature limits are 23 and 50 °C.8,10 At room temperature (23 °C), slow reaction rates and poor limonene conversion were observed (
