Intricate CSTR dynamics

Various dynamical characters of continuous stirred tank reaclors (CSTR) are introduced with respect to the effects of reaction types, extra thermal capacitance, periodic forcing, and coupling of CSTRs. The subject includes the classical dynamics of two-dimensional model and the variety of complex dynamics in three or higher dimensional systems such as periodic bifurcations to torus or chaos, aperiodic oscillations on invariant torus, and universal dynamics of alternating periodic-chaotic sequences with k.2^v-cycles for every natural number k. Particularly this review intends to bring about the problems that the engineers must be prepared to encounter in solving various physical systems including chemically reacting systems.     

Optimization-based predictive control of a simulated moving bed process using an identified model

For optimization-based dynamic control of simulated moving bed (SMB) process, a novel control strategy based on process identification, which is an extension of the earlier work (Song et al., 2006a. Identification and predictive control of a simulated moving bed process: purity control. Chemical Engineering Science 61, 1973-1986), is proposed. A linear output prediction model is obtained by the method of subspace identification and used for the dynamic control. The controller is designed for optimizing the production cost while maintaining the specified product purities. For all of these, the average purities over one switching period of the target components in extract and raffinate streams, the reciprocal productivity and the solvent consumption are selected as output variables, while the flow rates in 1, 2, 3 and 4 are chosen as the manipulated variables. The realization of this concept is discussed and assessed on a virtual eight column SMB unit for a system following a bi-Langmuir isotherm. The identified prediction model is proven to be in good agreement with the first principles model considered as the actual SMB process. For typical control objectives encountered in actual operation, i.e., disturbance rejection and set-point tracking, it is shown that the proposed controller exhibits excellent performance, hence it is an effective tool for optimization-based control of SMB process.     

Asymptotic solution to moving-bed exchange equations

Asymptotic solutions to countercurrent moving-bed exchange equations are discussed considering the effect of axial dispersion and interphase mass transfer. Existence conditions are derived by using perturbation theory in a properly defined moving coordinate system. The flow are ratio turns out to be a very important parameter and its effect on the exchange performance is carefully examined. In particular, the effect of interphase mass transfer disappears when the exchange zone becomes stationary. Applications are illustrated by using the Langmuir adsorption isotherm. Numerical solutions of the transient equations show that the asymptotic solution may be useful.     

Synthesis and catalytic application of Ni-supported carbon nanotubes for<Emphasis Type="Italic">n</Emphasis>-heptane cracking

Carbon nanotubes were synthesized by chemical vapor deposition and subsequently purified and oxidized by repeated treatment with nitric acid. After acid treatment the walls of carbon nanotubes became thinner and the surface area increased. The Ni-supported carbon nanotubes prepared by impregnation were applied to the cracking ofn- heptane to show an excellent activity. This indicates that the carbon nanotubes can serve as a good catalyst support with high dispersion of metallic components. The optimum Ni loading turned out to be about 5.2 mmol/g. The cracking product was found to contain mainly small hydrocarbons; thus the Ni-supported carbon nanotubes may be applied as a potential catalyst to the cracking of heavy hydrocarbons. A. M. Zhang was a visiting scholar at School of Chemical Engineering, Seoul National University. This paper is dedicated to Professor Hyun-Ku Rhee on the occasion of his retirement from Seoul National University.     

Active sites in Cu/ZnO/ZrO2 catalysts for methanol synthesis from CO/H2

Among various Cu/ZnO/ZrO₂ catalysts with the Cu/Zn ratio of 3/7, the one with 15 wt.% of ZrO₂ obtains the best activity for methanol synthesis by hydrogenation of CO. The TPR, TPO and XPS analyses reveal that a new copper oxide phase is formed in the calcined Cu/ZnO/ZrO₂ catalysts by the dissolution of zirconium ions in copper oxide. In addition, the Cu/ZnO/ZrO₂ catalyst with 15 wt.% of ZrO₂ turns out to contain the largest amount of the new copper oxide phase. When the Cu/ZnO/ZrO₂ catalysts is reduced, the Cu²⁺ species present in the ZrO₂ lattice is transformed to Cu⁺ species. This leads to the speculation that the addition of ZrO₂ to Cu/ZnO catalysts gives rise to the formation of Cu⁺ species, which is related to the methanol synthesis activity of Cu/ZnO/ZrO₂ catalyst in addition to Cu metal particles. Consequently, the ratio of Cu⁺/Cu⁰ is an important factor for the specific activity of Cu/ZnO/ZrO₂ catalyst for methanol synthesis.     

Epoxidation of n-hexene and cyclohexene over titanium-containing catalysts

TS-1, Ti-beta and Ti-MCM-41 molecular sieves have been prepared by direct hydrothermal synthesis method and applied to the epoxidation of n-hexene and cyclohexene with H₂O₂ under mild conditions. Ti-beta with extremely low Al content was synthesized by using a seed method to suppress the formation of diol produced by Brønsted acid sites present in Ti-beta. It was also found that a large amount of by-products (1-ol and 1-one) formed over hydrophilic Ti-MCM-41. We further modified Ti-MCM-41 by silylation with bis(trimethylsilyl) trifluoroacetamide (BSTFA). Among these catalysts, the Ti-beta with low content of Al enhanced the yield of epoxide and suppressed the formation of diol markedly. The silylated Ti-MCM-41 reduced the formation of by-products and promoted the yields of epoxide significantly. Based on experimental results, a reaction mechanism with two parallel and competitive reactions was proposed.     

Preparation of Titanium-Containing Carbon–Silica Composite Catalysts and Their Liquid-Phase Epoxidation Activity

Titanium-containing catalysts have been prepared by two different post-synthesis methods using activated carbon and carbon-silica composite as catalyst supports. They have been applied to the liquid-phase epoxidation of cyclohexene with tert-butyl hydroperoxide (TBHP) and H₂O₂. The carbon-silica composite catalyst showed a high conversion and selectivity to epoxide compared to the Ti-carbon catalyst and silica-based catalysts for the cyclohexene epoxidation with H₂O₂. The highest values of cyclohexene conversion and epoxide selectivity were obtained with the carbon-silica composite catalyst having a titanium content of 3 wt%.     

Application of optimal temperature trajectory to batch PMMA polymerization reactor

A mathematical model is developed for the polymerization of methyl methacrylate (MMA) in a batch reactor. The model includes chain transfers to the monomer and solvent and termination by both combination and disproportionation and also takes into account the density change of the reactor contents and the gel effect. The usual pseudo-steady-state assumption is relaxed here. The validity of the proposed model is tested by an isothermal experiment of batch PMMA polymerization. Indeed, the experimental results show that the proposed model can describe the real polymerization system very well in view of both monomer conversion and average molecular weights. The optimal control theory is applied together with Pontryagin's minimum principle to calculate the optimal temperature trajectory for a batch polymerization reactor system which would lead to a polymer product having the desired properties set a priori. The performance index of the control system is composed of three factors—the desired monomer conversion and number- and weight-average molecular weights. The desired values of number- and weight-average molecular weights are obtained at a specified monomer conversion within acceptable error ranges. Control experiments are conducted to track the optimal temperature trajectory obtained from the model and the results are found to be in good agreement with the desired values. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 69: 59–68, 1998     

Synthesis of MFI-type zeolites under atmospheric pressure

Silicalite and highly silicious ZSM-5 were synthesized using two reaction mixtures with different crystal growth environments, a dispersed low density mixture and a separated high density mixture, at 93 ±3 ‡C under the atmospheric pressure. Nucleation behavior and the transformation process of two mixtures were investigated utilizing various analytical techniques such as XRD, FT-IR, TGA, SEM, and pH measurement. During the induction period, the same intermediate phase was observed in both mixtures. The presence of this phase was found to be dependent on the degree of dilution of the reaction mixture. After the induction period, a sharp increase in both the degree of crystallization and the pH of the reaction mixture was detected. This indicates that the pH change in the reaction mixture is closely related to the crystallization process. From these observations, a crystallization mechanism is proposed on the basis of the appearance of stable silicate species and the role of OH^- ions during the induction period. According to this mechanism, MFI-type zeolite grows by condensation reaction among the stable silicate species formed during the induction period.     

Modeling and control of an LDPE autoclave reactor

A two-compartment four-cell model is developed for the adiabetic slim type autoclave reactor for free radical polymerization of low density polyethylene (LDPE). It is possible to determine not only the reactor performance represented by the monomer conversion and the reaction temperature but also the properties of the polymer product characterized by the average molecular weight and the polydispersity. It turns out that the reactor performance predicted is in good agreement with the plant data and the properties of the polymer product are estimated within reasonable ranges of actual values. The steady state multiplicity is found to exist and is examined by constructing the bifurcation diagram. The effects of various operation parameters on the reactor performance and the polymer properties are investigated systematically to show that the temperature distribution plays the central role for the properties of the polymer products. Therefore, it is essential to establish a good control strategy for the temperature in each compartment. The adaptive pole-placement control algorithm is applied to the temperature control of the adiabatic slim type autoclave reactor. The recursive least square method is used for the model identification. To accomplish a satisfactory control, the estimator and controller are initialized during the period of start-up. It is shown that the reactor system can be adaptively controlled by the pole-placement control algorithm, especially when the reactor temperature distribution is changed.