Safety aspects in modelling and operating of batch and semibatch stirred tank chemical reactors

Safety aspects in modelling of batch and semibatch stirred tank reactors as well as a model based safety analysis have been considered. Applicability of two basic types of models – i.e. the perfectly mixed reactor model and the CFD model, both formulated for laboratory scale as well as pilot plant scale reactors – has been discussed. A formulation of the appropriate reactor model, which is adequate to the considered case study has been demonstrated and tested experimentally. Particular attention has been devoted to the formulation of robust CFD models employed to simulate a performance of the stirred tank reactors. It has been found that models for perfectly mixed reactors may have quite wide range of application, while the CFD models should be definitely used in case of fast reactions, high viscosity of the reacting mixture as well as of failure leading to stopping of the impeller. The CFD models are able to predict a dynamic behaviour of reactors at any circumstances, so they can play a significant role in safety analysis carried out for industrial scale reactors, for which experimental safety tests are expensive and dangerous.     

CFD simulations of two stirred tank reactors with stationary catalytic basket

Among the different systems used for laboratory kinetic investigation, stationary catalytic basket stirred tank reactors (SCBSTRs) allow one to study triphasic reactions involving shaped catalyst with large size. The hydrodynamics of these complex reactors is not well known and has been studied experimentally in only a few cases. Despite the difference in the design of two commercial SCBSTRs reported in these works, the local measurements of the liquid-solid mass transfer coefficient inside the catalytic basket revealed the same velocity profile. The aim of the present work is therefore to investigate more accurately the hydrodynamics of the two reactors by means of CFD in order to compare the effect of the blade/baffle hydrodynamic interaction on the flow pattern. Owing to the geometrical complexity of the reactors, the hydrodynamic investigation is based on the k-ε model and the Brinkman-Forsheimer equations. The agreement at the local level with the experimental data (PIV and mass transfer measurements) validates this preliminary work performed with the standard values of the parameters present in the turbulent model and the Brinkman-Forsheimer equations. The simulations reveal in both reactors a ring-shaped vortex around the impeller in the agitation region. The high axial location of its centre induces a reverse flow at the tips of the basket. Owing to the fluid friction in the porous medium, the azimuthal flow in the core region is transformed into a radial flow in the basket where the flow decreases abruptly. Vertical vortices are located at the blade tips and at the downstream face of the baffles or they are located in the basket on both sides of the baffles, depending on the design and the location of the baffles. At the inner radius interface of the basket, the vertical blade impeller induces a rather homogeneous velocity profile, but the pitched blade impeller imposes a high velocity at the plane of symmetry. Therefore the simulations demonstrate that two different local velocity patterns and two different porous media may induce the same mass transfer properties.     

CFD modeling of gas entrainment in stirred tank systems

In the present work, CFD modeling was used to study the phenomenon of gas entrainment in stirred tank systems. Two types of impellers (DT, PBTD) were simulated. VOF method was used as surface tracking technique along with LES model to study interfacial behavior at the onset of gas entrainment. Simulations were performed to study cause of entrainment and underlying interfacial mechanism at the location of entrainment. CFD simulations clearly showed differences in onset and non onset conditions in terms of the magnitudes of interfacial turbulence. As per the predictions, phenomenon of surface aeration in stirred tank systems was characterized by exchange of momentum across the interface from water side to air side. Magnitudes of instantaneous axial velocities on air side, strain rates on air side and vorticities on air side exhibited a threshold at the onset of entrainment and reduced substantially after the onset.     

Simulation of reversible nylon-66 polymerization in homogeneous continuous-flow stirred tank reactors

Experimental data of Ogata¹ has been curve-fitted to obtain the forward and reverse rate constants for nylon-66 polymerization. Its molecular weight distribution (MWD) has been simulated in homogeneous continuous-flow stirred tank reactors (HCSTR) for 11 h of residence time when the reaction mass is very close to equilibrium. The set of algebraic equations have been solved using Brown's algorithm,² which was found to be more efficient compared to the Gauss-Jordon techniques of solution. The MWD thus obtained is compared with our earlier simulation of the molecular weight distribution from batch reactors³ and was found to differ significantly. In HCSTR, the weight fraction distribution does not undergo a maximum and the polydispersity index ρ of the polymer formed is much higher than that obtained from batch reactors. The number and weight average of the polymer formed in HCSTR is found to be significantly lower.     

搅拌槽中酯化反应热失控的CFD模拟

热失控是化工过程中常见的安全风险之一。在间歇釜式反应器中,桨叶的机械转动可以增强流体的循环流动、湍流强度、混合程度以及传热,进而有效防范热失控。防控效果与反应器结构和搅拌桨型密切相关。针对丙酸异丙酯酯化反应,采用计算流体力学模拟研究了桨型(Rushton桨、30o PBT桨及60o PBT桨)、转动方向和挡板对釜式反应器内温度演化的影响,从流动结构方面分析了原因。基于散度的失控判据比较了三种搅拌桨抑制热失控的能力,抑制能力为Rushton桨＞30° PBTD桨＞60° PBTD桨。本研究可为搅拌反应器热失控的优化设计提供一定的理论依据。     

On the dynamic behaviour of a class of homogeneous continuous stirred tank polymerization reactors

The steady state and dynamic behaviour of two typical vinyl polymerizations (polymethylmethacrylate and polystyrene with AIBN) carried out in a CSTR has been analyzed. Both the cases of constant and dynamically varying initiator concentration were treated for a wide range of reactor operating conditions. The results show that multiple steady states are possible even under isothermal conditions, but only unstable limit cycles appear possible for the systems studied.     

Scale-up of continuous flow stirred tank reactors

A model of a continuous flow stirred tank reactor based on laboratory experiments successfully describes the behavior of a pilot plant reactor. This model simulates the pilot plant performance over the full range of operating conditions: at high impeller speeds where performance approaches that of a perfectly mixed reactor and at low impeller speeds where performance significantly differs from perfect mixing. The micro-mixed feed model divides the continuous flow stirred tank reactor into a small micro-mixed impeller zone and a large macro-mixer.     

Response modes of continuous stirred tank reactors

The general applicability of stoichiometric constraints to reduce the dimensions of the differential equations describing the process dynamics of continuous stirred tank reactors has been disputed in the literature, and attempts have been made to disprove it.However, it turns out that the fundamental stoichiometric constraints on a set of chemical reactions carry over to the dynamics of open systems in the analysis of asymptomatic stability. In fact, the stoichiometric constraint becomes a new combined state variable, a general asymptomatic invariant, which is invariant to the way the chemical reactions proceed.Hence, only a reduced set of the stirred tank eigenvalues is changed by the reactions. The dimension of this set is equal to the number of independent reactions, also when temperature is included in the state vector. The remaining eigenvalues are left unchanged as if no reaction takes place.For global analysis, however, the reaction is valid only in the very special case when the initial conditions of the chemical species and the feed concentration vector obey the stoichiometric constraint.     

Periodic regimes of continuous stirred tank reactors

The scheme of analysis of the dynamic behaviour of continuous stirred tank reactors is developed. All classes of possible phase plots and their position in the parameter space are established for the case of the nth order exothermic reaction.     

Optimization of a cascade of stirred tank reactors

Dynamic programming is applied to the optimization of a cascade of stirred tank reactors in which an isothermal first-order reaction takes place. Use of this method is illustrated by calculation of polymerization parameters for a four-reactor cascade from experimental data available from the literature.     

Cellular automata modeling of continuous stirred tank reactors

The classical dynamical systems model of continuous stirred tank reactors (CSTR) in which a first order chemical reaction takes place is reformulated in terms of the stochastic cellular automata procedure developed in the works of Seyborg [2] and Neuforth [3], which is extended by including the feed flow of chemical reactants. We show that this cellular automata model is able to simulate the dilution rate and the mixing process in the CSTR, as well as the details of the heat removal due to the jacket. The cellular automata approach is expected to be of considerable applicability at any industrial scale and especially for any type of microchemical system.     

The quasi-steady-state approximation in continuous stirred tank reactors

The Quasi-steady-state-approximation (QSSA) applied lo continuous stirred tank reactors (CSTR) is examined. The induction period is found to be somewhat longer and the error in the QSSA larger than for batch reactors. This error is usually insignificant except when CSTR conversions are low. An alternative approximation is proposed for this case. The errors in the QSSA are also illustrated for the well known cases of Enzyme and Free-Radical polymerization kinetics.     

Segregated regions in continuous laminar stirred tank reactors

Using visualization techniques, including acid/base reactions and UV fluorescence, we provide experimental evidence of segregated regions (islands) during mixing of viscous Newtonian fluids under laminar flow conditions in continuous stirred tank reactors (CSTRs). The effect of inlet/outlet stream position and Reynolds number on the dynamics of the mixing processes is examined. Numerical experiments in 3-D map were able to capture the main features of the CSTR flow by perturbing a Batch system using an imposed axial flow. Asymmetric flow patterns produced by off-center positioning of inlet and outlet pipes cause a reduction in size of the segregated region, enlarging the chaotic region and leading to more efficient mixing. Under dynamic inlet flow conditions, the laminar steady flow is perturbed, giving rise to an asymmetric flow pattern that is able to destroy toroidal segregated regions. Counter-intuitively, higher agitation speed (higher Re) did not enhance overall mixing efficiency. Faster agitation stabilized the toroidal regions, making it harder to destroy them. In addition, dynamic mixing protocols are investigated to enhance mixing performance. We demonstrate that time-dependent pumping and stirring protocols are able to efficiently destroy long-lasting toroidal regions.     

搅拌反应器内计算流体力学模拟技术进展

综述了计算流体力学(CFD)技术应用在搅拌反应器的进展情况。重点对搅拌反应器内流动场模拟的各种处理方法,包括"黑箱"模型法、内外迭代法、多重参考系法和滑移网格法,进行了介绍与评价,指出了各种方法所具有的特点及存在的问题。阐述了搅拌反应器内CFD技术的发展方向,并就国内的研究现状进行了简单概述。     

Pattern formation in interacting continuous stirred tank reactors

The dynamic behavior of coupled continuous stirred tank reactors in which the nonisothermal Langmuir-Hinshelwood type reactions occur, exhibits several types of pattern formation. The regular and irregular multipeak patterns are detected for the endothermic reaction of a Langmuir-Hinshelwood type when the heat communication between the neighboring cells is larger than the mass interaction. These observations may imply the possible existence of spatial structure in a matrix of catalysis, the non-uniform distribution of concentration and temperature in packed bed reactors, and corrugated propagating fronts in combustion problems.     

Periodic control of continuous stirred tank reactors—III: Case of multistage reactors

The optimal periodic control of a multistage CSTR in which a nonisothermal parallel reaction is taking place is investigated. By applying the infinite-frequency pi criterion it is examined in what condition the optimal periodic control is proper. Then, the optimal steady control and the suboptimal periodic control are determined by numerical calculation. The results indicate that the improvement in the reactor performance for the periodic control relative to that for the steady control is very much increased with increase in the number of stages.     

Experimental measurements and simulation of mixing and chemical reaction in a stirred tank

Effects of mixing on the rate of second-order chemical reactions have been studied by measuring the time-average degree of conversion at enough points in a steady-state, continuous-flow stirred reactor to provide comparisons with numerical simulations of the same reactions using a standard Reynolds-averaged turbulence simulation code with an added closure. The reactants were introduced in widely separated feed streams in order to provide a difficult test for the measurements and simulations. Concentration and segregation measurements were made with two fluorescence based methods - one remote and one using a fiber optic probe. The rates of mixing and reaction were simulated using the Corrsin mixing term and the Spalding segregation production term with the Paired-Interaction reaction closure term.     

Transient response of continuous-flow stirred reactors containing heterogeneous systems for catalysis or sorption

Time domain solutions are presented for the transient response of an isothermal CFSR with one-dimensional diffusion and first-order irreversible chemical reaction in catalyst particles or liquid pools of regular geometry and with mass transfer resistance at the fluid-catalyst interface. Three different cases of feed perturbations have been considered, namely, step input, impulse input and the sudden introduction of pellets into the reactor. The solutions have been derived in a general manner, without specifying the particle shape, and are in terms of characteristic functions defined for each of the three particle geometries considered, i.e. slab with sealed edges, cylinder with sealed ends, and sphere. Asymptotic solutions suitable for large Thiele parameters (gf≥3) have also been derived and are particularly convenient when the series solutions converge slowly. Experimental verification of the exact and asymptotic solutions for a specific case of absorption and diffusion in a liquid pool is presented.     

On the dynamic behavior of continuous stirred tank reactors

The types of dynamic behavior possible for a single first order reaction carried out in a stirred tank reaction are classified according to values of the parameters and plots in parameter space used to define the various possibilites. Analytic criteria are developed which predict the existence and stability character of limit cycles as a function of the system parameters. The types of dynamic behavior predicted are illustrated by numerical computation of the temperature and concentration trajectories. Several kinds of new jump phenomena for this problem are observed and explained in terms of the parameter space plots. The theory and analysis methods can be easily generalized to other types of reaction systems.