Non-ideal Reactor Research Articles

A rigorous model for hydrogen response in industrial propylene polymerization loop reactors: From micro-mechanism to macro-behavior

In spite of playing a chain transfer agent role, the hydrogen activation effect in propylene polymerization with Ti-based Ziegler-Natta catalysts, so called “hydrogen response”, is usually explained by the dormant-site theory in polymer chemistry. However, how the micro-mechanism at the catalyst site scale affects the macro-behavior of industrial processes is unrevealed. This work aims at developing a rigorous model that can accurately describe hydrogen response and predict polymer chain microstructure for an industrial propylene polymerization process consisting of loop reactors in series. The model is comprised of a kinetic model, a thermodynamic model, and a macroscopic non-ideal loop reactor model. To describe hydrogen response, an elaborated kinetic model is established based on a consistent dormant site reactivation mechanism assuming a multi-site model. The model predictions are in good agreement with plant data, after taking the dormant sites reactivated by hydrogen into account. The proposed model is capable of fully assessing the effects of various process conditions, during steady-state and grade transition processes, on the macro-behavior (i.e., production, slurry density) as well as polymer properties (i.e., melt flow index, molecular weight distribution) in the industrial loop reactors. The underlying correlations are also discussed.

Surrogate-model-based optimization of a nonideal polymerization reactor for producing tailored molecular weight distribution

The optimization of polymerization reactors with nonideal mixing has been greatly hindered by a tremendous computation burden. In this study, a global optimization framework to integrate full MWD calculations and detailed reactor dynamics with nonideal mixing behaviors was developed by reducing the considerable computation time required for implementing full MWD. A combination of surrogate-model-based optimization and a computational fluid dynamics (CFD)-compartment reactor model was applied to produce the desired MWD in a nonideal reactor. A neural network (NN) surrogate model was trained using 3,000 MWD data produced from the mechanistic reactor model. The results showed that the model successfully described asymmetric MWD with bimodality resulting from the nonideal mixing behaviors in the reactor. The surrogate model was used to construct operation maps for the asymmetry and bimodality factors, with SHapley Additive exPlanations (SHAP) values showing that the flow rate of the chain transfer agent had the largest impact on the asymmetry factor, whereas temperature significantly influenced the bimodality factor. Finally, the optimization strategy based on the asymmetric and bimodality factors successfully determined operating conditions to produce four tailored MWDs, reported in actual polymerization reactors with R scores of 0.988–0.997.

Real gas effect on ignition in ideal and non-ideal reactors

Real gas effect on ignition in ideal and non-ideal reactors

A novel methodology to construct compartment models for a circulating fluidized bed riser

During the integrated modeling of a chemical process, there always exists a conflict between model accuracy and computational speed for non-ideal reactors. In view of this, a novel, easy to use, methodology to construct compartment or ideal reactor network models is proposed for a circulating fluidized bed (CFB) riser based on time-series. The pressure drop time-series is sampled during the Multi-Phase Particle-in-Cell (MP-PIC) simulation of the riser. Detailed procedures for mapping the time-series to a directed weighted complex network and the determination of model parameters are presented. Effects of the sampling frequency and division scheme for the time-series on compartment models are also investigated. Findings indicate that the MP-PIC simulation is reliable to record the time-series of pressure drop in the CFB riser. The non-ideal flow in the riser can be equivalently reproduced by a compartment model consisting of eight CSTRs with various sizes and backflow rates. The appropriate sampling frequency for the time-series should be greater than 200 Hz. The optimum division scheme for the time-series is with the predefined threshold value of K = [4025, 4150, 4275, 4400, 4525, 4650, 4775]. It is believed that the proposed methodology based on the time-series can be generalized to develop compartment models for non-ideal flow. It is also expected that compartment models can be readily integrated into a process simulator, e.g., Aspen Plus, to resolve the conflict between model accuracy and computational speed in process simulation, on-line analysis and real-time optimization.

Coeficiente de dispersión longitudinal obtenidos por medición hidroacústica y por trazador conservativo

The objective of the present work was to determine the value of the longitudinal dispersion coefficient (DL) of the Chicamtoltina stream (Alta Gracia) by means of two different techniques, in order to compare the values obtained. The first technique consisted of applying a developed formula that includes a detailed description of hydrodynamic parameters obtained by gauging with a hydroacoustic instrument, while the second technique consisted of injecting a conservative tracer, using the same approach as the non-ideal chemical reactor theory of flow with dispersion. This work was carried out at low flow conditions (dry period) and at high flow conditions (wet period). It was found that, either for high flow or low flow, the values of the dispersion coefficient obtained by both techniques have good agreement, fitting better in the dry period than in the wet period. Due to the fact that frequent gauging campaigns are carried out in this stream, it is concluded that with similar flow characteristics and morphology of the section, the gauging data can be used to determine the DL coefficient, in order to incorporate reliable data that can be applied to pollutant transport models.

RTD Modeling of a Non-Ideal Coiled-Tube Reactor Through Experimental Investigation for Pulse Input Using Methylene Blue Dye

This paper focuses on the grasp of a deep understanding of flow behavior in a coiled tube reactor through Residence Time Distribution (RTD) studies. The reactors, in general, are classified ideally: mixed and plug-flow patterns. Unfortunately, in the real world, it has been observed that they show very different behavior from that expected. Thus, the characterization of the nonideal coiled tube reactor is needed to carry out. The calculations were carried out in the Matlab for distribution of residence time of the coiled tube reactor that is used in the Chemical Reaction Engineering Laboratory at MIET College. Pulse input tests were used significantly to analyzed the flow behavior using methylene blue (MB) tracer. A significant disparity in RTD curves in the presence of the secondary flow was examined and data were recorded. Finally, a suitable mathematical model was selected from the Tank in Series (TIS) and Axial Dispersion Models (ADMs) based on residual error and was used to validate these outcomes. The deconvoluted of the signal was used to get Cin for the verification of the pulse input behavior. The results were compared with the experimental data that concluded the modeling of the reactor is in good agreement.

Combination of axial dispersion and velocity profile in parallel tanks-in-series compartment model for prediction of residence time distribution in a wide range of non-ideal laminar flow regimes

The residence time distribution is an important characteristic in the analysis of non-ideal reactors. In micro- reactors that operate predominantly under low Reynolds number, the axial dispersion is important. Since the channel length or residence time of fluid is usually not long enough, the axial dispersion model cannot predict an accurate RTD of the fluid in micro-reactors. In order to overcome this dilemma, a new model has been developed in the present work that combines the axial dispersion and velocity profile using the parallel tanks-in-series compartment model. The model comprises of two parameters, including the velocity profile exponent and Peclet number. It can be used for Newtonian and non-Newtonian fluid flow in the reactors with a wide range of Reynolds number and in all ranges of flow regime, including plug, laminar, perfectly mixed, and other profiles between these regimes. After verifying the model, the effects of velocity profile and Peclet number on the RTD of fluid in the tube for m-laminar and y-laminar velocity profiles were evaluated. Then, the RTDs of some previously reported systems such as straight Polytetrafluoroethylene (PTFE) tube, multi-laminated/elongational flow micro-mixer (MEFM-4) and standard T-junction micro-mixer (TjM) were adjusted to the proposed model.

CFD modeling of styrene polymerization in a CSTR

A computational fluid dynamics (CFD) approach coupled with polymerization kinetics is implemented to investigate styrene polymerization using azobisisobutyronitrile (AIBN) as initiator and toluene as solvent in a lab-scale continuous stirred tank reactor (CSTR). The integration of kinetic model and CFD model taking molecular weight distribution into consideration is accomplished by a user-defined function (UDF) code using the method of moments. The results predicted by CFD compare with literature data satisfactorily. The effects of operating variables such as species diffusion coefficient, impeller speed, residence time and reaction temperature are analyzed. As the impeller speed increases, the degree of mixing homogeneity is improved, which results in decreasing conversion and molecular weight distribution. The proposed method can be used to predict polymerization behaviors in non-ideal mixing industrial reactors.

Simulation and optimization of polymer molecular weight distribution with nonideal reactors

Molecular weight distribution (MWD) is essential for describing the microstructural quality of a polymer. However, most of the studies on MWD are limited to ideal reactors. Computational fluid dynamics (CFD) methods is a useful tool to deal with the nonideal reactors. Few studies on CFD have been extended to the simulation and optimization of polymer MWD due to the computational difficulties. In this study, a new strategy is proposed to simulate the spatial MWD for a type of nonideal reactors using the method of moments with interfacing to the CFD software. Subsequently, given a target MWD curve, process optimization is proposed to achieve the optimal operating conditions. The tubular and autoclave reactors of the low-density polyethylene process are demonstrated for the simulations and optimizations. The influences of the decision variables on the feasibility and objective function are also discussed.

Residence time calculations for complex swirling flow in a combustion chamber using large-eddy simulations

In order to appraise the residence time calculation for a fluid element within a complex combustion system, which features oxy-fuel combustion, large-eddy simulations (LES) are carried out under cold flow conditions in a complex swirled flow generic laboratory-scaled combustor. The quantities, like residence time distribution, mean residence time, cumulative distribution function, variance and skewness, are used to characterize the configuration under investigation. To accurately account for the influence of the flow and to capture the tracer concentration evolution, LES are first assessed by comparison with statistical moments from experiments and by various indices of quality and error analysis. They show that the investigated configuration features a non-ideal reactor based on the flow and tracer transport. The calculated residence time distribution is analyzed and compared with experimental findings providing an estimated mean residence time of about τ=1.9s. The derived residence time and functions are afterwards used to make predictions of tracer concentration at the reactor outlet. It turns out that such an appraised LES methodology is able to capture the residence time distribution in an accurate manner which allows its further extension to reacting conditions.

A new model for coal gasification on pressurized bubbling fluidized bed gasifiers

Many industries have taken interest in the use of coal gasification for the production of chemicals and fuels. This gasification can be carried out inside a fluidized bed reactor. This non-ideal reactor is difficult to predict due to the complex physical phenomena and the different chemical changes that the feedstock undergoes. The lack of a good model to simulate the reactor’s behavior produces less efficient processes and plant designs. Various approaches to the proper simulation of such reactor have been proposed. In this paper, a new model is developed for the simulation of a pressurized bubbling fluidized bed (PBFB) gasifier that rigorously models the physical phenomena and the chemical changes of the feedstock inside the reactor. In the model, the reactor is divided into three sections; devolatilization, volatile reactions and combustion-gasification. The simulation is validated against experimental data reported in the literature and compared with other models proposed by different authors; once the model is validated, the dependence of the syngas composition on operational pressure, temperature, steam/coal and air/coal ratios are studied. The results of this article show how this model satisfactorily predicts the performance of PBFB gasifiers.

Acid Gas to Syngas (AG2S™) technology applied to solid fuel gasification: Cutting H2S and CO2 emissions by improving syngas production

The paper deals with the application of the novel Acid Gas To Syngas (AG2S™) technology to the gasification of solid fuels. The AG2S technology is a completely new effective route of processing acid gases: H2S and CO2 are converted into syngas (CO and H2) by means of a regenerative thermal reactor. To show the application of the AG2S technology, modeling and simulation advances for gasification systems are initially discussed. The multi-scale, multi-phase, and multi-component coal gasification system is described by means of detailed kinetic mechanisms for coal pyrolysis, char heterogeneous reactions and for successive gas-phase reactions. These kinetic mechanisms are then coupled with transport resistances resulting in first-principles dynamic modeling of non-ideal reactors of different types (e.g., downdraft, updraft, traveling grate), also including the catalytic effect of ashes. The generalized approach pursued in developing the model allows characterizing the main phenomena involved in the coal gasification process, including the formation of secondary species (e.g., COS, CS2). This tool is here further validated on literature data and, then, adopted to demonstrate the AG2S effectiveness, where H2S and CO2 emissions are reduced with an increase of syngas production. The resulting process solution is more economically appealing with respect to the traditional Claus process and finds several application areas.

Study of Bunsen reaction in agitated reactor operating in counter current mode for iodine-sulphur thermo-chemical process

The iodine-sulphur (IS) thermo-chemical process is being studied as a potential process for production of hydrogen by water splitting. It consists of three chemical reactions: 1) Bunsen reaction, which is the acid production step, 2) sulphuric acid decomposition to produce oxygen; 3) hydrogen iodide decomposition to produce hydrogen. In this work, a detailed parametric study of the Bunsen reaction is presented, which was carried out in agitated reactor (ABR) in counter current mode of operation. Experiments have been carried out in the reactor at different temperatures by varying the sulphur dioxide (SO2) flow rate and partial pressure of SO2. Bunsen reaction rate and SO2 conversion are calculated experimentally from feed rate and scrubbing rate of SO2. It has been observed that the reaction rate and SO2 conversion increase with increase in SO2 flow, increase in SO2 partial pressure and decrease in temperature. 'Tanks-in-series' model, one of the non-ideal reactor models, has been proposed to describe the ABR reaction system. The model has been validated with experimental results. This approach can be useful for the design and scaling up of the agitated reactor.

Current Views on Hydrodynamic Models of Nonideal Flow Anaerobic Reactors

A critical review of the different hydrodynamic mathematical models available for nonideal flow configurations of both low-rate and high-rate anaerobic reactors is presented, including upflow anaerobic sludge blanket reactors, anaerobic fluidized bed reactors, anaerobic biofilters, wet and dry digesters. The review highlights the role of mathematical modeling on design and operational optimization of organic waste and wastewater treatment plants. For each reactor configuration the following approaches, proposed by various authors, are presented and compared: (a) plug flow model, (b) tank in series model, (c) dispersion model, and (d) computational fluid dynamic model. The review gives a general overview on mathematical modeling of anaerobic nonideal plug-flow reactors and compares different models indicating the advantages and disadvantages to apply them for different reactor type.

On Danckwerts’ Boundary Conditions for the Plug-Flow with Dispersion/Reaction Model

Accurate predictions of oxygen utilization with position in plug-flow like (aka serpentine) reactors employed for aerobic activated-sludge treatment of municipal and industrial wastewaters are desired. Three non-ideal reactor models—completely-mixed flow reactors (CMFRs) in series, segregated flow, and plug-flow with dispersion (PFD)—and the ideal plug-flow model were investigated considering typical reaction kinetics and a typical reactor configuration to perform such predictions. Significant differences arose between predictions from the PFD model relative to those from the CMFR in series and segregated flow models. These differences led to re-examination of the PFD model and the inlet/outlet boundary conditions postulated more than six decades ago by P. V. Danckwerts. Major criticisms are found in the literature addressing the PFD model arising from the concentration “jump” at the inlet boundary necessitated by specification of conservation of reactant flux at the expense of continuity of target reactant concentration. A fresh theoretical examination of the dispersive/reactive processes within a closed reactor with particular attention paid to the inlet and outlet boundary planes led to alternative statements for the inlet and outlet boundary conditions. Revisions proposed herein to Danckwerts’ boundary conditions for the PFD/reaction model preserve both continuity of reactant concentration and conservation of reactant flux at both inlet and outlet boundaries. Hypothetical computations based on pseudo-first-order kinetics for a reaction carried out within a serpentine reactor of typical configuration illustrate the differences between concentration profiles through the reactor predicted using the proposed and Danckwerts’ boundary conditions.

Kinetic analysis of TiO2-catalyzed heterogeneous photocatalytic oxidation of ethylene using computational fluid dynamics

Photocatalytic oxidation of ethylene was carried out over a TiO2 catalyst at 295K using two types of non-ideal fixed-bed flow reactors: a rectangular reactor and a cylindrical reactor. Computational fluid dynamics (CFD) analysis using a low Reynolds number-type k-ε turbulence model was conducted to investigate the ethylene oxidation behavior in the reactors at various gas flow rates and ethylene concentrations in the inlet gas (ethylene concentration of 50–250ppm and gas flow rate of 50–250mL/min). In the rectangular reactor, steady-state activities were obtained for ethylene oxidation under all conditions. The rate of ethylene oxidation on the TiO2 surface was analyzed in terms of Langmuir–Hinshelwood (L–H) type kinetics. The kinetic parameters for the surface reactions obtained via CFD analysis fit well with the experimental data. The CFD analysis also revealed that the ethylene concentration distribution in the reactor depended on the gas residence time distribution. We also carried out CFD analysis for the cylindrical reactor and compared the ethylene oxidation behavior with that in the rectangular reactor.

Hydrodynamic Mathematical Modelling of Aerobic Plug Flow and Nonideal Flow Reactors: A Critical and Historical Review

Existing mathematical models of wastewater treatment plants focus primarily on the bioconversion processes and often do not cope with the reactor hydrodynamics. However, in the literature several aerobic plug flow bioreactors with both kinetics modelling and hydrodynamics description are reported. The authors review mathematical models of aerobic plug flow reactors, such as activated sludge reactors, fluidized bed reactors, biofilters, and trickling filters focusing on their hydrodynamic approach and on the role of the reactor configuration on the process performance. For each reactor type the following modelling approach is compared: (a) ideal model, such as plug flow or complete mixed, (b) tank in series model, (c) dispersion model and (d) computational fluid dynamic model.

Cover Picture: Macromol. Theory Simul. 7∕2014

Cover: A novel hybrid simulation approach combines the deterministic and stochastic modeling of complex polymerization networks, for all types of polymerization reactions in ideal and non-ideal reactors. The fast deterministic simulation solves the heat and pressure balances and generates position-dependent event frequency profiles. The detailed stochastic simulation offers insight into the polymeric microstructure of each macromolecule. Further details can be found in the article by E. Neuhaus, T. Herrmann, I. Vittorias, D. Lilge, G. Mannebach, A. Gonioukh, and M. Busch* on page 415.

Comparative simulation of a fluidised bed reformer using industrial process simulators

A simulation model is developed by commercial simulators in order to predict the performance of a fluidised bed reformer. As many physical and chemical phenomena take place in the reformer, two sub-models (hydrodynamic and reaction sub-models) are needed. The hydrodynamic sub-model is based on the dynamic two-phase model and the reaction sub-model is derived from the literature. In the overall model, the bed is divided into several sections. In each section, the flow of the gas is considered as plug flow through the bubble phase and perfectly mixed through the emulsion phase. Experimental data from the literature were used to validate the model. Close agreement was found between the model of both ASPEN Plus (ASPEN PLUS 2004 ©) and HYSYS (ASPEN HYSYS 2004 ©) and the experimental data using various sectioning of the reactor ranged from one to four. The experimental conversion lies between one and four sections as expected. The model proposed in this work can be used as a framework in developing the complicated models for non-ideal reactors inside of the process simulators.

Multi-level Reactor Optimisation in the Conceptual Design of Processes with Heterogeneous Catalytic Reactors

The paper proposes a multi-level approach for process synthesis using process superstructure optimisation. More specifically, we address the introduction of detailed reactor models to explore the effects of non-ideal reactor behaviour during the process synthesis activity after the initial screening of design candidates has been completed using ideal reactor models and high-level design trends extracted to narrow the design space to a few promising process structures. The approach focuses on heterogeneously catalysed gas-phase reaction systems due to their prominence in industrial practice and is illustrated with examples in styrene and acetic acid production.