Ammonium Chloride Aerosol Nucleation and Growth in a Cross-Flow Impinging Jet Reactor

The nucleation and growth of an ammonium chloride aerosol starting from gaseous ammonia and hydrogen chloride was investigated experimentally and with the use of a mathematical model. The reactor was composed of 2 opposed jets perpendicular to a main stream and was operated under laminar/transition flow conditions. The reactants were segregated when they entered the reactor. The parameter observed was the particle size distribution of the aerosol described by its moments. Considerable scatter in the experimental results complicated their analysis, but some important trends could be identified. The model results were strongly affected by the fluid mechanics model, which influenced the predicted mixing inside the reactor. This work shows the importance of fluid mixing in controlling the aerosol size distribution.     

Simulation,estimation and control of size distribution in aerosol processes with simultaneous reaction,nucleation, condensation and coagulation

This article presents a comprehensive study on simulation, estimation and control of size distribution in aerosol processes with simultaneous chemical reaction, nucleation, condensation and coagulation. Initially, a typical aerosol process is considered and a detailed population balance model is presented which describes how the aerosol size distribution evolves with time. The population balance is complemented with mass and energy balances that describe the evolution of the continuous phase species and temperature of the system. Sectional representations and unimodal lognormal moment approximations of the population balance model are then derived and solved. It is found that the moment model provides reasonably accurate estimates of the average properties of the aerosol size distribution computed by the sectional model for long times. Then, a nonlinear state estimator is constructed on the basis of the moment model, which employs measurements of the geometric average particle diameter to compute the evolution of the average properties of the aerosol size distribution. Finally, a nonlinear controller is designed on the basis of the moment model and is implemented on the sectional model to achieve an aerosol size distribution with desired geometric average particle diameter. The robustness properties of the nonlinear estimator and controller with respect to significant parametric model uncertainty are successfully tested through computer simulations.     

A study of gain scheduling control applied to an exothermic CSTR

This paper describes how gain scheduling control is applied to a continuous stirred tank reactor model. The CSTR process, equipped with a cooling system, is modelled. Based on the resulting nonlinear model, a gain scheduling controller is designed. The gain scheduling follows a scheme denoted bias compensation. Compared to earlier reported gain scheduling schemes, the proposed scheme results in a controller that is less complex, which is advantageous in the controller implementation stage. Numerous simulations are performed, using the gain scheduling controller and two choices of control input to the reactor model. The simulation results indicate that a gain scheduling controller performs better than a linear controller. Simulations using different choices of control input to the reactor model indicate that proper process design is crucial for the controlled process performance.     

Size Distribution Change of Titania Nano-Particle Agglomerates Generated by Gas Phase Reaction,Agglomeration, and Sintering

In the manufacturing of nanometer-sized material particlulates by aerosol gas-to-particle conversion processes, it is important to analyze how the gas-phase chemical reaction, nucleation, agglomeration, and sintering rates control the size distribution and morphology of particles. In this study, titania particles were produced experimentally by the thermal decomposition of titanium tetraisopropoxide (TTIP) and oxidation of titanium tetrachloride (TiCl 4 ) using a laminar flow aerosol reactor. The effect of reaction temperature on the size and morphology of the generated particles was investigated under various conditions. The size distributions of agglomerates were measured using a DMA/CNC system. The size distributions of primary particles were measured using TEM pictures of the agglomerates sampled by a thermophoretic aerosol sampler. In order to model the growth of both agglomerates and primary particles simultaneously, a two-dimensional discrete-sectional representation of the size distribution was employed, solving the aerosol general dynamic equation for chemical reaction, agglomeration, and sintering. Qualitative agreement between the experimentally observed results and the simulation are satisfactory for the large variations in reactor temperature explored.     

A Mathematical Model for Ultrafine Iron Powder Growth in a Thermal Plasma

ABSTRACT

A two-dimensional model is developed for the growth of ultrafine metal powders in a thermal plasma reactor. The model accounts for particle formation by nucleation, and growth by condensation and Brownian coagulation. Transport of particles occurs by convection, thermophoresis, and Brownian diffusion. The conservation equations for the moments of the particle size distribution are solved, coupled to the equation for the conservation of metal vapor. Elliptic conservation equations result from the consideration of both axial and radial diffusion of the particles. This allows for simulations in complex, recirculating flows, which are likely to occur for numerous reactor configurations and parameters. A progressive grid refining technique is used to accelerate convergence. The model is applied to the case of a typical thermal plasma reactor for the production of ultrafine iron powders. The fields of the macroscopic properties of the aerosol population and the contribution of the different mechanisms are analyzed in various conditions, some of which involve important recirculations. The effect of operating parameters on the properties of the powder generated is studied. The results are compared for some of the conditions to those obtained numerically and experimentally by Girshick et al. (1993).     

A numerical investigation of aerosol dynamics in a wall-less reactor

This paper describes a numerical investigation of aerosol formation during silane decomposition in a wall-less reactor. The wall-less reactor is amenable to numerical investigation because the homogeneous chemical reactions leading to the formation of solid particles are isolated from heterogeneous effects, such as occur at the walls of a laminar flow aerosol reactor. The flow/heat transfer and gas-phase chemical kinetics are simulated utilizing separate one-way coupled models. The aerosol dynamics model is based on a simplified sectional model originally developed by Okuyama et al. This model is modified to allow for the simulation of particle growth via condensation. Simulations have been performed which indicate that particle growth via condensation may be an important process. Additionally, the effects of total reactor pressure, temperature and inlet silane concentration on the dynamics of the aerosol population have been investigated. Conditions which result in the formation of larger and more numerous particles have been identified.     

流化床反应器中气相丙烯聚合反应的动力学和预测控制(英文)

A two-phase dynamic model, describing gas phase propylene polymerization in a fluidized bed reactor, was used to explore the dynamic behavior and process control of the polypropylene production rate and reactor temperature. The open loop analysis revealed the nonlinear behavior of the polypropylene fluidized bed reactor, jus- tifying the use of an advanced control algorithm for efficient control of the process variables. In this case, a central- ized model predictive control （MPC） technique was implemented to control the polypropylene production rate and reactor temperature by manipulating the catalyst feed rate and cooling water flow rate respectively. The corre- sponding MPC controller was able to track changes in the setpoint smoothly for the reactor temperature and pro- duction rate while the setpoint tracking of the conventional proportional-integral （PI） controller was oscillatory with overshoots and obvious interaction between the reactor temperature and production rate loops. The MPC was able to produce controller moves which not only were well within the specified input constraints for both control vari- ables, but also non-aggressive and sufficiently smooth for practical implementations. Furthermore, the closed loop dynamic simulations indicated that the speed of rejecting the process disturbances for the MPC controller were also acceotable for both controlled variables.     

Model based control of a liquid swelling constrained batch reactor subject to recipe uncertainties

This work presents the application of nonlinear model predictive control (NMPC) to a simulated industrial batch reactor subject to safety constraint due to reactor level swelling, which can occur with relatively fast dynamics. Uncertainties in the implementation of recipes in batch process operation are of significant industrial relevance. The paper describes a novel control-relevant formulation of the excessive liquid rise problem for a two-phase batch reactor subject to recipe uncertainties. The control simulations are carried out using a dedicated NMPC and optimization software toolbox OptCon which implements efficient numerical algorithms. The open-loop optimal control problem is computed using the multiple-shooting technique and the arising nonlinear programming problem is solved using a sequential quadratic programming (SQP) algorithm tailored for large-scale problems, based on the freeware optimization environment HQP. The fast response of the NMPC controller is guaranteed by the initial value embedding and real-time iteration technologies. It is concluded that the OptCon implementation allows small sampling times and the controller is able to maintain safe and optimal operation conditions, with good control performance despite significant uncertainties in the implementation of the batch recipe.     

A NOVEL SPINNING DISC CONTINUOUS STIR TANK AND SETTLER REACTOR (SDCSTR) MODEL FOR CONTINUOUS SYNTHESIS OF TITANIA: A PHENOMENOLOGICAL MODEL

A novel phenomenological spinning disc continuous stir tank and settler reactor (SDCSTR) has been modeled for continuous synthesis of titania from its chloride precursor and water in which the desired polymorph, particle size, and distribution are controlled by the characteristics of the atomized inlet reagents, disc, and tank stir rate. This energy-efficient reactor generates seeding nuclei in the aerosol reacting volume that are then deployed for heterogeneous nucleation and particle growth in the metastable reacting volume of the aqueous (sol) process. Once at steady state, the enhanced TiO₂ nanoparticles due to the OH^?–H⁺ chemisorbed on the surface (with surface energy 0.5 < σ < 2.11 N/m) are continuously withdrawn at a rate equivalent to the particle settling rate from the settler. This reactor model eliminates the energy intensity required in traditional chemical vapor deposition (CVD) and aerosol reactors and provides better control for particle growth and size distribution by increasing particle residence time in the metastable zone of the aqueous (sol) reaction stage.     

Determination of Arbitrary Moments of Aerosol Size Distributions from Measurements with a Differential Mobility Analyzer

A method to determine arbitrary moments of aerosol size distributions from differential mobility analyzer measurements has been proposed. The proposed method is based on a modification of the algorithm developed by Knutson and Whitby to calculate the moments of electrical mobility distributions. For this modification, the electrical mobility and the charge distribution have been approximately expressed by power functions of the particle diameter. To evaluate the validity of the approximation, we have carried out numerical simulations for typical size distributions. We have found that for typical narrowly distributed aerosols such as polystyrene latex particles and particles that arise in the tandem differential mobility analyzer configuration, the distribution parameters can be accurately determined by this method. For a log-normally distributed aerosol, the accuracy of the distribution parameters determined by this method has been evaluated as a function of the geometric standard deviation. We have also compared the accuracy of the proposed method with other existing methods in the case of the asymmetric Gaussian distribution.     

Multi-scale modeling and control of fluidized beds for the production of solar grade silicon

In this paper we develop a multi-scale model to describe the growth of silicon particles due to chemical vapor deposition (CVD) in a fluidized bed reactor (FBR). The reactor system is designed to make poly-silicon for solar cell applications by thermal decomposition of silane. The complex interplay between the continuous and the disperse phases and CVD onto the silicon particles in the FBR is modeled using three modules — Computational Fluid Dynamics (CFD), Reaction Module and Population Balance Module (PBM). The Computational Fluid Dynamics (CFD) module describes the hydrodynamics via momentum, mass and heat transfer between different phases. The reaction module describes the homogeneous gas phase reactions and deposition on polycrystalline silicon particles. The population balance represents the dynamic evolution of the particle size distribution. By coupling together the modules, we provide a complete multi-scale model for the particulate CVD process. The resulting nonlinear, multi-scale model is solved using COMSOL Multi-physics and MATLAB. The results from the proposed model match the experimental data obtained from a pilot scale reactor. An inventory controller maintains the void fraction and in turn the average diameter of the silicon particles at the exit.     

Probabilistic reactor design in the framework of elementary process functions

Computational process models in combination with innovative design methodologies provide a powerful reactor design platform. Yet, model-based design is mostly done in a pure deterministic way. Possible uncertainties of the underlying model parameters, prediction errors due to simplifying assumptions regarding the reactor behavior and suboptimal realizations of the design along the reaction coordinate are in general not considered. Here we propose a systematic design approach to directly account for the impact of such variabilities during the design procedure. The three level design approach of Peschel et al. (2010) based on the concept of elementary process functions (EPF) serves as basis. The dynamic optimizations on each level are extended within a probabilistic framework to account for different sources of randomness. The impact of these sources on the performance prediction of a design is quantified and used to robustify the reactor design aiming at a more reliable performance and thus design prediction. The uncertainties of model parameters, non-idealities of the reactor behavior and inaccuracies in the design are included via statistical moments. By means of the sigma point method (Julier and Uhlmann, 1996) random variables are mapped to the design objective space via the nonlinear process model. Importantly, this work introduces a full probabilistic orthogonal collocation approach, i.e. random and stochastic variables can be described. Whereas the former one relates to randomness independent on the reaction time (e.g. kinetic model parameters or initial conditions), the latter one describes stochasticity along the reaction time (e.g. fluctuating pressure or temperature control). As an example process the hydroformylation of 1-dodecene in a thermomorphic solvent system consisting of n-decane and N,N-dimethylformamide is considered.Our probabilistic EPF approach allows designing robust optimal reactors, which operate within an estimated confidence at their expected optimum considering almost any kind of randomness arising in the design procedure. An additional value is that with increased predictive power of the reactor performance its embedding in an overall process is strongly simplified.     

Analysis of the Rapid Carbothermal Reduction Synthesis of Ultra-Fine Silicon Carbide Powders

A nondimensionalized and scaled nonisothermal model is developed for the "rapid carbothermal reduction" synthesis of sub-micron silicon carbide particles in an aerosol flow reactor to determine the minimum parametric representation of the system. Seven dimensionless groups are needed to completely describe the system, and these dimensionless groups are varied to determine the effects of the furnace wall temperature, inlet carbon particle size, carrier gas flow rate, and solids feed rate on final product quality. Analysis shows that radiation dominates the heating process, sintering dominates the primary particle growth, and conversion is controlled with precursor carbon particle size, wall temperature, and carrier gas flow rate.     

Low Pressure Aerosol Flow Reactor

In this work we report the development of a novel low pressure aerosol flow reactor for the determination of the kinetic parameters of fast heterogeneous processes. The experimental apparatus consists of a spray atomizer to introduce aerosols into a low pressure zone; a fast flow reactor for kinetic measurements and an IR spectrometer and mass spectrometer for concentration measurements. The surface area distribution and number density of the aerosol particles are determined from their infrared spectra and the decay kinetics are determined by monitoring the disappearance rates of the gas phase species (with a mass spectrometer) as a function of the aerosol properties. We report the application of this apparatus to the investigation of the uptake of acetone by liquid water aerosols (0.1–20 μ m diameter) at room temperature and a pressure of 35 Torr. These measurements yielded a value of the mass accommodation coefficient, α, of 3.6 _{? 2} ^{+ 3.1} × 10 ^{? 3} .     

Nonlinear control of rapid thermal chemical vapor deposition under uncertainty

This article focuses on nonlinear control of a rapid thermal chemical vapor deposition (RTCV'D) process in the presence of significant model uncertainty and disturbances. Initially, a detailed mathematical model of the RTCVD process is presented consisting of a nonlinear parabolic partial differential equation (PDE) which describes the time evolution of the wafer temperature across the radius of the wafer, coupled with a set of nonlinear ordinary differential equations (ODEs), which describe the time evolution of the concentrations of the various species. Then, the synthesis of a nonlinearoutput feedback controller based on the RTCVD process model by following a control methodology for nonlinear parabolic PDE systems introduced in (Baker and Christofides, 1998) is discussed. The controller uses measurements of wafer temperature at four locations to manipulate the power of the top lamps in order to achieve uniform temperature, and thus, uniform deposition of the thin film on the wafer over the entire process cycle. The nonlinearoutput feedback controller is successfully implemented through computer simulations and is shown to attenuate significant model uncertainty end disturbances and to outperform a proportional integral (PI) control scheme.     

Modal Aerosol Dynamics Modeling

ABSTRACT

The derivation of the governing equations for modal aerosol dynamics (MAD) models is presented. MAD models represent the aerosol size distribution as an assemblage of distinct populations of aerosol, where each population is distinguished by size or chemical composition. The size distribution of each population is approximated by an analytical modal distribution function; usually by a lognormal distribution function. By substituting the MAD representation of aerosol size distributions into the governing equation for aerosol processes, the governing differential equations for MAD models are derived. These differential equations express the time dependence of the moments of the aerosol size distribution and are called Moment Dynamics Equations (MDEs). The MDEs for Continuously-Stirred Tank Aerosol Reactors (CSTARs) are also derived.     

Simulation of nanoparticle synthesis in an aerosol flame reactor using a coupled flame dynamics–monodisperse population balance model

Flame aerosol synthesis is one of the commonly employed techniques for producing ultra fine particles of commodity chemicals such as titanium dioxide, silicon dioxide and carbon black. Large volumes of these materials are produced in industrial flame reactors. Particle size distribution of product powder is the most important variable and it depends strongly on flame dynamics inside the reactor, which in turn is a function of input process variables such as reactant flow rate and concentration, flow rates of air, fuel and the carrier gas and the burner geometry. A coupled flame dynamics–monodisperse population balance model for nanoparticle synthesis in an aerosol flame reactor is presented here. The flame dynamics was simulated using the commercial computational fluid dynamics software CFX and the particle population dynamics was represented using a monodisperse population balance model for continuous processes that predicts the evolution of particle number concentration, particle volume and surface area. The model was tested with published experimental data for synthesis of silica nanoparticles using different burner configurations and with different reactor operating conditions. The model predictions for radial flame temperature profiles and for the effects of process variables like precursor concentration and oxygen flow rate on particle specific surface area and mean diameter are in close agreement with published experimental data.     

Characteristics‐Based Model Predictive Control of a Catalytic Flow Reversal Reactor

This paper describes the formulation and tuning of a model‐based controller for a catalytic flow reversal reactor (CFRR). A plug flow non‐linear pseudo‐homogeneous mathematical representation of the process is used to model the mass and energy transport phenomena for the model‐based controller. A combination of the method of characteristics and model predictive control (MPC) technology is used to formulate the controller (Shang et al., Ind. Eng. Chem. Res. 43 (9) 2140–2149 (2004)). Mass extraction from the midsection of the reactor is used as the manipulated variable. Numerical simulations are used to show the performance of the formulated controller. The performance of the controller is evaluated on a simulated catalytic flow reversal reactor unit for combustion of lean methane streams for reduction of greenhouse gases emissions.     

Aerosol Growth in a Steady-State,Continuous Flow Chamber: Application to Studies of Secondary Aerosol Formation

An analytical solution for the steady-state aerosol size distribution achieved in a steady-state, continuous flow chamber is derived, where particle growth is occurring by gas-to-particle conversion and particle loss is occurring by deposition to the walls of the chamber. The solution is presented in the case of two condensing species. By fitting the predicted steady-state aerosol size distribution to that measured, one may infer information about the nature of the condensing species from the calculated values of the species's molecular weights. The analytical solution is applied to three sets of experiments on secondary organic aerosol formation carried out in the U.S. Environmental Protection Agency irradiated continuous flow reactor, with parent hydrocarbons: toluene, f -pinene, and a mixture of toluene and f -pinene. Fits to the observed size distributions are illustrated by assuming two condensing products for each parent hydrocarbon; this is a highly simplified picture of secondary organic aerosol formation, which is known to involve considerably more than two condensing products. While not based on a molecular-level model of the gas-to-particle conversion process, the model does allow one to evaluate the extent to which the observed size distribution agrees with that based on a simple, two-component picture of condensation, and to study the sensitivity of those size distributions to variation of the essential properties of the condensing compounds, such as molecular weight. An inherent limitation of the steady-state experiment is that it is not possible to calculate the vapor pressures of the condensing species.