Engineering Model of Friction of Gas‐Solids Flow in a Jet Mill Nozzle

In this study we develop a model for estimating particle friction against the wall of a jet mill nozzle. The computation is reduced to a definition of conventional force acting on particles in a polydispersed stream. It is assumed that energy losses due to friction are caused by multiple particle collisions against the nozzle walls. The proposed model is oriented to calculating jet mill nozzles and is much simpler than previously applied methods. A parametric study of the proposed model was carried out and the effect of particle friction on particle and gas velocities was derived.     

Modeling of Kinetic Expressions for the Reduction of NOx by Hydrogen in Oxygen‐Rich Exhausts Using a Gradient‐Free Loop Reactor

The reduction of NO_x by hydrogen under lean conditions is investigated in a gradient‐free loop reactor. Using this computer‐controlled reactor, the reaction rates can be measured under exact isothermal conditions. Systematic variation of the input concentrations of hydrogen, nitric oxide, oxygen as well as reaction temperature provides a complete data set of reaction rates for the given reaction system. A number of kinetic rate expressions were evaluated for their ability to fit the experimental data by using toolboxes of MATLAB. The temperature influence on reaction rate constants and adsorption equilibrium constants were correlated simultaneously using Arrhenius and van’t Hoff equations, respectively. The kinetic rate expression based on a Langmuir‐Hinshelwood‐type model describes the data and the model can be improved by introducing a correction term in square root of hydrogen partial pressure over the range of conditions investigated.     

Numerical Calculations of Spray Roasting Reactors of the Steel Industry with Special Emphasis on Fe2O3‐Particle Formation

This work presents numerical calculations for the lay‐out of spray roasting reactors for the steel industry. In these reactors, a pickling liquor based on water and HCl containing FeCl₂ is regenerated in a combustor leading to the formation of Fe₂O₃ particles. For the lay‐out of these reactors, detailed knowledge of the flow and temperature field, the associated gas phase reactions, and especially, of the formation of the Fe₂O₃ particles is required. An extended particle formation model is presented which is based on earlier work. Finally, results for an industrial spray roasting reactor are given showing the potential of the numerical tools developed for the improvement of the technical lay‐out of such thermal reactors.     

Practical Consequences of Non‐Linear Effects in Asymmetric Synthesis

The fundamental principles of non‐linear effects (NLE) are reviewed. Particular emphasis is placed on the case of asymmetric amplification, since it allows one to perform useful chemistry with a non‐enantiopure chiral auxiliary. A strong asymmetric depletion in a catalytic reaction may lead to an underestimation of the actual enantioselectivity of the fully resolved ligand. The study of NLE's is also proving useful as a mechanistic tool in asymmetric catalysis. Similar concepts may be extended to chiral reagents or to kinetic resolution. 1. What is a Non‐Linear Effect in Asymmetric Synthesis? 2. The Conditions for Observing a Non‐Linear Effect in Enantioselective Catalysis 3. Some Simple Models of NLE in Enantioselective Catalysis 4. Comparison of the Sizes of Asymmetric Amplifications 5. Rates and Non‐Linear Effects in Asymmetric Catalysis 6. Non‐Linear Effects Involving Chiral Reagents 7. Mechanistic Applications of Non‐Linear Effects 8. Synthetic Applications 9. Concluding Remarks     

Effects of Chaotic Temperature Fluctuations on the Heat Transfer Coefficient in Liquid‐Liquid‐Solid Fluidized Beds

The effect of chaotic temperature fluctuations on the immersed heater‐to‐bed heat transfer coefficient (h) are investigated in a liquid‐liquid‐solid fluidized bed (0.152 m ID × 2.5 m in height). The time series of temperature fluctuations are measured and analyzed by means of the multidimensional phase space portraits and Kolmogorov entropy (K), in order to characterize the chaotic behavior of heat transfer coefficient fluctuations in the bed. The overall heat transfer coefficient is inversely proportional to the Kolmogorov entropy of temperature fluctuations, as well as the fluctuation range of heat transfer coefficient (Δh_i). The Kolmogorov entropy and fluctuation range of the heat transfer coefficient (Δh_i) increase with increasing dispersed phase velocity, but decrease with increasing particle size. However, they attain their minima with variation of the continuous phase velocity as well as the bed porosity, at which point the flow regime of particles in the beds changes. The overall heat transfer coefficient is directly correlated with the Kolmogorov entropy, as well as the fluctuation range of heat transfer coefficient.     

Modeling Gas‐Solid Reactions in the Bed of a Rotary Kiln

When dealing with gas‐solid reactions in rotary kilns, it is necessary to realize that the total particle surface within the granular bed can be much larger than the outer surface of the bed. Depending on the reaction conditions this inner surface can contribute considerably to the chemical conversion in the kiln. In this paper, a model is presented, which describes the reaction within the bed for the case of bed movement according to the cascade mode. In this case, gas is drawn into the rotating bed together with the particles. As a key quantity, an effectiveness factor η of the bed is defined. It is the ratio of the actual conversion to the conversion that would occur if the concentration of the reacting component remained unchanged throughout the bed, i.e. at its entrance concentration. An evaluation for reactions of order mshows this factor to be more than 25 % when the Damköhler number is smaller than 2. It approaches 100 % as the Damköhler number approaches 0. The Damköhler number used in this paper contains the void fraction of the particle bed in its denominator.     

Fault Detection of Non‐Linear Processes Using Kernel Independent Component Analysis

In this paper, a new non‐linear process monitoring method based on kernel independent component analysis (KICA) is developed. Its basic idea is to use KICA to extract some dominant independent components capturing non‐linearity from normal operating process data and to combine them with statistical process monitoring techniques. The proposed method is applied to the fault detection in the Tennessee Eastman process and is compared with PCA, modified ICA, and KPCA. The proposed approach effectively captures the non‐linear relationship in the process variables and showed superior fault detectability compared to other methods while attaining comparable false alarm rates.     

Simulation of Barium Sulfate Precipitation using CFD and FM‐PDF Modeling in a Continuous Stirred Tank

A mixing‐precipitation model combining computational fluid dynamics (CFD), finite‐mode PDF (probability density function) model, population balance and kinetic modeling has been proposed to simulate the barium sulfate precipitation process in a continuous stirred tank agitated by a Rushton turbine. The effect of various operating conditions such as impeller speed, feed concentration, feed position and mean residence time on the barium sulfate precipitation process is clearly demonstrated. It is shown that the mean crystal size increases by increasing the impeller speed and mean residence time. However, when the feed concentration is increased, the mean crystal size decreases. The predictions are in reasonable agreement with the experimental data in the literature.     

Model Development for MEOR Process in Conventional Non‐Fractured Reservoirs and Investigation of Physico‐Chemical Parameter Effects

A three‐dimensional multi‐component transport model in a two‐phase oil‐water system was developed. The model includes separated terms to account for the dispersion, convection, injection, growth and death of microbes, and accumulation. For the first time, effects of both wettability alteration of reservoir rock from oil wet to water wet and reduction in interfacial tension (IFT) simultaneously on relative permeability and capillary pressure curves were included in a MEOR simulation model. Transport equations were considered for the bacteria, nutrients, and metabolite (bio‐surfactant) in the matrix, reduced interfacial tension on phase trapping, surfactant and polymer adsorption, and effect of polymer viscosity on mobility of the aqueous phase. The model was used to simulate effects of physico‐chemical parameters, namely flooding time schedules, washing water flowrate, substrate concentration, permeability, polymer and salinity concentration on Original Oil In Place (OOIP) in a hypothetical reservoir.     

Non‐Linear Predictive Control of a Three‐Phase Catalytic Reactor

In this work, the predictive control of a three‐phase catalytic reactor is considered. A predictive control algorithm, which has a non‐linear internal model represented by functional link networks, is proposed. This network structure has been shown to have a good non‐linear approximation capability, with the advantage that the estimation of its weight is a linear optimization problem. The results show the potential of the proposed procedure when it is applied to the 2‐methyl‐cyclohexanol production process, which is a non‐linear, distributed parameter and time‐varying process, typical of many important industrial systems.     

Dynamic Simulation and Optimization of a Dual‐Type Methanol Reactor Using Genetic Algorithms

In this investigation, a dynamic simulation and optimization for an auto‐thermal dual‐type methanol synthesis reactor was developed in the presence of catalyst deactivation. Theoretical investigation was performed in order to evaluate the performance, optimal operating conditions, and enhancement of methanol production in an auto‐thermal dual‐type methanol reactor. The proposed reactor model was used to simulate, optimize, and compare the performance of a dual‐type methanol reactor with a conventional methanol reactor. An auto‐thermal dual‐type methanol reactor is a shell‐and‐tube heat exchanger reactor in which the first reactor is cooled with cooling water and the second one is cooled with synthesis gas. The proposed model was validated against daily process data measured of a methanol plant recorded for a period of 4 years. Good agreement was achieved. The optimization was achieve by use of genetic algorithms in two steps and the results show there is a favorable profile of methanol production rate along the dual‐type reactor relative to the conventional‐type reactor. Initially, the optimal ratio of reactor lengths and temperature profiles along the reactor were obtained. Then, the approach was followed to get an optimal temperature profile at three periods of operation to maximize production rate. These optimization approaches increased by 4.7 % and 5.8 % additional yield, respectively, throughout 4 years, as catalyst lifetime. Therefore, the performance of the methanol reactor system improves using optimized dual‐type methanol reactor.     

Input Multiplicity Analysis in a Non‐Isothermal CSTR for Acid‐Catalyzed Hydrolysis of Acetic Anhydride

Multiplicity analysis gives practical guidance for process design to eliminate difficult operating regions associated with input and output multiplicities. Continuous stirred tank reactors (CSTRs) present challenging operational problems due to complex behavior such as input and output multiplicities, ignition/extinction, parametric sensitivity, and nonlinear oscillations. In the absence of a unified mathematical theory for representing various nonlinear system characteristics, the present study was aimed at understanding the dynamic behavior of CSTRs by means of experiments and to link the experimental data to theoretical considerations for further detection and elimination of operating problems. Theoretical modeling and analysis of a non‐isothermal CSTR with acid‐catalyzed hydrolysis of an acetic anhydride system for input multiplicity are discussed. Theoretical modeling of a non‐isothermal CSTR using a root‐finding technique was carried out for predicting steady‐state temperatures. Alternatively, a mathematical model for a non‐isothermal CSTR using unsteady‐state mass and energy balance equations is proposed. Computer‐based simulation was carried out using a program developed in MATLAB for final transient temperature and time‐temperature data of the CSTR system under investigation. The results of a theoretical analysis conducted for confirming the existence of input multiplicity in non‐isothermal CSTRs with acid‐catalyzed hydrolysis of acetic anhydride were compared with experimental investigations for validation.     

Microwave Super‐Heated Boiling of Organic Liquids: Origin,Effect and Application

This paper reports the state of the art of the microwave super‐heated boiling phenomenon. When a liquid is heated by microwaves, the temperature increases rapidly to reach a steady temperature while refluxing. It happens that this steady state temperature can be up to 40 K higher than the boiling point of the liquid. With the same reactor, overheating is not observed under conventional heating. The bulk temperature of a microwaved solvent under boiling depends on many factors: physical properties of the solvent, reactor geometry, mass flow, heat flow, and electric field distribution. The influence of these factors is studied and discussed. The kinetics of homogeneous organic reactions shows an extension of Arrhenius behaviour into the super‐heated temperature region. Reaction rate enhancement of order 10–100 can thus be achieved, which is normally only possible under pressure. Finally, we present a model predicting reaction kinetics and yields under classical and microwave heating, based on predicted temperature profiles in agreement with experimental data.     

Identifiability of Non‐Linear Differential Algebraic Systems via a Linearization Approach

A system is identifiable if there exists a unique relationship between its input‐output behaviour and the parameter values. Differential‐Algebraic Equation (DAE) systems have an input‐output behaviour that is described by a parameterized set of ordinary differential and algebraic equations. Methods proposed in the literature to test the identifiability of DAE systems are based on the tools of differential algebra and rely on time‐differentiation of model equations. As a result, even when dealing with a few states and parameters, the calculations required for these methods may become intractable. An alternative, which we propose, is to linearize the non‐linear DAE system about some rest point and then test the identifiability properties of the linearized system. In this work, we show that strong local identifiability of the linearized DAE system provides a sufficient condition for the strong local identifiability of the original non‐linear DAE system.     

Non–Pt Catalyst Layer Operation in a PEM Fuel Cell: A Variable‐thickness Regime

A recently pubilshed experimental polarization curve of a PEM fuel cell with the non–Pt cathode catalyst layer (CCL) exhibits unusual feature: in the region of small current densities, the curve is close to linear. We report a model for the CCL performance which explains this effect. The model includes finite rate of the oxygen adsorption on the catalyst surface. Qualitatively, due to a very high exchange current density of the non–Pt catalyst, the ORR rate close to the membrane is determined by the potential–independent oxygen adsorption rate. This leads to a specific regime of the CCL operation, when only part of the CCL thickness contributes to current production, while the rest part is completely inactive. With the growth of the cell current, the active part increases in width, while the inactive part shrinks. The resulting polarization curve appears to be close to linear.     

Applying a Thermodynamic Model to the Non‐Stoichiometric Precipitation of Barium Sulfate

Thermodynamic models for aqueous Ba²⁺‐SO₄^2–‐Na⁺‐Cl^–‐solutions are compared in their accuracy to predict ion activities in saturated and supersaturated solutions. The Pitzer and the Bromley model are employed, taking into account ion pair formation of barium sulfate. Such models are then used to describe particle nucleation and growth, and finally they are imbedded in a mechanistic mixing‐precipitation model for a single feed semibatch process. The effect of the key operating parameters on the mean particle size is analyzed through simulations. The results are compared with previous experimental data, thus highlighting the significance of a proper choice of the thermodynamic model.     

Modeling and Simulation of Laser‐Induced Ignition of RDX Using Detailed Chemical Kinetics

A laser‐induced ignition model of RDX is developed, in which a detailed chemical kinetics scheme, containing 45 species and 231 reactions, is employed to describe the reaction in the gas phase. The model is spatially one‐dimensional and includes the transient development of two regions: the condensed phase and the gas phase. The condensed phase is composed of solid RDX, liquid RDX, and some decomposition products. The main physicochemical processes include melting, decomposation, vaporization, and radiation absorption. The gas phase is composed of RDX vapor and reaction products and the main processes include convection, diffusion, heat conduction, chemical reaction, and radiation absorption. With interfacial boundary conditions, the governing parameters for the condensed phase are conservation equations of energy and species concentration, whereas those for the gas phase are the conservation equations of mass, momentum, energy, and species concentration. A finite difference program using FORTRAN is compiled and numerical simulation is carried out. The ignition process of RDX is discussed from the distribution and evolution of temperature and species concentration. The model can provide a reasonable prediction of the phenomenon that the flame moves towards the surface immediately after ignition, and then departed from the surface.     

Three‐Dimensional Numerical Simulation of Dense Pneumatic Conveying of Pulverized Coal in a Vertical Pipe at High Pressure

A two‐fluid model based on the kinetic theory of granular flow was used to study three‐dimensional steady state flow behavior of dense phase pneumatic conveying of pulverized coal in a vertical pipe, where the average solid concentration ranges from 11 % to 30 %, and the transport pressure ranges from 2.6 Mpa to 3.3 Mpa. Since the solid concentration is rather high, a k–?–k_p–?_p model which considers the turbulence interaction between the gas and particle phase, was incorporated into the two‐fluid model. The simulation results including profiles of gas and particle phase axial velocity, profiles of solid concentration, profiles of the turbulence intensity of the particle phase, as well as the value of the pressure gradient were reported. Then, the influences of solid concentration and transport pressure on the flow behaviors were discussed. The experiment was also carried out to validate the accuracy of the simulation results which showed that the predictions of pressure gradient were in good agreement with the experimental data. Simulation results indicate that the location of maximal solid concentration deviates from the pipe center and the deviation becomes more obvious with the solid concentration increasing, which is analogous to the phenomenon in the liquid/solid flow. Besides, pressure gradient declines as the transport pressure decreases, which is validated by experiment described in the paper. Moreover, the analysis indicates that it is necessary to consider the turbulence of particles for the simulation of dense phase pneumatic conveying at high pressure.     

Simulation of a Bubble Column by Computational Fluid Dynamics and Population Balance Equation Using the Cell Average Method

An axisymmetric computational fluid dynamics (CFD) simulation coupled with a population balance equation (PBE) has been applied in simulating the gas‐liquid flow in a bubble column with an in‐house code. The novel feature of this simulation is the application of the cell average method in a CFD‐PBE coupled model for the first time. The predicted results by this method are compared with those by the traditional fixed pivot method and experimental data. For both methods, the simulated results are in reasonable agreement with the reported experimentally measured values. However, the bubble size distributions determined by the cell average method are slightly better than those found by means of the fixed pivot method, i.e., the latter provides a smaller peak value and a wider bubble size distribution, and the probability density function of large bubbles is higher.