Global approximations of unsteady‐state adsorption,diffusion, and reaction in a porous catalyst

The pore diffusion model that describes unsteady‐state adsorption, diffusion, and reaction in a porous catalyst is in the form of a parabolic partial differential equation. To relieve computational loads, approximate ordinary differential equations are often used and they can be derived from the transfer function between the surface and average concentrations in the particle. The transfer function shows half‐order behaviors at the high‐frequency range. The rational transfer functions cannot describe well this half‐order behavior. Here, introducing the half‐order term to rational transfer function candidates for approximation, models valid throughout low‐ and high‐frequency ranges are derived. Since the proposed approximate models are valid globally, they can be applied to reactive porous catalysts easily. They can also be used for noninteger shape factors that will show better performances for adsorbents different from ideal geometries of infinite slab, infinite cylinder and sphere, and for biporous adsorbents. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2540–2548, 2013     

Closed-loop identification of systems using hybrid Box-Jenkins structure and its application to PID tuning

The paper describes a closed-loop system identification procedure for hybrid continuous-time Box-Jenkins models and demonstrates howit can be used for IMC based PID controller tuning. An instrumental variable algorithmis used to identify hybrid continuous-time transfer function models of the Box-Jenkins formfromdiscretetime prefiltered data, where the process model is a continuous-time transfer function, while the noise is represented as a discrete-time ARMA process. A novel penalizedmaximum-likelihood approach is used for estimating the discrete-time ARMA process and a circulatory noise elimination identification method is employed to estimate process model. The input-output data of a process are affected by additive circulatory noise in a closedloop. The noise-free input-output data of the process are obtained using the proposed method by removing these circulatory noise components. The process model can be achieved by using instrumental variable estimation method with prefiltered noise-free input-output data. The performance of the proposed hybrid parameter estimation scheme is evaluated by the Monte Carlo simulation analysis. Simulation results illustrate the efficacy of the proposed procedure. The methodology has been successfully applied in tuning of IMCbased flowcontroller and a practical application demonstrates the applicability of the algorithm.     

Similarity Solutions of Marangoni Convection Boundary Layer Flow with Gravity and External Pressure

This study is focused on a steady dissipative layer, which is generated by Marangoni convection flow over the surface resulted from an imposed temperature gradient, coupled with buoyancy effects due to gravity and external pressure. A model is proposed with Marangoni condition in the boundary conditions at the interface. The similarity equations are determined and approximate analytical solutions are obtained by an efficient transformation, asymptotic expansion and Pade approximant technique. For the cases that buoyancy force is favorable or unfavor-able to Marangoni flow, the features of flow and temperature fields are investigated in terms of Marangoni mixed convection parameter and Prantl number.     

Methodology to Estimate the Transfer Function of Individual Differential Mobility Analyzers

A method to estimate the nonideal features of the transfer function of individual differential mobility analyzers (DMA) was developed and tested experimentally. This was up to now an unsolved problem, which is important for the precision in DMA measurements. The method involves three DMAs of unknown characteristics, which are used in three rounds of experiments with two DMAs according to a fixed schedule. The width of the transfer functions of the three DMAs is obtained in a single fitting procedure where one parameter is fitted to each DMA transfer function and the particle losses in each DMA are calculated in direct relation to that parameter and parameters known from the experiment. It was shown that the proposed method could solve the apportioning problem and unambiguously estimate the transfer function width and the particle losses in each of the DMAs.     

Analysis of the dynamics of paste drying in a spouted bed

Although there are some models available in the literature for paste drying in spouted beds, few of them have focused on transient analysis of dynamical systems. Our objective was to integrate experiments and simulations of a dynamic model to investigate the transient response to disturbances and interruptions in the feed flow during paste drying in a spouted bed with inert particles. The spouted bed consisted of a cylindrical column with 50.0?cm of height and 20.0?cm of diameter. Drying tests were performed at inlet gas temperatures of 70?°C and 100?°C and inlet air flow 30% above the minimum spouting velocity. A 5% w/w suspension of calcium carbonate was used as paste material, and glass spheres of 2.2?mm were used as inert materials. Different patterns of step function changes were tested in the paste feed flow rate. A lumped parameter model was used to predict mass and heat transfer during the drying. Experiments and simulations were in good agreement.     

The mass and heat transfer process through the door seal of refrigeration

As one of the main reasons causing leakage heat load in a refrigerator, mass and heat transfer through refrigerator door seal is of great importance to be studied. In this paper, a model is presented for numerical simulation of mass and heat transfer process through refrigerator door seal, and an experiment apparatus is designed and set up as wel for comparison. A two-dimensional model and tracer gas method are used in simulation and experiment, respectively. It can be found that the relative deviations of air infiltration rate between the simulated results and experimental results were less than 1％, and the temperature difference errors at two special points of the door seal were less than 2.03 °C. In conclusion, the simulated results are in good agreement with the experimental results. This paper initially sets up a model that can accurately simulate the heat and mass transfer through the refrigerator door seal, and the model can be used in refrigerator door seal optimization research in the follow-up study.     

Electrochemical treatment of wastewater containing phenolic compounds: oxidation at boron-doped diamond electrodes

This work investigates the performance of BDD electrodes during oxidation of aqueous solutions of phenol. The main reaction intermediates are identified, the effect of operating conditions on the faradic yield of the process, and the degree of mineralization achievable under different experimental conditions are evaluated. Due to the crucial role of mass transfer in the process, an impinging jet cell is used for the experiments. The results indicate that if a minimum value of current density is imposed, suitable initial conditions can be set at which the removal of the reactant is always under mass transfer control and the process is carried out at a faradic yield of about unity, up to the near-complete disappearance of total organic load. High current density and high mass transfer coefficient must be used in order to carry out the process with high space-time yield. The performance of BDD is compared to that obtained at Ti/RuO₂ anodes.     

On the robustness of the soft sensors used to monitor a vial freeze-drying process

Process monitoring is a key issue in pharmaceutical freeze-drying to evaluate if the limit product temperature is approached, to identify the ending point of the main drying stage, and to estimate the value of some parameters of a mathematical model of the process so that it can be used for cycle optimization. Soft sensors can be used for this purpose: three algorithms, based on the extended Kalman filter and on product temperature measurement, have been compared in this study; they differ on the number of estimated parameters and on the way used to set their initial estimates. Results evidence that the accuracy of estimates is strongly dependent on the initial values of model parameters, and soft sensors #1 and #2 require a preliminary investigation to get accurate initial estimates of the heat and mass transfer coefficients. Soft sensor #2 should be preferred as it just requires an initial estimate of the heat transfer coefficient. Significant advantages are obtained with soft sensor #3: accurate estimates are obtained whichever values of the parameters are used to start the calculations (provided that reasonable values are used) and, thus, it can be effectively used to monitor the freeze-drying cycle without any preliminary investigation. Soft sensor #3 should thus be preferred to the other tools for freeze-drying monitoring.     

Reaction Delay of Aluminum in Condensed Explosives

A universal empirical relation is derived to predict the reaction delay times of aluminum particles as a function of particle diameter and gas temperature in explosives. The predicted delay times are shown to be in reasonable agreement with experimental data obtained in both low temperature and high temperature explosives. A convective heat transfer model is used to estimate the surface temperature of the solid aluminum particles. The reaction delay time of aluminum is shown to be close to the time when the particle surface reaches the pressure dependent melting point of aluminum.     

Approximation by Neural Network of the Effectiveness Factor in a Catalyst with Deactivation

A method for estimating the effectiveness factor in a catalytic pellet submitted to deactivation using neural networks is proposed. When a catalyst is deactivated by poisoning, the function η = η (t,ϕ) presents a minimum when strong diffusional resistances exist. In this particular case, the few methods published in the literature are not able to calculate η. A feedforward neural network trained with the back‐propagation algorithm was used to estimate the effectiveness factor. This methodology is especially useful when the function η = η (t,ϕ) presents a minimum. The predicted values using the neural network successfully fit those obtained solving the differential equation system. An extrapolation using temperatures outside the training range can be satisfactorily performed.     

An integrated computational fluid dynamics-process model of natural circulation steam generation in a coal-fired power plant

A semi-detailed 1D process model for steam generation in a natural circulation boiler (thermosyphon loop) is linked to a detailed 3D computational fluid dynamics (CFD) model of the coal-fired furnace. The CFD model has been validated against typical data from a 500 MW_e subcritical power plant. The heat flux distribution data from the CFD model are regressed into a function of height and used to drive the process model. The complex physics occurring in the furnace are coupled with the thermosyphon steam loop, resulting in circulation flows of around 4 times the feed flow. The steam side heat transfer coefficients are predicted in the process model and so the overall heat transfer coefficient for use in the CFD simulation can be re-evaluated as a function of height. The recalculated heat flux distribution is almost identical to the original, because the dominant resistance to heat flow is on the furnace side.     

Steady state hydrodynamics and mass transfer characteristics of a karr extraction column

The steady state hydrodynamics of the holdup in a 15 cm column agree quite well with mechanistic predictions at conditions approaching flooding. In the presence of mass transfer (acetic acid from the dispersed kerosene phase to the continuous water phase), the holdup data below flooding are not well predicted by the model due to enhanced droplet coalescence. The prediction of holdup at flooding is a function of the ratio of the flow rates but is independent of the physicochemical properties of the extraction system, and therefore can be used to estimate the flooding holdup regardless of the occurrence of mass transfer. In the second part of the paper, steady state mass transfer characteristics of the column were also simulated using a mechanistic model. Despite the difficulty of estimating parameters such as the mass transfer coefficient, the model curves could be arbitrarily adjusted to fit observed exit concentrations. These steady state results provide useful insights on the non-linearity of the system from a control viewpoint.     

Modeling of solid-state polymerization of poly(ethylene terephthalate)

A mathematical model for solid-state polymerization of poly(ethylene terephthalate) was developed. The effects of temperature and chain entanglement on chain mobility were considered to estimate the rate constants of chemical reactions. The diffusivities of volatile byproducts could be determined using the free volume theory.^13,14 The model predictions were validated with experimental data reported in the literature. In addition, assuming that the concentration profiles of volatile byproducts in spherical particles are described by a sinusoidal function, the mass transfer rate of the byproducts at a given time could be derived as an ordinary differential equation that can be easily treated. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 68:837–846, 1998     

Methods to measure and predict the transfer function size dependence of individual DMAs

In this study of the transfer function of copies of the Vienna-type differential mobility analyser (DMA) it was found that three, supposedly identical, DMAs exhibited distinct differences with respect to the width of the transfer function. This means that the transfer function of a DMA needs to be determined on an individual basis in order to obtain accurate results from DMA measurements. The size dependence of the transfer function width and the penetration of three DMAs were investigated experimentally in a broad range of Peclet numbers (400–400 000). Two of the three DMAs exhibited transfer function widths in excess of the broadening induced by diffusion. The size dependence of the width of all three DMAs could be explained within a few percents by assuming an instrument-specific, size-independent broadening in addition to diffusion broadening. The penetration was evaluated by relating to deposition in a circular tube. Excellent agreement between the experimental data and the simple model was obtained. The penetration study was extended to include literature data, showing that the simple model could be applied and that there are distinct differences between different DMA types. The results of this study indicate that the size dependence of the width of the transfer function and the penetration can be estimated by measuring the transfer function for a single particle size, thus greatly reducing the amount of work required by DMA users to characterise their instruments.     

Nonlinear observers for parameter estimation in a solution polymerization process using infrared spectroscopy

Adaptive and high gain nonlinear observers are used for state and parameter estimation in an industrial polymerization process. The solution homopolymerization of acrylic acid is considered. The process is monitored online by near infrared spectroscopy giving the residual amount of monomer. Using this measurement, a continuous adaptive observer is first constructed to estimate the concentration of radicals. A second high gain continuous-discrete observer uses off-line measurements of the polymer molecular weight to estimate the termination rate coefficient that might be time varying due to the gel effect. The transfer to solvent rate coefficient is estimated under steady-state conditions and is assumed to be constant during the reaction. The identified model is validated by varying the process parameters: the concentrations of solvent, monomer, radicals and the residence time in the reactor with interest of their impact on the polymer molecular weight.     

A heat and mass transfer study—analysis of continuous processes for the coloration of polyester fabric. I. Heat transmission to the fabric system—fabric,fiber, and dye particles

The three continuous processes (thermosol, high temperature steaming, and heat transfer printing) for the coloration of polyester and the involved equipment are briefly reviewed. A simple model for the transient heating of a body is developed, the model [eq.(22)] comprises a specific area of transfer parameter (A_s): area through which transport (of heat) takes place per unit mass of the body. This model is used in order to estimate the relative heating rates for the different geometrical approximations present in the fabric system: plate (fabric), cylinder (fiber), and sphere (dye particle). Results obtained from the more exact numerical analysis solution are used for investigating the limitations of the simple heat transfer model.     

Dynamic modeling of fixed-bed adsorption of flue gas using a variable mass transfer model

This study introduces a dynamic mass transfer model for the fixed-bed adsorption of a flue gas. The derivation of the variable mass transfer coefficient is based on pore diffusion theory and it is a function of effective porosity, temperature, and pressure as well as the adsorbate composition. Adsorption experiments were done at four different pressures (1.8, 5, 10 and 20 bars) and three different temperatures (30, 50 and 70 °C) with zeolite 13X as the adsorbent. To explain the equilibrium adsorption capacity, the Langmuir-Freundlich isotherm model was adopted, and the parameters of the isotherm equation were fitted to the experimental data for a wide range of pressures and temperatures. Then, dynamic simulations were performed using the system equations for material and energy balance with the equilibrium adsorption isotherm data. The optimal mass transfer and heat transfer coefficients were determined after iterative calculations. As a result, the dynamic variable mass transfer model can estimate the adsorption rate for a wide range of concentrations and precisely simulate the fixed-bed adsorption process of a flue gas mixture of carbon dioxide and nitrogen.     

应用傅立叶解析的参数估值法——固定床流体与颗粒间给热系数的测定

采用任意波形的输入温度信号对固定床进行温度应答实验,根据实验结果,对固定床的Disperison-Concentric模型进行傅立叶解析,在Re数0.5到229的范围内,拟合确定固定床中流体与颗粒的给热系数。 结果表明:在层流区,流体与颗粒间传热的Nu数并不随Re数的下降而减小。     

Design of stable steam injectors for continuous heating

Continuous direct steam injection systems are used in industry to rapidly raise the temperature of process streams either for heating or for sterilization purposes. High heat transfer rates can be achieved using this method, as compared with other methods e.g. shell and tube heat exchangers. Currently, there are no rational procedures available for designing steam injectors for stable operation. Flow visualization studies and pressure measurements have shown that three flow regimes; bubbling, jetting and intermittent steam/water flow exist, in direct steam injection into continuously flowing water. These flow regimes are a function of process conditions and orifice diameter. A semi-quantitative flow regime map for a range of process conditions has been drawn up. Bubbly flows give rise to the highest levels of noise due to bubble oscillations. This type of flow should therefore be avoided. The most stable flow regime, in terms of noise levels generated and hydrodynamic considerations is the jetting regime. Models have been derived for each flow regime; good agreement is found between experimental and theoretical data. A dimensionless number (Bubble/Jet number) has been defined, which can be used to predict transitions between bubbling and jetting flows. This dimensionless number, together with the flow regime map can be used to design stable, relatively quiet steam injection systems.