A MODEL FOR THE SOLID CIRCULATION RATE IN A RECIRCULATING FLUIDIZED BED

The present work is an experimental study on the solid circulation rate in a recirculating fluidized bed and mathematical modeling of the same based on the experimental results and existing literature. The effects of particle size, spacing between the draft tube bottom and distribution plate, inventory of solids, and superficial gas velocity on the solid circulation rate are studied experimentally on a semicircular cold model recirculating fluidized bed. A mathematical model is developed for the solid circulation rate incorporating the effect of the various operating and design parameters. The model is based on the present experimental work and data available in the literature for the same kind of reactors. Dimensional analysis and nonlinear regression models are used to develop the model. The final model equation is a non linear relationship between the different operating and design variables. The model equation gives good results for the same kind of systems and can be used with reasonable accuracy for a wide range of operating parameters.     

A MODEL FOR THE SOLID CIRCULATION RATE IN A RECIRCULATING FLUIDIZED BED

The present work is an experimental study on the solid circulation rate in a recirculating fluidized bed and mathematical modeling of the same based on the experimental results and existing literature. The effects of particle size, spacing between the draft tube bottom and distribution plate, inventory of solids, and superficial gas velocity on the solid circulation rate are studied experimentally on a semicircular cold model recirculating fluidized bed. A mathematical model is developed for the solid circulation rate incorporating the effect of the various operating and design parameters. The model is based on the present experimental work and data available in the literature for the same kind of reactors. Dimensional analysis and nonlinear regression models are used to develop the model. The final model equation is a non linear relationship between the different operating and design variables. The model equation gives good results for the same kind of systems and can be used with reasonable accuracy for a wide range of operating parameters.     

Modeling of a Reverse Flow Reactor for Methanol Synthesis Modeling of a Reverse Flow Reactor for Methanol Synthesis

An accurate one-dimensional, heterogeneous model taking account of axial dispersion and heat transfer to the reactor wall, and heat conduction through the reactor wall for methanol synthesis in a bench scale reactor under periodic reversal of flow direction is presented. Adjustable parameters in this model are the effectiveness factors for each of the three reactions occurring in the synthesis and a factor for the bed to wall heat transfer coefficient correlation. Experimental data were used to evaluate these parameters and reasonable values of these parameters were obtained. The model was found to closely predict the reactor performance under a wide range of operating conditions, such as carbon oxide concentrations, volumetric flow rate, and cyclic period.     

Analysis of combustion efficiency in CFB coal combustors

Fluidized bed technology is well known for its high combustion efficiency and is widely used in coal combustion. In this study, the combustor efficiency has been defined and investigated for CFB coal combustor based on the losses using a dynamic 2D model. The model is shown to agree well with the published data. The effect of operating parameters such as excess air ratio, bed operational velocity, coal particle diameter and combustor load and the effect of design variables such as bed height and bed diameter on the mean bed temperature, the overall CO emission and the combustion efficiency are analyzed for the small-scale of CFBC in the presently developed model. As a result of this analysis, it is observed that the combustion efficiency decreases with increasing excess air value. The combustion efficiency increases with the bed operational velocity. Increasing coal particle size results in higher combustion efficiency values. The coal feed rate has negative effect on the combustion efficiency. The combustor efficiency considerably increases with increasing combustor height and diameter if other parameters are kept unchanged.     

MATHEMATICAL AND EXPERIMENTAL INVESTIGATION ON NOX RECOVERY IN FLUIDIZED BED ADSORBERS FOR EXHAUST GASES OF NITRIC ACID PLANTS

A mathematical model for sorption of NOx from exhaust gas of nitric acid plants by activated carbon (AC) in a fluidized bed is proposed based on two-phase flow theory of fluidization. To solve the proposed model a computer program has been developed. The output of this program reveals the effects of various parameters such as temperature, inlet gas velocity, particle diameter, and inlet gas concentration on the rate of adsorption. To evaluate the proposed model, a pilot-scale plant was erected and the obtained experimental data were compared with the values predicted by the model. A good agreement is observed between these values. Once the validity of the proposed model is checked, it could be used for obtaining the optimum operating condition for this type of bed.     

MATHEMATICAL AND EXPERIMENTAL INVESTIGATION ON NOX RECOVERY IN FLUIDIZED BED ADSORBERS FOR EXHAUST GASES OF NITRIC ACID PLANTS

A mathematical model for sorption of NOx from exhaust gas of nitric acid plants by activated carbon (AC) in a fluidized bed is proposed based on two-phase flow theory of fluidization. To solve the proposed model a computer program has been developed. The output of this program reveals the effects of various parameters such as temperature, inlet gas velocity, particle diameter, and inlet gas concentration on the rate of adsorption. To evaluate the proposed model, a pilot-scale plant was erected and the obtained experimental data were compared with the values predicted by the model. A good agreement is observed between these values. Once the validity of the proposed model is checked, it could be used for obtaining the optimum operating condition for this type of bed.     

Numerical investigation and experimental validation of the performance of a tubular packed bed reactor for hydrogenation of diene‐based polymers

A process which comprised a tubular reactor (that can be packed with different internal structures) has been modeled and theoretically analyzed for conducting the hydrogenation of nitrile butadiene rubber (NBR). The dynamics of the tubular reactor and the intrinsic hydrogenation kinetics are coupled, and detailed numerical simulations are performed under isothermal and isobaric conditions. The proposed model thus obtained involves coupled, nonlinear, partial differential equations (distributed parameter system). The effect of different reactor design parameters such as Peclet number, carbon–carbon double bond loading, mass transfer to reaction resistance, and solubility of hydrogen with respect to hydrogenation of the NBR has been investigated numerically. The conversions predicted using the proposed model for tubular packed bed reactor are compared with those possible in conventional plug flow reactor and continuous stirred tank reactor models. The optimal parameters and operating conditions for efficient production of hydrogenated NBR are suggested. Finally, the validity of the proposed model is confirmed by comparing the predicted and the experimental degree of hydrogenation obtained in a tubular reactor packed with Intalox saddles. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers     

Estimation of Kinetic Parameters for Hydrogenation Reactions Using a Genetic Algorithm

The kinetics of acetylene hydrogenation in a fixed‐bed reactor of a commercial Pd/Al₂O₃ catalyst has been studied. The hydrogenation reactor considered in this work is an essential part of a vinyl chloride monomer (VCM) plant. Three well‐known kinetic models were used to simulate the hydrogenation reactor under industrial operating conditions. Since none of the models provide appropriate prediction, the industrial data and calculated values were compared and optimum kinetic parameters were evaluated utilizing a genetic algorithm (GA) technique. The best kinetic parameters for the three models were determined under specified industrial operating conditions. The hydrogenation reactor was simulated using the estimated optimum kinetic parameters of the three models. Simulation results from the three models were compared to industrial data and the best kinetic model was found. This kinetic model with the evaluated optimum kinetic parameters can well predict the behavior of the industrial hydrogenation reactor to improve the performance of the process.     

Simulation and Analysis of a Tubular Fixed‐Bed Fischer‐Tropsch Synthesis Reactor with Co‐Based Catalyst

A two‐dimensional pseudohomogeneous reactor model is proposed to simulate the performance of fixed‐bed Fischer‐Tropsch synthesis (FTS) reactors by lumped thought. A CO consumption kinetics equation and a carbon chain growth probability model were incorporated into the reactor model. The model equations discretized by a two‐dimensional orthogonal collocation method were solved by the Broyden method. Concentration and temperature profiles were obtained. The validity of the reactor model against the pilot plant test data was investigated. Satisfactory agreements between model prediction values and experiment results were obtained. Further simulations were carried out to investigate the effect of operating conditions on the reaction behavior of the fixed‐bed FTS reactor.     

A simplified mathematical modeling for thermo-catalytic decomposition of methane over carbon black catalyst in a fluidized bed reactor

A mathematical model for thermo-catalytic decomposition of methane over carbon black catalysts in a fluidized bed was proposed. The simplified isothermal, uniform flow model was considered and implemented into a computer code to predict the reactor performance. The experiment of methane decomposition into hydrogen and carbon was carried out in a fluidized bed of I.D of 0.055 m and height of 1.0 m. The range of reaction temperature was 850–900 °C, gas velocity was 1.0–3.0 U _mf , and catalyst loading was 50–200 g. The reaction parameters for model equation were determined from the curve fittings and the comparison of experimental data with simulation results showed good agreement for fluidized bed reactor system. From the simulation results, the fluidized bed performance with different operating conditions were obtained, and this simple model can be used to predict the performance of a larger scale fluidized bed reactor and also in determining the optimum operating conditions.     

Optimal hybrid modeling approach for polymerization reactors using parameter estimation techniques

The dynamics of polymerization catalytic reactors have been investigated by many researchers during the past five decades; however, the emphasis of these studies was directed towards correlating process model parameters using empirical investigation based on small scale experimental setup and not on real process conditions. The resulting correlations are of limited practical use for industrial scale operations. A statistical study for the relative correlation of each of the effective process parameters revealed the best combination of parameters that could be used for optimizing the process model performance. Parameter estimation techniques are then utilized to find the values of these parameters that minimize a predefined objective function. Published real industrial scale data for the process was used as a basis for validating the process model. To generalize the model, an artificial neural network approach is used to capture the functional relationship of the selected parameters with the process operating conditions. The developed ANN-based correlation was used in a conventional fluidized catalytic bed reactor (FCR) model and simulated under industrial operating conditions. The new hybrid model predictions of the melt-flow index and the emulsion temperature were compared to industrial measurements as well as published models. The predictive quality of the hybrid model was superior to other models. The suggested parameter estimation and modeling approach can be used for process analysis and possible control system design and optimization investigations.     

Preparation of carbon aerogels with different pore structures and their fixed bed adsorption properties for dye removal

Controlled porosity carbon aerogels are prepared by a sol–gel polymerization method and the prepared materials are used as fixed bed adsorbents for dye removal. The influences of operating conditions and preparation factors on the adsorption of C. I. Reactive Red 2, as a model compound, from aqueous solution were investigated. Many column parameters were estimated at different stages and the Bed-Depth-Service-Time model was used to analyze the experimental data. The results showed that the adsorption bed capacity increased with increasing bed height, decreasing liquid flow rate and decreasing initial dye concentration. Moreover, the work indicated that the adsorption ability of the carbon aerogel could be controlled by adjusting the molar ratio of resorcinol to surfactant and carbonization conditions. In addition, the adsorption capacity could be improved when the carbon aerogel was activated by CO₂. The reasons for the difference in adsorption ability could be related to the different pore structure characteristics of various samples.     

An Eulerian modeling approach of wood gasification in a bubbling fluidized bed reactor using char as bed material

We present an Eulerian multiphase approach for modeling the gasification of wood in fluidized beds. The kinetic theory of granular material is used to evaluate constitutive properties of the dispersed solid phase. Comprehensive models for wood pyrolysis, char gasification and homogeneous gas phase reactions are taken into account. The dispersed solid phase within the reactor is modeled as three continuous phases, i.e., one phase representing wood and two char phases with different diameters. In contrast to most other studies we investigate a fluidized bed which consists of wood and char particles without additional inert particles such as limestone or olivine. 2D simulation results for a lab-scale bubbling fluidized bed reactor are presented and compared with experimental data for product gas and tar concentrations and temperature. We investigate the influence of two different classes of parameters on product gas concentrations and temperature: (i) operating conditions such as initial bed height, wood feeding rate, and reactor throughput and (ii) model parameters like thermal boundary conditions, primary pyrolysis kinetics, and secondary pyrolysis model. Two different pyrolysis models are implemented and are compared against each other. The numerical results indicate (i) a relatively low influence of the investigated operating conditions on the main product gas components, (ii) a high sensitivity of main product gas components CO and CO₂ on the thermal boundary condition, and (iii) a very strong influence of operating conditions and model parameters on the tar content in the product gas.     

Adsorption of Carbamazepine in Fixed Bed Columns: Experimental and Modeling Studies

The adsorption of carbamazepine was evaluated on activated carbon in fixed bed columns. The effect of various parameters on breakthrough curves like carbamazepine initial concentrations (1.2, 1.6, and 2.5 mg/L), bed depths (0.4, 0.6, and 0.8 cm) and volumetric flow rates (1.0, 2.0, and 3.0 mL/min) was investigated. The breakthrough time increased with increase of bed depth, and decreased with increase of initial concentration and volumetric flow rate. In order to predict the theoretical breakthrough curves and to determine model parameters, BDST, Thomas, Yoon-Nelson and Clark models were applied to the experimental adsorption processes under the operational conditions described above. The Thomas and Yoon-Nelson models were in good agreement with the experimental data.     

Modelling of fluidized bed reactors—VI(b): The nonisothermal bed with stochastic bubbles

Two stochastic nonisothermal fluidized bed reactor models are developed to investigate the significance of the fluctuating nature of fluidized beds on reactor performance. Fluctuating bubble size distributions within the bed are simulated by stochastic mass and heat transfer coefficients. Results of hybrid computer simulations indicate that randomness can enhance or inhibit reactor performance depending on the operating parameters of the nonisothermal model. Bubble and dense phase concentration statistics are fairly similar to those of corresponding isothermal models because dense phase temperatures are relatively insensitive to transfer coefficient fluctuations due to the high dense phase beat capacity. However, the corresponding stochastic isothermal models predict decreases in conversion with increasing variance in the transfer coefficients for all operating conditions. Results indicate that a deterministic system with two stable steady states may have fewer stable random stationary solutions. The existence of the stationary states is dependent on fluctuation frequency and variance of the transfer coefficients.     

Hydrocracking: An improved Kinetic Model and Reactor Modeling

Stangeland's kinetic model for predicting hydrocracker yields was modified to explicitly account for the mass balance closure in each individual hydrocracking reaction and for the effect of hydrogen partial pressure on the hydrocracking reaction rate. This improved kinetic model has two additional parameters. The model was applied to the modeling of a fixed bed reactor for mild hydrocracking of vacuum gas oils in the framework of the Aspen Plus® process simulator. The kinetic parameters were regressed using the algorithm of Levenberg-Marquardt such that the mass balance in each individual hydrocracking reaction is satisfied. The reactor model assumed gas-liquid equilibrium and was used to quantify the effect upon conversion of the operating variables--liquid hourly spatial velocity, reactor pressure, and hydrogen-to-feed ratio--showing that both the kinetic and reactor models predict the appropriate trends compared to the reference data. The practical implications of explicitly introducing the mass balance closure for each hydrocracking reaction in the kinetic model are discussed.     

Simulation and validation of ethanol removal from water in an adsorption packed bed: Isotherm and mass transfer parameter determination in batch studies

Preferential adsorption of ethanol from ethanol/water mixtures in batch equilibrium and kinetic experiments were carried out on a commercially available activated carbon adsorbent Filtrasorb 600 (F‐600). A model based on finite difference method was developed and employed to determine the mass transfer parameters and equilibrium behaviour for the adsorption of ethanol from simple batch systems. The estimates of the adsorption isotherm along with the mass transfer parameters were used to simulate the transient performance that could be expected in a packed bed under various operating conditions (feed flow rate, feed concentration, and particle size). The applicability of the simulation results were found to be a good match with experimental packed bed experiments over the entire range of operating conditions tested.     

Preparation of Microfibrous Entrapped Activated Carbon Composites and its Application for Benzene Adsorption

Microfibrous composites consisting of 150-200 μm activated carbon particles entrapped in 6.5 μm stainless steel fibers were prepared by wet layup papermaking and sintering process. The effects of a variety of operation parameters on the properties of microfibrous composites were investigated. The composite bed with microfibrous entrapped activated carbon was developed to purify air contaminated with benzene. The experimental results showed that the microfibrous composite with a ratio of 13:6 (W/W, carbon/ fibers) was of a relatively higher carbon entrapment ratio under the conditions of adding 2 L water, stirring at 50 Hz for 10 min, and then sintering at 1050^°C for 20 min. The breakthrough time of 5.0 cm composite bed increased by 28 min compared with that of a 5.0 cm individual GACs bed, and bed utilization increased 18.4% at 1% breakthrough concentration. The Bohart-Adams and Yoon-Nelson models were applied to analyze the experimental data of composite bed. The Bohart-Adams model fitted well with the experimental data for the C/C₀ region up to 0.5 but showed large discrepancies above this value. The Yoon-Nelson model predicted values were in very good agreement with the experimental results in the C/C₀ region above 0.05.     

Transient behaviour of encapsulated enzyme reactor systems

Mathematical models are developed for the transient behaviour of encapsulated enzyme reactor systems such as the continuous stirred tank reactor (CSTR) and the packed bed tubular reactor. The rate processes taking place in the encapsulated enzyme bed are approximated by using a combined rate control model of enzyme reaction and membrane diffusion. The change in transient substrate concentration is obtained by using the developed rate expression in the material balance over the substrate as a function of time for the CSTR and as a function of time and position for the packed bed tubular reactor. The effects of various parameters such as the enzymic reaction rate constant, Michaelis constant, diffusional resistance of membranes, and Peclet number on the substrate concentration distribution, which varies with respect to operating time, are investigated. This study affords insight into the transient operating characteristics of the encapsulated enzyme reactor system. The results should be useful in understanding the start-up performance of the reactor systems and to control such reactor systems at desired operating conditions.     

Experimental Study and Mathematical Modeling of Green Pea Drying in a Spouted Bed

In this study, green pea drying is investigated experimentally in a laboratory-scale spouted bed dryer. A mathematical model is also developed to investigate the effect of operating conditions on the performance of the system. The effect of operating parameters such as inlet air temperature, particle size, and flow rate of the drying air on the performance of the dryer are studied experimentally. In order to build the process model, it is necessary to analyze the transport in both solid and gas phases. A complete set of equations with no adjustable parameters is derived for existing zones in the spouted bed dryer in order to predict variations in the temperature and moisture content of the solid and gas phases with time for batch drying conditions. Model results are compared with corresponding experimental data. Agreement between the model results and experimental data is good.