Heterogeneous Reactor Model Research Articles

Growth of carbon nanotubes inside porous anodic alumina membranes: Simulation and experiment

Porous anodic alumina (PAA) membranes represent a widely used and extensively studied template for production of carbon nanotubes (CNT). The PAA–CNT membranes possess a number of unique properties, such as controllable nanotube geometry, size– and chemically–based selectivity as well as high water permeability. In this work, we first propose a combination of gas phase and surface reaction models to quantitatively describe the growth of carbon nanotubes in PAA membranes in a commercial CVD reactor. A complimentary experimental study of CNT formation from ethanol precursor with argon as a carrier gas is performed. A new method for characterizing carbon nanotubes geometry by SEM and TEM image processing of membrane cross–sections is proposed. The simulations show that the carbon growth rate (in nm/min) averaged over the membrane remains constant during the deposition process until the pore diameter becomes relatively small, and rapidly falls to zero after that. The carbon nanotube thickness near the membrane surface is slightly higher than that in the membrane center. The carbon growth rate increases with synthesis temperature and pressure, while it decreases with the argon flow rate. The dependence of carbon growth rate on the ethanol/water flow rate reaches maximum at some intermediate value. These results are supported by the experimental data obtained from SEM/TEM image processing. It is found that the SEM data provide overestimated values of nanotube diameter and thickness in comparison with the TEM data. The obtained results provide new insights into the CNT growth kinetics in nanoporous media, and develop quantitative guidelines for synthesis of CNT–PAA membranes with precisely controlled nanopore geometry. It also validates the combined homogenous / heterogeneous reaction model by comparison with carbon deposition kinetics on a nanometer scale.

Multiscale Analysis to Determine the Sensitive Zones for Temperature Sensor Location in Tubular Reactors

AbstractThe sensitivity of benchmark tubular reactors subject to temperature and concentration of external perturbations was investigated. Two case studies were evaluated, a pseudo‐homogeneous axial dispersion dimensionless tubular reactor and a heterogeneous tubular reactor to produce maleic anhydride. For the dimensionless reactor model, the highest sensitivities in the reactor were located at the center and at the outlet for temperature and concentration disturbances, respectively, while for the heterogeneous reactor model the sensitivity does not undergo significant changes with feed disturbances. When variations in the most sensitive position occur, a cascade controller can be improved using multiple temperature sensors. The evaluation on weighting assignment of the temperature measurements for the cascade control scheme is also described.

Comparative study of conventional steam-methane-reforming (SMR) and auto-thermal-reforming (ATR) with their hybrid sorption enhanced (SE-SMR & SE-ATR) and environmentally benign process models for the hydrogen production

The paper presents a comparison of steam methane reforming (SMR), sorption enhanced steam methane reforming (SE-SMR), auto-thermal reforming (ATR), and sorption enhanced auto-thermal reforming (SE-ATR) in a fixed bed reformer for hydrogen production. A one-dimensional, unsteady-state heterogeneous reactor model for each process which includes mass and thermal dispersion in the direction of flow and axial pressure distribution, has been simulated using gPROMS® 4.0.1 model builder, while CEA and Aspen Plus® have been employed to analyze the equilibrium performance and simulate the process flowsheets of individual process respectively. The performance of the individual hydrogen production process has been analyzed in terms of CH4 conversion (%), H2 yield (wt. % of CH4), H2 purity and CO2 capture under the various operating conditions of temperature (773–1473 K) and pressure (5–40 bar). The simulation results were also compared with the thermodynamic calculations and literature data. An excellent agreement was observed between our reactor modelling outputs and literature data. The operating conditions of 923 K, 30 bar and S/C of 3.0, O2/CH4 of 0.45 have been chosen. At these conditions, the CH4 conversion for SMR, SE-SMR, ATR, and SE-ATR was found to be 32%, 66%, 51%, and 76% respectively while the composition of hydrogen produced on a dry basis was 55%, 87%, 55%, and 92% respectively. It has been concluded that there are significant advantages of both sorption enhanced processes over conventional reforming in terms of CH4 conversion, H2 purity and the amount of H2 energy produced per unit CH4 energy consumed (MJ).

Parameter estimation in kinetic models of complex heterogeneous catalytic reactions using Bayesian statistics

Kinetic analysis of the gas-phase and liquid phase hydrogenation of toluene to methylcyclohexane on Ni catalysts was performed. For complex reaction mechanisms comprising several kinetically significant steps, nonlinear regression, while giving an adequate description of experimental data, leads to kinetic parameters which are poorly defined. The approach based on Bayesian statistics allows identification of the values of such parameters which are the most statistically probable.

Reliable Efficient Difference Methods for Random Heterogeneous Diffusion Reaction Models with a Finite Degree of Randomness

This paper deals with the search for reliable efficient finite difference methods for the numerical solution of random heterogeneous diffusion reaction models with a finite degree of randomness. Efficiency appeals to the computational challenge in the random framework that requires not only the approximating stochastic process solution but also its expectation and variance. After studying positivity and conditional random mean square stability, the computation of the expectation and variance of the approximating stochastic process is not performed directly but through using a set of sampling finite difference schemes coming out by taking realizations of the random scheme and using Monte Carlo technique. Thus, the storage accumulation of symbolic expressions collapsing the approach is avoided keeping reliability. Results are simulated and a procedure for the numerical computation is given.

A multi-scale model for the Fischer-Tropsch synthesis in a wall-cooled packed bed reactor

A numerical model based on the fundamental continuum transport equations is developed to simulate the Fischer-Tropsch synthesis in a slender packed column. Internal and external mass transport limitations are considered in a fully resolved manner where a two-way coupling between mass and heat transport is accounted for. A Langmuir-Hinshelwood type kinetic model is used for the reaction rate in the catalyst phase which is then intrinsically coupled to the fluid phase transport by enforcing the appropriate boundary condition using the Immersed Boundary Method. The fixed bed reactor consists of 220 particles packed in a random manner using the Discrete Element Method where cooling from the wall to the bed is also considered. The influence of temperature and concentration on conversion and selectivity is investigated. The Direct Numerical Simulation of the Fischer-Tropsch reactor is then compared with an equivalent 1-D heterogeneous reactor model which employs empirical closures.

Small-scale production of hydrogen via auto-thermal reforming in an adiabatic packed bed reactor: Parametric study and reactor's optimization through response surface methodology

In this work, a two-dimensional (2-D) heterogeneous reactor model for ATR process is presented. In order to authenticate the developed reactor model outputs, literature results as well as thermodynamic findings produced by employing chemical equilibrium with applications (CEA) software were compared with the model predictions and an excellent agreement was evidenced that corroborates the model's accurate predictive capability. Response surface methodology combined with central composite design was used to investigate the significance of operational parameters on the performance of the ATR process and Parametric optimization was performed to find the optimal operating conditions. Further insights into the ATR process were obtained by studying the effect of temperature, pressure, S/C, oxygen to carbon ratio (O/C) and gas mass flow velocity (Gs) on CH4 conversion, H2 yield (wt. % of CH4) and H2 purity. It was concluded that 973 K, 1.5 bar, S/C of 3.0, O/C of 0.45 and Gs of 0.15 kg/m2s resulted in CH4 conversion and H2 purity up to 97.6% and 71.8%, respectively.

One-Dimensional Heterogeneous Reaction Model of a Drop-Tube Carbonator Reactor for Thermochemical Energy Storage Applications

Calcium looping systems constitute a promising candidate for thermochemical energy storage (TCES) applications, as evidenced by the constantly escalating scientific and industrial interest. However, the technologically feasible transition from the research scale towards industrial and highly competitive markets sets as a prerequisite the optimal design and operation of the process, especially corresponding reactors. The present study investigates for the first time the development of a detailed, one-dimensional mathematical model for the steady-state simulation of a novel drop-tube carbonator reactor as a core equipment unit in a concentrated solar power (CSP)-thermochemical energy storage integration plant. A validated kinetic mathematical model for a carbonation reaction (CaO(s) + CO2(g) → CaCO3(s)) focused on thermochemical energy storage conditions was developed and implemented for different material conditions. The fast gas–solid reaction kinetics conformed with the drop-tube reactor concept, as the latter is suitable for very fast reactions. Reaction kinetics were controlled by the reaction temperature. Varying state profiles were computed across the length of the reactor by using a mathematical model in which reactant conversions, the reaction rate, and the temperature and velocity of gas and solid phases provided crucial information on the carbonator’s performance, among other factors. Through process simulations, the model-based investigation approach revealed respective restrictions on a tailor-made reactor of 10 kWth, pointing out the necessity of detailed models as a provision for design and scale-up studies.

Influence of the pyrolysis and heterogeneous char reactions modeling in the simulation of sugarcane bagasse gasification in a bubbling fluidized bed reactor

The present work investigates different kinetic models for the pyrolysis and heterogeneous char reactions for numerical simulation of the sugarcane bagasse gasification in a bubbling fluidized bed reactor. A two-dimensional Euler-Euler approach is considered, and the reaction rate correlations are implemented in the open code MFIX (Multiphase Flow with Interphase eXchanges) via Fortran sub-routines. The impact of the considered kinetic models for pyrolysis and heterogeneous char reactions upon the prediction of the composition and temperature of the produced gas is evaluated. Six sets of kinetic correlations describing the reactions involved during the sugarcane bagasse gasification are used to perform the computational simulations. Results for the syngas composition obtained in all simulations are compared to available experimental data from literature. Axial profiles for the volumetric fractions of sugarcane bagasse and char, and gas temperature distribution along the reactor are analyzed. Based on the evaluations of this computational study, it is identified that the multiple components parallel competitive reactions pyrolysis model designated as RAN model is superior in the simulations of sugarcane bagasse gasification due to smaller deviations and better prediction of the char formed in the primary pyrolysis. Furthermore, it is shown that the Boudouard and steam gasification reactions modelling have a smaller impact over the predictive capability of the simulations than the char oxidation reaction. Finally, because the results tend to underpredict the O2 amount in the yielded gas, the present work suggests that an improved kinetic correlation for the sugarcane bagasse char oxidation can enhance the simulation predictive capability.

Macroscopic models for filtration and heterogeneous reactions in porous media

Derivation of macroscopic models for advection-diffusion processes in the presence of dominant heterogeneous (e.g., surface) reactions using homogenisation theory or volume averaging is often deemed unfeasible (Valdés-Parada et al., 2011; Battiato and Tartakovsky, 2011a) due to the strong coupling between scales that characterise such systems. In this work, we show how the upscaling can be carried out by applying and extending the methods presented in Allaire and Raphael (2007), Mauri (1991). The approach relies on the decomposition of the microscale concentration into a reactive component, given by the eigenfunction of the advection-diffusion operator, the associated eigenvalue which represents the macroscopic effective reaction rate, and a non-reactive component. The latter can be then upscaled with a two-scale asymptotic expansion and the final macroscopic equation is obtained for the leading order. The same method can also be used to overcome another classical assumption, namely of non solenoidal velocity fields, such as the case of deposition of charged colloidal particles driven by electrostatic potential forces. The whole upscaling procedure, which consists in solving three cell problems, is implemented for arbitrarily complex two- and three-dimensional periodic structures using the open-source finite volume library OpenFOAM®. We provide details on the implementation and test the methodology for two-dimensional periodic arrays of spheres, and we compare the results against fully resolved numerical simulations, demonstrating the accuracy and generality of the upscaling approach. The effective velocity, dispersion and reaction coefficients are obtained for a wide range of Péclet and surface Damköhler numbers, and for Coulomb-like forces to the grains. Noticeably, all the effective transport parameters are significantly different from the non-reactive (conserved scalar) case, as the heterogeneity introduced by the reaction strongly affects the micro-scale profiles.

Flow behaviors, reaction kinetics, and optimal design of fixed- and fluidized-beds for CO2 methanation

The performances of three catalytic reactors for CO2 methanation, i.e., single fixed-bed (1FxB), two-stage fixed-bed (2FxB), and bubbling fluidized-bed (BFB), were evaluated at a feed flow rate of 166.5 Nm3/h. A heterogeneous catalytic reaction model (HCRM) combining the one-dimensional plug-flow model on the reactor scale and the reaction–diffusion model on the particle scale was used for 1FxB and 2FxB. A two-phase reaction model (TPRM), including the mass transfer between the bubble and emulsion phases and axial dispersion, was proposed for the BFB. The results from HCRM and TPRM were in good agreement with experimental and modeling data. The 1FxB, 2FxB, and BFB were optimized via the parametric study considering the hot spot temperature, operating temperature and pressure, space velocity, flue gas recirculation ratio, and operational stability. The catalyst weights of 1FxB, 2FxB, and BFB required for a 90% CO2 conversion were 191, 40, and 34 kg, respectively. The proposed models were able to identify the flow behaviors, mass transfer, and reaction kinetics of the fixed- and fluidized-beds, which are useful for the optimal design of CO2 methanation reactors.

The Conversion Kinetics of Tincal to Boric Acid in Nitric Acid Solutions

Pure borax and various boron compounds are produced from the solutions in which tincal is dissolved with various reagents. Economically important boron compounds such as boric acid, borax, boric oxide, and refined hydrated sodium borates and perborates are produced from boron-containing ores. The production of boric acid by using nitric acid from tincal is more advantageous because it evaluates by-product NaNO3 as fertilizer production. In this study, the conversion kinetics of tincal to boric acid in nitric acid solutions were investigated by such parameters as particle size, 300-1500 µm; acid concentration,0.5-4 mol/L; solid-to-liquid ratio 0.04-0.10 g/mL; stirring speed 20.93-62.8 s-1, and reaction temperature, 30-60 oC. The conversion was found to increase with decreasing particle size and solid-to-liquid ratio and while it increased with increasing reaction temperature, acid concentration, and stirring speed. The conversion kinetics was examined using the heterogeneous and pseudo-homogeneous reaction models. The experimental results were found to be in better agreement with the correlation given in the following equation and the activation energy being 37.5 kJ/mol.

A modified model for isothermal homogeneous and heterogeneous reactions in the boundary-layer flow of a nanofluid

The homogeneous and heterogeneous reactions in the boundary-layer of a flat surface are considered. The autocatalysts are assumed to be of regular sizes, while the solution is a dilute nanofluid. The heat release due to the chemical reactions is taken into account. The Buongiorno’s model is used to describe the behaviors of this reaction system. This configuration makes the current model be different from all previous publications. Multiple solutions are given numerically to the rescaled nonlinear system, whose stability is verified. The results show that the strength coefficients of the homogeneous and heterogeneous reactions are key factors to cause the appearance of the multiple solutions in the distribution of the chemical reactions. Nanofluids enhance the diffusion of heat and help maintain the stability of chemical reactions.

Kinetics and Thermodynamics Studies of Ketalization of Glycerol and Acetone in the Presence of Basolite F300 as Catalyst

Acetalyzation of glycerol with acetone has been carried out using Basolite F300 as catalyst. Heterogeneous catalysis reaction model was employed and Langmuir Hinshelwood mechanism was simulated and validated to the experimental data. The experiment was conducted at varying temperature (30 – 55°C) with an initial molar ratio of glycerol to acetone of 1:4, agitation speed of 700 rpm and catalyst loading of 1% (w/w glycerol). The agitation speed of 700 rpm was sufficient to neglect the external mass transfer as the rate controlling step.The results showed that glycerol conversion as high as 83.33 % was obtained from one hour reaction time. The glycerol conversion was simulated and the results were compared with experimental data in a temperature range of 30°C to 55°C. From mathematical model, it was found that the pre-exponential factor of 0.0149 min–1 and activation energy of 15.7085 kJ.mole–1. Comparison of experimental data and calculation results showed that the proposed mathematical model was adequately able to approach the experimental data within the temperature range under investigation. Thermodynamics analysis on the ketalization resulted in ΔS°, ΔH° and ΔG° which values were 0.0834 kJ.mole–1 K–1, -29.7176 kJ.mole–1 and -4.8675 kJ.mole–1, respectively.

Optimal catalyst particle design for flexible fixed-bed CO2 methanation reactors

Power-to-Methane is a concept for energy storage harvested from renewable sources, for instance solar and wind power. A flexible operation of catalytic fixed-bed methanation reactors, according to the availability of energy, eliminates the need to store intermediate reactants in large buffer units. This requires reliable heat management, as the heat generation of the methanation reaction is a challenge even at steady-state conditions. For this purpose, many studies have been conducted on the reactor scale, but knowledge on how the catalyst particle design can influence reactor behavior is rather limited. Therefore, a heterogeneous reactor model is used in this study to investigate the influence of particle activity, permeability and heat conductivity on reactor performance. Subsequently, a nonlinear program is formulated and solved to find the optimal particle design depending on these three properties and their radial distribution in the catalyst particles. The designs include spherical particles with uniform properties (Case1), particles with two uniform zones of different properties (Case2) and particles with radially variable properties (Case3). Optimization, subsequent sensitivity analyses and dynamic simulations reveal that reactors filled with particles of Case2 should exhibit a particle core with high activity, which is surrounded by an inert, low-permeability shell (so-called ‘egg-yolk’ particles). In this way, the reactor shows a reduced parametric sensitivity and a high methane yield at the same time. In comparison to reactors filled with particles of Case1, they also exhibit a favorable behavior for dynamic and flexible reactor operation. The benefit of further particle zones to increase reactor performance appears insignificant, as shown by the results of Case3.

Numerical study on stability and influencing factors of heterogeneous reaction for hydrogen/oxygen mixture in planar catalytic micro combustor

The combustion and flow characteristics of H2/O2 mixture were numerically studied in a platinum-coated planar channel with a length of 20 mm and a height of 1 mm. Two-dimensional numerical models were built and verified by experimental data. The fundamental of generating unstable combustion and flow and its influencing factors were studied via changing the parameters (equivalent ratio, initial position of reaction, with or without homogeneous reaction). It was found that pure heterogeneous reaction could affect the flow state in the planar micro combustor because of the intense convective heat transfer on the inner wall. The critical Reynolds number in micro combustor calculated by pure heterogeneous reaction model was in the range of 650–1100. The reaction heat of catalyst surface and the thickness of boundary layer at the initial position of heterogeneous reaction are two main factors which influenced the stability of combustion and flow. Finally, the pure heterogeneous reaction had higher complete combustion efficiency than coupling reaction. Based on these conclusions, the applicable conditions for achieving stable flow and combustion in the microchannel were obtained, which could provide a theoretical basis for the application in micro-combustion.

Automated System for Identification of Conditions for Homogeneous and Heterogeneous Reactions in Multiobjective Optimization Problems

An automated system for identification of conditions for conduction of homogeneous and heterogeneous reactions includes mathematical modeling of a chemical reaction, determination of criteria for conditions of its optimization and variable parameters, setting and solving a multiobjective optimization problem and an optimal control problem, and development of efficient algorithms for a computing experiment. Modeling and optimization of homogeneous and heterogeneous catalytic reactions are done. Reaction conditions optimal for achievement of given criteria are determined.

A redox reaction model for self-heating and aging prediction of Al/CuO multilayers

Sputter-deposited Al/CuO multilayers capable of highly energetic reactions have been the subject of intense studies for tunable initiation and actuation. Designing high performance Al/CuO-based initiator devices definitively requires reliable prediction of their ignition and reaction kinetics including self-heating or ageing as a function of heating rate and environmental conditions. The paper proposes a heterogeneous reaction model integrating an ensemble of basic mechanisms (oxygen diffusion, structural transformations, polymorphic phase changes) that have been collected from recent experimental investigations. The reaction model assumes that the rate of reaction is limited by the transport of oxygen across the growing layer of Al2O3 separating Al and CuO. Importantly, we show that the model predicts reasonably all exotherms through a wide range of temperature (ambient – 1000°C), all resulting from a pure diffusion process as experimentally observed for such Al/CuO multilayers. The model shows how the temperature ramp affects the structure of the multilayer and especially the growth of alumina-based interfacial regions. It highlights the importance of the interfacial chemistry evolution such as the native mixture of AlxCuyOz transformation into a thin amorphous alumina, and the polymorphic phase transformation of this latter. The first one occurring at ∼350°C results in a loss of continuity of the interface leading to the accelerated redox reaction whereas the second one occurring between 500 and 600°C produces a denser barrier to oxygen diffusion leading to the stop of redox reaction. We finally use the model to simulate thermal annealing as usually performed in accelerated ageing experiments. We theoretically observe and experimentally validate that a two weeks exposure of the multilayers at 200°C starts degrading the multilayers thermal properties whereas when the temperature remains below 200°C, the material keeps its entire integrity.

Simulation of Acid–rock Heterogeneous Flow Reaction Based on the Lattice Boltzmann Method

Matrix acidizing is an essential strategy to maintain or increase the productivity or injectivity of hydrocarbon wells. However, for sandstone reservoirs, the heterogeneous flow reaction mechanism of acid–rock in porous media is very complex because of their complex mineral and chemical compositions. It is often difficult to match real formation conditions by experimental simulation. Also, traditional numerical simulation methods have the disadvantages of complex boundary processing and low computational efficiency. In this study, the lattice Boltzmann method (LBM) was used to establish the heterogeneous flow reaction model of acid–rock from a new perspective, which was solved by MATLAB to obtain the distribution of temperature, concentration of various substances, porosity, and permeability. The simulation results indicate that with increases in injection time and injection speed, the temperature and mass transfer distance of the acid will also increase. Changing the injection time had a more obvious influence on the transfer of temperature and mass than did changing the injection speed. The increasing rates of porosity and permeability in the middle of the flow channel were the highest. The fast-reaction mineral content, hydrofluoric acid injection concentration, and acid injection time had a great influence on the acidizing effect, whereas the slow-reaction mineral content, acid injection temperature, and injection speed had little influence on the acidizing effect. The results suggest that to improve the acidizing effect, priority should be given to improve the HF concentration and acid dose. It will be important for further guiding the optimization of acidizing process design parameters.

Non-equilibrium thermodynamics as a tool to compute temperature at the catalyst surface.

The surface temperature is computed for a heterogeneous catalytic reaction model, namely the oxidation of carbon monoxide on platinum. The surface temperature was found using non-equilibrium thermodynamic theory, a theory which provides the proper dependencies between heat and mass fluxes and the reaction rate. The theory predicts a possible coupling between the reaction rate and the thermal driving force and can help extend classical reaction kinetics. In the absence of direct measurements, we explore the coupling numerically. The results are able to capture experimental data reported in the literature, and give new insights into why Arrhenius plots may turn out to be non-linear.