Isothermal Plug Flow Reactor Research Articles

Physics-informed genetic programming for discovery of partial differential equations from scarce and noisy data

A novel framework is proposed that utilizes symbolic regression via genetic programming to identify free-form partial differential equations from scarce and noisy data. The framework successfully identified ground truth models for four synthetic systems (an isothermal plug flow reactor, a continuously stirred tank reactor, a nonisothermal reactor, and viscous flow governed by Burgers' equation) from time-variant data collected at one location. A comparative analysis against the so-called weak Sparse Identification of Nonlinear Dynamics (SINDy) demonstrated the proposed framework's superior ability to identify meaningful partial differential equation (PDE) models when data was scarce. The framework was further tested for robustness to noise and scarcity, showing successful model recovery from as few as eight time series data points collected at a single point in space with 50% noise. These results emphasize the potential of the proposed framework for the discovery of PDE models when data collection is expensive or otherwise difficult.

Investigation of the kinetics of methanation of a post-coelectrolysis mixture on a Ni/CZP oxide catalyst

The use of synthetic natural gas (SNG) as a plug-and-play fuel coming from renewables can help to overcome the limitations given by the intermittency of renewable energy. A way to implement the production of SNG pass through the co-electrolysis of CO2 to a mixture of hydrogen, carbon monoxide and carbon dioxide, steam and small amounts of methane, followed by CO and CO2 methanation. The presence of different reactants and processes requires the comprehension and quantification of the kinetics of the reactions involved with the aim of optimizing methanation. In this work a kinetic model that considers both the direct CO2 methanation and the indirect RWGS + CO methanation pathways has been developed over a Ni(10 %wt)/Ce0.33Zr0.63Pr0.04O2. The kinetic study made it possible to understand the influence of the reactants and products on the reactions through the calculation of reaction rates. This allowed to test, by linearization, the models found in the literature and their adjustment permitted to calculate sixteen kinetic parameters (activation energies, heats of adsorption and pre-exponential factors) present in the rate laws of methanation of CO2, CO and the Reverse Water Gas Shift reaction. The models then made it possible to simulate the evolution of partial flow rates in an isothermal plug flow reactor and were compared to experimental data.

Experimental and modeling investigation of partial oxidation of gasification tars

Among the methods to reduce tar emission, the partial oxidation (POX) of biomass gasification tars has been studied both experimentally at a pilot-scale and numerically. The gasification producer gas was obtained at a temperature of 800 °C in an air-blown fluidized bed with an equivalent ratio (ER) of 0.25. For the POX unit, two secondary ER values were selected: 0.05 and 0.10, with the option of pre-heating air or not. Multiple advanced analytical methods were employed to provide a detailed composition of the producer gas, tars and acid gases. The POX unit demonstrated the ability to reduce tar levels by 60 to 90% depending on the secondary ER (from 6.5 to 2.4 and 0.72 gtars/Nm3, excluding benzene). The lighter tars were almost completely eliminated. The permanent gases were barely modified while the light hydrocarbons (except C2H2) and benzene were significantly reduced. Consequently, there was a slight decrease in the lower heating value. These results were compared to an isothermal plug flow reactor model, which utilized a detailed radical kinetic scheme constructed from various sources to account for all the species measured during the experiments as well as soot mass yield. The model provided relatively accurate predictions of the hydrocarbon species variations, even though it did not consider the mixing between air and syngas at the inlet of the POX unit.

CPFD simulation of a pilot-scale CFB riser for sugar cracking to glycolaldehyde and other oxygenates: Coupling hydrodynamics and reaction kinetics

Cracking of sugars to glycolaldehyde and other value-added oxygenates has shown potential in lab-scale fluidized beds with high yield and selectivity towards glycolaldehyde. In this work, a homogeneous gas-phase kinetics model for sugar cracking available in literature is adopted and implemented into the Computational Particle Fluid Dynamics (CPFD) framework in order to simulate sugar cracking in a pilot-scale circulating fluidized bed riser operated at conditions relevant for continuous production of glycolaldehyde in the industry. An Eulerian-Lagrangian approach is applied to model the three-phase flow where liquid feed droplets are injected into the hot gas–solid fluidized bed. A modified gas-to-liquid ratio dependent Rosin-Rammler droplet size distribution is proposed to accurately represent the gas–liquid jet in the simulation. Simulated temperature and pressure distributions are in good agreement with measured ones. Prediction of the yield of glycolaldehyde at 60.9 wt%-C and other oxygenates using the the CPFD model corresponds closely to the results obtained from the same kinetic model implemented in an isothermal plug flow reactor model. This suggests that the CFB riser behaves essentially like a plug flow reactor, as hydrodynamic and thermal deviations from plug flow conditions do not have a considerable effect on the predicted yields. Comparing the model predictions to the measured yield of glycolaldehyde, a 50% overprediction is observed, suggesting that the hydrodynamic and cracking kinetics submodels need to be more closely coupled to more accurately predict the product yields, by means of e.g. heterogeneous cracking reactions.

Methanol production from biomass: Analysis and optimization

A methanol production kinetic model from syngas was prepared using an Aspen plus simulation software. The two most widely used kinetics from Vanden Bussche and Graaf’s was adopted for creation and validation of the methanol synthesis model. The model developed was then subjected to multivariable analysis. Methanol yield (%), carbon conversion (%), and methanol production (mol h−1) were the response studied from the model with change in the analysed factors. Stoichiometric number (S), reaction temperature, operating pressure, and the cooling condition involved during methanol production being the analysed input factors to the system. Prediction and the optimization of the analyzed responses was done with the help of the prepared surrogate model. The optimized values obtained for the methanol yield (%), carbon conversion (%) and methanol production (mol h−1) were, 46.95 %, 46.97 % and 1.21 mol h−1 respectively, when methanol reactor was cooled in an isothermal plug flow reactor at a stoichiometric number of 4.44 and by operating the reactor at 220 °C and 50 bars.

Modeling of thermal cracking reaction of kerosene range hydrocarbons

The present study deals with the modeling and simulation of a semi-mechanistic model of the thermal cracking reaction of a kerosene range hydrocarbon fuel. The objective of the present work is to investigate the concentration profile of various species specifically, H2, and C1-C4 hydrocarbons along the reactor length of a tubular reactor. The study will enable to optimize the reactor length for desirable products. An isothermal plug flow reactor (PFR) system is considered to investigate the variation of product distribution patterns along the axial direction. The simulation was performed considering 172 reactions and 51 species. The PFR temperature and pressure were maintained at 850 °C and 2.5 MPa, respectively. The cracked products obtained are grouped based on boiling temperature ranges. The study shows that the concentration profile of hydrogen, methane, ethylene, propane, and isobutylene increased monotonically with the increase of the characteristic length of the reactor. In contrast, the concentration of propylene and 1-butene passes through a maximum. Also, a variation in the characteristic length corresponding to the peak concentration of olefins is noted. The study may be useful for understanding the insight of pyrolysis reaction and selecting a characteristic reactor length for the optimization/maximization of lighter olefins.

Carbon dioxide methanation kinetic model on a commercial Ni/Al2O3 catalyst

Intrinsic kinetic characterization of the carbon dioxide methanation was determined over a commercial 14–17 wt.% Ni/Al2O3 between 623 K and 723 K at atmospheric pressure in the absence of heat and mass transfer limitations. Following a Hougen-Watson formalism, both direct path (CO2 methanation rate equation) and indirect path (Reverse Water Gas Shift rate equation +CO methanation rate equation) were described. As a first step, kinetic tests were performed operating in differential mode to evaluate the reaction rate dependence on reactants and products partial pressure at different temperatures in order to select the form of each reaction rate equation. Kinetic models available in the literature were evaluated and compared with the experimental results and model adaptations were proposed to identify the kinetic laws that fit the best the experimental values. Kinetic and adsorption parameters were calculated from these laws. Then, the identified parameters were adjusted simultaneously on experimental tests from 5% to 75% CO2 conversion using an isothermal plug-flow reactor. The three reaction rates and their reverse reactions were identified in order to minimize the error on CO2 conversion and CH4 and CO selectivities at 623 K, 673 K and 723 K. The final identified kinetic model was able to reflect the kinetics from differential conversion to thermodynamic equilibrium with an accuracy of 20% on the CH4 formation rate for the three temperatures.

Intrinsic kinetics of CO2 methanation over an industrial nickel-based catalyst

The intrinsic kinetics of CO2 methanation over an industrial nickel-based catalyst was determined for a temperature range between 250 °C to 350 °C. The kinetic experiments were performed operating an integral fixed-bed reactor far from equilibrium conditions, in the absence of heat and mass resistances and at the atmospheric pressure. Five mechanistic-based models for describing the reaction kinetics were taken from literature and used for fitting the experimental reaction rates. Model discrimination was based on the assessment of the thermodynamic consistency and statistical significance of inherent parameters (for 95% confidence level). Comparison of the adequacy of fit between accepted models was done through the determination of the corresponding F-values to select the best model. The selected model assumes a formyl intermediate mechanism with a hydroxyl group being the most abundant species. The proposed reaction kinetics was further validated by the simulation of an isothermal plug-flow reactor operating at the same experimental conditions employed in this work, where a reasonable agreement between model predictions and the observed values was obtained.

Analytical Determination of Rational Catalyst Lifetime for Consecutive Reaction in Isothermal Plug Flow Reactor

Background. The urgency of mathematical modeling of continuous chemical-technological processes in non-stationary con­ditions caused by the actions of various destabilizing factors is undoubted. In this case, analytical solutions have undeniable advantages over numerical ones, since they make it possible to clarify the nature of the cause-effect relationships in the properties of the modeling object under consideration and, as a practical result, to give physically grounded recommendations for increasing the efficiency of its functioning. For catalytic processes, the reason for non-stationarity is the deactivation of the solid catalyst (Kt). This leads to a decrease of the conversion degree \[{x_ \bullet } = 1 - {c_{1 \bullet }}\] of the A 1 reagent, and hence to a negative increase of its concentration \[{c_{1 \bullet }}\] in the reaction mixture at the outlet of the plug flow reactor (PFR) of length \[{L_{0 \bullet }},\] which leads to economic losses. Therefore, a rational (maximally expedient) catalyst lifetime \[{\theta _{\max }} > > 1\] has fundamental importance and is a significant part of the individual problem of selecting Kt. Objective . The aim of the paper is analytical calculation of the maximally expedient lifetime \[{\theta _{\max }} = {\tau _{\max }}/{\tau _{L \bullet }}\] of industrial Kt at the point \[{x_{0 \bullet }}\] of maximum of the nominal yield \[{\eta _{02 \bullet }} \equiv \eta _{02}^{\max }\] of the product A 2 for the isothermal system “PFR at the optimum resi­den­ce time \[{\tau _{L \bullet }} = {L_{0 \bullet }}/{u_0}\] of the reactants + consecutive catalytic reaction \[\mathrm{A}_{1}\xrightarrow[\mathrm{Kt},k_{\mathrm{d}1}]{k_{01},n_{1}=1}\alpha _{2}\mathrm{A}_{2}\xrightarrow[\mathrm{Kt},k_{\mathrm{d}2}]{k_{02},n_{2}=1}\alpha _{3}\mathrm{A}_{3}\] under the influence of the Kt deactivation destabilizing factor. Methods . A linearized mathematical model in the form of a system of ordinary differential equations of characteristics for calculating the relatively small Kt deactivation influence on the system operating mode stationarity has been used. Results . In the case of the first-order reaction for the conditions of the industrial Kt deactivation, the relative deviations \[\left | \varepsilon _{x\bullet } \right |=\left | (x_{\bullet }/x_{0\bullet })-1 \right |\sim k_{\mathrm{d}1}\tau _{\mathrm{max}} 0\] are determined by the simplex \[\gamma _{0k}=k_{01}/k_{02}\] of the nominal rate constants and by the simplex \[\gamma _{\mathrm{d}}=k_{\mathrm{d}2}/k_{\mathrm{d}1}\] of the Kt deactivation rate constants of the reaction stages. Conclusions . It is proved that with respect to the yield of A 2 product, there is a self-regulation effect \[({\varepsilon _{\eta 2 \bullet }} \approx 0)\] of the stationary mode at the condition of the equality \[\gamma _{\mathrm{d}}=1\] of the Kt deactivation rate constants. A nomogram for determining \[1 < <\theta _{max}< < (k_{\mathrm{d}1}\tau _{L\bullet })^{-1}\] on the maximum admissible value of \[\left | \varepsilon _{x\bullet } \right |_{max}^{\mathrm{adm}}< < 1.\] is calculated. For example, at a nominal degree of conversion \[{x_{0 \bullet }} = 75\% \Leftrightarrow {\gamma _{0k}} = 2\] of A 1 reagent and \[\left | \varepsilon _{x\bullet } \right |_{max}^{\mathrm{adm}}= 5\%\Rightarrow \theta _{max}\approx 1,1\cdot 10^{3}(k_{\mathrm{d}1}\tau _{L\bullet }=10^{-4}).\] It is shown that the rational catalyst lifetime \[{\theta _{\max }}\] is inversely proportional to the complex \[k_{\mathrm{d}1}\tau _{L\bullet }\] of the Kt deactivation rate constant of the first stage.

Characterization of Biomass Fuels in Isothermal Plug Flow Reactor (IPFR)

Spalovani fosilnich paliv je jednim z nejdůležitějsich zdrojů energie. Nicmeně nizkouhlikova politika a environmentalni zavazky ovlivňuji vývoj spalovacich a spolu-spalovacich technologii. Využivani paliv z biomasy může být odpovědi na nove výzvy, i když je zapotřebi vice výzkumu o efektivnim využiti těchto paliv. V soucasne době spalovani paliv z biomasy, zejmena slamy, způsobuje řadu technických problemů, zejmena tvorbu strusky, zanaseni výměniků tepla uvnitř spalovaci komory a nedostatecne vyhořeni paliva. Tento přispěvek se zaměřuje na analýzu spalovanibiomasy. Lepsi znalost chovani procesů při spalovani biomasy může přispět k optimalizaci navrhu praskoveho kotle a vyhnout se tim technickým problemům. Výsledky výzkumu ukazuji, že teplota a koncentrace kysliku v reaktoru hraji významnou roli v procesu tvorby prchave hořlaviny a vyhořeni tuheho zbytku. Napřiklad během experimentů s vyhořelým tuhým zbytkem při teplotě 850 ° C při 14% koncentraci kysliku po 200 ms bylo dosaženo vice než 80% ubytku hmotnosti. Ve srovnani se 700 ° C při 14% koncentraci kysliku byla stejna uroveň ubytku hmotnosti dosažena po 500 ms. Experimenty provedene na izotermickem reaktoru (IPFR) v Institutu energetických procesů a technologii paliv (IEVB) na TU Clausthal byly soucasti projektu mezi IEVB a „Karlsruhe Institute of Technology (KIT)“ v Německu.

Aluminium and rhodium co-doped ceria for water gas shift reaction and CO oxidation

This study presents the synthesis and application of aluminium and rhodium co-doped ceria for water gas shift (WGS) reaction and CO oxidation. The catalyst was synthesized using single step solution combustion method to obtain porous catalyst of relatively high surface area. The catalyst was characterized by various techniques. All the characterization results revealed successful substitution of the constituent dopants in ceria. The catalyst obtained was tested for its activity for WGS and CO oxidation. The catalyst exhibited higher catalytic activity in comparison to the other noble metal counterparts. A plausible dual site microkinetic model has been proposed in this study for WGS and CO oxidation over Rh/ceria based catalyst and a robust rate expression has been obtained. This rate expression in conjunction with the kinetic parameters and isothermal plug flow reactor model was used to predict the experimental CO conversion. As evident from the simulation results, the kinetic model developed in this study was able to predict the experimental trend with reasonable accuracy for both WGS and CO oxidation.

Zinc and platinum co-doped ceria for WGS and CO oxidation

This study presents the synthesis and application of zinc and platinum co-doped ceria for CO oxidation and water gas shift reaction (WGS). To synthesize the catalyst, novel combustion synthesis procedure at pH=10 has been employed, yielding the catalyst in single step without further purification procedures. The catalyst was found to be active under high temperature conditions (>350°C) thus asserting the functionality of the catalyst as single stage WGS catalyst. In this study, we have also developed a dual site redox mechanism to understand the intrinsic kinetics of WGS reaction. For the proposed mechanism, a plausible microkinetic model has been developed for WGS and CO oxidation reactions, respectively. In line with the application of reaction route (RR) analysis to the microkinetic models developed for single site pathway for WGS. In this study, we have extended the RR approach to dual site redox mechanism. From the above analysis, the surface dissociation of OH surface species was found to be rate determining step of the mechanism. The rate expression developed using RR analysis was validated through isothermal plug flow reactor (PFR) model. The PFR simulations predicted the experimental trend for wider range of temperature conditions thus portraying the significance of the microkinetic model developed in this study.

Estimation of the remaining lifetime of deactivated catalyst via the spatial average catalyst activity illustrated by the water–gas shift and steam methane reforming processes

In catalytic processes with catalyst deactivation, there is a big problem in estimating the remaining catalyst lifetime since industrial operating conditions are quite uncertain and consequently the non-uniform catalyst activity profile developed in the reactor during operation is unknown. In this article, a simple method for calculating the remaining catalyst lifetime from present operating data is reported. The spatial average catalyst activity, which indicates how much the catalyst has been deactivated, is proposed to denote the present catalyst activity in the reactor. For an isothermal plug flow reactor packed with non-porous catalyst, any catalyst activity profile determines the same reactant conversion if the spatial average activity related to this profile is the same. As a result, the average activity is easily calculated from present operating data without the information of the catalyst deactivation rate. The determined present average activity is used as an initial condition to estimate the remaining catalyst lifetime providing superbly accurate calculation results when the kinetic deactivation expression is characterized by the first order in the catalyst activity. The developed procedure is demonstrated using the water–gas shift reaction and methane steam reforming processes as examples.

Conceptual Approach in Multi-Objective Optimization of Packed Bed Membrane Reactor for Ethylene Epoxidation Using Real-coded Non-Dominating Sorting Genetic Algorithm NSGA-II

Abstract An isothermal plug flow reactor model with extended Fick diffusion model for transport through the porous membrane is utilized for simulation of ethylene oxide formation in a packed bed membrane reactor (PBMR). The model was verified and validated using published experimental data from an existing lab-scale unit. Sensitivity analysis was performed to determine robustness of the model. A conceptual approach on operation and design stage multi-objective optimization study is discussed. Real-coded NSGA-II is used and effect of its parameters on optimization of reactor performance is also studied. The results of three two-objective operation-stage (with 4 decision variables) and one two-objective design-stage (with 6 decision variables) optimization case studies are presented. Good convergence to a Pareto optimal solution is achieved for all cases. Significant improvement over current experimental operation is observed in terms of increase in conversion of ethylene, selectivity to ethylene oxide and ethylene oxide product flow rate.

Effect of dilution of fuel in CO2 on the conversion of NH3 to NO x during oxy-fuel combustion

The indirect chemical effects of fuel dilution by CO2 on NO formation were investigated numerically in this paper. CH4 doped with NH3 was used as fuel, while CO2 and O2 were mixed as oxidant. The dilution effect of CO2 was then investigated through adding extra CO2 to the reaction system. An isothermal plug flow reactor was used. An unbranched chain reaction mechanism is proposed to illustrate the chemical effects of CO2 on the H/O/OH radical pool and NO x . Due to the reaction between CO2 and H, extra NO will be formed in fuel-rich conditions, while NO will be inhibited in fuel-lean conditions and high CO2 dilution conditions. The reaction affected the radical pools of OH, H, and O of the branched chain reaction, and then the formation and reduction of NO. The pool of H had the greatest effect on NO reduction. The results suggest that the indirect chemical effects on NO formation differ between diluted fuel oxy-fuel combustion conditions and normal oxy-fuel conditions.

Characterization of high-temperature rapid char oxidation of raw and torrefied biomass fuels

The promising properties of torrefied biomass provide a valid co-firing option for large percentage biomass utilization in existing coal-fired boilers. Torrefied biomass is expected to have a better combustion stability than raw biomass and similar to that of coal. The present work will characterizes the oxidation properties of torrefied biomass char and compare with that of raw biomass char. The studied two chars are produced from raw and torrefied biomass in an Isothermal Plug Flow Reactor (IPFR) at high temperature and high heating rate, a sufficient residence time is applied for the completion of the high temperature devolatilization. Char oxidation tests are carried out in the IPFR by varying temperature, oxygen concentration and residence time. The reactivity of two studied chars are analyzed and compared with referenced biomass char and coal char, and the impact of torrefaction on char reactivity is also discussed in this paper. Finally, the char oxidation kinetic parameters are determined using a parameter optimization method, and the obtained kinetics are examined by comparing the experimental and predicted mass conversions.

Annular flow microreactor: An efficient tool for kinetic studies in gas phase at very short residence times

This study deals with the modelling of a tubular flow microreactor and an annular flow microreactor that are used for kinetic studies of thermal reactions (873–1273K) at very short residence times (10–100ms). The construction of a kinetic model on the basis of experimental reaction data requires the precise characterization of the thermal behaviour and the hydrodynamics of the reactor. In kinetic studies, the reactor is usually considered as an isothermal Plug Flow Reactor. In this paper, we demonstrate that an annular flow microreactor used at very short residence time not only leads to a temperature profile which is better controlled than in a tubular flow microreactor, but also to less axial dispersion for laminar flow. The comparison between both reactors is performed on the basis of temperature measurements, RTD measurements at room temperature, dimensionless numbers calculations and Computational Fluid Dynamics in typical reaction conditions.

Low temperature catalytic steam reforming of propane–methane mixture into methane-rich gas: Experiment and macrokinetic modeling

Steam reforming of propane–methane mixture into methane-rich gas was studied in a fixed-bed continuous-flow reactor in a temperature interval of 150–325°C under atmospheric pressure over Ni-based catalyst. It was found that the catalyst had good performance under low steam-to-carbon ratio of 0.39–0.58 and provided equilibrium product distribution at GHSV=670–3100h−1. Macrokinetic modeling of the experimental data obtained was performed in the framework of isothermal plug-flow reactor model. For the first time the two-step macro-kinetic scheme was suggested, that includes the reactions of irreversible propane steam reforming (first-order on propane): C3H8+6H2O→3CO2+10H2 with activation energy 112kJ/mole and reversible CO2 methanation (first-order on hydrogen): CO2+4H2⇄ CH4+2H2O with activation energy 50kJ/mole. It was shown that the proposed scheme describes quantitatively all the experimental results.

A generalized correlation for coal devolatilization kinetics at high temperature

The optimization of thermochemical (combustion, gasification, pyrolysis, oxyfiring) systems requires a comprehensive model, able to simulate conventional and innovative plants, for achieving the high levels of efficiency and low pollutant emissions required by the current applications. A devolatilization model is the basis of these processes and should be sufficiently simple and accurate to be implemented in commercial codes for simulating large scale plants. Kinetic parameters should be validated in qualified tests under severe thermal conditions and for coals of different ranks. In this work the experimental data from the isothermal plug flow reactor of IFRF (with temperatures up to 1673K and heating rates on the order of 104K/s), previously uniformed and organized in the solid fuel database SFDB, are elaborated to obtain the kinetic parameters according to a modified version of the single first order reaction model. The effective thermal history of the particles is estimated by simulating the devolatilization tests with a CFD model. A generalized correlation is obtained between the kinetic parameters and coal properties, preferably among those routinely reported in standard analyses. Finally, a practical and useful predictive tool is provided for studying the devolatilization of pulverized coal.

High-temperature rapid devolatilization of biomasses with varying degrees of torrefaction

Torrefied biomass is a coal-like fuel that can be burned in biomass boilers or co-fired with coal in co-firing furnaces. To make quantitative predictions regarding combustion behavior, devolatilization should be accurately described. In this work, the devolatilization of three torrefied biomasses and their parent material were tested in an isothermal plug flow reactor, which is able to rapidly heat the biomass particles to a maximum temperature of 1400°C at a rate of 104°C/s, similar to the conditions in actual power plant furnaces. During every devolatilization test, the devolatilized biomass particles were collected and analyzed to determine the weight loss based on the ash tracer method. According to the experimental results, it can be concluded that biomass decreases its reactivity after torrefaction, and the deeper of torrefaction conducted, the lower the biomass reactivity. Furthermore, based on a two-competing-step model, the kinetic parameters were determined by minimizing the difference between the modeled and experimental results based on the least-squares objective function, and the predicted weight losses exhibited a good agreement with experimental data from biomass devolatilization, especially at high temperatures. It was also detected that CO and H2 are the primary components of the released volatile matters from the devolatilization of the three torrefied biomasses, in which CO accounts for approximately 45–60%, and H2 accounts for 20–30% of the total volatile species.