Plug Flow Reactor Research Articles

Development of Steady-State and Dynamic Mass and Energy Constrained Neural Networks for Distributed Chemical Systems Using Noisy Transient Data.

The paper presents the development of algorithms for mass and energy constrained neural network models that can exactly conserve the overall mass and energy of distributed chemical process systems, even though the noisy transient data used for optimal model training violate the same. In contrast to approximately satisfying mass and energy balance constraints of a system by soft penalization of objective function, algorithms have been developed for solving equality-constrained nonlinear optimization problems, thus providing the guarantee of exactly satisfying the system mass and energy conservation laws. For developing dynamic mass-energy constrained network models for distributed systems, hybrid series and parallel dynamic-static neural networks have been leveraged. The developed algorithms for solving both the training and forward problems are validated using both steady-state and dynamic data in the presence of various noise characteristics. The developed data-driven algorithms are flexible to exactly satisfy mass and energy balance constraints for dynamic chemical processes if the system holdup information is available. The proposed network structures and algorithms are applied to the development of data-driven lumped and distributed models of an adiabatic superheater/reheater system, a nonisothermal continuous stirred tank reactor, as well as an electrically heated plug-flow reactor system where one form of energy gets transformed to another. It has been observed that the mass-energy constrained neural networks yield a root mean squared error of <1% with respect to the system truth for the case studies evaluated in this work.

Pilot Scale Electrolysis of Peroxodicarbonate as an Oxidizer for Lignin Valorization.

A pilot scale plant at Technology Readiness Level (TRL) 6 comprising an electrochemical ex-cell continuous production of sodium peroxodicarbonate and a thermal depolymerization plug flow reactor for kraft lignin conversion is established. Due to the labile nature of the "green" oxidizer peroxodicarbonate, special attention must be paid to the production parameters in order to optimize its use. A simplified design model describing steady-state and transient operations is formulated and finally validated against experimental data from the electrolysis setup. Design trade-offs are visualized, and their impact on specific energy consumption is evaluated. The pilot plant was operated for a 20-month period for more than 1200 h on-stream. Optimized process conditions result in vanillin yields of 8 wt % and thus prove the successful scale-up.

Scale-up of plug-flow reactors in anaerobic treatment of agro-industrial wastes

This study is aiming to evaluate the optimization potential of anaerobic digestion systems for the treatment of complex agro-industrial wastes at an industrial scale. In previous work, the performance of a 20 L pilot-scale Plug Flow Reactor (PFR) that was able to operate at Organic Loading Rates (OLRs) of up to 25 kg Chemical Oxygen Demand (COD) m−3 d−1, was demonstrated. This concept was then successfully transferred in a semi-industrial scale PFR of a volume equal to 50 m3, and the optimal operational parameters were evaluated. The construction of a full industrial scale facility followed, utilizing initially a 380 m3 PFR. Since PFR systems in practice do not behave ideally, due to short Length to Diameter ratio (L/D) and/or higher axial dispersion, the ideal PFR behavior was compared with real data of the non-ideal industrial-scale system; a performance reduction of 25–30 % was detected. However, the disadvantage of the non-ideal behavior of PFRs can be overcome by the cascaded arrangement of two such reactors (2 × 380 m3 PFRs), leading to a total volume reduction of 35 %, as depicted by experimentation on the industrial scale cascaded PFRs. The optimal design parameters for the PFRs are provided.

Redox and Kinetic Properties of Composition-Dependent Active Sites in Copper-Exchanged Chabazite for Direct Methane-to-Methanol Oxidation.

The CH4 oxidation performance of Cu-chabazite zeolites characterized by distinct Si/Al ratios and Cu loadings has been studied and the observed variations in reactivity have been correlated to the differences in the nature of the formed active centers. Plug flow reactor tests, in situ Fourier-transform infrared, and X-ray absorption spectroscopy demonstrate that a decrease in Cu loading shifts the reactivity/redox profile to higher temperatures and increases the CH3OH selectivity and Cu-efficiency. In situ electron paramagnetic resonance, Raman, ultraviolet-visible, Fourier-transform infrared, and photoluminescence spectroscopies reveal that this behavior is associated with the presence of monomeric Cu active sites, including bare Cu2+ and [CuOH]+ present at low Si/Al ratio and Cu loading. Formation of two distinct [Cu2(µ-O)]2+ moieties at higher Si/Al ratio or Cu loading forces these trends into the opposite direction. Operando electron paramagnetic resonance and ultraviolet-visible spectroscopy show that the apparent activation energy of monomeric Cu active species decreases with increasing Si/Al ratio, whereas the one of dimeric centers is unaffected.

Rim Driven Thruster as Innovative Propulsion Element for Dual Phase Flows in Plug Flow Reactors

The purpose of this work was to test a new setup to pump water with entrained air for application in gas fermentation. A mixed flow, where gas is contained in a liquid to be pumped, rapidly reduces the efficiency of a conventional pump, due to the compressibility of the gas. It is not always possible to degas the fluid, for instance in gas fermentation, which is preferably carried out in tubular reactors (loop fermenters) to achieve a high conversion rate of the gaseous feedstocks. Method: In this work, a rim-driven thruster (RDT) was tested in a lab-scale, cold flow model of a loop reactor with 5–30% (by volume) of gas fraction (air) in the liquid (water) as alternative propulsion element (6 m total pipe length, ambient temperature and pressure). As a result, it was found that the RDT, in connection with a guiding vane providing swirling motion to the two-phase fluid, could pump a mixed flow with up to 25.7% of gas content (by volume) at atmospheric pressure and 25 °C and 0.5 to 2 m/s flow speed. In conclusion, an RDT is advantageous over a classic propulsion element like a centrifugal pump or axial flow pump for transporting liquids with entrained gases. This article describes the potential of rim-driven thrusters, as known from marine propulsion, in biotechnology, the chemical industry, and beyond, to handle multiphase flows.

Scaling the polymerization of polyaldehydes through continuous flow synthesis

A plug flow reactor was constructed to scale the synthesis of metastable, phthalaldehyde-based polymers to achieve production rates of 1–2 kg per day. The flow-induced mixing and in-line polymerization quench and precipitation sequences resulted in improved polymer purity and long-term stability compared to the same materials made from a conventional batch process. Cryogenic rheology was used to probe the complex fluid dynamics encountered during the polymerization of PPA homopolymers. It is envisioned that this continuous flow manufacturing approach could be extended to other low ceiling temperature or aldehyde monomer systems to help implement and support a plastic circular economy.Graphical abstract

Demystifying group-4 polyolefin hydrogenolysis catalysis: Gaseous propane hydrogenolysis mechanism over the same catalysts

A kinetic/mechanistic investigation of gaseous propane hydrogenolysis over the single-site heterogeneous polyolefin depolymerization catalysts AlS/ZrNp2 and AlS/HfNp2 (AlS = sulfated alumina, Np = neopentyl), is use to probe intrinsic catalyst properties without the complexities introduced by time- and viscosity-dependent polymer medium effects. In a polymer-free automated plug-flow catalytic reactor, propane hydrogenolysis turnover frequencies approach 3,000 h-1 at 150 °C. Both catalysts exhibit approximately linear relationships between rate and [H2] at substoichiometric [H2] with rate law orders of 0.66 ± 0.09 and 0.48 ± 0.07 for Hf and Zr, respectively; at higher [H2], the rates approach zero-order in [H2]. Reaction orders in [C3H8] and [catalyst] are essentially zero-order under all conditions, with the former implying rapid, irreversible alkane binding/activation. This rate law, activation parameter, and DFT energy span analysis support a scenario in which [H2] is pivotal in one of two plausible and competing rate-determining transition states-bimolecular metal-alkyl bond hydrogenolysis vs. unimolecular β-alkyl elimination. The Zr and Hf catalyst activation parameters, ΔH‡ = 16.8 ± 0.2 kcal mol-1 and 18.2 ± 0.6 kcal mol-1, respectively, track the relative turnover frequencies, while ΔS‡ = -19.1 ± 0.8 and -16.7 ± 1.4 cal mol-1 K-1, respectively, imply highly organized transition states. These catalysts maintain activity up to 200 °C, while time-on-stream data indicate multiday activities with an extrapolated turnover number ~92,000 at 150 °C for the Zr catalyst. This methodology is attractive for depolymerization catalyst discovery and process optimization.

Hydrodynamic study of a flow-rig column by means of a radiotracer technique modelling with DTS-Pro 4

Abstract The residence time distribution (RTD) is very reliable, providing valuable information about the performance of process equipment such as reactors and columns. The aim of this work is to study the effect of agitation in the hydrodynamic column of flow-rig. In this case, residence time distribution (RTD) is determined using the radiotracer approach. The radiotracer is the Technetium Tc-99m with half decay 6 h. It also emits gamma rays with an energy of 0.140 MeV. 2 mL of approximately 9 mCi activity Tc-99m was injected inside the column. The results show that in the conditions studied the column presents the anomaly, dead volume. The Intensity function A(t) confirms this result. Agitation has a beneficial effect in the reduction of dead volume. To revise the conception of the column or study other parameters like the variation flow rate can reduce or eliminate the dead volume. The RTD model indicated the column behaved as a Plug flow reactor (PFR) with mixing cells in serie (J = 4) model and the RTD experiment verified the model well.

Uncertainty quantification and data consistency analysis for the development of hydrogen and syngas oxidation model

The exponential growth of contemporary chemical kinetics data coupled with the potential inherent high uncertainty poses significant challenges for developing chemical kinetic models. To obtain a high-quality dataset for the optimization of H2 and syngas oxidation model, this study developed a framework for data consistency analysis and uncertainty analysis of chemical kinetic data. The framework combines simulations based on solving conservation equations, data-driven metaheuristic algorithms, and statistical analysis. Over 2000 experimental data points, including ignition delay times measured in shock tubes, laminar flame speeds, and concentration profiles measured in perfectly stirred reactors and plug flow reactors, were collected and used to construct the experimental dataset. Seventeen parameters of a detailed H2 and syngas oxidation model were selected to build the reaction rate constant (RRC) dataset. The initially estimated experimental uncertainties and RRC uncertainty factors were updated by slack variables in the iterative algorithm. Some high-uncertainty data were identified and excluded from the optimization dataset. The final experimental dataset achieves data consistency, and the feasible parameter set of RRC shows good prediction capability. The experimental data with high uncertainties were highlighted, and the uncertainty sources were analyzed.

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.

Improve the thermal performance of precooler by enhancing the utilization of chemical heat sink: Refined design method and characteristic analysis

The chemical heat sink of the coolant plays a crucial role in enhancing the performance of the precooler, which affects the overall performance of the air-breathing precooled engines. The conventional thermal design method for precoolers cannot accurately evaluate the chemical heat sink of coolants. To address this crucial issue, this paper proposes a refined model that considers the chemical reaction processes of n-Decane, based on a two-dimensional discretization unit model and the plug flow reactor model incorporating molecular-level chemical reaction mechanisms. The validation of this model is conducted by comparing it with publicly accessible data and computational fluid dynamics simulations, thereby demonstrating its excellent accuracy. Subsequently, an analysis is conducted on the factors influencing the chemical heat sink release of the coolant within the precooler, and enhanced design criteria for optimizing chemical heat sink utilization are proposed. Building upon these considerations, the performance of a precooler with a design point of Mach number 5 under off-design conditions was analyzed. The findings indicate that employing rational design methods can enhance the chemical heat sink efficiency of endothermic fuels by 8.0%, along with a concurrent 10.3% increase in the total heat sink. This underscores the significance of considering the impact of the chemical heat sink of endothermic fuels in the design of precoolers. In the case presented in this paper, the contribution of the chemical heat sink to the total heat sink within the n-Decane precooler could reach 35.3%.

All‐nonlinear static‐dynamic neural networks versus Bayesian machine learning for data‐driven modelling of chemical processes

AbstractIn recent decades, the utilization of machine learning (ML) and artificial intelligence (AI) approaches have been explored for process modelling applications. However, different types of ML models may have contrasting advantages and disadvantages, which become critical during the optimal selection of a specific data‐driven model for a particular application as well as estimation of parameters during model training. This paper compares and contrasts two different types of data‐driven modelling approaches, namely the series/parallel all‐nonlinear static‐dynamic neural network models and models from a Bayesian ML approach. Both types of AI modelling approaches considered in this work have shown to significantly outperform several state‐of‐the‐art steady‐state and dynamic data‐driven modelling techniques for various performance measures, specifically, model sparsity, predictive capabilities, and computational expense. The performances of the proposed model structures and algorithms have been evaluated for two nonlinear dynamic chemical engineering systems—a plug‐flow reactor for vapour phase cracking of acetone for production of acetic anhydride and a pilot‐plant for post‐combustion CO2 capture using monoethanolamine as the solvent. For the validation data from the CO2 capture pilot plant, root mean squared error (RMSE) for flue gas outlet temperature, flowrate and CO2 concentration is 0.05%, 1.07%, and 5.0%, respectively, for the all‐nonlinear static‐dynamic neural networks and 0.1%, 1.75%, and 14.14%, respectively, for the Bayesian ML models. For the plug flow reactor data, the Bayesian ML models yield superior RMSE compared to the all‐nonlinear static‐dynamic neural networks when the measurement data are corrupted with Gaussian, auto‐correlated, or cross‐correlated noise.

Determining kinetics of fast exothermic reactions using a flow calorimeter

Continuous flow calorimeters are considered an emerging technique due to their ability to reduce safety issues associated with highly exothermic rapid reactions. In this study, a custom-made isoperibolic flow calorimeter was constructed, which uses a pyroelectric IR Sensor for temperature profile recording. The objective of this study is to validate the reactor concept for the determination kinetic parameters. Residence time distribution (RTD) analysis was conducted to assess the mixing performance of the packed-bed reactor employed in the calorimeter. This calorimeter was connected to a custom-made conductivity flow cell (CFC), to measure the in-line conductivity of the outlet stream. An axially dispersed plug flow reactor model (AD-PFR) is required to be able to incorporate the non-ideal behaviour of the flow. The experimental apparatus design and methodology was validated by conducting the hydrolysis of acetic anhydride. The activation energy, EA and the pre-exponential factor, ln(k0) for the hydrolysis of acetic anhydride were found to be 52.05 kJ mol−1 and 12.26 (s−1), respectively, which falls within the range of reported values. The new flow calorimeter proved to be effective, and accurate.

Optimized Spatial Configuration of Heterogeneous Biocatalysts Maximizes Cell-Free Biosynthesis of ω-Hydroxy and ω-Amino Acids.

Cell-free biocatalysis is gaining momentum in producing value-added chemicals, particularly in stepwise reaction cascades. However, the stability of enzyme cascades in industrial settings is often compromised when free enzymes are involved. In this study, we have developed a stable multifunctional heterogeneous biocatalyst coimmobilizing five enzymes on microparticles to transform 1,ω-diols into 1,ω-hydroxy acids. We improved the operational efficiency and stability of the heterogeneous biocatalyst by fine-tuning the enzyme loading and spatial organization. Stability issues are overcome through postimmobilization polymer coating. The general applicability of this heterogeneous biocatalyst is demonstrated by its scale-up in both batch and packed bed reactors, allowing a product yield of >80%. The continuous process is fed with H2O2 as the oxygen source, reaching a space-time yield (STY) of 0.76 g·L-1·h-1, maintained for the first 12 h. Finally, this flow system is telescoped with a second plug-flow reactor packed with a different heterogeneous biocatalyst integrating an additional transaminase. As a result, this 6-enzyme 2-reactor system sequentially transforms 1,ω-diols into 1,ω-amino acids while in situ recycling NAD+, depleting H2O2, and generating O2.

Plug Flow Reactor (PFR) Design for the Production of 100,000 tons per year of Cumene from the Catalytic Alkylation of Propylene and Benzene

In a bid to meet the ever-growing global demand for cumene based on its wide range of industrial applications and economic importance, the research considered the design of a plug-flow reactor (PFR) for the production of 100,000 tons of cumene per year from the catalytic alkylation of propylene and benzene. The PFR design models were developed by performing the mass and energy balance over the reactor at steady-state operation. The steady-state PFR performance models were simulated using the MATLAB R2023a version at an initial feed and operating temperature of 481.10 K and 483 K with varying fractional conversions from 0 to 0.95 at 0.05 intervals. At a maximum fractional conversion of 0.95, the PFR design specification for volume, height, diameter, space time, space velocity, quantity of heat generated, and quantity of heat generated per unit volume of the reactor was 19.7707 m3, 4.6523 m, 2.3261 m, 3.8766 s, 0.2580 s-1, 1.8035 J/s, and 0.03448 J/sm3, respectively. The profile behavior of the PFR functional parameters at changes in fractional conversion is in agreement with the trend for PFR operation at steady-state conditions, as shown in Figures 2–10. The evaluation of the PFR yearly production dependent on the reactor volume stood at $2,049.838. The article has shown that PFR is a suitable reaction medium for the catalytic alkylation process for optimum production of cumene and sustainability.

Shallow beds are not plug flow reactors – Analysis of kinetic data in the presence of axial dispersion effects

Laboratory-scale shallow beds filled with catalyst particles are frequently used in catalyst screening, activity tests and kinetic measurements. Often the experimental data are interpreted with plug flow or differential reactor models. Residence time measurements have shown large deviations from ideal plug flow behavior in shallow beds, indication the presence of axial dispersion effects, i.e. is backmixing and diffusion in the bed. The behavior of laboratory-scale bed reactors was investigated by theoretical considerations of the axial dispersion model and numerical simulations in the Damköhler-Péclet space. The results revealed that large errors in kinetic parameters can appear when the dispersion model is replaced by the plug flow model. This key effect was quantified using the ratio (F) of two Damköhler numbers: the real one, and the one wrongly estimated on experimental data affected by dispersion problems and interpreted with ideal plug-flow approach. Thus, the effect of back-mixing is evaluated varying a single parameter of the kinetic model, namely the rate constant. The conclusions are valid for power-law, Langmuir-Hinshelwood and Eley-Rideal kinetics.

Single mixed refrigerant biomethane liquefaction plant integrated with solar energy: Dynamic simulation for the decarbonization of the heavy road transport sector

This works proposes a dynamic thermoeconomic analysis of a liquefied biomethane production plant to meet the fuel demand of a fleet of heavy duty trucks in the south of Italy. The biomethane is obtained from the upgrading of the biogas produced by means of anaerobic digestion through a plug flow reactor fed by organic fraction of municipal solid waste. The upgrading of the biogas is realized using a three-stage membrane compression process, producing a 96 % pure biomethane. The biomethane liquefaction is realized using a single-mixed refrigerant process and compared to a Linde cycle process. The whole system is assisted by solar energy to reduce the fossil energy consumption of the process and feed-in tariffs are considered as funding policy. The models for the anaerobic digestion, the biogas upgrading, and the biomethane liquefaction are in detail developed in MatLab. The anaerobic digestion model is based on the ADM1 biological model, integrated with a suitable heat transfer model. The biogas upgrading model is based on a simplified Fick model. The liquefaction model is based on an equivalent two heat-exchangers model, taking into account the transient heat transfer. All the components are then integrated in TRNSYS to perform the dynamic simulation for one operating year of the whole system. Results from the thermoeconomic analysis are outstanding in terms of profitability, showing a payback period of less than 2 years and a Net Present Value of the system of 402 M€. The great environmental impact is also confirmed by a Primary Energy Saving of 91 % and a dramatic reduction of 86 % of the CO2 equivalent emissions.

Multiphase Numerical CFD Simulation of the Hydrothermal Liquefaction Process (HTL) of Sewage Sludge in a Tubular Reactor

This article presents multiphase numerical computational fluid dynamics (CFD) for simulating hydrothermal liquefaction of sewage sludge in a continuous plug-flow reactor. The discrete particle method (DPM) was used to analyze the solid particles’ interaction in liquid–solid high shear flows to investigate coupling computational fluid dynamics (CFD). Increasing solid particles’ interactions were observed with the increasing liquid velocity. The study examined the influence of parameters such as flow rate, temperature, and residence time on the efficiency of bio-oil production. An increase in temperature from 500 to 800 K caused an increase in the amount of biocrude oil produced from 12.4 to 32.9% within 60 min. In turn, an increase in the flow rate of the suspension from 10 to 60 mL/min caused a decrease in the amount of biocrude oil produced from 38.9 to 12.9%. This study offers insights into optimizing the flow channel of tubular reactors to enhance the HTL conversion efficiency of sewage sludge into biocrude oil. A parametric study was performed to investigate the effect of the slurry flow rate, temperature, and the external heat transfer coefficient on the biocrude oil production performance. The simulation data will be used in the future to design and scale up a large-scale HTL reactor.

Periodic Optimal Control of a Plug Flow Reactor Model with an Isoperimetric Constraint

We study a class of nonlinear hyperbolic partial differential equations with boundary control. This class describes chemical reactions of the type “A→\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A \\rightarrow $$\\end{document} product” carried out in a plug flow reactor (PFR) in the presence of an inert component. An isoperimetric optimal control problem with periodic boundary conditions and input constraints is formulated for the considered mathematical model in order to maximize the mean amount of product over the period. For the single-input system, the optimality of a bang-bang control strategy is proved in the class of bounded measurable inputs. The case of controlled flow rate input is also analyzed by exploiting the method of characteristics. A case study is performed to illustrate the performance of the reaction model under different control strategies.