Reactor-scale Simulations Research Articles

Reduced-order condensed-phase kinetic models for polyethylene, polypropylene and polystyrene thermochemical recycling

Thermochemical recycling of plastic waste (PW) into chemicals and energy vectors requires coupling particle and reactor-scale simulations to accurate condensed phase pyrolysis mechanisms for each constituent. This work proposes a methodology to derive reduced-order condensed-phase kinetic models from validated semi-detailed kinetic mechanisms. Two types of kinetic models are obtained for polyethylene (PE), polypropylene (PP) and polystyrene (PS): reduced semi-detailed models and multi-step fully lumped ones. These families offer different compromises between accuracy and computational cost. The former employ 50–100 gas + liquid species and describe both the radical degradation and the detailed carbon distribution of the products. Conversely, the latter involves 5–10 species per polymer tracking only the main petroleum cuts. The kinetic mechanisms are complemented by the definition of thermochemical properties of gas, liquid, and solid-phase species, accounting for phase-transitions through pseudo-chemical reactions. Model validations are performed by comparison with experimental data and the original semi-detailed mechanisms in terms of mass loss, heat fluxes and product distribution profiles. The resulting CHEMKIN-like condensed-phase models are attached as Supplementary Material and as a GitHub repository. Extending the proposed approach to other polymers and coupling it with existing subsets in the CRECK kinetic framework (e.g., biomass, PVC, PET) offers a powerful tool to model thermochemical recycling of PW and biomass/PW mixtures.

Investigations of atomic and molecular processes of NBI-heated discharges in the MAST Upgrade Super-X divertor with implications for reactors

This experimental study presents an in-depth investigation of the performance of the MAST-U Super-X divertor during NBI-heated operation (up to 2.5 MW) focussing on volumetric ion sources and sinks as well as power losses during detachment. The particle balance and power loss analysis revealed the crucial role of Molecular Activated Recombination and Dissociation (MAR and MAD) ion sinks in divertor particle and power balance, which remain pronounced in the change from ohmic to higher power (NBI heated) L-mode conditions. The importance of MAR and MAD remains with double the absorbed NBI heating. MAD results in significant power dissipation (up to ∼20% of PSOL ), mostly in the cold ( Te<5 eV) detached region. Theoretical and experimental evidence is found for the potential contribution of D− to MAR and MAD, which warrants further study. These results suggest that MAR and MAD can be relevant in higher power conditions than the ohmic conditions studied previously. Post-processing reactor-scale simulations suggests that MAR and MAD can play a significant role in divertor physics and synthetic diagnostic signals of reactor-scale devices, which are currently underestimated in exhaust simulations. This raises implications for the accuracy of reactor-scale divertor simulations of particularly tightly baffled (alternative) divertor configurations.

On the inaccuracies of point-particle approach for char conversion modeling

Char conversion is a complex phenomenon that involves not only heterogeneous reactions but also external and internal heat and mass transfer. Reactor-scale simulations often use a point-particle approach (PP approach) as sub-models for char conversion because of its low computational cost. Despite a number of simplifications involved in the PP approach, there are very few studies that systematically investigate the inaccuracies of the PP approach. This study aims to compare and identify when and why the PP approach deviates from resolved-particle simulations (RP approach). Simulations have been carried out for CO2 gasification of a char particle under zone II conditions (i.e., pore diffusion control) using both PP and RP approaches. Results showed significant deviations between the two approaches for the effectiveness factor, gas compositions, particle temperature, and particle diameter. The most significant sources of inaccuracies in the PP approach are negligence of the non-uniform temperature inside the particle and the inability to accurately model external heat transfer. Under the conditions with low effectiveness factors, the errors of intra-particle processes were dominant while the errors of external processes became dominant when effectiveness factors were close to unity. Because it assumes uniform internal temperature, the models applying the PP approach always predict higher effectiveness factors than the RP approach, despite its accurate estimation of intra-particle mass diffusion effects. As a consequence, the PP approach failed to predict the particle size changes accurately. Meanwhile, no conventional term for external heat transfer could explain the inaccuracy, indicating the importance of other sources of errors such as 2D/3D asymmetry or penetration of external flows inside the particles.

Towards modeling of ZrO2 atomic layer deposition at reactor scale based on experimental kinetic approximation

In this study, the growth kinetics of ZrO2 via the atomic layer deposition (ALD) using a mixed alkylamido-cyclopentadienyl zirconium precursor are proposed based on experimental data to evaluate the film growth behavior using reactor-scale simulation. In the ALD process, the hydroxyl concentration on the targeted surface govern the saturated growth per cycle values. However, we found that the bulkiness of remaining ligands on adsorbed species hinders the adsorption of Cp-Zr molecules.Considering this phenomenon, we proposed a kinetic model by calculating the energetic terms to quantify the “steric hindrance effect” of the first elementary surface reaction of CpZr(N(CH3)2)3 precursor (Cp-Zr), which enables the film growth prediction with the reactor-scale computational fluid dynamic (CFD) model.According to the experimental ALD process, the film growth was found to be influenced by the steric hindrance factor, especially at the temperature range from 150 °C to 250 °C, but the hindrance effect decreases with increasing temperature and disappears at 300 °C. The effective activation energy of the adsorption of Cp-Zr molecules on Si substrate was estimated to be 0.175 eV. Further understanding of the kinetic of ZrO2 deposition in this study is estimated to contribute to the optimization of the high-k metal oxides ALD deposition processes.

Methodology for designing solution polymerization reactors based on multiscale model construction and simulation

This work aims to develop a reliable methodology for designing solution polymerization reactors based on multiscale model construction and simulation. Firstly, accurate polymerization kinetic model, thermodynamic property model, transport property model, fluid dynamic model and simplified equipment model are established. Secondly, process and reactor scale simulations are employed in systematically studying the impact of various factors (e.g., operating variables, reactor type, combination mode, structure) through coupling the established models. The design of reactor system is conducted by deeply analyzing simulated results and comprehensively considering various influence factors. The research scheme for polymerization reactor design, along with the proposed methods for model construction, multiscale modeling, simulation cases design and data analysis, are explained in detail. Furthermore, taking a pilot-scale copolymerization of ethylene and 1-octene as an example, 248 simulation cases are carried out to provide a comprehensive description on the process of its model construction and multi-scale simulations.

Pore-Resolving Simulations of Biomass Char Particle Combustion

Biomass char morphology affects combustion behavior at the particle scale for zone II conditions, in which both heterogeneous reaction and intra-particle diffusion govern the overall rate. Furthermore, particle-scale processes affect reactor-scale outputs, and reactor-scale simulations are sensitive to particle-scale models. However, most char particle combustion models employ coarse-grained, effective-continuum approaches, which treat all porosity at the subgrid-scale. Effective-continuum approaches are not valid or accurate in the presence of large, irregular pores which can approach the size of the particle. A 3-D, pore-resolving CFD simulation approach using real biomass char particle geometries obtained from X-ray micro-computed tomography (micro-CT) is therefore used to examine the impact of morphology on zone II combustion for pulverized (∼100 µm) biomass char particles for the first time. In contrast to larger, millimeter to centimeter sized particles, the sub-millimeter, high aspect ratio biomass char particles exhibited localized reactant penetration into the innermost regions of the particles, facilitated by the presence of large pores connected to the external surface. The oxygen mole fraction distributions were governed by the large pore morphology, were non-monotonic with distance from the surface, and achieved minima in thick microporous char regions surrounding the large pores. A comparison between the pore-resolving simulation and an equivalent, spatially resolved, effective-continuum simulation revealed that even in the microporous char, the effective-continuum model underpredicted reactant penetration. A careful comparison was then performed between 30 pore-resolving particle simulations and several effectiveness factor models that employed particle-specific parameters. Commonly used uniform cylinder models significantly underpredicted effectiveness factors for these real pulverized pine char particles, while accessible hollow cylinder models achieved less than 10% relative error when averaged over all 30 particles.

A numerical approach on the selection of the purge flow rate in an atomic layer deposition (ALD) process

The variation of the purge flow rate is investigated in a reactor scale simulation of a typical atomic layer deposition (ALD) process. The investigation in its context addresses the possible issues of inadequate deposition rates with regard to the purge flow rate. A three-dimensional reactor is numerically implemented to simulate the physical and chemical processes to fabricate aluminum oxide (Al2O3) thin films. The purge flow rate disparity is focused to examine the effects within the fluid flow, mass transport, along with the chemical kinetics of the ALD process. The fabrication process employs trimethyl-aluminum and ozone (O3) as the metal and oxidant precursors, respectively, and inert argon as the purge gas. The reactor operation is set up to operate at a pressure of 10 torrs, with a substrate temperature of 200 °C. Three purge flow rates of 20, 10, and 5 sccm, respectively, have been examined. It was discovered that the slower flow rate showed, superior mass fraction distribution, reached unity surface coverage, and a time extensive surface deposition rate. A prolonged ozone exposure was crucial in providing an adequately oxidized substrate. The 20, 10, and 5 sccm purge flow rate growth obtained a 0.58, 0.85, and 1.6 Å/cycle, respectively. These findings revealing close similarities to experimental behaviors and recorded growths.

Multiscale CFD simulation of biomass fast pyrolysis with a machine learning derived intra-particle model and detailed pyrolysis kinetics

Coupling particle and reactor scale models is as essential as reactor fluid dynamics and particle motion for accurate Computational Fluid Dynamic (CFD) simulations of biomass fast pyrolysis reactors due to intraparticle heat transfer and chemical reactions controlling conversion time and product distributions. Direct online coupling of a particle model with a reactor model is computationally expensive, while offline coupling is case-dependent. In this research, solutions from a series of particle pyrolysis simulations were regressed with Artificial Neural Network (ANN). This machine learning-derived model predicted the same temperature and conversion profiles compared with particle resolved simulation while the isothermal approach overpredicted the temperature by 130 K and underpredicted the conversion time by 30 s. The ANN model was then integrated into CFD simulations of fluidized bed biomass fast pyrolysis with varied feedstocks via coupling PyTorch and MFiX. The averaged error of simulation predicted bio-oil yields with four feedstocks is 6.4%. This multi-scale approach provides an efficient tool for the coupled particle and reactor scale simulations of biomass pyrolysis.

Modeling and analysis of sulfur hexafluoride plasma etching for silicon microcavity resonators

Silicon microcavity resonators are an important component in modern photonics. In order to optimize their performance, it is fundamental to control their final shape, in particular with respect to the involved CMOS compatible, two-step sulfur hexafluoride plasma etching fabrication process. To that end, we use a ray-tracing based pseudo-particle model to enhance a level-set topography simulator enabling us to effectively capture the characteristics of sulfur hexafluoride plasma etching in the low-voltage-bias regime. By introducing a novel and robust calibration procedure and by applying it to experimental data of a reference two-step etching process, we are able to optimize the etch times and photoresist geometry without costly reactor-scale simulations and simultaneously explore beyond conventional statistical process modeling. Through defining objective design criteria by way of Gaussian beam analysis, we analyze the plasma etching process and provide new insights into alternative processing guidelines which impact shape measurements such as cavity opening and parabolic form. By means of scale analysis, we propose that the radius of curvature of the microcavity is optimized with a reduction of the photoresist opening diameter. After simulated fabrication runs, we surmise that the cavity quality parameters are improved by increasing the duration of the first etch step by a factor of 2 and by decreasing the second etch step duration by up to in comparison to the reference two-step etching process. This results in an overall reduction of etch time of at least , allowing to significantly optimize the overall fabrication process.

Reactor scale simulations of ALD and ALE: Ideal and non-ideal self-limited processes in a cylindrical and a 300 mm wafer cross-flow reactor

We have developed a simulation tool to model self-limited processes such as atomic layer deposition (ALD) and atomic layer etching inside reactors of arbitrary geometry as well the output of in situ quartz crystal microbalance and mass spectrometry. We have applied this model to two standard types of cross-flow reactors: a cylindrical tube reactor and a model 300 mm wafer reactor, and explored both ideal and nonideal self-limited kinetics. The model results are in agreement with experimental results and analytic expressions obtained using a simple plug-flow model for the cylindrical tube reactor. We also extended the simulations to consider two nonideal self-limited processes: soft-saturating processes characterized by a slow reaction pathway and processes where surface by-products can compete with the precursor for the same pool of adsorption sites. Our results show that it is possible to have a self-limited process with saturated yet inhomogeneous growth profiles due to the competition of reactor by-products. This is in agreement with experimental observations for titanium dioxide ALD from titanium tetraisopropoxide and titanium tetrachloride precursors.

Direct-simulation Monte Carlo modeling of reactor-scale gas-dynamic phenomena in a multiwafer atomic-layer deposition batch reactor

Atomic layer deposition (ALD) using multiwafer batch reactors has now emerged as the manufacturing process of choice for modern microelectronics at a massive scale. Stringent process requirements of thin film deposition uniformity within wafer (WiW) and wafer–wafer (WTW) in the batch, film conformity along submicrometer wafer features, thin film quality, and the utilization of expensive precursors in the reactor dictate ALD reactor design and process parameter optimization. This paper discusses a particle-based direct-simulation Monte Carlo (DSMC) of the full reactor scale simulation that overcomes the low Knudsen number limitation of typical continuum computational fluid dynamics approaches used for modeling low-pressure ALD reactors. A representative industrial multiwafer batch reactor used for the deposition of Si-based thin films with N2 and Si2Cl6 (hexachlorodisilane) as process feed gases with pressures in the range 43–130 Pa and a uniform reactor temperature of 600 °C is simulated. The model provides detailed insights into the flow physics associated with the transport of the precursor species from the inlets, through wafer feed nozzles, into the interwafer regions, and finally through the outlet. The reactor operating conditions are shown to be in the slip/transitional flow regime for much of the reactor volume and especially the feed gas nozzle and interwafer regions (where the Knudsen number approaches ∼0.2), justifying the need for a high-Knudsen number DSMC approach as in this work. For the simulated conditions, the nonuniformity of precursor species immediately above the wafer surface is predicted to be within &amp;lt;1% for a given wafer and &amp;lt;2% across the entire multiwafer stack. Results indicate that higher pressure degrades WiW and WTW uniformity. A reactor flow efficiency is defined and found to be ∼99%, irrespective of the chamber pressure.

Startup and Quench Electromagnetic Simulation of a Bitter Plate TF Coil Concept For the Fusion Nuclear Science Facility (FNSF)

Current distributions during startup and quench of very large reactor relevant coil systems will vary significantly from the smaller prototype magnets. A reactor scale simulation is needed. In this study, the FNSF magnet from the 2017 study is used as an example of a full sized reactor. The intent of the study is to investigate use of HTS conductors in the FNSF and how sizing and performance might be affected. A pancake or Bitter magnet like winding pattern is investigated to allow inductive and resistive redistribution of currents. A portion of the winding pack retains some resistivity to aid in redistribution of current during a transient or quench. Resistive materials can be used to support energy absorption for stability or to provide partial current dump capability during a quench, however, the primary quench mitigation mechanism is inductive redistribution of currents around the quench zone. In this implementation, the Bitter plate is both structural - similar to radial plates in ITER and electrical, intended, to limit current concentration during ramp-up. Use of localized resistors and parallel current paths are used to encourage more uniform startup currents. The analysis is a transient electromagnetic simulation using ANSYS. It is a cyclic symmetry modeling of an individual plate and is limited by the assumption that a local quench is repeated by the cyclic symmetry. This is a concession to the model size. Results are discussed in the context of performance needed for the FNSF.

Numerical simulation of a reacting porous char particle in supercritical water with structural evolution

A deep understanding of the particle conversion behavior is necessary for reactor-scale simulation and design, and the unqiue properties of supercritical water make it different from traditional gasification/combustion process. A 2-D transient numerical model coupling flow, heat transfer, species transport and porous structure evolution was therefore developed in this paper for supercritical water gasification of a single porous char particle. The gasification behavior was studied from 873 to 1023 K for particles of 0.1 and 0.5 mm, and the effects of convection and structural parameters were discussed. The results showed that the gasification shifted from kinetically controlled regime to diffusion controlled regime as temperature and particle size increased, and the conversion characteristics in each regime were quite different with the comprehensive effects of temperature and species distribution and porous structure. Under convective conditions, both heat and mass transfer was enhanced which significantly promoted char gasification, and asymmetric conversion was observed. Besides, the increase of the structural parameter ψ in random pore model and initial porosity shortened the char conversion time and showed more significant impact in kinetically controlled regime.

Bridging particle and reactor scales in the simulation of biomass fast pyrolysis by coupling particle resolved simulation and coarse grained CFD-DEM

Efficient utilization of biomass is challenging due to the complexity of the feedstock at molecular, particle, and reactor scales. Direct coupling of particle scale model and reactor scale simulation is computationally infeasible. In this research, the results from a particle resolved simulation were used to calibrate the heat transfer and reaction kinetics of particles. A hybrid drag model was used to consider the different fluidization properties of sands and biomass particles. The computation cost was reduced using a coarse-grained Discrete Element Method (DEM). The simulated conversion rate, char yield, tar yield, and pyrolysis gas yield compare well with experiment. The residence time and axial distributions of biomass were also analyzed. This novel multi-scale method provides an efficient and accurate tool for the modeling of biomass pyrolysis reactors.

Integrated Particle- and Reactor-Scale Simulation of Pine Pyrolysis in a Fluidized Bed

We report results from a multiscale computational modeling study of biomass fast pyrolysis in an experimental laboratory reactor that combined the hydrodynamics predicted by a two-fluid model (TFM)...

Electrons to Reactors Multiscale Modeling: Catalytic CO Oxidation over RuO2

First-principles kinetic Monte Carlo (1p-kMC) simulations for CO oxidation on two RuO2 facets, RuO2(110) and RuO2(111), were coupled to the computational fluid dynamics (CFD) simulations package MFIX, and reactor-scale simulations were then performed. 1p-kMC coupled with CFD has recently been shown as a feasible method for translating molecular scale mechanistic knowledge to the reactor scale, enabling comparisons to in situ and online experimental measurements. Only a few studies with such coupling have been published. This work incorporates multiple catalytic surface facets into the scale-coupled simulation, and three possibilities were investigated: the two possibilities of each facet individually being the dominant phase in the reactor, and also the possibility that both facets were present on the catalyst particles in the ratio predicted by an ab initio thermodynamics-based Wulff construction. When lateral interactions between adsorbates were included in the 1p-kMC simulations, the two surfaces, RuO2...

Field-Aligned Interpolation for Semi-Lagrangian Gyrokinetic Simulations

This work is devoted to the study of field-aligned interpolation in semi-Lagrangian codes. In the context of numerical simulations of magnetic fusion devices, this approach is motivated by the observation that gradients of the solution along the magnetic field lines are typically much smaller than along a perpendicular direction. In toroidal geometry, field-aligned interpolation consists of a 1D interpolation along the field line, combined with 2D interpolations on the poloidal planes (at the intersections with the field line). A theoretical justification of the method is provided in the simplified context of constant advection on a 2D periodic domain: unconditional stability is proven, and error estimates are given which highlight the advantages of field-aligned interpolation. The same methodology is successfully applied to the solution of the gyrokinetic Vlasov equation, for which we present the ion temperature gradient (ITG) instability as a classical test-case: first we solve this in cylindrical geometry (screw-pinch), and next in toroidal geometry (circular Tokamak). In the first case, the algorithm is implemented in Selalib (semi-Lagrangian library), and the numerical simulations provide linear growth rates that are in accordance with the linear dispersion analysis. In the second case, the algorithm is implemented in the Gysela code, and the numerical simulations are benchmarked with those employing the standard (not aligned) scheme. Numerical experiments show that field-aligned interpolation leads to considerable memory savings for the same level of accuracy; substantial savings are also expected in reactor-scale simulations.

Simulation of biomass particle evolution under pyrolysis conditions using lattice Boltzmann method

To accurately characterize biomass fast pyrolysis at the particle scale, intra-particle transport phenomena needs to be considered together with the gas flow surrounding the particle. In this study, a detailed numerical method was used to simulate the evolution of biomass particles under fast pyrolysis conditions. To conduct particle-scale simulations, the lattice Boltzmann method (LBM) was employed to solve the conservation equations, and pyrolysis kinetics were implemented to describe the chemical reactions. The present model was validated by comparing the numerical results with experimental data for a single biomass particle under pyrolysis conditions. The predicted temperature and conversion history agree with the experimental data. The temperature and density fields in the particle were found to be anisotropic due to the effect of the gas flow surrounding the particle, which was ignored by the 1D model. The non-uniform distributions of surface temperature indicate that using a constant temperature or heat flux as boundary conditions may cause numerical errors. Sensitivity analysis shows that density is the most influential parameter while porosity is the least. The heat of reaction converting the intermediate solid to char is more dominant than those of the three primary reactions. A parametric study was conducted to investigate the effect of particle shape on conversion time and final product yields. The simulation results show that the conversion time decreased when using the elliptic particle instead of the regular (circular) particle. The model also shows that more tar and syngas were produced, while less char was generated from an elliptic particle. The effect of particle shape on the center temperature of the biomass particle can be explained by comparing the heat transfer conditions at the front of the particle and the convective heat transfer at the top and bottom of the particle. The results demonstrated that the current LBM framework has the ability to reveal the detailed conversion process of biomass particles under various pyrolysis conditions, which can then be used to improve engineering models for reactor-scale simulation.

Modeling reaction–diffusion processes within catalyst washcoats: I. Microscale processes based on three-dimensional reconstructions

This paper develops a detailed analysis of reaction–diffusion processes within a porous rhodium-alumina catalyst washcoat. Focused-ion-beam–scanning-electron-microscope (FIB–SEM) techniques are developed and applied to reconstruct the actual catalyst-support microstructure. Three-dimensional transport processes within washcoat micro-pore structures are modeled using a dimensionless representation of reaction and diffusion rates based on the Damköhler number. Three-dimensional computational solutions for particular porous microstructures are modeled and interpreted. In a companion paper, these microstructural results are used to assist development of larger-scale models that can be incorporated into reactor-scale simulations.

Investigating atomic layer deposition characteristics in multi-outlet viscous flow reactors through reactor scale simulations

In order to minimize the operational time of atomic layer deposition (ALD) process, flow transports and film depositions are investigated in multi-outlet viscous flow reactors through reactor scale simulations. The simulation process is performed on depositions of Al2O3 films using trimethylaluminum and ozone as the precursors, and inert argon as the purge gas. The chemistry mechanism used includes both gas-phase and surface reactions. Simulations are performed at a fixed operating pressure of 10Torr (1330Pa) and at two substrate temperatures of 250°C and 300°C, respectively. Flows inside the reactors are following the continuum approach; as a result, the Navier–Stokes, energy and species transport equations can be used to simulate transient, laminar and multi-component reacting flows. Based on the chemistry mechanism adopted in this study, the amount of oxygen atoms produced from the ozone decomposition is found to be the major reason for discrepancies in oxidation times and deposition rates at different ALD processes. A reactor with fewer outlets minimizes the ALD operational times by reducing both oxidation time and second purge time. In addition, higher deposition rates at a shorter time are obtained by using a reactor with fewer outlets. However, assigning a long enough time for the ozone exposure results in independency of ALD characteristics from the number of outlets such that the growth rates of around 3.78angstrom/cycle and 4.52angstrom/cycle are obtained for the substrate temperatures of 250°C and 300°C, respectively.