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DOE OSTI2021

An Evolutionary Algorithm Approach to Multi-Pass ERL Optics Design

An Energy Recovery Experiment at CEBAF (ER@CEBAF) is aimed at demonstrating high energy, low current, multi-pass energy recovery at the existing 12 GeV CEBAF accelerator. The beam break-up instability, limiting the maximum beam current, can be controlled through minimizing beta functions for the lowest energy pass, which gives a preference to strongly focusing optics, e.g. a semi-periodic FODO lattice. On the other hand, one needs to limit beta function excursions, caused by under focusing, at the higher energy passes, which in turn favors weakly focusing linac optics. Balancing both effects is the main objective of proposed multi-pass linac optics optimization. Here, we discuss an optics design process for ER@CEBAF transverse optics using a genetic algorithm.

Neththikumara, I.↗

DOE OSTI2024

Defect Equilibria from First Principles: From Widegap Oxides to Topological Semimetals

Materials functionality and performance is rarely determined by the ideal crystal alone but is usually affected by formation of imperfections and the solution of impurities. In some applications, such as solar thermochemical hydrogen generation, defect formation is the fundamentally enabling mechanism of the desired functionality. In other cases, such as Cd3As2 topological semimetals, unintentional self-doping presents an obstacle to the access to the unique electronic properties. In either case, a quantitative understanding of the relevant defect mechanism is essential for developing design strategies. This presentation will touch upon numerous aspects in the computational simulation of defect equilibria, including non-equilibrium design strategies, the coupling of solid state and gas-phase reactions, dopant-defect and defect-defect interactions, both attractive and repulsive, the accuracy of total energy functionals and electronic structure methods, and the role of the shape of the density of states for the charge balance condition and Fermi level position, as well as machine-learning prediction of defect energies (1). Specific materials systems include Ga2O3 (2), Cd3As2 (3), and (Sr,Ce)MnO3 (4). (1) M.D. Witman, A. Goyal, T. Ogitsu, A.H. McDaniel, S. Lany, Nat. Comput. Sci. 3, 675 (2023). (2) A. Goyal, A. Zakutayev, V. Stevanovic, S. Lany, J. Appl. Phys. 129, 245704 (2021). (3) C. Brooks, M. van Schilfgaarde, D. Pashov, J.N. Nelson, K. Alberi, D.S. Dessau, S. Lany, Phys. Rev. B 107, 224110 (2023). (4) A. Goyal, M.D. Sanders, R.P. O'Hayre, S. Lany, PRX Energy 3, 013008 (2024).

CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS,M↗

DOE OSTI2021

Influence of functional groups on low-temperature combustion chemistry of biofuels

Ongoing progress in synthetic biology, metabolic engineering, and catalysis continues to produce a diverse array of advanced biofuels with complex molecular structure and functional groups. In order to integrate biofuels into existing combustion systems, and to optimize the design of next-generation combustion systems, understanding connections between molecular structure and ignition at low-temperature conditions (< 1000 K) remains a priority that is addressed in part using chemical kinetics modeling. The development of predictive models relies on detailed information, derived from experimental and theoretical studies, on molecular structure and chemical reactivity, both of which influence the balance of chain reactions that occur during combustion – propagation, termination, and branching. In broad context, three main categories of reactions affect ignition behavior: (i) initiation reactions that generate a distribution of organic radicals, ; (ii) competing unimolecular decomposition of and bimolecular reaction of with O2; (iii) decomposition mechanisms of peroxy radical adducts (RO), including isomerization via RO ⇌ OOH. Furthermore, all three categories are influenced by functional groups in different ways, which causes a shift in the balance of chain reactions that unfold over complex temperature- and pressure-dependent mechanisms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

In-situ magnetic alignment model for additive manufacturing of anisotropic bonded magnets

In this work, we report a mathematical framework which predicts the degree of alignment (DoA) in an in-situ aligned additively manufactured 3D printed bonded magnets. A multiphysics model is developed which couples the harmonious interactions of magnetic particles in a viscous flowing polymer under the presence of an external magnetic field. The hydrodynamic fluid-particle interaction is paired with the magnetophoretic force to predict the particle trajectory and distribution during extrusion through a 3D printer nozzle. Succeeding the force balance, a magnetohydrodynamic torque equilibrium analysis is performed to predict the net-orientation of the magnetic particles as a function of the applied field strength, viscous forces, and particle-to-particle interactions (P2P). Experimental validation of the DoA predictions is performed using 65 vol% Nd-Fe-B+Sm-Fe-N in Nylon12 (DoA exp = 0.620 and DoA theory = 0.686) and 15 vol% Sm-Co in PLA (DoA exp = 0.830 and DoA theory = 0.863). A parametric analysis is performed to analyze the effect of operating and design parameters like alignment field strength, magnetic loading fraction, extrusion load, and particle size. The model predicts a competing behavior between particle-fluid and particle-particle interactions under the presence of an applied field. Lastly, the model provides a framework to efficiently predict the DoA in tandem with a functionalized-magnetic 3D printer and allows the user to adjust the operating parameters according to the desired DoA.

36 MATERIALS SCIENCE↗

DOE OSTI2025

A Variational Autoencoder Model Toward Molecular Structure Representation Learning of Fuels

Here, in this work, a Variational Autoencoder (VAE)-based data-driven modeling framework is developed with the overarching goal of enabling fuel design. The VAE model is trained on a large dataset with several chemical species to learn a compressed latent space molecular representation. Chemical structure in the form of Simplified Molecular Input Line Entry System (SMILES) string is fed as input, encoded into the VAE latent space, and decoded back to the SMILES string using Long Short-Term Memory (LSTM) networks. Complexities of the VAE training loss function are thoroughly examined by varying the weightage (beta (𝜷) parameter) of the latent space regularization term, thereby assessing the balance between reconstruction accuracy and validity, and focusing on both accurate molecular structure reconstruction and latent space consistency. Two different strategies for 𝜷 variation are evaluated: linear annealing and cyclic annealing. In addition, the impact of total correlation adjustment and hierarchical priors is also studied with regard to the balance between reconstruction fidelity and latent space regularization, and potential issues such as posterior collapse, over-regularization, and poor disentanglement of latent variables. Overall, the best performance of the model is achieved with hierarchical priors and incrementally increasing 𝜷 from 0 to a threshold value of 0.25 over 75 epochs. The generative VAE model can be readily coupled with Quantitative Structure–Property Relationship (QSPR) analysis to develop an integrated end-to-end framework for fuel-property prediction and molecular design of novel promising fuels.

fuel design↗

DOE OSTI2025

Urban weather modeling using WRF: linking physical assumptions, code implementation, and observational needs

The Weather Research and Forecasting (WRF) model includes urban schemes that simulate the influence of urban surfaces on the atmosphere using parameterizations for flux, and radiative exchanges. Three core schemes – the Bulk urban parameterization, Single-Layer Urban Canopy Model (SLUCM), and Multi-Layer Urban Canopy Model (MLUCM) – represent increasing levels of complexity. Although the parameterizations within these urban schemes are described in the literature, their specific implementation remains poorly documented, thus slowing down model development efforts. This manuscript provides a roadmap to the three urban schemes in WRF version 4.5.2, presenting equations using the same symbols as in the model code, along with references to code lines, and including graphics and explanations that connect the code to its physical foundations. Our thorough review of the urban parameterizations implemented in WRF version 4.5.2 highlighted a handful of parameters that may introduce discontinuities in simulations: (i) in the SLUCM, a 1 mm h −1 rain rate threshold is employed to switch between two minimum moisture availability parameterizations, thus impacting latent heat flux calculations; (ii) in the SLUCM a threshold is used to partition shortwave radiation into direct and diffuse components; (iii) in all three urban schemes, the bulk Richardson number is employed to select the similarity function, which influences the vertical distribution of heat and momentum. We also identified a highly simplified treatment of the radiative balance on roof surfaces. The implications of these simplifications can be assessed through targeted observations across relevant conditions, including varying precipitation rates, cloud cover, and transitions between stability regimes. Furthermore, the widespread application of the Monin-Obukhov similarity theory in these urban schemes warrants model evaluation under highly stable and unstable conditions and in heterogeneous urban settings with variable land cover and building heights on scales finer than model resolution. To address these challenges, we offer guidance on observational strategies, emphasizing the need for multi-parametric measurements to capture potential compensating biases and multi-height measurements that align with the levels where quantities are diagnostic and prognosed in the model (i.e., the lowest atmospheric level of the WRF model). Finally, our inspection of the code revealed implementation bugs that have now been corrected in WRF versions 4.6.0 and 4.6.1. Sensitivity tests over the Atlanta urban area show that these corrections affect surface temperatures, underscoring the importance of performing rigorous documentation and verification of the implementation of parameterizations in model code.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Multi-objective optimization of root phenotypes for nutrient capture using evolutionary algorithms

Root phenotypes are avenues to the development of crop cultivars with improved nutrient capture, which is an important goal for global agriculture. The fitness landscape of root phenotypes is highly complex and multidimensional. It is difficult to predict which combinations of traits (phene states) will create the best performing integrated phenotypes in various environments. Brute force methods to map the fitness landscape by simulating millions of phenotypes in multiple environments are computationally challenging. Evolutionary optimization algorithms may provide more efficient avenues to explore high dimensional domains such as the root phenotypic space. We coupled the three-dimensional functional–structural plant model, SimRoot, to the Borg Multi-Objective Evolutionary Algorithm (MOEA) and the evolutionary search over several generations facilitated the identification of optimal root phenotypes balancing trade-offs across nutrient uptake, biomass accumulation, and root carbon costs in environments varying in nutrient availability. Our results show that several combinations of root phenes generate optimal integrated phenotypes where performance in one objective comes at the cost of reduced performance in one or more of the remaining objectives, and such combinations differed for mobile and non-mobile nutrients and for maize (a monocot) and bean (a dicot). Functional–structural plant models can be used with multi-objective optimization to identify optimal root phenotypes under various environments, including future climate scenarios, which will be useful in developing the more resilient, efficient crops urgently needed in global agriculture.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

Integrating subsystem embedding subalgebras and coupled cluster Green’s function: a theoretical foundation for quantum embedding in excitation manifold

Here, in this study, we introduce a novel approach to coupled-cluster Green's function (CCGF) embedding by seamlessly integrating conventional CCGF theory with the state-of-the-art sub-system embedding sub-algebras coupled cluster (SES-CC) formalism. This integration focuses primarily on delineating the characteristics of the sub-system and the corresponding segments of the Green's function, defined explicitly by active orbitals. Crucially, our work involves the adaptation of the SES-CC paradigm, addressing the left eigenvalue problem through a distinct form of Hamiltonian similarity transformation. This advancement not only facilitates a comprehensive representation of the interaction between the embedded sub-system and its surrounding environment but also paves the way for the quantum mechanical description of multiple embedded domains, particularly by employing the emergent quantum flow algorithms. Our theoretical underpinnings further set the stage for a generalization to multiple embedded sub-systems. This expansion holds significant promise for the exploration and application of non-equilibrium quantum systems, enhancing the understanding of system–environment interactions. In doing so, the research underscores the potential of SES-CC embedding within the realm of quantum computations and multi-scale simulations, promising a good balance between accuracy and computational efficiency.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Theory of the thermionic current beyond the traditional space charge limit enabled by trapped ions in the virtual cathode

We show that trapped ions in virtual cathode potential wells can raise the transmitted current of emitted electrons into a plasma much closer to the full emission than is predicted by cathode sheath theories without trapped ions. The transmitted current is controlled by the well barrier voltage, which must adjust to balance the creation of low-energy ions within the well, and their loss. Our model considers the case of a plasma-facing cathode where trapped ions are created passively via charge-exchange collisions and lost passively via thermal leakage over the well. We quantify these rates and estimate the current in terms of system parameters for thermionic emission into a plasma with several cathode geometries. A general prediction is that the current as a function of emitted flux does not saturate at the traditional space charge limit (the onset of a well) but can reach far higher values until the trapped ion balance breaks down, causing instability. The maximum stable current depends on parameters but in principle can be arbitrarily high if active techniques are used to manipulate the trapped ion balance. We conclude that major improvements in plasma technologies with hot cathodes might be achieved by optimizing the current enhancement enabled by trapped ions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Gold-Standard Chemical Database 137 (GSCDB137): A Diverse Set of Accurate Energy Differences for Assessing and Developing Density Functionals

We present GSCDB137, a rigorously curated benchmark library of 137 data sets (8377 entries) covering main-group and transition-metal reaction energies and barrier heights, (intra- and intermolecular) noncovalent interactions, dipole moments, polarizabilities, electric-field response energies, and vibrational frequencies. Legacy data from GMTKN55 and MGCDB84 have been updated to today's best reference values; redundant or low-quality points were removed, and many new, property-focused sets were added. Testing 29 popular density functional approximations (DFAs) confirms the expected Jacob's-ladder hierarchy overall but also reveals notable exceptions: functional performance for frequencies and electric-field properties correlates poorly with that for other ground-state energetics. ωB97M-V and ωB97X-V are the most balanced hybrid meta-GGA and hybrid GGA, respectively; B97M-V and revPBE-D4 lead the meta-GGA and GGA classes. Double hybrids lower mean errors by about 30% versus their hybrid analogues but demand careful frozen-core, basis set, and spin contamination treatment. GSCDB137 offers a comprehensive, openly documented platform for rigorous validation of DFA and universal machine learning potentials, and training of the next generation of exchange-correlation functionals.

Liang, Jiashu [University of California, Berkeley,↗

DOE OSTI2025

Disruption of histone acetylation homeostasis reveals multilayered chromatin regulation for transcriptional resiliency

Background Epigenetic modifications, nucleosome occupancy, and three-dimensional chromatin architecture collectively create a multi-layered, highly interactive regulatory system for controlling genomic functionality. Dysregulation of epigenetic processes leads to a plethora of abnormalities including disease states. Therapies focused on epigenetic modulation can alter gene expression to correct dysfunction, though the perpetuation of these states and the relationships among chromatin regulatory layers is not well understood. Results Here, we investigated global and local chromatin structural and functional responses after acute histone deacetylase inhibitor treatment (suberoylanilide hydroxamic acid) in lung cancer cells across time. Treatment substantially increased global histone acetylation resulting in a pervasive but not distinctive signature. The spread of acetylation did not significantly impact global chromatin accessibility, and nucleosome remodeling largely occurred at finer scales in functionally relevant genomic regions. Indeed, both H 3 K 4 trimethylation, a mark of active transcription, and gene expression changes were altered in a controlled locus-specific manner, suggesting aberrant acetylation indirectly leads to balanced and bidirectional gene expression profiles from tighter regulation of other chromatin features. HDACi treatment induced (13%) genomic rearrangement in chromatin compartmentalization and moderate weakening of topologically associating domains. Conclusions Continuous wavelet analysis of these features demonstrates that scale-dependent, locus-specific factors influence the relationship between chromatin architecture and functional output, suggesting that regulation of transcription and nucleosome remodeling is not entirely (nor linearly) dependent upon large scale compartment exchange. Structural and functional responses are most pronounced early after treatment with partial persistence of differential local chromatin features and expression later in time; this highlights the plasticity of chromatin regulation, which may have implications for the efficacy of epigenetic treatments. These results demonstrate the effectiveness of multi-layered regulation of transcription: in resilient systems, disruption of one chromatin feature does not distort the regulation of other features in supporting a transcriptional program that allows for survival.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

How the Hydrophobic Interface between a Perfluorosulfonic Acid Polymer and Water Vapor Controls Membrane Hydration

Stable hydration in perfluorinated polyelectrolyte membranes such as Nafion is essential to maintain good ion conductivity and manage permeation, especially in vapor-fed devices where water content depends on relative humidity in a gas stream. Extensive studies in the literature have shown that Nafion hydration in water vapor is controlled by its interfacial transport resistance. Nafion forms a fluorine-rich layer at the polymer-gas interface, and it has been proposed that this layer blocks water transport due to its hydrophobicity. To develop a molecular-level description of the physics underlying transport resistance in this system, we have performed a computational reaction-diffusion kinetics study of water evaporation from Nafion. Two distinct models are examined, one mimicking the blocking function proposed in the literature and the other assuming that there is no blocking, treating instead water evaporation as a dynamic balance between uptake from the gas and desorption from the polymer surface. Simulation results are compared to time-dependent infrared data over a range of 100-0% relative humidity from the literature. Only the dynamic model successfully reproduces experimental observations. This indicates that the physical nature of interfacial transport resistance is not slow diffusion across an interfacial layer; rather, it is due to the competition between dehydration and rehydration. The simulation data provide details on the accompanying water distributions throughout the membrane and on interfacial kinetics, showing that they are characterized by strong fluctuations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Non-monotonic magnetic anisotropy behavior as a function of adsorbate coverage in Fe ultrathin films near the spin reorientation transition

Carbon monoxide (CO) adsorption on ultrathin fcc Fe films is known to result in the rotation of magnetization from out-of-plane to in-plane. By imaging in real time the magnetic domain structure of perpendicularly magnetized Fe/(2 ML)Ni/Cu(100) films during exposure to CO, we demonstrate that the effect of adsorption on the magnetic properties occurs in two distinct stages. Initially, when CO bonds preferentially on bridge sites, perpendicular magnetic anisotropy is enhanced. Later, when on-top adsorption dominates, magnetization rotates towards in-plane in agreement with previous studies. This CO-induced spin reorientation transition (SRT) is not reversible by annealing, as CO desorption would require high temperature cycles which yield permanent structural changes in the metal films. This study demonstrates the existence of a novel non-monotonic behavior of the magnetic anisotropy as a function of adsorbate coverage. The influence of CO on ultrathin film magnetism in real time near critical points, where the anisotropy balance is extremely sensitive to small variations, reveals the previously elusive complexity of this adsorbate induced SRT.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Time propagation of electronic wavefunctions using nonorthogonal determinant expansions

The use of truncated configuration interaction in real-time time-dependent simulations of electron dynamics provides a balance of computational cost and accuracy, while avoiding some of the failures associated with real-time time-dependent density functional theory. However, low-order truncated configuration interaction also has limitations, such as overestimation of polarizability in configuration interaction singles, even when perturbative doubles are included. Increasing the size of the determinant expansion may not be computationally feasible, and so, in this work, we investigate the use of nonorthogonality in the determinant expansion to establish the extent to which higher-order substitutions can be recovered, providing an improved description of electron dynamics. Model systems are investigated to quantify the extent to which different methods accurately reproduce the (hyper)polarizability, including the high-harmonic generation spectrum of H 2 , water, and butadiene.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Improving leaf spring phenology modelling for temperate tree species: An integration of the Farquhar–Medlyn photosynthesis model with the optimality‐based approach

Spring leaf phenology in temperate tree species is highly sensitive to climate change and significantly affects plant photosynthetic performance, resource utilization, competition and trophic interactions, thereby impacting various ecosystem functions. Although optimality-based (OPT) approaches for modelling spring phenology are increasingly recognized, the optimal representation of the underlying principle (balancing photosynthesis gains with chilling risks) remains controversial. Here, we integrated a coupled Farquhar–Medlyn photosynthesis model into an existing OPT model, and termed the resulting model R-OPT, and evaluated its performance using the PEP725 dataset, which includes 409,144 site-species-year records from across Europe. Our results show that R-OPT outperforms both the default OPT and non-optimality-based models (e.g. the chilling-forcing trade-off and growing degree day models). This improved performance is consistent within and across five focal tree species but varies by region: R-OPT excels in lowland, moist environments but is less effective in high-altitude, cold, and dry areas, possibly due to an incomplete representation of environmental constraints on photosynthetic carbon gain in these regions. Our research advances leaf spring phenology modelling by emphasizing an optimality principle that balances photosynthetic carbon gain with chilling risk, improving the representation of plant photosynthesis processes and enhancing understanding of environmental factors influencing phenology in the context of climate change.

coupled Farquhar–Medlyn photosynthesis model↗

DOE OSTI2022

Excited State Phenomena in Correlated Nanostructures: Transition Metal Oxide Clusters and Nanocrystals

The primary goal of our research program was to apply advanced computational techniques to predict electronic properties of molecular species. These include transition metal monoxide and dioxide clusters and negatively charged copper oxide clusters which are important systems for their utilization in a variety of technological applications. The enhanced electron-electron interactions inherent in these systems make it challenging to model their excited state properties within a parameter-free approach. The excited state properties in question include the interaction of light with these molecules which results in ejection of electrons from the system, or the absorption of light by the molecular system resulting in a molecule in a higher-energy state. Our overall goal was to investigate the impact of various computational and theoretical approaches on such electronic and optical excitations in these systems. Comparing several variants of theoretical approaches with available experimental data, and high-level quantum chemistry computations helped us identify the level of theory and approximations that are needed to achieve a reasonable balance between accuracy and computational demand.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2023

IDAES-PSE 2.0 Release

The Institute for the Design of Advanced Energy Systems (IDAES) Integrated Platform is a versatile computational environment offering extensive process systems engineering (PSE) capabilities for optimizing the design and operation of complex, interacting technologies and systems. IDAES enables users to efficiently search vast, complex design spaces to discover the lowest cost, most environmentally sustainable solutions while supporting the full process modeling lifecycle, from conceptual design to dynamic optimization and control. The extensible, open platform empowers users to create models of novel processes and rapidly develop custom analyses, workflows, and end-user applications. IDAES-PSE 2.0.0 Release Highlights Removal of deprecated features from IDAES v1 Update to Pyomo v6.5 – this required a number of updates to support the new NL solver writer and to address some changes in Pyomo Creation of new testing suite for backward compatibility, model robustness and verification More general implementation of the Helmholtz EoS. This brings some new features like standard property diagrams, choice of mass or mole basis, and new state variable options Standardizing names in Heat Exchanger models (breaking change from v2.0.0a2): Control Volumes named hot_side and cold_side Ports names hot_side_inlet, hot_side_outlet, cold_side_inlet and cold_side_outlet Config Blocks names hot_side_config and cold_side_config Config arguments for user provided names for each side: hot_side_name and cold_side_name. Updating Keras surrogate tool to use v1.1 of OMLT New prototype API for model initialization (idaes.core.initialization) The new API uses "Model Initializer" objects instead of class methods, allowing for the definition of multiple initialization routines for a single model A number of common, model agnostic initialization routines have also been defined, including initialization from data, block-decomposition and a general hierarchical approach equivalent to the existing method for common unit models New metadata for thermophysical properties – valid_range This can be used to record the range of values over which a property value can be trusted, such as the range of experimental data used to regress parameters A number of new utility functions have been added to check for properties with values outside the valid range and to set bounds based on this metadata Updated construction of balance expressions in Control Volumes to remove unneeded terms In the past, unneeded terms were added as a constant 0 term, however they will now be dropped entirely from the expression This was necessary due to more strict unit checking in the new Pyomo solver writer which no longer ignores 0 terms Updates to metadata for thermophysical properties to better define known properties and units of measurement This results in more strict enforcement of standard naming for thermophysical and reaction properties Users can still define custom properties, but these must be done explicitly using the define_custom_properties() method instead of being implicitly created by add_property() Updated convergence tester utility tool to support definition of benchmark files (JSON format) and comparison of performance to benchmarks Set default iteration limit for IPOPT in IDAES config to 200 iterations Update scaling of example models to work with new Pyomo NL solver writer Improve testing of extensions and examples infrastructure to avoid need for downloading files Updated distillation column to centralize common functionality and remove a number of Pyomo warnings

IDAES↗

DOE OSTI2022

Enhancing reactant selectivity for Ni/Mg reforming catalysts using silicalite-1 shells: A modeling study

The ability of a zeolite shell to enhance the selective conversion of hydrocarbons through diffusional limitations was investigated using a multi-scale model of a fixed-bed reactor. The impact of shell thickness and molecule/pore size on the catalytic performance of silicalite-1 zeolite encapsulated nickel catalyst pellets for steam reforming of C1-C7 hydrocarbons is reported. A reaction–diffusion model using kinetic expressions established in literature was employed. The model was verified through comparison with reported experimental results for steam reforming data over a temperature range of 748 – 1113 K and pressure of 1 – 10 bar. Comparisons are also made against experimental data for steam reforming in the presence of a zeolite shell. Evaluation of the Weisz-Prater criterion for both the core and encapsulated catalyst confirmed mass transfer limitation induced by the utilization of a zeolite shell. The model was used to suggest an optimal thickness that balances diffusional limitations imposed by the zeolite layer on methane versus that of the heavier hydrocarbons. The optimum thickness varied as a function of hydrocarbon size and shape which determined the diffusion rates. For toluene and heptane, a 50 nm thick shell was sufficient to wholly prevent reaction. Hydrocarbons like propane and butane required a shell 7.5 and 5 μm thick. Increasing the gas-hourly-space-velocity from 10,000 to 60,000 h –1 caused a decrease in the optimum shell thickness. Furthermore, this approach can be modified for application to other mixed hydrocarbon systems to predict optimal catalyst design.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗