Computational model of ammonia synthesis with catalyst pellets: Linking the structure and performance

In a fixed bed of porous catalyst pellets, there are developed two composition and temperature fields, one in the fluid phase and the other one at the level of solid pellets. The objective of this work is to evaluate, by numerical simulation, the unsteady state behavior of a catalyst pellet in typical operating conditions for methanol synthesis reactors. The process kinetics was described by the model published by Graaf et al (1990) and the reaction-diffusion process inside the pellet is based on the Wilke-Bosanquet model. The results showed a short composition and temperature stabilization time, generally below 4 seconds, for a spherical catalyst pellet having typical dimensions for industrial applications.

Computational Model of Ammonia Synthesis with Catalyst Pellets: Linking the Structure and Performance

PREFACE NOTATION 1. GETTING STARTED AND BEYOND 1.1 When Not to Model Illustration 1.1 The Challenger Space Shuttle Disaster Illustration 1.2 Loss of Blood Vessel Patency 1.2 Some Initial Tools and Steps 1.3 Closure Illustration 1.3 Discharge of Plant Effluent into a River Illustration 1.4 Electrical Field Due to a Dipole Illustration 1.5 Design of a Thermocouple Illustration 1.6 Newton's Law for Systems of Variable Mass: A False Start and the Remedy Illustration 1.7 Release of a Substance into a Flowing Fluid. Determination of a Mass Transfer Coefficient Practice Problems 2. SOME MATHEMATICAL TOOLS 2.1 Vector Algebra 2.1.1 Definition of a Vector 2.1.2 Vector Equality 2.1.3 Vector Addition and Subtraction 2.1.4 Multiplication by a Scalar 2.1.5 The Scalar or Dot Product 2.1.6 The Vector or Cross Product Illustration 2.1 Distance of a Point from a Plane Illustration 2.2 Shortest Distance Between Two Lines Illustration 2.3 Work as an Application of the Scalar Product Illustration 2.4 Extension of the Scalar Product to n Dimensions. A Sale of Stocks Illustration 2.5 A Model Economy 2.2 Matrices 2.2.1 Types of Matrices 2.2.2 The Echelon Form. Rank r 2.2.3 Matrix Equality 2.2.4 Matrix Addition Illustration 2.6 Acquisition Costs 2.2.5 Multiplication by a Scalar 2.2.6 Matrix Multiplication Illustration 2.7 The Product of Two Matrices Illustration 2.8 Matrix-Vector Representation of Linear Algebraic Equation 2.2.7 Elementary Row Operations Illustration 2.9 Application of Elementary Row Operation. Algebraic Equivalence 2.2.8 Solution of Sets of Linear Algebraic Equations. Gaussian Elimination Illustration 2.10 An Overspecified System of Equations with a Unique Solution Illustration 2.11 A Normal System of Equations with no Solutions 2.3 Ordinary Differential Equations Illustration 2.12 A Population Model Illustration 2.13 Newton's Law of Cooling 2.3.1 Order of an ODE 2.3.2 Linear and Non-linear ODE's 2.3.3 Boundary and Initial Conditions Illustration 2.14 Classification of ODE's and Boundary Conditions 2.3.4 Equivalent Systems Illustration 2.15 Equivalence of Vibrating Mechanical Systems and an Electrical RLC Circuit 2.3.5 Analytical Methods A. Solution by Separation of Variables Illustration 2.16 Solution of Non-Linear ODE's by Separation of Variables B. The D-Operator and Eigenvalue Methods. Particular Integrals Illustration 2.17 Mass on a Spring Subjected to a Sinusoidal Forcing Function C. The Laplace Transformation Illustration 2.18 Application of Inversion Procedures Illustration 2.19 The Mass-Spring System Revisited. Resonance Practice Problems 3. GEOMETRICAL CONCEPTS 3.1 Introduction Illustration 3.1 A Simple Geometry Problem: Crossing of a River Illustration 3.2 The Formation of Quasi Crystals and Tilings from Two Quadrilateral Polygons Illustration 3.3 Charting of Market Price Dynamics: The Japanese Candlestick Method Illustration 3.4 Surveying: The Join Calculation. The Triangulation Intersection Illustration 3.5 The Global Positioning System (GPS) Illustration 3.6 The Orthocenter of a Triangle Illustration 3.7 Relative Velocity and the Wind Triangle Illustration 3.8 Interception of an Airplane Illustration 3.9 Path of Pursuit Illustration 3.10 Trilinear Coordinates. The Three Jug Problem Illustration 3.11 Inflecting Production Rates and Multiple Steady States. The Van Heerden Diagram Illustration 3.12 Linear Programming: A Geometrical Construction Illustration 3.13 Stagewise Adsorption Purification of Liquids. The Operating Diagram Illustration 3.14 Supercoiled DNA Practice Problems 4. THE EFFECT OF FORCES 4.1 Introduction Illustration 4.1 The Stress-Strain Relation. Stored Strain Energy. Stress Due to the Impact of a Falling Mass Illustration 4.2 Bending of Beams. Euler's Formula for the Buckling of a Strut Illustration 4.3 Electrical and Magnetic Forces. Thomson's Determination of e/m Illustration 4.4 Pressure of a Gas in Terms of its Molecular Properties. Boyle's Law and the Ideal Gas Law. Velocity of Gas Molecules Illustration 4.5 Path of a Projectile Illustration 4.6 The Law of Universal Gravitation. Escape Velocity. The Synchronous Satellite Illustration 4.7 Fluid Forces. Bernoulli's Equation and Its Applications. The Continuity Equation Illustration 4.8 Lift Capacity of a Hot Air Balloon Illustration 4.9 Work and Energy. Compression of a Gas. Power Output of a Bumblebee Practice Problems 5. COMPARTMENTAL MODELS 5.1 Introduction Illustration 5.1 Measurement of Plasma Volume and Cardiac Output by the Dye Dilution Method Illustration 5.2 The Continuous Stirred Tank Reactor (CSTR). Model and Optimum Size Illustration 5.3 Modeling of a Bioreactor. Monod Kinetics. The Optimum Dilution Rate Illustration 5.4 Non-Idealities in a Stirred Tank. Residence-Time Distributions from Tracer Experiments Illustration 5.5 A Moving Boundary Problem: The Shrinking Core Model and the Quasi-Steady State Illustration 5.6 More on Moving Boundaries. The Crystallization Process Illustration 5.7 Moving Boundaries in Medicine: Controlled Release Drug Delivery Illustration 5.8 Evaporation of a Pollutant into the Atmosphere Illustration 5.9 Ground Penetration from an Oil Spill Illustration 5.10 Concentration Variations in Stratified Layers Illustration 5.11 One-Compartment Pharmocokinetics Illustration 5.12 Deposition of Platelets from Flowing Blood Illustration 5.13 Dynamics of the Human Immunodeficiency Virus (HIV) Practice Problems 6. ONE-DIMENSIONAL DISTRIBUTED SYSTEMS 6.1 Introduction Illustration 6.1 The Hypsometric Formula Illustration 6.2 Poiseuille's Equation for Laminar Flow in a Pipe Illustration 6.3 Compressible Laminar Flow in a Horizontal Pipe Illustration 6.4 Conduction of Heat Through Various Geometries Illustration 6.5 Conduction in Systems with Heat Sources Illustration 6.6 The Countercurrent Heat Exchanger Illustration 6.7 Diffusion and Reaction in a Catalyst Pellet. The Effectiveness Factor Illustration 6.8 The Heat Exchanger Fin Illustration 6.9 Polymer Sheet Extrusion. The Uniformity Index Illustration 6.10 The Streeter-Phelps River Pollution Model. The Oxygen Sag Curve Illustration 6.11 Conduction in a Thin Wire Carrying an Electrical Current Illustration 6.12 Electrical Potential Due to a Charged Disk Illustration 6.13 Production of Silicon Crystals: Getting Lost and Staging a Recovery Practice Problems 7. SOME SIMPLE NETWORKS 7.1 Introduction Illustration 7.1 A Thermal Network: External Heating of a Stirred Tank Illustration 7.2 A Chemical Reaction Network. The Radioactive Decay Series Illustration 7.3 Hydraulic Networks Illustration 7.4 An Electrical Network: Hitting a Brick Wall and Going Around It Illustration 7.5 A Mechanical Network. Resonance of Two Vibrating Masses Illustration 7.6 Application of Matrix Methods to Stoichiometric Calculations Illustration 7.7 Diagnosis of a Plant Flow Sheet Illustration 7.8 Manufacturing Costs. Use of Matrix-Vector Products Illustration 7.9 More About Electrical Circuits. The Electrical Ladder Networks Illustration 7.10 Networks in Plant Physiology: Photosynthesis and Respiration Practice Problems 8. MORE MATHEMATICAL TOOLS: DIMENSIONAL ANALYSIS AND NUMERICAL METHODS 8.1 Dimensional Analysis 8.1.1 Introduction Illustration 8.1 Time of Swing of a Simple Pendulum Illustration 8.2 Vibration of a One-Dimensional Structure 8.1.2 Systems with More Variables than Dimensions. The Buckingham pi Theorem Illustration 8.3 Heat Transfer to a Fluid in Turbulent Flow Illustration 8.4 Drag on Submerged Bodies. Horsepower of a Car Illustration 8.5 Design of a Depth Charge Practice Problems 8.2 Numerical Methods 8.2.1 Introduction 8.2.2 Numerical Software Packages 8.2.3 Numerical Solution of Simultaneous Linear Algebraic Equations. Gaussian Elimination Illustration 8.6 The Global Positioning System Revisited: Gaussian Elimination Using the MATHEMATICA Package 8.2.4 Numerical Solution of Single Nonlinear Equations. Newton's Method Illustration 8.7 Chemical Equilibrium: The Synthesis of Ammonia by the Haber Process 8.2.5 Numerical Solution of Simultaneous, Non-Linear Equations. The Newton-Raphson Method Illustration 8.8 More Chemical Equilibria: Producing Silicon Films by Chemical Vapor Deposition (CVD) 8.2.6 Numerical Solution of Ordinary Differential Equations. The Euler and Runge-Kutta Methods Illustration 8.9 The Effect of Drag on the Trajectory of an Artillery Piece Practice Problems Index

Ammonia production is generally carried out in multiphase catalytic reactors. In this paper we analyze an industrial reactor for ammonia production with a dynamic heterogeneous model that accounts for transport resistance both inside and outside catalyst pellets. The work is aimed at investigating the possible appearance of periodic solutions in normal operating conditions for their relevance in terms of safety and control strategy. The analysis is based on a continuation approach to determine the bifurcational characterization of model predictions. This description is compared with that derived in a previous work (Mancusi et al. 2000), which was based on a simpler pseudo-homogeneous model of the same process.

Advance in computational rheology allows for in silico predictions of the viscoelastic responses of arbitrarily branched polymer melts. While detailed branching structure is required for the rheology predictions, rheology itself is often the most sensitive tool to detect low levels of branching. With rheological experiments and computational modeling of a set of nominally linear and model comb ethylene-butene copolymers, we show that coupled models for the synthesis and rheology can integrate diverse measurements, incorporating inherent experimental uncertainties. This approach allows us to achieve tight bounds on the branching structures of the constituent molecules. Next, we numerically explore the effects of the numbers and molar masses of side arms in comb polymers on the viscoelastic responses in both the linear and nonlinear regimes. Such computational exploration can aid in designing specific polymers suitable for a given processing scenario.Graphical abstractCoupled models for synthesis and rheology allow tight bounds on branching architecture and parametric exploration of flow properties of statistically branched polymers.

Radially layered configuration for improved performance of packed bed reactors

In this work, a particle‐resolved computational fluid dynamics model of the acetylene hydrogenation process is developed to investigate the effects of catalyst particle structures on the reaction–diffusion behaviors aiming to improve selectivity toward target ethylene. The effects of packing structures on mass and heat transfer are explored by employing particles with varying shapes, wall thicknesses, and external diameters. The simulation results reveal that decreasing diffusion paths and elevating reactor bed temperature will enhance ethylene selectivity, and cylinder and Raschig ring packing structures exhibit the lowest and highest ethylene selectivity of 35.6% and 48.9% at 70% of acetylene conversion, respectively. Reducing wall thicknesses of Raschig ring particles facilitates the diffusion of generated ethylene from the interior zone of catalysts but concurrently inhibits the conversion of acetylene to ethylene. The Raschig ring catalyst particle with 1.9 mm of wall thickness and 3.5 mm of external diameter is finally revealed to exhibit the highest ethylene selectivity.

In this paper, we propose a novel, semi-analytic approach for the two-scale, computational modeling of concentration transport in packed bed reactors. Within the reactor, catalytic pellets are stacked, which alter the concentration evolution. Firstly, the considered experimental setup is discussed and a naive one-scale approach is presented. This one-scale model motivates, due to unphysical fitted values, to enrich the computational procedure by another scale. The computations on the second scale, here referred to as microscale, are based on a proper investigation of the diffusion process in the catalytic pellets from which, after continuum-consistent considerations, a sink term for the macroscopic advection–diffusion–reaction process can be identified. For the special case of a spherical catalyst pellet, the parabolic partial differential equation at the microscale can be reduced to a single ordinary differential equation in time through a semi-analytic approach. After the presentation of our model, we show results for its calibration against the macroscopic response of a simple standard mass transport experiment. Based thereon, the effective diffusion parameters of the catalyst pellets can be identified.

Hydrogen spillover on carbon-supported precious metal catalysts has been investigated with inelastic neutron scattering (INS) spectroscopy. The aim, which was fully realized, was to identify spillover hydrogen on the carbon support. The inelastic neutron scattering spectra of Pt/C, Ru/C, and PtRu/C fuel cell catalysts dosed with hydrogen were determined in two sets of experiments: with the catalyst in the neutron beam and, using an annular cell, with carbon in the beam and catalyst pellets at the edge of the cell excluded from the beam. The vibrational modes observed in the INS spectra were assigned with reference to the INS of a polycyclic aromatic hydrocarbon, coronene, taken as a molecular model of a graphite layer, and with the aid of computational modeling. Two forms of spillover hydrogen were identified: H at edge sites of a graphite layer (formed after ambient dissociative chemisorption of H-2), and a weakly bound layer of mobile H atoms (formed by surface diffusion of H atoms after dissociative chernisorption of H-2 at 500 K). The INS spectra exhibited characteristic riding modes of H on carbon and on Pt or Ru. In these riding modes H atoms move in phase with vibrations of the carbon and metal lattices. The lattice modes are amplified by neutron scattering from the H atoms attached to lattice atoms. Uptake of hydrogen, and spillover, was greater for the Ru containing catalysts than for the Pt/C catalyst. The INS experiments have thus directly demonstrated H spillover to the carbon support of these metal catalysts.

Evaluation of published kinetic models for tert-amyl ethyl ether synthesis

Modeling of ammonia synthesis to produce supercritical steam for solar thermochemical energy storage

Dopamine is an important neurotransmitter responsible for regulating various brain functions such as learning and cognition. Dysfunctions within the dopaminergic system are implicated in many neurological and neuropsychiatric disorders. To understand such a complex system, biologically realistic multiscale computational models are necessary. Such models require the extraction of relevant and important factors or processes from one scale to bridge and interact with systems at other scales. In this paper, we analyze an influential computational model of dopamine synthesis and release within a pre-synaptic terminal by systematically perturbing its variables/substrates. Based on the relative changes in steady states and the time to reach the new perturbed steady states, we found that the substrates within the cascade of intracellular biochemical reactions can vary widely in terms of influence and timescale. We then categorize the substrates according to their relative timescales and changes in steady states. The perturbation results are then used to guide our selection for the most appropriate equations and functions to be approximated in developing reduced models of the original model. Our preliminary simulation results show that either a slow or fast version of the reduced model can be simulated significantly faster than the original model. Our work demonstrates, through perturbation analysis, the feasibility of reduced models of the dopaminergic presynaptic terminal to improve computational efficiency, implement in multiscale modelling, and in silico neuropharmacology.

Correlations between the energies of elementary steps limit the rates of thermally catalysed reactions at surfaces. Here, we show how these limitations can be circumvented in ammonia synthesis by coupling catalysts to a non-thermal plasma. We postulate that plasma-induced vibrational excitations in N2 decrease dissociation barriers without influencing subsequent reaction steps. We develop a density-functional-theory-based microkinetic model to incorporate this effect, and parameterize the model using N2 vibrational excitations observed in a dielectric-barrier-discharge plasma. We predict plasma enhancement to be particularly great on metals that bind nitrogen too weakly to be active thermally. Ammonia synthesis rates observed in a dielectric-barrier-discharge plasma reactor are consistent with predicted enhancements and predicted changes in the optimal metal catalyst. The results provide guidance for optimizing catalysts for application with plasmas. Plasma catalysis holds promise for overcoming the limitations of conventional catalysis. Now, a kinetic model for ammonia synthesis is reported to predict optimal catalysts for use with plasmas. Reactor measurements at near-ambient conditions confirm the predicted catalytic rates, which are similar to those obtained in the Haber–Bosch process.

Continuous ammonia synthesis using Ru nanoparticles based on Li–N2 battery

On the structure sensitivity of ammonia synthesis on promoted and unpromoted iron