The UKOOA ignition model [Ignition Probability Review, Model Development and Look-up Correlations; The Energy Institute, London; 2006] is the UK offshore industry standard for determining the ignition probability of flammable releases on offshore installations. As the model is dependent on a large number of parameters, several look-up correlations were developed for typical onshore and offshore modules, to reduce the model to a limited set of parameters. There remains some debate about how these look-up correlations can best be applied in order to describe all conditions satisfactorily. A number of enhancements and clarification to the existing look-up correlations for offshore installations are proposed. The hot-work hours for a typical offshore module was defined in the original model as 15 hours/year, however, this may be considered very low if substantial works are undertaken. Therefore, an enhancement to the look-up correlations is proposed to account for increased hot-work hours. A change to the model to allow users to specify different splits between immediate and delayed ignition is also proposed.

The formation of soot in an n-heptane fuelled HCCI engine, operated at a rich equivalence ratio of 1.93, has been studied by means of in-cylinder snatch sampling as well as by applying a new engine model, which features a highly detailed description of soot. The study has been conducted by scientists of the Department of Chemical Engineering and Biotechnology at Cambridge University (UK), the Institute of Clean and Secure Energy at the University of Utah (USA), Ibiden and Toyota. This new computationally efficient model can provide aggregate and primary particle size distribution functions and detailed information on aggregate morphology and chemical composition such as images similar to those produced with TEMs.

In this study the coagulation, condensation, and sintering of nanoparticles is investigated using a stochastic particle model. Each stochastic particle consists of interacting polydisperse primary particles that are connected to each other. In the model sintering occurs between each individual pair of neighboring primary particles. This is important for particles in which the range of the size of the primary particles varies significantly. The sintering time is obtained from the viscous flow model. The model is solved using a stochastic particle algorithm. The particles are represented in a binary tree that contains the connectivity as well as the degree of sintering information. Particles are forme, coagulate, sinter, and experience condensation according to known rate laws. The particle binary tree, along with it the degree of sintering, is updated after each time step according to the rates of the different processes. The stochastic particle method uses the technique of fictitious jumps and linear process deferment. The theoretical results are fitted against experimental values for the formation of SiO2 nanoparticles and computer generated TEM pictures are presented and compared to experiments.

In this paper a novel predictor–corrector algorithm is presented for the solution of coupled gas-phase – particulate systems. The emphasis of this work is the study of soot formation, but the concepts can be applied to other systems. This algorithm couples a stiff ODE solver to a Monte Carlo population balance solver. Such coupling has been achieved previously for similar systems using a Strang operator splitting algorithm, however, that algorithm demonstrated several numerical issues which resulted in a high computational cost to acquire adequate precision. In particular a source-sink instability was identified whereby a large-magnitude source term present in the ODE system was competing with a similarly sized sink term in the population balance. This instability required that the splitting step size was very small in order to keep numerical error sufficiently low. A predictor–corrector algorithm has been formulated to negate this instability. An additional efficiency is gained with this algorithm as a principal computational cost of the Strang splitting algorithm is removed: the requirement to re-initialise the ODE solver every splitting step. The numerical convergence of the new algorithm is demonstrated, and its efficiency is compared to that of the Strang splitting algorithm. Substantial computation time savings are demonstrated, which allow a fixed error in three studied system functionals to be achieved with an order-of-magnitude reduction in computation time.

A detailed PAH growth model is developed, which is solved using a kinetic Monte Carlo algorithm. The model describes the structure and growth of planar PAH molecules, and is referred to as the kinetic Monte Carlo–aromatic site (KMC-ARS) model. A detailed PAH growth mechanism based on reactions at radical sites available in the literature, and additional reactions obtained from quantum chemistry calculations are used to model the PAH growth processes. New rates for the reactions involved in the cyclodehydrogenation process for the formation of 6-member rings on PAHs are calculated in this work based on density functional theory simulations. The KMC-ARS model is validated by comparing experimentally observed ensembles on PAHs with the computed ensembles for a C2H2 and a C6H6 flame at different heights above the burner. The motivation for this model is the development of a detailed soot particle population balance model which describes the evolution of an ensemble of soot particles based on their PAH structure. However, at present incorporating such a detailed model into a population balance is computationally unfeasible. Therefore, a simpler model referred to as the site-counting model has been developed, which replaces the structural information of the PAH molecules by their functional groups augmented with statistical closure expressions. This closure is obtained from the KMC-ARS model, which is used to develop correlations and statistics in different flame environments which describe such PAH structural information. These correlations and statistics are implemented in the site-counting model, and results from the site-counting model and the KMC-ARS model are in good agreement. Additionally the effect of steric hindrance in large PAH structures is investigated and correlations for sites unavailable for reaction are presented.

An updated rate of O2 oxidation of one to four ring polyaromatic hydrocarbons in premixed flames is presented based on density function theory simulations of oxygen attack at different radical sites on various PAHs. The rate is in agreement with other rates found in the literature; however, it is several orders of magnitude lower than the currently accepted oxidation rate of multi-ring aromatic species, including soot. Simulations are presented of a premixed flame using this improved rate and a new advanced soot particle model, which is developed in this paper. This model includes unprecedented detail of the particles in the ensemble, including the aromatic content, C/H composition and primary-particle aggregate structure. The O2 oxidation rate calculated in this paper is shown to give a better prediction of particle number density and soot volume fraction for a premixed flame. The predicted particle size distributions are shown also to describe better the experimental data. Predicted C/H ratio and PAH size distributions are shown for the flame. Computed TEM-style images are compared to experimental TEM images, which show that the aggregate structure of the particles is well predicted.

A simple model for the gas-phase synthesis of carbon nanotubes on iron catalyst particles has been developed. It includes a growth model for the catalyst particles and describes nanotube growth processes through carbon monoxide disproportionation and hydrogenation. Models for particle–particle interactions and sintering are also included. When carbon arrives at a catalyst particle it can either dissolve in the particle until a saturation limit is reached, or form a graphene layer on the particle, or go on to form a nanotube. Two models for incipient nanotube growth are considered. The first allows nanotubes to form once a catalyst particle reaches the saturation condition. The second only allows nanotubes to form on the collision of two saturated particles. The particle system is solved using a multivariate stochastic solver coupled to the gas-phase iron chemistry using an operator splitting algorithm. Comparison with experimental data gives a good prediction of the nanotube length, and reasonable values of catalyst particle diameter and nanotube diameter. A parametric study is presented in which the carbon monoxide reaction rate constants are varied, as is the fraction of carbon allowed to form nanotubes relative to surface layers. The assumptions of the coagulation and sintering models are also discussed.

In this study the formation processes of catalyst nanoparticles and single walled carbon nanotubes (SWCNTs) in a premixed flame doped with Fe(CO)5 were first modelled using a three-step SWCNT growth model including a detailed surface chemistry model. The growth of SWCNTs was experimentally studied by the length measurement of the SWCNT using Raman radial breathing mode (RBM) and size measurements of the iron oxide catalyst particles using XRD and TEM. The flame chemistry and the formation of the catalyst particles were modelled in detail by means of a sectional model. In a post-processing step the SWCNT population balance growth model was numerically solved using a multivariate stochastic population balance solver. The model was able to capture the growth characteristics and revealed the role of the monolayer. The computational study on the adsorption, dissociation, and reactions of CO, H2 and H2O on iron nanoparticles showed that carbon, hydrogen and oxygen atoms form at the surface of the catalyst. Their ratio, which is controlled by the surface reaction pathways, affects the growth of SWCNTs, the formation of monolayers and the phase transformation of catalyst particles.

A new, advanced soot particle model is developed that describes soot particles by their aromatic structure, including functional site descriptions and a detailed surface chemistry mechanism. A methodology is presented for the description of polyaromatic hydrocarbon (PAH) structures by their functional sites. The model is based on statistics that describe aromatic structural information in the form of easily computed correlations, which were generated using a kinetic Monte Carlo algorithm to study the growth of single PAH molecules. A comprehensive surface reaction mechanism is presented to describe the growth and desorption of aromatic rings on PAHs. The model is capable of simulating whole particle ensembles which allows bulk properties such as soot volume fraction and number density to be found, as well as joint particle size and surface area distributions. The model is compared to the literature-standard soot model [J. Appel, H. Bockhorn, M. Frenklach, Combust. Flame 121 (2000) 122–136] in a plug-flow reactor and is shown to predict well the experimental results of soot mass, average particle size, and particle size distributions at different flow times. Finally, the carbon/hydrogen ratio and the distribution of average PAH sizes in the ensemble, as predicted by the model, are discussed.

A previously developed bivariate surface-volume model has been extended to a new particle structure and composition model (PSCM). The PSCM is capable of providing information about the shape of a soot particle by approximately tracking its aggregate structure and holding size information of the primary particles, of which a soot particle is comprised. Information about the aggregate composition is provided by counting the number of carbon and hydrogen atoms per aggregate particle. Thus, the new model makes it possible to produce representative TEMs for soot particles in a flame at different heights above the burner, with only a small increase in the computational expense.

The combustion of TiCl4 to synthesize TiO2 nanoparticles is a multimillion tonne per year industrial process. The objective of this paper is to further the understanding of this process. Work toward three aspects of this multiscale problem is presented herein: gas-phase chemistry, surface chemistry, and the solution of a multidimensional population balance problem coupled to detailed chemical mechanisms. Presented here is the first thermodynamically consistent mechanism with physically realistic elementary-step rate constants by which TiCl4 is oxidized to form a stable Ti2OxCly species that lies on the path to formation of TiO2 nanoparticles. Second, progress toward a surface chemistry mechanism based on density functional theory (DFT) calculations is described. Third, the extension of a stochastic two-dimensional (surface-volume) population balance solver is presented. For the first time, the number and size of primary particles within each agglomerate particle in the population is tracked. The particle model, which incorporates inception, coagulation, growth, and sintering, is coupled to the new gas-phase kinetic model using operator splitting, and is used to simulate a heated furnace laboratory reactor and an industrial reactor. Using the primary particle information, transmission electron microscopy (TEM)-style images of the particles are generated, demonstrating the potential utility of first-principles modeling for the prediction of particle morphology in complex industrial systems.

The feasibility of coupling a stochastic soot algorithm to a deterministic gas-phase chemistry solver is investigated for homogeneous combusting systems. A second-order splitting technique was used to decouple the particle population and gas phase in order to solve. A numerical convergence study is presented that demonstrates convergence with splitting step size and particle count for a batch reactor and a perfectly stirred reactor. Simulation results are presented alongside experimental data for a plug flow reactor (PFR) and are compared to a method of moments simulation of a perfectly stirred reactor. Coupling of the soot and chemistry solvers is shown to converge for both systems; however, numerical instabilities present significant challenges in the PSR case. Comparison with the experimental data for a PFR showed good agreement of the soot mass and reasonable agreement of the particle size distribution. Two different soot particle models were used to simulate the PFR: a spherical particle model and a surface–volume model that takes some account of particle shape. The results for the two models are compared. Additionally, the stochastic soot solver is used to track the evolution of the C/H ratio of individual soot particles in the PFR for the first time.

The combustion of TiCl 4 to synthesize titanium dioxide nanoparticles is a multi-million tonne per year industrial process. The size and shape of these particles affects properties important to both the industrial processing and the final product, such as ease of milling and opacity of the powder. Although used in industry for decades, the understanding of the process is poor and experimental optimization is incremental and costly. As such, the ability to simulate a multi-variate distribution (for example mass, surface area, amount of agglomeration) of a population of nanoparticles created in this process is important.We propose to present work towards a model spanning processes on all length and time scales from the molecular up to the industrial plant level. A previously published TiO 2 particle model including particle inception, surface growth, coagulation, and sintering, was based on approximate one-step chemistry [1]. Using an operator splitting method we have coupled a stochastic particle model with solvers for detailed gas phase and surface chemistry mechanisms to solve a 2-dimensional (surface-volume) population balance. This generalized model has been successfully used with existing chemistry mechanisms for the detailed simulation of soot formation in flames. The aim is to use the generalized model together with new chemistry, described below, to model the entire TiO 2 synthesis process.