Carbon nanotube fiber, as a material, promises superior material properties to ordinary carbon fiber. It has higher tensile strength, as well as high electrical and thermal conductivity. The production process is implemented in several university rigs, as well as in some industrial settings, but the process is not well understood or modelled physically. This thesis investigates several different components of this process, presents computational models of the key physical processes, and assimilates experimental data into those models in order to improve their accuracy. The production process consists of a heated quartz reactor tube that is continuously fed with hydrogen, methane, ferrocene, and thiophene. First, a hydrodynamic computational fluid dynamics solver is developed to simulate the flow in the reactor and to model the temperature gradient in the flow. This solver is also extended to model the hydrodynamic stability of the flow through a gas exchange valve attached to the outlet of the production reactor. A simplistic model of the finished carbon nanotube aerogel is presented to evaluate the influence of a convecting solid structure on the flow through the gas valve. Further detail of the production process is then investigated by calculating the decomposition rate of thiophene from experimental observations. The problem of finding the decomposition rate is set up using a Bayesian inference framework and the resulting objective function is minimised using a gradient-based method. An adjoint method is used to calculate the gradient of the objective function with respect to the model parameters. This decomposition rate of thiophene in a hydrogen atmosphere is then used to compare the decomposition of ferrocene and thiophene in the reactor using two different reactor inlet conditions. The implications for the production of carbon nanotubes are presented. Finally the nucleation, growth and evaporation of the catalyst nanoparticles in the reactor is investigated. A simple particle model that can quantitatively describe the mass fraction of the particles in the flow is developed. This model is first applied to predict how the radial particle mass fraction distribution varies with flow rate and the input ferrocene concentration. Then the particle model is fitted using the Bayesian inference framework, again using gradient-based minimisation with an adjoint method to calculate the gradient of the objective function with respect to the model parameters. The implications of the best-fit parameters are discussed, and a parameter set that is closer to the decomposition rate of thiophene than the decomposition rate of ferrocene is found to describe the experimental results best. The models presented in this study can be used to guide further experimental studies into the carbon nanotube production process, and to improve the design of the reactor used. The adjoint method presented can be applied to other fields in which analytical and quantitative models can be paired with experimental data to improve the model’s parameters. Further experimental data can be easily assimilated into the models presented here, because the Bayesian interference framework is a rigorous process to assimilate both new and existing data. Finally this thesis can also explain why the final carbon nanotube product forms a sock-like structure, and highlights that the availability of sulphur is critical to the formation of the catalyst nanoparticles from which carbon nanotubes can grow.