Abstract:
Dynamic simulation programs were created in the Python programming language, to describe a laboratory scale, sub-zero distillation column, that is used to separate mixtures of tetrafluoroethylene (TFE), hexafluoropropylene (HFP) and octafluorocyclobutane (OFCB). Both the equilibrium and rate-based modelling approaches were taken, to generate a comparison between the efficiency and simulation time of both models.
A physical properties data bank for the three components had to be created, as the main and many of the sub-models require physical or thermodynamic properties for evaluation. The different physical property models, found in literature, were programmed into functions that could easily return the wanted property, given a set of required inputs. The applicable mixing rules for each property type was also programmed into functions, to allow for easy retrieval.
The vapour-liquid equilibrium (VLE) model used, is also one that comes from literature and is based on parameters for the three binary systems. The VLE model consists of the Peng-Robinson equation of state, that utilises the Mathias-Copeman alpha function and the Wong-Sandler mixing rules, to describe the vapour phase. The liquid phase is described by the non-random two liquid (NRTL) activity coefficient model. Furthermore, the γ-Φ VLE formulation was used to put the thermodynamic model together. These models were also written into functions to serve as simulation building blocks.
Mass and energy transfer on packed sections in the rate-based model was described by the Maxwell-Stefan diffusion model. The form of this model that was utilised, is the matrix-based, exact solution of the Maxwell-Stefan equations, under the two-film theory. This model was slightly simplified by assuming that the corrective flux matrix reduces to the identity matrix- an assumption that is regularly made in distillation modelling.
Emphasis was laid in documenting how the models are put together to build the simulations. Dynamic simulation algorithms rarely accompany distillation models reported in literature, or authors make use of commercial software to order the modelling equations for them. One of the objectives of the research presented here was, therefore, to report on the process developed to solve the problem.
Both simulation programs delivered typical responses that can be expected of distillation systems. The actual change in the magnitude of the values, however, proved to be significantly small. The cause of this, being the large liquid molar hold-up values that were produced by the model initialisation. The feed flow rate, in comparison, is too small to bring about a significant effect when suddenly increased. This could mean that the system is not capable of reaching the steady-state produced by the initialisation (as the feed cylinder may be too small to contain the required amount of feed gas) and that the column may have to be run in a continuous dynamic state. To be sure of this, however, the model will first need to be validated against experimental data. Furthermore, the simulation programs proved to progress very slowly, particularly the simulation built around the rate-based model. A time step-size of 0.5 resulted in an integration time around 1 minute and 20 seconds for the equilibrium model, while the rate model ran for over 19 minutes, both for a timespan of 300 s.
It is recommended that future research focuses on building start-up simulations for the models, to provide better initial results and to give more insight into the operation of the column. Experimental validation of the models is also important, to establish their accuracies. Finally, work has to be done to improve the simulation speeds, especially if it is required that one of the models are integrated into the column's control system.
