Phase rule | EPFL Graph Search

In thermodynamics, the phase rule is a general principle governing "pVT" systems, whose thermodynamic states are completely described by the variables pressure (p), volume (V) and temperature (T), in thermodynamic equilibrium. If F is the number of degrees of freedom, C is the number of components and P is the number of phases, then :F = C - P + 2 It was derived by American physicist Josiah Willard Gibbs in his landmark paper titled On the Equilibrium of Heterogeneous Substances, published in parts between 1875 and 1878. The rule assumes the components do not react with each other. The number of degrees of freedom is the number of independent intensive variables, i.e. the largest number of thermodynamic parameters such as temperature or pressure that can be varied simultaneously and arbitrarily without determining one another. An example of one-component system is a system involving one pure ch

Integrating Rate Based Models into a Multi-Objective Process Design & Optimisation Framework using Surrogate Models

Levent Sinan Teske

In the development of energy and chemical processes, the process engineers extensively apply computer aided methods to design & optimise these processes and corresponding process units. Such applications are multi-scale modelling and multi-objective optimisation methods. Multi-objective optimisation of super-structured process designs are expensive in CPU-time due to the high number of potential configurations and operation conditions to be calculated. Thus single process units are generally represented by simple models like equilibrium based (chemical or phase equilibrium) or specific short cut models. In the development of new processes, kinetic effects or mass transport limitations in certain process units may play an important role, especially in multiphase chemical reactors. Therefore, it is desirable to represent such process units by experimentally derived rate based models (i.e. reaction rates and mass transport rates) in the process flowsheet simulators used for the extensive multi-objective optimisation. This increases the trust engineers have in the results and allows enriching the process simulations with newest experimental findings. As most rate based models are iteratively solved, a direct incorporation would cause higher CPU-time that penalises the use of multi-objective optimisation. A global surrogate model (SUMO) of a rate based model was successfully generated to allow its incorporation into a process design & optimisation tool which makes use of an evolutionary multi-objective optimisation. The methodology was applied to a fluidised bed methanation reactor in the process chain from wood to Synthetic Natural Gas (SNG). Two types of surrogate model, an ordinary Kriging interpolation and an artificial neural network, were generated and compared to its underlying rate based model and the chemical equilibrium model. The analysis showed that kinetic limitations have significant influence on the result already for standard bulk gas chemical components. A case study applying the previous version of the process design model and the revised version (with rate based model introduced as a set of five surrogate models) will demonstrate that the prediction uncertainties of the process design & optimisation methodology are reduced due to the integration of the rate based model of the fluidised bed methanation reactor. It will be shown that the different process design models predict considerably different optimal operating conditions of the Wood-to-SNG process. This emphasises the importance of the integration of rate based models into the process design models. The presented approach has been developed for the fluidised bed methanation reactor, however, it is a generic approach which can be applied to other process unit technologies as well. Future investigations will target other technologies to further improve the process design & optimisation predictions and support project development.

EPFL2014

Phase and microstructure selection in peritectic alloys under high G-V ratio

Stéphane Dobler, Wilfried Kurz

A new model for the case of a superposition of a phase transformation and a microstructure transition from columnar plane front to equiaxed dendritic growth for peritectic alloys is presented. This model is applied to Fe-Ni alloys where a phase transition from gamma to delta takes place when the solute content decreases. The results of the model are compared with predictions of the nucleation constitutional undercooling model. They show that the peritectic two-(solid) phase region is restricted and may completely disappear depending on nucleation undercooling and dendrite growth kinetics.

WALTER DE GRUYTER GMBH2022

Integrating rate based models into multi-objective optimisation of process designs using surrogate models

François Maréchal, Levent Sinan Teske

Multi-objective optimisation (MOO) of super-structured process designs are expensive in CPU- time because of the high number of potential configurations and operation conditions to be calculated. Thus single process units are generally represented by simple models like equilibrium based (chemical or phase equilibrium) or specific short cut models. In the development of new processes, kinetic effects or mass transport limitations in certain process units may play an important role, especially in multiphase chemical reactors. Therefore, it is desirable to represent such process unit by experimentally derived RBMs (rate based models) in the process flowsheet simulators used for the extensive MOO. This increases the trust engineers have in the results and allows enriching the process simulations with newest experimental findings. As most RBMs are iteratively solved, a direct incorporation would cause higher CPU-time that penalises the use of MOO. A global surrogate model (SUMO) of a RBM was successfully generated to allow its incorporation into a process design & optimisation (PDO) tool which makes use of an evolutionary MOO. The methodology was applied to a fluidised bed methanation reactor in the process chain from wood to Synthetic Natural Gas (SNG). Two types of surrogate model, an ordinary Kriging interpolation and an artificial neural network, were generated and compared to its underlying rate based model and the chemical equilibrium model. The analysis showed that kinetic limitations have significant influence on the result already for standard bulk gas chemical components. From experimental experience it can be stated that a significant amount of chemical compounds, which are near to complete conversion according the thermodynamic equilibrium, are measured in the gas phase after the reactor. Thus including RBMs in PDO improves the quality of results. This approach allows a significant improvement of information exchange between process design & optimisation workflow and experimental development of PUs in early stages of process development.