Vapor-liquid equilibria (VLE) appear in many processes in the chemical industry. Their accurate prediction is therefore important for the design and operation of such processes. A typical approach is to describe the liquid-phase non-idealities using activity coefficients calculated from g^E models. Of these, the non-random two-liquid (NRTL) model is one of the most popular choices. However, estimation of the parameters is known to exhibit poor identifiability, with multiple non-unique combinations leading to the same activity coefficients and VLE diagrams.
Typically, VLE model parameters are estimated based on discrete equilibrium measurements under controlled conditions. Here, an alternative approach is proposed in which the NRTL parameters are estimated based on dynamic trajectories measured from batch distillation experiments. The objective of the thesis is to investigate whether dynamic trajectory data provides additional information content that can aid parameter estimation and improve parameter identifiability. To this end, a dynamic batch distillation model should be developed based on the MESH equations and the NRTL parameters regressed so that the model reproduces the trajectories.
Estimation of model parameters is typically performed using least squares minimization. Recently, we have investigated an alternative machine learning (ML) approach for parameter estimation of dynamic models, in which Time Series Extrinsic Regression (TSER) is used to learn the inverse mapping of the time series output to the underlying time-invariant parameters. The method has shown success for the estimation of kinetic parameters, and its applicability to thermodynamic parameters is to be explored in this project. The parameter estimation and analysis are to be performed based on a synthetically generated dataset.
About Division 2.2 at BAM:
In division 2.2, research focuses on the development of dynamic process models to describe all system states from start-up to shutdown, supported by an open library of dynamic, pressure-driven models. The division uses machine learning, uncertainty quantification and hybrid modeling methods to drive forward real-time application and plant monitoring. For the comprehensive digitalization of process engineering, the division is also researching information and data modelling as well as process models from engineering to the operation of chemical plants. This is supplemented by the development of methods for the safe and optimal transformation of chemical plants.
Task Description:
- Development of a dynamic batch distillation model based on the MESH equations
- Estimation of the NRTL model parameters using (i) conventional least squares minimization and (ii) the TSER machine learning approach
- Investigation of parameter identifiability and potential non-uniqueness of NRTL parameters estimated from discrete equilibrium measurements
- Assessment of whether dynamic trajectory data introduces additional information that improves parameter identifiability
Desirable Knowledge and Skills:
- Pursuing a degree in chemical engineering, process engineering or similar
- Knowledge of process modeling and thermodynamics
- Knowledge of optimization and machine learning methods
- Programming experience with Python
Start: immediately
Contact person: John Paul Gerakis, M.Sc - john-paul.gerakis@bam.de