# [PhD proposal] Data-driven models for prediction and feasibility space reduction of gas and liquid separation processes.

### Supervision

Team OPTIMIST, Loria

Supervisor : Bernardetta ADDIS (HDR)

bernardetta.addis@loria.fr

Co-supervisor: Christophe CASTEL (LRGP)

### Keywords

Global optimization, machine learning, process engineering

### Description

Process synthesis plays a central role in process engineering. More specifically, for applications with high environmental impact: CO2 capture, hydrogen purification, desalination of seawater, and waste-water treatment processes. Those separation processes are usually high energy demanding and may have high economic and environmental costs if not well designed.

Although there exist scientific contributions to optimization-based process design, these are not integrated into industrial practices [Chen2017]. This phenomenon can be explained by the missing the generality of the proposed methods and the excessive simplification of the process modeling. Indeed, current equation-based models contain the discretization of differential equations. Therefore, they become difficult to solve when the size of the problem is large and discrete variables are involved [Floudas1998, Biegler2010, Belotti2013].

A possible alternative is to use optimization coupled with simulation-based approaches. This strategy suffers from another issue, the search space is not mathematically defined and, therefore, cannot be explored efficiently. Furthermore, simulation is a time-consuming procedure leading to slow convergence for the resulting optimization methods [Neveux2019].

A way to combine the quality of the two approaches is to work on data-driven models. Our research group (involving LORIA and LRGP laboratories) started to work in this direction for gas membrane separations processes [Ramirez-Santos2018, Bozorg 2020]. The idea is to use machine learning methods to represent the physical behavior of the membrane. For example, training a neural network model using data obtained by a simulator to mimic its behavior. After the training, we inject the governing equation of the neural network into the model (instead of using the discretized differential equations). Two important factors are related to the success of the overall method: the quality of the regression model (in our example, the neural network) and the introduction of additional constraints to limit the space search to physically meaningful regions. For example, we used a support vector machine to cut away a part of the space where the simulation cannot converge. Indeed, equation-based optimization methods explore (implicitly) all the search space defined by the model. Therefore the overall model must represent only the physically meaningful research space. Preliminary results [Addis2020] show that this strategy leads to a fast and stable optimization algorithm.

Motivated by these results, we decided to extend the work to other separation processes and explore different machine learning approaches to obtain the necessary models. We will focus first on liquid membrane separation, a problem similar to the gas one, but characterized by more complicated physical equations. Then, we will move on to hybrid separation processes and reactive systems.

The thesis will focus on the proposal and training of new models to represent the physics of the different components of the system (liquid separation membranes, reactors, etc). Both regression and classification models will be studied. The regression models for predicting the physical behaviors of each device. The classification models for space reduction. Space reduction must cut away regions with no physical meaning. In addition, it can allow removing not promising from an energetic point of view. This second feature can boost the successive search strategy. The aim is to produce high-quality predictive models, with the simplest structure. Indeed, the resulting models need to be integrated into an optimization strategy. The possibility to translate them into a system of equations is of paramount importance. The work will start with membranes for liquid separation, which is the natural extension of our preliminary work, and then will move on to reaction models. All produced models will be validated on several industrial case studies using the simulation tool [Bounaceur2016] and data provided by LRGP.

### Skills

Required:

Good programming skills

Good optimization and machine learning knowledge

Preferred:

non-linear optimization

Desired (but not compulsory):

global optimization

knowledge of the pyomo library

The candidate must be fluent in English (thesis in collaboration with Italy).

### Bibliography

[Addis2020] B. Addis, A. Calamita, C. Castel, F. Di Luzio, E. Favre, A. Macali, V. Piccialli.

“Membrane Separation Processes Using Machine Learning Based Mathematical Programming

Models”, Annual conference of the Institute for Operations Research and the Management

Sciences (INFORMS20), online meeting 7-13 November 2020

[Belotti2013] P. Belotti, C. Kirches, S. Leyffer, J. Linderoth, J. Luedtke, A. Mahajan.

“Mixed-integer nonlinear optimization”. Acta Numerica, 22, 1-131, 2013.

[Biegler2010] L.T. Biegler. “Nonlinear Programming: Concepts, Algorithms, and Applications to

Chemical Processes”, MOS–SIAM Series on Optimization, 2010.

[Bounaceur2016] R. Bounaceur, E. Berger, M. Pfister, A. A. Ramirez Santos, E. Favre.

“Rigorous variable permeability modelling and process simulation for the design of polymeric

membrane gas separation units: MEMSIC simulation tool”, Journal of Membrane Science,

Elsevier, 2016, 523, pp.77 – 91.

[Bozorg 2020] M. Bozorg, Álvaro A. Ramı r ́ ez-Santos, B. Addis, V. Piccialli, C. Castel, E. Favre,

”Optimal process design of biogas upgrading membrane systems: Polymeric vs high

performance inorganic membrane materials”, Chemical Engineering Science 225, 115769, 2020

[Chen2017] A. Chen, I. Grossmann. “Recent developments and challenges in

optimization-based process synthesis”. Ann. Rev. Chem. Biomolec. Eng. 8 (1), 249–283, 2017.

[Floudas1998] C.A. Floudas. “Nonlinear and Mixed–Integer Optimization. Fundamentals and

Applications”. Oxford University Press, 1998.

[Neveux2019] T. Neveux, B. Addis, C. Castel, V. Piccialli, E. Favre. “Comparison of process

synthesis methods: case study of the design of membrane separation processes”, The 12th

EUROPEAN CONGRESS OF CHEMICAL ENGINEERING, Florence 15-19 September 2019

[Ramirez-Santos2018] A. A. Ramirez-Santos, M. Bozorg, B. Addis, V. Piccialli, C. Castel, E.

Favre. ”Optimization of multistage membrane gas separation processes. Example of application

to CO2 capture from blast furnace gas”, Journal of Membrane Science, 566, pp 346-366, 2018

### How to apply

Deadline: May 16, 2022 (midnight Paris time)

Applications must be sent as soon as possible.

Send a file with the following documents:

- Your CV;
- A cover letter/motivation letter describing your interest in this topic;
- A brief description (one-page maximum) of your Master’s thesis (or equivalent) or work in progress if not yet completed;
- Your diplomas and transcripts for the Bachelor’s and Master’s degrees (or the last 5 years);

In addition, a letter of recommendation from the person who supervised or has supervised your Master’s thesis (or research project or internship) is welcome.