Publications

Clapeyron.jl: An extensible, open-source fluid-thermodynamics toolkit

Published in Ind. Eng. Chem. Res., 2022

Equations of state are a vital tool when modelling natural gas, electrolyte, polymer, pharmaceutical and biological systems. However, their implementations have historically been abstruse and cumbersome, and as such, the only options available were black-box commercial tools. Recently, there has been a rise in open-source alternatives. Clapeyron.jl is one of the pioneering attempts at a thermodynamics framework to build and make use of equations of state. This framework is built in Julia, a modern language for scientific computing known for its ease of use, extensibility, and first-class support for differentiable programming. We currently support more equations than any package available, including standard cubic (SRK, PR, PSRK, etc.), activity-coefficient (NRTL, UNIFAC, etc.), COSMO-based, and the venerable SAFT equations. The property-estimation methods supported are extensive, including bulk, VLE, LLE and VLLE properties. With Clapeyron.jl, researchers and enthusiasts alike will be able to focus on the application and worry less about the implementation.

Recommended citation: Walker, P.J., Yew, H-W., Riedemann, A.. ‘Clapeyron.jl: An extensible, open-source fluid-thermodynamics toolkit’, Ind. Eng. Chem. Res. 2022, XXXX, XXX, XXX-XXX https://pubs.acs.org/doi/10.1021/acs.iecr.2c00326

Ab initio development of generalized Lennard-Jones (Mie) force fields for predictions of thermodynamic properties in advanced molecular-based SAFT equations of state

Published in J. Chem. Phys., 2022

A methodology for obtaining molecular parameters of a modified statistical associating fluid theory for variable-range interactions of Mie form (SAFT-VR Mie) equation of state (EoS) from ab initio calculations is proposed for non-associative species that can be modeled as single spherical segments. The methodology provides a strategy to map interatomic or intermolecular potentials obtained from ab initio quantum-chemistry calculations to the corresponding Mie potentials that can be used within the SAFT-VR Mie EoS. The inclusion of corrections for quantum and many-body effects allows for an excellent, fully predictive description of the vapor–liquid envelope and other bulk thermodynamic properties of noble gases; this description is of similar or superior quality to that obtained using SAFT-VR Mie with parameters regressed in the traditional way using experimental thermodynamic-property data. The methodology is extended to an anisotropic species, methane, where similar levels of accuracy are obtained. The efficacy of using less-accurate quantum-chemistry methods in this methodology is explored, showing that these methods do not provide satisfactory results, although we note that the description is nevertheless substantially better than those obtained using the conductor-like screening model for describing real solvents (COSMO-RS), the only other fully predictive ab initio method currently available. Overall, the reliance on thermophysical data is completely dispensed with, providing the first extensible, wholly predictive SAFT-type EoSs.

Recommended citation: Walker, P.J., Zhao, T., Haslam, A.J., Jackson, G.. ‘Ab initio development of generalized Lennard-Jones (Mie) force fields for predictions of thermodynamic properties in advanced molecular-based SAFT equations of state’, J. Chem. Phys., 156, 154106 https://aip.scitation.org/doi/full/10.1063/5.0087125

Group contribution and machine learning approaches to predict Abraham solute parameters, solvation free energy, and solvation enthalpy

Published in J. Chem. Inf. Mod., 2022

We present a group contribution method (SoluteGC) and a machine learning model (SoluteML) to predict the Abraham solute parameters, as well as a machine learning model (DirectML) to predict solvation free energy and enthalpy at 298 K. The proposed group contribution method uses atom-centered functional groups with corrections for ring and polycyclic strain while the machine learning models adopt a directed message passing neural network. The solute parameters predicted from SoluteGC and SoluteML are used to calculate solvation energy and enthalpy via linear free energy relationships. Extensive data sets containing 8366 solute parameters, 20,253 solvation free energies, and 6322 solvation enthalpies are compiled in this work to train the models. The three models are each evaluated on the same test sets using both random and substructure-based solute splits for solvation energy and enthalpy predictions. The results show that the DirectML model is superior to the SoluteML and SoluteGC models for both predictions and can provide accuracy comparable to that of advanced quantum chemistry methods. Yet, even though the DirectML model performs better in general, all three models are useful for various purposes. Uncertain predicted values can be identified by comparing the three models, and when the 3 models are combined together, they can provide even more accurate predictions than any one of them individually. Finally, we present our compiled solute parameter, solvation energy, and solvation enthalpy databases (SoluteDB, dGsolvDBx, dHsolvDB) and provide public access to our final prediction models through a simple web-based tool, software packages, and source code.

Recommended citation: Chung, Y., Vermeire, F.H., Wu, O.H., Walker, P.J., Abraham, M.H., Green, W.H.. ‘Group Contribution and Machine Learning Approaches to Predict Abraham Solute Parameters, Solvation Free Energy, and Solvation Enthalpy’, J. Chem. Inf. Mod., 62, 3, 433-446 https://pubs.acs.org/doi/abs/10.1021/acs.jcim.1c01103

Importance of the Relative Static Permittivity in electrolyte SAFT-VR Mie Equations of State

Published in Fluid Phase Equilib., 2022

The influence and importance of the relative static permittivity (RSP) in electrolyte equations of state is examined for the case of aqueous sodium chloride. Using the SAFT-VR Mie model, the Debye-Hückel (DH) or Mean-Spherical Approximation (MSA) terms, as well as the Born-solvation term, are used to formulate an electrolyte equation of state. The RSP is obtained from a variety of models, each differing in their dependencies; we consider constant, temperature-, density- and composition-dependent models. For a fair comparison between different combinations of electrostatic and RSP models, all ion-related parameters are obtained a priori. A novel combining rule is proposed to obtain the unlike parameters between solvents and ions; its reliability is examined for a variety of electrolyte systems. We also compare its performance relative to parameterised electrolyte models. Both the DH and MSA terms yield similar results for almost all properties and conditions. The RSP models used have the more-significant impact. Liquid densities and solvent saturation pressures showed limited changes between RSP models whereas osmotic coefficients, mean ionic activity coefficients and carbon dioxide solubilities observed drastically different behaviour. Analysing the contributions of the various terms to the activities of each species in an electrolyte mixture reveals an important balance between the Born-solvation and the DH or MSA terms where the RSP models have a significant influence over this balance, particularly when these carry a solvent- or ion-composition dependence.

Recommended citation: Walker, P.J., Liang, X., Kontogeorgis, G.M.. ‘Importance of the Relative Static Permittivity in Electrolyte SAFT-VR Mie Equations of state’, Fluid Phase Equilib., 551, 113256 https://www.sciencedirect.com/science/article/pii/S0378381221003198

Introducing students to research codes: a short course on solving partial differential equations in Python

Published in Education for Chemical Engineers, 2021

Recent releases of open-source research codes and solvers for numerically solving partial differential equations in Python present a great opportunity for educators to integrate these codes into the classroom in a variety of ways. The ease with which a problem can be implemented and solved using these codes reduce the barrier to entry for users. We demonstrate how one of these codes, FiPy, can be introduced to students through a short course using progression as the guiding philosophy. Four exercises of increasing complexity were developed. Basic concepts from more advanced numerical methods courses are also introduced at appropriate points. To further engage students, we demonstrate how an open research problem can be readily implemented and also incorporate the use of ParaView to post-process their results. Student engagement and learning outcomes were evaluated through a pre and post-course survey and a focus group discussion. Students broadly found the course to be engaging and useful with the ability to easily visualise the solution to PDEs being greatly valued. Due to the introductory nature of the course, due care in terms of set-up and the design of learning activities during the course is essential. This course, if integrated with appropriate level of support, can encourage students to use the provided codes and improve their understanding of concepts used in numerical analysis and PDEs.

Recommended citation: Inguva, P., Bhute, V.J., Cheng, T.N., Walker, P.J.. ‘Introducing Students to Solving Partial Differential Equations in Python’, Education for Chemical Engineers, 36, 1-11 https://www.sciencedirect.com/science/article/pii/S1749772821000117

Continuum-scale modelling of polymer blends using the Cahn–Hilliard equation: transport and thermodynamics

Published in Soft Matter, 2021

The Cahn–Hilliard equation is commonly used to study multi-component soft systems such as polymer blends at continuum scales. We first systematically explore various features of the equation system, which give rise to a deep connection between transport and thermodynamics-specifically that the Gibbs free energy of mixing function is central to formulating a well-posed model. Accordingly, we explore how thermodynamic models from three broad classes of approach (lattice-based, activity-based and perturbation methods) can be incorporated within the Cahn–Hilliard equation and examine how they impact the numerical solution for two model polymer blends, noting that although the analysis presented here is focused on binary mixtures, it is readily extensible to multi-component mixtures. It is observed that, although the predicted liquid–liquid interfacial tension is quite strongly affected, the choice of thermodynamic model has little influence on the development of the morphology.

Recommended citation: Inguva, P. Walker, P.J., K., Zhu, K., Yew, H-W., Haslam, A.J., Matar, O.K.. ‘Continuum-scale modelling of polymer blends using the Cahn–Hilliard equation: Transport and thermodynamics’, Soft Matter, 2021, 17, 5645-5665 https://pubs.rsc.org/en/content/articlehtml/2021/sm/d1sm00272d

A new predictive group-contribution ideal-heat-capacity model, and its influence on second-derivative properties calculated using a free-energy equation of state

Published in J. Chem. Eng. Data, 2020

A statistical-thermodynamics-based group contribution (GC) method, commensurate with the GC methodology used in SAFT-$\gamma$ Mie, is proposed to model ideal heat capacities. Special treatment of halogenated groups allows many halogenated molecules to be modeled with few parameters. Parameters for small, single-group species agree well with experimental vibrational temperatures. Parameters corresponding to groups used for larger species highlight effects such as anharmonicity and torsional modes. The proposed correlation consistently demonstrates higher accuracy than that of Joback and Reid. Ideal heat capacities are seldom used in isolation, but contribute to other properties that may be used to assess the quality of an equation of state. The importance of the ideal free energy to various second-derivative properties, as calculated using the SAFT-$\gamma$ Mie equation of state, is examined. In the majority of cases, using the proposed correlation to calculate the ideal free energy results in more-accurately estimated second-derivative properties—sometimes substantially so. Further studies of the contribution of the ideal free energy are carried out revealing interesting behavior near the critical point that may relate to the Widom-Fisher and Widom lines.

Recommended citation: Walker, P. J., Haslam, A. J., ‘A new predictive group-contribution ideal-heat-capacity model, and its influence on second-derivative properties calculated using a free-energy equation of state’, J. Chem. Eng. Data 2020, 65, 12, 5809–5829 https://pubs.acs.org/doi/abs/10.1021/acs.jced.0c00723

Facilitating Independent Learning: Student Perspectives on the Value of Student-Led Maker Spaces in Engineering Education

Published in IJEE, 2020

Embedding and effectively managing independent learning within engineering curricula can be somewhat challenging. This work examines the development of a student-led maker space to facilitate independent learning and explores the value that these spaces can add to engineering curricula from a student perspective. Student-led maker spaces as used here, refer to learning environments created and developed solely by students, generally outside of the university setting and with minimal faculty support, to explore concepts related to their studies. We examine the experiences of two undergraduate engineering students involved in creating a student-led maker space to develop and produce a working prototype of a 3D printed modular separation column. The results show that these spaces can provide rewarding independent learning situations that encourage entrepreneurship and promote life-long learning.

Recommended citation: Kalogeropoulos, N., Walker, P., Hale, C., Hellgardt, K., Macey, A., Shah, U.V., Maraj, M.P.. ‘Facilitaing Independent Learning: Student Perspectives on the Value of Student-Led Maker Spaces in Engineering Education’, IJEE 2020, 36, 4, 1220-1233 https://www.ijee.ie/contents/c360420.html

Pierre J. Walker

Publications