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Hulikal Chakrapani T, Hajibeygi H, Moultos OA, Vlugt TJH. Mutual Diffusivities of Mixtures of Carbon Dioxide and Hydrogen and Their Solubilities in Brine: Insight from Molecular Simulations. Ind Eng Chem Res 2024; 63:10456-10481. [PMID: 38882502 PMCID: PMC11177264 DOI: 10.1021/acs.iecr.4c01078] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2024] [Revised: 05/14/2024] [Accepted: 05/20/2024] [Indexed: 06/18/2024]
Abstract
H2-CO2 mixtures find wide-ranging applications, including their growing significance as synthetic fuels in the transportation industry, relevance in capture technologies for carbon capture and storage, occurrence in subsurface storage of hydrogen, and hydrogenation of carbon dioxide to form hydrocarbons and alcohols. Here, we focus on the thermodynamic properties of H2-CO2 mixtures pertinent to underground hydrogen storage in depleted gas reservoirs. Molecular dynamics simulations are used to compute mutual (Fick) diffusivities for a wide range of pressures (5 to 50 MPa), temperatures (323.15 to 423.15 K), and mixture compositions (hydrogen mole fraction from 0 to 1). At 5 MPa, the computed mutual diffusivities agree within 5% with the kinetic theory of Chapman and Enskog at 423.15 K, albeit exhibiting deviations of up to 25% between 323.15 and 373.15 K. Even at 50 MPa, kinetic theory predictions match computed diffusivities within 15% for mixtures comprising over 80% H2 due to the ideal-gas-like behavior. In mixtures with higher concentrations of CO2, the Moggridge correlation emerges as a dependable substitute for the kinetic theory. Specifically, when the CO2 content reaches 50%, the Moggridge correlation achieves predictions within 10% of the computed Fick diffusivities. Phase equilibria of ternary mixtures involving CO2-H2-NaCl were explored using Gibbs Ensemble (GE) simulations with the Continuous Fractional Component Monte Carlo (CFCMC) technique. The computed solubilities of CO2 and H2 in NaCl brine increased with the fugacity of the respective component but decreased with NaCl concentration (salting out effect). While the solubility of CO2 in NaCl brine decreased in the ternary system compared to the binary CO2-NaCl brine system, the solubility of H2 in NaCl brine increased less in the ternary system compared to the binary H2-NaCl brine system. The cooperative effect of H2-CO2 enhances the H2 solubility while suppressing the CO2 solubility. The water content in the gas phase was found to be intermediate between H2-NaCl brine and CO2-NaCl brine systems. Our findings have implications for hydrogen storage and chemical technologies dealing with CO2-H2 mixtures, particularly where experimental data are lacking, emphasizing the need for reliable thermodynamic data on H2-CO2 mixtures.
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Affiliation(s)
- Thejas Hulikal Chakrapani
- Reservoir Engineering, Geoscience and Engineering Department, Faculty of Civil Engineering and Geosciences, Delft University of Technology, Delft 2628 CN, The Netherlands
| | - Hadi Hajibeygi
- Reservoir Engineering, Geoscience and Engineering Department, Faculty of Civil Engineering and Geosciences, Delft University of Technology, Delft 2628 CN, The Netherlands
| | - Othonas A Moultos
- Engineering Thermodynamics, Process and Energy Department, Faculty of Mechanical Engineering, Delft University of Technology, Delft 2628 CB, The Netherlands
| | - Thijs J H Vlugt
- Engineering Thermodynamics, Process and Energy Department, Faculty of Mechanical Engineering, Delft University of Technology, Delft 2628 CB, The Netherlands
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2
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Olowookere FV, Turner CH. Predicting Gaseous Solute Diffusion in Viscous Multivalent Ionic Liquid Solvents. J Phys Chem B 2023; 127:9144-9154. [PMID: 37831616 DOI: 10.1021/acs.jpcb.3c03858] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/15/2023]
Abstract
Calculating solute diffusion in dense, viscous solvents can be particularly challenging in molecular dynamics simulations due to the long time scales involved. Here, a new scaling approach is developed for predicting solute diffusion based on analyses of CO2 and SO2 diffusion in two different multivalent ionic liquid solvents. Various scaling approaches are initially evaluated, including single and separate thermostats for the solute and solvent, as well as the application of the Arrhenius relationship and the Speedy-Angell power law. A very strong logarithmic correlation is established between the solvent-accessible surface area and solute diffusion. This relationship, reflecting Danckwerts' surface renewal theory and the Vrentas-Duda free volume model, presents a valuable method for estimating diffusion behavior from short simulation trajectories at elevated temperatures. The approach may be beneficial for enhancing predictive modeling in similar challenging systems and should be more broadly evaluated.
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Affiliation(s)
- Feranmi V Olowookere
- Department of Chemical and Biological Engineering, The University of Alabama, Tuscaloosa, Alabama 35487-0203, United States
| | - C Heath Turner
- Department of Chemical and Biological Engineering, The University of Alabama, Tuscaloosa, Alabama 35487-0203, United States
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3
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Saric D, Guevara-Carrion G, Gaponenko Y, Shevtsova V, Vrabec J. Diffusion of hydrocarbons diluted in supercritical carbon dioxide. Sci Rep 2023; 13:16107. [PMID: 37752219 PMCID: PMC10522683 DOI: 10.1038/s41598-023-42892-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2023] [Accepted: 09/15/2023] [Indexed: 09/28/2023] Open
Abstract
Mutual diffusion of six hydrocarbons (methane, ethane, isobutane, benzene, toluene or naphthalene) diluted in supercritical carbon dioxide ([Formula: see text]) is studied by molecular dynamics simulation near the Widom line, i.e., in the temperature range from 290 to 345 K along the isobar 9 MPa. The [Formula: see text] + aromatics mixtures are additionally sampled at 10 and 12 MPa and an experimental database with Fick diffusion coefficient data for those systems is provided. Taylor dispersion experiments of [Formula: see text] with benzene, toluene, n-dodecane and 1,2,3,4-tetrahydronaphthalene are conducted along the [Formula: see text] 10 MPa isobar. Maxwell-Stefan and Fick diffusion coefficients are analyzed, together with the thermodynamic factor that relates them. It is found that the peculiar behavior of the Fick diffusion coefficient of some [Formula: see text] mixtures in the extended critical region is a consequence of the thermodynamic factor minimum due to pronounced clustering on the molecular scale. Further, the strong dependence of the Fick diffusion coefficient on the molecular mass of the solute as well as the breakdown of the Stokes-Einstein relation near the Widom line are confirmed. Eleven correlations for the prediction of the Fick diffusion coefficient of [Formula: see text] mixtures are assessed. An alternative two-step approach for the prediction of the infinite dilution Fick diffusion coefficient of supercritical [Formula: see text] mixtures is proposed. It requires only the state point in terms of temperature and pressure (or density) as well as the molecular solute mass as input parameters. First, entropy scaling is applied to estimate the self-diffusion coefficient of [Formula: see text]. Subsequently, this coefficient is used to determine the infinite dilution Fick diffusion coefficient of the mixture, based on the finding that these two diffusion coefficients exhibit a linear relationship, where the slope depends only on the molecular solute mass.
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Affiliation(s)
- Denis Saric
- Thermodynamics, Technical University of Berlin, Ernst-Reuter-Platz 1, 10587, Berlin, Germany
| | | | - Yury Gaponenko
- MRC, CP-165/62, Université libre de Bruxelles (ULB), Ave. F.D. Roosevelt 50, B-1050, Brussels, Belgium
| | - Valentina Shevtsova
- Fluid Mechanics Group, Faculty of Engineering, Mondragon University, 20500, Mondragon, Spain
- IKERBASQUE, Basque Foundation for Science, Plaza Euskadi 5, 48009, Bilbao, Spain
| | - Jadran Vrabec
- Thermodynamics, Technical University of Berlin, Ernst-Reuter-Platz 1, 10587, Berlin, Germany.
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4
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Leverant CJ, Greathouse JA, Harvey JA, Alam TM. Machine Learning Predictions of Simulated Self-Diffusion Coefficients for Bulk and Confined Pure Liquids. J Chem Theory Comput 2023. [PMID: 37192538 DOI: 10.1021/acs.jctc.2c01040] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/18/2023]
Abstract
Diffusion properties of bulk fluids have been predicted using empirical expressions and machine learning (ML) models, suggesting that predictions of diffusion also should be possible for fluids in confined environments. The ability to quickly and accurately predict diffusion in porous materials would enable new discoveries and spur development in relevant technologies such as separations, catalysis, batteries, and subsurface applications. In this work, we apply artificial neural network (ANN) models to predict the simulated self-diffusion coefficients of real liquids in both bulk and pore environments. The training data sets were generated from molecular dynamics (MD) simulations of Lennard-Jones particles representing a diverse set of 14 molecules ranging from ammonia to dodecane over a range of liquid pressures and temperatures. Planar, cylindrical, and hexagonal pore models consisted of walls composed of carbon atoms. Our simple model for these liquids was primarily used to generate ANN training data, but the simulated self-diffusion coefficients of bulk liquids show excellent agreement with experimental diffusion coefficients. ANN models based on simple descriptors accurately reproduced the MD diffusion data for both bulk and confined liquids, including the trend of increased mobility in large pores relative to the corresponding bulk liquid.
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Affiliation(s)
- Calen J Leverant
- Nanoscale Sciences Department, Sandia National Laboratories, Albuquerque, New Mexico 87185, United States
| | - Jeffery A Greathouse
- Nuclear Waste Disposal Research & Analysis Department, Sandia National Laboratories, Albuquerque, New Mexico 87185, United States
| | - Jacob A Harvey
- Geochemistry Department, Sandia National Laboratories, Albuquerque, New Mexico 87185, United States
| | - Todd M Alam
- Department of Organic Materials Science, Sandia National Laboratories, Albuquerque, New Mexico 87185, United States
- ACC Consulting New Mexico, Cedar Crest, New Mexico 87008, United States
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5
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Rehner P, Bauer G, Gross J. FeO s: An Open-Source Framework for Equations of State and Classical Density Functional Theory. Ind Eng Chem Res 2023. [DOI: 10.1021/acs.iecr.2c04561] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/11/2023]
Affiliation(s)
- Philipp Rehner
- Energy and Process Systems Engineering, Department of Mechanical and Process Engineering, ETH Zurich, Tannenstrasse 3, Zurich 8092, Switzerland
| | - Gernot Bauer
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, Stuttgart 70569, Germany
| | - Joachim Gross
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, Stuttgart 70569, Germany
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6
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Zeng F, Wan R, Xiao Y, Song F, Peng C, Liu H. Predicting the Self-Diffusion Coefficient of Liquids Based on Backpropagation Artificial Neural Network: A Quantitative Structure–Property Relationship Study. Ind Eng Chem Res 2022. [DOI: 10.1021/acs.iecr.2c03342] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Fazhan Zeng
- School of Chemistry & Molecular Engineering, East China University of Science and Technology, Shanghai200237, China
| | - Ren Wan
- School of Chemistry & Molecular Engineering, East China University of Science and Technology, Shanghai200237, China
| | - Yongjun Xiao
- School of Chemistry & Molecular Engineering, East China University of Science and Technology, Shanghai200237, China
| | - Fan Song
- School of Chemistry & Molecular Engineering, East China University of Science and Technology, Shanghai200237, China
| | - Changjun Peng
- School of Chemistry & Molecular Engineering, East China University of Science and Technology, Shanghai200237, China
| | - Honglai Liu
- School of Chemistry & Molecular Engineering, East China University of Science and Technology, Shanghai200237, China
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7
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Crossover Residual Entropy Scaling of the Viscosity and Thermal Conductivity of Carbon Dioxide. J Mol Liq 2022. [DOI: 10.1016/j.molliq.2022.120799] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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8
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Li N, Wang X, Chen G, Gao N. Linking Thermal Conductivity and Self-Diffusion Coefficient with a Simple Dimensionless Calorimetric Parameter for Saturated Liquids. Ind Eng Chem Res 2022. [DOI: 10.1021/acs.iecr.2c02447] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Nian Li
- Ningbo Research Institute, Zhejiang University, Ningbo315100, China
- NingboTech University, Ningbo315100, China
- Zhejiang Engineering Research Center for Intelligent Marine Ranch Equipment, Ningbo315100, China
| | - Xuehui Wang
- Department of Chemical Engineering, Imperial College London, LondonSW7 2AZ, U.K
| | - Guangming Chen
- Ningbo Research Institute, Zhejiang University, Ningbo315100, China
- NingboTech University, Ningbo315100, China
| | - Neng Gao
- NingboTech University, Ningbo315100, China
- Zhejiang Engineering Research Center for Intelligent Marine Ranch Equipment, Ningbo315100, China
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9
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Dehlouz A, Jaubert JN, Galliero G, Bonnissel M, Privat R. Entropy Scaling-Based Correlation for Estimating the Self-Diffusion Coefficients of Pure Fluids. Ind Eng Chem Res 2022. [DOI: 10.1021/acs.iecr.2c01086] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Aghilas Dehlouz
- Université de Lorraine, École Nationale Supérieure des Industries Chimiques, Laboratoire Réactions et Génie des Procédés (UMR CNRS 7274), 1 rue Grandville, 54000 Nancy, France
- Gaztransport & Technigaz (GTT), 1 route de Versailles, 78470 Saint-Rémy-lès-Chevreuse, France
| | - Jean-Noël Jaubert
- Université de Lorraine, École Nationale Supérieure des Industries Chimiques, Laboratoire Réactions et Génie des Procédés (UMR CNRS 7274), 1 rue Grandville, 54000 Nancy, France
| | - Guillaume Galliero
- Université de Pau et des Pays de l’Adour, E2S UPPA, CNRS TotalEnergies, LFCR UMR 5150, 64013 Pau, France
| | - Marc Bonnissel
- Gaztransport & Technigaz (GTT), 1 route de Versailles, 78470 Saint-Rémy-lès-Chevreuse, France
| | - Romain Privat
- Université de Lorraine, École Nationale Supérieure des Industries Chimiques, Laboratoire Réactions et Génie des Procédés (UMR CNRS 7274), 1 rue Grandville, 54000 Nancy, France
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10
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Transport Properties of Binary Lennard-Jones Mixtures: Insights from Entropy Scaling and Conformal Solution Theory. J Mol Liq 2022. [DOI: 10.1016/j.molliq.2022.120401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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11
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Alam TM, Allers JP, Leverant CJ, Harvey JA. Symbolic regression development of empirical equations for diffusion in Lennard-Jones fluids. J Chem Phys 2022; 157:014503. [DOI: 10.1063/5.0093658] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
Symbolic regression (SR) with a multi-gene genetic program has been used to elucidate new empirical equations describing diffusion in Lennard-Jones (LJ) fluids. Examples include equations to predict self-diffusion in pure LJ fluids and equations describing the finite-size correction for self-diffusion in binary LJ fluids. The performance of the SR-obtained equations was compared to that of both the existing empirical equations in the literature and to the results from artificial neural net (ANN) models recently reported. It is found that the SR equations have improved predictive performance in comparison to the existing empirical equations, even though employing a smaller number of adjustable parameters, but show an overall reduced performance in comparison to more extensive ANNs.
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Affiliation(s)
- Todd M. Alam
- ACC Consulting New Mexico, Cedar Crest, New Mexico 87008, USA
- Department of Organic Materials Science, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - Joshua P. Allers
- Department of Organic Materials Science, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - Calen J. Leverant
- Department of WMD Threats and Aerosol Science, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
- Department of Chemical Engineering, University of Florida, Gainesville, Florida 32611, USA
| | - Jacob A. Harvey
- Geochemistry Department, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
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12
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Stierle R, Gross J. Hydrodynamic density functional theory for mixtures from a variational principle and its application to droplet coalescence. J Chem Phys 2021; 155:134101. [PMID: 34624998 DOI: 10.1063/5.0060088] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Abstract
Dynamic density functional theory (DDFT) allows the description of microscopic dynamical processes on the molecular scale extending classical DFT to non-equilibrium situations. Since DDFT and DFT use the same Helmholtz energy functionals, both predict the same density profiles in thermodynamic equilibrium. We propose a molecular DDFT model, in this work also referred to as hydrodynamic DFT, for mixtures based on a variational principle that accounts for viscous forces as well as diffusive molecular transport via the generalized Maxwell-Stefan diffusion. Our work identifies a suitable expression for driving forces for molecular diffusion of inhomogeneous systems. These driving forces contain a contribution due to the interfacial tension. The hydrodynamic DFT model simplifies to the isothermal multicomponent Navier-Stokes equation in continuum situations when Helmholtz energies can be used instead of Helmholtz energy functionals, closing the gap between micro- and macroscopic scales. We show that the hydrodynamic DFT model, although not formulated in conservative form, globally satisfies the first and second law of thermodynamics. Shear viscosities and Maxwell-Stefan diffusion coefficients are predicted using an entropy scaling approach. As an example, we apply the hydrodynamic DFT model with a Helmholtz energy density functional based on the perturbed-chain statistical associating fluid theory equation of state to droplet and bubble coalescence in one dimension and analyze the influence of additional components on coalescence phenomena.
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Affiliation(s)
- Rolf Stierle
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany
| | - Joachim Gross
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany
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13
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Dehlouz A, Privat R, Galliero G, Bonnissel M, Jaubert JN. Revisiting the Entropy-Scaling Concept for Shear-Viscosity Estimation from Cubic and SAFT Equations of State: Application to Pure Fluids in Gas, Liquid and Supercritical States. Ind Eng Chem Res 2021. [DOI: 10.1021/acs.iecr.1c01386] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Aghilas Dehlouz
- École Nationale Supérieure des Industries Chimiques, Laboratoire Réactions et Génie des Procédés (UMR CNRS 7274), Université de Lorraine, 1 rue Grandville, 54000 Nancy, France
- Gaztransport & Technigaz (GTT), 1 route de Versailles, 78470 Saint-Rémy-lès-Chevreuse, France
| | - Romain Privat
- École Nationale Supérieure des Industries Chimiques, Laboratoire Réactions et Génie des Procédés (UMR CNRS 7274), Université de Lorraine, 1 rue Grandville, 54000 Nancy, France
| | - Guillaume Galliero
- E2S UPPA, CNRS Total Energies, LFCR UMR 5150, Université de Pau et des Pays de l’Adour 64000 Pau, France
| | - Marc Bonnissel
- Gaztransport & Technigaz (GTT), 1 route de Versailles, 78470 Saint-Rémy-lès-Chevreuse, France
| | - Jean-Noël Jaubert
- École Nationale Supérieure des Industries Chimiques, Laboratoire Réactions et Génie des Procédés (UMR CNRS 7274), Université de Lorraine, 1 rue Grandville, 54000 Nancy, France
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14
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Gonçalves CIS, Silva GM, Ndiaye PM, Tavares FW. Helmholtz Scaling: An Alternative Approach to Calculate Viscosity with the PCP-SAFT Equation of State. Ind Eng Chem Res 2021. [DOI: 10.1021/acs.iecr.1c00837] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Cliff I. S. Gonçalves
- Programa de Engenharia Química—COPPE, Universidade Federal do Rio de Janeiro, C.P. 68542 Rio de Janeiro, Brazil
| | - Gabriel M. Silva
- Escola de Química, Universidade Federal do Rio de Janeiro, C.P. 68542 Rio de Janeiro, Brazil
| | - Papa M. Ndiaye
- Programa de Engenharia Química—COPPE, Universidade Federal do Rio de Janeiro, C.P. 68542 Rio de Janeiro, Brazil
- Escola de Química, Universidade Federal do Rio de Janeiro, C.P. 68542 Rio de Janeiro, Brazil
| | - Frederico W. Tavares
- Programa de Engenharia Química—COPPE, Universidade Federal do Rio de Janeiro, C.P. 68542 Rio de Janeiro, Brazil
- Escola de Química, Universidade Federal do Rio de Janeiro, C.P. 68542 Rio de Janeiro, Brazil
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15
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Scheiner B, Yoon TJ. Calculation of self-diffusion coefficients in supercritical carbon dioxide using mean force kinetic theory. J Chem Phys 2021; 154:134101. [PMID: 33832259 DOI: 10.1063/5.0045211] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
This paper presents an application of mean force kinetic theory (MFT) to the calculation of the self-diffusivity of CO2 in the supercritical fluid regime. Two modifications to the typical application of MFT are employed to allow its application to a system of molecular species. The first is the assumption that the inter-particle potential of mean force can be obtained from the molecule center-of-mass pair correlation function, which in the case of CO2 is the C-C pair correlation function. The second is a new definition of the Enskog factor that describes the effect of correlations at the surface of the collision volume. The new definition retains the physical picture that this quantity represents a local density increase, resulting from particle correlations, relative to that in the zero density homogeneous fluid limit. These calculations are facilitated by the calculation of pair correlation functions from molecular dynamics (MD) simulations using the FEPM2 molecular CO2 model. The self-diffusivity calculated from theory is in good agreement with that from MD simulations up to and slightly beyond the density at the location of the Frenkel line. The calculation is compared with and is found to perform similarly well to other commonly used models but has a greater potential for application to systems of mixed species and to systems of particles with long range interatomic potentials due to electrostatic interactions.
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Affiliation(s)
- Brett Scheiner
- Los Alamos National Laboratory, Los Alamos, New Mexico 87544, USA
| | - Tae Jun Yoon
- Los Alamos National Laboratory, Los Alamos, New Mexico 87544, USA
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16
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Zmpitas J, Gross J. Modified Stokes–Einstein Equation for Molecular Self-Diffusion Based on Entropy Scaling. Ind Eng Chem Res 2021. [DOI: 10.1021/acs.iecr.0c06090] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Julia Zmpitas
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany
| | - Joachim Gross
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany
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17
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Allers JP, Garzon FH, Alam TM. Artificial neural network prediction of self-diffusion in pure compounds over multiple phase regimes. Phys Chem Chem Phys 2021; 23:4615-4623. [PMID: 33620369 DOI: 10.1039/d0cp06693a] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
Artificial neural networks (ANNs) were developed to accurately predict the self-diffusion constants for pure components in liquid, gas and super critical phases. The ANNs were tested on an experimental database of 6625 self-diffusion constants for 118 different chemical compounds. The presence of multiple phases results in a heavy skew in the distribution of diffusion constants and multiple approaches were used to address this challenge. First, an ANN was developed with the raw diffusion values to assess what the main drawbacks of this direct method were. The first approach for improving the predictions involved taking the log 10 of diffusion to provide a more uniform distribution and reduce the range of target output values used to develop the ANN. The second approach involved developing individual ANNs for each phase using the raw diffusion values. Results show that the log transformation leads to a model with the best self-diffusion constant predictions and an overall average absolute deviation (AAD) of 6.56%. The resultant ANN is a generalized model that can be used to predict diffusion across all three phases and over a diverse group of compounds. The importance of each input feature was ranked using a feature addition method revealing that the density of the compound has the largest impact on the ANN prediction of self-diffusion constants in pure compounds.
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Affiliation(s)
- Joshua P Allers
- Department of Organic Materials Science, Sandia National Laboratories, Albuquerque, NM 87185, USA.
| | - Fernando H Garzon
- Advanced Materials Laboratory, Sandia National Laboratories, Albuquerque, NM 87185, USA and Center of Micro-Engineered Materials, University of New Mexico, Albuquerque, NM 87106, USA
| | - Todd M Alam
- Department of Organic Materials Science, Sandia National Laboratories, Albuquerque, NM 87185, USA.
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18
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Mairhofer J. A Residual Entropy Scaling Approach for Viscosity Based on the GERG-2008 Equation of State. Ind Eng Chem Res 2021. [DOI: 10.1021/acs.iecr.0c04938] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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19
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Fouad WA, Alasiri H. Molecular dynamic simulation and SAFT modeling of the viscosity and self-diffusion coefficient of low global warming potential refrigerants. J Mol Liq 2020. [DOI: 10.1016/j.molliq.2020.113998] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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20
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Bell IH. Entropy Scaling of Viscosity - II: Predictive Scheme for Normal Alkanes. JOURNAL OF CHEMICAL AND ENGINEERING DATA 2020; 65:10.1021/acs.jced.0c00749. [PMID: 34121765 PMCID: PMC8191377 DOI: 10.1021/acs.jced.0c00749] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
In this work, a residual entropy value 6/10 of the way between the critical point and a value of -2/3 of Boltzmann's constant is shown to collapse the scaled viscosity for the family of normal alkanes. Based on this approach, a nearly universal correlation is proposed that can reproduce 95% of the experimental data for normal alkanes within ±18% (without removal of clearly erroneous data). This universal correlation has no new fluid-specific empirical parameters and is based on experimentally accessible values. This collapse is shown to be valid to a residual entropy half way between the critical point and the triple point, beyond which the macroscopically-scaled viscosity has a super-exponential dependence on residual entropy, terminating at the triple point. A key outcome of this study is a better understanding of entropy scaling for fluids with intramolecular degrees of freedom. A study of the transport and thermodynamic properties at the triple point rounds out the analysis.
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Affiliation(s)
- Ian H Bell
- Applied Chemicals and Materials Division, National Institute of Standards and Technology, Boulder, CO 80305
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21
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Celebi AT, Jamali SH, Bardow A, Vlugt TJH, Moultos OA. Finite-size effects of diffusion coefficients computed from molecular dynamics: a review of what we have learned so far. MOLECULAR SIMULATION 2020. [DOI: 10.1080/08927022.2020.1810685] [Citation(s) in RCA: 28] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Affiliation(s)
- Alper T. Celebi
- Engineering Thermodynamics, Process & Energy Department, Faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology, Delft, The Netherlands
| | - Seyed Hossein Jamali
- Engineering Thermodynamics, Process & Energy Department, Faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology, Delft, The Netherlands
| | - André Bardow
- Energy & Process Systems Engineering, Department of Mechanical and Process Engineering, ETH Zurich, Zürich, Switzerland
| | - Thijs J. H. Vlugt
- Engineering Thermodynamics, Process & Energy Department, Faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology, Delft, The Netherlands
| | - Othonas A. Moultos
- Engineering Thermodynamics, Process & Energy Department, Faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology, Delft, The Netherlands
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22
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Binti Mohd Taib M, Trusler JPM. Residual entropy model for predicting the viscosities of dense fluid mixtures. J Chem Phys 2020; 152:164104. [PMID: 32357798 DOI: 10.1063/5.0002242] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
In this work, we have investigated the mono-variant relationship between the reduced viscosity and residual entropy in pure fluids and in binary mixtures of hydrocarbons and hydrocarbons with dissolved carbon dioxide. The mixtures considered were octane + dodecane, decane + carbon dioxide, and 1,3-dimethylbenzene (m-xylene) + carbon dioxide. The reduced viscosity was calculated according to the definition of Bell, while the residual entropy was calculated from accurate multi-parameter Helmholtz-energy equations of state and, for mixtures, the multi-fluid Helmholtz energy approximation. The mono-variant dependence of reduced viscosity upon residual molar entropy was observed for the pure fluids investigated, and by incorporating two scaling factors (one for reduced viscosity and the other for residual molar entropy), the data were represented by a single universal curve. To apply this method to mixtures, the scaling factors were determined from a mole-fraction weighted sum of the pure-component values. This simple model was found to work well for the systems investigated. The average absolute relative deviation (AARD) was observed to be between 1% and 2% for pure components and a mixture of similar hydrocarbons. Larger deviations, with AARDs of up to 15%, were observed for the asymmetric mixtures, but this compares favorably with other methods for predicting the viscosity of such systems. We conclude that the residual-entropy concept can be used to estimate the viscosity of mixtures of similar molecules with high reliability and that it offers a useful engineering approximation even for asymmetric mixtures.
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Affiliation(s)
- Malyanah Binti Mohd Taib
- Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
| | - J P Martin Trusler
- Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
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23
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Fischer M, Bauer G, Gross J. Transferable Anisotropic United-Atom Mie (TAMie) Force Field: Transport Properties from Equilibrium Molecular Dynamic Simulations. Ind Eng Chem Res 2020. [DOI: 10.1021/acs.iecr.0c00848] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Matthias Fischer
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany
| | - Gernot Bauer
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany
| | - Joachim Gross
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany
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24
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Schilling J, Horend C, Bardow A. Integrating superstructure‐based design of molecules, processes, and flowsheets. AIChE J 2020. [DOI: 10.1002/aic.16903] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Johannes Schilling
- Institute of Technical ThermodynamicsRWTH Aachen University Aachen Germany
| | - Christian Horend
- Institute of Technical ThermodynamicsRWTH Aachen University Aachen Germany
| | - André Bardow
- Institute of Technical ThermodynamicsRWTH Aachen University Aachen Germany
- Institute of Energy and Climate Research – Energy Systems Engineering (IEK‐10)Forschungszentrum Jülich GmbH Jülich Germany
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25
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Bell IH. Entropy Scaling of Viscosity - I: A Case Study of Propane. JOURNAL OF CHEMICAL AND ENGINEERING DATA 2020; 65:10.1021/acs.jced.0c00209. [PMID: 33364635 PMCID: PMC7754705 DOI: 10.1021/acs.jced.0c00209] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
In this work, a broadly-applicable and simple approach for building high accuracy viscosity correlations is demonstrated for propane. The approach is based on the combination of a number of recent insights related to the use of residual entropy scaling, especially a new way of scaling the viscosity for consistency with the dilute-gas limit. With three adjustable parameters in the dense phase, the primary viscosity data for propane are predicted with a mean absolute relative deviation of 1.38%, and 95% of the primary data are predicted within a relative error band of less than 5%. The dimensionality of the dense-phase contribution is reduced from the conventional two dimensional approach (temperature and density) to a one-dimensional correlation with residual entropy as the independent variable. The simplicity of the model formulation ensures smooth extrapolation behavior (barring errors in the equation of state itself). The approach proposed here should be applicable to a wide range of chemical species. The supporting information includes the relevant data in tabular form and a Python implementation of the model.
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Affiliation(s)
- Ian H Bell
- Applied Chemicals and Materials Division, National Institute of Standards and Technology, Boulder, CO 80305
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26
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Hopp M, Gross J. Thermal Conductivity from Entropy Scaling: A Group-Contribution Method. Ind Eng Chem Res 2019. [DOI: 10.1021/acs.iecr.9b04289] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Madlen Hopp
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, 70569 Stuttgart, Germany
| | - Joachim Gross
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, 70569 Stuttgart, Germany
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27
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Hopp M, Mele J, Hellmann R, Gross J. Thermal Conductivity via Entropy Scaling: An Approach That Captures the Effect of Intramolecular Degrees of Freedom. Ind Eng Chem Res 2019. [DOI: 10.1021/acs.iecr.9b03998] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Madlen Hopp
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, 70569 Stuttgart, Germany
| | - Julia Mele
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, 70569 Stuttgart, Germany
| | - Robert Hellmann
- Institute of Chemistry, University of Rostock, 18055 Rostock, Germany
| | - Joachim Gross
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, 70569 Stuttgart, Germany
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28
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Probing the link between residual entropy and viscosity of molecular fluids and model potentials. Proc Natl Acad Sci U S A 2019; 116:4070-4079. [PMID: 30770449 DOI: 10.1073/pnas.1815943116] [Citation(s) in RCA: 33] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
This work investigates the link between residual entropy and viscosity based on wide-ranging, highly accurate experimental and simulation data. This link was originally postulated by Rosenfeld in 1977 [Rosenfeld Y (1977) Phys Rev A 15:2545-2549], and it is shown that this scaling results in an approximately monovariate relationship between residual entropy and reduced viscosity for a wide range of molecular fluids [argon, methane, [Formula: see text], [Formula: see text], refrigerant R-134a (1,1,1,2-tetrafluoroethane), refrigerant R-125 (pentafluoroethane), methanol, and water] and a range of model potentials (hard sphere, inverse power, Lennard-Jones, and Weeks-Chandler-Andersen). While the proposed "universal" correlation of Rosenfeld is shown to be far from universal, when used with the appropriate density scaling for molecular fluids, the viscosity of nonassociating molecular fluids can be mapped onto the model potentials. This mapping results in a length scale that is proportional to the cube root of experimentally measurable liquid volume values.
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29
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Abstract
This article gives an overview of excess-entropy scaling, the 1977 discovery by Rosenfeld that entropy determines properties of liquids like viscosity, diffusion constant, and heat conductivity. We give examples from computer simulations confirming this intriguing connection between dynamics and thermodynamics, counterexamples, and experimental validations. Recent uses in application-related contexts are reviewed, and theories proposed for the origin of excess-entropy scaling are briefly summarized. It is shown that if two thermodynamic state points of a liquid have the same microscopic dynamics, they must have the same excess entropy. In this case, the potential-energy function exhibits a symmetry termed hidden scale invariance, stating that the ordering of the potential energies of configurations is maintained if these are scaled uniformly to a different density. This property leads to the isomorph theory, which provides a general framework for excess-entropy scaling and illuminates, in particular, why this does not apply rigorously and universally. It remains an open question whether all aspects of excess-entropy scaling and related regularities reflect hidden scale invariance in one form or other.
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Affiliation(s)
- Jeppe C Dyre
- Glass and Time, IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
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