Industrial Requirements for Thermodynamic and Transport Properties: 2020.

This paper reports the results of an investigation of industrial requirements for thermodynamic and transport properties carried out during the years 2019-2020. It is a follow-up of a similar investigation performed and published 10 years ago by the Working Party (WP) of Thermodynamics and Transport Properties of European Federation of Chemical Engineering (EFCE).1 The main goal was to investigate the advances in this area over the past 10 years, to identify the limitations that still exist, and to propose future R&D directions that will address the industrial needs. An updated questionnaire, with two new categories, namely, digitalization and comparison to previous survey/changes over the past 10 years, was sent to a broad number of experts in companies with a diverse activity spectrum, in oil and gas, chemicals, pharmaceuticals/biotechnology, food, chemical/mechanical engineering, consultancy, and power generation, among others, and in software suppliers and contract research laboratories. Very comprehensive answers were received by 37 companies, mostly from Europe (operating globally), but answers were also provided by companies in the USA and Japan. The response rate was about 60%, compared to 47% in the year 2010. The paper is written in such a way that both the majority and minority points of view are presented, and although the discussion is focused on needs and challenges, the benefits of thermodynamics and success stories are also reported. The results of the survey are thematically structured and cover changes, challenges, and further needs for a number of areas of interest such as data, models, systems, properties, and computational aspects (molecular simulation, algorithms and standards, and digitalization). Education and collaboration are discussed and recommendations on the future research activities are also outlined. In addition, a few initiatives, books, and reviews published in the past decade are briefly discussed. It is a long paper and, to provide the reader with a more complete understanding of the survey, many (anonymous) quotations (indicated with "..." and italics) from the industrial colleagues who have participated in the survey are provided. To help disseminate the specific information of interest only to particular industrial sectors, the paper has been written in such a way that the individual sections can also be read independently of each other.

Ab initio intermolecular potential energy surface for the CO2-N2 system and related thermophysical properties.

A four-dimensional potential energy surface (PES) for the interaction between a rigid carbon dioxide molecule and a rigid nitrogen molecule was constructed based on quantum-chemical ab initio calculations up to the coupled-cluster level with single, double, and perturbative triple excitations. Interaction energies for a total of 1893 points on the PES were calculated using the counterpoise-corrected supermolecular approach and basis sets of up to quintuple-zeta quality with bond functions. The interaction energies were extrapolated to the complete basis set limit, and an analytical site-site potential function with seven sites for carbon dioxide and five sites for nitrogen was fitted to the interaction energies. The CO2-N2 cross second virial coefficient as well as the dilute gas shear viscosity, thermal conductivity, and binary diffusion coefficient of CO2-N2 mixtures were calculated for temperatures up to 2000 K to validate the PES and to provide reliable reference values for these important properties. The calculated values are in very good agreement with the best experimental data.

Thermodiffusion in multicomponent n-alkane mixtures.

Compositional grading within a mixture has a strong impact on the evaluation of the pre-exploitation distribution of hydrocarbons in underground layers and sediments. Thermodiffusion, which leads to a partial diffusive separation of species in a mixture due to the geothermal gradient, is thought to play an important role in determining the distribution of species in a reservoir. However, despite recent progress, thermodiffusion is still difficult to measure and model in multicomponent mixtures. In this work, we report on experimental investigations of the thermodiffusion of multicomponent n-alkane mixtures at pressure above 30 MPa. The experiments have been conducted in space onboard the Shi Jian 10 spacecraft so as to isolate the studied phenomena from convection. For the two exploitable cells, containing a ternary liquid mixture and a condensate gas, measurements have shown that the lightest and heaviest species had a tendency to migrate, relatively to the rest of the species, to the hot and cold region, respectively. These trends have been confirmed by molecular dynamics simulations. The measured condensate gas data have been used to quantify the influence of thermodiffusion on the initial fluid distribution of an idealised one dimension reservoir. The results obtained indicate that thermodiffusion tends to noticeably counteract the influence of gravitational segregation on the vertical distribution of species, which could result in an unstable fluid column. This confirms that, in oil and gas reservoirs, the availability of thermodiffusion data for multicomponent mixtures is crucial for a correct evaluation of the initial state fluid distribution.

Calculation of the thermal conductivity of low-density CH4-N2 gas mixtures using an improved kinetic theory approach.

The thermal conductivity of low-density CH4-N2 gas mixtures has been calculated by means of the classical trajectory method using state-of-the-art intermolecular potential energy surfaces for the CH4-CH4, N2-N2, and CH4-N2 interactions. Results are reported in the temperature range from 70 K to 1200 K. Since the thermal conductivity is influenced by the vibrational degrees of freedom of the molecules, which are not included in the rigid-rotor classical trajectory computations, a new correction scheme to account for vibrational degrees of freedom in a dilute gas mixture is presented. The calculations show that the vibrational contribution at the highest temperature studied amounts to 46% of the total thermal conductivity of an equimolar mixture compared to 13% for pure nitrogen and 58% for pure methane. The agreement with the available experimental thermal conductivity data at room temperature is good, within ±1.4%, whereas at higher temperatures, larger deviations up to 4.5% are observed, which can be tentatively attributed to deteriorating performance of the measuring technique employed. Results are also reported for the magnitude and temperature dependence of the rotational collision number, Z(rot), for CH4 relaxing in collisions with N2 and for N2 relaxing in collisions with CH4. Both collision numbers increase with temperature, with the former being consistently about twice the value of the latter.

Influence of a magnetic field on the viscosity of a dilute gas consisting of linear molecules.

The viscomagnetic effect for two linear molecules, N2 and CO2, has been calculated in the dilute-gas limit directly from the most accurate ab initio intermolecular potential energy surfaces presently available. The calculations were performed by means of the classical trajectory method in the temperature range from 70 K to 3000 K for N2 and 100 K to 2000 K for CO2, and agreement with the available experimental data is exceptionally good. Above room temperature, where no experimental data are available, the calculations provide the first quantitative information on the magnitude and the behavior of the viscomagnetic effect for these gases. In the presence of a magnetic field, the viscosities of nitrogen and carbon dioxide decrease by at most 0.3% and 0.7%, respectively. The results demonstrate that the viscomagnetic effect is dominated by the contribution of the jj¯ polarization at all temperatures, which shows that the alignment of the rotational axes of the molecules in the presence of a magnetic field is primarily responsible for the viscomagnetic effect.

Intermolecular potential energy surface and thermophysical properties of the CH4-N2 system.

A five-dimensional potential energy surface (PES) for the interaction of a rigid methane molecule with a rigid nitrogen molecule was determined from quantum-chemical ab initio calculations. The counterpoise-corrected supermolecular approach at the CCSD(T) level of theory was utilized to compute a total of 743 points on the PES. The interaction energies were calculated using basis sets of up to quadruple-zeta quality with bond functions and were extrapolated to the complete basis set limit. An analytical site-site potential function with nine sites for methane and five sites for nitrogen was fitted to the interaction energies. The PES was validated by calculating the cross second virial coefficient as well as the shear viscosity and binary diffusion coefficient in the dilute-gas limit for CH4-N2 mixtures. An improved PES was obtained by adjusting a single parameter of the analytical potential function in such a way that quantitative agreement with the most accurate experimental values of the cross second virial coefficient was achieved. The transport property values obtained with the adjusted PES are in good agreement with the best experimental data.

Calculation of the transport properties of a dilute gas consisting of Lennard-Jones chains.

The transport properties in the dilute gas limit have been calculated by the classical-trajectory method for a gas consisting of chain-like molecules. The molecules were modelled as rigid chains consisting of spherical segments that interact through a combination of site-site Lennard-Jones 12-6 potentials. Results are reported for shear viscosity, self-diffusion, and thermal conductivity for chains consisting of 1, 2, 3, 4, 5, 6, 7, 8, 10, 13, and 16 segments in the reduced temperature range of 0.3-50. The results indicate that the transport properties increase with temperature and decrease with chain length. At high temperatures the dependence of the transport properties is governed effectively by the repulsive part of the potential. No simple scaling with chain length has been observed. The higher order correction factors are larger than observed for real molecules so far, reaching asymptotic values of 1.019-1.033 and 1.060-1.072 for viscosity and thermal conductivity, respectively. The dominant contribution comes from the angular momentum coupling. The agreement with molecular dynamics calculations for viscosity is within the estimated accuracy of the two methods for shorter chains. However, for longer chains differences of up to 7% are observed.

Viscosity of liquid mixtures: the Vesovic-Wakeham method for chain molecules.

New expressions for the viscosity of liquid mixtures, consisting of chain-like molecules, are derived by means of Enskog-type analysis. The molecules of the fluid are modelled as chains of equally sized, tangentially joined, and rigid spheres. It is assumed that the collision dynamics in such a fluid can be approximated by instantaneous collisions. We determine the molecular size parameters from the viscosity of each pure species and show how the different effective parameters can be evaluated by extending the Vesovic-Wakeham (VW) method. We propose and implement a number of thermodynamically consistent mixing rules, taking advantage of SAFT-type analysis, in order to develop the VW method for chain molecules. The predictions of the VW-chain model have been compared in the first instance with experimental viscosity data for octane-dodecane and methane-decane mixtures, thus, illustrating that the resulting VW-chain model is capable of accurately representing the viscosity of real liquid mixtures.

Ab initio intermolecular potential energy surface and thermophysical properties of hydrogen sulfide.

A six-dimensional potential energy hypersurface (PES) for two interacting rigid hydrogen sulfide molecules was determined from high-level quantum-mechanical ab initio computations. A total of 4016 points for 405 different angular orientations of two molecules were calculated utilizing the counterpoise-corrected supermolecular approach at the CCSD(T) level of theory and extrapolating the calculated interaction energies to the complete basis set limit. An analytical site-site potential function with eleven sites per hydrogen sulfide molecule was fitted to the interaction energies. The PES has been validated by computing the second pressure virial coefficient, shear viscosity, thermal conductivity and comparing with the available experimental data. The calculated values of volume viscosity were not used to validate the potential as the low accuracy of the available data precluded such an approach. The second pressure virial coefficient was evaluated by means of the Takahashi and Imada approach, while the transport properties, in the dilute limit, were evaluated by utilizing the classical trajectory method. In general, the agreement with the primary experimental data is within the experimental error for temperatures higher than 300 K. For lower temperatures the lack of reliable data indicates that the values of the second pressure virial coefficient and of the transport properties calculated in this work are currently the most accurate estimates for the thermophysical properties of hydrogen sulfide.

What happens inside a fuel cell? Developing an experimental functional map of fuel cell performance.

Fuel cell performance is determined by the complex interplay of mass transport, energy transfer and electrochemical processes. The convolution of these processes leads to spatial heterogeneity in the way that fuel cells perform, particularly due to reactant consumption, water management and the design of fluid-flow plates. It is therefore unlikely that any bulk measurement made on a fuel cell will accurately represent performance at all parts of the cell. The ability to make spatially resolved measurements in a fuel cell provides one of the most useful ways in which to monitor and optimise performance. This Minireview explores a range of in situ techniques being used to study fuel cells and describes the use of novel experimental techniques that the authors have used to develop an 'experimental functional map' of fuel cell performance. These techniques include the mapping of current density, electrochemical impedance, electrolyte conductivity, contact resistance and CO poisoning distribution within working PEFCs, as well as mapping the flow of reactant in gas channels using laser Doppler anemometry (LDA). For the high-temperature solid oxide fuel cell (SOFC), temperature mapping, reference electrode placement and the use of Raman spectroscopy are described along with methods to map the microstructural features of electrodes. The combination of these techniques, applied across a range of fuel cell operating conditions, allows a unique picture of the internal workings of fuel cells to be obtained and have been used to validate both numerical and analytical models.

Calculation of the transport and relaxation properties of dilute water vapor.

Transport properties of dilute water vapor have been calculated in the rigid-rotor approximation using four different potential energy hypersurfaces and the classical-trajectory method. Results are reported for shear viscosity, self-diffusion, thermal conductivity, and volume viscosity in the dilute-gas limit for the temperature range of 250-2500 K. Of these four surfaces the CC-pol surface of Bukowski et al. [J. Chem. Phys. 128, 094314 (2008)] is in best accord with the available measurements. Very good agreement is found with the most accurate results for viscosity in the whole temperature range of the experiments. For thermal conductivity the deviations of the calculated values from the experimental data increase systematically with increasing temperature to around 5% at 1100 K. For both self-diffusion and volume viscosity, the much more limited number of available measurements are generally consistent with the calculated values, apart from the lower temperature isotopically labeled diffusion measurements.

Calculation of the transport and relaxation properties of methane. II. Thermal conductivity, thermomagnetic effects, volume viscosity, and nuclear-spin relaxation.

Transport properties of pure methane have been calculated in the rigid-rotor approximation using the recently proposed intermolecular potential energy hypersurface [R. Hellmann et al., J. Chem. Phys. 128, 214303 (2008)] and the classical-trajectory method. Results are reported in the dilute-gas limit for the temperature range of 80-1500 K. The calculated thermal conductivity values are in very good agreement with the measured data and correlations. In the temperature range of 310-480 K the calculated values underestimate the best experimental data by 0.5%-1.0%. We suggest that the calculated values are more accurate, especially at low and high temperatures, than the currently available correlations based on the experimental data. Our results also agree well with measurements of thermal transpiration and of the thermomagnetic coefficients. We have shown that although the dominant contribution to the thermomagnetic coefficients comes from the Wjj polarization in the spherical approximation, the contribution of a second polarization, Wj, cannot be neglected nor can a full description of the Wjj polarization. The majority of the volume viscosity measurements around room temperature are consistent with the calculated values but this is not the case at high and low temperatures. However, for nuclear-spin relaxation the calculated values consistently exceed the measurements, which are mutually consistent within a few percent.

Calculation of the transport and relaxation properties of methane. I. Shear viscosity, viscomagnetic effects, and self-diffusion.

Transport properties of pure methane gas have been calculated in the rigid-rotor approximation using the recently proposed intermolecular potential energy hypersurface [R. Hellmann et al., J. Chem. Phys. 128, 214303 (2008)] and the classical-trajectory method. Results are reported in the dilute-gas limit for shear viscosity, viscomagnetic coefficients, and self-diffusion in the temperature range of 80-1500 K. Compared with the best measurements, the calculated viscosity values are about 0.5% too high at room temperature, although the temperature dependence of the calculated values is in very good agreement with experiment between 210 and 390 K. For the shear viscosity, the calculations indicate that the corrections in the second-order approximation and those due to the angular-momentum polarization are small, less than 0.7%, in the temperature range considered. The very good agreement of the calculated values with the experimental viscosity data suggests that the rigid-rotor approximation should be very reasonable for the three properties considered. In general, the agreement for the other measured properties is within the experimental error.

A kinetic theory description of the viscosity of dense fluids consisting of chain molecules.

An expression for the viscosity of a dense fluid is presented that includes the effect of molecular shape. The molecules of the fluid are approximated by chains of equal-sized, tangentially jointed, rigid spheres. It is assumed that the collision dynamics in such a fluid can be approximated by instantaneous collisions between two rigid spheres belonging to different chains. The approach is thus analogous to that of Enskog for a fluid consisting of rigid spheres. The description is developed in terms of two molecular parameters, the diameter sigma of the spherical segment and the chain length (number of segments) m. It is demonstrated that an analysis of viscosity data of a particular pure fluid alone cannot be used to obtain independently effective values of both sigma and m. Nevertheless, the chain lengths of n-alkanes are determined by assuming that the diameter of each rigid sphere making up the chain can be represented by the diameter of a methane molecule. The effective chain lengths of n-alkanes are found to increase linearly with the number C of carbon atoms present. The dependence can be approximated by a simple relationship m=1+(C-1)3. The same relationship was reported within the context of a statistical associating fluid theory equation of state treatment of the fluid, indicating that both the equilibrium thermodynamic properties and viscosity yield the same value for the chain lengths of n-alkanes.

Calculation of the transport properties of carbon dioxide. III. Volume viscosity, depolarized Rayleigh scattering, and nuclear spin relaxation.

Transport properties of pure carbon dioxide have been calculated from the intermolecular potential using the classical trajectory method. Results are reported in the dilute-gas limit for volume viscosity, depolarized Rayleigh scattering, and nuclear spin relaxation for temperatures ranging from 200 to 1000 K. Three recent carbon dioxide potential energy hypersurfaces have been investigated. Calculated values for the rotational collision number for all three intermolecular surfaces are consistent with the measurements and indicate that the temperature dependence of the Brau-Jonkman correlation is not applicable for carbon dioxide. The results for the depolarized Rayleigh scattering cross section and the nuclear spin relaxation cross section show that calculated values for the generally more successful potentials differ from the observations by 9% at about 290 K, although agreement is obtained for nuclear spin relaxation at about 400 K.

Calculation of the transport properties of carbon dioxide. II. Thermal conductivity and thermomagnetic effects.

The transport properties of pure carbon dioxide have been calculated from the intermolecular potential using the classical trajectory method. Results are reported in the dilute-gas limit for thermal conductivity and thermomagnetic coefficients for temperatures ranging from 200 K to 1000 K. Three recent carbon dioxide potential energy hypersurfaces have been investigated. Since thermal conductivity is influenced by vibrational degrees of freedom, not included in the rigid-rotor classical trajectory calculation, a correction for vibration has also been employed. The calculations indicate that the second-order thermal conductivity corrections due to the angular momentum polarization (< 2%) and velocity polarization (< 1%) are both small. Thermal conductivity values calculated using the potential energy hypersurface by Bukowski et al. (1999) are in good agreement with the available experimental data. They underestimate the best experimental data at room temperature by 1% and in the range up to 470 K by 1%-3%, depending on the data source. Outside this range the calculated values, we believe, may be more reliable than the currently available experimental data. Our results are consistent with measurements of the thermomagnetic effect at 300 K only when the vibrational degrees of freedom are considered fully. This excellent agreement for these properties indicates that particularly the potential surface of Bukowski et al. provides a realistic description of the anisotropy of the surface.