Thermal Conductivity Of Carbon Dioxide Research Articles

Modeling of nonequilibrium processes behind a shock wave in a mixture of carbon dioxide and argon

A closed self-consistent model of a nonequilibrium flow of a mixture of carbon dioxide and argon behind the front of a plane shock wave is developed. The generalized Chapman - Enskog method is used in the three-temperature approach, taking into account various channels of vibrational relaxation in a carbon dioxide molecule. An extended system of Navier - Stokes - Fourier equations is written, consisting of the equations of conservation of mass, momentum and energy, supplemented by the diffusion equations of the mixture components and relaxation equations for the vibrational modes of the CO2 molecule. The closing relations for the stress tensor, diffusion velocity, heat flux and vibrational energy fluxes are obtained. An algorithm for calculating the coefficients of shear and bulk viscosity, thermal conductivity of various degrees of freedom, diffusion and thermal diffusion has been developed and implemented. The model was validated by comparison with experimental data for the viscosity and thermal conductivity of carbon dioxide and argon, as well as for the binary diffusion coefficient. Satisfactory agreement with the experiment was obtained. The dependence of the transport coefficients on the gas temperature, temperatures of vibrational modes and mixture composition is analyzed. The developed model is ready for use in numerical simulation of shock waves in a mixture of CO2-Ar.

Al2O3-CO2 Nanofluid Transport Properties: A Molecular Dynamics Study and Machine Learning Predictive Modelling

Nanofluids are recognized to have significant difference in thermal/transport properties in contrast to the corresponding heat transfer fluids. The viscosity and thermal conductivity of carbon dioxide, which are the transport properties, play the vital role in swiftly growing applications of enhanced oil recovery process and industrial refrigeration. The current study presents different machine learning models to predict the transport properties of alumina-carbon dioxide nanofluid along with the molecular simulation approach. Several machine learning methods with linear regression, K-Nearest Neighbors, and Decision Tree are used to see the accuracy in determining these transport properties. The input variables taken to predict these transport properties are temperature, nanoparticle volume fraction and size. Molecular dynamics simulations using Large-scale Atomic/Molecular Massively Parallel Simulator are executed to determine the properties. Pearson correlation was established between the independent and dependent variables to check the dependency of the input variables on thermal conductivity and µ. Finally, we performed the statistical coefficients of determination to resolute the accuracy of the results obtained. It is concluded from the study that, the decision tree model with an accuracy of 99% is the best suited model for the prediction of transport properties of current nanofluid over the temperature range, volume fractions, and varied nanoparticle sizes.

Crossover residual entropy scaling of the viscosity and thermal conductivity of carbon dioxide

The crossover method is applied to the residual entropy scaling of viscosity and thermal conductivity to overcome the failure of the original model in the description of critical enhancement. Carbon dioxide is selected as a demonstration. One can derive the thermodynamic properties and fluid characteristic parameters required by the residual entropy scaling and critical enhancement term from the crossover multiparameter equation of state or crossover volume-translated Soave-Redlich-Kwong equation of state. The critical enhancement effects on viscosity and thermal conductivity are calculated using crossover functions based on the mode-coupling theory. It is found that the reduced value of the background part extracted from the near-critical viscosity and thermal conductivity data follows a univariate function of residual entropy, which is unified for the gaseous, liquid, and supercritical regions. The crossover models better represent the viscosity and thermal conductivity near the critical point with no deterioration in accuracy in the crossover region. The model incorporating the multiparameter equation of state takes advantage of the faithful representation of experimental data while the model of the volume-translated Soave-Redlich-Kwong equation of state is more feasible to be extended to other fluids and mixtures.

Low Thermal Conductivity of Carbon Dioxide at High Pressure: Implications for Icy Planetary Interiors

AbstractCarbon dioxide is commonly found in terrestrial planets and its thermal property is relevant to the dynamics and evolution of those terrestrial planets. In this work, we combine time‐domain thermoreflectance measurements and first‐principles calculations to determine the thermal conductivity of CO2 up to 70 GPa at room temperature. Our results show that the thermal conductivity of liquid CO2 is ∼0.22 W m−1 K−1 at 0.3–0.5 GPa and increases to ∼0.28 W m−1 K−1 when the liquid CO2 transforms into molecular solid phase I (dry ice). Upon further compression, the mean value of thermal conductivity of phase I increases to 1.4–2.1 W m−1 K−1 at ∼10 GPa and then slightly drops across the phase I‐III boundary. Phase III exhibits a gentle increase of thermal conductivity with pressure and reaches to a maximum value of ∼4 W m−1 K−1 at ∼45 GPa, but shows an abrupt drop when transforming into a non‐molecular amorphous solid. The pressure evolution of CO2 thermal conductivity across different phases may have significant implications for the heat flow and temperature distribution in the interiors of planets and moons containing CO2.

초임계 상태에서 질소가 포함된 이산화탄소의 열전도율 측정

In this study, the thermal conductivity of carbon dioxide with nitrogen in the supercritical state was experimentally measured. A non-stationary hot wire method, was used as a method for measuring thermal conductivity. The experimental equipment comprised a Wheatstone Bridge, a power supply, an oscilloscope, a gas inlet, a thermocouple, and a pressure gauge. The pressure vessel of the test section is designed to sufficiently withstand high pressure of 100 bar or more. As the heating wire, a platinum wire was used due to relation between temperature and resistance. When a voltage of 20V was applied, the platinum wire was heated and the thermal conductivity was measured using the slope of the voltage difference caused by the change in resistance. The molar concentration of nitrogen in the carbon dioxide and nitrogen mixture was changed to 1%, 3%, and 5%, the temperature was set to 35℃, 40℃, 45℃, and the pressure was varied from 80 to 100 bar. The experimental results were verified by measuring the thermal conductivity of pure CO₂ and pure N₂. The effect of the temperature, pressure, and the molar concentration of nitrogen on the thermal conductivity was physically explained by introducing the thermophysical properties of the mixture.

Predicting thermal conductivity of carbon dioxide using group of data-driven models

Thermal conductivity of carbon dioxide (CO2) is a vital thermophysical parameter that significantly affects the heat transfer modeling related to CO2 transportation, pipelines design and associated process industries. The current study lays emphasis on implementing powerful soft computing approaches to develop novel paradigms for estimation of CO2 thermal conductivity. To achieve this, a massive database including 5893 experimental datapoints was acquired from the experimental investigations. The collected data, covering pressure values from 0.097 to 209.763 MPa and temperature between 217.931 and 961.05 K, were employed for establishing various models based on multilayer perceptron (MLP) optimized by different back-propagation algorithms, and radial basis function neural network (RBFNN) coupled with particle swarm optimization (PSO). Then, the two best found models were linked under two committee machine intelligent systems (CMIS) using weighted averaging and group method of data handling (GMDH). The obtained results showed that CMIS-GMDH is the most accurate paradigm with an overall AARD% and R2 values of 0.8379% and 0.9997, respectively. In addition, CMIS-GMDH outperforms the best prior explicit models. Finally, the leverage technique confirmed the validity of the model and more than 96% of the data are within its applicability realm.

A study on thermodynamic and transport properties of carbon dioxide using molecular dynamics simulation

Molecular dynamics simulation was applied to test and evaluate the ability of several models of carbon dioxide on predicting thermodynamics and transport properties. Firstly, we compared the liquid-vapor coexist curves of seven kinds of carbon dioxide models by molecular dynamics simulations. It was found that the Cygan_flex model and EPM2 model were more accurate than the others. Then we investigated the structural properties of carbon dioxide using NPT ensemble molecular dynamics simulation. The fluid became less dense with the increasing temperature. Thirdly, the self-diffusion coefficients were studied at temperature and pressure up to 600 K and 80 MPa, respectively. The results showed that the self-diffusion coefficient decreased with the increasing pressure and increased with increasing temperature. Finally, we calculated the thermal conductivity of carbon dioxide at 250 K using EPM2_flex model, Cygan_flex model and TraPPE_flex model. So, we should pay attention to the selection of appropriate carbon dioxide models to obtain different carbon dioxide properties.

A New Correlation Method for Estimating Thermal Conductivity of Carbon Dioxide in Liquid, Vapor and Supercritical Phases

In this study, a new correlation for estimating thermal conductivity (TC) of carbon dioxide was developed based on 2319 data points. The data points were at the temperature ranging from 250 to 1100 K, pressure ranging from 1 to 3000 bar and density ranging from 0.3 to 1400 Kg.m-3 in different phases of liquid, vapor and supercritical. The statistical parameters including average absolute deviation (AAD%), average percent relative error (ARE%), sum of absolute residual (SAR) and the coefficient of determination (R2) have been calculated to evaluate the accuracy of present correlation. The obtained values of AAD%, ARE%, SAR and R2 were 1.98, −0.64, 3510.1 and 0.995, respectively. The predictions of proposed correlation were also compared with three widely used correlations. The results showed that the proposed correlation is able to accurately calculate thermal conductivity of carbon dioxide. In addition, the proposed model is superior to all the existing empirical models considered.

Predictive model based on ANFIS for estimation of thermal conductivity of carbon dioxide

Developing accurate and reliable modeling techniques for prediction of different properties of supercritical fluids (SCFs) such as thermal conductivity is of crucial importance due to growing application of these fluids in various fields of industrial and supercritical processes. This study aims to develop a predictive model for CO2 thermal conductivity predictions based on Adaptive Neuro-Fuzzy Inference System (ANFIS). An extensive number of 1042 experimental data were gathered from the literature covering wide ranges of operational temperatures and pressures. The combination of Hybrid and Particle Swarm Optimization (PSO) methods were used to train the model. The predictions of the developed Conjugate ANFIS model were compared with two literature correlations. Results show that the developed model is accurate and effective in prediction of experimental data. In addition, the proposed model is superior to two literature correlations in prediction of actual thermal conductivity data.

Reference Correlation of the Thermal Conductivity of Carbon Dioxide from the Triple Point to 1100 K and up to 200 MPa.

This paper contains new, representative reference equations for the thermal conductivity of carbon dioxide. The equations are based in part upon a body of experimental data that has been critically assessed for internal consistency and for agreement with theory whenever possible. In the case of the dilute-gas thermal conductivity, we incorporated recent theoretical calculations to extend the temperature range of the experimental data. Moreover, in the critical region, the experimentally observed enhancement of the thermal conductivity is well represented by theoretically based equations containing just one adjustable parameter. The correlations are applicable for the temperature range from the triple point to 1100 K and pressures up to 200 MPa. The overall uncertainty (at the 95% confidence level) of the proposed correlation varies depending on the state point from a low of 1% at very low pressures below 0.1 MPa between 300 K and 700 K, to 5% at the higher pressures of the range of validity.

An intelligent modeling approach for prediction of thermal conductivity of CO2

In the design of a carbon dioxide capture and storage (CCS) process, the thermal conductivity of carbon dioxide is of special concern. Hence, it is quite important to search for a quick and accurate determination of thermal conductivity of CO2 for precise modeling and evaluation of such a process. To achieve this aim, a robust computing methodology, entitled least square support vector machine (LSSVM) modeling, which is coupled with an optimization approach, was used to model this transport property. The model was constructed and evaluated employing a comprehensive data bank (more than 550 data series) covering wide ranges of pressures and temperatures. Before constructing the model, outlier detection was performed on the whole data bank to diagnose and delete erroneous measurements and doubtful data from the experimental dataset. It was found that the proposed LSSVM model had a very accurate prediction of thermal conductivity of CO2 with an average absolute relative error of 0.79% and a coefficient of determination of 0.999. In addition, more than 90% of the experimental data points were estimated with an absolute relative error smaller than 2% by the developed model.

Thermal conductivity of carbon dioxide from non-equilibrium molecular dynamics: a systematic study of several common force fields.

We report a systematic investigation of the thermal conductivity of various three-site models of carbon dioxide (CO2) using nonequilibrium molecular dynamics in the temperature range 300-1000 K and for pressures up to 200 MPa. A direct comparison with experimental data is made. Three popular CO2 force fields (MSM, EPM2, and TraPPE) and two flexible models (based on EPM2) were investigated. All rigid force fields accurately predict the equation of state for carbon dioxide for the given range of variables. They can also reproduce the thermal conductivity of CO2 at room temperature and predict a decrease of the thermal conductivity with increasing temperature. At high temperatures, the rigid models underestimate the thermal conductivity.

The effect of gas environment on electrical heating in suspended carbon nanotubes

We report micro-Raman spectroscopy measurements of the temperature distribution of current-carrying, 5 μm long, suspended carbon nanotubes in different gas environments near atmospheric pressure. At the same heating power, the measured G band phonon temperature of the nanotube is found to be significantly lower in gaseous environments than in vacuum. Theoretical analysis of these results suggests that about 50%–60% of the heat dissipated in the suspended nanotube is removed by its surrounding gas molecules, and that the thermal boundary conductance is higher in carbon dioxide than in nitrogen, argon, and helium, despite the lower thermal conductivity of carbon dioxide.

Predictive tool for an accurate estimation of carbon dioxide transport properties

In the present work, simple-to-use predictive tool, which is simpler than current available models and involves a fewer number of parameters, requiring less complicated and shorter computations, is formulated to arrive at an appropriate estimation of the transport properties (namely viscosity and thermal conductivity) of carbon dioxide (CO 2) as a function of pressure and temperature. The correlation developed accurately works for temperatures between 260 and 450 K as well as pressures between 10 and 70 MPa which is the range of pressure that is widely considered in CO 2 sequestration. Results have been compared with the reported data and excellent agreement has been obtained between the predicted results and observed values. The average absolute deviations were found to be 1.1 and 1.3% for viscosity and thermal conductivity of carbon dioxide respectively. Proposed simple predictive tool and can be of immense practical value for the engineers to have a quick check on the transport properties (namely viscosity and thermal conductivity) of carbon dioxide at various temperatures and pressures without performing any experimental measurements. In particular, personnel dealing with regulatory bodies of greenhouse gas control and process industries would find the proposed approach to be user friendly involving transparent calculations with no complex expressions.

Contributions of the Van der Waals Laboratory to the Knowledge of Transport Properties of Fluids

After the presentation of Enskog's theory of the transport phenomena at high densities in 1922, one of the aims of the Van der Waals Laboratory was to check this theory with accurate experimental results. As early as 1931, Michels and Gibson published data on the viscosity of nitrogen taken by means of the Van der Waals vertical-capillary viscometer. In 1952, Michels and Botzen presented thermal-conductivity measurements on nitrogen taken by means of the parallel-plate heat-conductivity apparatus. Finally, in 1968 Trappeniers and Oosting presented data on the self-diffusion coefficient of methane obtained with a nuclear magnetic resonance spin-echo spectrometer. In all of these cases agreement with either the Enskog theory or the modified Enskog theory was not obtained. In 1973 Trappeniers and J. Michels showed that the self-diffusion coefficient of krypton obtained with a tracer method deviates from Enskog theory due to the formation of clusters. Measurements of the thermal conductivity of argon in 1955 motivated a study of transport phenomena of fluids in the critical region. This resulted, in 1962, in the first proof of the existence of a rather strong divergence in the thermal conductivity of carbon dioxide, by Michels, Sengers, and Van der Gulik. In 1978 Offringa showed that the viscosity has only a small critical anomaly, while Oosting showed as early as 1968 that, for selfdiffusion, such an anomaly could not be detected. In 1991 Mostert, and in 1996 Sakonidou, showed that the anomaly in the thermal conductivity is finite in mixtures near the vapor–liquid critical line. In the 1970s a vibrating-wire viscometer suited for measuring the viscosity near the melting line of simple gases was developed to check predictions by computer simulations of the viscosity of hard spheres. From the comparisons, it could be concluded that in the density range from the critical density up to twice this density, a special version of the hard-sphere Enskog theory describes the measurements within the experimental accuracy. With this result it was possible to describe the viscosity in the low-density range, up to the critical density, by a model of a gradual transition from intercluster transport described by the Chapman–Enskog theory to intracluster transport described by the hard-sphere Enskog theory, a model inspired by J. Michels' conclusion that the formation of clusters influences the transport properties.

Vapor-phase thermal conductivity of 1,1,1,2,2-pentafluoropropane, 1,1,1,3,3-pentafluoropropane, 1,1,2,2,3-pentafluoropropane and carbon dioxide

The insulation efficiency of polyurethane foam is mainly (60 to 65%) determined by the thermal conductivity of the cell gas, which is a mixture of carbon dioxide (CO 2) and a blowing agent. Until recently CFC-11 (trichlorofluoromethane) was the most widely used blowing agent. To find adequate substitutes for CFC-11, the vapor-phase thermal conductivity of several potential blowing agents has been measured. The experimental procedure is based on the transient hot-wire method. The apparatus was designed in cooperation with the University of Stuttgart (Prof. K. Stephan). The measuring cell (stainless steel, 1.4571) with a length of 270 mm and a diameter of 48 mm consists of two parallel chambers with platinum wires of different lengths. In this paper experimental results for the vapor-phase thermal conductivity of carbon dioxide (CO 2), 1,1,1,2,2-pentafluoropropane (HFC-245cb), 1,1,1,3,3-pentafluoropropane (HFC-245fa), and 1,1,2,2,3-pentafluoropropane (HFC-245ca) are given. Experiments have been performed at pressures between 0.2 MPa and 1.5 MPa and temperatures between 298 K and 419.91 K.

Ab initio Calculation of Transport Properties of Supercritical Carbon Dioxide

Self diffusion, shear viscosity and thermal conductivity of carbon dioxide are determined fully ab initio using two different intermolecular potential energy surfaces. These properties are calculated using the time-correlation formalism in classical equilibrium molecular dynamics simulations. The self diffusion constant is in addition determined from the Einstein relation. For the shear viscosity we use two different models of momentum localization: at the center of mass of the molecules, or at each atom. For the thermal conductivity we apply the formulae for rigid and flexible molecules assuming energy localization at the center of mass of the molecules. The results obtained are in good agreement with experiment. A fully ab initio calculation of transport properties allows for a prediction of these quantities even at state points where experiments are hardly possible.

Nonequilibrium molecular dynamics study of molecular contributions to the thermal conductivity of carbon dioxide

We calculate the thermal conductivity of supercritical and liquid carbon dioxide using a recently developed nonequilibrium molecular dynamics (NEMD) algorithm for molecular fluids. We evaluate the translational, rotational, potential energy and force contributions to the heat flux separately. We find that at high density both the rotational contribution for a nonspherical molecule and the contribution from the total force acting on the molecule are important for predicting the thermal conductivity accurately. The NEMD results for the thermal conductivity agree well with experimental data. At a near critical state point, we observed a phase separation induced by the fictitious external field. The contribution to the thermal conductivity from the Lennard-Jones potential energy becomes important at this state point.

The Transport Properties of Carbon Dioxide

The paper contains new, representative equations for the viscosity and thermal conductivity of carbon dioxide. The equations are based in part upon a body of experimental data that have been critically assessed for internal consistency and for agreement with theory whenever possible. In the case of the low-density thermal conductivity at high temperatures, all available data are shown to be inconsistent with theoretical expectation and have therefore been abandoned in favor of a theoretical prediction. Similarly, the liquid-phase thermal conductivity has been predicted owing to the small extent and poor quality of the experimental information. In the same phase the inconsistencies between the various literature reports of viscosity measurements cannot be resolved and new measurements are necessary. In the critical region the experimentally observed enhancements of both transport properties are well represented by theoretically based equations containing just one adjustable parameter. The complete correlations cover the temperature range 200 K≤T<1500 K for viscosity and 200 K≤T≤1000 K for thermal conductivity, and pressures up to 100 MPa. The uncertainties associated with the correlation vary according to the thermodynamic state from ±0.3% for the viscosity of the dilute gas near room temperature to ±5% for the thermal conductivity in the liquid phase. Tables of the viscosity and thermal conductivity generated by the representative equations are provided to assist with the confirmation of computer implementations of the calculation procedure.

Thermal conductivity of argon, nitrogen and carbon dioxide at elevated temperatures and pressures

The transient hot-wire technique has been used to measure the thermal conductivity of argon at 427 and 470 K, nitrogen at 430 K and carbon dioxide at 380, 430 and 470 K at various pressures, the maximum being 30 MPa. The argon results served to test the apparatus, which has been adapted to operate at these higher temperatures. The low-density limits for the argon thermal conductivities were found to be consistent with published viscosity values. The density dependence of the thermal conductivity of argon was found at both temperatures to be equal, within experimental uncertainties, to that observed at lower temperatures. The results for nitrogen were compared with earlier results and the low-density limit gave an Eucken factor consistent with previous trends. The results for carbon dioxide are compared with previous measurements made at low densities by other techniques and with a theoretically predicted surface for the thermal conductivity of carbon dioxide in the region of the critical point.