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Thermodynamics, Transport, and Fluid MechanicsOctober 15, 2024

Linking Thermal Conductivity to Equations of State Using the Residual Entropy Scaling Theory
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Zhuo Li
Zhuo Li
Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Beijing Key Laboratory for CO2 Utilization and Reduction Technology, Tsinghua University, Beijing 100084,People’s Republic of China
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Yuanyuan Duan*
Yuanyuan Duan
Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Beijing Key Laboratory for CO2 Utilization and Reduction Technology, Tsinghua University, Beijing 100084,People’s Republic of China
Southwest United Graduate School, Kunming 650092, People’s Republic of China
*Email: [email protected]
More by Yuanyuan Duan
https://orcid.org/0000-0002-4117-7545
Xiaoxian Yang*
Xiaoxian Yang
Applied Thermodynamics, Chemnitz University of Technology, Chemnitz 09107, Germany
*Email: [email protected]
More by Xiaoxian Yang
https://orcid.org/0000-0003-4655-3156

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Industrial & Engineering Chemistry Research

Cite this: Ind. Eng. Chem. Res. 2024, 63, 42, 18160–18175

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https://doi.org/10.1021/acs.iecr.4c02946

Published October 15, 2024

CC-BY 4.0 .

Abstract

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In recent years, the application of the residual entropy scaling (RES) method for modeling transport properties has become increasingly prominent. Based on Yang et al. (Ind. Eng. Chem. Res. 2021, 60, 13052) in modeling the thermal conductivity of refrigerants, we present here an RES model that extends Yang et al.’s approach to a wider range of pure fluids and their mixtures. All fluids available in the REFPROP 10.0 software, i.e., those with reference equations of state (EoS), were studied. A total of 71,554 experimental data of 125 pure fluids and 16,702 experimental data of 164 mixtures were collected from approximately 647 references, mainly based on the NIST ThermoData Engine (TDE) database 10.1. As a result, over 68.2% (corresponding to the standard deviation of a normal distribution) of the well-screened experimental data agree with the developed RES model within 3.1% and 4.6% for pure fluids and mixtures, respectively. Comparative analysis against the various models implemented in the REFPROP 10.0 (one of the state-of-the-art software packages for thermophysical property calculations) reveals that our RES model demonstrates analogous statistical agreement with experimental data yet with much fewer parameters. Regarding the average absolute value of the relative deviation (AARD) from experimental values to model predictions, the developed RES model shows a smaller or equal AARD for 74 pure fluids out of 125 and 76 mixtures out of 164. Besides, a detailed examination of the impact of the critical enhancement term on mixture calculations was conducted. To use our model easily, a software package written in Python is provided in the Supporting Information.

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You are free to share(copy and redistribute) this article in any medium or format and to adapt(remix, transform, and build upon) the material for any purpose, even commercially within the parameters below:
- Creative Commons (CC): This is a Creative Commons license.
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Subjects

1. Introduction

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Thermal conductivity, an essential transport property, represents the spontaneous energy transfer process resulting from temperature differences. Experimental and modeling studies on the thermal conductivity of fluids are of great scientific importance. In contrast to extensively studied thermophysical properties such as density, experimental data on the thermal conductivity of fluids are relatively sparse and limited to certain temperature and pressure ranges. (1−3) This limitation poses a challenge to constructing empirical multiparameter models, which rely heavily on extensive experimental data, especially as the scope of investigation expands to include a growing number of pure fluids and fluid mixtures. Consequently, the pursuit of semiempirical models, which require fewer parameters and less experimental data for parameter-fitting, is becoming an important focus in thermal conductivity modeling.

Current semiempirical thermal conductivity models include those depending on the free volume theory, (4) the hard-sphere theory, (5) the friction theory, (6,7) the extended corresponding states (ECS), (8,9) and the residual entropy scaling (RES). (10) Among these models, the RES one is attracting more and more attention. According to the isomorph theory, (11,12) the dimensionless transport properties of fluids, especially viscosity and thermal conductivity, can be expressed as a univariate function of residual entropy within a group of similar fluids. As a result, the RES model requires a significantly smaller number of experimental data points for parameter fitting than most other models. Furthermore, owing to the analogous nature of the relation between dimensionless transport properties and dimensionless residual entropy of different fluids, ideally, no additional fitting parameters are required to predict mixtures. Researchers such as Bell et al., (13−16) Yang et al., (17−22) Liu et al., (23−26) Kang et al., (27−29) Hopp et al., (30−32) and Lötgering-Lin et al. (33−35) have effectively utilized this approach to model both the viscosity and thermal conductivity of pure fluids, yielding promising results.

In this paper, we focus on developing RES methods for thermal conductivity. In recent years, numerous researchers have made significant progress. Hopp and Gross (30) developed a RES model for the thermal conductivity of water and 147 organic substances by using the equation of state (EOS) of the perturbed-chain polar statistical associating fluid theory (PCP-SAFT) (36,37) to determine the residual entropy. The RES model showed an average relative deviation of 4.2% from the experimental data. They also investigated a universal modeling approach integrating RES with the group contribution method. (31) Dehlouz et al. (38) introduced a new dimensionless mathematical form for the relation of thermal conductivity and residual entropy similar to that initially proposed by Rosenfeld. (39) They used tc-PR EOS (40) and I-PC-SAFT EOS (41) to calculate the residual entropy and developed a RES model for 119 pure fluids with an average deviation of about 3.4%. Liu et al. (26) created a RES model with critical enhancement correction for CO₂ using the crossover multiparameter EOS. (42) Regarding mixtures, the research focus was primarily on refrigerants and their mixtures. Fouad (43) and Kang et al. (28) used the PC-SAFT EOS, (44) while Liu et al. (24) used the cubic-plus-association (CPA) EOS (45) to calculate the residual entropy. In addition, Rokni et al. (46,47) developed RES models based on Hopp and Gross’s research (30) for typical fluids in combustion processes, including hydrocarbon mixtures, to predict the thermal conductivity of fluids under extreme conditions. The studies above on mixtures are all tailored to a single class of fluids; therefore, one of the main objectives of this study is to extend the model to cover a broader range of fluids.

The RES model developed by Yang et al. (48,49) is an essential foundation of this work. Yang et al. (48) utilized REFPROP 10.0 (50) for the residual entropy calculation, formulating an RES model for the thermal conductivity of refrigerants and their mixtures and integrating the critical enhancement crossover model developed by Olchowy and Sengers. (51) Satisfactory agreements with experimental data were achieved for the mixtures without any additional adjustable binary interaction parameters (BIP). Later, for viscosity, Yang et al. (49) classified different fluids into different groups and developed a RES model for 124 fluids ranging from light gases (e.g., helium) to dense fluids (e.g., hexadecane). This work aims to use the same fluid classification method of viscosity (49) to extend the thermal conductivity model developed by Yang et al. (48) from 39 refrigerants to 125 pure fluids. This study will also employ reference EOS to calculate residual entropy, fully capitalizing on the benefits of REFPROP 10.0 in thermodynamic property computations. All fluids implemented in the REFPROP 10.0, namely those with reference EOS, were studied. A total of 71,554 experimental data points for 125 pure fluids and 16,702 experimental data points for 164 mixtures were compiled from approximately 647 references, mainly based on the NIST ThermoData Engine (TDE) database 10.1. (52) Given the significantly expanded range of fluid types considered, the analysis focused mainly on the results of mixtures from a fluid-group perspective. Furthermore, a detailed examination of the impact of the critical enhancement term on the mixtures was conducted.

2. Theory

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Fluid thermal conductivity λ is calculated with the sum of the dilute gas term λ_ρ→0(T), the residual term λ_res(s^r), and the critical enhancement term Δλ_C(T,ρ), expressed as follows:

λ = λ_{ρ \to 0} (T) + λ_{res} (s^{r}) + Δ λ_{c} (T, ρ)

(1)

The dilute gas thermal conductivity λ_ρ→0(T) is a function of temperature T. For pure fluids, a polynomial expression is employed:

λ_{ρ \to 0} / (W \cdot m^{- 1} \cdot K^{- 1}) = \sum_{i = 0}^{4} a_{i} (T / K)^{i}

(2)

The parameters a_i were determined by fitting them to calculations from REFPROP 10.0 (50) for each pure fluid. These values are listed in Table S1 in the Supporting Information (SI) and have been implemented in the OilMixProp 1.0 software package. (53) We could potentially use REFPROP 10.0 to calculate λ_ρ→0. However, REFPROP 10.0 uses a variety of different methods to calculate λ_ρ→0, which are hard to replicate in our coding. Besides, REFPROP 10.0 fails to calculate dilute gas thermal conductivity of many mixtures especially those involving alcohols. Therefore, the proposed eq 2 could be used in combination with a proper mixing rule for calculating the thermal conductivity of the dilute gas thermal conductivity (see the following).

As described by Bell (13) and Yang et al., (48) the residual term of thermal conductivity λ_res(s^r) can be determined using the formula:

λ_{res} (s^{r}) = \frac{λ_{res}^{+} k_{B} ρ_{N}^{2 / 3} \sqrt{k_{B} T / m}}{(s^{+})^{2 / 3}}

(3)

where

s^{+} = - s^{r} / R

(4)

Here, ρ_N in units of m^–3 represents the number density, m in units of kg is the mass of one molecule, s^r in units of J·mol^–1·K^–1 denotes the molar residual entropy, which is the difference between the actual fluid entropy and the ideal gas entropy at the same temperature and density, and R = 8.31446261815324 J·mol^–1·K^–1 is the molar gas constant. In this study, the number density ρ_N and molar residual entropy s^r were computed using the reference EOS implemented in REFPROP 10.0, with the interface of Python CoolProp package version 6.4.1. (54) The reference EOS and thermal conductivity models used in REFPROP 10.0 are listed in Table S2 of the SI. The plus-scaled dimensionless residual thermal conductivity is related to the plus-scaled dimensionless residual entropy s⁺ using the following polynomial equations

λ_{res}^{+} = n_{1} \cdot (s^{+}) + n_{2} \cdot (s^{+})^{1.5} + n_{3} \cdot (s^{+})^{2} + n_{4} \cdot (S^{+})^{2.5}

(5)

λ_{res}^{+} = n_{g 1} \cdot (s^{+} / ξ) + n_{g 2} \cdot (s^{+} / ξ)^{1.5} + n_{g 3} \cdot (s^{+} / ξ)^{2} + n_{g 4} \cdot (S^{+} / ξ)^{2.5}

(6)

Equation 5 is tailored for a pure fluid with fluid-specific fitted parameter n_k (k = 1, 2, 3, 4), while eq 6 is designed for a group of pure fluids with group-specific fitted parameters n_gk (k = 1, 2, 3, 4) and a fluid-specific scaling factor ξ for each individual fluid.

The critical enhancement of thermal conductivity is determined using a crossover model introduced by Olchowy and Sengers (51) as

Δ λ_{c} (T, ρ) = \frac{ρ c_{p} R_{D} K_{B} T}{6 π η φ} (\bar{Ω} - \bar{Ω})

(7)

\bar{Ω} = \frac{2}{π} [\frac{(c_{p} - c_{V})}{c_{p}} \arctan (q_{D} φ) + \frac{c_{V}}{c_{p}} q_{D} φ]

(8)

\bar{Ω} = \frac{2}{π} [1 - \exp (- \frac{1}{(q_{D} φ)^{- 1} + (q_{D} φ ρ_{crit} / ρ)^{2} / 3})]

(9)

φ = φ_{0} {(\frac{p_{crit} ρ}{Γ ρ_{crit}^{2}})}^{ν / γ} {[\frac{\partial ρ (T, p)}{\partial p} |_{T} - (\frac{T_{ref}}{T}) \frac{\partial ρ (T_{ref}, p)}{\partial p} |_{T}]}^{ν / γ}

(10)

Here, η represents the viscosity, c_p and c_V denote the isobaric and isochoric specific heat capacities, respectively, and ρ_crit and p_crit stand for the molar density and pressure at the critical point, respectively. These parameters are calculated using the default models in REFPROP 10.0. The values of R_D = 1.02, ν = 0.63, and γ = 1.239 are universal constants, while Γ, φ₀, T_ref, and q_D are fluid-specific parameters acquired from REFPROP 10.0 and detailed in Table S3 in the SI.

A predictive mixing rule is adopted to extend the RES model to mixtures. Similar to the previous work, (48) the dilute gas thermal conductivity for mixtures λ_ρ→0,mix is calculated with REFPROP 10.0 via the Python package CoolProp 6.4.1. (54,55) However, REFPROP 10.0 cannot calculate the dilute gas thermal conductivity λ_ρ→0,mix of some mixture especially those involving alcohols and water. For these mixtures, a mixing rule similar to the Wilke approximation (56) was adopted:

λ_{ρ \to 0, mix} = \sum_{i} \frac{x_{i} λ_{ρ \to 0, i}}{\sum_{j} x_{j} φ_{i j}}

(11)

with

φ_{i j} = \frac{(1 - k_{i j, λ}) (1 + (λ_{ρ \to 0, i} / λ_{ρ \to 0, j})^{1 / 2} (m_{j} / m_{i})^{1 / 4})^{2}}{(8 (1 + m_{i} / m_{j}))^{1 / 2}}

(12)

where x_i is the mole fraction of component i and m_i is the mass of one molecule of component i. The binary interaction coefficients for dilute gases k_ij,λ are all set to 0, which could be fitted if sufficient accurate dilute gas data for a mixture are available. Different from our previous work, (48) a new mass fraction weighted mixing rule was used to as the effective mass of one particle of the mixture (to replace m in eq 3 for mixture calculation):

m_{mix} = {(\sum_{i} y_{i} \sqrt{m_{i}})}^{2} = \sum_{i j} y_{i} y_{j} \sqrt{m_{i} m_{j}}

(13)

where y_i is the mass fraction of component i. This will be discussed in more detail in Section 3.2. Subsequently, in contrast to our previous work, (48) the mole fraction weighted average coefficient n_k,mix is employed to substitute the parameters n_k in eq 6, i.e.,

n_{k, mix} = \sum_{i} x_{i} n_{k, i} (k = 1, 2, 3, 4)

(14)

where n_k,i (k = 1,2,3,4) are fluid-specific fitted parameters n_k of component i. It is essential to mention that n_k (k = 1, 2, 3, 4) parameters of a pure fluid are replaced by n_g1/ξ, n_g2/ξ^1.5, n_g3/ξ², and n_g4/ξ^2.5, respectively, only if the pure fluid does not have fluid-specific fitted parameters.

For the critical enhancement term of the thermal conductivity of fluid mixtures, we implemented the identical mixing rule as the ECS model devised by Chichester and Huber, (57) wherein, for mixtures, the parameter Γ, φ₀, T_ref, and q_D in eqs 7–10 are replaced with the mole-fraction-weighted average of each individual component

Z_{mix} = \sum_{i} x_{i} Z_{i}

(15)

where x_i is the mole fraction of component i and Z is one of the parameters Γ, φ₀, T_ref, and q_D. The critical parameters (T_crit, ρ_crit, and p_crit) of the mixtures were also acquired from REFPROP 10.0 as well.

3. Results

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3.1. Data Collection and Selection

A total of 71,554 experimental thermal conductivity values (λ, T, p) for 125 pure fluids and 16,702 values (λ, T, p, x) for 164 mixtures (including binary and multicomponent) from approximately 647 references were collected. Detailed citation information is provided in the Supporting Information─Detailed Plots and References (SI-DPR). The literature is primarily sourced from the NIST TDE 10.1, (52) supplemented by recently published experimental data we gathered. All data were carefully examined to address issues such as units, magnitudes, or transcription errors. Subsequently, the same methods (see footnote in Table 1) as used in our previous work (48,49) were adopted to filter out approximately 3.9% pure fluid data and 5.7% of mixture data. Table 1 presents the number of experimental data collected, the number of sources, and the number and proportion of data filtered out by each filter. Figure 1 shows experimental data of two example fluids (ammonia (58−64) and R22 (65−81)) processed with these three filters. Data filtered by filter 1 are all concentrated at zero because their s⁺ and λ_res⁺ cannot be correctly calculated. To a certain extent, these filters also serve for data evaluation, e.g., data filtered out by filter 3 are usually of low quality as they are obviously not consistent with other data. For detailed information on Table 1 for each fluid, please refer to Tables S4 and S5 in the Supporting Information (SI). The experimental data’s temperature, pressure, and composition ranges are also summarized in these two tables.

Table 1. Statistical Experimental Data Summary of Pure Fluids and Their Mixtures^a

		S_D	N_tot	N_use	N_lim	N_phase	N_dev	N_REFPROP,fail
pure fluids	total	567	71554	68765	1544	468	777	72
pure fluids	N/N_tot			96.10%	2.16%	0.65%	1.09%	0.10%
mixtures	total	124	16702	15758	685	156	103	1976
mixtures	N/N_tot			94.35%	4.10%	0.93%	0.62%	11.83%

^{^a}

S_D: number of data sources; N_tot: total number of experimental data; N_use: number of adopted data for parameter-fitting and comparison analysis; N_lim: number of data filtered by Filter 1, which removed those exceeding limits of the reference EoS in REFPROP 10.0; N_phase: number of data filtered by Filter 2, which removed those reported in conflicting phases; N_dev: number of data filtered by Filter 3, which removed those deviating from the RES model by more than 30%. N_REFPROP,fail: number of data whose thermal conductivity cannot be calculated with the recommended models in REFPROP 10.0 using the given temperature and pressure while these data will still be used for the evaluation of the RES model. Please note: some literature have both data of pure fluid and mixtures; therefore, the total number of literature source was 647.

Figure 1. Characteristic λ_res⁺ vs s⁺ curves of (a) ammonia (58−63) and (b) R22. (64−80) The definitions of Filter 1, 2, and 3 can be found in the footnote of Table 1.

All experimental data, except those removed by Filter 1, are displayed in characteristic λ_res⁺ vs s⁺ curves as provided in the SI-DPR. For each pure fluid, the experimental (s⁺, λ_res⁺) points collapse into a characteristic single line with some noise due to the poor quality of some data. A few fluids (such as He and CO) only have experimental data with s⁺ values close to zero, so the range of residual entropy corresponding to characteristic lines is limited.

3.2. Correlation for Pure Fluids

In this section, the RES model for 125 pure fluids, whose reference EoS and experimental thermal conductivity data are both available, was established. These pure fluids were divided into 8 groups, similar to our previous work. (49) The number and detailed description of each group are presented in Table 2. The classification of groups meets the following objectives: with as few groups as possible, the group-specific parameter n_gk fitted to each group and the fluid-specific scaling factor ξ can produce the best statistical consistency. For pure fluids with sufficient quantity and good quality experimental data, the fluid-specific parameter n_k could also be fitted. The results are listed in Tables 3 and 4. In Table 3, for the additional 26 (= 151–125) pure fluids implemented in REFPROP 10.0 (151 pure fluids in total) without available data, the group number was determined by the following steps. (1) Carrying out calculations using REFPROP 10.0 in both liquid and gas phases and using these data as reference data; (2) fitting ξ using each group’s group-specific fitted parameters with these reference data; (3) assigning the group number of this fluid where its ξ is most close to 1.

Table 2. Fluid Groups and Their Brief Descriptions

group number	group abbreviation	detailed description
1	LG	light gases with quantum effects at low temperatures, mainly hydrogen and its spin isomers and helium
2	G	gaseous fluids, e.g., the noble gases
3	LHC	a majority of light hydrocarbons and halogenated hydrocarbons (refrigerants)
4	B	fluids with benzene rings and similar fluids
5	MHC	medium hydrocarbons and similar fluids
6	HHC	heavy hydrocarbons and dense fluids
7	LA	fluids with light intermolecular association among molecules like methanol
8	SA	fluids with strong intermolecular association among molecules, such as water

Table 3. Fluid Information and the Fluid-Specific Fitted Parameters

REFPROP fluid name	group number	ξ	Z^a	n₁	n₂	n₃	n₄
13BUTADIENE	2	0.971	1	0.000000	5.379592	–3.515631	1.143689
1BUTENE	5	0.8916	1	0.000000	4.218309	–2.607745	0.973758
1BUTYNE	4	1	0
1PENTENE	4	0.9643	0
22DIMETHYLBUTANE	3	0.9836	1	0.000000	2.787455	–0.347996	0.254597
23DIMETHYLBUTANE	3	0.9782	1	0.000000	3.418932	–0.754166	0.319323
3METHYLPENTANE	5	0.9109	1	0.000000	5.003443	–2.239168	0.664843
ACETONE	4	1.059	0
ACETYLENE	3	1.1945	1	0.000000	1.750292	–0.098956	0.143796
AMMONIA	7	0.9804	1	0.357901	2.508824	0.437440	–0.007305
ARGON	2	0.9929	1	2.212697	–4.335464	4.685634	–0.731662
BENZENE	4	0.9864	1	6.114857	–11.805067	9.165699	–1.624275
BUTANE	3	0.9873	1	9.914508	–15.844874	9.840589	–1.467766
C11	5	0.7956	1	5.167730	–5.907157	4.958787	–0.634295
C12	5	0.8045	0
C16	5	0.7121	1	12.868089	–9.340009	5.387528	–0.571729
C1CC6	3	1.0211	1	12.813721	–19.138957	10.658325	–1.477798
C22	6	0.741	1	0.000000	10.736853	–2.041242	0.296740
C2BUTENE	5	0.9302	1	0.888244	3.084085	–2.425022	0.976326
C3CC6	4	0.9774	1	13.331441	–19.894384	11.138446	–1.554099
C4F10	3	1	0
C5F12	5	0.8689	0
C6F14	5	0.8686	0
CF3I	3	1	0
CHLORINE	3	0.9156	1	0.000000	–1.813594	4.704503	–1.005004
CHLOROBENZENE	4	1.0177	1	0.000000	0.813486	1.321055	–0.125706
CO	2	1	0
CO2	3	1.002	1	1.706852	–2.225083	2.920715	–0.376879
COS	3	1	0
CYCLOBUTENE	3	1	0
CYCLOHEX	3	1.008	1	0.000000	2.971082	–0.481603	0.256643
CYCLOPEN	3	0.9864	0
CYCLOPRO	3	1.235	1	4.574498	–12.114472	10.732103	–2.418843
D2	1	0.9476	0
D2O	8	1.1823	1	5.261652	–6.384364	5.908181	–1.256585
D4	6	0.8105	1	0.000000	–4.121521	6.562392	–0.964812
D5	6	0.7271	1	0.000000	–5.170102	7.532869	–1.060288
D6	5	1	0
DEA	7	0.9878	0
DECANE	5	0.8113	1	4.264299	–3.187923	3.467454	–0.428095
DEE	3	0.9879	1	5.071657	–14.357684	11.583587	–2.101609
DMC	3	0.9874	1	0.000000	–1.097291	2.780174	–0.374842
DME	3	1.0457	1	0.759606	–0.891232	2.426799	–0.393419
EBENZENE	4	0.996	1	5.914624	–8.923543	6.023321	–0.807386
EGLYCOL	7	1.2492	1	0.000000	–0.071257	2.106998	–0.414900
ETHANE	3	1.0094	1	2.264652	–2.973246	2.834533	–0.168146
ETHANOL	7	1.6238	1	0.256349	7.523893	–4.554179	0.861844
ETHYLENE	3	0.982	1	0.889433	–0.284962	2.094853	–0.445207
ETHYLENEOXIDE	3	1.2018	1	0.000000	0.098128	1.778352	–0.332378
FLUORINE	2	0.9429	1	0.000000	–0.114084	2.560271	–0.433969
H2S	7	1.445	1	0.432501	2.740587	–1.819681	0.938402
HCL	7	0.8174	0
HELIUM	1	1.2966	0
HEPTANE	5	0.8636	1	1.639500	–4.109500	4.754431	–0.712181
HEXANE	5	0.8867	1	12.117771	–17.462543	10.233398	–1.465975
HYDROGEN	1	1.0925	1	2.263272	–7.356751	10.699531	–3.575533
IBUTENE	3	1.0042	1	4.864538	–6.452786	4.039782	–0.328573
IHEXANE	5	0.8797	1	0.000000	0.813682	1.580508	–0.152544
IOCTANE	5	0.8769	1	8.197005	–15.049807	9.373205	–1.270155
IPENTANE	3	0.9565	0
ISOBUTAN	3	1.0344	1	7.423475	–12.623751	8.360390	–1.271135
KRYPTON	2	0.9803	1	4.126446	–6.776568	5.542582	–0.773972
MD2M	6	1	0
MD3M	6	1	0
MD4M	6	1	0
MDM	6	0.8909	1	8.916267	2.640074	–2.421293	0.851311
MEA	7	1.2444	0
METHANE	2	0.9897	1	2.149868	–3.171791	3.076996	–0.191412
METHANOL	7	1.6895	1	3.286199	3.920777	–3.533019	0.823359
MILPRF23699	6	1	0
MLINOLEA	6	0.8121	1	0.000000	5.038723	1.660785	–0.324476
MLINOLEN	6	1	0
MM	6	0.9762	1	0.000000	–2.998729	4.897334	–0.700838
MOLEATE	6	0.7932	1	0.000000	7.481170	0.592821	–0.199701
MPALMITA	6	1	0
MSTEARAT	6	0.7428	0
MXYLENE	4	0.9819	0
N2O	2	1.0618	1	2.513468	–5.101075	5.298646	–1.002263
NEON	2	1	0
NEOPENTN	3	1	0
NF3	3	1	0
NITROGEN	2	0.9628	1	2.343833	–4.109131	4.450635	–0.669527
NONANE	5	0.8295	1	1.426501	–10.319122	8.964770	–1.374319
NOVEC649	4	1	0
OCTANE	5	0.853	1	0.000000	3.192025	0.047318	0.121680
ORTHOHYD	1	1	0
OXYGEN	2	0.9973	1	3.578576	–7.686498	7.651484	–1.602941
OXYLENE	4	1.0148	1	13.315169	–19.183399	10.385784	–1.404669
PARAHYD	1	1	0
PENTANE	3	0.9701	1	17.306659	–19.435781	9.257508	–1.127877
POE5	6	1	0
POE7	6	1	0
POE9	6	1	0
PROPADIENE	3	1	0
PROPANE	3	0.9964	1	8.726474	–13.787569	8.781108	–1.303329
PROPYLEN	4	0.9227	1	2.978741	–3.719802	3.952515	–0.647533
PROPYLENEOXIDE	3	1.0695	0
PROPYNE	3	1.0758	0
PXYLENE	4	0.9924	1	10.975030	–14.386000	7.788535	–0.960621
R11	3	0.9455	1	2.448812	–3.077300	3.779976	–0.574054
R1123	3	1	0
R113	3	0.976	1	0.408042	–1.181694	3.113587	–0.513467
R114	3	0.9883	0
R115	3	0.9707	1	0.832945	–0.549647	1.989828	–0.178955
R116	3	0.8263	0
R12	3	0.9634	1	3.952520	–5.736267	5.068745	–0.778955
R1216	3	1	0
R1224YDZ	3	1.0468	1	0.000000	5.697113	–3.681056	1.095443
R123	3	1.0185	1	11.296696	–16.704536	9.929254	–1.487969
R1233ZDE	3	1.015	1	1.381582	–2.889227	3.573098	–0.518453
R1234YF	3	1.0446	1	0.000000	0.561791	1.133353	–0.022522
R1234ZEE	3	1.0445	1	0.000000	–0.195660	1.970080	–0.248027
R1234ZEZ	3	1	0
R124	3	1.0364	1	1.936501	–1.918713	2.181608	–0.162050
R1243ZF	3	1	0
R125	3	1.0138	1	2.118214	–2.548352	2.867573	–0.336718
R13	3	0.9743	1	4.401745	–6.523089	5.339968	–0.796013
R1336MZZZ	3	1.0718	1	0.000000	2.110048	–0.096833	0.183517
R134A	3	1.0434	1	1.388264	–0.760952	1.664978	–0.125953
R14	3	0.9856	1	0.000000	1.856857	–0.091191	0.328629
R141B	3	1.0224	1	5.244290	–12.966918	10.001388	–1.724927
R142B	3	1.0185	1	1.585603	–1.288917	1.985725	–0.151916
R143A	3	1.0277	1	0.000000	0.808867	1.155897	–0.078609
R150	3	1.0501	1	0.000000	3.214526	–0.336963	0.125032
R152A	3	1.0498	1	0.986161	–0.163102	1.481922	–0.139125
R161	3	1.0454	1	0.000000	–1.364383	3.073718	–0.504590
R21	3	1.0163	1	0.000000	0.905175	1.252424	–0.118433
R218	3	0.943	1	4.546313	–5.628770	4.395302	–0.546137
R22	3	1.0388	1	4.091164	–5.280935	4.457871	–0.683280
R227EA	3	1.0511	1	4.622243	–14.334938	12.669269	–2.640429
R23	3	1.046	1	4.763672	–5.377349	4.149939	–0.596530
R236EA	3	1	0
R236FA	3	1.022	1	2.665792	–7.207912	6.766258	–1.198062
R245CA	3	0.883	0
R245FA	3	1.0533	1	0.259408	–2.453743	3.588802	–0.553704
R32	3	0.9671	1	0.833010	0.496007	1.424641	–0.174255
R365MFC	3	1.0094	0
R40	3	1	0
R41	3	0.8575	1	0.000000	5.494781	–1.103109	0.051828
RC318	3	0.9223	1	0.000000	6.665295	–3.424906	0.930574
RE143A	3	1	0
RE245CB2	3	1.0231	1	1.713390	–1.188678	1.611470	–0.019372
RE245FA2	3	1.7541	0
RE347MCC	3	0.9543	0
SF6	2	0.854	1	0.000000	5.719873	–2.019152	0.506107
SO2	2	0.8837	1	0.000000	1.707698	1.647666	–0.360041
T2BUTENE	3	1	0
TOLUENE	4	1.0079	1	9.949329	–15.028331	9.102394	–1.327497
VINYLCHLORIDE	3	1	0
WATER	8	1.182	1	0.000000	–0.482377	4.465204	–1.296961
XENON	2	0.9925	1	1.370170	–1.432450	1.997402	0.005468

^{^a}

The quantity and quality of the experimental data are good (Z = 1) or not good (Z = 0) enough to fit fluid-specific n₁, n₂, n₃, and n₄ parameters.

Table 4. Group-Specific Fitted Parameters of Each Group

group number	n_g1	n_g2	n_g3	n_g4
1	2.391631	–8.1473	12.52226	–4.38311
2	2.173335	–4.8767	5.754321	–1.18193
3	3.629822	–5.32944	4.534105	–0.64328
4	10.62084	–16.0687	9.495404	–1.35573
5	0	–0.15825	1.789146	–0.20526
6	0	0.895835	2.305079	–0.32201
7	9.110479	–7.56132	4.512561	–0.63366
8	0	2.124187	3.034116	–1.08806

Note that, for the 39 pure refrigerants studied in our previous work, (48) apart from n-hexane in group 5 and ammonia in group 7, the remaining 37 fluids are all in group 3. Group 3 is the largest group containing 77 pure fluids mainly light hydrocarbons and halogenated hydrocarbons. With the new classification, a few additional experimental data and more comprehensive parameter fitting strategy, this study refitted the parameters of the 39 fluids, achieving a good consistency. Experimental data of each group collapse into the λ_res⁺ vs s⁺/ξ curves are shown in Figure 3.

As shown in Tables 3 and 4, the first group-specific fitted parameter n_g1 is zero for groups 5, 6, and 8, and the first fluid-specific fitted parameter n₁ is also zero for many pure fluids. The first fitted parameters (n₁ and n_g1) being zero indicates the potential of constructing the RES model with simpler equations, i.e., one term less than eqs 5 and 6. One strategy is to optimize the functional form (e.g., exponents of s⁺) of eqs 5 and 6, which are, however, outside the scope of this study and will be explored in the future.

In our previous work, Yang et al. (49) found a relation between the fluid-specific scaling factor ξ_μ of the viscosity’s RES model and the s_crit⁺ (plus-scaled dimensionless residual entropy at the critical point). Subsequently, Jager et al. (81) studied ξ_μ of long-chain alkane and applied the results to a new RES model. (82) Inspired by this work on viscosity’s ξ_μ, the scaling factor of the thermal conductivity was also analyzed in this work. Figure 2 shows how the scaling factor ξ of the thermal conductivity of each pure fluid varies with s_crit⁺. The ξ/s_crit⁺ of each pure fluid is similar in each group, and the value of the fluid ξ/s_crit⁺ of Group 3, which contains the largest number of fluids, is roughly 0.7; this is consistent with the viscosity’s RES model of Yang et al. (49) However, the scaling factor of the thermal conductivity model is more dispersed (for fluids in Group 3: the standard deviation of the viscosity scaling factor is 0.054, while the thermal conductivity scaling factor is 0.100). Experimental data of each group collapse into the individual global λ_res⁺ vs s⁺/ξ curves are shown in Figure 3.

Figure 2. Scaling factor ξ. The denominator s_crit⁺ is the plus-scaled dimensionless residual entropy at the critical point calculated with REFPROP 10.0 (50) of each pure fluid. The number at the top right of each box indicates the group number. The vertical dashed dotted line denotes ξ/s_crit⁺ = 0.7. Values not shown in the figure: C16:0.29, C22:0.26, methyl stearate: 0.26, parahydrogen: 1.63, orthohydrogen: 1.61, hydrogen: 1.76, helium: 4.21, and deuterium (D2): 1.31. The names used in REFPROP 10.0 were adopted.

Figure 3. Values of λ_res⁺ as a function of s⁺/ξ of each group of pure fluids, where λ_res⁺ is the dimensionless residual thermal conductivity, s⁺ is the dimensionless residual entropy, and ξ is the scaling factor. The curves are calculated with the global n_gk parameters. All groups are shown at the bottom; at the top, each group is individually illustrated but stacked by powers of 20 and with group number labeled.

Figure 4 shows the relative deviation of the experimental value λ_exp from the λ_RES calculated with the RES model; see SI-DPR for more detailed plots of each pure fluid. Please note that in calculating λ_RES, the fluid-specific fitted parameter n_k is always preferred, while the global parameter n_gk is used only if n_k is not available in Table 3. The results showed that over 68.2% (corresponding to the standard deviation of a normal distribution) of the experimental data deviated from the RES model by less than 3.1%. To better reproduce some results of this work, a Python package implementing the developed RES method were provided in the SI, and the example calculations of each pure fluid and mixture are available in Table S6 and S7 in the SI. Here, we define the average relative deviation (ARD) of the experimental values λ_exp from model calculations and the average of the absolute value of the relative deviation (AARD) as

ARD = \frac{\sum_{i}^{N} [(λ_{EXP, i} - λ_{RES, i}) / λ_{RES, i}]}{N}

(16)

AARD = \frac{\sum_{i}^{N} [| (λ_{EXP, i} - λ_{RES, i}) / λ_{RES, i} |]}{N}

(17)

where N is the total number of experimental data points of a given fluid, and the ARD and AARD represent the system offset and scatter from the experimental data to the model, respectively. ARD for each pure fluid is shown in Figure 4, and AARD is listed in Table S4 of the SI. Considering the presence of low-quality data and the uncertainties introduced by dilute-gas calculation, only 86 and 105 of the 125 pure fluids have ARD absolute values less than 1.0% and 2.0%, respectively. For fluids with larger ARD, the possible reasons are as follows: very few experimental data are available (RE347mcc: ARD = −5.0%, 4 points; isopentane: ARD = 4.9%, 6 points); the experimental data cover a limited range of temperature and pressure (neon: ARD = 3.5%, experimental data are available only in the gas phase, i.e., near s⁺ = 0); the dilute gas thermal conductivity is inaccurate (acetylene: ARD = −2.9%; R245fa: ARD = −3.5%); the consistency of experimental data was poor (R41: ARD = −7.7%). For the 18 pure fluids of which more than 1000 experimental data points are available, absolute values of ARD are mainly less than 1.5% except propane (ARD = −2.2%) and water (ARD = 1.7%). For the 61 fluids with more than 200 experimental data points, the absolute ARD of RES model compared to experimental data is less than 2.5% except R245FA (ARD = −3.5%) and R123 (ARD = 4.6%).

Figure 4. Relative deviations of the experimental thermal conductivity λ_exp from values λ_RES calculated with the RES model. The short line indicates the average relative deviation; the shape shows the distribution of the relative deviation; and the colors are for a clear illustration only. Fluid-specific n_k parameters are preferred, and only if they are not available in Table 3, global parameters n_gk are used.

At last, the performance of the RES model was compared to the various recommended models implemented in REFPROP 10.0. The REFPROP models cannot calculate very few experimental data (0.10%, see Table 1). According to Table S4, the RES model shows smaller or equal AARD for 74 pure fluids out of 125 compared to REFPROP 10.0.

3.3. Prediction for Mixtures

In this section, the mixing rules described in Section 2 were utilized to calculate thermal conductivity of mixtures, and the results were compared to experimental data. At first, various mixing rules for m_mix of mixtures in eq 3 were investigated. In the previous work, (49)m_mix was determined as the mass fraction weighted average

(m_{mix} = \sum_{i} y_{i} m_{i})

. In this work, a few other mixing rules for m_mix were studied, see Figure 5, and as a result,

m_{mix} = {(\sum_{i} y_{i} \sqrt{m_{i}})}^{2}

yielded the best performance. The slightly better performance of the mass fraction weighted average of

\sqrt{m}

over m is consistent with the factor that

\sqrt{m}

is in eq 3 rather than m.

Figure 5. Influence of different mixing rules of for m_mix on the prediction of thermal conductivity of mixtures, where x_i represents the mole fraction, y_i represents the mass fraction, and m_i is the molecular mass for component i. Deviation represents the maximum deviation corresponding to the standard deviation of a normal distribution (≈68.2%) of the selected experiment data.

With the new mixing rule for m_mix, over 68.2% of the well-evaluated experimental data (see Table 1) exhibit agreement with the RES model within 4.6%. The performance of the RES model varies for mixtures from different groups, see Figure 6. For group LHC + LHC (“group a + b″ denotes binary mixtures with one component from group a and another from b), 7210 filtered experimental data points are available, and the ARD is a mere −0.4%. For group G + LHC, the ARD is only 0.6% and there are 1,575 experimental data points. Of course, there are also bad cases, e.g., for group LHC + MHC, there are 490 data points while the ARD is as high as 11.1%. It should be noted that the relatively large ARD and AARD for group LG + LG (ARD = 6.6%, AARD = 6.8%) may be attributed, in part, to the limited availability of experimental data (only 69 points) and the failure of the RES methods for quantum fluids, as reported by Yang et al. (49) Bell et al. (83) proposed a simple empirical model that introduces a thermal length scale relative to the packing length scale

L

to modify the classical residual entropy, quantifying the impact of quantum effects on the residual entropy scaling. This approach will improve the accuracy of residual entropy scaling models for quantum fluids such as hydrogen. However, in this study, a consistent mathematical expression was pursued for all fluids, and thus this improvement was not adopted.

Figure 6. Statistical summary of the relative deviation of the experimental data from model calculations for binary mixtures. All selected data: all experimental data collected and passed the three filters; Further filtered data: experimental data further filtered so that they can be calculated with the REFPROP models. ARD and AARD: the average relative deviation and the average of the absolute value of relative deviation of the experimental values from the model calculations, respectively. Please note that the blank areas in the figure indicate either the absence of available data or the inability of REFPROP to perform calculations.

The performance of the RES model for the mixture prediction was also compared to the REFPROP models. Each binary mixture has up to four additional binary interaction parameters in the ECS model (the most used model in REFPROP), while the RES model developed in this work does not require any additional adjustable parameters. The REFPROP models failed to calculate approximately 12% of the well-evaluated experimental data (see Table 1), mainly for mixtures of water and alcohol, as detailed in Table S5. After filtering out these data, the statistical results of both the RES and REFPROP models compared to the experimental data are shown in Figure 6. Detailed information is given in the 164 figures of each mixture in the SI-DPR. According to Table S5 in the SI, the RES model yields equal or lower AARD for 76 of all 164 mixtures compared to REFPROP models. Overall, without introducing any adjustable parameters, the developed RES model achieved a similar level of agreement with mixture experimental data as the REFPROP models.

The deviation from experimental data to both the RES and the REFPROP models exhibit certain similarities. For group LHC + MHC, both models have an AARD exceeding 10%, and the deviations for the mixtures of group LG + LG and LG + G also surpass 6%, which all exceed the typical uncertainty (5%) of experimental thermal conductivity data. This reflects the limitations of existing models in mixture calculation and might also imply that higher-quality experimental data is needed for some mixture groups. For cyclohexane (group LG) + decane (group MHC), (84,85) the ARD for the RES and REFPROP models are 14.8% and 12%, respectively, and for D₂ (group LG) + H₂ (group LG), (86−88) both models exhibit significant negative deviations (RES: −7.7%, REFPROP: −7.6%). These indicate the need for adding adjustable parameters to the mixing rules to improve model performance, which will be our future work.

To better illustrate the calculation results of mixtures, the s⁺ vs λ_res⁺ plots of nine mixtures of which more than 500 experimental data were available, are illustrated in Figure 7. Figures of other mixtures are provided in the SI-DPR. Five mixtures have more than 1000 data (ethanol + water, (89−101) R125 + R134a, (102−104) R32 + R134a, (103,104) propane + R32, (104) and R32 + R125 + R134a (103)) and four mixtures have data between 500 and 1000 (ethylene glycol + water, (97,105−115) heptane + isooctane, (116−119) R125 + R32, (103,120−125) and propane + R134a (104)). Among these 9 mixtures, for binary mixtures of heptane + isooctane, R125 + R134a, R32 + R134a, and R125 + R32, the s⁺ vs λ_res⁺ characteristic lines are distinct, and the AARD of the experimental data from model prediction is less than 3%. The model prediction is worse for group LA + SA: the AARD is 5.4% for water + ethanol, and 6.3% for ethylene glycol + water. Especially, the maximum absolute deviation for water + ethanol and ethylene glycol + water exceeds 20% (21.2% and 23.7%, respectively). Cautions should be taken when using this model to calculate the thermal conductivity of fluids containing water and alcohols. For propane + R32 and propane + R134a, there are “no data” between s⁺ = 1 and 2, and the deviation from the s⁺ vs λ_res⁺ characteristic line increases at s⁺ ≈ 2. This is because the experimental data in this range are either considered to be in the two-phase region by REFPROP 10.0 and thus filtered out by Filter 2, or have high deviation but not reaching the criteria of Filter 3. Data of three multicomponent mixtures: R32 + R125 + R134a, (103) R32 + R1234yf + CO₂, (103) and R32 + R125 + R134a + R1234yf + CO₂ (103) were also collected in this work. Without introducing additional adjustable parameters, the AARD of the RES model is 2.3%, 4.0%, and 1.5% for these mixtures, respectively.

Figure 7. Relation between λ_res⁺ and s⁺ for mixtures that have more than 500 experimental data points: (a) heptane + isooctane, (116−119) (b) R125 + R134a, (102−104) (c) R32 + R134a, (103,104) (d) R125 + R32, (103,120−125) (e) ethanol + water, (89−101) (f) ethylene glycol + water, (97,105−115) (g) propane + R134a, (104) (h) propane + R32, (104) and (i) R32 + R125 + R134a. (103) Different colors and symbols represent experimental data from different sources. For specific literature information, please refer to SI-DPR.

The critical enhancement model proposed by Olchowy and Sengers (51) was incorporated in many multiparameter thermal conductivity models for pure fluids, including propane (126) and CO₂ (127) and was successfully applied to refrigerants in our previous work. (48) When the critical enhancement model was applied to mixtures in this work, a “strange behavior” was observed: For certain mixtures, the calculated critical term Δλ_C,mix at conditions far away from the critical point is less than zero, which is abnormal. Further investigation reveals that REFPROP 10.0 considered these experimental points in a two-phase region and yielded negative infinity value of specific heat capacities needed in eqs 7 and 8. To solve this problem, Δλ_C,mix was forced to be zero if it was calculated to be negative. As a result, the critical enhancement model proposed by Olchowy and Sengers (51) obviously improved the accuracy of the model. Although there are a few cases where the deviation increases, the introduction of the critical enhancement term reduces the AARD of 29 mixtures, and the AARD of 7 mixtures is reduced by more than 2%. All mixtures with a change in AARD for more than 1% and with sufficient experimental data are shown in Table 5. It is worth mentioning that for CO₂+ethane, the ARD decreases significantly from 10.2% to 1.7%.

Table 5. Mixtures for Which the Critical Enhancement Term Changes AARD by More than 1%

	with critical enhancement		without critical enhancement
mixture name	ARD/%	AARD/%	ARD/%	AARD/%	AARD change/%
CO₂ + ethane	1.7	5.8	10.2	10.9	5.1
helium + R14	–3.4	3.6	8	8	4.4
R14 + R22	1.7	5.9	8.1	9.4	3.5
CO₂ + ethylene	–1.9	2.8	4.1	5.5	2.7
argon + R14	–0.7	3	4.8	5.1	2.1
R143a + R1234yf	0.6	1.7	2.9	3.5	1.8
R134a + R1234ze(E)	1.6	5.7	3.2	7.3	1.6
R143a + R1234ze(E)	–0.8	2.7	0.8	4.1	1.4
R125 + R1234ze(E)	0	2.4	1.3	3.4	1
R152a + R218	–8.2	10.2	–7	9.2	–1
R125 + R143a	–8.4	8.4	–4.6	5.5	–2.9

Three fluid mixtures were selected to show the impact of the critical enhancement term with their λ vs p_r plots shown in Figure 7. For CO₂ + ethane (128) and CO₂ + ethylene, (129) the thermal conductivity values predicted by the RES model without the critical enhancement term are generally lower than the experimental data, while those with the critical enhancement term are generally closer to the experimental data. Of course, the critical enhancement model of Olchowy and Sengers (51) is not perfect: (1) As shown by the data of CO₂ + ethane (129) in Figure 8a, the peak values of experiment data cannot be predicted by the model; (2) the AARD increases for some mixtures (e.g., R125 + R143a, (121) see Figure 8c) after introducing the critical term, likely due to the overcorrection of critical effects by the critical term.

Figure 8. Thermal conductivity experimental data and model prediction of some fluid mixtures with temperature close to the critical point, where p_r = p/p_c is the reduced pressure relative to critical pressure: (a) CO₂ + ethane, (128) (b) CO₂ + ethylene, (129) and (c) R125 + R143a. (121) The molar fraction of each component is indicated. The critical temperature and pressure were calculated with REFPROP 10.0.

4. Conclusion, Discussion, and Future Work

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In this work, we collected experimental thermal conductivity data for 125 pure fluids and 164 mixtures and developed a residual entropy scaling (RES) model for thermal conductivity. Using a simple polynomial equation, this method uses reference equations of state (EOS) in REFPROP 10.0 to calculate the residual entropy and link residual thermal conductivity to residual entropy. The 125 fluids were classified into 8 different groups, and data of each group collapsed into a characterized residual thermal conductivity vs residual entropy curve. More than 68.2% (corresponding to a standard deviation of a normal distribution) of the evaluated experimental data agree with the RES model within 3.1% for pure fluids. Compared to the various models implemented in REFPROP 10.0, the RES model provides a smaller or equal AARD for 74 out of 125 pure fluids, indicating a similar accuracy level with fewer adjustable parameters. The accuracy of the RES model is affected by the accuracy of the residual entropy, and this implies that the accuracy of our model can be further improved with updates to the reference EOS in REFPROP.

Using simple mixing rules without adjustable parameters, more than 68.2% of the well-evaluated experimental data agree with the RES model within 4.6% for mixtures. The mixing rules proposed in this work lead to a promising result for mixtures of the same group. The situation is different for mixtures from different groups, which may be related to the degree of asymmetry within the system. Nevertheless, without introducing new parameters, the RES model yielded a lower AARD than the REFPROP model for 76 of the 164 mixtures. Further refinement of the mixing rules for different pairs of fluid properties will be carried out to achieve better prediction results.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.iecr.4c02946.

Tables of dilute gas calculation parameters of pure fluids; of reference equation of state and the recommended thermal conductivity model in REFPROP 10.0; of names, group, and constants of pure fluids; for statistics of the experimental data of pure fluids; for statistics of the experimental data of fluid mixtures; for sample thermal conductivity calculations of pure substances with the recommended models in REFPROP 10.0 and the RES model; for sample thermal conductivity calculations of binaries with the recommended models in REFPROP 10.0 and the RES model; and for thermal conductivity as a function of residual entropy for each group and figures for relative deviation from experimental data of pure fluids to model predictions and relative deviation from experimental data of fluid mixtures to model predictions (PDF)
Python package for residual entropy scaling model calculation (ZIP)
Detailed plots and references of all collected experimental data (PDF)

Terms & Conditions

Most electronic Supporting Information files are available without a subscription to ACS Web Editions. Such files may be downloaded by article for research use (if there is a public use license linked to the relevant article, that license may permit other uses). Permission may be obtained from ACS for other uses through requests via the RightsLink permission system: http://pubs.acs.org/page/copyright/permissions.html.

Author Information

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Corresponding Authors
- Yuanyuan Duan - Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Beijing Key Laboratory for CO2 Utilization and Reduction Technology, Tsinghua University, Beijing 100084,People’s Republic of China; Southwest United Graduate School, Kunming 650092, People’s Republic of China; https://orcid.org/0000-0002-4117-7545; Email: [email protected]
- Xiaoxian Yang - Applied Thermodynamics, Chemnitz University of Technology, Chemnitz 09107, Germany; https://orcid.org/0000-0003-4655-3156; Email: [email protected]
Author
- Zhuo Li - Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Beijing Key Laboratory for CO2 Utilization and Reduction Technology, Tsinghua University, Beijing 100084,People’s Republic of China
Notes
The authors declare no competing financial interest.

Acknowledgments

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The realization of the project and the scientific work was supported by the National Science and Technology Major Project of China (J2019-I-0009-0009), the German Federal Ministry of Education and Research on the basis of a decision by the German Bundestag (funding code 03SF0623A), and the Yunnan Provincial Science and Technology Project at Southwest United Graduate School (202302AO370018). The authors gratefully acknowledge this support and carry the full responsibility for the content of this paper. The authors would also like to thank Dr. Ian. H. Bell of the National Institute of Standards and Technology for his help in compiling the reference list of experimental data.

References

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This article references 129 other publications.

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Li, H. L.; Dong, B. B.; Yu, Z. X.; Yan, J. Y.; Zhu, K. Thermo-physical properties of CO2 mixtures and their impacts on CO2 capture, transport and storage: Progress since 2011. Appl. Energy 2019, 255, 113789 DOI: 10.1016/j.apenergy.2019.113789
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Thermo-physical properties of CO2 mixtures and their impacts on CO2 capture, transport and storage: Progress since 2011
Li, Hailong; Dong, Beibei; Yu, Zhixin; Yan, Jinyue; Zhu, Kai
Applied Energy (2019), 255 (), 113789CODEN: APENDX; ISSN:0306-2619. (Elsevier Ltd.)
A review. The knowledge of accurate thermo-phys. properties is crucial for the development and deployment of CO2 capture, transport and storage (CCS). The progress on the exptl. data and theor. models regarding thermo-phys. properties of CO2 mixts. as well as the property impact on the design and operation of different CCS processes has been updated. The newly published exptl. data since 2011 have been collected and reviewed based on which the new knowledge gaps regarding measurements have been identified. There have also been some advanced models proposed recently, which have shown good performances. The collected model performances don't show there exist a model that is superior to others; but they still provide a good guideline regarding model selection. However, developing more-complex models as the complexity may not necessarily improve the accuracy when empirical parameters were included and well-tuned. By comparing the importance of the properties and the accuracy of existing models, suggestions were given regarding the development of property models that should be prioritized.
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Huber, M. L.; Lemmon, E. W.; Bell, I. H.; McLinden, M. O. The NIST REFPROP Database for Highly Accurate Properties of Industrially Important Fluids. Ind. Eng. Chem. Res. 2022, 61 (42), 15449– 15472, DOI: 10.1021/acs.iecr.2c01427
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The NIST REFPROP Database for Highly Accurate Properties of Industrially Important Fluids
Huber, Marcia L.; Lemmon, Eric W.; Bell, Ian H.; McLinden, Mark O.
Industrial & Engineering Chemistry Research (2022), 61 (42), 15449-15472CODEN: IECRED; ISSN:0888-5885. (American Chemical Society)
The NIST REFPROP software program is a powerful tool for calcg. thermophys. properties of industrially important fluids, and this manuscript describes the models implemented in, and features of, this software. REFPROP implements the most accurate models available for selected pure fluids and their mixts. that are valid over the entire fluid range including gas, liq., and supercrit. states, with the goal of uncertainties approaching the level of the underlying exptl. data. The equations of state for thermodn. properties are primarily of the Helmholtz energy form; a variety of models are implemented for the transport properties. The models are documented for the 147 fluids included in the current version. A graphical user interface generates tables and provides extensive plotting capabilities. Properties can also be accessed through third-party apps. or user-written code via the core property subroutines compiled into a shared library. REFPROP disseminates international stds. in both the natural gas and refrigeration industries, as well as stds. for water/steam.
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Li, J.; Peng, X.; Yang, Z.; Hu, S.; Duan, Y. Design, improvements and applications of dual-pressure evaporation organic Rankine cycles: A review. Appl. Energy 2022, 311, 118609 DOI: 10.1016/j.apenergy.2022.118609
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Wang, F. A.; Zhu, J. Q.; Chen, H. S.; Wang, W. C.; Jiang, Y. L. A new model of thermal conductivity for liquids. Chem. Eng. J. 2000, 78 (2–3), 187– 191, DOI: 10.1016/S1385-8947(00)00152-2
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Kandiyoti, R.; Mclaughlin, E. Viscosity and Thermal Conductivity of Dense Hard Sphere Fluid Mixtures. Mol. Phys. 1969, 17 (6), 643– 653, DOI: 10.1080/00268976900101521
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Quiñones-Cisneros, S. E.; Pollak, S.; Schmidt, K. A. G. Friction Theory Model for Thermal Conductivity. J. Chem. Eng. Data 2021, 66 (11), 4215– 4227, DOI: 10.1021/acs.jced.1c00400
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Jia, H.; Hu, Y.; Wang, X.; Gao, B. Viscosity and Thermal Conductivity Model of HFOs and HFO/HFC Mixtures Based on Friction Theory. Int. J. Thermophys. 2023, 44 (5), 76, DOI: 10.1007/s10765-023-03189-z
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Huber, M. L. Models for Viscosity, Thermal Conductivity, and Surface Tension of Selected Pure Fluids as Implemented in REFPROP v10.0; NIST Interagency/Internal Report (NISTIR) 8209; National Institute of Standards and Technology: Gaithersburg, MD, 2018.
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McLinden, M. O.; Klein, S. A.; Perkins, R. A. An extended corresponding states model for the thermal conductivity of refrigerants and refrigerant mixtures. Int. J. Refrig. 2000, 23 (1), 43– 63, DOI: 10.1016/S0140-7007(99)00024-9
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An extended corresponding states model for the thermal conductivity of refrigerants and refrigerant mixtures
McLinden, Mark O.; Klein, Sanford A.; Perkins, Richard A.
International Journal of Refrigeration (1999), 23 (1), 43-63CODEN: IJRFDI; ISSN:0140-7007. (Elsevier Science Ltd.)
The extended corresponding states (ECS) model of Huber et al. (1992) for calcg. the thermal cond. of a pure fluid or fluid mixt. is modified by the introduction of a thermal cond. shape factor which is detd. from exptl. data. An addnl. empirical correction to the traditional Eucken correlation for the dil. gas cond. was necessary, esp. for highly polar fluids. For pure fluids, these addnl. factors result in significantly improved agreement between the ECS predictions and exptl. data. A further modification for mixts. eliminates discontinuities at the pure component limits. The method has been applied to 11 halocarbon refrigerants, propane, ammonia, and carbon dioxide as well as mixts. of these fluids. The av. abs. deviations between the calcd. and exptl. values ranged from 1.08 to 5.57% for the 14 pure fluids studied. Deviations for the 12 mixts. studied ranged from 2.98 to 9.40%. Deviations increase near the crit. point, esp. for mixts.
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Rosenfeld, Y. A quasi-universal scaling law for atomic transport in simple fluids. J. Phys.: Condens.Matter 1999, 11 (28), 5415– 5427, DOI: 10.1088/0953-8984/11/28/303
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A quasi-universal scaling law for atomic transport in simple fluids
Rosenfeld, Yaakov
Journal of Physics: Condensed Matter (1999), 11 (28), 5415-5427CODEN: JCOMEL; ISSN:0953-8984. (Institute of Physics Publishing)
A semiempirical "universal" corresponding-states relationship, for the dimensionless transport coeffs. of dense fluids as functions of the reduced configurational entropy, was proposed more than twenty years ago and established by many simulations. Here it is shown anal., by appealing to Enskog's original results for the inverse-power potentials, that the quasi-universal entropy scaling can be extended also to dil. gases. The analytic form and the possible origin for the entropy scaling for dense fluids are discussed in view of this unexpected result. On the basis of the entropy scaling we predict a min. in the shear viscosity as a function of temp. for all soft inverse-power potentials, in quant. agreement with the available simulations.
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Gnan, N.; Schrøder, T. B.; Pedersen, U. R.; Bailey, N. P.; Dyre, J. C. Pressure-energy correlations in liquids. IV. ″Isomorphs″ in liquid phase diagrams. J. Chem. Phys. 2009, 131 (23), 234504, DOI: 10.1063/1.3265957
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Schrøder, T. B.; Gnan, N.; Pedersen, U. R.; Bailey, N. P.; Dyre, J. C. Pressure-energy correlations in liquids. V. Isomorphs in generalized Lennard-Jones systems. J. Chem. Phys. 2011, 134 (16), 164505, DOI: 10.1063/1.3582900
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Bell, I. H. Probing the link between residual entropy and viscosity of molecular fluids and model potentials. Proc. Natl. Acad. Sci. U. S. A. 2019, 116 (10), 4070– 4079, DOI: 10.1073/pnas.1815943116
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Probing the link between residual entropy and viscosity of molecular fluids and model potentials
Bell, Ian H.
Proceedings of the National Academy of Sciences of the United States of America (2019), 116 (10), 4070-4079CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
This work investigates the link between residual entropy and viscosity based on wide-ranging, highly accurate exptl. 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 approx. monovariate relationship between residual entropy and reduced viscosity for a wide range of mol. fluids [argon, methane, CO2, SF6, 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 d. scaling for mol. fluids, the viscosity of nonassocg. mol. fluids can be mapped onto the model potentials. This mapping results in a length scale that is proportional to the cube root of exptl. measurable liq. vol. values.
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Bell, I. H. Entropy Scaling of Viscosity-I: A Case Study of Propane. J. Chem. Eng. Data 2020, 65 (6), 3203– 3215, DOI: 10.1021/acs.jced.0c00209
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Bell, I. H. Entropy Scaling of Viscosity-II: Predictive Scheme for Normal Alkanes. J. Chem. Eng. Data 2020, 65 (11), 5606– 5616, DOI: 10.1021/acs.jced.0c00749
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Bell, I. H.; Messerly, R.; Thol, M.; Costigliola, L.; Dyre, J. C. Modified Entropy Scaling of the Transport Properties of the Lennard-Jones Fluid. J. Phys. Chem. B 2019, 123 (29), 6345– 6363, DOI: 10.1021/acs.jpcb.9b05808
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Modified Entropy Scaling of the Transport Properties of the Lennard-Jones Fluid
Bell, Ian H.; Messerly, Richard; Thol, Monika; Costigliola, Lorenzo; Dyre, Jeppe C.
Journal of Physical Chemistry B (2019), 123 (29), 6345-6363CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
Rosenfeld proposed two different scaling approaches to model the transport properties of fluids, sepd. by 22 years, one valid in the dil. gas, and another in the liq. phase. In this work, we demonstrate that these two limiting cases can be connected through the use of a novel approach to scaling transport properties and a bridging function. This approach, which is empirical and not derived from theory, is used to generate ref. correlations for the transport properties of the Lennard-Jones 12-6 fluid of viscosity, thermal cond., and self-diffusion. This approach, with a very simple functional form, allows for the reprodn. of the most accurate simulation data to within nearly their statistical uncertainty. The correlations are used to confirm that for the Lennard-Jones fluid the appropriately scaled transport properties are nearly monovariate functions of the excess entropy from low-d. gases into the supercooled phase and up to extreme temps. This study represents the most comprehensive metastudy of the transport properties of the Lennard-Jones fluid to date.
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Yang, X. X.; Xiao, X.; May, E. F.; Bell, I. H. Entropy Scaling of Viscosity-III: Application to Refrigerants and Their Mixtures. J. Chem. Eng. Data 2021, 66 (3), 1385– 1398, DOI: 10.1021/acs.jced.0c01009
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Al Ghafri, S. Z.; Akhfash, M.; Hughes, T. J.; Xiao, X.; Yang, X.; May, E. F. High pressure viscosity measurements of ternary (methane+ propane+ heptane) mixtures. Fuel Process. Technol. 2021, 223, 106984 DOI: 10.1016/j.fuproc.2021.106984
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Kim, D.; Liu, H. T.; Yang, X. X.; Yang, F. F.; Morfitt, J.; Arami-Niya, A.; Ryu, M.; Duan, Y. Y.; May, E. F. Thermal conductivity measurements and correlations of pure R1243zf and binary mixtures of R32+R1243zf and R32+R1234yf Int. J. Refrig. 2021, 131, 990– 999, DOI: 10.1016/j.ijrefrig.2021.07.019
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Yang, X. X.; Hanzelmann, C.; Feja, S.; Trusler, J. P. M.; Richter, M. Thermophysical Property Modeling of Lubricant Oils and Their Mixtures with Refrigerants Using a Minimal Set of Experimental Data. Ind. Eng. Chem. Res. 2023, 62 (44), 18736– 18749, DOI: 10.1021/acs.iecr.3c02474
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Yang, X. X.; Liu, H. T.; Chen, S. H.; Kim, D.; Yang, F. F.; Arami-Niya, A.; Duan, Y. Y. Viscosity of binary refrigerant mixtures of R32+R1234yf and R32+R1243zf. Int. J. Refrig. 2021, 128, 197– 205, DOI: 10.1016/j.ijrefrig.2020.11.020
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Viscosity of binary refrigerant mixtures of R32 + R1234yf and R32 + R1243zf
Yang, Xiaoxian; Liu, Hangtao; Chen, Shi Hai; Kim, Dongchan; Yang, Fufang; Arami-Niya, Arash; Duan, Yuanyuan
International Journal of Refrigeration (2021), 128 (), 197-205CODEN: IJRFDI; ISSN:0140-7007. (Elsevier Ltd.)
Viscosity measurements of six binary mixts. of R32+R1234yf and R32+R1243zf at different compns. were conducted in the homogenous liq. and gas phases with a vibrating-wire viscometer in the temp. range from (254 to 383) K and pressures from (1 to 8) MPa. The measurement system was verified with the measurements of pure carbon dioxide and R32 in homogenous liq. and gas phases. The relative combined expanded uncertainties (k = 2) in the exptl. viscosity of the mixts. are generally from 3.2% to 5.0%. The measured viscosities agree with the calcns. of the extended corresponding state model implemented in the software package REFPROP 10.0 within 10% and mainly within 5%. The parameters of the residual entropy scaling model incorporating cubic-plus-assocn. equation of state (RES-CPA model) for the viscosity of pure R1243zf and binary R32 + R1243zf mixt. were detd. The relative deviation of the measured viscosities from values calcd. with the RES-CPA model is mainly within 6% in the liq. phase and 10% in the gas phase.
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Yang, X.; Xiao, X.; Thol, M.; Richter, M.; Bell, I. A Residual Entropy Scaling Approach for Viscosity of Refrigerants, Other Fluids, and Their Mixtures. In Proceedings of the 6th International Congress of Refrigeration; Paris, France, August 21–25, 2023.
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Liu, H.; Yang, F.; zhang, K.; Duan, Y.; Yang, Z. Residual Entropy Scaling Model for the Viscosity of Noble Gases. Gongcheng Rewuli Xuebao 2021, 42, 1– 8
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Liu, H. T.; Yang, F. F.; Yang, X. X.; Yang, Z.; Duan, Y. Y. Modeling the thermal conductivity of hydrofluorocarbons, hydrofluoroolefins and their binary mixtures using residual entropy scaling and cubic-plus-association equation of state. J. Mol. Liq. 2021, 330, 115612 DOI: 10.1016/j.molliq.2021.115612
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Modeling the thermal conductivity of hydrofluorocarbons, hydrofluoroolefins and their binary mixtures using residual entropy scaling and cubic-plus-association equation of state
Liu, Hangtao; Yang, Fufang; Yang, Xiaoxian; Yang, Zhen; Duan, Yuanyuan
Journal of Molecular Liquids (2021), 330 (), 115612CODEN: JMLIDT; ISSN:0167-7322. (Elsevier B.V.)
Thermal cond. strongly impacts heat transfer, and thus is an important thermophys. property for refrigeration and medium-low-temp. heat utilization systems. In this work, the residual entropy scaling incorporating cubic-plus-assocn. equation of state, as a convenient and robust modeling approach for the transport properties of pure and mixt. fluids of which the exptl. data are scarce or unavailable, is extended to the thermal cond. of hydrofluorocarbons, hydrofluoroolefins, and their binary mixts. For all the investigated pure and mixt. fluids, the dependence of the thermal cond. on the thermodn. state is reduced to a 'universal' univariate function of the rescaled residual entropy with one adjustable parameter for each pure fluid and no further adjustable parameter for mixts. A new formulation of the ref. thermal cond. is proposed to improve the accuracy for the binary mixts. The model reproduces the thermal cond. of the investigated pure and mixt. fluids with the root mean square deviation of 2.9% in gas, liq., and supercrit. regions. The lack or uneven distribution of the data is overcome based on the residual entropy scaling with the extensive data of R134a as a ref.
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Liu, H. T.; Yang, F. F.; Yang, Z.; Duan, Y. Y. Modeling the viscosity of hydrofluorocarbons, hydrofluoroolefins and their binary mixtures using residual entropy scaling and cubic-plus-association equation of state. J. Mol. Liq. 2020, 308, 113027 DOI: 10.1016/j.molliq.2020.113027
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Modeling the viscosity of hydrofluorocarbons, hydrofluoroolefins and their binary mixtures using residual entropy scaling and cubic-plus-association equation of state
Liu, Hangtao; Yang, Fufang; Yang, Zhen; Duan, Yuanyuan
Journal of Molecular Liquids (2020), 308 (), 113027CODEN: JMLIDT; ISSN:0167-7322. (Elsevier B.V.)
Hydrofluorocarbons (HFCs), hydrofluoroolefins (HFOs), and their binary mixts. are widely-used working fluids in moderate and low temp. energy systems. An accurate viscosity model is the cornerstone for the economic and conceptual optimization of the energy utilization systems. In this work, we apply residual entropy scaling and the cubic-plus-assocn. (CPA) equation of state to HFCs, HFOs, and their binary mixts. The reduced viscosity (real fluid viscosity divided by dil. gas viscosity) of 14 pure fluids are correlated to a univariate function of the residual entropy, which is calcd. with the CPA equation of state, a model that was recently adapted for the thermodn. properties of HFCs/HFOs. Then the viscosity of 10 binary mixts. are predicted by the model without introducing any further adjustable parameters. The present model reproduces the viscosity of the investigated pure fluids and mixts. accurately in both the gas and liq. phases and presents reliable predictions in temp. and pressure ranges in which the exptl. data are scarce or unavailable.
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Liu, H. T.; Yang, F. F.; Yang, Z.; Duan, Y. Y. Crossover residual entropy scaling of the viscosity and thermal conductivity of carbon dioxide. J. Mol. Liq. 2022, 368, 120799 DOI: 10.1016/j.molliq.2022.120799
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Kang, K.; Gu, Y. X.; Wang, X. P. Assessment and development of the viscosity prediction capabilities of entropy scaling method coupled with a modified binary interaction parameter estimation model for refrigerant blends. J. Mol. Liq. 2022, 358, 119184 DOI: 10.1016/j.molliq.2022.119184
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Kang, K.; Li, X. L.; Gu, Y. X.; Wang, X. P. Thermal conductivity prediction of pure refrigerants and mixtures based on entropy-scaling concept. J. Mol. Liq. 2022, 368, 120568 DOI: 10.1016/j.molliq.2022.120568
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Kang, K.; Yang, S.; Gu, Y.; Wang, X. Density and viscosity measurement of R513A and a modified residual entropy scaling model for predicting the viscosity of HFC/HFO refrigerants. Int. J. Refrig. 2024, 162, 204– 214, DOI: 10.1016/j.ijrefrig.2024.04.008
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Hopp, M.; Gross, J. Thermal Conductivity of Real Substances from Excess Entropy Scaling Using PCP-SAFT. Ind. Eng. Chem. Res. 2017, 56 (15), 4527– 4538, DOI: 10.1021/acs.iecr.6b04289
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Thermal Conductivity of Real Substances from Excess Entropy Scaling Using PCP-SAFT
Hopp, Madlen; Gross, Joachim
Industrial & Engineering Chemistry Research (2017), 56 (15), 4527-4538CODEN: IECRED; ISSN:0888-5885. (American Chemical Society)
Entropy scaling is an intriguingly simple approach for correlating and predicting transport properties of real substances and mixts. It is convincingly documented in the literature that entropy scaling is indeed a firm concept for the shear viscosity of real substances, including hydrogen bonding species and strongly nonspherical species. We investigate whether entropy scaling is applicable for thermal cond. It is shown that the dimensionless thermal cond. (thermal cond. divided by a ref. thermal cond.) does not show a single-variable dependence on residual entropy, for obvious choices of a ref. thermal cond. We perform a detailed anal. of exptl. data and propose a ref. thermal cond. that is itself a simple function of the residual entropy. We then obtain good scaling behavior for the entire fluid region for water and 147 org. substances from various chem. families: linear and branched alkanes, alkenes, aldehydes, aroms., ethers, esters, ketones, alcs., and acids. The residual entropy is calcd. from the Perturbed Chain Polar Statistical Assocg. Fluid Theory equation of state. The correlation of exptl. data requires two parameters for pure substances with scarce exptl. data and up to five parameters for exptl. well-characterized species. The correlation results for all substances lead to av. relative deviations of 4.2% to exptl. data. To further assess the approach, we analyze extrapolations to states not covered by exptl. data and find very satisfying results.
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Hopp, M.; Gross, J. Thermal Conductivity from Entropy Scaling: A Group-Contribution Method. Ind. Eng. Chem. Res. 2019, 58 (44), 20441– 20449, DOI: 10.1021/acs.iecr.9b04289
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Thermal Conductivity from Entropy Scaling: A Group-Contribution Method
Hopp, Madlen; Gross, Joachim
Industrial & Engineering Chemistry Research (2019), 58 (44), 20441-20449CODEN: IECRED; ISSN:0888-5885. (American Chemical Society)
Entropy scaling has proven to be a powerful method for calcg. transport properties. The applicability of the entropy scaling approach to predict the viscosity, thermal cond. and self-diffusion coeffs. of pure substances based on substance-specific parameters was over last years convincingly demonstrated in literature. In this work we derive a predictive method for the thermal cond. based on entropy scaling. The model is developed as a group-contribution approach, where substances are considered to be composed of chem. (functional) groups. The excess entropy is calcd. using the group-contribution PCP-SAFT equation of state. The model is applicable for gaseous phases and for liq.-phase conditions covering wide ranges of temp. and pressure. We consider pure fluids from various chem. families, namely alkanes, branched alkanes, cyclic alkanes, alkenes, aldehydes, aroms., esters, ethers, ketones and alcs., and some individual substances, such as water, carbon dioxide and alike. We propose parameters of 29 chem. groups, by considering 231 substances with more than 50,000 exptl. data points The group-contribution method for the thermal cond. proposed in this work is shown to be in convincing agreement with exptl. data, with 6.17% av. abs. deviation for all considered data points.
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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, 58 (39), 18432– 18438, DOI: 10.1021/acs.iecr.9b03998
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Thermal Conductivity via Entropy Scaling: An Approach That Captures the Effect of Intramolecular Degrees of Freedom
Hopp, Madlen; Mele, Julia; Hellmann, Robert; Gross, Joachim
Industrial & Engineering Chemistry Research (2019), 58 (39), 18432-18438CODEN: IECRED; ISSN:0888-5885. (American Chemical Society)
The thermal cond. of gases depends strongly on the vibrational and rotational degrees of freedom of the mol. under consideration. Entropy scaling is based on the residual entropy, which does not capture the intramol. and rotational contributions. This study proposes a model for the thermal cond. that accounts for these degrees of freedom. We use the Chapman-Cowling approxn., where contributions of internal degrees of freedom to the thermal cond. of an ideal gas are related to the self-diffusion coeff. A resulting expression for the thermal cond. is used as a ref. in entropy scaling. We find exptl. values for thermal conductivities in the entire fluid range to be (to good approxn.) a function of residual entropy only. This study shows that entropy scaling is a strong approxn. also for thermal cond., provided a suitable expression is chosen for the ref. thermal cond.
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Lötgering-Lin, O.; Fischer, M.; Hopp, M.; Gross, J. Pure Substance and Mixture Viscosities Based on Entropy Scaling and an Analytic Equation of State. Ind. Eng. Chem. Res. 2018, 57 (11), 4095– 4114, DOI: 10.1021/acs.iecr.7b04871
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Lötgering-Lin, O.; Gross, J. Group Contribution Method for Viscosities Based on Entropy Scaling Using the Perturbed-Chain Polar Statistical Associating Fluid Theory. Ind. Eng. Chem. Res. 2015, 54 (32), 7942– 7952, DOI: 10.1021/acs.iecr.5b01698
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Lötgering-Lin, O.; Schöniger, A.; Nowak, W.; Gross, J. Bayesian Model Selection Helps To Choose Objectively between Thermodynamic Models: A Demonstration of Selecting a Viscosity Model Based on Entropy Scaling. Ind. Eng. Chem. Res. 2016, 55 (38), 10191– 10207, DOI: 10.1021/acs.iecr.6b02671
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Sauer, E.; Stavrou, M.; Gross, J. Comparison between a Homo- and a Heterosegmented Group Contribution Approach Based on the Perturbed-Chain Polar Statistical Associating Fluid Theory Equation of State. Ind. Eng. Chem. Res. 2014, 53 (38), 14854– 14864, DOI: 10.1021/ie502203w
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Comparison between a Homo- and a Heterosegmented Group Contribution Approach Based on the Perturbed-Chain Polar Statistical Associating Fluid Theory Equation of State
Sauer, Elmar; Stavrou, Marina; Gross, Joachim
Industrial & Engineering Chemistry Research (2014), 53 (38), 14854-14864CODEN: IECRED; ISSN:0888-5885. (American Chemical Society)
Depending on the mol. model, group contribution (GC) approaches based on the statistical assocg. fluid theory (SAFT) can be classified in homosegmented and heterosegmented GC approaches. In homosegmented GC approaches, mols. are modeled as chains composed of identical segments. Heterosegmented GC approaches, on the other hand, consider mol. chains composed of different segment types and thus maintain a more detailed picture of real mols. Therefore, heterosegmented GC approaches are arguably more phys. realistic and ought to give more accurate descriptions of thermodn. properties. In this work, we evaluate the performance of a homosegmented and a heterosegmented GC approach based on the perturbed-chain polar SAFT (PCP-SAFT) equation of state (EoS). To ensure a meaningful comparison between both GC approaches, a dipole term for the heterosegmented GC approach is formulated. Group parameters of 22 functional groups were adjusted to pure component property data. The comparison between both GC approaches shows that the heterosegmented GC approach leads to significantly better agreement with exptl. data for various chem. families.
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Vijande, J.; Piñeiro, M. M.; Bessières, D.; Saint-Guirons, H.; Legido, J. L. Description of PVT behaviour of hydrofluoroethers using the PC-SAFT EOS. Phys. Chem. Chem. Phys. 2004, 6 (4), 766– 770, DOI: 10.1039/B312223A
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Dehlouz, A.; Jaubert, J. N.; Galliero, G.; Bonnissel, M.; Privat, R. Combining the entropy-scaling concept and cubic- or SAFT equations of state for modelling thermal conductivities of pure fluids. Int. J. Heat Mass Transfer 2022, 196, 123286 DOI: 10.1016/j.ijheatmasstransfer.2022.123286
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Combining the entropy-scaling concept and cubic- or SAFT equations of state for modelling thermal conductivities of pure fluids
Dehlouz, Aghilas; Jaubert, Jean-Noel; Galliero, Guillaume; Bonnissel, Marc; Privat, Romain
International Journal of Heat and Mass Transfer (2022), 196 (), 123286CODEN: IJHMAK; ISSN:0017-9310. (Elsevier Ltd.)
The transport properties of a fluid show a complex dependence with temp. and pressure due to the combination of different phenomena occurring at the microscopic scale. The entropy scaling concept aims at describing this complex behavior by expressing reduced transport properties as one-variable functions of the Tv-residual entropy, a thermodn. quantity that can be straightforwardly estd. with an equation of state (EoS). In this work, a reformulated version of Rosenfeld's original entropy scaling approach is proposed in order to calc. the thermal conductivities of pure fluids. A specifically developed reduced thermal cond. expression was correlated to a function of the Tv-residual entropy that was recently proposed by our group to correlate viscosities and self-diffusion coeffs. The thermodn. properties involved in the definition of the entropy-scaling variables (that are the residual entropies, densities, heat capacities) were estd. with either the I-PC-SAFT or the tc-PR equations of state (EoSs) thus leading to the definition of two different models. Each of them was validated against a large database of around 90,000 exptl. thermal conductivities encompassing liq., gas and supercrit. states for 119 chem. species belonging to 11 chem. families such as n-alkanes, alkenes, alcs., HFC-CFC etc. For each model, component-specific, chem.-family specific and universal parameters were proposed. Working with the I-PC-SAFT and tc-PR EoSs, the obtained MAPEs (Mean Abs. Percent Errors) are resp. 3.3% and 3.4% when the model parameters are considered as component-specific, 9.7% and 5.6% when they are selected as chem.-family specific meanwhile they are 11.2% and 9.2% when they are assumed to be universal.
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Rosenfeld, Y. Quasi-universal scaling law for atomic transport in simple fluids. J. Phys. IV 2000, 10 (P5), 129– 134, DOI: 10.1051/jp4:2000517
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Le Guennec, Y.; Privat, R.; Jaubert, J.-N. Development of the translated-consistent tc-PR and tc-RK cubic equations of state for a safe and accurate prediction of volumetric, energetic and saturation properties of pure compounds in the sub-and super-critical domains. Fluid Phase Equilib. 2016, 429, 301– 312, DOI: 10.1016/j.fluid.2016.09.003
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Development of the translated-consistent tc-PR and tc-RK cubic equations of state for a safe and accurate prediction of volumetric, energetic and saturation properties of pure compounds in the sub- and super-critical domains
Le Guennec, Yohann; Privat, Romain; Jaubert, Jean-Noel
Fluid Phase Equilibria (2016), 429 (), 301-312CODEN: FPEQDT; ISSN:0378-3812. (Elsevier B.V.)
In this paper, translated and consistent versions of the Peng-Robinson (tc-PR) and Redlich-Kwong (tc-RK) cubic equations of state (CEoS) are developed. The adjective consistent means that the α-function used in such models passes the consistency test we recently developed and which guarantees safe extrapolation in the supercrit. region and safe VLE calcn. in multi-component systems. The adjective translated means that a vol. translation aimed at exactly reproducing the exptl. satd. liq. vol. at a reduced temp. of 0.8 was used. The key conclusion of this paper is that the tc-PR EoS is certainly the safest and the most accurate 3-parameter cubic EoS ever published. Indeed the av. deviations over roughly 1000 compds. belonging to different chem. families are: ΔPsat<1 %, ΔvapH = ΔcsatP,L = 2% and ΔvsatL(Tr < 0.9) = 2.3%. In the case of a lack of exptl. data to fit the 3 parameters of the α-function and to det. the value of the vol. correction, the second part of this study aims at providing a generalized version of the tc-PR and tc-RK CEoS in which all parameters can be estd. from the mere knowledge of the acentric factor.
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Moine, E.; Piña-Martinez, A.; Jaubert, J. N.; Sirjean, B.; Privat, R. I-PC-SAFT: An Industrialized Version of the Volume-Translated PC-SAFT Equation of State for Pure Components, Resulting from Experience Acquired All through the Years on the Parameterization of SAFT-Type and Cubic Models. Ind. Eng. Chem. Res. 2019, 58 (45), 20815– 20827, DOI: 10.1021/acs.iecr.9b04660
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Yang, F. F.; Liu, Q.; Duan, Y. Y.; Yang, Z. Crossover multiparameter equation of state: General procedure and demonstration with carbon dioxide. Fluid Phase Equilib. 2019, 494, 161– 171, DOI: 10.1016/j.fluid.2019.04.035
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Crossover multiparameter equation of state: General procedure and demonstration with carbon dioxide
Yang, Fufang; Liu, Qiang; Duan, Yuanyuan; Yang, Zhen
Fluid Phase Equilibria (2019), 494 (), 161-171CODEN: FPEQDT; ISSN:0378-3812. (Elsevier B.V.)
The multiparameter equation of state represents exptl. data in wide ranges of temp. and d. with superb accuracy. However, at the crit. point, all classical models fail in describing the asymptotic behavior of thermodn. properties, which is governed by the renormalization group (RG) theory. Using the crossover method, the classical models far from the crit. point can be transformed to the RG theory at the crit. point. Here we validate the procedure of combining the crossover method with the multiparameter equation of state through comparison with exptl. data and the original multiparameter equation of state, and testing against the qual. criterion of characteristic curves. We select carbon dioxide as a demonstration due to its data availability and qualification as a benchmark fluid for thermodn. property modeling. We describe in detail the contribution of different types of terms in the crossover method and original multiparameter equation of state to thermodn. properties. Furthermore, we propose twin Gaussian terms to compensate for the loss of accuracy near the coexistence curve upon removing the non-anal. terms and leave the anal. part of the formulation unaltered. With a slight and acceptable loss of accuracy in the crossover region, the crossover method enforces the asymptotic singular behavior and crit. exponents at the crit. point. Far from the crit. point, the present model transforms to the original model and retains the superb accuracy of the latter.
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Fouad, W. A. Thermal Conductivity of Pure Fluids and Multicomponent Mixtures Using Residual Entropy Scaling with PC-SAFT-Application to Refrigerant Blends. J. Chem. Eng. Data 2020, 65 (12), 5688– 5697, DOI: 10.1021/acs.jced.0c00682
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Gross, J.; Sadowski, G. Perturbed-chain SAFT: An equation of state based on a perturbation theory for chain molecules. Ind. Eng. Chem. Res. 2001, 40 (4), 1244– 1260, DOI: 10.1021/ie0003887
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Perturbed-Chain SAFT: An Equation of State Based on a Perturbation Theory for Chain Molecules
Gross, Joachim; Sadowski, Gabriele
Industrial & Engineering Chemistry Research (2001), 40 (4), 1244-1260CODEN: IECRED; ISSN:0888-5885. (American Chemical Society)
A modified statistical assocg. fluid theory (SAFT) equation of state is developed by applying the perturbation theory of Barker and Henderson to a hard-chain ref. fluid. With conventional one-fluid mixing rules, the equation of state is applicable to mixts. of small spherical mols. such as gases, nonspherical solvents, and chainlike polymers. The three pure-component parameters required for nonassocg. mols. were identified for 78 substances by correlating vapor pressures and liq. vols. The equation of state gives good fits to these properties and agrees well with caloric properties. When applied to vapor-liq. equil. of mixts., the equation of state shows substantial predictive capabilities and good precision for correlating mixts. Comparisons to the SAFT version of Huang and Radosz reveal a clear improvement of the proposed model. A brief comparison with the Peng-Robinson model is also given for vapor-liq. equil. of binary systems, confirming the good performance of the suggested equation of state. The applicability of the proposed model to polymer systems was demonstrated for high-pressure liq.-liq. equil. of a polyethylene mixt. The pure-component parameters of polyethylene were obtained by extrapolating pure-component parameters of the n-alkane series to high mol. wts.
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Yang, F. F.; Chu, Q. F.; Liu, Q.; Duan, Y. Y.; Yang, Z. The cubic-plus-association equation of state for hydrofluorocarbons, hydrofluoroolefins, and their binary mixtures. Chem. Eng. Sci. 2019, 209, 115182 DOI: 10.1016/j.ces.2019.115182
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The cubic-plus-association equation of state for hydrofluorocarbons, hydrofluoroolefins, and their binary mixtures
Yang, Fufang; Chu, Qingfu; Liu, Qiang; Duan, Yuanyuan; Yang, Zhen
Chemical Engineering Science (2019), 209 (), 115182CODEN: CESCAC; ISSN:0009-2509. (Elsevier Ltd.)
Hydrofluorocarbons, hydrofluoroolefins, and their mixts. are widely used as working fluids in energy systems. Weak hydrogen bond exists in these fluids and thus contribute to their thermodn. properties. In this work, we account for the contribution of the weak hydrogen bond by tailoring the cubic-plus-assocn. (CPA) equation of state (EoS) and its parameter fitting procedure. Overfitting to the liq. properties is avoided by introducing the satd. vapor d. into the fitting objective function. The EoS is extended to binary mixts. using the van der Waals mixing rules and Elliot combining rule in which process solving the cross-assocn. fraction is reduced from an equation set consisting of 4 nonlinear equations to a single nonlinear equation. The performance of the present model is investigated in terms of the vapor-liq. equil. (VLE) and volumetric properties of 15 pure fluids and 40 binary mixts. using fitted and zero binary interaction parameter, and is compared with the ref. data, a CPA EoS that uses the traditional parameter fitting procedure, the Soave-Redlich-Kwong (SRK) EoS, and a vol.-translated SRK EoS. The present model (including the EoS and fitting procedure) accurately reproduces the vapor pressure, d., and second virial coeff. for the pure fluids and binary mixts., and is the only valid model among the investigated models for both the VLE and the volumetric properties in both liq. and vapor phases. The contribution of the assocn. term to the pressure is also shown in the temp.-d. diagram, presenting a similar behavior as that in water in which the effect of the hydrogen bond is comparatively more pronounced.
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Rokni, H. B.; Moore, J. D.; Gavaises, M. Entropy-scaling based pseudo-component viscosity and thermal conductivity models for hydrocarbon mixtures and fuels containing iso-alkanes and two-ring saturates. Fuel 2021, 283, 118877 DOI: 10.1016/j.fuel.2020.118877
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Entropy-scaling based pseudo-component viscosity and thermal conductivity models for hydrocarbon mixtures and fuels containing iso-alkanes and two-ring saturates
Rokni, Houman B.; Moore, Joshua D.; Gavaises, Manolis
Fuel (2021), 283 (), 118877CODEN: FUELAC; ISSN:0016-2361. (Elsevier Ltd.)
Recently, Rokni et al. developed entropy-scaling based pseudo-component techniques to predict the viscosity and thermal cond. of hydrocarbon mixts. and fuels up to high temp. and pressure conditions using only two calcd. or measured mixt. properties (no. av. mol. wt. and hydrogen-to-carbon ratio). The models are accurate for many hydrocarbon mixts. that do not contain branched compds. (7 and 2% mean abs. percent deviation (MAPD) for viscosity and thermal cond., resp., on av.). However, predictions for some hydrocarbon mixts. and fuels contg. iso-alkanes are often less accurate (16 and 19% MAPD for viscosity and thermal cond., resp., on av.). To improve predictions, it was proposed Rokni et al. to fit one model parameter using an exptl. ref. viscosity or thermal cond. data point, which may not be ideal if exptl. ref. data are not available. In order to make these models more practical, this study fits empirical correlations for the model parameters, so that accurate predictions can be made without fitting model parameters. The correlations enable viscosity and thermal cond. predictions for a wide range of hydrocarbon mixts. and fuels, including those contg. branched alkanes, and no longer require input of any exptl. ref. viscosity or thermal cond. data. The correlations are temp. (fit to data from 288 to 550 K) and pressure (fit to data from 1 to 4,400 bar) dependent and are functions of av. mol. wt., hydrogen-to-carbon ratio, iso-alkane and two-ring sat. concns. Viscosity and thermal cond. predictions were found to improve to within 5 and 2% av. MAPD, resp., relative to exptl. data for the hydrocarbon mixts. and fuels considered in this study.
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Rokni, H. B.; Moore, J. D.; Gupta, A.; McHugh, M. A.; Mallepally, R. R.; Gavaises, M. General method for prediction of thermal conductivity for well-characterized hydrocarbon mixtures and fuels up to extreme conditions using entropy scaling. Fuel 2019, 245, 594– 604, DOI: 10.1016/j.fuel.2019.02.044
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General method for prediction of thermal conductivity for well-characterized hydrocarbon mixtures and fuels up to extreme conditions using entropy scaling
Rokni, Houman B.; Moore, Joshua D.; Gupta, Ashutosh; Hugh, Mark A.; Mallepally, Rajendar R.; Gavaises, Manolis
Fuel (2019), 245 (), 594-604CODEN: FUELAC; ISSN:0016-2361. (Elsevier Ltd.)
A general and efficient technique is developed to predict the thermal cond. of well-characterized hydrocarbon mixts., rocket propellant (RP) fuels, and jet fuels up to high temps. and high pressures (HTHP). The technique is based upon entropy scaling using the group contribution method coupled with the Perturbed-Chain Statistical Assocg. Fluid Theory (PC-SAFT) equation of state. The mixt. no. averaged mol. wt. and hydrogen to carbon ratio are used to define a single pseudo-component to represent the compds. in a well-characterized hydrocarbon mixt. or fuel. With these two input parameters, thermal cond. predictions are less accurate when the mixt. contains significant amts. of iso-alkanes, but the predictions improve when a single thermal cond. data point at a ref. condition is used to fit one model parameter. For eleven binary mixts. and three ternary mixts. at conditions from 288 to 360 K and up to 4,500 bar, thermal conductivities are predicted with mean abs. percent deviations (MAPDs) of 16.0 and 3.0% using the two-parameter and three-parameter models, resp. Thermal conductivities are predicted for three RP fuels and three jet fuels at conditions from 293 to 598 K and up to 700 bar with MAPDs of 14.3 and 2.0% using the two-parameter and three-parameter models, resp.
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Yang, X. X.; Kim, D. C.; May, E. F.; Bell, I. H. Entropy Scaling of Thermal Conductivity: Application to Refrigerants and Their Mixtures. Ind. Eng. Chem. Res. 2021, 60 (35), 13052– 13070, DOI: 10.1021/acs.iecr.1c02154
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Entropy scaling of thermal conductivity: Application to refrigerants and their mixtures
Yang, Xiaoxian; Kim, Dongchan; May, Eric F.; Bell, Ian H.
Industrial & Engineering Chemistry Research (2021), 60 (35), 13052-13070CODEN: IECRED; ISSN:0888-5885. (American Chemical Society)
Residual entropy scaling (RES) of thermal cond. was applied to pure refrigerants, including natural and halogenated refrigerants, and their mixts. The ref. equations of state and the mixt. models implemented in the REFPROP software package were adopted to calc. the residual entropy, and the crit. enhancement of thermal cond. was taken into account with the RES approach for the first time. Exptl. data of 39 pure fluids with more than 38,000 data points and of 31 mixts. with more than 7600 points were collected and analyzed. More than 95.4% of the data (within two std. deviations of the mean) of pure fluids collapse into a global dimensionless residual thermal cond. vs. scaled dimensionless residual entropy curve within 11.1% and those of mixts. are within 8.3%. This smooth, monotonically increasing curve was correlated with a polynomial function contg. only four fitted parameters and one fluid-specific scaling factor. Each pure fluid has its individual scaling factor, and a simple mole-fraction-weighted mixing rule was applied for mixts. The correlation function provides a reliable thermal cond. prediction of pure fluids and, without any addnl. parameters, of mixts. The proposed model yields a similar level of statistical agreement with the exptl. data as the extended corresponding states model, which is the current state-of-the-art and has as many as four more parameters for each pair of components.
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Yang, X.; Xiao, X.; Thol, M.; Richter, M.; Bell, I. H. Linking Viscosity to Equations of State Using Residual Entropy Scaling Theory. Int. J. Thermophys. 2022, 43 (12), 183, DOI: 10.1007/s10765-022-03096-9
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Lemmon, E. W.; Bell, I. H.; Huber, M.; McLinden, M. NIST standard reference database 23: reference fluid thermodynamic and transport properties-REFPROP, Version 10.0. In Natl. Stand. Ref. Data Ser.; (NIST NSRDS); National Institute of Standards and Technology: Gaithersburg, MD, 2018.
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Olchowy, G. A.; Sengers, J. V. A Simplified Representation for the Thermal-Conductivity of Fluids in the Critical Region. Int. J. Thermophys. 1989, 10 (2), 417– 426, DOI: 10.1007/BF01133538
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Frenkel, M.; Chirico, R. D.; Diky, V.; Yan, X.; Dong, Q.; Muzny, C. ThermoData Engine (TDE): software implementation of the dynamic data evaluation concept. J. Chem. Inf. Model 2005, 45 (4), 816– 838, DOI: 10.1021/ci050067b
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ThermoData Engine (TDE): Software Implementation of the Dynamic Data Evaluation Concept
Frenkel, Michael; Chirico, Robert D.; Diky, Vladimir; Yan, Xinjian; Dong, Qian; Muzny, Chris
Journal of Chemical Information and Modeling (2005), 45 (4), 816-838CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
The first full-scale software implementation of the dynamic data evaluation concept {ThermoData Engine (TDE)} is described for thermophys. property data. This concept requires the development of large electronic databases capable of storing essentially all exptl. data known to date with detailed descriptions of relevant metadata and uncertainties. The combination of these electronic databases with expert-system software, designed to automatically generate recommended data based on available exptl. data, leads to the ability to produce critically evaluated data dynamically or 'to order'. Six major design tasks are described with emphasis on the software architecture for automated crit. evaluation including dynamic selection and application of prediction methods and enforcement of thermodn. consistency. The direction of future enhancements is discussed.
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Yang, X.; Richter, M. OilMixProp 1.0: Package for thermophysical properties of oils, common fluids and their mixtures. In International Conference on Screw Machines 2024, September 3–5, Germany, Dortmund.
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Bell, I. H.; Wronski, J.; Quoilin, S.; Lemort, V. Pure and Pseudo-pure Fluid Thermophysical Property Evaluation and the Open-Source Thermophysical Property Library CoolProp. Ind. Eng. Chem. Res. 2014, 53 (6), 2498– 2508, DOI: 10.1021/ie4033999
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Pure and Pseudo-pure Fluid Thermophysical Property Evaluation and the Open-Source Thermophysical Property Library CoolProp
Bell, Ian H.; Wronski, Jorrit; Quoilin, Sylvain; Lemort, Vincent
Industrial & Engineering Chemistry Research (2014), 53 (6), 2498-2508CODEN: IECRED; ISSN:0888-5885. (American Chemical Society)
Over the last few decades, researchers have developed a no. of empirical and theor. models for the correlation and prediction of the thermophys. properties of pure fluids and mixts. treated as pseudo-pure fluids. In this paper, a survey of all the state-of-the-art formulations of thermophys. properties is presented. The most-accurate thermodn. properties are obtained from multiparameter Helmholtz-energy-explicit-type formulations. For the transport properties, a wider range of methods has been employed, including the extended corresponding states method. All of the thermophys. property correlations described here have been implemented into CoolProp, an open-source thermophys. property library. This library is written in C++, with wrappers available for the majority of programming languages and platforms of tech. interest. As of publication, 110 pure and pseudo-pure fluids are included in the library, as well as properties of 40 incompressible fluids and humid air. The source code for the CoolProp library is included as an electronic annex.
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Bell, I. H.; Quoilin, S.; Wronski, J.; Lemort, V. CoolProp: An Open-Source Reference-Quality Thermophysical Property Library. In ASME ORC 2nd International Seminar on ORC Power Systems; DTU Library: Rotterdam, The Netherlands, 2013.
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Wilke, C. R. A Viscosity Equation for Gas Mixtures. J. Chem. Phys. 1950, 18 (4), 517– 519, DOI: 10.1063/1.1747673
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A viscosity equation for gas mixtures
Wilke, C. R.
Journal of Chemical Physics (1950), 18 (), 517-19CODEN: JCPSA6; ISSN:0021-9606.
By application of the kinetic theory, with several simplifying assumptions, the previous equation of Buddenberg and Wilke (C.A. 43, 7281f) was modified to give a general equation for viscosity as a function of mol. wts. and viscosities of the pure components of the mixt. Agreement of the equation with exptl. data is demonstrated for a number of highly irregular binary gas systems and mixts. of 3 to 7 components.
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Chichester, J.; Huber, M. L. Documentation and Assessment of the Transport Property Model for Mixtures Implemented in NIST REFPROP, Version 8.0; National Institute of Standards and Technology:: Gaithersburg, MD, 2008.
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Golubev, I. F.; Sokolova, V. P. Thermal Conductivity of Ammonia at Various Temperatures and Pressures. Teploenergetika 1964, 11 (9), 64– 67
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Richter, G. N.; Sage, B. H. Thermal Conductivity of Fluids. Ammonia. J. Chem. Eng. Data 1964, 9, 75– 78, DOI: 10.1021/je60020a022
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New values of thermal conductivity and specific heat at different temperatures for a series of gases
Senftleben, Hermann
Zeitschrift fuer Angewandte Physik (1964), 17 (2), 86-7CODEN: ZAPHAX; ISSN:0044-2283.
Thermal cond. values from 0 to 400°, and sp. heat values from 0 to 200° were detd. (CA 55, 7952g) and fitted to a power series with 3 consts. The gases included CO2, air, Ar, Kr, HCN, NH3, MeCl, CH2Cl2, EtCl, C2H3Cl, C2H2Cl2, C2HCl3, C2H3CN, CH4, C2H2, C2H6, C2H4, ethylene oxide, C3H8, C3H6, C4H10, C4H8, C4H6, C5H12.
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Shamsetdinov, F. N.; Zaripov, Z. I.; Abdulagatov, I. M.; Huber, M. L.; Gumerov, F. M.; Gabitov, F. R.; Kazakov, A. F. Experimental study of the thermal conductivity of ammonia D water refrigerant mixtures at temperatures from 278 to 356 K and at pressures up to 20 MPa. Int. J. Refrig. 2013, 36, 1347– 1368, DOI: 10.1016/j.ijrefrig.2013.02.008
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Varlashkin, P. G.; Thompson, J. C. Thermal Conductivity of Liquid Ammonia. J. Chem. Eng. Data 1963, 8, 526– 526, DOI: 10.1021/je60019a014
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Measurements of the Thermal Conductivity of Chlorodifluoromethane (HCFC-22) in the Temperature Range from 300 K to 515 K and at Pressures up to 55 MPa
Le Neindre, Bernard; Garrabos, Yves; Sabirzianov, Aidar; Goumerov, Farid
Journal of Chemical and Engineering Data (2001), 46 (2), 193-201CODEN: JCEAAX; ISSN:0021-9568. (American Chemical Society)
We report measurements of the thermal cond. of chlorodifluoromethane (HCFC-22) with a coaxial cylinder cell operating in the steady state. The measurements of the thermal cond. of HCFC-22 were performed along several quasi-isotherms between 300 and 515 K, in the gas phase, in the liq. phase, and in the crit. region. The pressure range covered varies from 0.1 MPa to 55 MPa. On the basis of the fitting of exptl. data, a background equation is provided to calc. the thermal cond. outside the crit. region as a function of temp. and d. A careful anal. of the various sources of errors leads to an estd. uncertainty of the thermal cond., of the order of ± 1.5 %.
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Makita, T.; Tanaka, Y.; Morimoto, Y.; Noguchi, M.; Kubota, H. Thermal Conductivity of Gaseous Fluorocarbon Refrigerants R 12, R13, and R 23, Under Pressure. Int. J. Thermophys. 1981, 2, 249– 268, DOI: 10.1007/BF00504188
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Thermal conductivity of gaseous fluorocarbon refrigerants R 12, R 13, R 22 and R 23, under pressure
Makita, T.; Tanaka, Y.; Morimoto, Y.; Noguchi, M.; Kubota, H.
International Journal of Thermophysics (1981), 2 (3), 249-68CODEN: IJTHDY; ISSN:0195-928X.
The thermal conductivities of 4 gaseous fluorocarbon refrigerants (R 12, R 12, R 22, and R 23) were measured by using a vertical coaxial cylinder app. from about room temp. to 393 K and pressures to ∼7 MPa. The thermal conductivities increase with increasing pressure. The temp. coeff. of thermal cond. at const. pressure, (.vdelta.λ/.vdelta.T)p, is pos. at low pressures and becomes neg. at high pressures. Steep increases occur near the crit. points.
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Tsvetkov, O. B.; Laptev, Y. A. Thermal Conductivities of Freons and Their Binary Mixtures. In Proc Eighth Symposium on Thermophysical Properties; ASME: New York, 1982.
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Tsvetkov, O. B.; Laptyev, Y. A. Thermal-Conductivity of Difluoromonochloromethane in the Critical Region. Int. J. Thermophys. 1991, 12 (1), 53– 65, DOI: 10.1007/BF00506122
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Tsvetkov, O. B.; Laptev, Y. A.; Asambaev, A. G. The thermal conductivity of binary mixtures of liquid R22 with R142b and R152a at low temperatures. Int. J. Thermophys. 1996, 17 (3), 597– 606, DOI: 10.1007/BF01441506
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The thermal conductivity of binary mixtures of liquid R22 and R142b and R152a at low temperatures
Tsvetkov, O. B.; Laptev, Yu. A.; Asambaev, A. G.
International Journal of Thermophysics (1996), 17 (3), 597-606CODEN: IJTHDY; ISSN:0195-928X. (Plenum)
The paper presents the thermal cond. of mixts. of liq. refrigerants. R22/R142b and R22/R152a. The measurements were carried out in the temp. range 160-300 K for pressures from 0.2 to 8.0 MPa in a transient coaxial-cylinder instrument. The uncertainty of the thermal cond. data was estd. to be ±2%. The exptl. method and app. were validated by using the measurements of refrigerant R22. The results presented were used to develop a correlation for the description of the thermal cond. of refrigerants.
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Thermal conduction in H2-D2 mixtures
Archer, C. T.
Proceedings of the Royal Society of London, Series A: Mathematical, Physical and Engineering Sciences (1938), 165 (), 474-85CODEN: PRLAAZ; ISSN:1364-5021.
The thermal conds. at 0° of H2 and D2 are 0.0004182 and 0.0003080 cal. cm.-1 sec.-1. deg.-1, and the accommodation coeffs. (on Pt) are 0.296 and 0.376, resp. Data are given for thermal conds. of 7 mixts., and for 3 temp. coeffs.
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Saxena, S. C.; Tondon, P. K. Experimental Data and Procedures for Predicting Thermal Conductivity of Binary Mixtures of Nonpolar Gases. J. Chem. Eng. Data 1971, 16 (2), 212– 220, DOI: 10.1021/je60049a032
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Experimental data and procedures for predicting thermal conductivity of binary mixtures of nonpolar gases
Saxena, Satish C.; Tondon, P. K.
Journal of Chemical and Engineering Data (1971), 16 (2), 212-20CODEN: JCEAAX; ISSN:0021-9568.
The thermal conds. of Ne, Ar, Kr, Xe, H2, D2 N2, and O2 were measured by using a thick hot-wire metal cell at 5 temps. in the range 40-175°. The soln. of the heat balance equation as developed by Oldham and Luchsinger is employed, and an accuracy was estd. of 1-2% in the recommended abs. cond. values. In this temp. range, the thermal conds. of the binary systems Ne-H2, Ne-N2, Ne-O2, H2-D2, N2-D2, H2-N2, N2-O2, Kr-H2, Xe-H2, Xe-D2, and Xe-Ar are also detd. as a function of compn. On the basis of these exptl. data, the methods of prediction of thermal cond. of mixts. due to Hirschfelder, Mason and Saxena, Mathur and Saxena, Lindsay and Bromley, Ulybin, et al., and Burgoyne and Weinberg are examd. to ascertain their relative accuracies. The framework of Chapman-Enskog kinetic theory in conjunction with the exptl. data on thermal cond. is used to generate the diffusion and viscosity coeffs. for Xe-Ar, Xe-D2, Ne-H2, Ne-N2, and Ne-O2, as representative systems.
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Thermal conductivity of liquids. Binary mixtures of water-methyl alcohol and water-ethyl alcohol
Bates, Oscar Kenneth; Hazzard, George; Palmer, Gerald
Industrial and Engineering Chemistry, Analytical Edition (1938), 10 (), 314-18CODEN: IENAAD; ISSN:0096-4484.
Thermal conds. and temp. coeffs. of thermal cond. for mixts. of water-MeOH and water-EtOH are given. Thermal cond. decreases with percentage of alc., the rate of decrease being greatest for the highest mean temp. and lowest for the lowest mean temp. investigated. The thermal cond. of water increases with increase of temp.; whereas the conds. of both MeOH and EtOH decrease with increase of temp. Mixts. of approx. 50% water with either MeOH or EtOH exhibit a const.-temp. coeff.
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Rastorguev, Y. L.; Ganiev, Y. A. Thermal Conductivity of Aqueous Solutions of Organic Liquids. Russ. J. Phys. Chem. 1966, 40, 869– 871
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Riedel, L. Chem.-Ing.-Technol. 1951, 23, 465, DOI: 10.1002/cite.330231902
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Zhou, J. C.; Che, Y. Y.; Wu, K. J.; Shen, J.; He, C. H. Thermal Conductivity of DMSO + C2H5OH, DMSO + H2O, and DMSO + C2H5OH + H2O Mixtures at T = (278.15 to 338.15) K. J. Chem. Eng. Data 2013, 58, 663– 670, DOI: 10.1021/je301171y
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Thermal Conductivity of DMSO + C2H5OH, DMSO + H2O, and DMSO + C2H5OH + H2O Mixtures at T = (278.15 to 338.15) K
Zhou, Jun-Chao; Che, Yuan-Yuan; Wu, Ke-Jun; Shen, Jian; He, Chao-Hong
Journal of Chemical & Engineering Data (2013), 58 (3), 663-670CODEN: JCEAAX; ISSN:0021-9568. (American Chemical Society)
The thermal conductivities of DMSO + ethanol, DMSO + water, and DMSO + ethanol + water were reported. The measurements, covering a temp. range from (278.15 to 338.15) K were performed by a transient hot-wire technique over the whole concn. range at atm. pressure. The exptl. data of thermal cond. were correlated by the second-order Scheffe polynomial in terms of temp. and wt. fraction. The av. abs. deviation of those correlated values from the exptl. data was 1.35 %. The uncertainty of thermal cond. was ± 2.0 % with a coverage factor of k = 2.
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102
Jeong, S. U.; Kim, M. S.; Ro, S. T. Liquid Thermal Conductivity of Binary Mixtures of Pentafluoroethane (R125) and 1,1,1,2-Tetrafluoroethane (R134a). Int. J. Thermophys. 1999, 20, 55– 62, DOI: 10.1023/A:1021469928377
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103
Kim, D.; Yang, X. X.; Arami-Niya, A.; Rowland, D.; Xiao, X.; Al Ghafri, S. Z. S.; Tsuji, T.; Tanaka, Y.; Seiki, Y.; May, E. F. Thermal Conductivity Measurements of Refrigerant Mixtures Containing Hydrofluorocarbons (HFC-32, HFC-125, HFC-134a), Hydrofluoroolefins (HFO-1234yf), and Carbon Dioxide (CO2). J. Chem. Thermodyn. 2020, 151, 106248 DOI: 10.1016/j.jct.2020.106248
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103
Thermal conductivity measurements of refrigerant mixtures containing hydrofluorocarbons (HFC-32, HFC-125, HFC-134a), hydrofluoroolefins (HFO-1234yf), and carbon dioxide (CO2)
Kim, Dongchan; Yang, Xiaoxian; Arami-Niya, Arash; Rowland, Darren; Xiao, Xiong; Al Ghafri, Saif Z. S.; Tsuji, Tomoya; Tanaka, Yukio; Seiki, Yoshio; May, Eric F.
Journal of Chemical Thermodynamics (2020), 151 (), 106248CODEN: JCTDAF; ISSN:0021-9614. (Elsevier Ltd.)
Thermal cond. measurements of eight binary refrigerant mixts. were conducted in the homogeneous liq. and vapor phases with the transient hot-wire technique. The temp. range of the measurements spanned from (224.3 to 386.6) K with pressures ranging between (1.0 and 6.5) MPa. The binary mixts. were equimolar (R125 + R32), (R32 + R134a), (R32 + CO2), (R125 + R134a), (R125 + CO2), (R134a + R1234yf), (R134a + CO2) and (R1234yf + CO2). Addnl., two multi-component mixts., (R32 + R1234yf + CO2) and (R32 + R1234yf + R134a + R125 + CO2), were investigated. The transient hot-wire app. was validated with measurements of pure CO2 in the liq. and vapor regions. The relative combined expanded uncertainty (k = 2) in the exptl. thermal cond. was on the order of 2.0%. The relative deviations of the measured thermal conductivities in the vapor phase from those calcd. using the extended corresponding states (ECS) model with default binary interaction parameters (BIPs), as implemented in the software REFPROP 10, were between (-12 and +8) %, while those in the liq. phase were between (-15 and +4) %. The new exptl. data were used to tune the BIPs in the ECS model. Significant improvements were obsd. esp. in the liq. phase of the five-component mixt., with the root-mean-square of the relative difference between the exptl. data and the model estn. reduced by a factor of nearly three.
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104
Perkins, R.; Schwarzberg, E.; Gao, X. Experimental Thermal Conductivity Values for Mixtures of R32, R125, R134a, and Propane; NIST Interagency/Internal Report (NISTIR); National Institute of Standards and Technology: Gaithersburg, MD, 1999.
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Assael, M. J.; Charitidou, E.; Avgoustiniatos, S.; Wakeham, W. A. Absolute Measurements of the Thermal Conductivity of Mixtures of Alkene-Glycols with Water. Int. J. Thermophys. 1989, 10, 1127– 1140, DOI: 10.1007/BF00500567
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Absolute measurements of the thermal conductivity of mixtures of alkene-glycols with water
Assael, M. J.; Charitidou, E.; Avgoustiniatos, S.; Wakeham, W. A.
International Journal of Thermophysics (1989), 10 (6), 1127-40CODEN: IJTHDY; ISSN:0195-928X.
New abs. measurements of the thermal cond. of ethylene and propylene glycol and their mixts. with water are presented. The measurements were performed in a tantalum-type transient hot-wire instrument at atm. pressure, in the temp. range 295-360 K. The overall uncertainty of the reported values is estd. to be less than ±0.5%, an est. confirmed by measurements of the thermal cond. of water. The mixts. with water studied have compns. of 25, 50, and 75%, by wt. A recently proposed semiempirical scheme for the prediction of the thermal cond. of pure liqs. is extended to allow the prediction of the thermal cond. of these mixts. from the pure components, as a function of both compn. and temp.
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Bates, O. K.; Hazzard, G. Thermal Conductivity of Alcohols and Glycols. Ind. Eng. Chem. 1945, 37, 193– 195, DOI: 10.1021/ie50422a021
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Bogacheva, I. S.; Zemdikhanov, K. B.; Mukhamedzyanov, G. K.; Sadykov, A. K.; Usmanov, A. G. Heat Conductivity of Mixtures of Organic Liquids. Zh. Fiz. Khim 1980, 54, 1468– 1470
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Thermal conductivity of solutions of some organic liquids
Bogacheva, I. S.; Zemdikhanov, K. B.; Mukhamedzyanov, G. Kh.; Sadykov, A. Kh.; Usmanov, A. G.
Zhurnal Fizicheskoi Khimii (1980), 54 (6), 1468-70CODEN: ZFKHA9; ISSN:0044-4537.
Thermal conductivities were measured at 298-363 K of binary solns. monoethylene glycol(I)-H2O, triethylene glycol(II)-H2O, I-II, I-diethylene glycol, and monoethanolamine-diethanolamine, over the entire concn. ranges.
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Bohne, D.; Fischer, S.; Obermeier, E. Thermal Conductivity, Density, Viscosity, and Prandtl Numbers of Ethylene Glycol-Water Mixtures. Ber. Bunsen-Ges. Phys. Chem. 1984, 88, 739– 742, DOI: 10.1002/bbpc.19840880813
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Thermal conductivity, density, viscosity, and Prandtl-numbers of ethylene glycol-water mixtures
Bohne, D.; Fischer, S.; Obermeier, E.
Berichte der Bunsen-Gesellschaft (1984), 88 (8), 739-42CODEN: BBPCAX; ISSN:0005-9021.
Thermal cond., d., and viscosity were detd. of (CH2OH)2-H2O. The measurements were performed at -20 to 180° for thermal cond., -10 to 150° for d., and -10 to 100° for viscosity. Prandtl nos. calcd. with the own exptl. data and literature values of sp. heat capacity are presented in dependence of temp. and concn.
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Ganiev, Y. A.; Rastorgu, Y. L. Thermal Conductivity of Mixed Non-Electrolyte Solutions. Russ. J. Phys. Chem. 1968, 42, 68
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Grigrev, A. Thermal Conductivity: Water and Water-Organic Systems. Sov. Un. Gov. Bur. Stand., Grozny Oil Inst., Infor. Seri 1985.
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Rastorguev, Y. L.; Ganiev, Y. A. Thermal Conductivity of Organic Liquids. Zh. Fiz. Khim. 1967, 41, 1352
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Riedel, L. Measurement of Thermal Conductivity of Mixtures of Several Organic Compounds with Water. Chem.-Ing.-Technol. 1951, 23, 465, DOI: 10.1002/cite.330231902
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Sun, T.; Teja, A. S. Density, Viscosity and Thermal Conductivity of Aqueous Ethylene, Diethylene and Triethylene Glycol Mixtures between 290 and 450 K. J. Chem. Eng. Data 2003, 48, 198– 202, DOI: 10.1021/je025610o
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Density, Viscosity, and Thermal Conductivity of Aqueous Ethylene, Diethylene, and Triethylene Glycol Mixtures between 290 K and 450 K
Sun, Tongfan; Teja, Amyn S.
Journal of Chemical and Engineering Data (2003), 48 (1), 198-202CODEN: JCEAAX; ISSN:0021-9568. (American Chemical Society)
The d., viscosity, and thermal cond. of ethylene glycol + water, diethylene glycol + water, and triethylene glycol + water mixts. were measured at temps. ranging from 290 to 450 K and concns. ranging from 25 to 100 mol% of glycol. The data obtained are generally in agreement with the limited data available in the literature. Correlation of the data was performed using simple empirical expressions and the generalized corresponding states principle (GCSP). The GCSP method, with two adjustable parameters for each property, offers the potential for judicious extrapolation of d. and transport property data for all glycol + water mixts.
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Abstract
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Figure 1
Figure 1. Characteristic λ_res⁺ vs s⁺ curves of (a) ammonia (58−63) and (b) R22. (64−80) The definitions of Filter 1, 2, and 3 can be found in the footnote of Table 1.
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Figure 2
Figure 2. Scaling factor ξ. The denominator s_crit⁺ is the plus-scaled dimensionless residual entropy at the critical point calculated with REFPROP 10.0 (50) of each pure fluid. The number at the top right of each box indicates the group number. The vertical dashed dotted line denotes ξ/s_crit⁺ = 0.7. Values not shown in the figure: C16:0.29, C22:0.26, methyl stearate: 0.26, parahydrogen: 1.63, orthohydrogen: 1.61, hydrogen: 1.76, helium: 4.21, and deuterium (D2): 1.31. The names used in REFPROP 10.0 were adopted.
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Figure 3
Figure 3. Values of λ_res⁺ as a function of s⁺/ξ of each group of pure fluids, where λ_res⁺ is the dimensionless residual thermal conductivity, s⁺ is the dimensionless residual entropy, and ξ is the scaling factor. The curves are calculated with the global n_gk parameters. All groups are shown at the bottom; at the top, each group is individually illustrated but stacked by powers of 20 and with group number labeled.
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Figure 4
Figure 4. Relative deviations of the experimental thermal conductivity λ_exp from values λ_RES calculated with the RES model. The short line indicates the average relative deviation; the shape shows the distribution of the relative deviation; and the colors are for a clear illustration only. Fluid-specific n_k parameters are preferred, and only if they are not available in Table 3, global parameters n_gk are used.
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Figure 5
Figure 5. Influence of different mixing rules of for m_mix on the prediction of thermal conductivity of mixtures, where x_i represents the mole fraction, y_i represents the mass fraction, and m_i is the molecular mass for component i. Deviation represents the maximum deviation corresponding to the standard deviation of a normal distribution (≈68.2%) of the selected experiment data.
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Figure 6
Figure 6. Statistical summary of the relative deviation of the experimental data from model calculations for binary mixtures. All selected data: all experimental data collected and passed the three filters; Further filtered data: experimental data further filtered so that they can be calculated with the REFPROP models. ARD and AARD: the average relative deviation and the average of the absolute value of relative deviation of the experimental values from the model calculations, respectively. Please note that the blank areas in the figure indicate either the absence of available data or the inability of REFPROP to perform calculations.
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Figure 7
Figure 7. Relation between λ_res⁺ and s⁺ for mixtures that have more than 500 experimental data points: (a) heptane + isooctane, (116−119) (b) R125 + R134a, (102−104) (c) R32 + R134a, (103,104) (d) R125 + R32, (103,120−125) (e) ethanol + water, (89−101) (f) ethylene glycol + water, (97,105−115) (g) propane + R134a, (104) (h) propane + R32, (104) and (i) R32 + R125 + R134a. (103) Different colors and symbols represent experimental data from different sources. For specific literature information, please refer to SI-DPR.
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Figure 8
Figure 8. Thermal conductivity experimental data and model prediction of some fluid mixtures with temperature close to the critical point, where p_r = p/p_c is the reduced pressure relative to critical pressure: (a) CO₂ + ethane, (128) (b) CO₂ + ethylene, (129) and (c) R125 + R143a. (121) The molar fraction of each component is indicated. The critical temperature and pressure were calculated with REFPROP 10.0.
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  A quasi-universal scaling law for atomic transport in simple fluids
  Rosenfeld, Yaakov
  Journal of Physics: Condensed Matter (1999), 11 (28), 5415-5427CODEN: JCOMEL; ISSN:0953-8984. (Institute of Physics Publishing)
  A semiempirical "universal" corresponding-states relationship, for the dimensionless transport coeffs. of dense fluids as functions of the reduced configurational entropy, was proposed more than twenty years ago and established by many simulations. Here it is shown anal., by appealing to Enskog's original results for the inverse-power potentials, that the quasi-universal entropy scaling can be extended also to dil. gases. The analytic form and the possible origin for the entropy scaling for dense fluids are discussed in view of this unexpected result. On the basis of the entropy scaling we predict a min. in the shear viscosity as a function of temp. for all soft inverse-power potentials, in quant. agreement with the available simulations.
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11. 11
  Gnan, N.; Schrøder, T. B.; Pedersen, U. R.; Bailey, N. P.; Dyre, J. C. Pressure-energy correlations in liquids. IV. ″Isomorphs″ in liquid phase diagrams. J. Chem. Phys. 2009, 131 (23), 234504, DOI: 10.1063/1.3265957
  There is no corresponding record for this reference.
12. 12
  Schrøder, T. B.; Gnan, N.; Pedersen, U. R.; Bailey, N. P.; Dyre, J. C. Pressure-energy correlations in liquids. V. Isomorphs in generalized Lennard-Jones systems. J. Chem. Phys. 2011, 134 (16), 164505, DOI: 10.1063/1.3582900
  There is no corresponding record for this reference.
13. 13
  Bell, I. H. Probing the link between residual entropy and viscosity of molecular fluids and model potentials. Proc. Natl. Acad. Sci. U. S. A. 2019, 116 (10), 4070– 4079, DOI: 10.1073/pnas.1815943116
  13
  Probing the link between residual entropy and viscosity of molecular fluids and model potentials
  Bell, Ian H.
  Proceedings of the National Academy of Sciences of the United States of America (2019), 116 (10), 4070-4079CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
  This work investigates the link between residual entropy and viscosity based on wide-ranging, highly accurate exptl. 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 approx. monovariate relationship between residual entropy and reduced viscosity for a wide range of mol. fluids [argon, methane, CO2, SF6, 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 d. scaling for mol. fluids, the viscosity of nonassocg. mol. fluids can be mapped onto the model potentials. This mapping results in a length scale that is proportional to the cube root of exptl. measurable liq. vol. values.
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14. 14
  Bell, I. H. Entropy Scaling of Viscosity-I: A Case Study of Propane. J. Chem. Eng. Data 2020, 65 (6), 3203– 3215, DOI: 10.1021/acs.jced.0c00209
  There is no corresponding record for this reference.
15. 15
  Bell, I. H. Entropy Scaling of Viscosity-II: Predictive Scheme for Normal Alkanes. J. Chem. Eng. Data 2020, 65 (11), 5606– 5616, DOI: 10.1021/acs.jced.0c00749
  There is no corresponding record for this reference.
16. 16
  Bell, I. H.; Messerly, R.; Thol, M.; Costigliola, L.; Dyre, J. C. Modified Entropy Scaling of the Transport Properties of the Lennard-Jones Fluid. J. Phys. Chem. B 2019, 123 (29), 6345– 6363, DOI: 10.1021/acs.jpcb.9b05808
  16
  Modified Entropy Scaling of the Transport Properties of the Lennard-Jones Fluid
  Bell, Ian H.; Messerly, Richard; Thol, Monika; Costigliola, Lorenzo; Dyre, Jeppe C.
  Journal of Physical Chemistry B (2019), 123 (29), 6345-6363CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
  Rosenfeld proposed two different scaling approaches to model the transport properties of fluids, sepd. by 22 years, one valid in the dil. gas, and another in the liq. phase. In this work, we demonstrate that these two limiting cases can be connected through the use of a novel approach to scaling transport properties and a bridging function. This approach, which is empirical and not derived from theory, is used to generate ref. correlations for the transport properties of the Lennard-Jones 12-6 fluid of viscosity, thermal cond., and self-diffusion. This approach, with a very simple functional form, allows for the reprodn. of the most accurate simulation data to within nearly their statistical uncertainty. The correlations are used to confirm that for the Lennard-Jones fluid the appropriately scaled transport properties are nearly monovariate functions of the excess entropy from low-d. gases into the supercooled phase and up to extreme temps. This study represents the most comprehensive metastudy of the transport properties of the Lennard-Jones fluid to date.
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17. 17
  Yang, X. X.; Xiao, X.; May, E. F.; Bell, I. H. Entropy Scaling of Viscosity-III: Application to Refrigerants and Their Mixtures. J. Chem. Eng. Data 2021, 66 (3), 1385– 1398, DOI: 10.1021/acs.jced.0c01009
  There is no corresponding record for this reference.
18. 18
  Al Ghafri, S. Z.; Akhfash, M.; Hughes, T. J.; Xiao, X.; Yang, X.; May, E. F. High pressure viscosity measurements of ternary (methane+ propane+ heptane) mixtures. Fuel Process. Technol. 2021, 223, 106984 DOI: 10.1016/j.fuproc.2021.106984
  There is no corresponding record for this reference.
19. 19
  Kim, D.; Liu, H. T.; Yang, X. X.; Yang, F. F.; Morfitt, J.; Arami-Niya, A.; Ryu, M.; Duan, Y. Y.; May, E. F. Thermal conductivity measurements and correlations of pure R1243zf and binary mixtures of R32+R1243zf and R32+R1234yf Int. J. Refrig. 2021, 131, 990– 999, DOI: 10.1016/j.ijrefrig.2021.07.019
  There is no corresponding record for this reference.
20. 20
  Yang, X. X.; Hanzelmann, C.; Feja, S.; Trusler, J. P. M.; Richter, M. Thermophysical Property Modeling of Lubricant Oils and Their Mixtures with Refrigerants Using a Minimal Set of Experimental Data. Ind. Eng. Chem. Res. 2023, 62 (44), 18736– 18749, DOI: 10.1021/acs.iecr.3c02474
  There is no corresponding record for this reference.
21. 21
  Yang, X. X.; Liu, H. T.; Chen, S. H.; Kim, D.; Yang, F. F.; Arami-Niya, A.; Duan, Y. Y. Viscosity of binary refrigerant mixtures of R32+R1234yf and R32+R1243zf. Int. J. Refrig. 2021, 128, 197– 205, DOI: 10.1016/j.ijrefrig.2020.11.020
  21
  Viscosity of binary refrigerant mixtures of R32 + R1234yf and R32 + R1243zf
  Yang, Xiaoxian; Liu, Hangtao; Chen, Shi Hai; Kim, Dongchan; Yang, Fufang; Arami-Niya, Arash; Duan, Yuanyuan
  International Journal of Refrigeration (2021), 128 (), 197-205CODEN: IJRFDI; ISSN:0140-7007. (Elsevier Ltd.)
  Viscosity measurements of six binary mixts. of R32+R1234yf and R32+R1243zf at different compns. were conducted in the homogenous liq. and gas phases with a vibrating-wire viscometer in the temp. range from (254 to 383) K and pressures from (1 to 8) MPa. The measurement system was verified with the measurements of pure carbon dioxide and R32 in homogenous liq. and gas phases. The relative combined expanded uncertainties (k = 2) in the exptl. viscosity of the mixts. are generally from 3.2% to 5.0%. The measured viscosities agree with the calcns. of the extended corresponding state model implemented in the software package REFPROP 10.0 within 10% and mainly within 5%. The parameters of the residual entropy scaling model incorporating cubic-plus-assocn. equation of state (RES-CPA model) for the viscosity of pure R1243zf and binary R32 + R1243zf mixt. were detd. The relative deviation of the measured viscosities from values calcd. with the RES-CPA model is mainly within 6% in the liq. phase and 10% in the gas phase.
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22. 22
  Yang, X.; Xiao, X.; Thol, M.; Richter, M.; Bell, I. A Residual Entropy Scaling Approach for Viscosity of Refrigerants, Other Fluids, and Their Mixtures. In Proceedings of the 6th International Congress of Refrigeration; Paris, France, August 21–25, 2023.
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23. 23
  Liu, H.; Yang, F.; zhang, K.; Duan, Y.; Yang, Z. Residual Entropy Scaling Model for the Viscosity of Noble Gases. Gongcheng Rewuli Xuebao 2021, 42, 1– 8
  There is no corresponding record for this reference.
24. 24
  Liu, H. T.; Yang, F. F.; Yang, X. X.; Yang, Z.; Duan, Y. Y. Modeling the thermal conductivity of hydrofluorocarbons, hydrofluoroolefins and their binary mixtures using residual entropy scaling and cubic-plus-association equation of state. J. Mol. Liq. 2021, 330, 115612 DOI: 10.1016/j.molliq.2021.115612
  24
  Modeling the thermal conductivity of hydrofluorocarbons, hydrofluoroolefins and their binary mixtures using residual entropy scaling and cubic-plus-association equation of state
  Liu, Hangtao; Yang, Fufang; Yang, Xiaoxian; Yang, Zhen; Duan, Yuanyuan
  Journal of Molecular Liquids (2021), 330 (), 115612CODEN: JMLIDT; ISSN:0167-7322. (Elsevier B.V.)
  Thermal cond. strongly impacts heat transfer, and thus is an important thermophys. property for refrigeration and medium-low-temp. heat utilization systems. In this work, the residual entropy scaling incorporating cubic-plus-assocn. equation of state, as a convenient and robust modeling approach for the transport properties of pure and mixt. fluids of which the exptl. data are scarce or unavailable, is extended to the thermal cond. of hydrofluorocarbons, hydrofluoroolefins, and their binary mixts. For all the investigated pure and mixt. fluids, the dependence of the thermal cond. on the thermodn. state is reduced to a 'universal' univariate function of the rescaled residual entropy with one adjustable parameter for each pure fluid and no further adjustable parameter for mixts. A new formulation of the ref. thermal cond. is proposed to improve the accuracy for the binary mixts. The model reproduces the thermal cond. of the investigated pure and mixt. fluids with the root mean square deviation of 2.9% in gas, liq., and supercrit. regions. The lack or uneven distribution of the data is overcome based on the residual entropy scaling with the extensive data of R134a as a ref.
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25. 25
  Liu, H. T.; Yang, F. F.; Yang, Z.; Duan, Y. Y. Modeling the viscosity of hydrofluorocarbons, hydrofluoroolefins and their binary mixtures using residual entropy scaling and cubic-plus-association equation of state. J. Mol. Liq. 2020, 308, 113027 DOI: 10.1016/j.molliq.2020.113027
  25
  Modeling the viscosity of hydrofluorocarbons, hydrofluoroolefins and their binary mixtures using residual entropy scaling and cubic-plus-association equation of state
  Liu, Hangtao; Yang, Fufang; Yang, Zhen; Duan, Yuanyuan
  Journal of Molecular Liquids (2020), 308 (), 113027CODEN: JMLIDT; ISSN:0167-7322. (Elsevier B.V.)
  Hydrofluorocarbons (HFCs), hydrofluoroolefins (HFOs), and their binary mixts. are widely-used working fluids in moderate and low temp. energy systems. An accurate viscosity model is the cornerstone for the economic and conceptual optimization of the energy utilization systems. In this work, we apply residual entropy scaling and the cubic-plus-assocn. (CPA) equation of state to HFCs, HFOs, and their binary mixts. The reduced viscosity (real fluid viscosity divided by dil. gas viscosity) of 14 pure fluids are correlated to a univariate function of the residual entropy, which is calcd. with the CPA equation of state, a model that was recently adapted for the thermodn. properties of HFCs/HFOs. Then the viscosity of 10 binary mixts. are predicted by the model without introducing any further adjustable parameters. The present model reproduces the viscosity of the investigated pure fluids and mixts. accurately in both the gas and liq. phases and presents reliable predictions in temp. and pressure ranges in which the exptl. data are scarce or unavailable.
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26. 26
  Liu, H. T.; Yang, F. F.; Yang, Z.; Duan, Y. Y. Crossover residual entropy scaling of the viscosity and thermal conductivity of carbon dioxide. J. Mol. Liq. 2022, 368, 120799 DOI: 10.1016/j.molliq.2022.120799
  There is no corresponding record for this reference.
27. 27
  Kang, K.; Gu, Y. X.; Wang, X. P. Assessment and development of the viscosity prediction capabilities of entropy scaling method coupled with a modified binary interaction parameter estimation model for refrigerant blends. J. Mol. Liq. 2022, 358, 119184 DOI: 10.1016/j.molliq.2022.119184
  There is no corresponding record for this reference.
28. 28
  Kang, K.; Li, X. L.; Gu, Y. X.; Wang, X. P. Thermal conductivity prediction of pure refrigerants and mixtures based on entropy-scaling concept. J. Mol. Liq. 2022, 368, 120568 DOI: 10.1016/j.molliq.2022.120568
  There is no corresponding record for this reference.
29. 29
  Kang, K.; Yang, S.; Gu, Y.; Wang, X. Density and viscosity measurement of R513A and a modified residual entropy scaling model for predicting the viscosity of HFC/HFO refrigerants. Int. J. Refrig. 2024, 162, 204– 214, DOI: 10.1016/j.ijrefrig.2024.04.008
  There is no corresponding record for this reference.
30. 30
  Hopp, M.; Gross, J. Thermal Conductivity of Real Substances from Excess Entropy Scaling Using PCP-SAFT. Ind. Eng. Chem. Res. 2017, 56 (15), 4527– 4538, DOI: 10.1021/acs.iecr.6b04289
  30
  Thermal Conductivity of Real Substances from Excess Entropy Scaling Using PCP-SAFT
  Hopp, Madlen; Gross, Joachim
  Industrial & Engineering Chemistry Research (2017), 56 (15), 4527-4538CODEN: IECRED; ISSN:0888-5885. (American Chemical Society)
  Entropy scaling is an intriguingly simple approach for correlating and predicting transport properties of real substances and mixts. It is convincingly documented in the literature that entropy scaling is indeed a firm concept for the shear viscosity of real substances, including hydrogen bonding species and strongly nonspherical species. We investigate whether entropy scaling is applicable for thermal cond. It is shown that the dimensionless thermal cond. (thermal cond. divided by a ref. thermal cond.) does not show a single-variable dependence on residual entropy, for obvious choices of a ref. thermal cond. We perform a detailed anal. of exptl. data and propose a ref. thermal cond. that is itself a simple function of the residual entropy. We then obtain good scaling behavior for the entire fluid region for water and 147 org. substances from various chem. families: linear and branched alkanes, alkenes, aldehydes, aroms., ethers, esters, ketones, alcs., and acids. The residual entropy is calcd. from the Perturbed Chain Polar Statistical Assocg. Fluid Theory equation of state. The correlation of exptl. data requires two parameters for pure substances with scarce exptl. data and up to five parameters for exptl. well-characterized species. The correlation results for all substances lead to av. relative deviations of 4.2% to exptl. data. To further assess the approach, we analyze extrapolations to states not covered by exptl. data and find very satisfying results.
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31. 31
  Hopp, M.; Gross, J. Thermal Conductivity from Entropy Scaling: A Group-Contribution Method. Ind. Eng. Chem. Res. 2019, 58 (44), 20441– 20449, DOI: 10.1021/acs.iecr.9b04289
  31
  Thermal Conductivity from Entropy Scaling: A Group-Contribution Method
  Hopp, Madlen; Gross, Joachim
  Industrial & Engineering Chemistry Research (2019), 58 (44), 20441-20449CODEN: IECRED; ISSN:0888-5885. (American Chemical Society)
  Entropy scaling has proven to be a powerful method for calcg. transport properties. The applicability of the entropy scaling approach to predict the viscosity, thermal cond. and self-diffusion coeffs. of pure substances based on substance-specific parameters was over last years convincingly demonstrated in literature. In this work we derive a predictive method for the thermal cond. based on entropy scaling. The model is developed as a group-contribution approach, where substances are considered to be composed of chem. (functional) groups. The excess entropy is calcd. using the group-contribution PCP-SAFT equation of state. The model is applicable for gaseous phases and for liq.-phase conditions covering wide ranges of temp. and pressure. We consider pure fluids from various chem. families, namely alkanes, branched alkanes, cyclic alkanes, alkenes, aldehydes, aroms., esters, ethers, ketones and alcs., and some individual substances, such as water, carbon dioxide and alike. We propose parameters of 29 chem. groups, by considering 231 substances with more than 50,000 exptl. data points The group-contribution method for the thermal cond. proposed in this work is shown to be in convincing agreement with exptl. data, with 6.17% av. abs. deviation for all considered data points.
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32. 32
  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, 58 (39), 18432– 18438, DOI: 10.1021/acs.iecr.9b03998
  32
  Thermal Conductivity via Entropy Scaling: An Approach That Captures the Effect of Intramolecular Degrees of Freedom
  Hopp, Madlen; Mele, Julia; Hellmann, Robert; Gross, Joachim
  Industrial & Engineering Chemistry Research (2019), 58 (39), 18432-18438CODEN: IECRED; ISSN:0888-5885. (American Chemical Society)
  The thermal cond. of gases depends strongly on the vibrational and rotational degrees of freedom of the mol. under consideration. Entropy scaling is based on the residual entropy, which does not capture the intramol. and rotational contributions. This study proposes a model for the thermal cond. that accounts for these degrees of freedom. We use the Chapman-Cowling approxn., where contributions of internal degrees of freedom to the thermal cond. of an ideal gas are related to the self-diffusion coeff. A resulting expression for the thermal cond. is used as a ref. in entropy scaling. We find exptl. values for thermal conductivities in the entire fluid range to be (to good approxn.) a function of residual entropy only. This study shows that entropy scaling is a strong approxn. also for thermal cond., provided a suitable expression is chosen for the ref. thermal cond.
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33. 33
  Lötgering-Lin, O.; Fischer, M.; Hopp, M.; Gross, J. Pure Substance and Mixture Viscosities Based on Entropy Scaling and an Analytic Equation of State. Ind. Eng. Chem. Res. 2018, 57 (11), 4095– 4114, DOI: 10.1021/acs.iecr.7b04871
  There is no corresponding record for this reference.
34. 34
  Lötgering-Lin, O.; Gross, J. Group Contribution Method for Viscosities Based on Entropy Scaling Using the Perturbed-Chain Polar Statistical Associating Fluid Theory. Ind. Eng. Chem. Res. 2015, 54 (32), 7942– 7952, DOI: 10.1021/acs.iecr.5b01698
  There is no corresponding record for this reference.
35. 35
  Lötgering-Lin, O.; Schöniger, A.; Nowak, W.; Gross, J. Bayesian Model Selection Helps To Choose Objectively between Thermodynamic Models: A Demonstration of Selecting a Viscosity Model Based on Entropy Scaling. Ind. Eng. Chem. Res. 2016, 55 (38), 10191– 10207, DOI: 10.1021/acs.iecr.6b02671
  There is no corresponding record for this reference.
36. 36
  Sauer, E.; Stavrou, M.; Gross, J. Comparison between a Homo- and a Heterosegmented Group Contribution Approach Based on the Perturbed-Chain Polar Statistical Associating Fluid Theory Equation of State. Ind. Eng. Chem. Res. 2014, 53 (38), 14854– 14864, DOI: 10.1021/ie502203w
  36
  Comparison between a Homo- and a Heterosegmented Group Contribution Approach Based on the Perturbed-Chain Polar Statistical Associating Fluid Theory Equation of State
  Sauer, Elmar; Stavrou, Marina; Gross, Joachim
  Industrial & Engineering Chemistry Research (2014), 53 (38), 14854-14864CODEN: IECRED; ISSN:0888-5885. (American Chemical Society)
  Depending on the mol. model, group contribution (GC) approaches based on the statistical assocg. fluid theory (SAFT) can be classified in homosegmented and heterosegmented GC approaches. In homosegmented GC approaches, mols. are modeled as chains composed of identical segments. Heterosegmented GC approaches, on the other hand, consider mol. chains composed of different segment types and thus maintain a more detailed picture of real mols. Therefore, heterosegmented GC approaches are arguably more phys. realistic and ought to give more accurate descriptions of thermodn. properties. In this work, we evaluate the performance of a homosegmented and a heterosegmented GC approach based on the perturbed-chain polar SAFT (PCP-SAFT) equation of state (EoS). To ensure a meaningful comparison between both GC approaches, a dipole term for the heterosegmented GC approach is formulated. Group parameters of 22 functional groups were adjusted to pure component property data. The comparison between both GC approaches shows that the heterosegmented GC approach leads to significantly better agreement with exptl. data for various chem. families.
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37. 37
  Vijande, J.; Piñeiro, M. M.; Bessières, D.; Saint-Guirons, H.; Legido, J. L. Description of PVT behaviour of hydrofluoroethers using the PC-SAFT EOS. Phys. Chem. Chem. Phys. 2004, 6 (4), 766– 770, DOI: 10.1039/B312223A
  There is no corresponding record for this reference.
38. 38
  Dehlouz, A.; Jaubert, J. N.; Galliero, G.; Bonnissel, M.; Privat, R. Combining the entropy-scaling concept and cubic- or SAFT equations of state for modelling thermal conductivities of pure fluids. Int. J. Heat Mass Transfer 2022, 196, 123286 DOI: 10.1016/j.ijheatmasstransfer.2022.123286
  38
  Combining the entropy-scaling concept and cubic- or SAFT equations of state for modelling thermal conductivities of pure fluids
  Dehlouz, Aghilas; Jaubert, Jean-Noel; Galliero, Guillaume; Bonnissel, Marc; Privat, Romain
  International Journal of Heat and Mass Transfer (2022), 196 (), 123286CODEN: IJHMAK; ISSN:0017-9310. (Elsevier Ltd.)
  The transport properties of a fluid show a complex dependence with temp. and pressure due to the combination of different phenomena occurring at the microscopic scale. The entropy scaling concept aims at describing this complex behavior by expressing reduced transport properties as one-variable functions of the Tv-residual entropy, a thermodn. quantity that can be straightforwardly estd. with an equation of state (EoS). In this work, a reformulated version of Rosenfeld's original entropy scaling approach is proposed in order to calc. the thermal conductivities of pure fluids. A specifically developed reduced thermal cond. expression was correlated to a function of the Tv-residual entropy that was recently proposed by our group to correlate viscosities and self-diffusion coeffs. The thermodn. properties involved in the definition of the entropy-scaling variables (that are the residual entropies, densities, heat capacities) were estd. with either the I-PC-SAFT or the tc-PR equations of state (EoSs) thus leading to the definition of two different models. Each of them was validated against a large database of around 90,000 exptl. thermal conductivities encompassing liq., gas and supercrit. states for 119 chem. species belonging to 11 chem. families such as n-alkanes, alkenes, alcs., HFC-CFC etc. For each model, component-specific, chem.-family specific and universal parameters were proposed. Working with the I-PC-SAFT and tc-PR EoSs, the obtained MAPEs (Mean Abs. Percent Errors) are resp. 3.3% and 3.4% when the model parameters are considered as component-specific, 9.7% and 5.6% when they are selected as chem.-family specific meanwhile they are 11.2% and 9.2% when they are assumed to be universal.
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39. 39
  Rosenfeld, Y. Quasi-universal scaling law for atomic transport in simple fluids. J. Phys. IV 2000, 10 (P5), 129– 134, DOI: 10.1051/jp4:2000517
  There is no corresponding record for this reference.
40. 40
  Le Guennec, Y.; Privat, R.; Jaubert, J.-N. Development of the translated-consistent tc-PR and tc-RK cubic equations of state for a safe and accurate prediction of volumetric, energetic and saturation properties of pure compounds in the sub-and super-critical domains. Fluid Phase Equilib. 2016, 429, 301– 312, DOI: 10.1016/j.fluid.2016.09.003
  40
  Development of the translated-consistent tc-PR and tc-RK cubic equations of state for a safe and accurate prediction of volumetric, energetic and saturation properties of pure compounds in the sub- and super-critical domains
  Le Guennec, Yohann; Privat, Romain; Jaubert, Jean-Noel
  Fluid Phase Equilibria (2016), 429 (), 301-312CODEN: FPEQDT; ISSN:0378-3812. (Elsevier B.V.)
  In this paper, translated and consistent versions of the Peng-Robinson (tc-PR) and Redlich-Kwong (tc-RK) cubic equations of state (CEoS) are developed. The adjective consistent means that the α-function used in such models passes the consistency test we recently developed and which guarantees safe extrapolation in the supercrit. region and safe VLE calcn. in multi-component systems. The adjective translated means that a vol. translation aimed at exactly reproducing the exptl. satd. liq. vol. at a reduced temp. of 0.8 was used. The key conclusion of this paper is that the tc-PR EoS is certainly the safest and the most accurate 3-parameter cubic EoS ever published. Indeed the av. deviations over roughly 1000 compds. belonging to different chem. families are: ΔPsat<1 %, ΔvapH = ΔcsatP,L = 2% and ΔvsatL(Tr < 0.9) = 2.3%. In the case of a lack of exptl. data to fit the 3 parameters of the α-function and to det. the value of the vol. correction, the second part of this study aims at providing a generalized version of the tc-PR and tc-RK CEoS in which all parameters can be estd. from the mere knowledge of the acentric factor.
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41. 41
  Moine, E.; Piña-Martinez, A.; Jaubert, J. N.; Sirjean, B.; Privat, R. I-PC-SAFT: An Industrialized Version of the Volume-Translated PC-SAFT Equation of State for Pure Components, Resulting from Experience Acquired All through the Years on the Parameterization of SAFT-Type and Cubic Models. Ind. Eng. Chem. Res. 2019, 58 (45), 20815– 20827, DOI: 10.1021/acs.iecr.9b04660
  There is no corresponding record for this reference.
42. 42
  Yang, F. F.; Liu, Q.; Duan, Y. Y.; Yang, Z. Crossover multiparameter equation of state: General procedure and demonstration with carbon dioxide. Fluid Phase Equilib. 2019, 494, 161– 171, DOI: 10.1016/j.fluid.2019.04.035
  42
  Crossover multiparameter equation of state: General procedure and demonstration with carbon dioxide
  Yang, Fufang; Liu, Qiang; Duan, Yuanyuan; Yang, Zhen
  Fluid Phase Equilibria (2019), 494 (), 161-171CODEN: FPEQDT; ISSN:0378-3812. (Elsevier B.V.)
  The multiparameter equation of state represents exptl. data in wide ranges of temp. and d. with superb accuracy. However, at the crit. point, all classical models fail in describing the asymptotic behavior of thermodn. properties, which is governed by the renormalization group (RG) theory. Using the crossover method, the classical models far from the crit. point can be transformed to the RG theory at the crit. point. Here we validate the procedure of combining the crossover method with the multiparameter equation of state through comparison with exptl. data and the original multiparameter equation of state, and testing against the qual. criterion of characteristic curves. We select carbon dioxide as a demonstration due to its data availability and qualification as a benchmark fluid for thermodn. property modeling. We describe in detail the contribution of different types of terms in the crossover method and original multiparameter equation of state to thermodn. properties. Furthermore, we propose twin Gaussian terms to compensate for the loss of accuracy near the coexistence curve upon removing the non-anal. terms and leave the anal. part of the formulation unaltered. With a slight and acceptable loss of accuracy in the crossover region, the crossover method enforces the asymptotic singular behavior and crit. exponents at the crit. point. Far from the crit. point, the present model transforms to the original model and retains the superb accuracy of the latter.
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43. 43
  Fouad, W. A. Thermal Conductivity of Pure Fluids and Multicomponent Mixtures Using Residual Entropy Scaling with PC-SAFT-Application to Refrigerant Blends. J. Chem. Eng. Data 2020, 65 (12), 5688– 5697, DOI: 10.1021/acs.jced.0c00682
  There is no corresponding record for this reference.
44. 44
  Gross, J.; Sadowski, G. Perturbed-chain SAFT: An equation of state based on a perturbation theory for chain molecules. Ind. Eng. Chem. Res. 2001, 40 (4), 1244– 1260, DOI: 10.1021/ie0003887
  44
  Perturbed-Chain SAFT: An Equation of State Based on a Perturbation Theory for Chain Molecules
  Gross, Joachim; Sadowski, Gabriele
  Industrial & Engineering Chemistry Research (2001), 40 (4), 1244-1260CODEN: IECRED; ISSN:0888-5885. (American Chemical Society)
  A modified statistical assocg. fluid theory (SAFT) equation of state is developed by applying the perturbation theory of Barker and Henderson to a hard-chain ref. fluid. With conventional one-fluid mixing rules, the equation of state is applicable to mixts. of small spherical mols. such as gases, nonspherical solvents, and chainlike polymers. The three pure-component parameters required for nonassocg. mols. were identified for 78 substances by correlating vapor pressures and liq. vols. The equation of state gives good fits to these properties and agrees well with caloric properties. When applied to vapor-liq. equil. of mixts., the equation of state shows substantial predictive capabilities and good precision for correlating mixts. Comparisons to the SAFT version of Huang and Radosz reveal a clear improvement of the proposed model. A brief comparison with the Peng-Robinson model is also given for vapor-liq. equil. of binary systems, confirming the good performance of the suggested equation of state. The applicability of the proposed model to polymer systems was demonstrated for high-pressure liq.-liq. equil. of a polyethylene mixt. The pure-component parameters of polyethylene were obtained by extrapolating pure-component parameters of the n-alkane series to high mol. wts.
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45. 45
  Yang, F. F.; Chu, Q. F.; Liu, Q.; Duan, Y. Y.; Yang, Z. The cubic-plus-association equation of state for hydrofluorocarbons, hydrofluoroolefins, and their binary mixtures. Chem. Eng. Sci. 2019, 209, 115182 DOI: 10.1016/j.ces.2019.115182
  45
  The cubic-plus-association equation of state for hydrofluorocarbons, hydrofluoroolefins, and their binary mixtures
  Yang, Fufang; Chu, Qingfu; Liu, Qiang; Duan, Yuanyuan; Yang, Zhen
  Chemical Engineering Science (2019), 209 (), 115182CODEN: CESCAC; ISSN:0009-2509. (Elsevier Ltd.)
  Hydrofluorocarbons, hydrofluoroolefins, and their mixts. are widely used as working fluids in energy systems. Weak hydrogen bond exists in these fluids and thus contribute to their thermodn. properties. In this work, we account for the contribution of the weak hydrogen bond by tailoring the cubic-plus-assocn. (CPA) equation of state (EoS) and its parameter fitting procedure. Overfitting to the liq. properties is avoided by introducing the satd. vapor d. into the fitting objective function. The EoS is extended to binary mixts. using the van der Waals mixing rules and Elliot combining rule in which process solving the cross-assocn. fraction is reduced from an equation set consisting of 4 nonlinear equations to a single nonlinear equation. The performance of the present model is investigated in terms of the vapor-liq. equil. (VLE) and volumetric properties of 15 pure fluids and 40 binary mixts. using fitted and zero binary interaction parameter, and is compared with the ref. data, a CPA EoS that uses the traditional parameter fitting procedure, the Soave-Redlich-Kwong (SRK) EoS, and a vol.-translated SRK EoS. The present model (including the EoS and fitting procedure) accurately reproduces the vapor pressure, d., and second virial coeff. for the pure fluids and binary mixts., and is the only valid model among the investigated models for both the VLE and the volumetric properties in both liq. and vapor phases. The contribution of the assocn. term to the pressure is also shown in the temp.-d. diagram, presenting a similar behavior as that in water in which the effect of the hydrogen bond is comparatively more pronounced.
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46. 46
  Rokni, H. B.; Moore, J. D.; Gavaises, M. Entropy-scaling based pseudo-component viscosity and thermal conductivity models for hydrocarbon mixtures and fuels containing iso-alkanes and two-ring saturates. Fuel 2021, 283, 118877 DOI: 10.1016/j.fuel.2020.118877
  46
  Entropy-scaling based pseudo-component viscosity and thermal conductivity models for hydrocarbon mixtures and fuels containing iso-alkanes and two-ring saturates
  Rokni, Houman B.; Moore, Joshua D.; Gavaises, Manolis
  Fuel (2021), 283 (), 118877CODEN: FUELAC; ISSN:0016-2361. (Elsevier Ltd.)
  Recently, Rokni et al. developed entropy-scaling based pseudo-component techniques to predict the viscosity and thermal cond. of hydrocarbon mixts. and fuels up to high temp. and pressure conditions using only two calcd. or measured mixt. properties (no. av. mol. wt. and hydrogen-to-carbon ratio). The models are accurate for many hydrocarbon mixts. that do not contain branched compds. (7 and 2% mean abs. percent deviation (MAPD) for viscosity and thermal cond., resp., on av.). However, predictions for some hydrocarbon mixts. and fuels contg. iso-alkanes are often less accurate (16 and 19% MAPD for viscosity and thermal cond., resp., on av.). To improve predictions, it was proposed Rokni et al. to fit one model parameter using an exptl. ref. viscosity or thermal cond. data point, which may not be ideal if exptl. ref. data are not available. In order to make these models more practical, this study fits empirical correlations for the model parameters, so that accurate predictions can be made without fitting model parameters. The correlations enable viscosity and thermal cond. predictions for a wide range of hydrocarbon mixts. and fuels, including those contg. branched alkanes, and no longer require input of any exptl. ref. viscosity or thermal cond. data. The correlations are temp. (fit to data from 288 to 550 K) and pressure (fit to data from 1 to 4,400 bar) dependent and are functions of av. mol. wt., hydrogen-to-carbon ratio, iso-alkane and two-ring sat. concns. Viscosity and thermal cond. predictions were found to improve to within 5 and 2% av. MAPD, resp., relative to exptl. data for the hydrocarbon mixts. and fuels considered in this study.
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47. 47
  Rokni, H. B.; Moore, J. D.; Gupta, A.; McHugh, M. A.; Mallepally, R. R.; Gavaises, M. General method for prediction of thermal conductivity for well-characterized hydrocarbon mixtures and fuels up to extreme conditions using entropy scaling. Fuel 2019, 245, 594– 604, DOI: 10.1016/j.fuel.2019.02.044
  47
  General method for prediction of thermal conductivity for well-characterized hydrocarbon mixtures and fuels up to extreme conditions using entropy scaling
  Rokni, Houman B.; Moore, Joshua D.; Gupta, Ashutosh; Hugh, Mark A.; Mallepally, Rajendar R.; Gavaises, Manolis
  Fuel (2019), 245 (), 594-604CODEN: FUELAC; ISSN:0016-2361. (Elsevier Ltd.)
  A general and efficient technique is developed to predict the thermal cond. of well-characterized hydrocarbon mixts., rocket propellant (RP) fuels, and jet fuels up to high temps. and high pressures (HTHP). The technique is based upon entropy scaling using the group contribution method coupled with the Perturbed-Chain Statistical Assocg. Fluid Theory (PC-SAFT) equation of state. The mixt. no. averaged mol. wt. and hydrogen to carbon ratio are used to define a single pseudo-component to represent the compds. in a well-characterized hydrocarbon mixt. or fuel. With these two input parameters, thermal cond. predictions are less accurate when the mixt. contains significant amts. of iso-alkanes, but the predictions improve when a single thermal cond. data point at a ref. condition is used to fit one model parameter. For eleven binary mixts. and three ternary mixts. at conditions from 288 to 360 K and up to 4,500 bar, thermal conductivities are predicted with mean abs. percent deviations (MAPDs) of 16.0 and 3.0% using the two-parameter and three-parameter models, resp. Thermal conductivities are predicted for three RP fuels and three jet fuels at conditions from 293 to 598 K and up to 700 bar with MAPDs of 14.3 and 2.0% using the two-parameter and three-parameter models, resp.
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48. 48
  Yang, X. X.; Kim, D. C.; May, E. F.; Bell, I. H. Entropy Scaling of Thermal Conductivity: Application to Refrigerants and Their Mixtures. Ind. Eng. Chem. Res. 2021, 60 (35), 13052– 13070, DOI: 10.1021/acs.iecr.1c02154
  48
  Entropy scaling of thermal conductivity: Application to refrigerants and their mixtures
  Yang, Xiaoxian; Kim, Dongchan; May, Eric F.; Bell, Ian H.
  Industrial & Engineering Chemistry Research (2021), 60 (35), 13052-13070CODEN: IECRED; ISSN:0888-5885. (American Chemical Society)
  Residual entropy scaling (RES) of thermal cond. was applied to pure refrigerants, including natural and halogenated refrigerants, and their mixts. The ref. equations of state and the mixt. models implemented in the REFPROP software package were adopted to calc. the residual entropy, and the crit. enhancement of thermal cond. was taken into account with the RES approach for the first time. Exptl. data of 39 pure fluids with more than 38,000 data points and of 31 mixts. with more than 7600 points were collected and analyzed. More than 95.4% of the data (within two std. deviations of the mean) of pure fluids collapse into a global dimensionless residual thermal cond. vs. scaled dimensionless residual entropy curve within 11.1% and those of mixts. are within 8.3%. This smooth, monotonically increasing curve was correlated with a polynomial function contg. only four fitted parameters and one fluid-specific scaling factor. Each pure fluid has its individual scaling factor, and a simple mole-fraction-weighted mixing rule was applied for mixts. The correlation function provides a reliable thermal cond. prediction of pure fluids and, without any addnl. parameters, of mixts. The proposed model yields a similar level of statistical agreement with the exptl. data as the extended corresponding states model, which is the current state-of-the-art and has as many as four more parameters for each pair of components.
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49. 49
  Yang, X.; Xiao, X.; Thol, M.; Richter, M.; Bell, I. H. Linking Viscosity to Equations of State Using Residual Entropy Scaling Theory. Int. J. Thermophys. 2022, 43 (12), 183, DOI: 10.1007/s10765-022-03096-9
  There is no corresponding record for this reference.
50. 50
  Lemmon, E. W.; Bell, I. H.; Huber, M.; McLinden, M. NIST standard reference database 23: reference fluid thermodynamic and transport properties-REFPROP, Version 10.0. In Natl. Stand. Ref. Data Ser.; (NIST NSRDS); National Institute of Standards and Technology: Gaithersburg, MD, 2018.
  There is no corresponding record for this reference.
51. 51
  Olchowy, G. A.; Sengers, J. V. A Simplified Representation for the Thermal-Conductivity of Fluids in the Critical Region. Int. J. Thermophys. 1989, 10 (2), 417– 426, DOI: 10.1007/BF01133538
  There is no corresponding record for this reference.
52. 52
  Frenkel, M.; Chirico, R. D.; Diky, V.; Yan, X.; Dong, Q.; Muzny, C. ThermoData Engine (TDE): software implementation of the dynamic data evaluation concept. J. Chem. Inf. Model 2005, 45 (4), 816– 838, DOI: 10.1021/ci050067b
  52
  ThermoData Engine (TDE): Software Implementation of the Dynamic Data Evaluation Concept
  Frenkel, Michael; Chirico, Robert D.; Diky, Vladimir; Yan, Xinjian; Dong, Qian; Muzny, Chris
  Journal of Chemical Information and Modeling (2005), 45 (4), 816-838CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
  The first full-scale software implementation of the dynamic data evaluation concept {ThermoData Engine (TDE)} is described for thermophys. property data. This concept requires the development of large electronic databases capable of storing essentially all exptl. data known to date with detailed descriptions of relevant metadata and uncertainties. The combination of these electronic databases with expert-system software, designed to automatically generate recommended data based on available exptl. data, leads to the ability to produce critically evaluated data dynamically or 'to order'. Six major design tasks are described with emphasis on the software architecture for automated crit. evaluation including dynamic selection and application of prediction methods and enforcement of thermodn. consistency. The direction of future enhancements is discussed.
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53. 53
  Yang, X.; Richter, M. OilMixProp 1.0: Package for thermophysical properties of oils, common fluids and their mixtures. In International Conference on Screw Machines 2024, September 3–5, Germany, Dortmund.
  There is no corresponding record for this reference.
54. 54
  Bell, I. H.; Wronski, J.; Quoilin, S.; Lemort, V. Pure and Pseudo-pure Fluid Thermophysical Property Evaluation and the Open-Source Thermophysical Property Library CoolProp. Ind. Eng. Chem. Res. 2014, 53 (6), 2498– 2508, DOI: 10.1021/ie4033999
  54
  Pure and Pseudo-pure Fluid Thermophysical Property Evaluation and the Open-Source Thermophysical Property Library CoolProp
  Bell, Ian H.; Wronski, Jorrit; Quoilin, Sylvain; Lemort, Vincent
  Industrial & Engineering Chemistry Research (2014), 53 (6), 2498-2508CODEN: IECRED; ISSN:0888-5885. (American Chemical Society)
  Over the last few decades, researchers have developed a no. of empirical and theor. models for the correlation and prediction of the thermophys. properties of pure fluids and mixts. treated as pseudo-pure fluids. In this paper, a survey of all the state-of-the-art formulations of thermophys. properties is presented. The most-accurate thermodn. properties are obtained from multiparameter Helmholtz-energy-explicit-type formulations. For the transport properties, a wider range of methods has been employed, including the extended corresponding states method. All of the thermophys. property correlations described here have been implemented into CoolProp, an open-source thermophys. property library. This library is written in C++, with wrappers available for the majority of programming languages and platforms of tech. interest. As of publication, 110 pure and pseudo-pure fluids are included in the library, as well as properties of 40 incompressible fluids and humid air. The source code for the CoolProp library is included as an electronic annex.
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55. 55
  Bell, I. H.; Quoilin, S.; Wronski, J.; Lemort, V. CoolProp: An Open-Source Reference-Quality Thermophysical Property Library. In ASME ORC 2nd International Seminar on ORC Power Systems; DTU Library: Rotterdam, The Netherlands, 2013.
  There is no corresponding record for this reference.
56. 56
  Wilke, C. R. A Viscosity Equation for Gas Mixtures. J. Chem. Phys. 1950, 18 (4), 517– 519, DOI: 10.1063/1.1747673
  56
  A viscosity equation for gas mixtures
  Wilke, C. R.
  Journal of Chemical Physics (1950), 18 (), 517-19CODEN: JCPSA6; ISSN:0021-9606.
  By application of the kinetic theory, with several simplifying assumptions, the previous equation of Buddenberg and Wilke (C.A. 43, 7281f) was modified to give a general equation for viscosity as a function of mol. wts. and viscosities of the pure components of the mixt. Agreement of the equation with exptl. data is demonstrated for a number of highly irregular binary gas systems and mixts. of 3 to 7 components.
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57. 57
  Chichester, J.; Huber, M. L. Documentation and Assessment of the Transport Property Model for Mixtures Implemented in NIST REFPROP, Version 8.0; National Institute of Standards and Technology:: Gaithersburg, MD, 2008.
  There is no corresponding record for this reference.
58. 58
  Golubev, I. F.; Sokolova, V. P. Thermal Conductivity of Ammonia at Various Temperatures and Pressures. Teploenergetika 1964, 11 (9), 64– 67
  There is no corresponding record for this reference.
59. 59
  Gutweiler, J.; Raw, C. J. G. Transport Properties of Polar Gas Mixtures II. Heat Conductivities of Ammonia-Methylamine Mixtures. J. Chem. Phys. 1968, 48, 2413– 2415, DOI: 10.1063/1.1669462
  There is no corresponding record for this reference.
60. 60
  Richter, G. N.; Sage, B. H. Thermal Conductivity of Fluids. Ammonia. J. Chem. Eng. Data 1964, 9, 75– 78, DOI: 10.1021/je60020a022
  There is no corresponding record for this reference.
61. 61
  Senftleben, H. New values of thermal conductivity and specific heat at different temperatures for a series of gases. Z. Angew. Phys. 1964, 17, 86– 87
  61
  New values of thermal conductivity and specific heat at different temperatures for a series of gases
  Senftleben, Hermann
  Zeitschrift fuer Angewandte Physik (1964), 17 (2), 86-7CODEN: ZAPHAX; ISSN:0044-2283.
  Thermal cond. values from 0 to 400°, and sp. heat values from 0 to 200° were detd. (CA 55, 7952g) and fitted to a power series with 3 consts. The gases included CO2, air, Ar, Kr, HCN, NH3, MeCl, CH2Cl2, EtCl, C2H3Cl, C2H2Cl2, C2HCl3, C2H3CN, CH4, C2H2, C2H6, C2H4, ethylene oxide, C3H8, C3H6, C4H10, C4H8, C4H6, C5H12.
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62. 62
  Shamsetdinov, F. N.; Zaripov, Z. I.; Abdulagatov, I. M.; Huber, M. L.; Gumerov, F. M.; Gabitov, F. R.; Kazakov, A. F. Experimental study of the thermal conductivity of ammonia D water refrigerant mixtures at temperatures from 278 to 356 K and at pressures up to 20 MPa. Int. J. Refrig. 2013, 36, 1347– 1368, DOI: 10.1016/j.ijrefrig.2013.02.008
  There is no corresponding record for this reference.
63. 63
  Varlashkin, P. G.; Thompson, J. C. Thermal Conductivity of Liquid Ammonia. J. Chem. Eng. Data 1963, 8, 526– 526, DOI: 10.1021/je60019a014
  There is no corresponding record for this reference.
64. 64
  Assael, M. J.; Karagiannidis, E. Measurements of the Thermal-Conductivity of R22, R123, and R134a in the Temperature-Range 250–340-K at Pressures up to 30 MPa. Int. J. Thermophys. 1993, 14 (2), 183– 197, DOI: 10.1007/BF00507807
  There is no corresponding record for this reference.
65. 65
  Chaikovskiy, V. F.; Geller, V. Z.; Gorykin, S. F.; Artamonov, S. D.; Bondar, G. E.; Ivanchenko, S. I.; Lenskiy, L. R.; Peredriy, V. G. Comprehensive Investigation of the Thermophysical Properties of Most Important and Promising Refrigerants in Liquid and Gaseous Phase. Teplofiz. Svoistva Zhidk., Collect. Vol. 1976, 108– 117
  There is no corresponding record for this reference.
66. 66
  Cherneeva, L. I. Investigation of the Thermal Conductivity of Freon-22. Kholod. Tekhn. 1953, 30, 60– 63
  There is no corresponding record for this reference.
67. 67
  Cherneeva, L. I. Investigation of the Thermal Conductivity of Freons. Kholod. Tekhn. 1955, 32, 23– 24
  There is no corresponding record for this reference.
68. 68
  Fellows, B. R.; Richard, R. G.; Shankland, I. R. Thermal Conductivity Data for Some Environmentally Acceptable Fluorocarbons. Therm. Conduct. 1990, 21, 311– 325
  There is no corresponding record for this reference.
69. 69
  Geller, V. Z.; Ivanchenko, S. I.; Peredriy, V. G. Experimental Investigation of Dynamic Viscosity and Thermal Conductivity Coefficients of Difluorudichloromethane. Izv. Vyssh. Uchebn. Zaved., Neft Gaz 1973, 61– 65
  There is no corresponding record for this reference.
70. 70
  Hammerschmidt, U. Thermal-Conductivity of a Wide-Range of Alternative Refrigerants Measured with an Improved Guarded Hot-Plate Apparatus. Int. J. Thermophys. 1995, 16 (5), 1203– 1211, DOI: 10.1007/BF02081288
  There is no corresponding record for this reference.
71. 71
  Kim, S. H.; Kim, D. S.; Kim, M. S.; Ro, S. T. The Thermal-Conductivity of R22, R142b, R152a, and Their Mixtures in the Liquid-State. Int. J. Thermophys. 1993, 14 (4), 937– 950, DOI: 10.1007/BF00502116
  There is no corresponding record for this reference.
72. 72
  Le Neindre, B.; Garrabos, Y.; Sabirzianov, A.; Goumerov, F. Measurements of the Thermal Conductivity of Chlorodifluoromethane in the Temperature Range of 300K to 515K and at Pressures up to 55 MPa. J. Chem. Eng. Data 2001, 46, 193– 201, DOI: 10.1021/je0002078
  72
  Measurements of the Thermal Conductivity of Chlorodifluoromethane (HCFC-22) in the Temperature Range from 300 K to 515 K and at Pressures up to 55 MPa
  Le Neindre, Bernard; Garrabos, Yves; Sabirzianov, Aidar; Goumerov, Farid
  Journal of Chemical and Engineering Data (2001), 46 (2), 193-201CODEN: JCEAAX; ISSN:0021-9568. (American Chemical Society)
  We report measurements of the thermal cond. of chlorodifluoromethane (HCFC-22) with a coaxial cylinder cell operating in the steady state. The measurements of the thermal cond. of HCFC-22 were performed along several quasi-isotherms between 300 and 515 K, in the gas phase, in the liq. phase, and in the crit. region. The pressure range covered varies from 0.1 MPa to 55 MPa. On the basis of the fitting of exptl. data, a background equation is provided to calc. the thermal cond. outside the crit. region as a function of temp. and d. A careful anal. of the various sources of errors leads to an estd. uncertainty of the thermal cond., of the order of ± 1.5 %.
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73. 73
  Makita, T.; Tanaka, Y.; Morimoto, Y.; Noguchi, M.; Kubota, H. Thermal Conductivity of Gaseous Fluorocarbon Refrigerants R 12, R13, and R 23, Under Pressure. Int. J. Thermophys. 1981, 2, 249– 268, DOI: 10.1007/BF00504188
  73
  Thermal conductivity of gaseous fluorocarbon refrigerants R 12, R 13, R 22 and R 23, under pressure
  Makita, T.; Tanaka, Y.; Morimoto, Y.; Noguchi, M.; Kubota, H.
  International Journal of Thermophysics (1981), 2 (3), 249-68CODEN: IJTHDY; ISSN:0195-928X.
  The thermal conductivities of 4 gaseous fluorocarbon refrigerants (R 12, R 12, R 22, and R 23) were measured by using a vertical coaxial cylinder app. from about room temp. to 393 K and pressures to ∼7 MPa. The thermal conductivities increase with increasing pressure. The temp. coeff. of thermal cond. at const. pressure, (.vdelta.λ/.vdelta.T)p, is pos. at low pressures and becomes neg. at high pressures. Steep increases occur near the crit. points.
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74. 74
  Potapov, M. D. The Thermal Conductivity of Liquid Binary Mixtures of Halogenated Hydrocarbons. Ph. D. Thesis, Odessa Technological Institute of Food Industry: Odessa, USSR, 1988.
  There is no corresponding record for this reference.
75. 75
  Sadyikov, A. K. Experimental Investigation of Some Thermophysical Properties of Polyoxy Compounds; Kazan Technical Institute for Refrigeration: Kazan, USSR, 1978.
  There is no corresponding record for this reference.
76. 76
  Shestova, A. I. The Investigation of Thermal Conductivity of Freons of the Methane Type; Institute of Theoretical Physics: Novosibirsk, USSR, 1977.
  There is no corresponding record for this reference.
77. 77
  Tsvetkov, O. B.; Laptev, Y. A. Thermal Conductivities of Freons and Their Binary Mixtures. In Proc Eighth Symposium on Thermophysical Properties; ASME: New York, 1982.
  There is no corresponding record for this reference.
78. 78
  Tsvetkov, O. B.; Laptyev, Y. A. Thermal-Conductivity of Difluoromonochloromethane in the Critical Region. Int. J. Thermophys. 1991, 12 (1), 53– 65, DOI: 10.1007/BF00506122
  There is no corresponding record for this reference.
79. 79
  Tsvetkov, O. B.; Laptev, Y. A.; Asambaev, A. G. The thermal conductivity of binary mixtures of liquid R22 with R142b and R152a at low temperatures. Int. J. Thermophys. 1996, 17 (3), 597– 606, DOI: 10.1007/BF01441506
  79
  The thermal conductivity of binary mixtures of liquid R22 and R142b and R152a at low temperatures
  Tsvetkov, O. B.; Laptev, Yu. A.; Asambaev, A. G.
  International Journal of Thermophysics (1996), 17 (3), 597-606CODEN: IJTHDY; ISSN:0195-928X. (Plenum)
  The paper presents the thermal cond. of mixts. of liq. refrigerants. R22/R142b and R22/R152a. The measurements were carried out in the temp. range 160-300 K for pressures from 0.2 to 8.0 MPa in a transient coaxial-cylinder instrument. The uncertainty of the thermal cond. data was estd. to be ±2%. The exptl. method and app. were validated by using the measurements of refrigerant R22. The results presented were used to develop a correlation for the description of the thermal cond. of refrigerants.
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80. 80
  Zaporozhan, G. V. Investigation of the Thermal Conductivity of Some Freons at Low Temperatures; Grozny Petroleum Institute: Grozny, USSR, 1978.
  There is no corresponding record for this reference.
81. 81
  Jäger, A.; Steinberg, L.; Mickoleit, E.; Thol, M. Residual entropy scaling for long-chain linear alkanes and isomers of alkanes. Ind. Eng. Chem. Res. 2023, 62 (8), 3767– 3791, DOI: 10.1021/acs.iecr.2c04238
  There is no corresponding record for this reference.
82. 82
  Mickoleit, E.; Jäger, A.; Turuelo, C. G.; Thol, M.; Bell, I. H.; Breitkopf, C. Group Contribution Method for the Residual Entropy Scaling Model for Viscosities of Branched Alkanes. Int. J. Thermophys. 2023, 44 (12), 176, DOI: 10.1007/s10765-023-03289-w
  There is no corresponding record for this reference.
83. 83
  Bell, I. H.; Leachman, J. W.; Rigosi, A. F.; Hill, H. M. Quantum Entropic Effects in the Liquid Viscosities of Hydrogen, Deuterium, and Neon. Phys. Fluids 2023, 35 (8), 081703 DOI: 10.1063/5.0164037
  There is no corresponding record for this reference.
84. 84
  Kravchun, S. N. Thermal-Conductivity of Binary-Liquid Systems. Zh. Fiz. Khim. 1986, 60 (9), 2176– 2179
  There is no corresponding record for this reference.
85. 85
  Naziev, Y. M.; Gumbatov, A. M.; Akhmedov, A. K.; Abasov, A. A.; Abasov, R. A. Experimental study of thermal conductivity of liquid binary cyclohexane-n-decane mixtures at high pressures. Izv. Vyssh. Uchebdn. Zaved. 1985, 28, 57
  There is no corresponding record for this reference.
86. 86
  Archer, C. T. Thermal Conduction in Hydrogen-Deuterium Mixtures. Proc. R. Soc. London, Ser. A 1938, 165, 474– 485, DOI: 10.1098/rspa.1938.0072
  86
  Thermal conduction in H2-D2 mixtures
  Archer, C. T.
  Proceedings of the Royal Society of London, Series A: Mathematical, Physical and Engineering Sciences (1938), 165 (), 474-85CODEN: PRLAAZ; ISSN:1364-5021.
  The thermal conds. at 0° of H2 and D2 are 0.0004182 and 0.0003080 cal. cm.-1 sec.-1. deg.-1, and the accommodation coeffs. (on Pt) are 0.296 and 0.376, resp. Data are given for thermal conds. of 7 mixts., and for 3 temp. coeffs.
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87. 87
  Minter, C.; Schuldiner, S. Thermal Conductivity of Equilibrated Mixtures of H2’, D2’, and HD. J. Chem. Eng. Data 1959, 4 (3), 223– 226, DOI: 10.1021/je60003a010
  There is no corresponding record for this reference.
88. 88
  Saxena, S. C.; Tondon, P. K. Experimental Data and Procedures for Predicting Thermal Conductivity of Binary Mixtures of Nonpolar Gases. J. Chem. Eng. Data 1971, 16 (2), 212– 220, DOI: 10.1021/je60049a032
  88
  Experimental data and procedures for predicting thermal conductivity of binary mixtures of nonpolar gases
  Saxena, Satish C.; Tondon, P. K.
  Journal of Chemical and Engineering Data (1971), 16 (2), 212-20CODEN: JCEAAX; ISSN:0021-9568.
  The thermal conds. of Ne, Ar, Kr, Xe, H2, D2 N2, and O2 were measured by using a thick hot-wire metal cell at 5 temps. in the range 40-175°. The soln. of the heat balance equation as developed by Oldham and Luchsinger is employed, and an accuracy was estd. of 1-2% in the recommended abs. cond. values. In this temp. range, the thermal conds. of the binary systems Ne-H2, Ne-N2, Ne-O2, H2-D2, N2-D2, H2-N2, N2-O2, Kr-H2, Xe-H2, Xe-D2, and Xe-Ar are also detd. as a function of compn. On the basis of these exptl. data, the methods of prediction of thermal cond. of mixts. due to Hirschfelder, Mason and Saxena, Mathur and Saxena, Lindsay and Bromley, Ulybin, et al., and Burgoyne and Weinberg are examd. to ascertain their relative accuracies. The framework of Chapman-Enskog kinetic theory in conjunction with the exptl. data on thermal cond. is used to generate the diffusion and viscosity coeffs. for Xe-Ar, Xe-D2, Ne-H2, Ne-N2, and Ne-O2, as representative systems.
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89. 89
  Bates, O. K.; Hazzard, G.; Palmer, G. Ind. Eng. Chem. Anal. Ed. 1938, 10, 314– 318, DOI: 10.1021/ac50122a006
  89
  Thermal conductivity of liquids. Binary mixtures of water-methyl alcohol and water-ethyl alcohol
  Bates, Oscar Kenneth; Hazzard, George; Palmer, Gerald
  Industrial and Engineering Chemistry, Analytical Edition (1938), 10 (), 314-18CODEN: IENAAD; ISSN:0096-4484.
  Thermal conds. and temp. coeffs. of thermal cond. for mixts. of water-MeOH and water-EtOH are given. Thermal cond. decreases with percentage of alc., the rate of decrease being greatest for the highest mean temp. and lowest for the lowest mean temp. investigated. The thermal cond. of water increases with increase of temp.; whereas the conds. of both MeOH and EtOH decrease with increase of temp. Mixts. of approx. 50% water with either MeOH or EtOH exhibit a const.-temp. coeff.
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90. 90
  Filippov, L. P. Vestn. Mosk. Univ., Ser. 3: Fiz. Astr. 1960, 15, 43- 50 DOI:.
  There is no corresponding record for this reference.
91. 91
  Gillam, D. G.; Lamm, O. Certain Liquids using the Hot Wire Method. Acta Chem. Scand. 1955, 9, 657– 660
  There is no corresponding record for this reference.
92. 92
  Henneberg, H. Ueber das wärmeleitungsvermögen der mischungen von aethylalkohol und wasser; Druck C. Gerold's sohn: 1888.
  There is no corresponding record for this reference.
93. 93
  Lees, C. H. X. On the Thermal Conductivities of Single and Mixed Solids and Liquids and Their Variation with Temperature. Philos. Trans. R. Soc. London, Ser. A 1898, 191, 339– 440, DOI: 10.1098/rsta.1898.0010
  There is no corresponding record for this reference.
94. 94
  Loewen, J. A.; Popov, V. N.; Malov, B. A. Comparative Theories of Social Change ; 1969, 87- 89. DOI: DOI: 10.1177/009182966901600205 .
  There is no corresponding record for this reference.
95. 95
  Popov, V. N.; Malov, B. A. Teploenergetika 1971, 18, 88- 90DOI: DOI: 10.1093/nq/18-3-88 .
  There is no corresponding record for this reference.
96. 96
  Qun-Fang, L.; Ruisen, L.; Dan-Yan, N.; Yu-Chun, H. Thermal Conductivities of Some Organic Solvents and Their Binary Mixtures. J. Chem. Eng. Data 1997, 42 (5), 971– 974, DOI: 10.1021/je960351m
  There is no corresponding record for this reference.
97. 97
  Rastorguev, Y. L.; Ganiev, Y. A. Thermal Conductivity of Aqueous Solutions of Organic Liquids. Russ. J. Phys. Chem. 1966, 40, 869– 871
  There is no corresponding record for this reference.
98. 98
  Rastorguev, Y. L.; Ganiev, Y. A. Thermal Conductivity of Nonelectrolytes. Zh. Fiz. Khim. 1967, 41 (11), 2901– 2907
  There is no corresponding record for this reference.
99. 99
  Riedel, L. Chem.-Ing.-Technol. 1951, 23, 465, DOI: 10.1002/cite.330231902
  There is no corresponding record for this reference.
100. 100
  Tsederberg, N. V. Teploenergetika 1956, 3, 42- 48
  There is no corresponding record for this reference.
101. 101
  Zhou, J. C.; Che, Y. Y.; Wu, K. J.; Shen, J.; He, C. H. Thermal Conductivity of DMSO + C2H5OH, DMSO + H2O, and DMSO + C2H5OH + H2O Mixtures at T = (278.15 to 338.15) K. J. Chem. Eng. Data 2013, 58, 663– 670, DOI: 10.1021/je301171y
  101
  Thermal Conductivity of DMSO + C2H5OH, DMSO + H2O, and DMSO + C2H5OH + H2O Mixtures at T = (278.15 to 338.15) K
  Zhou, Jun-Chao; Che, Yuan-Yuan; Wu, Ke-Jun; Shen, Jian; He, Chao-Hong
  Journal of Chemical & Engineering Data (2013), 58 (3), 663-670CODEN: JCEAAX; ISSN:0021-9568. (American Chemical Society)
  The thermal conductivities of DMSO + ethanol, DMSO + water, and DMSO + ethanol + water were reported. The measurements, covering a temp. range from (278.15 to 338.15) K were performed by a transient hot-wire technique over the whole concn. range at atm. pressure. The exptl. data of thermal cond. were correlated by the second-order Scheffe polynomial in terms of temp. and wt. fraction. The av. abs. deviation of those correlated values from the exptl. data was 1.35 %. The uncertainty of thermal cond. was ± 2.0 % with a coverage factor of k = 2.
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102. 102
  Jeong, S. U.; Kim, M. S.; Ro, S. T. Liquid Thermal Conductivity of Binary Mixtures of Pentafluoroethane (R125) and 1,1,1,2-Tetrafluoroethane (R134a). Int. J. Thermophys. 1999, 20, 55– 62, DOI: 10.1023/A:1021469928377
  There is no corresponding record for this reference.
103. 103
  Kim, D.; Yang, X. X.; Arami-Niya, A.; Rowland, D.; Xiao, X.; Al Ghafri, S. Z. S.; Tsuji, T.; Tanaka, Y.; Seiki, Y.; May, E. F. Thermal Conductivity Measurements of Refrigerant Mixtures Containing Hydrofluorocarbons (HFC-32, HFC-125, HFC-134a), Hydrofluoroolefins (HFO-1234yf), and Carbon Dioxide (CO2). J. Chem. Thermodyn. 2020, 151, 106248 DOI: 10.1016/j.jct.2020.106248
  103
  Thermal conductivity measurements of refrigerant mixtures containing hydrofluorocarbons (HFC-32, HFC-125, HFC-134a), hydrofluoroolefins (HFO-1234yf), and carbon dioxide (CO2)
  Kim, Dongchan; Yang, Xiaoxian; Arami-Niya, Arash; Rowland, Darren; Xiao, Xiong; Al Ghafri, Saif Z. S.; Tsuji, Tomoya; Tanaka, Yukio; Seiki, Yoshio; May, Eric F.
  Journal of Chemical Thermodynamics (2020), 151 (), 106248CODEN: JCTDAF; ISSN:0021-9614. (Elsevier Ltd.)
  Thermal cond. measurements of eight binary refrigerant mixts. were conducted in the homogeneous liq. and vapor phases with the transient hot-wire technique. The temp. range of the measurements spanned from (224.3 to 386.6) K with pressures ranging between (1.0 and 6.5) MPa. The binary mixts. were equimolar (R125 + R32), (R32 + R134a), (R32 + CO2), (R125 + R134a), (R125 + CO2), (R134a + R1234yf), (R134a + CO2) and (R1234yf + CO2). Addnl., two multi-component mixts., (R32 + R1234yf + CO2) and (R32 + R1234yf + R134a + R125 + CO2), were investigated. The transient hot-wire app. was validated with measurements of pure CO2 in the liq. and vapor regions. The relative combined expanded uncertainty (k = 2) in the exptl. thermal cond. was on the order of 2.0%. The relative deviations of the measured thermal conductivities in the vapor phase from those calcd. using the extended corresponding states (ECS) model with default binary interaction parameters (BIPs), as implemented in the software REFPROP 10, were between (-12 and +8) %, while those in the liq. phase were between (-15 and +4) %. The new exptl. data were used to tune the BIPs in the ECS model. Significant improvements were obsd. esp. in the liq. phase of the five-component mixt., with the root-mean-square of the relative difference between the exptl. data and the model estn. reduced by a factor of nearly three.
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104. 104
  Perkins, R.; Schwarzberg, E.; Gao, X. Experimental Thermal Conductivity Values for Mixtures of R32, R125, R134a, and Propane; NIST Interagency/Internal Report (NISTIR); National Institute of Standards and Technology: Gaithersburg, MD, 1999.
  There is no corresponding record for this reference.
105. 105
  Assael, M. J.; Charitidou, E.; Avgoustiniatos, S.; Wakeham, W. A. Absolute Measurements of the Thermal Conductivity of Mixtures of Alkene-Glycols with Water. Int. J. Thermophys. 1989, 10, 1127– 1140, DOI: 10.1007/BF00500567
  105
  Absolute measurements of the thermal conductivity of mixtures of alkene-glycols with water
  Assael, M. J.; Charitidou, E.; Avgoustiniatos, S.; Wakeham, W. A.
  International Journal of Thermophysics (1989), 10 (6), 1127-40CODEN: IJTHDY; ISSN:0195-928X.
  New abs. measurements of the thermal cond. of ethylene and propylene glycol and their mixts. with water are presented. The measurements were performed in a tantalum-type transient hot-wire instrument at atm. pressure, in the temp. range 295-360 K. The overall uncertainty of the reported values is estd. to be less than ±0.5%, an est. confirmed by measurements of the thermal cond. of water. The mixts. with water studied have compns. of 25, 50, and 75%, by wt. A recently proposed semiempirical scheme for the prediction of the thermal cond. of pure liqs. is extended to allow the prediction of the thermal cond. of these mixts. from the pure components, as a function of both compn. and temp.
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106. 106
  Bates, O. K.; Hazzard, G. Thermal Conductivity of Alcohols and Glycols. Ind. Eng. Chem. 1945, 37, 193– 195, DOI: 10.1021/ie50422a021
  There is no corresponding record for this reference.
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107. 107
  Bogacheva, I. S.; Zemdikhanov, K. B.; Mukhamedzyanov, G. K.; Sadykov, A. K.; Usmanov, A. G. Heat Conductivity of Mixtures of Organic Liquids. Zh. Fiz. Khim 1980, 54, 1468– 1470
  107
  Thermal conductivity of solutions of some organic liquids
  Bogacheva, I. S.; Zemdikhanov, K. B.; Mukhamedzyanov, G. Kh.; Sadykov, A. Kh.; Usmanov, A. G.
  Zhurnal Fizicheskoi Khimii (1980), 54 (6), 1468-70CODEN: ZFKHA9; ISSN:0044-4537.
  Thermal conductivities were measured at 298-363 K of binary solns. monoethylene glycol(I)-H2O, triethylene glycol(II)-H2O, I-II, I-diethylene glycol, and monoethanolamine-diethanolamine, over the entire concn. ranges.
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108. 108
  Bohne, D.; Fischer, S.; Obermeier, E. Thermal Conductivity, Density, Viscosity, and Prandtl Numbers of Ethylene Glycol-Water Mixtures. Ber. Bunsen-Ges. Phys. Chem. 1984, 88, 739– 742, DOI: 10.1002/bbpc.19840880813
  108
  Thermal conductivity, density, viscosity, and Prandtl-numbers of ethylene glycol-water mixtures
  Bohne, D.; Fischer, S.; Obermeier, E.
  Berichte der Bunsen-Gesellschaft (1984), 88 (8), 739-42CODEN: BBPCAX; ISSN:0005-9021.
  Thermal cond., d., and viscosity were detd. of (CH2OH)2-H2O. The measurements were performed at -20 to 180° for thermal cond., -10 to 150° for d., and -10 to 100° for viscosity. Prandtl nos. calcd. with the own exptl. data and literature values of sp. heat capacity are presented in dependence of temp. and concn.
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109. 109
  Ganiev, Y. A.; Rastorgu, Y. L. Thermal Conductivity of Mixed Non-Electrolyte Solutions. Russ. J. Phys. Chem. 1968, 42, 68
  There is no corresponding record for this reference.
110. 110
  Grigrev, A. Thermal Conductivity: Water and Water-Organic Systems. Sov. Un. Gov. Bur. Stand., Grozny Oil Inst., Infor. Seri 1985.
  There is no corresponding record for this reference.
111. 111
  Rastorguev, Y. L.; Ganiev, Y. A. Thermal Conductivity of Organic Liquids. Zh. Fiz. Khim. 1967, 41, 1352
  There is no corresponding record for this reference.
112. 112
  Riedel, L. Measurement of Thermal Conductivity of Mixtures of Several Organic Compounds with Water. Chem.-Ing.-Technol. 1951, 23, 465, DOI: 10.1002/cite.330231902
  There is no corresponding record for this reference.
113. 113
  Sun, T.; Teja, A. S. Density, Viscosity and Thermal Conductivity of Aqueous Ethylene, Diethylene and Triethylene Glycol Mixtures between 290 and 450 K. J. Chem. Eng. Data 2003, 48, 198– 202, DOI: 10.1021/je025610o
  113
  Density, Viscosity, and Thermal Conductivity of Aqueous Ethylene, Diethylene, and Triethylene Glycol Mixtures between 290 K and 450 K
  Sun, Tongfan; Teja, Amyn S.
  Journal of Chemical and Engineering Data (2003), 48 (1), 198-202CODEN: JCEAAX; ISSN:0021-9568. (American Chemical Society)
  The d., viscosity, and thermal cond. of ethylene glycol + water, diethylene glycol + water, and triethylene glycol + water mixts. were measured at temps. ranging from 290 to 450 K and concns. ranging from 25 to 100 mol% of glycol. The data obtained are generally in agreement with the limited data available in the literature. Correlation of the data was performed using simple empirical expressions and the generalized corresponding states principle (GCSP). The GCSP method, with two adjustable parameters for each property, offers the potential for judicious extrapolation of d. and transport property data for all glycol + water mixts.
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114. 114
  Usmanov, I. U.; Salikhov, A. S. The Concentration Variation of the Thermal Conductivities of Certain Aqueous Solutions of Organic Liquids. Russ. J. Phys. Chem. 1977, 51, 1488– 1489
  There is no corresponding record for this reference.
115. 115
  Vanderkooi, W. N.; Hildenbrand, D. L.; Stull, D. R. Liquid Thermal Conductivities: The Apparatus, Values for Several Glycols and Their Aqueous Solutions, and Five High Molecular Weight Hydrocarbons. J. Chem. Eng. Data 1967, 12, 377– 379, DOI: 10.1021/je60034a023
  115
  Liquid thermal conductivities. The apparatus, values for several glycols and their aqueous solutions, and five high molecular weight hydrocarbons
  Vanderkooi, William N.; Hildenbrand, Donald L.; Stull, Daniel R.
  Journal of Chemical and Engineering Data (1967), 12 (3), 377-9CODEN: JCEAAX; ISSN:0021-9568.
  An a pp. is described for measuring the thermal conds. of liquids at ≤150° with a probable error of <1%. A thin layer of liquid occupies the annular space between a sphere and a spherical cavity in a surrounding copper block. The thermal cond. is calcd. from the slope of the heat dissipation of the sphere vs. the temp. difference between the sphere and the block. Thermal cond. data are given for mono-, di-, and triethylene glycol; mono and dipropylene glycol; aq. solns. of these glycols; and for 1-phenyl-3-(2-phenethyl)hendecane, 1-cyclohexyl-3-(2-cyclohexylethyl)-hendecane, 9-N-octylheptadecane, 9-(2-phenylethyl)heptadecane, 1-cyclopentyl-4(3-cyclopentylpropyl)dodecane.
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116. 116
  Fareleira, J. M. N. A.; Li, S. F. Y.; Wakeham, W. A. The Thermal Conductivity of Liquid Mixtures at Elevated Pressures. Int. J. Thermophys. 1989, 10, 1041– 1051, DOI: 10.1007/BF00503172
  116
  The thermal conductivity of liquid mixtures at elevated pressures
  Fareleira, J. M. N. A.; Li, S. F. Y.; Wakeham, W. A.
  International Journal of Thermophysics (1989), 10 (5), 1041-51CODEN: IJTHDY; ISSN:0195-928X.
  New, abs. measurements are reported of the thermal conductivities of liq. mixts. of heptane and isooctane in the pressure range 0.1 to 430 MPa for temps. of 307.85 and 337.15 K. The results represent a preliminary investigation of the advantages of attempting to describe the isothermal compn. dependence of the thermal cond. of liq. mixts. along isochores, rather than isobars as has been traditional. However, no significant differences were found between the compn. dependences for these two conditions, possibly due to the lack of exptl. data on the d. of these mixts.
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117. 117
  Naziev, D. Y.; Aliev, A. M. Research of Thermal Conductivity of Binary Mixtures of n-Heptane-Isooctane at High Parameters of State. Teplofiz. Vys. Temp. 1992, 30, 294– 298
  117
  Study of the thermal conductivity of n-heptane-isooctane binary mixtures for high state parameters
  Naziev, D. Ya.; Aliev, A. M.; Naziev, Ya. M.
  Teplofizika Vysokikh Temperatur (1992), 30 (2), 294-8CODEN: TVYTAP; ISSN:0040-3644.
  A special cylindric calorimetric app. was used to measure the thermal conductivities of binary mixts. of heptane with isooctane, in gases and liq. states.
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118. 118
  Wakeham, W. A.; Yu, H. R.; Zalaf, M. The Thermal Conductivity of the Mixtures of Liquid Hydrocarbons at Pressures up to 400 MPa. Int. J. Thermophys. 1990, 11, 987– 1000, DOI: 10.1007/BF00500554
  118
  The thermal conductivity of the mixtures of liquid hydrocarbons at pressures up to 400 MPa
  Wakeham, W. A.; Yu, H. R.; Zalaf, M.
  International Journal of Thermophysics (1990), 11 (6), 987-1000CODEN: IJTHDY; ISSN:0195-928X.
  Results are presented of thermal cond. measurements of three binary mixts. of heptane and 2,2,4-tri-Me pentane. The measurements were carried out within the temp. range 308-359 K and over the pressure range 0.1-410 MPa with a transient hot-wire instrument. The exptl. data are represented by simple polynomials along isotherms as 9 functions of pressure for each compn. for the purpose of interpolation. However, an alternative scheme of representation, based upon an heuristic extention of the hard-sphere theory, is shown to give a much more concise representation capable of extrapolation. A procedure for the prediction of the thermal cond. of the mixts., based on the same theory, which uses no information derived from the present measurements, is shown to yield results of an accuracy sufficient for many purposes.
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119. 119
  Yu, H. The Measurement of the Thermal Conductivity for Liquid with the Transient Hot-Wire Instrument. Beijing Shiyou Huagong Xueyuan Xuebao 1993, 1, 29– 36
  There is no corresponding record for this reference.
120. 120
  Gao, X.; Nagasaka, Y.; Nagashima, A. Thermal Conductivity of Binary Refrigerant Mixtures of HFC-32/125 and HFC-32/134a in the Liquid Phase. Int. J. Thermophys. 1999, 20, 1403– 1415, DOI: 10.1023/A:1021432920199
  There is no corresponding record for this reference.
121. 121
  Geller, V. Z.; Nemzer, B. V.; Cheremnykh, U. V. Thermal Conductivity of the Refrigerant Mixtures R404A, R407C, R410A, and R507A. Int. J. Thermophys. 2001, 22, 1035– 1043, DOI: 10.1023/A:1010691504352
  121
  Thermal conductivity of the refrigerant mixtures R 404A, R 407C, R 410A, and R 507A
  Geller, V. Z.; Nemzer, B. V.; Cheremnykh, U. V.
  International Journal of Thermophysics (2001), 22 (4), 1035-1043CODEN: IJTHDY; ISSN:0195-928X. (Kluwer Academic/Plenum Publishers)
  New thermal cond. data of the refrigerant mixts. R 404A, R 407C, R 410A, and R 507C are presented. For all these refrigerants, the thermal cond. was measured in the vapor phase at atm. pressure over a temp. range from 250 to 400 K and also at moderate pressures. A modified steady-state hot-wire method was used for these measurements. The cumulative correction for end effects, eccentricity of the wire, and radiation heat transfer did not exceed 2 %. Calcd. uncertainties in exptl. thermal cond. are, in general, less than ±1.5 %. All available literature thermal cond. data for R 404A, R 407C, R 410A, and R 507C were evaluated to identify the most accurate data on which to base the thermal cond. model. The thermal cond. is modeled with the residual concept. In this representation, the thermal cond. was composed of two contributions. One of the contributions is a dil. gas term which is a function only of temp. The second contribution is a residual term which is a function only of d. The models cover a wide range of conditions except for the region of the thermal cond. crit. enhancement. The resulting correlations are applicable for the thermal cond. of dil. gas, superheated vapor, and satd. liq. and vapor far away from the crit. point. Comparisons are made for all available literature data.
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122. 122
  Matsuo, S.; Tanaka, Y. Measurements of Transport Properties and Their Problems. Rev. High Press. Sci. Technol. 1994, 3 (4), 346– 353, DOI: 10.4131/jshpreview.3.346
  There is no corresponding record for this reference.
123. 123
  Ro, S. T.; Kim, M. S.; Jeong, S. U. Liquid Thermal Conductivity of Binary Mixtures of Difluoromethane (R32) and Pentafluoroethane (R125). Int. J. Thermophys. 1997, 18, 991– 999, DOI: 10.1007/BF02575243
  123
  Liquid thermal conductivity of binary mixtures of difluoromethane (R32) and pentafluoroethane (R125)
  Ro, S. T.; Kim, M. S.; Jeong, S. U.
  International Journal of Thermophysics (1997), 18 (4), 991-999CODEN: IJTHDY; ISSN:0195-928X. (Plenum)
  The thermal conductivities of refrigerant mixts. of difluoromethane (R32) and pentafluoroethane (R125) in the liq. phase are presented. The thermal conductivities were measured with the transient hot-wire method with one bare platinum wire. The expts. were conducted in the temp. range of 233-323 K and in the pressure range of 2-20 MPa. An empirical equation to describe the thermal cond. of a near-azeotropic mixt., R32 + R125, is provided based on the measured 168 thermal cond. data as a function of temp. and pressure. The dependence of thermal cond. on the compn. at different temps. and pressures is also presented. The uncertainty of the measurements is estd. to be ±2%.
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124. 124
  Tanaka, Y.; Matsuo, S.; Taya, S. Gaseous Thermal Conductivity of Difluoromethane (HFC-32), Pentafluoroethane (HFC-125), and Their Mixtures. Int. J. Thermophys. 1995, 16, 121– 131, DOI: 10.1007/BF01438963
  124
  Gaseous thermal conductivity of difluoromethane (HFC-32), pentafluoroethane (HFC-125), and their mixtures
  Tanaka, Y.; Matsuo, S.; Taya, S.
  International Journal of Thermophysics (1995), 16 (1), 121-31CODEN: IJTHDY; ISSN:0195-928X. (Plenum)
  The gaseous thermal conductivities of difluoromethane (HFC-32), pentafluoroethane (HFC-125), and their binary mixts. were measured with a transient hot-wire app. in the temp. ranges 283-333 K at pressures up to satn. The uncertainty of the data is estd. to be within 1%. The thermal cond. as a function of compn. of the mixts. at const. pressure and temp. is found to have a small max. near 0.3-0.4 mol fraction of HFC-32. The gaseous thermal-cond. data obtained for pure HFC-32 and HFC-125 were correlated with temp. and d. together with the liq. thermal-cond. data from the literature, based on the excess thermal-cond. concept. The compn. dependence of the thermal cond. at a const. temp. is represented with the aid of the Wassiljewa equation.
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125. 125
  Tomimura, T.; Maki, S.; Zhang, X.; Fujii, M. Measurements of Thermal Conductivity and Thermal Diffusivity of Alternative Refrigerants in Liquid Phase with a Transient Short-Hot-Wire Method. Jpn. J. Thermophys. Prop. 2001, 15, 9– 14, DOI: 10.2963/jjtp.15.9
  There is no corresponding record for this reference.
126. 126
  Marsh, K. N.; Perkins, R. A.; Ramires, M. L. V. Measurement and Correlation of the Thermal Conductivity of Propane from 86 to 600 K at Pressures to 70 MPa. J. Chem. Eng. Data 2002, 47 (4), 932– 940, DOI: 10.1021/je010001m
  126
  Measurement and Correlation of the Thermal Conductivity of Propane from 86 K to 600 K at Pressures to 70 MPa
  Marsh, Kenneth N.; Perkins, Richard A.; Ramires, Maria L. V.
  Journal of Chemical and Engineering Data (2002), 47 (4), 932-940CODEN: JCEAAX; ISSN:0021-9568. (American Chemical Society)
  Data tables are reported on the thermal cond. of propane. Previous correlations have been limited by a lack of thermal-cond. data for the vapor at temps. below 300 K and liq. data near the crit. point. In addn., significant discrepancies were noted in the high-temp. dil.-gas thermal cond. The present data cover the temp. range from the triple point at 85.5 K to 600 K and the pressure range 0.1 to 70 MPa. They are estd. to have an uncertainty of 1 % for measurements removed from the crit. point and at pressures above 1 MPa, which increases to 3 % in the crit. region and 4 % at low pressures (< 1 MPa). These new exptl. data are used together with the previously available data to develop improved correlations for the thermal cond. of propane. The thermal-cond. correlation for propane is estd. to have an uncertainty of about 3 % at a 95 % confidence level, with the exception of state points near the crit. point and the dil. gas, where the uncertainty of the correlation increases to 5 %.
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127. 127
  Huber, M. L.; Sykioti, E. A.; Assael, M. J.; Perkins, R. A. Reference Correlation of the Thermal Conductivity of Carbon Dioxide from the Triple Point to 1100 K and up to 200 MPa. J. Phys. Chem. Ref. Data 2016, 45 (1), 013102 DOI: 10.1063/1.4940892
  127
  Reference Correlation of the Thermal Conductivity of Carbon Dioxide from the Triple Point to 1100 K and up to 200 MPa
  Huber, M. L.; Sykioti, E. A.; Assael, M. J.; Perkins, R. A.
  Journal of Physical and Chemical Reference Data (2016), 45 (1), 013102/1-013102/18CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
  This paper contains new, representative ref. equations for the thermal cond. of carbon dioxide. The equations are based in part upon a body of exptl. data that has been critically assessed for internal consistency and for agreement with theory whenever possible. In the case of the dil.-gas thermal cond., we incorporated recent theor. calcns. to extend the temp. range of the exptl. data. Moreover, in the crit. region, the exptl. obsd. enhancement of the thermal cond. is well represented by theor. based equations contg. just one adjustable parameter. The correlation is applicable for the temp. 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 and 700 K, to 5% at the higher pressures of the range of validity. (c) 2016 American Institute of Physics.
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128. 128
  Mostert, R.; Sengers, J. V. Thermal Conductivity of Mixtures of Carbon Dioxide and Ethane in the Critical Region. Int. J. Thermophys. 2008, 29 (4), 1205– 1221, DOI: 10.1007/s10765-008-0482-1
  There is no corresponding record for this reference.
129. 129
  Junk, W. A.; Comings, E. W. Thermal Conductivity of Gas Mixtures at High Pressure: Ethylene-Nitrogen and Ethylene-Carbon Dioxide. Chem. Eng. Prog. 1953, 49, 263– 266
  There is no corresponding record for this reference.
Supporting Information
Supporting Information
The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.iecr.4c02946.
- Tables of dilute gas calculation parameters of pure fluids; of reference equation of state and the recommended thermal conductivity model in REFPROP 10.0; of names, group, and constants of pure fluids; for statistics of the experimental data of pure fluids; for statistics of the experimental data of fluid mixtures; for sample thermal conductivity calculations of pure substances with the recommended models in REFPROP 10.0 and the RES model; for sample thermal conductivity calculations of binaries with the recommended models in REFPROP 10.0 and the RES model; and for thermal conductivity as a function of residual entropy for each group and figures for relative deviation from experimental data of pure fluids to model predictions and relative deviation from experimental data of fluid mixtures to model predictions (PDF)
- Python package for residual entropy scaling model calculation (ZIP)
- Detailed plots and references of all collected experimental data (PDF)
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1. Introduction

2. Theory

3. Results

3.1. Data Collection and Selection

Figure 1

3.2. Correlation for Pure Fluids

Figure 2

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Figure 4

3.3. Prediction for Mixtures

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Figure 7

Figure 8

4. Conclusion, Discussion, and Future Work

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Linking Thermal Conductivity to Equations of State Using the Residual Entropy Scaling Theory
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