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Thermophysical and Thermochemical PropertiesJanuary 10, 2025

Entropy Scaling of Viscosity IV─Application to 124 Industrially Important Fluids
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Viktor Martinek
Viktor Martinek
Interdisciplinary Center for Scientific Computing, Heidelberg University, 69120 Heidelberg, Germany
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https://orcid.org/0000-0001-6215-4783
Ian Bell
Ian Bell
Applied Chemicals and Materials Division, National Institute of Standards and Technology, Boulder, Colorado 80305, United States
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Roland Herzog
Roland Herzog
Interdisciplinary Center for Scientific Computing, Heidelberg University, 69120 Heidelberg, Germany
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Markus Richter
Markus Richter
Faculty of Mechanical Engineering, Applied Thermodynamics, Chemnitz University of Technology, 09107 Chemnitz, Germany
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https://orcid.org/0000-0001-8120-5646
Xiaoxian Yang*
Xiaoxian Yang
Faculty of Mechanical Engineering, Applied Thermodynamics, Chemnitz University of Technology, 09107 Chemnitz, Germany
*Email: [email protected]
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https://orcid.org/0000-0003-4655-3156

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Journal of Chemical & Engineering Data

Cite this: J. Chem. Eng. Data 2025, 70, 2, 727–742

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https://doi.org/10.1021/acs.jced.4c00451

Published January 10, 2025

CC-BY 4.0 .

Abstract

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In our previous work [Yang, X. J. Chem. Eng. Data 2021, 66, 1385–1398], a residual entropy scaling (RES) approach was developed to link viscosity to residual entropy using a 4-term power function for 39 refrigerants. In further research [Yang, X. Int. J. Thermophys. 2022, 43, 183], this RES approach was extended to 124 pure fluids containing fluids from light gases (hydrogen and helium) to dense fluids (e.g., heavy hydrocarbons) and fluids with strong association force (e.g., water). In these previous research studies, the model was developed by manual optimization of the power function. The average absolute relative deviation (AARD) of experimental data from the RES model is approximately 3.36%, which is higher than the 2.74% obtained with the various models in REFPROP 10.0. In the present work, the power function was optimized by iteratively fitting the global (fluid-independent power terms) and local parameters (fluid-specific and group-specific parameters) and screening the experimental data. The resulting equation has only three terms instead of four. Most notably, the AARD of the new RES model is reduced down to 2.76%; this is very close to the various multiparameter models in REFPROP 10.0, while the average relative deviation (ARD) amounts to 0.03%, which is smaller than REFPROP 10.0’s 0.7%. A Python package is provided for the use of the developped model.

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License Summary*
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.
- Attribution (BY): Credit must be given to the creator.
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Subjects

1. Introduction

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With a residual entropy scaling (RES) approach, the residual part of the transport properties (mainly viscosity, thermal conductivity, and self-diffusion) of pure fluids can be expressed using a single variable: residual entropy. The residual entropy is a thermodynamic property and can be easily calculated with many well-developed and accurate equations of state (EOS). With this feature, the RES approach has been attracting attention in recent years and has been developed in many ways and used successfully by different authors. For example for viscosity, RES approaches have been applied to the Lennard-Jones (L-J) fluid and other spherically symmetric simple potentials, (1,2) as well as hundreds of real fluids including hydrocarbons, (3−5) refrigerants, (6−9) and other fluids of industrial interest. (10−13) Specifically, Lötgering-Lin et al. (11) and Dehlouz et al. (14) developed a generalized RES approach for viscosity of more than 100 pure fluids. For the thermal conductivity, RES approaches are also successful for many real fluids. (9,15−19)

In our previous work, (6) an RES approach was developed to link residual viscosity to residual entropy using a 4-term power function for 39 refrigerants. Later, this approach was extended to 124 pure fluids (12,13) containing a variety of fluids from light gases (hydrogen and helium) to dense fluids (e.g., heavy hydrocarbons) and fluids with strong association (e.g., water). This simple 4-term power function consists of different types of parameters: global parameters (i.e., the structure and power terms) for all fluids, group-specific parameters for a group of similar fluids, and fluid-specific parameters for each fluid. These parameters are explained in detail in Section 2.2. In the above-mentioned papers, (6,12,13) the global parameters (structure and power terms) were determined manually by choosing the ones that best fit the approximately 50,000 well-evaluated experimental data points. With such a trial-and-error method, the average absolute relative deviation (AARD) (corresponding to scattering) of these experimental data from the RES model is approximately 3.36%, which is higher than the 2.74% obtained with the various state-of-the-art models in REFPROP 10.0. (20)

The primary aim of this work is to optimize these global parameters of the power function by means of a self-developed constrained numerical optimization routine. We aim at delivering an RES approach that has the same level of accuracy as the state-of-the-art models implemented in REFPROP 10.0, while using fewer parameters and an approach that is reproducible.

The RES approach calculates only the residual part of the viscosity; the remaining dilute gas viscosity η_ρ→0(T) still needs to be determined by another method. If the highest accuracy is the aim, η_ρ→0(T) should be calculated with the pure-fluid correlations implemented in REFPROP 10.0. These fluid-specific correlations are available when low-density viscosity data are available in the literature. REFPROP 10.0 cannot calculate η_ρ→0(T) for some mixtures, especially those involving alcohols. Therefore, in the present work, other methods are also adopted for pure-fluid η_ρ→0(T) calculations: (1) η_ρ→0(T) is modeled as a polynomial of temperature with parameters fitted against REFPROP 10.0 results, (2) calculation with known L-J parameters as in our previous work, (6) and (3) calculation with L-J parameters which are estimated according to critical point information. The first method aims at achieving high accuracy, while the latter two aim at using fewer parameters for the viscosity calculation, allowing for a broader predictive application.

This work is structured as follows. In Section 2.1, we provide a brief overview of the RES approach and methods to calculate η_ρ→0(T). Thereafter, in Section 2.2, we discuss the design of the power function, the different types of parameters, how and when they are used, and how they were determined. In Section 3, the results are presented and compared to previous work and to REFPROP version 10.0. Finally, conclusions are drawn in Section 4. Part of this endeavor was supported by subproject 3 of the KETEC (Research Platform Refrigeration and Energy Technology) project. (21) One important goal within KETEC subproject 3 is to model thermophysical properties of lubricant + refrigerant mixtures, and this work focuses on the viscosity of more general types of fluids.

2. Computational Methods

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2.1. Fundamentals

In this section, we provide an overview of the RES approach and various methods to calculate the dilute gas viscosity η_ρ→0(T). The fluid viscosity η at temperature T can be expressed as the sum of the dilute gas part η_ρ→0(T) and the residual part η_res(s^r)

η = η_{ρ \to 0} (T) + η_{res} (s^{r}, T, ρ_{N})

(1)

Here s^r denotes the molar residual entropy.

Table 1. Brief Descriptions for Each of the Fluid Groups

Gr.	description
1	light gaseous fluids with quantum effects in the low temperature range, mainly hydrogen, its spin isomers, and helium
2	gaseous fluids, e.g., the noble gases
3	a majority of light hydrocarbons and halogenated hydrocarbons (most of refrigerants belong to this group)
4	fluids with benzene rings and similar fluids
5	medium hydrocarbons and similar fluids
6	heavy hydrocarbons and dense fluids
7	fluids with light intermolecular association among molecules like methanol
8	fluids with strong intermolecular association among molecules like water

Table 2. Group-Specific Parameters n_g,1, n_g,2, and n_g,3 for the Eight Groups of Fluids

group	n_g,1	n_g,2	n_g,3
1	1.297005	–3.104217	2.257168
2	0.363576	–0.074938	0.005159
3	0.392983	–0.167528	0.037984
4	0.305935	–0.128391	0.028658
5	0.286312	–0.111090	0.022642
6	0.220249	–0.070232	0.011963
7	0.305932	–0.171762	0.050058
8	0.297539	–0.209949	0.068151

Table 3. Parameters for All Pure Fluids Considered in This Work^a

REFPROP fluid name	best available	group	ξ	z^a	n₁	n₂	n₃
13BUTADIENE	REFPROP 10.0	2	1.2847	1	0.258856	–0.078886	0.017208
1BUTENE	both	5	0.8356	1	0.430921	–0.203191	0.047206
1BUTYNE	predictive	4	0.9723	0	0.305935	–0.128391	0.028658
1PENTENE	predictive	4	0.9938	0	0.305935	–0.128391	0.028658
22DIMETHYLBUTANE	proposed model	3	0.9674	1	0.644029	–0.388594	0.104904
23DIMETHYLBUTANE	proposed model	3	1.0369	1	0.328817	–0.118197	0.023611
3METHYLPENTANE	REFPROP 10.0	5	0.8682	1	0.516076	–0.282909	0.0711
ACETONE	REFPROP 10.0	4	0.9358	1	0.442736	–0.224432	0.054166
ACETYLENE	proposed model	3	0.9977	0	0.392983	–0.167528	0.037984
AMMONIA	REFPROP 10.0	7	0.9102	1	0.238911	–0.07776	0.017714
ARGON	REFPROP 10.0	2	0.957	1	0.441631	–0.198307	0.064599
BENZENE	REFPROP 10.0	4	0.8377	1	0.252163	–0.043119	0.000423
BUTANE	REFPROP 10.0	3	1.0263	1	0.369686	–0.148651	0.032041
C11	proposed model	5	1.0597	1	0.298732	–0.119667	0.024296
C12	REFPROP 10.0	5	1.1021	1	0.26995	–0.10285	0.020241
C16	REFPROP 10.0	5	1.2385	1	0.236788	–0.085333	0.015984
C1CC6	REFPROP 10.0	3	0.9783	1	0.418776	–0.188387	0.044392
C22	proposed model	6	1.159	1	0.191955	–0.062655	0.01086
C2BUTENE	proposed model	5	0.8195	1	0.512632	–0.272262	0.067693
C3CC6	predictive	3	1.1154	0	0.392983	–0.167528	0.037984
C4F10	predictive	3	1.0628	0	0.392983	–0.167528	0.037984
C5F12	few data	5	0.852	1	0.409441	–0.185661	0.04174
C6F14	both	5	0.8902	1	0.443823	–0.211872	0.048157
CF3I	few data	3	0.9358	1	0.697509	–0.480812	0.145142
CHLORINE	REFPROP 10.0	3	0.8866	0	0.392983	–0.167528	0.037984
CHLOROBENZENE	proposed model	4	0.9249	1	0.323888	–0.130118	0.028328
CO	proposed model	2	1	0	0.363576	–0.074938	0.005159
CO2	REFPROP 10.0	3	1.0174	1	0.2335	0.007837	–0.023471
COS	predictive	3	0.9325	0	0.392983	–0.167528	0.037984
CYCLOBUTENE	predictive	3	0.9789	0	0.392983	–0.167528	0.037984
CYCLOHEX	proposed model	3	0.8973	1	0.741397	–0.472354	0.132227
CYCLOPEN	REFPROP 10.0	3	0.9495	1	0.41325	–0.175764	0.040135
CYCLOPRO	few data	3	0.9517	0	0.392983	–0.167528	0.037984
D2	proposed model	1	1.3518	1	0.396609	–0.510562	0.40281
D2O	REFPROP 10.0	8	1.0445	1	0.280658	–0.182178	0.056524
D4	both	6	0.8426	1	0.3353	–0.131842	0.026054
D5	both	6	0.8501	1	0.33123	–0.124703	0.023571
D6	predictive	5	1.0959	0	0.286312	–0.11109	0.022642
DEA	proposed model	7	1.301	1	0.365242	–0.196452	0.04811
DECANE	REFPROP 10.0	5	1.026	1	0.306021	–0.125138	0.02603
DEE	REFPROP 10.0	3	1.148	1	0.319833	–0.124679	0.025516
DMC	REFPROP 10.0	3	1.1865	1	0.322188	–0.139703	0.031902
DME	REFPROP 10.0	3	1.0772	1	0.357695	–0.15162	0.03393
EBENZENE	REFPROP 10.0	4	0.9678	1	0.371309	–0.168943	0.038494
EGLYCOL	both	7	1.2176	1	0.422328	–0.22843	0.056447
ETHANE	REFPROP 10.0	3	0.9456	1	0.404667	–0.168529	0.0384
ETHANOL	proposed model	7	1.1362	1	0.292038	–0.160178	0.043583
ETHYLENE	both	3	0.9348	1	0.391366	–0.159554	0.036436
ETHYLENEOXIDE	proposed model	3	1.046	1	0.599879	–0.367331	0.099849
FLUORINE	both	2	1.0632	1	0.453053	–0.206686	0.053423
H2S	proposed model	7	0.7585	1	0.225851	–0.00749	–0.007898
HCL	proposed model	7	0.7276	1	0.028574	0.241739	–0.097719
HELIUM	both	1	1.2661	0	1.297005	–3.104217	2.257168
HEPTANE	REFPROP 10.0	5	0.9283	1	0.321695	–0.130973	0.027822
HEXANE	proposed model	5	0.8913	1	0.355662	–0.151115	0.032927
HYDROGEN	REFPROP 10.0	1	1.0136	1	2.272439	–6.277765	4.310689
IBUTENE	both	3	1.0146	1	0.406355	–0.188449	0.045383
IHEXANE	proposed model	5	0.87	1	0.368669	–0.158143	0.034655
IOCTANE	proposed model	5	0.8323	1	0.416715	–0.191216	0.043679
IPENTANE	proposed model	3	1.0344	1	0.391104	–0.168977	0.038118
ISOBUTAN	proposed model	3	0.9504	1	0.443856	–0.203979	0.048521
KRYPTON	REFPROP 10.0	2	0.9497	1	0.574447	–0.432866	0.18256
MD2M	predictive	6	1.0013	0	0.220249	–0.070232	0.011963
MD3M	predictive	6	1.0947	0	0.220249	–0.070232	0.011963
MD4M	predictive	6	1.1733	0	0.220249	–0.070232	0.011963
MDM	proposed model	6	0.9043	1	0.272782	–0.094278	0.01691
MEA	proposed model	7	1.179	1	0.394192	–0.200601	0.048884
METHANE	REFPROP 10.0	2	1.0301	1	0.436026	–0.208491	0.062506
METHANOL	proposed model	7	1.0736	1	0.3169	–0.194229	0.056838
MILPRF23699	predictive	6	1.3482	0	0.220249	–0.070232	0.011963
MLINOLEA	REFPROP 10.0	6	1.2558	1	0.151958	–0.041349	0.006241
MLINOLEN	REFPROP 10.0	6	1.2728	1	0.153776	–0.044009	0.006933
MM	few data	6	0.8248	1	0.575147	–0.299109	0.069042
MOLEATE	REFPROP 10.0	6	1.1938	1	0.183461	–0.055158	0.008903
MPALMITA	both	6	1.0704	1	0.254341	–0.090117	0.016221
MSTEARAT	few data	6	1.11	1	0.078226	–0.007601	–0.000082
MXYLENE	REFPROP 10.0	4	0.996	1	0.317989	–0.135573	0.030302
N2O	proposed model	2	1.2009	1	0.102561	0.326024	–0.210582
NEON	REFPROP 10.0	2	0.8561	1	0.375722	–0.010707	–0.018149
NEOPENTN	both	3	0.8922	1	0.415494	–0.153463	0.030807
NF3	proposed model	3	0.8253	0	0.392983	–0.167528	0.037984
NITROGEN	REFPROP 10.0	2	1.0092	1	0.340291	–0.091078	0.021042
NONANE	proposed model	5	0.9937	1	0.35713	–0.159116	0.034753
NOVEC649	predictive	4	1.048	0	0.305935	–0.128391	0.028658
OCTANE	REFPROP 10.0	5	0.9592	1	0.327911	–0.138181	0.029726
ORTHOHYD	predictive	1	1	0	1.297005	–3.104217	2.257168
OXYGEN	both	2	0.5879	0	0.363576	–0.074938	0.005159
OXYLENE	REFPROP 10.0	4	0.9475	1	0.381394	–0.178626	0.041899
PARAHYD	predictive	1	1.0284	0	1.297005	–3.104217	2.257168
PENTANE	proposed model	3	1.0806	1	0.404638	–0.184815	0.042214
POE5	predictive	6	1.2675	0	0.220249	–0.070232	0.011963
POE7	predictive	6	1.4492	0	0.220249	–0.070232	0.011963
POE9	predictive	6	1.706	0	0.220249	–0.070232	0.011963
PROPADIENE	predictive	3	0.9724	0	0.392983	–0.167528	0.037984
PROPANE	REFPROP 10.0	3	0.9744	1	0.406055	–0.178357	0.041571
PROPYLEN	proposed model	4	0.8228	1	0.511568	–0.269974	0.067762
PROPYLENEOXIDE	proposed model	3	1.074	1	0.490791	–0.265874	0.067684
PROPYNE	few data	3	1.0069	0	0.392983	–0.167528	0.037984
PXYLENE	REFPROP 10.0	4	0.9814	1	0.35906	–0.16616	0.038731
R11	proposed model	3	0.9674	1	0.424119	–0.188906	0.04421
R1123	predictive	3	1.1188	0	0.392983	–0.167528	0.037984
R113	proposed model	3	0.9528	1	0.470361	–0.225442	0.054716
R114	both	3	0.9733	1	0.615057	–0.378672	0.10544
R115	proposed model	3	0.9497	1	0.416234	–0.185289	0.044498
R116	both	3	1.1981	0	0.392983	–0.167528	0.037984
R12	proposed model	3	0.9752	1	0.336945	–0.094121	0.011411
R1216	predictive	3	1.1017	0	0.392983	–0.167528	0.037984
R1224YDZ	REFPROP 10.0	3	1.1264	1	0.146773	0.050263	–0.031134
R123	proposed model	3	1.0434	1	0.34979	–0.135478	0.028526
R1233ZDE	REFPROP 10.0	3	1.1227	1	0.3948	–0.184015	0.042551
R1234YF	REFPROP 10.0	3	1.0676	1	0.267769	–0.055341	0.001703
R1234ZEE	proposed model	3	1.0887	1	0.307227	–0.107687	0.020815
R1234ZEZ	predictive	3	1.1051	0	0.392983	–0.167528	0.037984
R124	proposed model	3	1.0288	1	0.41212	–0.18945	0.044478
R1243ZF	predictive	3	1.0406	0	0.392983	–0.167528	0.037984
R125	REFPROP 10.0	3	1.0298	1	0.326005	–0.109154	0.019807
R13	REFPROP 10.0	3	0.9866	1	0.385255	–0.158415	0.035273
R1336MZZZ	REFPROP 10.0	3	1.1513	1	0.095382	0.091688	–0.043208
R134A	REFPROP 10.0	3	1.0588	1	0.310059	–0.106155	0.020416
R14	both	3	1.0194	1	0.450154	–0.30721	0.112828
R141B	proposed model	3	0.9981	1	0.368577	–0.146787	0.032034
R142B	REFPROP 10.0	3	1.0054	1	0.198686	0.025088	–0.024214
R143A	REFPROP 10.0	3	1.0306	1	0.151459	0.08917	–0.050429
R150	proposed model	3	1.0268	1	0.535701	–0.305261	0.080679
R152A	REFPROP 10.0	3	1.0587	1	0.265764	–0.066609	0.008754
R161	proposed model	3	1.0527	0	0.392983	–0.167528	0.037984
R21	both	3	1.0294	1	0.335415	–0.112703	0.019639
R218	REFPROP 10.0	3	0.9965	1	0.361546	–0.142715	0.031279
R22	both	3	1.0343	1	0.392154	–0.174282	0.040375
R227EA	proposed model	3	1.0571	1	0.333557	–0.123002	0.02453
R23	REFPROP 10.0	3	1.0851	1	0.23995	–0.053348	0.006059
R236EA	proposed model	3	1.0467	1	0.336455	–0.126899	0.026339
R236FA	REFPROP 10.0	3	1.0897	1	0.323674	–0.119077	0.023505
R245CA	proposed model	3	1.0442	1	0.3904	–0.168551	0.037777
R245FA	REFPROP 10.0	3	1.0804	1	0.354663	–0.153191	0.035329
R32	REFPROP 10.0	3	1.1102	1	0.015284	0.220607	–0.095156
R365MFC	predictive	3	1.0755	0	0.392983	–0.167528	0.037984
R40	REFPROP 10.0	3	0.9811	1	0.142319	0.110023	–0.057116
R41	few data	3	0.9871	0	0.392983	–0.167528	0.037984
RC318	both	3	0.9792	1	0.490322	–0.247741	0.061422
RE143A	predictive	3	1.0141	0	0.392983	–0.167528	0.037984
RE245CB2	predictive	3	1.09	0	0.392983	–0.167528	0.037984
RE245FA2	proposed model	3	1.1249	1	0.386539	–0.176311	0.040336
RE347MCC	both	3	1.119	1	0.314588	–0.111438	0.020902
SF6	REFPROP 10.0	2	1.0969	1	0.182282	0.122179	–0.070003
SO2	proposed model	2	1.3355	1	0.000376	0.167659	–0.062185
T2BUTENE	predictive	3	1.0062	0	0.392983	–0.167528	0.037984
TOLUENE	REFPROP 10.0	4	0.9191	1	0.377943	–0.174981	0.041297
VINYLCHLORIDE	predictive	3	1.0429	0	0.392983	–0.167528	0.037984
WATER	REFPROP 10.0	8	1.0038	1	0.294605	–0.21161	0.069198
XENON	proposed model	2	0.9514	1	0.421622	–0.101908	0.008931

^{^a}

The column “best available” indicates whether the proposed model is the best available based solely on our data set. The entries are as follows: If ARD and AARD are both lower compared to using REFPROP 10.0’s default model, “proposed model” is assigned. If the AARD of the proposed model is lower, while the ARD is higher, “both” is indicated. For fluids, where REFPROP 10.0’s default models perform better on both indicators, “REFPROP 10.0” is written. In cases, where our data set contains less than 20 data points, “few data” is specified. “predictive” is used in cases, where the coefficients are determined without any data. The column z^a indicates whether fluid-specific parameters are available (z^a = 1) or not (z^a = 0). If fluid-specific parameters are available, then ξ = 1 is used in the calculation instead of the shown value for ξ. The equation with appropriate global exponents is .

Figure 1. AARD (upper plot) and ARD (lower plot) of the filtered (or analyzable) experimental data from the model predictions. REF. models refers to the default viscosity models in REFPROP 10.0. For the remaining models, the labels comprise two parts connected by a “+” symbol. The former part denotes the method for dilute gas viscosity η_ρ→0(T) calculation (see Section 2.1): oLJ uses L-J parameters, oREF uses REFPROP 10.0, oP3 uses a third-order polynomial, oP4 uses a fourth-order polynomial, and oCP uses the critical point information. The latter part refers to the residual viscosity calculation method: rP4 is a 4-term power function used in the previous work (6) and rP3 is the 3-term power function developed in the present work.

Figure 2. AARD of the REFPROP 10.0 models and the oREF + rP3 model predictions to the filtered experimental data for each pure fluid. The fluids are further classified according to the model types used by REFPROP 10.0: (a) reference correlations, (32−67) (b) ECS model with fitted parameters or friction theory models, (47,58,61) and (c) ECS model without fitted parameters and other models. (68−70) Fluid names in REFPROP 10.0 are adopted (see the Appendix for their respective IUPAC chemical names and CAS registry numbers). The entries are sorted primarily by whether the proposed RES model has a lower AARD than that of REFPROP 10.0 and secondarily according to increasing AARD of the proposed model. The green background indicates that the proposed model is better.

Figure 3. ARD of the REFPROP 10.0 models and the oREF + rP3 model predictions to the filtered experimental data for each pure fluid. The fluids are further classified according to the model types used by REFPROP 10.0: (a) reference correlations, (32−67) (b) ECS model with fitted parameters or friction theory models, (47,58,61) and (c) ECS model without fitted parameters and other models. (68−70) Fluid names in REFPROP 10.0 are adopted (see the Appendix for their respective IUPAC chemical names and CAS registry numbers). The entries are sorted primarily by whether the proposed RES model has a lower absolute ARD than that of REFPROP 10.0 and secondarily according to increasing ARD of the proposed model. The green background indicates that the proposed model is better.

Figure 4. Plus-scaled dimensionless residual viscosity η_res⁺ as a function of $s^{+} / ξ$ for each group of pure fluids, where s⁺ is the plus-scaled residual entropy and ξ is the fluid-specific scaling factor. The group-specific parameters n_i,g are used to calculate the curves. All groups are shown at the bottom. Each group is also illustrated and annotated stacked by a power of 20 at the top to highlight the qualitative differences.

Figure 5. Ratio $ξ / s_{crit}^{+}$ of all considered pure fluids, where ξ is the fluid-specific scaling factor and s_crit⁺ is the plus-scaled dimensionless residual entropy at the critical point, which is obtained from REFPROP 10.0. The group numbers are annotated in the top right of each box. At $ξ / s_{crit}^{+} = 0.7$ , a vertical dashed dotted line is drawn. Values for group 1 exceed the plot limits, i.e., PARAHYD: 1.67, ORTHOHYD: 1.61, HYDROGEN: 1.64, HELIUM: 4.09, D2:1.86.

Figure 6. ARD and AARD of the experimental data of 351 binary mixtures from predictions of models. “All selected data”: for calculations with the RES model, similar filters as used in pure fluids were applied for mixture data. “Further filtered data”: one more filter is applied to the “All selected data” so that calculations are also available with REFPROP 10.0 models. For combinations with no available data, 0.0 is given.

For pure fluids, four methods are used for the η_ρ→0(T) calculation in the present work. The first method (denoted as oREF) is simply using REFPROP 10.0, which implements a variety of different methods depending on the particular fluid. The second method (denoted as oP3 and oP4) is to use a polynomial as a function of temperature

η_{ρ \to 0} (T) = m_{4} T^{4} + m_{3} T^{3} + m_{2} T^{2} + m_{1} T + m_{0}

(2)

where T is the temperature in K. The parameters m₀, m₁, m₂, m₃, m₄ are fitted against calculations of REFPROP 10.0 from the triple point temperature to generally 1000 K or the highest calculable temperature and are implemented in the software package oilmixprop 1.0. (22) The parameters are also included in the Supporting Information (SI) of the present work. Note that the fourth-order polynomial for η_ρ→0(T) (denoted as oP4) yields better results than the third-order polynomial (denoted as oP3), while a fifth-order polynomial does not achieve notably better results. The third method (denoted as oLJ) is the same as the one used in our previous work (6) and is described below. Assuming the molecular interactions can be approximated by those of L-J particles, η_ρ→0(T) can be calculated using the Chapman–Enskog (23) solution of the Boltzmann transport equation

η_{ρ \to 0} (T) = \frac{5}{16} \sqrt{\frac{m k_{B} T}{π}} \frac{1}{σ^{2} Ω^{(2, 2) *}}

(3)

where m is the molecular mass in units of kg, k_B = 1.380649 × 10^–23 J/K is the Boltzmann constant, σ is the collision diameter of the L-J particle in unit of m, and Ω^(2,2)* is the reduced collision integral obtained by integrating the possible approach trajectories of the particles. An empirical correlation of Ω^(2,2)* for the Lennard–Jones fluid as a function of T was used

Ω^{(2, 2) *} = 1.16145 \cdot T^{* - 0.14874} + 0.52487 \cdot e^{- 0.77320 \cdot T *} + 2.16178 \cdot e^{- 2.43787 \cdot T *}

(4)

where T* = k_BT/ϵ is the dimensionless temperature, and ϵ/k_B is the reduced L-J pair-potential energy. This equation is also used in REFPROP 10.0 (20) and is a simplification of the original one proposed by Neufeld et al. (24) In the third method, σ and ϵ were obtained from REFPROP 10.0 and are listed in the SI of our previous work. (6) The fourth method (denoted as oCP) is almost the same as the third one, except that the L–J parameters σ and ϵ are estimated according to the predictive correlations of Chung et al. (25)

ϵ / K_{B} = T_{c} / 1.2593

(5)

σ^{3} = 0.3189 / ρ_{c}

(6)

where T_c and ρ_c are critical temperature in units of K and critical density in units of m^–3, respectively. These fluid constants were obtained from REFPROP 10.0 and can be found in the SI of our previous work. (13) Please note that in the third and fourth methods of calculating the dilute gas viscosity, the molecular interactions are approximated by those of L-J particles. However, this does not mean that all molecules are assumed to be spherical in this work. It only means that only the dilute gas portion is treated in that manner.

Now, we discuss the residual part of viscosity η_res(s^r), which, as introduced by Bell et al., (3,10) can be calculated by

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

(7)

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

(8)

Here, ρ_N is the number density in unit of 1/m³, s^r is the molar residual entropy in unit of J/(mol K), defined as the difference between the real fluid entropy and the ideal gas entropy at the same temperature and density, i.e., s^r(T, ρ) = s(T, ρ) – s⁰(T, ρ), and R ≈ 8.3145 J/(mol K) is the molar gas constant. (26) The plus-scaled dimensionless residual viscosity η_res⁺ (see eq 7) is linked to the plus-scaled dimensionless residual entropy s⁺ (see eq 8) using power functions to be discussed in the following section; see eq 13.

The Python interface of package CoolProp 6.4.1 (27) was used to call REFPROP 10.0 (20) and calculate the number density ρ_N and molar residual entropy s^r for both pure fluids and mixtures in the present work. The reference EOS used for each pure fluid are listed in Table S2 in the SI in our previous work. (13)

For mixtures, a predictive mixing rule was utilized to allow the RES model to predict the viscosity of mixtures without any additional adjustable parameters. The dilute gas viscosity for mixtures η_ρ→0,mix is obtained with the approximation of Wilke (28)

η_{ρ \to 0, mix} = \sum_{f = 1}^{N} \frac{x_{f} \cdot η_{ρ \to 0, f}}{\sum_{j = 1}^{N} x_{j} \cdot ϕ_{fj}}

(9)

with

ϕ_{fj} = \frac{{[1 + {(η_{ρ \to 0, f} / η_{ρ \to 0, j})}^{1 / 2} \cdot {(m_{j} / m_{f})}^{1 / 4}]}^{2}}{{8 \cdot [1 + (m_{f} / m_{j})]}^{1 / 2}}

(10)

where x_f and m_f are the mole fraction and the mass of one molecule of component f. In eqs 7 and 8, the effective mass of one particle m is substituted by the mole fraction weighted average m_mix

m_{mix} = \sum_{f} x_{f} \cdot m_{f}

(11)

Then, the mole fraction weighted average coefficients n_i,mix are utilized to substitute the fluid-specific and group-specific parameters n_i, i.e.

n_{i, mix} = \sum_{f} x_{f} \cdot n_{i, f}

(12)

where n_i,f (i = 1, 2, 3) are fitted parameters of pure fluid f (see the following section). The utilized mixing rules allow predictions of not only binaries but also multicomponent mixtures.

2.2. Equation Design, Predictions, and Parameter Identification

As mentioned in our previous work, (6,12,13) the plus-scaled dimensionless residual viscosity η_res⁺ is linked to the plus-scaled dimensionless residual entropy s⁺ with the following equation

\ln (η_{res}^{+} + 1) = n_{1, X} {(s^{+} / ξ_{f})}^{p_{1}} + n_{2, X} {(s^{+} / ξ_{f})}^{p_{2}} + n_{3, X} {(s^{+} / ξ_{f})}^{p_{3}} + n_{4, X} {(s^{+} / ξ_{f})}^{p_{4}}

(13)

In eq 13, p_i (i = 1, 2, 3, 4) are global parameters that are the same for all fluids. n_i,X (i = 1, 2, 3, 4) are either fluid-specific (X = f) parameters, which are different for each fluid f, or group-specific parameters (X = g), which are different for each group of fluids g. The classification of the studied 124 pure fluids into eight groups is exactly the same as in our previous work. (13) In Table 1, a short description for each group is provided, while the group numbers for each fluid are indicated in Table 3.

For a pure fluid, when there are sufficient good-quality data, fluid-specific parameters n_i,f can be obtained; otherwise, group-specific parameters n_i,g must be used. ξ_f is the fluid-specific scaling factor, which is equal to 1 when n_i,f is in use, or is a fitted value when n_i,g is in use.

In the previous work, p_i values (i = 1, 2, 3, 4) were taken equal to 1.0, 1.5, 2.0, 2.5, respectively, which were determined by the trial-and-error method. In the present work, p_i values were optimized with a comprehensive optimization procedure as summarized in Algorithms 1 and 2.

The same data filters F₁, F₂, F₃ as in the previous work (13) were adopted. The first filter F₁ removes data that exceed the limitation of the used EOS in calculating density and residual entropy. These data amount to approximately 3.5% of all data. The second filter F₂ removes data that suggest conflicting phase information. For instance, a high viscosity value suggests the fluid is in the liquid phase while the given temperature and pressure indicates that the fluid is in the gas phase. About 1.3% of the data were screened out with this filter. To handle outliers, the third filter F₃ removes data whose relative deviation from the model prediction is larger than a set threshold. We used 30% for the threshold, which is the same as in the previous work. Filter F₃ is involved in the iteration of Algorithm 1, and, in the end, only approximately 1.1% of the data are filtered out with this filter. Due to the very few data filtered out, there is limited risk that filter F₃ is too selective, making the model appear to have a small deviation while actually steering the model in the wrong direction. For each fluid, the number of all data and of those filtered by each filter are summarized in a table in the SI of the present work.

As shown in Algorithm 1, the third filter F₃ is carried out in every optimization loop. In each loop, the method to determine n_i,f, n_i,g, and ξ_f is the same as in the previous work, (13) while the method to determine p_i is inspired by the literature (29−31) and summarized in Algorithm 2.

In Algorithm 2, for p_i optimization, only fluids with fluid-specific parameters n_i,f, i.e., with data of sufficiently good quality, are involved. This reduces the complexity of Algorithm 2 while there are still more than 90% of all screened data in use. For each studied fluid in Algorithm 2, an objective function is defined

Minimize

\frac{1}{n} \sum_{k = 1}^{n} {(η_{res, k}^{+} - f (s_{k}^{+}, p_{f}, n_{f}))}^{2} + σ_{j} \sum_{i = 1}^{3} (p_{i, f} - {\bar{p}}_{i})^{2}

(14)

w.r.t. p_f, n_f, where p_i,f are the fluid-specific p_i parameters for fluid f, p̅_i is the mean of p_i,f across all fluids, σ_j is a penalty weighting factor in the iteration step j, and η_res,k⁺ and s_k⁺ are the k-th data points to be fitted. This objective function couples the individual optimization problems (the first term in the objective function) by applying a penalty (the second term in the objective function) to the parameters intended to be global for each individual problem. The strategy to push fluid-specific p_i,f toward their mean p̅_i is to start with a very small penalty weighting factor, i.e., σ_j = 10^–5, and then increase it step by step σ_j = σ_j · σ_increase with an increasing factor σ_increase = 1.2.

3. Results and Discussion

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3.1. New RES Model

With the algorithms described in the previous section, the final optimized global parameters p_i (i = 1, 2, 3) are 1.8, 2.4, and 2.8, respectively. The fluid-specific parameters n_i,f are listed in Table 3, the group-specific parameters are listed in Table 2 and their fluid-specific scaling factors are listed in Table 3.

To note, the 4-term power function is reduced to a 3-term one. The 4-term power function is denoted as rP4, while the 3-term one is denoted as rP3. There are two key arguments for this simplification. First, to avoid negative slope of the ln(η_res⁺ + 1) vs. s⁺ curve at the condition s⁺ = 0, the lower bound of n_1,X in the lowest power term is zero in the fitting. Although a negative slope is physical, (3) a positive slope helps to avoid overfitting for those fluids without data in the gas phase. As a result, n_1,X = 0 holds in many fluids and groups. Second, compared to the 4-term equation, a 3-term one allows more fluids, particularly those without gas phase data, to have fluid-specific parameters. This is because, when there are no data in the gas phase, the 4-term equation overfits the data and delivers unreasonable parameters, while this problem is avoided by using the 3-term one.

To evaluate the new RES model, two statistical values AARD and the average relative deviation (ARD) are defined

AARD = \frac{1}{n} \sum_{k = 1}^{n} | \frac{η_{\exp, k} - η_{calc, k}}{η_{\exp, k}} |

(15)

ARD = \frac{1}{n} \sum_{k = 1}^{n} \frac{η_{\exp, k} - η_{calc, k}}{η_{\exp, k}}

(16)

where η_exp,k is the experimental viscosity of data point k and η_calc,k is the prediction by a model. The AARD is a measure of the scattering, while the ARD denotes systematic offsets. The AARD (upper plot) and ARD (lower plot) plots of the filtered (or analyzable) experimental data from different models are presented in Figure 1. REFPROP 10.0, as the state-of-the-art software package to accurately calculate thermophysical properties, was adopted as a baseline. For the fluids studied here, the default viscosity models in REFPROP 10.0 are reference correlations (32−67) for 43 pure fluids, extended corresponding states models (58,68−70) for 77 pure fluids, and friction theory models (47,61) for three pure fluids. For fluid NF3, REFPROP 10.0 does not provide a viscosity model. The various RES-based models with different η_ρ→0(T) calculation methods (see Section 2.1) and residual viscosity calculation with different power functions (the 4-term one from the previous work and the 3-term one in the present work) are also shown in Figure 1.

As can be seen in Figure 1, REFPROP 10.0 yields the lowest AARD (2.74%), i.e., the lowest scattering of experimental data from model, but with almost the largest ARD (0.7%), i.e., the largest systematic offset from experimental data to the model. The best RES approach is the one with η_ρ→0(T) calculated using REFPROP 10.0 (oREF in Figure 1) and with residual viscosity calculated using the 3-term power function (rP3) from the present work. Compared to REFPROP 10.0, it yields slightly higher AARD (only 0.02% higher) but almost zero absolute ARD and with 1% more data analyzable (or 1% fewer data filtered out). Of course, the comparison to REFPROP 10.0 models is not entirely fair. A fair comparison should be that only data used to develop the REFPROP 10.0 models were adopted to assess our models. Such a comparison is however not straightforward to achieve given the documentary standards in the open literature, so it was not attempted. The parameters listed in Tables 2 and 3 are all based on this RES approach (oREF + rP3). A Python package containing the proposed model including the corresponding parameters is provided in the SI.

If η_ρ→0(T) is calculated with polynomials (oP3 or oP4), the AARD slightly increases (less than 0.1%). This method is favored as the η_ρ→0(T) is a relatively simple correlation with few parameters, and it helps to develop an RES approach more independent of REFPROP 10.0 in the future. If η_ρ→0(T) is calculated with reliable L-J parameters (oLJ), the AARD reaches up to 3.4%; the benefits here are that fewer parameters are needed and fluids not implemented in REFPROP 10.0 can also be studied. If η_ρ→0(T) is calculated with L-J parameters estimated using critical point information (oCP), the AARD reaches up to 4.5%. In this case, if critical point, mole mass, and acentric factor of a pure or quasi-pure fluid are known, only three additional n_i,f (i = 1, 2, 3) parameters are needed to enable reliable viscosity prediction (with an estimated standard uncertainty of 4.5%). Such applications have been seen in our previous work in fluid optimization (71) and oil property modeling. (72)

Compared to the previous work (13) in which a 4-term power function is used for residual viscosity calculation (rP4), the 3-term equation, in the present work, rP3 yields improved performance. The key reasons are (1) the function form with power terms is optimized and (2) overfitting is avoided so that more fluids have individual fluid-specific parameters.

3.2. Details for Pure-Fluid Correlation

The previous section provides the overall statistics of the performance of the best RES approach (oREF + rP3), while this section presents the details of its correlation of each pure fluid.

The AARD and ARD of the filtered experimental data from model predictions for each pure fluid are illustrated in Figures 2 and 3, respectively. Although overall REFPROP 10.0 has a lower AARD than the proposed RES model (see Figure 1), the proposed RES model shows a smaller AARD than REFPROP 10.0 for more than half of the 124 fluids. The proposed approach yields both, a lower AARD and ARD, for 48 of the pure fluids. The new RES model could be considered as the best available one according to the considered data. Direct comparison with the primary data sets selected by the authors of the reference correlation is required to make a more authoritative comparison. Such a comparison is not feasible to do because many of the data sets are not included in the NIST Thermo Data Engine database. This is also indicated in Table 3. The standard uncertainty of the RES model is estimated to be 2.8%, as approximately 68.4% (corresponding to one standard deviation of a normal distribution) of the data agree with the model within this threshold. The ARD of the proposed RES model for most of the pure fluids is significantly lower than that of REFPROP 10.0. One hundred and one fluids exhibit an absolute ARD of less than 1%, while 117 are below 2%. Most fluids with more than 1000 points have an absolute ARD of below 1%, while all are 1.5% or lower. Fluids with an absolute ARD larger than 2% are generally those with data only in the gas phase (e.g., R161), with very few data (e.g., CYCLOPRO, R41), or with less accurate dilute gas viscosity calculations (e.g., KRYPTON). The AARD and ARD of some fluids seem to be zero because either no model is available, e.g., for NF3 in REFPROP 10.0, or only dilute gas viscosity data are available, e.g., for CO.

Figure 4 shows the values of η_res⁺ + 1 as a function of

s^{+} / ξ

for each group of pure fluids. As expected and similar to the previous work, (13) each group’s fluids collapse into one curve. The fluid-specific scaling factors ξ_f of each fluid are listed in Table 3 and the ratio

ξ / s_{crit}^{+}

are shown in Figure 5, where s_crit⁺ is the plus-scaled dimensionless residual entropy at the critical point obtained from REFPROP 10.0. The ratios in group 3 are approximately 0.7, and for groups with heavier components, the ratios generally decrease, which is in good agreement to literature. (4,13,73) With the group-specific parameters and the almost-constant

ξ / s_{crit}^{+}

ratio in each group, one may obtain rough estimates of viscosity for fluids without data if the EOS yields a reasonable value for the residual entropy at the critical point. This can be done by classifying a fluid into one of the groups and use its constant

ξ / s_{crit}^{+}

ratio to estimate its ξ_f, based on the similarity of molecular structure, or on existing models. For example, the latter method has been applied to some fluids in the present work. These are indicated with “predictive” in the “best available” column in Table 3. For these 27 pure fluids, which are available in REFPROP 10.0 but for which no viscosity were available in the NIST ThermoDataEngine, 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 “experimental data”; (2) fitting ξ_f using each group’s group-specific parameters with these “experimental data”; (3) assigning the group number of this fluid where its ξ_f is the most close to 1. These results are listed in Table 3. Finally, we would like to mention, compared to our previous work, (13) group 1 is still a noticeable outlier in terms of fluid-specific scaling factors ξ_f as shown in Figure 5.

Group 1 comprises fluids with quantum effects at low temperatures, i.e., hydrogen, deuterium, and helium. Not only is the data availability low but also it is crucially low in areas where we expect the RES approach to worsen for those fluids. A simple empirical means of handling at least some of the quantum correction to the RES approach for the cryogens has been proposed, (74) but further study is required. Furthermore, the results for water look better than they actually are, as the available data in the NIST ThermoDataEngine is not comprehensive. More experimental data of water and maybe alcohols need to be collected to further evaluate the RES model for these fluids.

3.3. Prediction for Mixtures

For fluid mixtures, the developed RES approach is a pure prediction method, i.e., no additional adjustable parameter is needed. In total, 33,109 data were collected from 351 binary mixtures as used in our previous work. (13) An overview of statistical measures of the prediction performance of the developed RES approach is shown in Figure 6. Please note: (1) REFPROP 10.0 does not calculate dilute gas viscosity of many mixtures, especially those involving alcohols. Therefore, for the dilute gas viscosity of a mixture, the fourth-order polynomial (eq 2) was adopted for pure component calculation with the mixing rule of the approximation of Wilke (28) as described in Section 2.2. (2) For all the collected mixture data, similar filters as used in pure fluids were applied, and the remaining data were named “all selected data” in Figure 6. REFPROP 10.0 cannot calculate about 20.5% of “all selected data”; therefore, one more filter was applied so that calculations were also available with REFPROP 10.0 models, and the remaining data are named “Further filtered data” in Figure 6. In summary, the proposed model agrees with 68.2% of “all selected data” within 7.8%.

With the RES model, for binary mixtures of the same group, the ARD is generally less than 2.7%. Mixtures within group 5 show particularly low ARD, namely 0.2%. The ARD for mixtures of different groups varies widely, ranging from 0.8% for groups 1 and 2 (with 1982 data points) up to 16.3% for groups 7 and 8 (with 3625 data points). As shown in Figure 6, the AARD of the all selected data has a relatively wide range depending on the group combination. The scatter for different groups are, however, mostly in the same order of magnitude as REFPROP 10.0’s, while some are lower. In total, the proposed model has a lower AARD than REFPROP 10.0 for 185 out of the 351 considered mixtures.

Modeling the viscosity of mixtures has been a challenging issue, especially for those composed of molecules of very different sizes. For instance, the AARD are very high for both the new RES model and the models in REFPROP 10.0 in comparison to experimental data of groups 1 and 8 (light gas and liquid with strong association force) and those involving group 6 (heavy molecules). One of the key reasons is that the viscosity changes thousands of times from a pure component of small molecular size (for example, a refrigerant R32 in group 3) to a pure component in group 6 of large molecular size (for example, dodecane as a lubricant oil in group 6). This, on the one hand, makes accurate measurements very hard and, on the other hand, makes the model generally yield very large deviations (e.g., on the order of 30%) if the given composition has a 1% uncertainty. Modeling mixtures using proper mixing rules is an important and interesting topic of future work.

4. Conclusions

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The RES approach developed in our previous work was successfully improved. The approach demonstrates an accuracy on par with that of the fluids in REFPROP 10.0 not modeled by fluid-specific correlations. The key improvement lies in the optimization of the relations between the residual viscosity and the residual entropy. In the previous work, they are related by a 4-term power function determined manually, while in the present work they are related by a 3-term power function determined with a comprehensive fitting procedure. As a result, the average absolute relative deviation, corresponding to scattering of the experimental data from the model, is reduced down to 2.76%; this is very close to 2.74% obtained with the various multiparameter models in REFPROP 10.0. Meanwhile, the average relative deviation, corresponding to systematic offset of the experimental data to the model, is 0.03%, which is significantly better than REFPROP 10.0’s 0.7%. Based solely on the data available to us, for 48 of the 124 pure fluids, the proposed approach yields both a lower AARD and ARD. For mixture predictions, the RES approach is a pure prediction method, which agree with more than 68.4% of the data within 7.8%. Therefore, we could roughly estimate our RES having a standard uncertainty of 2.8% for pure fluids and 7.8% for mixtures.

The present work also investigates various methods to calculate the dilute gas viscosity. The method using REFPROP 10.0 calculation yields the best agreement with the experimental data. A fourth-order polynomial for dilute gas viscosity was developed in the present work which yields slightly worse results compared to REFPROP 10.0 but has a simple functional form which can be used for all studied fluids. Methods based on L-J parameters either obtained from reliable sources or estimations with critical point information were evaluated, as well. Both yield higher AARD. Nonetheless, with the last method, no additional parameters are needed for dilute gas viscosity calculation, while it yields AARD only twice (4.49% compared to 2.76%) of the best RES method here. To use the model developed in the present work, a Python package is provided in the SI. Fluid-specific parameters are suggested to be used, and only if they are not available should group-specific parameters with the fluid-specific scaling factor be used.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jced.4c00451.

main.py (PY): implementation of the core of the RES model; Dilute_gas_viscosity.txt (TXT): parameters for the calculation of the dilute gas viscosity; RES_Parameter.txt (TXT): parameters for the models; Samples_* (TXT): all files beginning with “Samples_” are sample calculations that may be used to verify the model; Data_evaluation_REF_15.txt (TXT): various statistics concerned with the data used for the pure fluid calculations; Data_evaluation_mix.txt (TXT): various statistics concerned with the data used for the mixtures calculations; Table_multi.txt (TXT): information about the experimental data of mixtures; Table_pure_REF_15.txt (TXT): various statistics of the model qualities for the pure fluids; Fluid_Constants.txt (TXT): fluid constants used; pure-fluid data and literature.docx (DOCX): detailed information on pure fluid data and the literature; figure_pure_devs (folder/*PNG): relative deviation for all used data points for the RES model and REFPROP models for all substances; figure_pure_groups (folder/*PNG): η_res⁺ + 1 as a function of $s^{+} / ξ$ for one group each; mix_dev_exp_res_ecs (folder/*PNG): relative deviations for all mixtures for the RES model and the REFPROP models individually, as well as their data sources; mix_s_eta_all_data (folder/*PNG): η_res⁺ + 1 as a function of $s^{+} / ξ$ for each mixture individually for all data, as well as the data sources; mix_s_eta_select_data (folder/*PNG): η_res⁺ + 1 as a function of $s^{+} / ξ$ for each mixtures individually for the filtered data, as well as the data sources; pure_dev_exp_res_ecs (folder/*PNG): relative deviations for all pure fluids for the RES model and the REFPROP models individually, as well as the data sources; pure_s_eta_all_data (folder/*PNG): η_res⁺ + 1 as a function of $s^{+} / ξ$ for each pure fluid individually for all data, as well as the data sources; pure_s_eta_fitted_data (folder/*PNG): η_res⁺ + 1 as a function of $s^{+} / ξ$ for each pure fluid individually for the filtered data, as well as the data sources (ZIP)

je4c00451_si_001.zip (111.11 MB)

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Author Information

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Corresponding Author
- Xiaoxian Yang - Faculty of Mechanical Engineering, Applied Thermodynamics, Chemnitz University of Technology, 09107 Chemnitz, Germany; https://orcid.org/0000-0003-4655-3156; Email: [email protected]
Authors
- Viktor Martinek - Interdisciplinary Center for Scientific Computing, Heidelberg University, 69120 Heidelberg, Germany; https://orcid.org/0000-0001-6215-4783
- Ian Bell - Applied Chemicals and Materials Division, National Institute of Standards and Technology, Boulder, Colorado 80305, United States
- Roland Herzog - Interdisciplinary Center for Scientific Computing, Heidelberg University, 69120 Heidelberg, Germany
- Markus Richter - Faculty of Mechanical Engineering, Applied Thermodynamics, Chemnitz University of Technology, 09107 Chemnitz, Germany; https://orcid.org/0000-0001-8120-5646
Author Contributions
Study conception and design: X.Y.; data collection: X.Y., I.B.; optimization methodology: V.M., R.H., X.Y.; analysis and interpretation of results: V.M., X.Y.; draft manuscript preparation: V.M.; manuscript major revision: I.B., X.Y.; funding acquisition: R.H., M.R. All authors reviewed the results and approved the final version of the manuscript.
Notes
The authors declare no competing financial interest.

Acknowledgments

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This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)─HE 6077/14-1 and RI 2482/10-1─within the Priority Programme “SPP 2331: Machine Learning in Chemical Engineering”. Partial support was provided by NIST. This work was also supported by the German Federal Ministry of Education and Research on the basis of a decision by the German Bundestag (Funding Code 03SF0623A).

Appendix: Fluid Name Glossary

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In the following, the REFPROP 10.0 names of all considered fluids are listed with their corresponding IUPAC chemical names and their CAS Registry numbers:

References

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This article references 74 other publications.

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In this work, a residual entropy value of 6/10 of the way between the crit. point and a value of -2/3 of Boltzmann const. is shown to collapse the scaled viscosity for the family of normal alkanes. Based on this approach, a nearly universal correlation is proposed that can reproduce 95% of the exptl. data for normal alkanes within ±18% (without removal of clearly erroneous data). This universal correlation has no new fluid-specific empirical parameters and is based on exptl. accessible values. This collapse is shown to be valid to a residual entropy half-way between the crit. point and the triple point, beyond which the macroscopically scaled viscosity has a superexponential dependence on residual entropy, terminating at the triple point. A key outcome of this study is a better understanding of entropy scaling for fluids with intramol. degrees of freedom. A study of the transport and thermodn. properties at the triple point rounds out the anal.
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Journal of Chemical Physics (2020), 152 (16), 164104CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
In this work, we have investigated the mono-variant relationship between the reduced viscosity and residual entropy in pure fluids and in binary mixts. of hydrocarbons and hydrocarbons with dissolved carbon dioxide. The mixts. considered were octane + dodecane, decane + carbon dioxide, and 1,3-dimethylbenzene (m-xylene) + carbon dioxide. The reduced viscosity was calcd. according to the definition of Bell, while the residual entropy was calcd. from accurate multi-parameter Helmholtz-energy equations of state and, for mixts., the multi-fluid Helmholtz energy approxn. The mono-variant dependence of reduced viscosity upon residual molar entropy was obsd. for the pure fluids investigated, and by incorporating two scaling factors (one for reduced viscosity and the other for residual molar entropy), the data were represented by a single universal curve. To apply this method to mixts., the scaling factors were detd. from a mole-fraction weighted sum of the pure-component values. This simple model was found to work well for the systems investigated. The av. abs. relative deviation (AARD) was obsd. to be between 1% and 2% for pure components and a mixt. of similar hydrocarbons. Larger deviations, with AARDs of up to 15%, were obsd. for the asym. mixts., but this compares favorably with other methods for predicting the viscosity of such systems. We conclude that the residual-entropy concept can be used to est. the viscosity of mixts. of similar mols. with high reliability and that it offers a useful engineering approxn. even for asym. mixts. (c) 2020 American Institute of Physics.
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Yang, 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, 1385– 1398, DOI: 10.1021/acs.jced.0c01009
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Liu, H.; Yang, F.; Yang, Z.; Duan, 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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Bell, I.; Laesecke, A. In Viscosity of Refrigerants and Other Working Fluids from Residual Entropy Scaling , 16th International Refrigeration and Air Conditioning Conference at Purdue, 2016; p 2287. https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=920655.
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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, 4070– 4079, DOI: 10.1073/pnas.1815943116
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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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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, 4095– 4114, DOI: 10.1021/acs.iecr.7b04871
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Yang, X.; Xiao, X.; Thol, M.; Richter, M.; Bell, I. In A Residual Entropy Scaling Approach for Viscosity of Refrigerants, Other Fluids and Their Mixtures , 26th International Congress of Refrigeration, 2023.
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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, 183, DOI: 10.1007/s10765-022-03096-9
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Linking Viscosity to Equations of State Using Residual Entropy Scaling Theory
Yang, Xiaoxian; Xiao, Xiong; Thol, Monika; Richter, Markus; Bell, Ian H.
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Abstr.: In our previous work (J Chem Eng Data 2021, 66(3):1385-1398), a residual entropy scaling (RES) approach was developed to link viscosity to residual entropy [a thermodn. property calcd. with an equation of state (EoS)] using a simple polynomial equation for refrigerants. Here, we present an extension of this approach to a much wider range of fluids: all pure fluids and their mixts. whose ref. EoS and exptl. viscosity data are available. A total of 84 877 exptl. points for 124 pure fluids and 351 mixts. are collected from 1846 refs. The investigated pure fluids contain a wide variety of fluids from light gases with quantum effects at low temps. to dense fluids and fluids with strong intermol. assocn. More than 68.2 % (corresponding to the std. deviation) of the evaluated exptl. data agree with the RES model within 3.2 % and 8.0 % for pure fluids and mixts., resp. Compared to the recommended models implemented in the REFPROP 10.0 software (the state-of-the-art for thermophys. property calcn.), if the dil. gas viscosity is calcd. in the same way, our RES approach yields similar statistical agreement with the exptl. data while having a much simpler formulation and fewer parameters. To use our RES model, a software package written in Python is provided in the supporting information. Graphical Abstr.: [graphic not available: see fulltext].
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Dehlouz, A.; Privat, R.; Galliero, G.; Bonnissel, M.; Jaubert, J.-N. Revisiting the entropy-scaling concept for shear-viscosity estimation from cubic and SAFT equations of state: application to pure fluids in gas, liquid and supercritical states. Ind. Eng. Chem. Res. 2021, 60, 12719– 12739, DOI: 10.1021/acs.iecr.1c01386
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Industrial & Engineering Chemistry Research (2021), 60 (34), 12719-12739CODEN: IECRED; ISSN:0888-5885. (American Chemical Society)
The entropy scaling concept postulates that reduced transport properties of fluids are related to the residual entropy, a property that reveals intermol. interactions and can be estd. from equations of state (EoS) in a straightforward way. In that framework, two models for dynamic viscosity are presented in this paper: in both models, similar expressions inspired from Rosenfeld's seminal idea are used to reduce transport properties and are related to a carefully selected function of the Tν-residual entropy. This latter is estd. from the PC-SAFT EoS for one model or the tc-PR cubic EoS for the other. The two models are able to predict the viscosities in the entire fluid region (liq., gas, and supercrit. states), which is a great advantage, in comparison to most of the correlations available in the open literature that are specific to a phys. state. Model parameters were fitted over a large database contg. more than 100 000 pure-fluid exptl. data assocd. with 142 chem. species. For each model, different sets of parameters are provided, each of them being likely to be used in specific situations: first, component-specific parameters were estd. for 142 pure compds.; second, chem.-family specific parameters were proposed for describing components not included in our database but belonging to one of the chem. families we considered. Eventually, for compds. present neither in the original database, nor in the considered chem. families, universal parameters (leading to lower accuracy but applicable to any species) are proposed. The accuracy of the models is obviously maximal when using component-specific parameters and minimal with universal parameters. Thus, the entropy-scaling formulation presented in this work can be used for routinely modeling the dynamic viscosity of any pure fluid. As main advantages, it can be applied to any pure species without restriction and is valid for all fluid states, from the dil. gas to the liq. and even the supercrit. state.
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Liu, H.; Yang, F.; Yang, X.; Yang, Z.; Duan, 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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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, 5688– 5697, DOI: 10.1021/acs.jced.0c00682
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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, 4527– 4538, DOI: 10.1021/acs.iecr.6b04289
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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.; 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, 18432– 18438, DOI: 10.1021/acs.iecr.9b03998
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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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Yang, X.; Kim, D.; May, E. F.; Bell, I. H. Entropy scaling of thermal conductivity: application to refrigerants and their mixtures. Ind. Eng. Chem. Res. 2021, 60, 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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Neufeld, P. D.; Janzen, A. R.; Aziz, R. A. Empirical equations to calculate 16 of the transport collision integrals Ω^{(l,s)^*} for the Lennard-Jones (12–6) potential. J. Chem. Phys. 1972, 57, 1100– 1102, DOI: 10.1063/1.1678363
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Empirical equations to calculate 16 of the transport collision integrals Ω(1,s)* for the Lennard-Jones (12-6) potential
Neufeld, Philip D.; Janzen, A. R.; Aziz, R. A.
Journal of Chemical Physics (1972), 57 (3), 1100-102CODEN: JCPSA6; ISSN:0021-9606.
Sixteen of the reduced transport collision integrals Ω(l,s)* are calcd. as a function of reduced temp. T* for the Lennard-Jones (12-6) potential. These calcns. are more accurate than those of Hirschfelder, Curtiss, and Bird, which are frequently used. Empirical equations are presented which allow the calcn. of the collision integrals for any reduced temp. in the range 0.3 ≤ T* ≤ 100 without interpolation from tables. The error in the values so obtained is probably less than 0.1%.
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Chung, T. H.; Lee, L. L.; Starling, K. E. Applications of kinetic gas theories and multiparameter correlation for prediction of dilute gas viscosity and thermal conductivity. IInd. Eng. Chem. Fundam. 1984, 23, 8– 13, DOI: 10.1021/i100013a002
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Applications of kinetic gas theories and multiparameter correlation for prediction of dilute gas viscosity and thermal conductivity
Chung, Ting Horng; Lee, Lloyd L.; Starling, Kenneth E.
Industrial & Engineering Chemistry Fundamentals (1984), 23 (1), 8-13CODEN: IECFA7; ISSN:0196-4313.
Kinetic gas theories have been applied for the development of a correlation of gas viscosity and thermal cond. Employing the acentric factor (ω), the dipole moment (μ), and the assocn. parameter (κ) to characterize the effects of mol. shape and anisotropic intermol. forces, the resultant multiparameter correlations are self-consistent for viscosity and thermal cond. and generalized for polar and nonpolar gases. The results for pure gases are outstanding, not only in accuracy but also in applicability for such wide classes of fluids which include polar and H-bonding compds.
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Tiesinga, E.; Mohr, P. J.; Newell, D. B.; Taylor, B. N. CODATA recommended values of the fundamental physical constants: 2018. J. Phys. Chem. Ref. Data 2021, 50, 033105 DOI: 10.1063/5.0064853
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CODATA Recommended Values of the Fundamental Physical Constants: 2018
Tiesinga, Eite; Mohr, Peter J.; Newell, David B.; Taylor, Barry N.
Journal of Physical and Chemical Reference Data (2021), 50 (3), 033105CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
A review. We report the 2018 self-consistent values of consts. and conversion factors of physics and chem. recommended by the Committee on Data of the International Science Council. The recommended values can also be found at physics.nist.gov/consts. The values are based on a least-squares adjustment that takes into account all theor. and exptl. data available through 31 Dec. 2018. A discussion of the major improvements as well as inconsistencies within the data is given. The former include a decrease in the uncertainty of the dimensionless fine-structure const. and a nearly two orders of magnitude improvement of particle masses expressed in units of kg due to the transition to the revised International System of Units (SI) with an exact value for the Planck const. Further, because the elementary charge, Boltzmann const., and Avogadro const. also have exact values in the revised SI, many other consts. are either exact or have significantly reduced uncertainties. Inconsistencies remain for the g and the muon magnetic-moment anomaly. The proton charge radius puzzle has been partially resolved by improved measurements of hydrogen energy levels. This review article contains the 2018 self-consistent set of values of the consts. and conversion factors of physics and chem. recommended by the Committee on Data for Science and Technol. (CODATA). The CODATA values are based on a least-squares adjustment that takes into account all data available up to the end of 2018. Details of the data selection and methodol. are described. (c) 2021 American Institute of Physics.
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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, 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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Wilke, C. R. A viscosity equation for gas mixtures. J. Chem. Phys. 1950, 18, 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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Glowinski, R.; Marroco, A. Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité, d’une classe de problèmes de Dirichlet non linéaires. Rev. Fr. Autom. Inf. Rech. Oper. 1975, 9, 41– 76, DOI: 10.1051/m2an/197509r200411
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Gabay, D.; Mercier, B. A dual algorithm for the solution of nonlinear variational problems via finite element approximations. Comput. Math. Appl. 1976, 2, 17– 40, DOI: 10.1016/0898-1221(76)90003-1
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Boyd, S.; Parikh, N.; Chu, E.; Peleato, B.; Eckstein, J. Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Mach. Learn. 2010, 3, 1– 122, DOI: 10.1561/2200000016
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Lemmon, E. W.; Jacobsen, R. T. Viscosity and thermal conductivity equations for nitrogen, oxygen, argon, and air. Int. J. Thermophys. 2004, 25, 21– 69, DOI: 10.1023/B:IJOT.0000022327.04529.f3
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Viscosity and Thermal Conductivity Equations for Nitrogen, Oxygen, Argon, and Air
Lemmon, E. W.; Jacobsen, R. T.
International Journal of Thermophysics (2004), 25 (1), 21-69CODEN: IJTHDY; ISSN:0195-928X. (Kluwer Academic/Plenum Publishers)
New formulations for the viscosity and thermal cond. for nitrogen, oxygen, argon, and air are given. Air is treated as a pseudo-pure fluid using an approach adopted from previous research on the equation of state for air. The equations are valid over all liq. and vapor states, and a simplified cross-over equation was used to model the behavior of the crit. enhancement for thermal cond. The extrapolation behavior of the equations for nitrogen and argon well below their triple points was monitored so that both could be used as ref. equations for extended corresponding states applications. The uncertainties of calcd. values from the equations are generally within 2% for nitrogen and argon and within 5% for oxygen and air, except in the crit. region where the uncertainties are higher. Comparisons with the available exptl. data are given.
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Avgeri, S.; Assael, M. J.; Huber, M. L.; Perkins, R. A. Reference correlation of the viscosity of toluene from the triple point to 675 K and up to 500 MPa. J. Phys. Chem. Ref. Data 2015, 44, 033101 DOI: 10.1063/1.4926955
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Reference Correlation of the Viscosity of Toluene from the Triple Point to 675 K and up to 500 MPa
Avgeri, S.; Assael, M. J.; Huber, M. L.; Perkins, R. A.
Journal of Physical and Chemical Reference Data (2015), 44 (3), 033101/1-033101/16CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
This paper contains new, representative ref. equations for the viscosity of toluene. The equations are based in part upon a body of exptl. data that have been critically assessed for internal consistency and for agreement with theory whenever possible. The correlations are valid from the triple point (178.0 K) to 675 K, and at pressures up to 500 MPa. The estd. uncertainty at a 95% confidence level varies depending on the region of temp. and pressure from a low of 0.3% for the low-d. gas at temps. from 305 to 640 K at pressures to 0.3 MPa (essentially the uncertainty of the best exptl. data) to 0.7% for the satd. liq. at temps. from 263 to 373 K, to 5% for the low-temp. liq. from 187 to 210 K at pressures to 15 MPa. (c) 2015 American Institute of Physics.
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Herrmann, S.; Vogel, E. New formulation for the viscosity of n-butane. J. Phys. Chem. Ref. Data 2018, 47, 013104 DOI: 10.1063/1.5020802
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New Formulation for the Viscosity of n-Butane
Herrmann, Sebastian; Vogel, Eckhard
Journal of Physical and Chemical Reference Data (2018), 47 (1), 013104/1-013104/32CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
A review. A new viscosity formulation for n-butane, based on the residual quantity concept, uses the ref. equation of state by Bucker and Wagner [J. Phys. Chem. Ref. Data 35, 929 (2006)] and is valid in the fluid region from the triple point to 650 K and to 100 MPa. The contributions for the zero-d. viscosity and for the initial-d. dependence were sep. developed, whereas those for the crit. enhancement and for the higher-d. terms were pretreated. All contributions were given as a function of the reciprocal reduced temp. τ, while the last two contributions were correlated as a function of τ and of the reduced d. δ. The different contributions were based on specific primary data sets, whose evaluation and choice were discussed in detail. The final formulation incorporates 13 coeffs. derived employing a state-of-the-art linear optimization algorithm. The viscosity at low pressures p ≤ 0.2 MPa is described with an expanded uncertainty of 0.5% (coverage factor k = 2) for temps. 293 ≤ T/K ≤ 626. The expanded uncertainty in the vapor phase at subcrit. temps. T ≥ 298 K as well as in the supercrit. thermodn. region T ≤ 448 K at pressures p ≤ 30 MPa is estd. to be 1.5%. It is raised to 4.0% in regions where only less reliable primary data sets are available and to 6.0% in ranges without any primary data, but in which the equation of state is valid. A weakness of the ref. equation of state in the near-crit. region prevents estn. of the expanded uncertainty in this region. Viscosity tables for the new formulation are presented in Appendix B for the single-phase region, for the vapor-liq. phase boundary, and for the near-crit. region. (c) 2018 American Institute of Physics.
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Assael, M. J.; Papalas, T. B.; Huber, M. L. Reference correlations for the viscosity and thermal conductivity of n-undecane. J. Phys. Chem. Ref. Data 2017, 46, 033103 DOI: 10.1063/1.4996885
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Reference Correlations for the Viscosity and Thermal Conductivity of n-Undecane
Assael, M. J.; Papalas, T. B.; Huber, M. L.
Journal of Physical and Chemical Reference Data (2017), 46 (3), 033103/1-033103/12CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
A review. This paper presents new, wide-ranging correlations for the viscosity and thermal cond. of n-undecane based on critically evaluated exptl. data. The correlations are designed to be used with a recently published equation of state that is valid from the triple point to 700 K, at pressures up to 500 MPa, with densities below 776.86 kg m-3. The estd. uncertainty for the dil.-gas viscosity is 2.4%, and the estd. uncertainty for viscosity in the liq. phase for pressures up to 60 MPa over the temp. range 260 K-520 K is 5%. The estd. uncertainty is 3% for the thermal cond. of the low-d. gas and 3% for the liq. over the temp. range from 284 K to 677 K at pressures up to 400 MPa. Both correlations behave in a phys. reasonable manner when extrapolated to the full range of the equation of state, but care should be taken when using the correlations outside of the validated range. The uncertainties will be larger outside of the validated range and also in the crit. region. (c) 2017 American Institute of Physics.
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Huber, M. L.; Laesecke, A.; Perkins, R. Transport properties of n-dodecane. Energy Fuels 2004, 18, 968– 975, DOI: 10.1021/ef034109e
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Transport Properties of n-Dodecane
Huber, Marcia L.; Laesecke, Arno; Perkins, Richard
Energy & Fuels (2004), 18 (4), 968-975CODEN: ENFUEM; ISSN:0887-0624. (American Chemical Society)
The authors have surveyed literature data and developed correlations for the viscosity and thermal cond. of n-dodecane that are valid over a wide range of fluid states. The new correlations are applicable from the triple point (263.59 °K) to 800 °K, and at pressures up to 200 MPa. The viscosity correlation has an estd. uncertainty of 0.5% along the satn. boundary in the liq. phase, 3% in the compressed liq. region, and 3% in the vapor (the uncertainties can be considered as ests. of a combined expanded uncertainty with a coverage factor of 2). The thermal cond. correlation has an estd. uncertainty of 4% along the liq. satn. boundary and in the compressed liq., and ∼5% in the vapor region.
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Meng, X. Y.; Sun, Y. K.; Cao, F. L.; Wu, J. T.; Vesovic, V. Reference correlation of the viscosity of n-hexadecane from the triple point to 673 K and up to 425 MPa. J. Phys. Chem. Ref. Data 2018, 47, 033102 DOI: 10.1063/1.5039595
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Reference Correlation of the Viscosity of n-Hexadecane from the Triple Point to 673 K and up to 425 MPa
Meng, X. Y.; Sun, Y. K.; Cao, F. L.; Wu, J. T.; Vesovic, V.
Journal of Physical and Chemical Reference Data (2018), 47 (3), 033102/1-033102/12CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
A review. A new correlation for the viscosity of n-hexadecane is presented. The correlation is based upon a body of exptl. data that has been critically assessed for internal consistency and for agreement with theory. It is applicable in the temp. range from the triple point to 673 K at pressures up to 425 MPa. The overall uncertainty of the proposed correlation, estd. as the combined expanded uncertainty with a coverage factor of 2, varies from 1% for the viscosity at atm. pressure to 10% for the viscosity of the vapor phase at low temps. Tables of the viscosity generated by the relevant equations are provided at selected temps. and pressures and along the satn. line. (c) 2018 American Institute of Physics.
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Laesecke, A.; Muzny, C. D. Reference correlation for the viscosity of carbon dioxide. J. Phys. Chem. Ref. Data 2017, 46, 013107 DOI: 10.1063/1.4977429
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Reference Correlation for the Viscosity of Carbon Dioxide
Laesecke, Arno; Muzny, Chris D.
Journal of Physical and Chemical Reference Data (2017), 46 (1), 013107/1-013107/28CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
A review. A comprehensive database of exptl. and computed data for the viscosity of carbon dioxide (CO2) was compiled and a new ref. correlation was developed. Literature results based on an ab initio potential energy surface were the foundation of the correlation of the viscosity in the limit of zero d. in the temp. range from 100 to 2000 K. Guided symbolic regression was employed to obtain a new functional form that extrapolates correctly to 0 and to 10 000 K. Coordinated measurements at low d. made it possible to implement the temp. dependence of the Rainwater-Friend theory in the linear-in-d. viscosity term. The residual viscosity could be formulated with a scaling term ργ/T, the significance of which was confirmed by symbolic regression. The final viscosity correlation covers temps. from 100 to 2000 K for gaseous CO2 and from 220 to 700 K with pressures along the melting line up to 8000 MPa for compressed and supercrit. liq. states. The data representation is more accurate than with the previous correlations, and the covered pressure and temp. range is significantly extended. The crit. enhancement of the viscosity of CO2 is included in the new correlation. (c) 2017 American Institute of Physics.
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Tariq, U.; Jusoh, A. R. B.; Riesco, N.; Vesovic, V. Reference correlation of the viscosity of cyclohexane from the triple point to 700 K and up to 110 MPa. J. Phys. Chem. Ref. Data 2014, 43, 033101 DOI: 10.1063/1.4891103
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Reference Correlation of the Viscosity of Cyclohexane from the Triple Point to 700 K and up to 110 MPa
Tariq, U.; Jusoh, A. R. B.; Riesco, N.; Vesovic, V.
Journal of Physical and Chemical Reference Data (2014), 43 (3), 033101/1-033101/18CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
A new correlation for the viscosity of cyclohexane is presented. The correlation is based upon a body of exptl. data that has been critically assessed for internal consistency and for agreement with theory. It is applicable in the temp. range from the triple point to 700 K at pressures up to 110 MPa. In the dil. gas region, at pressures below 0.3 MPa, the correlation is valid up to 873 K. The overall uncertainty of the proposed correlation, estd. as the combined expanded uncertainty with a coverage factor of 2, varies from 0.5% for the viscosity of the dil. gas and of liq. at ambient pressure to 5% for the viscosity at high pressures and temps. Tables of the viscosity generated by the relevant equations, at selected temps. and pressures and along the satn. line, are provided. (c) 2014 American Institute of Physics.
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Muzny, C. D.; Huber, M. L.; Kazakov, A. F. Correlation for the viscosity of normal hydrogen obtained from symbolic regression. J. Chem. Eng. Data 2013, 58, 969– 979, DOI: 10.1021/je301273j
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Correlation for the Viscosity of Normal Hydrogen Obtained from Symbolic Regression
Muzny, Chris D.; Huber, Marcia L.; Kazakov, Andrei F.
Journal of Chemical & Engineering Data (2013), 58 (4), 969-979CODEN: JCEAAX; ISSN:0021-9568. (American Chemical Society)
We report the results of a symbolic-regression methodol. to obtain both the functional form and the coeffs. for a wide-ranging correlation for the viscosity of normal hydrogen. The correlation covers the temp. range from the triple-point temp. to 1000 K and pressures up to 200 MPa and extrapolates in a phys. reasonable manner to 2000 K. The estd. uncertainty is 4 % for the satd. liq. from the triple point to 31 K, with larger deviations as the crit. region is approached. The estd. uncertainty is 4 % for the supercrit. fluid phase at pressures to 200 MPa. For the limited range of 200 K to 400 K at pressures up to 0.1 MPa, the uncertainty is 0.1 %.
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Huber, M. L.; Laesecke, A.; Xiang, H. W. Viscosity correlations for minor constituent fluids in natural gas: n-octane, n-nonane and n-decane. Fluid Phase Equilib. 2005, 228–229, 401– 408, DOI: 10.1016/j.fluid.2005.03.008
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Viscosity correlations for minor constituent fluids in natural gas: n-octane, n-nonane and n-decane
Huber, Marcia L.; Laesecke, Arno; Xiang, Hong Wei
Fluid Phase Equilibria (2005), 228-229 (), 401-408CODEN: FPEQDT; ISSN:0378-3812. (Elsevier B.V.)
Natural gas, although predominantly comprised of methane, often contains small amts. of heavier hydrocarbons that contribute to its thermodn. and transport properties. In this manuscript, we review the current literature and present new correlations for the viscosity of the pure fluids n-octane, n-nonane, and n-decane that are valid over a wide range of fluid states, from the dil. gas to the dense liq. The new correlations represent the viscosity to within the uncertainty of the best exptl. data and will be useful for engineers working on viscosity models for natural gas and other hydrocarbon mixts.
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Meng, X.; Zhang, J.; Wu, J.; Liu, Z. Experimental measurement and modeling of the viscosity of dimethyl ether. J. Chem. Eng. Data 2012, 57, 988– 993, DOI: 10.1021/je201297j
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Experimental Measurement and Modeling of the Viscosity of Dimethyl Ether
Meng, Xianyang; Zhang, Jianbo; Wu, Jiangtao; Liu, Zhigang
Journal of Chemical & Engineering Data (2012), 57 (3), 988-993CODEN: JCEAAX; ISSN:0021-9568. (American Chemical Society)
The viscosities of di-Me ether in the temp. range of (243 to 373) K from satd. pressure up to 30 MPa are reported. These new exptl. data were measured with a vibrating-wire viscometer. The combined expanded uncertainty of the results with a level of confidence of 0.95 (k = 2) is about ± 2.0 % over all ranges of temp. and pressure. The exptl. data are used to develop correlations for the viscosity, including a satd. liq. equation and a multiparameter formulation covering liq. and vapor region. On the basis of the uncertainty of and comparisons with the exptl. data, the estd. uncertainty of viscosity correlation is 2 % in the liq. phase and 3 % in the gas region.
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Meng, X. Y.; Cao, F. L.; Wu, J. T.; Vesovic, V. Reference correlation of the viscosity of ethylbenzene from the triple point to 673 K and up to 110 MPa. J. Phys. Chem. Ref. Data 2017, 46, 013101 DOI: 10.1063/1.4973501
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Reference Correlation of the Viscosity of Ethylbenzene from the Triple Point to 673 K and up to 110 MPa
Meng, X. Y.; Cao, F. L.; Wu, J. T.; Vesovic, V.
Journal of Physical and Chemical Reference Data (2017), 46 (1), 013101/1-013101/13CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
A new correlation for the viscosity of ethylbenzene is presented. The correlation is based upon a body of exptl. data that has been critically assessed for internal consistency and for agreement with theory. It is applicable in the temp. range from the triple point to 673 K at pressures up to 110 MPa. The overall uncertainty of the proposed correlation, estd. as the combined expanded uncertainty with a coverage factor of 2, varies from 1% for the viscosity at atm. pressure to 5% for the highest temps. and pressures of interest. Tables of the viscosity, generated by the relevant equations at selected temps. and pressures and along the satn. line, are provided. Comparison of viscosity of xylene isomers indicated that at very high temps. the viscosity correlation of para-xylene has higher uncertainty than previously postulated. Thus, in this work we also provide a revised viscosity correlation for p-xylene. (c) 2017 American Institute of Physics.
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Vogel, E.; Span, R.; Herrmann, S. Reference correlation for the viscosity of ethane. J. Phys. Chem. Ref. Data 2015, 44, 043101 DOI: 10.1063/1.4930838
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Reference Correlation for the Viscosity of Ethane
Vogel, Eckhard; Span, Roland; Herrmann, Sebastian
Journal of Physical and Chemical Reference Data (2015), 44 (4), 043101/1-043101/39CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
A new representation of the viscosity for the fluid phase of ethane includes a zero-d. correlation and a contribution for the crit. enhancement, initially both developed sep., but based on exptl. data. The higher-d. contributions are correlated as a function of the reduced d. δ = ρ/ρc and of the reciprocal reduced temp. τ = Tc/T (ρc-crit. d. and Tc-crit. temp.). The final formulation contains 14 coeffs. obtained using a state-of-the-art linear optimization algorithm. The evaluation and choice of the selected primary data sets is reviewed, in particular with respect to the assessment used in earlier viscosity correlations. The new viscosity surface correlation makes use of the ref. equation of state for the thermodn. properties of ethane by Bucker and Wagner [J. Phys. Chem. Ref. Data 35, 205 (2006)] and is valid in the fluid region from the melting line to temps. of 675 K and pressures of 100 MPa. The viscosity in the limit of zero d. is described with an expanded uncertainty of 0.5% (coverage factor k = 2) for temps. 290 < T/K < 625, increasing to 1.0% at temps. down to 212 K. The uncertainty of the correlated values is 1.5% in the range 290 < T/K < 430 at pressures up to 30 MPa on the basis of recent measurements judged to be very reliable as well as 4.0% and 6.0% in further regions. The uncertainty in the near-crit. region (1.001 < 1/τ < 1.010 and 0.8 < δ < 1.2) increases with decreasing temp. up to 3.0% considering the available reliable data. Tables of the viscosity calcd. from the correlation are listed in an appendix for the single-phase region, for the vapor-liq. phase boundary, and for the near-crit. region. (c) 2015 American Institute of Physics.
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Kiselev, S. B.; Ely, J. F.; Abdulagatov, I. M.; Huber, M. L. Generalized SAFT-DFT/DMT model for the thermodynamic, interfacial, and transport properties of associating fluids: application for n-alkanols. Ind. Eng. Chem. Res. 2005, 44, 6916– 6927, DOI: 10.1021/ie050010e
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Generalized SAFT-DFT/DMT Model for the Thermodynamic, Interfacial, and Transport Properties of Associating Fluids: Application for n-Alkanols
Kiselev, S. B.; Ely, J. F.; Abdulagatov, I. M.; Huber, M. L.
Industrial & Engineering Chemistry Research (2005), 44 (17), 6916-6927CODEN: IECRED; ISSN:0888-5885. (American Chemical Society)
We have developed a "global" crossover (GC) statistical assocg. fluid theory (SAFT) equation of state (EOS) for assocg. fluids that incorporates non-analytic scaling laws in the crit. region and in the limit of low densities, ρ → 0, that is transformed into the ideal-gas EOS. Unlike the crossover SAFT EOS developed earlier, the new GC SAFT EOS contains a so-called kernel term and reproduces the asymptotic scaling behavior of the isochoric heat capacity in the one- and two-phase regions. In addn., we develop on the basis of the d. functional theory (DFT) a GC SAFT-DFT model for the surface tension. In the second step, using the GC SAFT EOS and the decoupled-mode theory (DMT), we have developed a generalized GC SAFT-DMT model for transport coeffs. that reproduces the singular behavior of the thermal cond. of pure fluids in the crit. region. Unlike the DMT model based on the asymptotic crossover EOS, the GC SAFT-DMT model is valid in the entire fluid state region at T ≥ Tb (where Tb is the binodal temp.), and at ρ → 0 reproduces the dil. gas contributions for the transport coeffs. A comparison was made with exptl. data for methanol, ethanol, and higher n-alkanols. For n-alkanols, the GC SAFT-DFT/DMT model contains the same no. of the adjustable parameters as the original classical SAFT EOS, but reproduces with high accuracy the PVT, VLE, isochoric, and isobaric sp. heats, surface tension, and thermal cond. data close to and far from the crit. point.
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Holland, P. M.; Eaton, B. E.; Hanley, H. J. M. A correlation of the viscosity and thermal conductivity data of gaseous and liquid ethylene. J. Phys. Chem. Ref. Data 1983, 12, 917– 932, DOI: 10.1063/1.555701
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A correlation of the viscosity and thermal conductivity data of gaseous and liquid ethylene
Holland, P. M.; Eaton, B. E.; Hanley, H. J. M.
Journal of Physical and Chemical Reference Data (1983), 12 (4), 917-32CODEN: JPCRBU; ISSN:0047-2689.
Data for the viscosity and thermal cond. coeff. of gaseous and liq. C2H4 were evaluated and represented by an empirical function. Tables of values are presented for the range 110-500 K for pressures to 50 MPa (≈500 atm). Both the viscosity and thermal cond. coeff. data have uncertainties of about ±5% increasing to 10% in the dense liq. The anomalous contribution to the thermal cond. in the vicinity of the crit. point is included.
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Schmidt, K. A. G.; Quiñones-Cisneros, S. E.; Carroll, J. J.; Kvamme, B. Hydrogen sulfide viscosity modeling. Energy Fuels 2008, 22, 3424– 3434, DOI: 10.1021/ef700701h
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Hydrogen Sulfide Viscosity Modeling
Schmidt, Kurt A. G.; Quinones-Cisneros, Sergio E.; Carroll, John J.; Kvamme, Bjoern
Energy & Fuels (2008), 22 (5), 3424-3434CODEN: ENFUEM; ISSN:0887-0624. (American Chemical Society)
As regulations for emissions of carbon dioxide and hydrogen sulfide into the atm. are becoming stricter and the penalty for violation increases, new and economical ways of reducing these emissions are becoming increasingly important to everyday operations. One promising sequestering option is the injection of acid gas mixts. into formations for disposal/storage. During the design of these acid gas injection schemes a comprehensive knowledge of the thermo-phys. properties is of utmost importance in detg. the feasibility and size of these operations. Recently, the friction theory (f-theory) for viscosity modeling was shown to accurately det. the viscosity behavior of a wide range of petroleum fluid systems ranging from natural gases to heavy crude oils. This technique also was shown to accurately model mixts. contg. various concns. of CO2. However, in the development of the f-theory hydrogen sulfide was not explicitly studied and therefore needs to be accounted for to ensure it is accurately modeled. The development/validation of any modeling approach requires a thorough knowledge of the available data. With this in mind, an exhaustive collection of the data available in the literature was performed revealing a very limited no. of exptl. points available in the open literature for the viscosity of pure H2S and H2S mixts. Although limited data for pure H2S exists in the literature, a crit. evaluation of the data was performed and a ref. viscosity model based on the generalized friction theory (f-theory) was developed. The developed ref. viscosity model gives reasonable modeling results over the T-η-P surface for H2S. The one parameter f-theory was also extended to include H2S, and the model was shown to accurately reproduce existing exptl. viscosities of hydrogen sulfide and its mixts. in ranges relevant to the natural gas and petroleum industry.
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Michailidou, E. K.; Assael, M. J.; Huber, M. L.; Abdulagatov, I. M.; Perkins, R. A. Reference correlation of the viscosity of n-heptane from the triple point to 600 K and up to 248 MPa. J. Phys. Chem. Ref. Data 2014, 43, 023103 DOI: 10.1063/1.4875930
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Reference Correlation of the Viscosity of n-Heptane from the Triple Point to 600 K and up to 248 MPa
Michailidou, E. K.; Assael, M. J.; Huber, M. L.; Abdulagatov, I. M.; Perkins, R. A.
Journal of Physical and Chemical Reference Data (2014), 43 (2), 023103/1-023103/13CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
This paper contains a new wide-ranging correlation for the viscosity of n-heptane based on critically evaluated exptl. data. The correlation is valid from the triple point (182.55 K) to 600 K, and at pressures up to 248 MPa. The estd. uncertainty at a 95% confidence level is 3.5% over the whole range (with the exception of the near-crit. region). Along the satd. liq. curve, the estd. uncertainty is 1% below 292 K, 0.6% in the region from 292 to 346 K, rising to 2% between 346 and 363 K, and 0.3% for the low-d. gas at temps. from 317 to 600 K and pressures to 0.3 MPa. (c) 2014 American Institute of Physics.
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Michailidou, E. K.; Assael, M. J.; Huber, M. L.; Perkins, R. A. Reference correlation of the viscosity of n-hexane from the triple point to 600 K and up to 100 MPa. J. Phys. Chem. Ref. Data 2013, 42, 033104 DOI: 10.1063/1.4818980
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Reference Correlation of the Viscosity of n-Hexane from the Triple Point to 600 K and up to 100 MPa
Michailidou, E. K.; Assael, M. J.; Huber, M. L.; Perkins, R. A.
Journal of Physical and Chemical Reference Data (2013), 42 (3), 033104/1-033104/12CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
This paper contains new, representative ref. equations for the viscosity of n-hexane. 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. The correlations are valid from the triple point to 600 K, and at pressures up to 100 MPa. We est. the expanded uncertainty at a 95% confidence level to be 2% for the liq. phase at temps. from the triple point to 450 K and pressures to 100 MPa. For the liq. at 450-600 K at pressures to 100 MPa, the expanded uncertainty at the 95% confidence level is 6%, and is 0.3% for the low-d. gas at pressures to 0.3 MPa. (c) 2013 American Institute of Physics.
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Vogel, E.; Küchenmeister, C.; Bich, E. Viscosity correlation for isobutane over wide ranges of the fluid region. Int. J. Thermophys. 2000, 21, 343– 356, DOI: 10.1023/A:1006623310780
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Viscosity correlation for isobutane over wide ranges of the fluid region
Vogel, E.; Kuchenmeister, C.; Bich, E.
International Journal of Thermophysics (2000), 21 (2), 343-356CODEN: IJTHDY; ISSN:0195-928X. (Kluwer Academic/Plenum Publishers)
A new representation of the viscosity of isobutane has been developed. The representative equations include zero-d. and initial-d. dependence correlations. The higher d. contributions to the residual viscosity are formed by a combination of double polynomials in d. and reciprocal temp. and of a free-vol. term with a temp.-dependent close-packed d. The new full surface correlation is based on primary exptl. data sets selected as a result of a crit. assessment of the available information. The validity of the representation extends from the triple point to 600 K and 35 MPa in accordance with the modified Benedict-Webb-Rubin equation of state by Younglove and Ely (1987). The uncertainty of the representation varies from ± 0.4 % in the dil. gas phase between room temp. and 600 K to ± 3% in the thermodn. ranges in which the equation of state is valid as well as where primary exptl. data are available.
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51
Xiang, H. W.; Laesecke, A.; Huber, M. L. A new reference correlation for the viscosity of methanol. J. Phys. Chem. Ref. Data 2006, 35, 1597– 1620, DOI: 10.1063/1.2360605
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A new reference correlation for the viscosity of methanol
Xiang, Hong Wei; Laesecke, Arno; Huber, Marcia L.
Journal of Physical and Chemical Reference Data (2006), 35 (4), 1597-1620CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
A new ref.-quality correlation for the viscosity of methanol is presented that is valid over the entire fluid region, including vapor, liq., and metastable phases. To describe the zero-d. viscosity with kinetic theory for polar gases, a new expression for the collision integral of the Stockmayer potential is introduced. The initial d. dependence is based on the Rainwater-Friend theory. A new correlation for the third viscosity virial coeff. is developed from exptl. data and applied to methanol. The high-d. contribution to the viscosity is based on the Chapman-Enskog theory and includes a new expression for the hard-sphere diam. that is a function of both temp. and d. The resulting correlation is applicable for temps. from the triple point to 630 K at pressures up to 8 GPa. The estd. uncertainty of the resulting correlation (with a coverage factor of 2) varies from 0.6% in the dil.-gas phase between room temp. and 630 K, to less than 2% for the liq. phase at pressures up to 30 MPa at temps. between 273 and 343 K, 3% for pressures from 30 to 100 MPa, 5% for the liq. from 100 to 500 MPa, and 10% between 500 MPa and 4 GPa. At very high pressures, from 4 to 8 GPa, the correlation has an estd. uncertainty of 30% and can be used to indicate qual. behavior.
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Cao, F. L.; Meng, X. Y.; Wu, J. T.; Vesovic, V. Reference correlation of the viscosity of meta-xylene from 273 to 673 K and up to 200 MPa. J. Phys. Chem. Ref. Data 2016, 45, 013103 DOI: 10.1063/1.4941241
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Reference Correlation of the Viscosity of meta-Xylene from 273 to 673 K and up to 200 MPa
Cao, F. L.; Meng, X. Y.; Wu, J. T.; Vesovic, V.
Journal of Physical and Chemical Reference Data (2016), 45 (1), 013103/1-013103/12CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
A new correlation for the viscosity of meta-xylene is presented. The correlation is based upon a body of exptl. data that has been critically assessed for internal consistency and for agreement with theory. It is applicable in the temp. range from 273 to 673 K at pressures up to 200 MPa. The overall uncertainty of the proposed correlation, estd. as the combined expanded uncertainty with a coverage factor of 2, varies from 1% for the viscosity at atm. pressure to 5% for the highest temps. and pressures of interest. Tables of the viscosity, generated by the relevant equations, at selected temps. and pressures, and along the satn. line, are provided. (c) 2016 American Institute of Physics.
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Cao, F. L.; Meng, X. Y.; Wu, J. T.; Vesovic, V. Reference correlation of the viscosity of ortho-xylene from 273 to 673 K and up to 110 MPa. J. Phys. Chem. Ref. Data 2016, 45, 023102 DOI: 10.1063/1.4945663
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Reference Correlation of the Viscosity of ortho-Xylene from 273 to 673 K and up to 110 MPa
Cao, F. L.; Meng, X. Y.; Wu, J. T.; Vesovic, V.
Journal of Physical and Chemical Reference Data (2016), 45 (2), 023102/1-023102/11CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
A review. A new correlation for the viscosity of ortho-xylene (o-xylene) is presented. The correlation is based upon a body of exptl. data that has been critically assessed for internal consistency and for agreement with theory. It is applicable in the temp. range from 273 to 673 K at pressures up to 110 MPa. The overall uncertainty of the proposed correlation, estd. as the combined expanded uncertainty with a coverage factor of 2, varies from 1% for the viscosity at atm. pressure to 5% for the highest temps. and pressures of interest. Tables of the viscosity generated by the relevant equations, at selected temps. and pressures and along the satn. line, are provided. (c) 2016 American Institute of Physics.
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Balogun, B.; Riesco, N.; Vesovic, V. Reference correlation of the viscosity of para-xylene from the triple point to 673 K and up to 110 MPa. J. Phys. Chem. Ref. Data 2015, 44, 013103 DOI: 10.1063/1.4908048
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Reference Correlation of the Viscosity of para-Xylene from the Triple Point to 673 K and up to 110 MPa
Balogun, B.; Riesco, N.; Vesovic, V.
Journal of Physical and Chemical Reference Data (2015), 44 (1), 013103/1-013103/13CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
A new correlation for the viscosity of para-xylene (p-xylene) is presented. The correlation is based upon a body of exptl. data that has been critically assessed for internal consistency and for agreement with theory. It is applicable in the temp. range from the triple point to 673 K at pressures up to 110 MPa. The overall uncertainty of the proposed correlation, estd. as the combined expanded uncertainty with a coverage factor of 2, varies from 0.5% for the viscosity of the dil. gas to 5% for the highest temps. and pressures of interest. Tables of the viscosity generated by the relevant equations, at selected temps. and pressures and along the satn. line, are provided. (c) 2015 American Institute of Physics.
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Tanaka, Y.; Sotani, T. Thermal conductivity and viscosity of 2,2-dichloro-1,1,1-trifluoroethane (HCFC-123). Int. J. Thermophys. 1996, 17, 293– 328, DOI: 10.1007/BF01443394
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Thermal conductivity and viscosity of 2,2-dichloro-1,1,1-trifluoroethane (HCFC-123)
Tanaka, Y.; Sotani, T.
International Journal of Thermophysics (1996), 17 (2), 293-328CODEN: IJTHDY; ISSN:0195-928X. (Plenum)
The thermal cond. and the viscosity data of CFC alternative refrigerant HCFC-123 (2,2-dichloro-1,1,1-trifluoroethane; CHCl2-CF3) were critically evaluated and correlated on the basis of a comprehensive literature survey. Using the residual transport-property concept, the authors have developed the three-dimensional surfaces of the thermal cond.-temp.-d. and the viscosity-temp.-d. A dil.-gas function and an excess function of simple form were established for each property. The crit. enhancement contribution was taken no account because reliable crossover equations of state and the thermal cond. data are still missing in the crit. region. The correlation for the thermal cond. is valid at temps. from 253 to 373 K, pressures up to 30 MPa, and densities up to 1623 kg·m-3. The correlation for the viscosity is valid at temps. from 253 to 423 K, pressures up to 20 MPa, and densities up to 1608 kg·m-3. The uncertainties of the present correlations are estd. to be 5% for both properties, since the exptl. data are still scarce and somewhat contradictory in the vapor phase at present.
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Huber, M. L.; Assael, M. J. Correlations for the viscosity of 2,3,3,3-tetrafluoroprop-1-ene (R1234yf) and trans-1,3,3,3-tetrafluoropropene (R1234ze(E)). Int. J. Refrig. 2016, 71, 39– 45, DOI: 10.1016/j.ijrefrig.2016.08.007
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Correlations for the viscosity of 2,3,3,3-tetrafluoroprop-1-ene (R1234yf) and trans-1,3,3,3-tetrafluoropropene (R1234ze(E))
Huber, Marcia L.; Assael, Marc J.
International Journal of Refrigeration (2016), 71 (), 39-45CODEN: IJRFDI; ISSN:0140-7007. (Elsevier Ltd.)
Due to concerns about global warming, there is interest in 2,3,3,3-tetrafluoroprop-1-ene (R1234yf) and trans-1,3,3,3-tetrafluoropropene (R1234ze(E)) as potential replacements for refrigerants with high global warming potential (GWP). In this paper we survey available data and provide viscosity correlations that cover the entire fluid range including vapor, liq., and supercrit. regions. The correlation for R1234yf is valid from the triple point (220 K) to 410 K at pressures up to 30 MPa, and the correlation for R1234ze(E) is valid from the triple point (169 K) to 420 K at pressures up to 100 MPa. The estd. uncertainty for both correlations at a 95% confidence level is 2% for the liq. phase over the temp. range 243 K to 363 K at pressures to 30 MPa, and 3% for the gas phase at atm. pressure.
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Huber, M. L.; Laesecke, A. Correlation for the viscosity of pentafluoroethane (R125) from the triple point to 500 K at pressures up to 60 MPa. Ind. Eng. Chem. Res. 2006, 45, 4447– 4453, DOI: 10.1021/ie051367l
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Correlation for the Viscosity of Pentafluoroethane (R125) from the Triple Point to 500 K at Pressures up to 60 MPa
Huber, Marcia L.; Laesecke, Arno
Industrial & Engineering Chemistry Research (2006), 45 (12), 4447-4453CODEN: IECRED; ISSN:0888-5885. (American Chemical Society)
We present a correlation for the viscosity of pentafluoroethane (R125) based on a compilation and crit. assessment of the available exptl. data. The correlation covers a wide range of fluid states, including the supercrit. region. It is applicable from the triple point at 172.52 to 500 K, with pressures varying up to 60 MPa. The formulation includes a zero-d. contribution, initial d. dependence based on the Rainwater-Friend theory, and a residual contribution for higher densities that combines virial terms with a free-vol. term, both being temp.-dependent. The estd. uncertainty of the viscosity correlation (coverage factor of 2) is 3% along the liq.-phase satn. boundary, 3% in the compressed liq. phase at pressures to 60 MPa, and 0.8% in the vapor.
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Huber, M. L.; Laesecke, A.; Perkins, R. A. Model for the viscosity and thermal conductivity of refrigerants, including a new correlation for the viscosity of R134a. Ind. Eng. Chem. Res. 2003, 42, 3163– 3178, DOI: 10.1021/ie0300880
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Model for the Viscosity and Thermal Conductivity of Refrigerants, Including a New Correlation for the Viscosity of R134a
Huber, Marcia L.; Laesecke, Arno; Perkins, Richard A.
Industrial & Engineering Chemistry Research (2003), 42 (13), 3163-3178CODEN: IECRED; ISSN:0888-5885. (American Chemical Society)
We present modifications to an extended corresponding states (ECS) model for thermal cond. and viscosity originally developed by Ely and Hanley (Ind. Eng. Chem. Fundam. 1981, 20, 323-332). We apply the method to 17 pure refrigerants and present coeffs. for the model and comparisons with exptl. data. The av. abs. viscosity deviation for the 17 pure fluids studied ranges from a low of 0.56% for R236ea to a high of 5.68% for propylene, with an av. abs. deviation for all fluids of 3.13% based on a total of 3737 points. The av. abs. thermal cond. deviation for the 17 pure fluids studied ranges from a low of 1.37% for R116 to a high of 6.78% for R115, with an av. abs. deviation for all fluids of 3.75% based on a total of 12 156 points. We also present a new correlation for the viscosity of R134a (1,1,1,2-tetrafluoroethane), which is used as a ref. fluid for the description of properties of some refrigerants. The new correlation represents the viscosity to within the uncertainty of the best exptl. data.
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Tsolakidou, C. M.; Assael, M. J.; Huber, M. L.; Perkins, R. A. Correlations for the viscosity and thermal conductivity of ethyl fluoride (R161). J. Phys. Chem. Ref. Data 2017, 46, 023103 DOI: 10.1063/1.4983027
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Correlations for the Viscosity and Thermal Conductivity of Ethyl Fluoride (R161)
Tsolakidou, Ch. M.; Assael, M. J.; Huber, M. L.; Perkins, R. A.
Journal of Physical and Chemical Reference Data (2017), 46 (2), 023103/1-023103/12CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
This paper presents new wide-ranging correlations for the viscosity and thermal cond. of Et fluoride (R161) based on critically evaluated exptl. data. The correlations are designed to be used with a recently published equation of state that is valid from 130 to 450 K, at pressures up to 100 MPa. The estd. uncertainty at a 95% confidence level is 2% for the viscosity of low-d. gas (pressures below 0.5 MPa) and 3% for the viscosity of the liq. over the temp. range from 243 to 363 K at pressures up to 30 MPa. The estd. uncertainty is 3% for the thermal cond. of the low-d. gas and 3% for the liq. over the temp. range from 234 to 374 K at pressures up to 20 MPa. Both correlations may be used over the full range of the equation of state, but the uncertainties will be larger, esp. in the crit. region. (c) 2017 American Institute of Physics.
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Perkins, R. A.; Huber, M. L.; Assael, M. J. Measurements of the thermal conductivity of 1,1,1,3,3-pentafluoropropane (R245fa) and correlations for the viscosity and thermal conductivity surfaces. J. Chem. Eng. Data 2016, 61, 3286– 3294, DOI: 10.1021/acs.jced.6b00350
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Measurements of the Thermal Conductivity of 1,1,1,3,3-Pentafluoropropane (R245fa) and Correlations for the Viscosity and Thermal Conductivity Surfaces
Perkins, Richard A.; Huber, Marcia L.; Assael, Marc J.
Journal of Chemical & Engineering Data (2016), 61 (9), 3286-3294CODEN: JCEAAX; ISSN:0021-9568. (American Chemical Society)
New exptl. data on the thermal cond. of 1,1,1,3,3-pentafluoropropane (R245fa) are reported that cover a wide range of liq. conditions. These new exptl. data were made with a transient hot-wire app. and cover the liq. phase over a temp. range of 173-344 K and a pressure range of 0.1-71 MPa. The exptl. data reported here have an expanded uncertainty (0.95 level of confidence) of less than 1%. The measurements are used with selected literature data to develop correlations for the thermal cond. On the basis of this expanded uncertainty and comparisons with exptl. data, the thermal cond. correlation for R245fa is estd. to have a relative expanded uncertainty (0.95 level of confidence) of about 2% at a 95% confidence level for the liq. phase at pressures to 70 MPa and 2% for the vapor phase. In addn., we surveyed literature data and developed a correlation for the viscosity of R245fa. The estd. relative expanded uncertainty (0.95 level of confidence) of this correlation is 3% for the liq. phase at pressures to 40 MPa and 2% for the vapor phase.
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Quiñones-Cisneros, S. E.; Huber, M. L.; Deiters, U. K. Correlation for the viscosity of sulfur hexafluoride (SF6) from the triple point to 1000 K and pressures to 50 MPa. J. Phys. Chem. Ref. Data 2012, 41, 023102-023102-11 DOI: 10.1063/1.3702441
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New International Formulation for the Viscosity of H2O
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Journal of Physical and Chemical Reference Data (2009), 38 (2), 101-125CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
The International Assocn. for the Properties of Water and Steam (IAPWS) encouraged an extensive research effort to update the IAPS Formulation 1985 for the Viscosity of Ordinary Water Substance, leading to the adoption of a Release on the IAPWS Formulation 2008 for the Viscosity of Ordinary Water Substance. This manuscript describes the development and evaluation of the 2008 formulation, which provides a correlating equation for the viscosity of water for fluid states up to 1173 K and 1000 MPa with uncertainties from less than 1% to 7% depending on the state point. (c) 2009 American Institute of Physics.
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Avgeri, S.; Assael, M. J.; Huber, M. L.; Perkins, R. A. Reference correlation of the viscosity of benzene from the triple point to 675 K and up to 300 MPa. J. Phys. Chem. Ref. Data 2014, 43, 033103 DOI: 10.1063/1.4892935
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The present publication contains data on the thermophys. properties of deuterium oxide (heavy water). The properties are represented by equations which can be readily programmed on a computer and incorporated in data banks. All data have been carefully and crit. analyzed. The compendium represents the best available data for fluid D2O.
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Wen, Chenyang; Meng, Xianyang; Huber, Marcia L.; Wu, Jiangtao
Journal of Chemical & Engineering Data (2017), 62 (10), 3603-3609CODEN: JCEAAX; ISSN:0021-9568. (American Chemical Society)
The Paris Agreement on climate change, in which many nations have agreed to limit greenhouse gas emissions, has spurred interest in developing working fluids with low global warming potential (GWP) that can satisfy environmental concerns and have thermophys. properties that can meet engineering performance requirements. One such fluid is 1,1,1,2,2,4,5,5,5-nonafluoro-4-(trifluoromethyl)-3-pentanone (also known as Novec-649 and Novec-1230), which has potential applications in org. Rankine cycles (ORC), electronics cooling, computer/data center cooling, and fire extinguishing. In this work, the viscosity measurements of Novec-649 were reported. The measurements were performed over the temp. range of (243 to 373) K and at pressures up to 40 MPa using a vibrating-wire viscometer. The combined expanded uncertainty of the reported viscosity was 2% with a confidence level of 0.95 (k = 2). These exptl. data were used to develop a viscosity correlation that covers a wide temp. and pressure range, with an estd. uncertainty at a 95% confidence level of 2% for the liq. phase from (240 to 400) K at pressures up to 40 MPa.
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A review. A new viscosity formulation for propane, using the ref. equation of state for its thermodn. properties by Lemmon et al. [J. Chem. Eng. Data 54, 3141 (2009)] and valid in the fluid region from the triple-point temp. to 650 K and pressures up to 100 MPa, is presented. At the beginning, a zero-d. contribution and one for the crit. enhancement, each based on the exptl. data, were independently generated in parts. The higher-d. contributions are correlated as a function of the reciprocal reduced temp. τ = Tc/T and of the reduced d. δ = ρ/ρc (Tc-crit. temp., ρc-crit. d.). The final formulation includes 17 coeffs. inferred by applying a state-of-the-art linear optimization algorithm. The evaluation and choice of the primary data sets are detailed due to its importance. The viscosity at low pressures p ≤ 0.2 MPa is represented with an expanded uncertainty of 0.5% (coverage factor k = 2) for temps. 273 ≤ T/K ≤ 625. The expanded uncertainty in the vapor phase at subcrit. temps. T ≥ 273 K as well as in the supercrit. thermodn. region T ≤ 423 K at pressures p ≤ 30 MPa is assumed to be 1.5%. In the near-crit. region (1.001 < 1/τ < 1.010 and 0.8 < δ < 1.2), the expanded uncertainty increases with decreasing temp. up to 3.0%. It is further increased to 4.0% in regions of less reliable primary data sets and to 6.0% in ranges in which no primary data are available but the equation of state is valid. Tables of viscosity computed for the new formulation are given in an Appendix for the single-phase region, for the vapor-liq. phase boundary, and for the near-crit. region. (c) 2016 American Institute of Physics.
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An improved extended corresponding states method for estimation of viscosity of pure refrigerants and mixtures
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The extended corresponding states method for calcg. the viscosity of pure refrigerants and mixts. is investigated. The accuracy of pure fluid viscosity values is significantly improved by introducing a third shape factor evaluated using available pure fluid viscosity data. A modification to the method of Huber and Ely (Fluid Phase Equil., 1992, 80, 45-46) is proposed for estn. of the viscosity of mixts.; this modification eliminates the possibility of discontinuities at the crit. point, ensures that the pure component viscosity is provided in the limit of a component mole fraction approaching 1, and improves the overall accuracy of the method. The method was applied to 12 pure refrigerants including three hydrocarbons and mixts. The av. abs. deviations between the calcd. and exptl. viscosity values are within 4% for all of the pure fluids and most of the mixts. investigated.
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Dynamic Crossover in Fluids: From Hard Spheres to Molecules
Bell, Ian H.; Delage-Santacreu, Stephanie; Hoang, Hai; Galliero, Guillaume
Journal of Physical Chemistry Letters (2021), 12 (27), 6411-6417CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
We propose a simple and generic definition of a demarcation reconciling structural and dynamic frameworks when combined with the entropy scaling framework. This crossover line between gas- and liq.-like behaviors is defined as the curve for which an individual property, the contribution to viscosity due to mols.' translation, is exactly equal to a collective property, the contribution to viscosity due to mol. interactions. Such a definition is shown to be consistent with the one based on the min. of the kinematic viscosity. For the hard sphere, this is shown to be an exact soln. For Lennard-Jones spheres and dimers and for some simple real fluids, this relation holds very well. This crossover line passes nearby the crit. point, and for all studied fluids, it is well captured by the crit. excess entropy curve for at. fluids, emphasizing the link between transport properties and local structure.
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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, 081703 DOI: 10.1063/5.0164037
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Xiaoxian Yang. Viscosity and Thermal Conductivity Models of 151 Common Fluids Based on Residual Entropy Scaling and Cubic Equations of State. ACS Omega 2025, 10 (6) , 6124-6134. https://doi.org/10.1021/acsomega.4c10815

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Abstract
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Figure 1
Figure 1. AARD (upper plot) and ARD (lower plot) of the filtered (or analyzable) experimental data from the model predictions. REF. models refers to the default viscosity models in REFPROP 10.0. For the remaining models, the labels comprise two parts connected by a “+” symbol. The former part denotes the method for dilute gas viscosity η_ρ→0(T) calculation (see Section 2.1): oLJ uses L-J parameters, oREF uses REFPROP 10.0, oP3 uses a third-order polynomial, oP4 uses a fourth-order polynomial, and oCP uses the critical point information. The latter part refers to the residual viscosity calculation method: rP4 is a 4-term power function used in the previous work (6) and rP3 is the 3-term power function developed in the present work.
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Figure 2
Figure 2. AARD of the REFPROP 10.0 models and the oREF + rP3 model predictions to the filtered experimental data for each pure fluid. The fluids are further classified according to the model types used by REFPROP 10.0: (a) reference correlations, (32−67) (b) ECS model with fitted parameters or friction theory models, (47,58,61) and (c) ECS model without fitted parameters and other models. (68−70) Fluid names in REFPROP 10.0 are adopted (see the Appendix for their respective IUPAC chemical names and CAS registry numbers). The entries are sorted primarily by whether the proposed RES model has a lower AARD than that of REFPROP 10.0 and secondarily according to increasing AARD of the proposed model. The green background indicates that the proposed model is better.
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Figure 3
Figure 3. ARD of the REFPROP 10.0 models and the oREF + rP3 model predictions to the filtered experimental data for each pure fluid. The fluids are further classified according to the model types used by REFPROP 10.0: (a) reference correlations, (32−67) (b) ECS model with fitted parameters or friction theory models, (47,58,61) and (c) ECS model without fitted parameters and other models. (68−70) Fluid names in REFPROP 10.0 are adopted (see the Appendix for their respective IUPAC chemical names and CAS registry numbers). The entries are sorted primarily by whether the proposed RES model has a lower absolute ARD than that of REFPROP 10.0 and secondarily according to increasing ARD of the proposed model. The green background indicates that the proposed model is better.
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Figure 4
Figure 4. Plus-scaled dimensionless residual viscosity η_res⁺ as a function of $s^{+} / ξ$ for each group of pure fluids, where s⁺ is the plus-scaled residual entropy and ξ is the fluid-specific scaling factor. The group-specific parameters n_i,g are used to calculate the curves. All groups are shown at the bottom. Each group is also illustrated and annotated stacked by a power of 20 at the top to highlight the qualitative differences.
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Figure 5
Figure 5. Ratio $ξ / s_{crit}^{+}$ of all considered pure fluids, where ξ is the fluid-specific scaling factor and s_crit⁺ is the plus-scaled dimensionless residual entropy at the critical point, which is obtained from REFPROP 10.0. The group numbers are annotated in the top right of each box. At $ξ / s_{crit}^{+} = 0.7$ , a vertical dashed dotted line is drawn. Values for group 1 exceed the plot limits, i.e., PARAHYD: 1.67, ORTHOHYD: 1.61, HYDROGEN: 1.64, HELIUM: 4.09, D2:1.86.
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Figure 6
Figure 6. ARD and AARD of the experimental data of 351 binary mixtures from predictions of models. “All selected data”: for calculations with the RES model, similar filters as used in pure fluids were applied for mixture data. “Further filtered data”: one more filter is applied to the “All selected data” so that calculations are also available with REFPROP 10.0 models. For combinations with no available data, 0.0 is given.
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References
This article references 74 other publications.
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  Entropy Scaling of Viscosity-II: Predictive Scheme for Normal Alkanes
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  In this work, a residual entropy value of 6/10 of the way between the crit. point and a value of -2/3 of Boltzmann const. is shown to collapse the scaled viscosity for the family of normal alkanes. Based on this approach, a nearly universal correlation is proposed that can reproduce 95% of the exptl. data for normal alkanes within ±18% (without removal of clearly erroneous data). This universal correlation has no new fluid-specific empirical parameters and is based on exptl. accessible values. This collapse is shown to be valid to a residual entropy half-way between the crit. point and the triple point, beyond which the macroscopically scaled viscosity has a superexponential dependence on residual entropy, terminating at the triple point. A key outcome of this study is a better understanding of entropy scaling for fluids with intramol. degrees of freedom. A study of the transport and thermodn. properties at the triple point rounds out the anal.
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  Binti Mohd Taib, Malyanah; Trusler, J. P. Martin
  Journal of Chemical Physics (2020), 152 (16), 164104CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  In this work, we have investigated the mono-variant relationship between the reduced viscosity and residual entropy in pure fluids and in binary mixts. of hydrocarbons and hydrocarbons with dissolved carbon dioxide. The mixts. considered were octane + dodecane, decane + carbon dioxide, and 1,3-dimethylbenzene (m-xylene) + carbon dioxide. The reduced viscosity was calcd. according to the definition of Bell, while the residual entropy was calcd. from accurate multi-parameter Helmholtz-energy equations of state and, for mixts., the multi-fluid Helmholtz energy approxn. The mono-variant dependence of reduced viscosity upon residual molar entropy was obsd. for the pure fluids investigated, and by incorporating two scaling factors (one for reduced viscosity and the other for residual molar entropy), the data were represented by a single universal curve. To apply this method to mixts., the scaling factors were detd. from a mole-fraction weighted sum of the pure-component values. This simple model was found to work well for the systems investigated. The av. abs. relative deviation (AARD) was obsd. to be between 1% and 2% for pure components and a mixt. of similar hydrocarbons. Larger deviations, with AARDs of up to 15%, were obsd. for the asym. mixts., but this compares favorably with other methods for predicting the viscosity of such systems. We conclude that the residual-entropy concept can be used to est. the viscosity of mixts. of similar mols. with high reliability and that it offers a useful engineering approxn. even for asym. mixts. (c) 2020 American Institute of Physics.
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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
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  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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8. 8
  Bell, I.; Laesecke, A. In Viscosity of Refrigerants and Other Working Fluids from Residual Entropy Scaling , 16th International Refrigeration and Air Conditioning Conference at Purdue, 2016; p 2287. https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=920655.
  There is no corresponding record for this reference.
9. 9
  Wang, X.; Wright, E.; Gao, N.; Li, Y. Evaluation on excess entropy scaling method predicting thermal transport properties of liquid HFC/HFO refrigerants. J. Therm. Sci. 2022, 31, 1465– 1475, DOI: 10.1007/s11630-020-1383-2
  There is no corresponding record for this reference.
10. 10
  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, 4070– 4079, DOI: 10.1073/pnas.1815943116
  10
  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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11. 11
  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, 4095– 4114, DOI: 10.1021/acs.iecr.7b04871
  There is no corresponding record for this reference.
12. 12
  Yang, X.; Xiao, X.; Thol, M.; Richter, M.; Bell, I. In A Residual Entropy Scaling Approach for Viscosity of Refrigerants, Other Fluids and Their Mixtures , 26th International Congress of Refrigeration, 2023.
  There is no corresponding record for this reference.
13. 13
  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, 183, DOI: 10.1007/s10765-022-03096-9
  13
  Linking Viscosity to Equations of State Using Residual Entropy Scaling Theory
  Yang, Xiaoxian; Xiao, Xiong; Thol, Monika; Richter, Markus; Bell, Ian H.
  International Journal of Thermophysics (2022), 43 (12), 183CODEN: IJTHDY; ISSN:0195-928X. (Springer)
  Abstr.: In our previous work (J Chem Eng Data 2021, 66(3):1385-1398), a residual entropy scaling (RES) approach was developed to link viscosity to residual entropy [a thermodn. property calcd. with an equation of state (EoS)] using a simple polynomial equation for refrigerants. Here, we present an extension of this approach to a much wider range of fluids: all pure fluids and their mixts. whose ref. EoS and exptl. viscosity data are available. A total of 84 877 exptl. points for 124 pure fluids and 351 mixts. are collected from 1846 refs. The investigated pure fluids contain a wide variety of fluids from light gases with quantum effects at low temps. to dense fluids and fluids with strong intermol. assocn. More than 68.2 % (corresponding to the std. deviation) of the evaluated exptl. data agree with the RES model within 3.2 % and 8.0 % for pure fluids and mixts., resp. Compared to the recommended models implemented in the REFPROP 10.0 software (the state-of-the-art for thermophys. property calcn.), if the dil. gas viscosity is calcd. in the same way, our RES approach yields similar statistical agreement with the exptl. data while having a much simpler formulation and fewer parameters. To use our RES model, a software package written in Python is provided in the supporting information. Graphical Abstr.: [graphic not available: see fulltext].
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14. 14
  Dehlouz, A.; Privat, R.; Galliero, G.; Bonnissel, M.; Jaubert, J.-N. Revisiting the entropy-scaling concept for shear-viscosity estimation from cubic and SAFT equations of state: application to pure fluids in gas, liquid and supercritical states. Ind. Eng. Chem. Res. 2021, 60, 12719– 12739, DOI: 10.1021/acs.iecr.1c01386
  14
  Revisiting the Entropy-Scaling Concept for Shear-Viscosity Estimation from Cubic and SAFT Equations of State: Application to Pure Fluids in Gas, Liquid and Supercritical States
  Dehlouz, Aghilas; Privat, Romain; Galliero, Guillaume; Bonnissel, Marc; Jaubert, Jean-Noel
  Industrial & Engineering Chemistry Research (2021), 60 (34), 12719-12739CODEN: IECRED; ISSN:0888-5885. (American Chemical Society)
  The entropy scaling concept postulates that reduced transport properties of fluids are related to the residual entropy, a property that reveals intermol. interactions and can be estd. from equations of state (EoS) in a straightforward way. In that framework, two models for dynamic viscosity are presented in this paper: in both models, similar expressions inspired from Rosenfeld's seminal idea are used to reduce transport properties and are related to a carefully selected function of the Tν-residual entropy. This latter is estd. from the PC-SAFT EoS for one model or the tc-PR cubic EoS for the other. The two models are able to predict the viscosities in the entire fluid region (liq., gas, and supercrit. states), which is a great advantage, in comparison to most of the correlations available in the open literature that are specific to a phys. state. Model parameters were fitted over a large database contg. more than 100 000 pure-fluid exptl. data assocd. with 142 chem. species. For each model, different sets of parameters are provided, each of them being likely to be used in specific situations: first, component-specific parameters were estd. for 142 pure compds.; second, chem.-family specific parameters were proposed for describing components not included in our database but belonging to one of the chem. families we considered. Eventually, for compds. present neither in the original database, nor in the considered chem. families, universal parameters (leading to lower accuracy but applicable to any species) are proposed. The accuracy of the models is obviously maximal when using component-specific parameters and minimal with universal parameters. Thus, the entropy-scaling formulation presented in this work can be used for routinely modeling the dynamic viscosity of any pure fluid. As main advantages, it can be applied to any pure species without restriction and is valid for all fluid states, from the dil. gas to the liq. and even the supercrit. state.
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15. 15
  Liu, H.; Yang, F.; Yang, X.; Yang, Z.; Duan, 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
  15
  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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16. 16
  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, 5688– 5697, DOI: 10.1021/acs.jced.0c00682
  There is no corresponding record for this reference.
17. 17
  Hopp, M.; Gross, J. Thermal conductivity of real substances from excess entropy scaling using PCP-SAFT. Ind. Eng. Chem. Res. 2017, 56, 4527– 4538, DOI: 10.1021/acs.iecr.6b04289
  17
  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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18. 18
  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, 18432– 18438, DOI: 10.1021/acs.iecr.9b03998
  18
  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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19. 19
  Yang, X.; Kim, D.; May, E. F.; Bell, I. H. Entropy scaling of thermal conductivity: application to refrigerants and their mixtures. Ind. Eng. Chem. Res. 2021, 60, 13052– 13070, DOI: 10.1021/acs.iecr.1c02154
  19
  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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20. 20
  Huber, M.; Harvey, A.; Lemmon, E.; Hardin, G.; Bell, I.; McLinden, M. NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties (REFPROP), Version 10 , 2018. https://www.nist.gov/srd/refprop.
  There is no corresponding record for this reference.
21. 21
  Urbaneck, T.; Matthes, M.; Richter, M.; Hempel, O.; Safarik, M.; Franzke, U. Research Platform Refrigeration and Energy Technology (KETEC) 2022, 2022. www.ketec.online.
  There is no corresponding record for this reference.
22. 22
  Yang, X.; Richter, M. OilMixProp 1.0: Package for Thermophysical Properties of Oils, Common Fluids, and Their Mixtures. IOP Conf. Ser. Mater. Sci. Eng. 2024, 1322, 012009 DOI: 10.1088/1757-899X/1322/1/012009
  There is no corresponding record for this reference.
23. 23
  Hirschfelder, J. O.; Curtiss, C. F.; Bird, R. B. Molecular Theory of Gases and Liquids; John Wiley & Sons, Ltd, 1966.
  There is no corresponding record for this reference.
24. 24
  Neufeld, P. D.; Janzen, A. R.; Aziz, R. A. Empirical equations to calculate 16 of the transport collision integrals Ω^{(l,s)^*} for the Lennard-Jones (12–6) potential. J. Chem. Phys. 1972, 57, 1100– 1102, DOI: 10.1063/1.1678363
  24
  Empirical equations to calculate 16 of the transport collision integrals Ω(1,s)* for the Lennard-Jones (12-6) potential
  Neufeld, Philip D.; Janzen, A. R.; Aziz, R. A.
  Journal of Chemical Physics (1972), 57 (3), 1100-102CODEN: JCPSA6; ISSN:0021-9606.
  Sixteen of the reduced transport collision integrals Ω(l,s)* are calcd. as a function of reduced temp. T* for the Lennard-Jones (12-6) potential. These calcns. are more accurate than those of Hirschfelder, Curtiss, and Bird, which are frequently used. Empirical equations are presented which allow the calcn. of the collision integrals for any reduced temp. in the range 0.3 ≤ T* ≤ 100 without interpolation from tables. The error in the values so obtained is probably less than 0.1%.
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25. 25
  Chung, T. H.; Lee, L. L.; Starling, K. E. Applications of kinetic gas theories and multiparameter correlation for prediction of dilute gas viscosity and thermal conductivity. IInd. Eng. Chem. Fundam. 1984, 23, 8– 13, DOI: 10.1021/i100013a002
  25
  Applications of kinetic gas theories and multiparameter correlation for prediction of dilute gas viscosity and thermal conductivity
  Chung, Ting Horng; Lee, Lloyd L.; Starling, Kenneth E.
  Industrial & Engineering Chemistry Fundamentals (1984), 23 (1), 8-13CODEN: IECFA7; ISSN:0196-4313.
  Kinetic gas theories have been applied for the development of a correlation of gas viscosity and thermal cond. Employing the acentric factor (ω), the dipole moment (μ), and the assocn. parameter (κ) to characterize the effects of mol. shape and anisotropic intermol. forces, the resultant multiparameter correlations are self-consistent for viscosity and thermal cond. and generalized for polar and nonpolar gases. The results for pure gases are outstanding, not only in accuracy but also in applicability for such wide classes of fluids which include polar and H-bonding compds.
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26. 26
  Tiesinga, E.; Mohr, P. J.; Newell, D. B.; Taylor, B. N. CODATA recommended values of the fundamental physical constants: 2018. J. Phys. Chem. Ref. Data 2021, 50, 033105 DOI: 10.1063/5.0064853
  26
  CODATA Recommended Values of the Fundamental Physical Constants: 2018
  Tiesinga, Eite; Mohr, Peter J.; Newell, David B.; Taylor, Barry N.
  Journal of Physical and Chemical Reference Data (2021), 50 (3), 033105CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
  A review. We report the 2018 self-consistent values of consts. and conversion factors of physics and chem. recommended by the Committee on Data of the International Science Council. The recommended values can also be found at physics.nist.gov/consts. The values are based on a least-squares adjustment that takes into account all theor. and exptl. data available through 31 Dec. 2018. A discussion of the major improvements as well as inconsistencies within the data is given. The former include a decrease in the uncertainty of the dimensionless fine-structure const. and a nearly two orders of magnitude improvement of particle masses expressed in units of kg due to the transition to the revised International System of Units (SI) with an exact value for the Planck const. Further, because the elementary charge, Boltzmann const., and Avogadro const. also have exact values in the revised SI, many other consts. are either exact or have significantly reduced uncertainties. Inconsistencies remain for the g and the muon magnetic-moment anomaly. The proton charge radius puzzle has been partially resolved by improved measurements of hydrogen energy levels. This review article contains the 2018 self-consistent set of values of the consts. and conversion factors of physics and chem. recommended by the Committee on Data for Science and Technol. (CODATA). The CODATA values are based on a least-squares adjustment that takes into account all data available up to the end of 2018. Details of the data selection and methodol. are described. (c) 2021 American Institute of Physics.
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27. 27
  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, 2498– 2508, DOI: 10.1021/ie4033999
  27
  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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28. 28
  Wilke, C. R. A viscosity equation for gas mixtures. J. Chem. Phys. 1950, 18, 517– 519, DOI: 10.1063/1.1747673
  28
  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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29. 29
  Glowinski, R.; Marroco, A. Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité, d’une classe de problèmes de Dirichlet non linéaires. Rev. Fr. Autom. Inf. Rech. Oper. 1975, 9, 41– 76, DOI: 10.1051/m2an/197509r200411
  There is no corresponding record for this reference.
30. 30
  Gabay, D.; Mercier, B. A dual algorithm for the solution of nonlinear variational problems via finite element approximations. Comput. Math. Appl. 1976, 2, 17– 40, DOI: 10.1016/0898-1221(76)90003-1
  There is no corresponding record for this reference.
31. 31
  Boyd, S.; Parikh, N.; Chu, E.; Peleato, B.; Eckstein, J. Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Mach. Learn. 2010, 3, 1– 122, DOI: 10.1561/2200000016
  There is no corresponding record for this reference.
32. 32
  Lemmon, E. W.; Jacobsen, R. T. Viscosity and thermal conductivity equations for nitrogen, oxygen, argon, and air. Int. J. Thermophys. 2004, 25, 21– 69, DOI: 10.1023/B:IJOT.0000022327.04529.f3
  32
  Viscosity and Thermal Conductivity Equations for Nitrogen, Oxygen, Argon, and Air
  Lemmon, E. W.; Jacobsen, R. T.
  International Journal of Thermophysics (2004), 25 (1), 21-69CODEN: IJTHDY; ISSN:0195-928X. (Kluwer Academic/Plenum Publishers)
  New formulations for the viscosity and thermal cond. for nitrogen, oxygen, argon, and air are given. Air is treated as a pseudo-pure fluid using an approach adopted from previous research on the equation of state for air. The equations are valid over all liq. and vapor states, and a simplified cross-over equation was used to model the behavior of the crit. enhancement for thermal cond. The extrapolation behavior of the equations for nitrogen and argon well below their triple points was monitored so that both could be used as ref. equations for extended corresponding states applications. The uncertainties of calcd. values from the equations are generally within 2% for nitrogen and argon and within 5% for oxygen and air, except in the crit. region where the uncertainties are higher. Comparisons with the available exptl. data are given.
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33. 33
  Avgeri, S.; Assael, M. J.; Huber, M. L.; Perkins, R. A. Reference correlation of the viscosity of toluene from the triple point to 675 K and up to 500 MPa. J. Phys. Chem. Ref. Data 2015, 44, 033101 DOI: 10.1063/1.4926955
  33
  Reference Correlation of the Viscosity of Toluene from the Triple Point to 675 K and up to 500 MPa
  Avgeri, S.; Assael, M. J.; Huber, M. L.; Perkins, R. A.
  Journal of Physical and Chemical Reference Data (2015), 44 (3), 033101/1-033101/16CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
  This paper contains new, representative ref. equations for the viscosity of toluene. The equations are based in part upon a body of exptl. data that have been critically assessed for internal consistency and for agreement with theory whenever possible. The correlations are valid from the triple point (178.0 K) to 675 K, and at pressures up to 500 MPa. The estd. uncertainty at a 95% confidence level varies depending on the region of temp. and pressure from a low of 0.3% for the low-d. gas at temps. from 305 to 640 K at pressures to 0.3 MPa (essentially the uncertainty of the best exptl. data) to 0.7% for the satd. liq. at temps. from 263 to 373 K, to 5% for the low-temp. liq. from 187 to 210 K at pressures to 15 MPa. (c) 2015 American Institute of Physics.
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34. 34
  Herrmann, S.; Vogel, E. New formulation for the viscosity of n-butane. J. Phys. Chem. Ref. Data 2018, 47, 013104 DOI: 10.1063/1.5020802
  34
  New Formulation for the Viscosity of n-Butane
  Herrmann, Sebastian; Vogel, Eckhard
  Journal of Physical and Chemical Reference Data (2018), 47 (1), 013104/1-013104/32CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
  A review. A new viscosity formulation for n-butane, based on the residual quantity concept, uses the ref. equation of state by Bucker and Wagner [J. Phys. Chem. Ref. Data 35, 929 (2006)] and is valid in the fluid region from the triple point to 650 K and to 100 MPa. The contributions for the zero-d. viscosity and for the initial-d. dependence were sep. developed, whereas those for the crit. enhancement and for the higher-d. terms were pretreated. All contributions were given as a function of the reciprocal reduced temp. τ, while the last two contributions were correlated as a function of τ and of the reduced d. δ. The different contributions were based on specific primary data sets, whose evaluation and choice were discussed in detail. The final formulation incorporates 13 coeffs. derived employing a state-of-the-art linear optimization algorithm. The viscosity at low pressures p ≤ 0.2 MPa is described with an expanded uncertainty of 0.5% (coverage factor k = 2) for temps. 293 ≤ T/K ≤ 626. The expanded uncertainty in the vapor phase at subcrit. temps. T ≥ 298 K as well as in the supercrit. thermodn. region T ≤ 448 K at pressures p ≤ 30 MPa is estd. to be 1.5%. It is raised to 4.0% in regions where only less reliable primary data sets are available and to 6.0% in ranges without any primary data, but in which the equation of state is valid. A weakness of the ref. equation of state in the near-crit. region prevents estn. of the expanded uncertainty in this region. Viscosity tables for the new formulation are presented in Appendix B for the single-phase region, for the vapor-liq. phase boundary, and for the near-crit. region. (c) 2018 American Institute of Physics.
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35. 35
  Assael, M. J.; Papalas, T. B.; Huber, M. L. Reference correlations for the viscosity and thermal conductivity of n-undecane. J. Phys. Chem. Ref. Data 2017, 46, 033103 DOI: 10.1063/1.4996885
  35
  Reference Correlations for the Viscosity and Thermal Conductivity of n-Undecane
  Assael, M. J.; Papalas, T. B.; Huber, M. L.
  Journal of Physical and Chemical Reference Data (2017), 46 (3), 033103/1-033103/12CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
  A review. This paper presents new, wide-ranging correlations for the viscosity and thermal cond. of n-undecane based on critically evaluated exptl. data. The correlations are designed to be used with a recently published equation of state that is valid from the triple point to 700 K, at pressures up to 500 MPa, with densities below 776.86 kg m-3. The estd. uncertainty for the dil.-gas viscosity is 2.4%, and the estd. uncertainty for viscosity in the liq. phase for pressures up to 60 MPa over the temp. range 260 K-520 K is 5%. The estd. uncertainty is 3% for the thermal cond. of the low-d. gas and 3% for the liq. over the temp. range from 284 K to 677 K at pressures up to 400 MPa. Both correlations behave in a phys. reasonable manner when extrapolated to the full range of the equation of state, but care should be taken when using the correlations outside of the validated range. The uncertainties will be larger outside of the validated range and also in the crit. region. (c) 2017 American Institute of Physics.
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36. 36
  Huber, M. L.; Laesecke, A.; Perkins, R. Transport properties of n-dodecane. Energy Fuels 2004, 18, 968– 975, DOI: 10.1021/ef034109e
  36
  Transport Properties of n-Dodecane
  Huber, Marcia L.; Laesecke, Arno; Perkins, Richard
  Energy & Fuels (2004), 18 (4), 968-975CODEN: ENFUEM; ISSN:0887-0624. (American Chemical Society)
  The authors have surveyed literature data and developed correlations for the viscosity and thermal cond. of n-dodecane that are valid over a wide range of fluid states. The new correlations are applicable from the triple point (263.59 °K) to 800 °K, and at pressures up to 200 MPa. The viscosity correlation has an estd. uncertainty of 0.5% along the satn. boundary in the liq. phase, 3% in the compressed liq. region, and 3% in the vapor (the uncertainties can be considered as ests. of a combined expanded uncertainty with a coverage factor of 2). The thermal cond. correlation has an estd. uncertainty of 4% along the liq. satn. boundary and in the compressed liq., and ∼5% in the vapor region.
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37. 37
  Meng, X. Y.; Sun, Y. K.; Cao, F. L.; Wu, J. T.; Vesovic, V. Reference correlation of the viscosity of n-hexadecane from the triple point to 673 K and up to 425 MPa. J. Phys. Chem. Ref. Data 2018, 47, 033102 DOI: 10.1063/1.5039595
  37
  Reference Correlation of the Viscosity of n-Hexadecane from the Triple Point to 673 K and up to 425 MPa
  Meng, X. Y.; Sun, Y. K.; Cao, F. L.; Wu, J. T.; Vesovic, V.
  Journal of Physical and Chemical Reference Data (2018), 47 (3), 033102/1-033102/12CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
  A review. A new correlation for the viscosity of n-hexadecane is presented. The correlation is based upon a body of exptl. data that has been critically assessed for internal consistency and for agreement with theory. It is applicable in the temp. range from the triple point to 673 K at pressures up to 425 MPa. The overall uncertainty of the proposed correlation, estd. as the combined expanded uncertainty with a coverage factor of 2, varies from 1% for the viscosity at atm. pressure to 10% for the viscosity of the vapor phase at low temps. Tables of the viscosity generated by the relevant equations are provided at selected temps. and pressures and along the satn. line. (c) 2018 American Institute of Physics.
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38. 38
  Laesecke, A.; Muzny, C. D. Reference correlation for the viscosity of carbon dioxide. J. Phys. Chem. Ref. Data 2017, 46, 013107 DOI: 10.1063/1.4977429
  38
  Reference Correlation for the Viscosity of Carbon Dioxide
  Laesecke, Arno; Muzny, Chris D.
  Journal of Physical and Chemical Reference Data (2017), 46 (1), 013107/1-013107/28CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
  A review. A comprehensive database of exptl. and computed data for the viscosity of carbon dioxide (CO2) was compiled and a new ref. correlation was developed. Literature results based on an ab initio potential energy surface were the foundation of the correlation of the viscosity in the limit of zero d. in the temp. range from 100 to 2000 K. Guided symbolic regression was employed to obtain a new functional form that extrapolates correctly to 0 and to 10 000 K. Coordinated measurements at low d. made it possible to implement the temp. dependence of the Rainwater-Friend theory in the linear-in-d. viscosity term. The residual viscosity could be formulated with a scaling term ργ/T, the significance of which was confirmed by symbolic regression. The final viscosity correlation covers temps. from 100 to 2000 K for gaseous CO2 and from 220 to 700 K with pressures along the melting line up to 8000 MPa for compressed and supercrit. liq. states. The data representation is more accurate than with the previous correlations, and the covered pressure and temp. range is significantly extended. The crit. enhancement of the viscosity of CO2 is included in the new correlation. (c) 2017 American Institute of Physics.
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39. 39
  Tariq, U.; Jusoh, A. R. B.; Riesco, N.; Vesovic, V. Reference correlation of the viscosity of cyclohexane from the triple point to 700 K and up to 110 MPa. J. Phys. Chem. Ref. Data 2014, 43, 033101 DOI: 10.1063/1.4891103
  39
  Reference Correlation of the Viscosity of Cyclohexane from the Triple Point to 700 K and up to 110 MPa
  Tariq, U.; Jusoh, A. R. B.; Riesco, N.; Vesovic, V.
  Journal of Physical and Chemical Reference Data (2014), 43 (3), 033101/1-033101/18CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
  A new correlation for the viscosity of cyclohexane is presented. The correlation is based upon a body of exptl. data that has been critically assessed for internal consistency and for agreement with theory. It is applicable in the temp. range from the triple point to 700 K at pressures up to 110 MPa. In the dil. gas region, at pressures below 0.3 MPa, the correlation is valid up to 873 K. The overall uncertainty of the proposed correlation, estd. as the combined expanded uncertainty with a coverage factor of 2, varies from 0.5% for the viscosity of the dil. gas and of liq. at ambient pressure to 5% for the viscosity at high pressures and temps. Tables of the viscosity generated by the relevant equations, at selected temps. and pressures and along the satn. line, are provided. (c) 2014 American Institute of Physics.
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40. 40
  Muzny, C. D.; Huber, M. L.; Kazakov, A. F. Correlation for the viscosity of normal hydrogen obtained from symbolic regression. J. Chem. Eng. Data 2013, 58, 969– 979, DOI: 10.1021/je301273j
  40
  Correlation for the Viscosity of Normal Hydrogen Obtained from Symbolic Regression
  Muzny, Chris D.; Huber, Marcia L.; Kazakov, Andrei F.
  Journal of Chemical & Engineering Data (2013), 58 (4), 969-979CODEN: JCEAAX; ISSN:0021-9568. (American Chemical Society)
  We report the results of a symbolic-regression methodol. to obtain both the functional form and the coeffs. for a wide-ranging correlation for the viscosity of normal hydrogen. The correlation covers the temp. range from the triple-point temp. to 1000 K and pressures up to 200 MPa and extrapolates in a phys. reasonable manner to 2000 K. The estd. uncertainty is 4 % for the satd. liq. from the triple point to 31 K, with larger deviations as the crit. region is approached. The estd. uncertainty is 4 % for the supercrit. fluid phase at pressures to 200 MPa. For the limited range of 200 K to 400 K at pressures up to 0.1 MPa, the uncertainty is 0.1 %.
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41. 41
  Huber, M. L.; Laesecke, A.; Xiang, H. W. Viscosity correlations for minor constituent fluids in natural gas: n-octane, n-nonane and n-decane. Fluid Phase Equilib. 2005, 228–229, 401– 408, DOI: 10.1016/j.fluid.2005.03.008
  41
  Viscosity correlations for minor constituent fluids in natural gas: n-octane, n-nonane and n-decane
  Huber, Marcia L.; Laesecke, Arno; Xiang, Hong Wei
  Fluid Phase Equilibria (2005), 228-229 (), 401-408CODEN: FPEQDT; ISSN:0378-3812. (Elsevier B.V.)
  Natural gas, although predominantly comprised of methane, often contains small amts. of heavier hydrocarbons that contribute to its thermodn. and transport properties. In this manuscript, we review the current literature and present new correlations for the viscosity of the pure fluids n-octane, n-nonane, and n-decane that are valid over a wide range of fluid states, from the dil. gas to the dense liq. The new correlations represent the viscosity to within the uncertainty of the best exptl. data and will be useful for engineers working on viscosity models for natural gas and other hydrocarbon mixts.
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42. 42
  Meng, X.; Zhang, J.; Wu, J.; Liu, Z. Experimental measurement and modeling of the viscosity of dimethyl ether. J. Chem. Eng. Data 2012, 57, 988– 993, DOI: 10.1021/je201297j
  42
  Experimental Measurement and Modeling of the Viscosity of Dimethyl Ether
  Meng, Xianyang; Zhang, Jianbo; Wu, Jiangtao; Liu, Zhigang
  Journal of Chemical & Engineering Data (2012), 57 (3), 988-993CODEN: JCEAAX; ISSN:0021-9568. (American Chemical Society)
  The viscosities of di-Me ether in the temp. range of (243 to 373) K from satd. pressure up to 30 MPa are reported. These new exptl. data were measured with a vibrating-wire viscometer. The combined expanded uncertainty of the results with a level of confidence of 0.95 (k = 2) is about ± 2.0 % over all ranges of temp. and pressure. The exptl. data are used to develop correlations for the viscosity, including a satd. liq. equation and a multiparameter formulation covering liq. and vapor region. On the basis of the uncertainty of and comparisons with the exptl. data, the estd. uncertainty of viscosity correlation is 2 % in the liq. phase and 3 % in the gas region.
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43. 43
  Meng, X. Y.; Cao, F. L.; Wu, J. T.; Vesovic, V. Reference correlation of the viscosity of ethylbenzene from the triple point to 673 K and up to 110 MPa. J. Phys. Chem. Ref. Data 2017, 46, 013101 DOI: 10.1063/1.4973501
  43
  Reference Correlation of the Viscosity of Ethylbenzene from the Triple Point to 673 K and up to 110 MPa
  Meng, X. Y.; Cao, F. L.; Wu, J. T.; Vesovic, V.
  Journal of Physical and Chemical Reference Data (2017), 46 (1), 013101/1-013101/13CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
  A new correlation for the viscosity of ethylbenzene is presented. The correlation is based upon a body of exptl. data that has been critically assessed for internal consistency and for agreement with theory. It is applicable in the temp. range from the triple point to 673 K at pressures up to 110 MPa. The overall uncertainty of the proposed correlation, estd. as the combined expanded uncertainty with a coverage factor of 2, varies from 1% for the viscosity at atm. pressure to 5% for the highest temps. and pressures of interest. Tables of the viscosity, generated by the relevant equations at selected temps. and pressures and along the satn. line, are provided. Comparison of viscosity of xylene isomers indicated that at very high temps. the viscosity correlation of para-xylene has higher uncertainty than previously postulated. Thus, in this work we also provide a revised viscosity correlation for p-xylene. (c) 2017 American Institute of Physics.
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44. 44
  Vogel, E.; Span, R.; Herrmann, S. Reference correlation for the viscosity of ethane. J. Phys. Chem. Ref. Data 2015, 44, 043101 DOI: 10.1063/1.4930838
  44
  Reference Correlation for the Viscosity of Ethane
  Vogel, Eckhard; Span, Roland; Herrmann, Sebastian
  Journal of Physical and Chemical Reference Data (2015), 44 (4), 043101/1-043101/39CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
  A new representation of the viscosity for the fluid phase of ethane includes a zero-d. correlation and a contribution for the crit. enhancement, initially both developed sep., but based on exptl. data. The higher-d. contributions are correlated as a function of the reduced d. δ = ρ/ρc and of the reciprocal reduced temp. τ = Tc/T (ρc-crit. d. and Tc-crit. temp.). The final formulation contains 14 coeffs. obtained using a state-of-the-art linear optimization algorithm. The evaluation and choice of the selected primary data sets is reviewed, in particular with respect to the assessment used in earlier viscosity correlations. The new viscosity surface correlation makes use of the ref. equation of state for the thermodn. properties of ethane by Bucker and Wagner [J. Phys. Chem. Ref. Data 35, 205 (2006)] and is valid in the fluid region from the melting line to temps. of 675 K and pressures of 100 MPa. The viscosity in the limit of zero d. is described with an expanded uncertainty of 0.5% (coverage factor k = 2) for temps. 290 < T/K < 625, increasing to 1.0% at temps. down to 212 K. The uncertainty of the correlated values is 1.5% in the range 290 < T/K < 430 at pressures up to 30 MPa on the basis of recent measurements judged to be very reliable as well as 4.0% and 6.0% in further regions. The uncertainty in the near-crit. region (1.001 < 1/τ < 1.010 and 0.8 < δ < 1.2) increases with decreasing temp. up to 3.0% considering the available reliable data. Tables of the viscosity calcd. from the correlation are listed in an appendix for the single-phase region, for the vapor-liq. phase boundary, and for the near-crit. region. (c) 2015 American Institute of Physics.
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45. 45
  Kiselev, S. B.; Ely, J. F.; Abdulagatov, I. M.; Huber, M. L. Generalized SAFT-DFT/DMT model for the thermodynamic, interfacial, and transport properties of associating fluids: application for n-alkanols. Ind. Eng. Chem. Res. 2005, 44, 6916– 6927, DOI: 10.1021/ie050010e
  45
  Generalized SAFT-DFT/DMT Model for the Thermodynamic, Interfacial, and Transport Properties of Associating Fluids: Application for n-Alkanols
  Kiselev, S. B.; Ely, J. F.; Abdulagatov, I. M.; Huber, M. L.
  Industrial & Engineering Chemistry Research (2005), 44 (17), 6916-6927CODEN: IECRED; ISSN:0888-5885. (American Chemical Society)
  We have developed a "global" crossover (GC) statistical assocg. fluid theory (SAFT) equation of state (EOS) for assocg. fluids that incorporates non-analytic scaling laws in the crit. region and in the limit of low densities, ρ → 0, that is transformed into the ideal-gas EOS. Unlike the crossover SAFT EOS developed earlier, the new GC SAFT EOS contains a so-called kernel term and reproduces the asymptotic scaling behavior of the isochoric heat capacity in the one- and two-phase regions. In addn., we develop on the basis of the d. functional theory (DFT) a GC SAFT-DFT model for the surface tension. In the second step, using the GC SAFT EOS and the decoupled-mode theory (DMT), we have developed a generalized GC SAFT-DMT model for transport coeffs. that reproduces the singular behavior of the thermal cond. of pure fluids in the crit. region. Unlike the DMT model based on the asymptotic crossover EOS, the GC SAFT-DMT model is valid in the entire fluid state region at T ≥ Tb (where Tb is the binodal temp.), and at ρ → 0 reproduces the dil. gas contributions for the transport coeffs. A comparison was made with exptl. data for methanol, ethanol, and higher n-alkanols. For n-alkanols, the GC SAFT-DFT/DMT model contains the same no. of the adjustable parameters as the original classical SAFT EOS, but reproduces with high accuracy the PVT, VLE, isochoric, and isobaric sp. heats, surface tension, and thermal cond. data close to and far from the crit. point.
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46. 46
  Holland, P. M.; Eaton, B. E.; Hanley, H. J. M. A correlation of the viscosity and thermal conductivity data of gaseous and liquid ethylene. J. Phys. Chem. Ref. Data 1983, 12, 917– 932, DOI: 10.1063/1.555701
  46
  A correlation of the viscosity and thermal conductivity data of gaseous and liquid ethylene
  Holland, P. M.; Eaton, B. E.; Hanley, H. J. M.
  Journal of Physical and Chemical Reference Data (1983), 12 (4), 917-32CODEN: JPCRBU; ISSN:0047-2689.
  Data for the viscosity and thermal cond. coeff. of gaseous and liq. C2H4 were evaluated and represented by an empirical function. Tables of values are presented for the range 110-500 K for pressures to 50 MPa (≈500 atm). Both the viscosity and thermal cond. coeff. data have uncertainties of about ±5% increasing to 10% in the dense liq. The anomalous contribution to the thermal cond. in the vicinity of the crit. point is included.
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47. 47
  Schmidt, K. A. G.; Quiñones-Cisneros, S. E.; Carroll, J. J.; Kvamme, B. Hydrogen sulfide viscosity modeling. Energy Fuels 2008, 22, 3424– 3434, DOI: 10.1021/ef700701h
  47
  Hydrogen Sulfide Viscosity Modeling
  Schmidt, Kurt A. G.; Quinones-Cisneros, Sergio E.; Carroll, John J.; Kvamme, Bjoern
  Energy & Fuels (2008), 22 (5), 3424-3434CODEN: ENFUEM; ISSN:0887-0624. (American Chemical Society)
  As regulations for emissions of carbon dioxide and hydrogen sulfide into the atm. are becoming stricter and the penalty for violation increases, new and economical ways of reducing these emissions are becoming increasingly important to everyday operations. One promising sequestering option is the injection of acid gas mixts. into formations for disposal/storage. During the design of these acid gas injection schemes a comprehensive knowledge of the thermo-phys. properties is of utmost importance in detg. the feasibility and size of these operations. Recently, the friction theory (f-theory) for viscosity modeling was shown to accurately det. the viscosity behavior of a wide range of petroleum fluid systems ranging from natural gases to heavy crude oils. This technique also was shown to accurately model mixts. contg. various concns. of CO2. However, in the development of the f-theory hydrogen sulfide was not explicitly studied and therefore needs to be accounted for to ensure it is accurately modeled. The development/validation of any modeling approach requires a thorough knowledge of the available data. With this in mind, an exhaustive collection of the data available in the literature was performed revealing a very limited no. of exptl. points available in the open literature for the viscosity of pure H2S and H2S mixts. Although limited data for pure H2S exists in the literature, a crit. evaluation of the data was performed and a ref. viscosity model based on the generalized friction theory (f-theory) was developed. The developed ref. viscosity model gives reasonable modeling results over the T-η-P surface for H2S. The one parameter f-theory was also extended to include H2S, and the model was shown to accurately reproduce existing exptl. viscosities of hydrogen sulfide and its mixts. in ranges relevant to the natural gas and petroleum industry.
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48. 48
  Michailidou, E. K.; Assael, M. J.; Huber, M. L.; Abdulagatov, I. M.; Perkins, R. A. Reference correlation of the viscosity of n-heptane from the triple point to 600 K and up to 248 MPa. J. Phys. Chem. Ref. Data 2014, 43, 023103 DOI: 10.1063/1.4875930
  48
  Reference Correlation of the Viscosity of n-Heptane from the Triple Point to 600 K and up to 248 MPa
  Michailidou, E. K.; Assael, M. J.; Huber, M. L.; Abdulagatov, I. M.; Perkins, R. A.
  Journal of Physical and Chemical Reference Data (2014), 43 (2), 023103/1-023103/13CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
  This paper contains a new wide-ranging correlation for the viscosity of n-heptane based on critically evaluated exptl. data. The correlation is valid from the triple point (182.55 K) to 600 K, and at pressures up to 248 MPa. The estd. uncertainty at a 95% confidence level is 3.5% over the whole range (with the exception of the near-crit. region). Along the satd. liq. curve, the estd. uncertainty is 1% below 292 K, 0.6% in the region from 292 to 346 K, rising to 2% between 346 and 363 K, and 0.3% for the low-d. gas at temps. from 317 to 600 K and pressures to 0.3 MPa. (c) 2014 American Institute of Physics.
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49. 49
  Michailidou, E. K.; Assael, M. J.; Huber, M. L.; Perkins, R. A. Reference correlation of the viscosity of n-hexane from the triple point to 600 K and up to 100 MPa. J. Phys. Chem. Ref. Data 2013, 42, 033104 DOI: 10.1063/1.4818980
  49
  Reference Correlation of the Viscosity of n-Hexane from the Triple Point to 600 K and up to 100 MPa
  Michailidou, E. K.; Assael, M. J.; Huber, M. L.; Perkins, R. A.
  Journal of Physical and Chemical Reference Data (2013), 42 (3), 033104/1-033104/12CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
  This paper contains new, representative ref. equations for the viscosity of n-hexane. 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. The correlations are valid from the triple point to 600 K, and at pressures up to 100 MPa. We est. the expanded uncertainty at a 95% confidence level to be 2% for the liq. phase at temps. from the triple point to 450 K and pressures to 100 MPa. For the liq. at 450-600 K at pressures to 100 MPa, the expanded uncertainty at the 95% confidence level is 6%, and is 0.3% for the low-d. gas at pressures to 0.3 MPa. (c) 2013 American Institute of Physics.
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50. 50
  Vogel, E.; Küchenmeister, C.; Bich, E. Viscosity correlation for isobutane over wide ranges of the fluid region. Int. J. Thermophys. 2000, 21, 343– 356, DOI: 10.1023/A:1006623310780
  50
  Viscosity correlation for isobutane over wide ranges of the fluid region
  Vogel, E.; Kuchenmeister, C.; Bich, E.
  International Journal of Thermophysics (2000), 21 (2), 343-356CODEN: IJTHDY; ISSN:0195-928X. (Kluwer Academic/Plenum Publishers)
  A new representation of the viscosity of isobutane has been developed. The representative equations include zero-d. and initial-d. dependence correlations. The higher d. contributions to the residual viscosity are formed by a combination of double polynomials in d. and reciprocal temp. and of a free-vol. term with a temp.-dependent close-packed d. The new full surface correlation is based on primary exptl. data sets selected as a result of a crit. assessment of the available information. The validity of the representation extends from the triple point to 600 K and 35 MPa in accordance with the modified Benedict-Webb-Rubin equation of state by Younglove and Ely (1987). The uncertainty of the representation varies from ± 0.4 % in the dil. gas phase between room temp. and 600 K to ± 3% in the thermodn. ranges in which the equation of state is valid as well as where primary exptl. data are available.
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51. 51
  Xiang, H. W.; Laesecke, A.; Huber, M. L. A new reference correlation for the viscosity of methanol. J. Phys. Chem. Ref. Data 2006, 35, 1597– 1620, DOI: 10.1063/1.2360605
  51
  A new reference correlation for the viscosity of methanol
  Xiang, Hong Wei; Laesecke, Arno; Huber, Marcia L.
  Journal of Physical and Chemical Reference Data (2006), 35 (4), 1597-1620CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
  A new ref.-quality correlation for the viscosity of methanol is presented that is valid over the entire fluid region, including vapor, liq., and metastable phases. To describe the zero-d. viscosity with kinetic theory for polar gases, a new expression for the collision integral of the Stockmayer potential is introduced. The initial d. dependence is based on the Rainwater-Friend theory. A new correlation for the third viscosity virial coeff. is developed from exptl. data and applied to methanol. The high-d. contribution to the viscosity is based on the Chapman-Enskog theory and includes a new expression for the hard-sphere diam. that is a function of both temp. and d. The resulting correlation is applicable for temps. from the triple point to 630 K at pressures up to 8 GPa. The estd. uncertainty of the resulting correlation (with a coverage factor of 2) varies from 0.6% in the dil.-gas phase between room temp. and 630 K, to less than 2% for the liq. phase at pressures up to 30 MPa at temps. between 273 and 343 K, 3% for pressures from 30 to 100 MPa, 5% for the liq. from 100 to 500 MPa, and 10% between 500 MPa and 4 GPa. At very high pressures, from 4 to 8 GPa, the correlation has an estd. uncertainty of 30% and can be used to indicate qual. behavior.
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52. 52
  Cao, F. L.; Meng, X. Y.; Wu, J. T.; Vesovic, V. Reference correlation of the viscosity of meta-xylene from 273 to 673 K and up to 200 MPa. J. Phys. Chem. Ref. Data 2016, 45, 013103 DOI: 10.1063/1.4941241
  52
  Reference Correlation of the Viscosity of meta-Xylene from 273 to 673 K and up to 200 MPa
  Cao, F. L.; Meng, X. Y.; Wu, J. T.; Vesovic, V.
  Journal of Physical and Chemical Reference Data (2016), 45 (1), 013103/1-013103/12CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
  A new correlation for the viscosity of meta-xylene is presented. The correlation is based upon a body of exptl. data that has been critically assessed for internal consistency and for agreement with theory. It is applicable in the temp. range from 273 to 673 K at pressures up to 200 MPa. The overall uncertainty of the proposed correlation, estd. as the combined expanded uncertainty with a coverage factor of 2, varies from 1% for the viscosity at atm. pressure to 5% for the highest temps. and pressures of interest. Tables of the viscosity, generated by the relevant equations, at selected temps. and pressures, and along the satn. line, are provided. (c) 2016 American Institute of Physics.
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53. 53
  Cao, F. L.; Meng, X. Y.; Wu, J. T.; Vesovic, V. Reference correlation of the viscosity of ortho-xylene from 273 to 673 K and up to 110 MPa. J. Phys. Chem. Ref. Data 2016, 45, 023102 DOI: 10.1063/1.4945663
  53
  Reference Correlation of the Viscosity of ortho-Xylene from 273 to 673 K and up to 110 MPa
  Cao, F. L.; Meng, X. Y.; Wu, J. T.; Vesovic, V.
  Journal of Physical and Chemical Reference Data (2016), 45 (2), 023102/1-023102/11CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
  A review. A new correlation for the viscosity of ortho-xylene (o-xylene) is presented. The correlation is based upon a body of exptl. data that has been critically assessed for internal consistency and for agreement with theory. It is applicable in the temp. range from 273 to 673 K at pressures up to 110 MPa. The overall uncertainty of the proposed correlation, estd. as the combined expanded uncertainty with a coverage factor of 2, varies from 1% for the viscosity at atm. pressure to 5% for the highest temps. and pressures of interest. Tables of the viscosity generated by the relevant equations, at selected temps. and pressures and along the satn. line, are provided. (c) 2016 American Institute of Physics.
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54. 54
  Balogun, B.; Riesco, N.; Vesovic, V. Reference correlation of the viscosity of para-xylene from the triple point to 673 K and up to 110 MPa. J. Phys. Chem. Ref. Data 2015, 44, 013103 DOI: 10.1063/1.4908048
  54
  Reference Correlation of the Viscosity of para-Xylene from the Triple Point to 673 K and up to 110 MPa
  Balogun, B.; Riesco, N.; Vesovic, V.
  Journal of Physical and Chemical Reference Data (2015), 44 (1), 013103/1-013103/13CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
  A new correlation for the viscosity of para-xylene (p-xylene) is presented. The correlation is based upon a body of exptl. data that has been critically assessed for internal consistency and for agreement with theory. It is applicable in the temp. range from the triple point to 673 K at pressures up to 110 MPa. The overall uncertainty of the proposed correlation, estd. as the combined expanded uncertainty with a coverage factor of 2, varies from 0.5% for the viscosity of the dil. gas to 5% for the highest temps. and pressures of interest. Tables of the viscosity generated by the relevant equations, at selected temps. and pressures and along the satn. line, are provided. (c) 2015 American Institute of Physics.
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55. 55
  Tanaka, Y.; Sotani, T. Thermal conductivity and viscosity of 2,2-dichloro-1,1,1-trifluoroethane (HCFC-123). Int. J. Thermophys. 1996, 17, 293– 328, DOI: 10.1007/BF01443394
  55
  Thermal conductivity and viscosity of 2,2-dichloro-1,1,1-trifluoroethane (HCFC-123)
  Tanaka, Y.; Sotani, T.
  International Journal of Thermophysics (1996), 17 (2), 293-328CODEN: IJTHDY; ISSN:0195-928X. (Plenum)
  The thermal cond. and the viscosity data of CFC alternative refrigerant HCFC-123 (2,2-dichloro-1,1,1-trifluoroethane; CHCl2-CF3) were critically evaluated and correlated on the basis of a comprehensive literature survey. Using the residual transport-property concept, the authors have developed the three-dimensional surfaces of the thermal cond.-temp.-d. and the viscosity-temp.-d. A dil.-gas function and an excess function of simple form were established for each property. The crit. enhancement contribution was taken no account because reliable crossover equations of state and the thermal cond. data are still missing in the crit. region. The correlation for the thermal cond. is valid at temps. from 253 to 373 K, pressures up to 30 MPa, and densities up to 1623 kg·m-3. The correlation for the viscosity is valid at temps. from 253 to 423 K, pressures up to 20 MPa, and densities up to 1608 kg·m-3. The uncertainties of the present correlations are estd. to be 5% for both properties, since the exptl. data are still scarce and somewhat contradictory in the vapor phase at present.
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56. 56
  Huber, M. L.; Assael, M. J. Correlations for the viscosity of 2,3,3,3-tetrafluoroprop-1-ene (R1234yf) and trans-1,3,3,3-tetrafluoropropene (R1234ze(E)). Int. J. Refrig. 2016, 71, 39– 45, DOI: 10.1016/j.ijrefrig.2016.08.007
  56
  Correlations for the viscosity of 2,3,3,3-tetrafluoroprop-1-ene (R1234yf) and trans-1,3,3,3-tetrafluoropropene (R1234ze(E))
  Huber, Marcia L.; Assael, Marc J.
  International Journal of Refrigeration (2016), 71 (), 39-45CODEN: IJRFDI; ISSN:0140-7007. (Elsevier Ltd.)
  Due to concerns about global warming, there is interest in 2,3,3,3-tetrafluoroprop-1-ene (R1234yf) and trans-1,3,3,3-tetrafluoropropene (R1234ze(E)) as potential replacements for refrigerants with high global warming potential (GWP). In this paper we survey available data and provide viscosity correlations that cover the entire fluid range including vapor, liq., and supercrit. regions. The correlation for R1234yf is valid from the triple point (220 K) to 410 K at pressures up to 30 MPa, and the correlation for R1234ze(E) is valid from the triple point (169 K) to 420 K at pressures up to 100 MPa. The estd. uncertainty for both correlations at a 95% confidence level is 2% for the liq. phase over the temp. range 243 K to 363 K at pressures to 30 MPa, and 3% for the gas phase at atm. pressure.
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57. 57
  Huber, M. L.; Laesecke, A. Correlation for the viscosity of pentafluoroethane (R125) from the triple point to 500 K at pressures up to 60 MPa. Ind. Eng. Chem. Res. 2006, 45, 4447– 4453, DOI: 10.1021/ie051367l
  57
  Correlation for the Viscosity of Pentafluoroethane (R125) from the Triple Point to 500 K at Pressures up to 60 MPa
  Huber, Marcia L.; Laesecke, Arno
  Industrial & Engineering Chemistry Research (2006), 45 (12), 4447-4453CODEN: IECRED; ISSN:0888-5885. (American Chemical Society)
  We present a correlation for the viscosity of pentafluoroethane (R125) based on a compilation and crit. assessment of the available exptl. data. The correlation covers a wide range of fluid states, including the supercrit. region. It is applicable from the triple point at 172.52 to 500 K, with pressures varying up to 60 MPa. The formulation includes a zero-d. contribution, initial d. dependence based on the Rainwater-Friend theory, and a residual contribution for higher densities that combines virial terms with a free-vol. term, both being temp.-dependent. The estd. uncertainty of the viscosity correlation (coverage factor of 2) is 3% along the liq.-phase satn. boundary, 3% in the compressed liq. phase at pressures to 60 MPa, and 0.8% in the vapor.
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58. 58
  Huber, M. L.; Laesecke, A.; Perkins, R. A. Model for the viscosity and thermal conductivity of refrigerants, including a new correlation for the viscosity of R134a. Ind. Eng. Chem. Res. 2003, 42, 3163– 3178, DOI: 10.1021/ie0300880
  58
  Model for the Viscosity and Thermal Conductivity of Refrigerants, Including a New Correlation for the Viscosity of R134a
  Huber, Marcia L.; Laesecke, Arno; Perkins, Richard A.
  Industrial & Engineering Chemistry Research (2003), 42 (13), 3163-3178CODEN: IECRED; ISSN:0888-5885. (American Chemical Society)
  We present modifications to an extended corresponding states (ECS) model for thermal cond. and viscosity originally developed by Ely and Hanley (Ind. Eng. Chem. Fundam. 1981, 20, 323-332). We apply the method to 17 pure refrigerants and present coeffs. for the model and comparisons with exptl. data. The av. abs. viscosity deviation for the 17 pure fluids studied ranges from a low of 0.56% for R236ea to a high of 5.68% for propylene, with an av. abs. deviation for all fluids of 3.13% based on a total of 3737 points. The av. abs. thermal cond. deviation for the 17 pure fluids studied ranges from a low of 1.37% for R116 to a high of 6.78% for R115, with an av. abs. deviation for all fluids of 3.75% based on a total of 12 156 points. We also present a new correlation for the viscosity of R134a (1,1,1,2-tetrafluoroethane), which is used as a ref. fluid for the description of properties of some refrigerants. The new correlation represents the viscosity to within the uncertainty of the best exptl. data.
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59. 59
  Tsolakidou, C. M.; Assael, M. J.; Huber, M. L.; Perkins, R. A. Correlations for the viscosity and thermal conductivity of ethyl fluoride (R161). J. Phys. Chem. Ref. Data 2017, 46, 023103 DOI: 10.1063/1.4983027
  59
  Correlations for the Viscosity and Thermal Conductivity of Ethyl Fluoride (R161)
  Tsolakidou, Ch. M.; Assael, M. J.; Huber, M. L.; Perkins, R. A.
  Journal of Physical and Chemical Reference Data (2017), 46 (2), 023103/1-023103/12CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
  This paper presents new wide-ranging correlations for the viscosity and thermal cond. of Et fluoride (R161) based on critically evaluated exptl. data. The correlations are designed to be used with a recently published equation of state that is valid from 130 to 450 K, at pressures up to 100 MPa. The estd. uncertainty at a 95% confidence level is 2% for the viscosity of low-d. gas (pressures below 0.5 MPa) and 3% for the viscosity of the liq. over the temp. range from 243 to 363 K at pressures up to 30 MPa. The estd. uncertainty is 3% for the thermal cond. of the low-d. gas and 3% for the liq. over the temp. range from 234 to 374 K at pressures up to 20 MPa. Both correlations may be used over the full range of the equation of state, but the uncertainties will be larger, esp. in the crit. region. (c) 2017 American Institute of Physics.
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60. 60
  Perkins, R. A.; Huber, M. L.; Assael, M. J. Measurements of the thermal conductivity of 1,1,1,3,3-pentafluoropropane (R245fa) and correlations for the viscosity and thermal conductivity surfaces. J. Chem. Eng. Data 2016, 61, 3286– 3294, DOI: 10.1021/acs.jced.6b00350
  60
  Measurements of the Thermal Conductivity of 1,1,1,3,3-Pentafluoropropane (R245fa) and Correlations for the Viscosity and Thermal Conductivity Surfaces
  Perkins, Richard A.; Huber, Marcia L.; Assael, Marc J.
  Journal of Chemical & Engineering Data (2016), 61 (9), 3286-3294CODEN: JCEAAX; ISSN:0021-9568. (American Chemical Society)
  New exptl. data on the thermal cond. of 1,1,1,3,3-pentafluoropropane (R245fa) are reported that cover a wide range of liq. conditions. These new exptl. data were made with a transient hot-wire app. and cover the liq. phase over a temp. range of 173-344 K and a pressure range of 0.1-71 MPa. The exptl. data reported here have an expanded uncertainty (0.95 level of confidence) of less than 1%. The measurements are used with selected literature data to develop correlations for the thermal cond. On the basis of this expanded uncertainty and comparisons with exptl. data, the thermal cond. correlation for R245fa is estd. to have a relative expanded uncertainty (0.95 level of confidence) of about 2% at a 95% confidence level for the liq. phase at pressures to 70 MPa and 2% for the vapor phase. In addn., we surveyed literature data and developed a correlation for the viscosity of R245fa. The estd. relative expanded uncertainty (0.95 level of confidence) of this correlation is 3% for the liq. phase at pressures to 40 MPa and 2% for the vapor phase.
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61. 61
  Quiñones-Cisneros, S. E.; Huber, M. L.; Deiters, U. K. Correlation for the viscosity of sulfur hexafluoride (SF6) from the triple point to 1000 K and pressures to 50 MPa. J. Phys. Chem. Ref. Data 2012, 41, 023102-023102-11 DOI: 10.1063/1.3702441
  There is no corresponding record for this reference.
62. 62
  Huber, M. L.; Perkins, R. A.; Laesecke, A.; Friend, D. G.; Sengers, J. V.; Assael, M. J.; Metaxa, I. N.; Vogel, E.; Mareš, R.; Miyagawa, K. New international formulation for the viscosity of H₂O. J. Phys. Chem. Ref. Data 2009, 38, 101– 125, DOI: 10.1063/1.3088050
  62
  New International Formulation for the Viscosity of H2O
  Huber, M. L.; Perkins, R. A.; Laesecke, A.; Friend, D. G.; Sengers, J. V.; Assael, M. J.; Metaxa, I. N.; Vogel, E.; Mares, R.; Miyagawa, K.
  Journal of Physical and Chemical Reference Data (2009), 38 (2), 101-125CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
  The International Assocn. for the Properties of Water and Steam (IAPWS) encouraged an extensive research effort to update the IAPS Formulation 1985 for the Viscosity of Ordinary Water Substance, leading to the adoption of a Release on the IAPWS Formulation 2008 for the Viscosity of Ordinary Water Substance. This manuscript describes the development and evaluation of the 2008 formulation, which provides a correlating equation for the viscosity of water for fluid states up to 1173 K and 1000 MPa with uncertainties from less than 1% to 7% depending on the state point. (c) 2009 American Institute of Physics.
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63. 63
  Avgeri, S.; Assael, M. J.; Huber, M. L.; Perkins, R. A. Reference correlation of the viscosity of benzene from the triple point to 675 K and up to 300 MPa. J. Phys. Chem. Ref. Data 2014, 43, 033103 DOI: 10.1063/1.4892935
  63
  Reference Correlation of the Viscosity of Benzene from the Triple Point to 675 K and up to 300 MPa
  Avgeri, S.; Assael, M. J.; Huber, M. L.; Perkins, R. A.
  Journal of Physical and Chemical Reference Data (2014), 43 (3), 033103/1-033103/13CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
  This paper contains new, representative ref. equations for the viscosity of benzene. 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. The correlation is valid from the triple point (278.647 K) to 675 K, and at pressures up to 300 MPa, with the exception of temps. lower than 350 K where the pressure is restricted to 200 MPa. For the liq. phase, at temps. from 288 to 373 K at pressures up to 80 MPa, we est. the uncertainty (at a 95% confidence level) to be 1.8%, increasing to 3.4% at 200 MPa, and 5% at pressures up to the correlation max. For the liq. at temps. from 373 to 523 K, the uncertainty is 2.7% at pressures from satn. to 50 MPa, rising to 3.6% at 300 MPa. For temps. above 523 K, we est. the uncertainty in the liq. phase to be 5%. The uncertainty for the low-d. fluid phase at temps. from 305 to 640 K and pressures to 0.3 MPa is estd. to be 0.2%. (c) 2014 American Institute of Physics.
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64. 64
  Kestin, J.; Sengers, J. V.; Kamgar-Parsi, B.; Sengers, J. M. H. L. Thermophysical properties of fluid D₂O. J. Phys. Chem. Ref. Data 1984, 13, 601– 609, DOI: 10.1063/1.555714
  64
  Thermophysical properties of fluid heavy water (D2O)
  Kestin, J.; Sengers, J. V.; Kamgar-Parsi, B.; Sengers, J. M. H. Levelt
  Journal of Physical and Chemical Reference Data (1984), 13 (2), 601-9CODEN: JPCRBU; ISSN:0047-2689.
  The present publication contains data on the thermophys. properties of deuterium oxide (heavy water). The properties are represented by equations which can be readily programmed on a computer and incorporated in data banks. All data have been carefully and crit. analyzed. The compendium represents the best available data for fluid D2O.
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65. 65
  Wen, C.; Meng, X.; Huber, M. L.; Wu, J. Measurement and correlation of the viscosity of 1,1,1,2,2,4,5,5,5-nonafluoro-4-(trifluoromethyl)-3-pentanone. J. Chem. Eng. Data 2017, 62, 3603– 3609, DOI: 10.1021/acs.jced.7b00572
  65
  Measurement and Correlation of the Viscosity of 1,1,1,2,2,4,5,5,5-Nonafluoro-4-(trifluoromethyl)-3-pentanone
  Wen, Chenyang; Meng, Xianyang; Huber, Marcia L.; Wu, Jiangtao
  Journal of Chemical & Engineering Data (2017), 62 (10), 3603-3609CODEN: JCEAAX; ISSN:0021-9568. (American Chemical Society)
  The Paris Agreement on climate change, in which many nations have agreed to limit greenhouse gas emissions, has spurred interest in developing working fluids with low global warming potential (GWP) that can satisfy environmental concerns and have thermophys. properties that can meet engineering performance requirements. One such fluid is 1,1,1,2,2,4,5,5,5-nonafluoro-4-(trifluoromethyl)-3-pentanone (also known as Novec-649 and Novec-1230), which has potential applications in org. Rankine cycles (ORC), electronics cooling, computer/data center cooling, and fire extinguishing. In this work, the viscosity measurements of Novec-649 were reported. The measurements were performed over the temp. range of (243 to 373) K and at pressures up to 40 MPa using a vibrating-wire viscometer. The combined expanded uncertainty of the reported viscosity was 2% with a confidence level of 0.95 (k = 2). These exptl. data were used to develop a viscosity correlation that covers a wide temp. and pressure range, with an estd. uncertainty at a 95% confidence level of 2% for the liq. phase from (240 to 400) K at pressures up to 40 MPa.
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66. 66
  Vogel, E.; Herrmann, S. New formulation for the viscosity of propane. J. Phys. Chem. Ref. Data 2016, 45, 043103 DOI: 10.1063/1.4966928
  66
  New Formulation for the Viscosity of Propane
  Vogel, Eckhard; Herrmann, Sebastian
  Journal of Physical and Chemical Reference Data (2016), 45 (4), 043103/1-043103/31CODEN: JPCRBU; ISSN:0047-2689. (American Institute of Physics)
  A review. A new viscosity formulation for propane, using the ref. equation of state for its thermodn. properties by Lemmon et al. [J. Chem. Eng. Data 54, 3141 (2009)] and valid in the fluid region from the triple-point temp. to 650 K and pressures up to 100 MPa, is presented. At the beginning, a zero-d. contribution and one for the crit. enhancement, each based on the exptl. data, were independently generated in parts. The higher-d. contributions are correlated as a function of the reciprocal reduced temp. τ = Tc/T and of the reduced d. δ = ρ/ρc (Tc-crit. temp., ρc-crit. d.). The final formulation includes 17 coeffs. inferred by applying a state-of-the-art linear optimization algorithm. The evaluation and choice of the primary data sets are detailed due to its importance. The viscosity at low pressures p ≤ 0.2 MPa is represented with an expanded uncertainty of 0.5% (coverage factor k = 2) for temps. 273 ≤ T/K ≤ 625. The expanded uncertainty in the vapor phase at subcrit. temps. T ≥ 273 K as well as in the supercrit. thermodn. region T ≤ 423 K at pressures p ≤ 30 MPa is assumed to be 1.5%. In the near-crit. region (1.001 < 1/τ < 1.010 and 0.8 < δ < 1.2), the expanded uncertainty increases with decreasing temp. up to 3.0%. It is further increased to 4.0% in regions of less reliable primary data sets and to 6.0% in ranges in which no primary data are available but the equation of state is valid. Tables of viscosity computed for the new formulation are given in an Appendix for the single-phase region, for the vapor-liq. phase boundary, and for the near-crit. region. (c) 2016 American Institute of Physics.
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67. 67
  Bruno, T. J.; Fortin, T. J.; Huber, M. L.; Laesecke, A.; Lemmon, E. W.; Mansfield, E.; McLinden, M. O.; Outcalt, S. L.; Perkins, R. A.; Urness, K. N.; Widegren, J. A. Thermophysical Properties of Polyol Ester Lubricants , 2019.
  There is no corresponding record for this reference.
68. 68
  Chichester, J. C.; Huber, M. L. Documentation and Assessment of the Transport Property Model for Mixtures Implemented in NIST REFPROP (Version 8.0) , 2008.
  There is no corresponding record for this reference.
69. 69
  Huber, M. L. Models for Viscosity, Thermal Conductivity, and Surface Tension of Selected Pure Fluids as Implemented in REFPROP v10.0 , Techreport Report, 2018.
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  Klein, S.; McLinden, M.; Laesecke, A. An improved extended corresponding states method for estimation of viscosity of pure refrigerants and mixtures. Int. J. Refrig. 1997, 20, 208– 217, DOI: 10.1016/S0140-7007(96)00073-4
  70
  An improved extended corresponding states method for estimation of viscosity of pure refrigerants and mixtures
  Klein, S.A.; Mclinden, M.O.; Laesecke, A.
  International Journal of Refrigeration (1997), 20 (3), 208-217CODEN: IJRFDI; ISSN:0140-7007. (Elsevier)
  The extended corresponding states method for calcg. the viscosity of pure refrigerants and mixts. is investigated. The accuracy of pure fluid viscosity values is significantly improved by introducing a third shape factor evaluated using available pure fluid viscosity data. A modification to the method of Huber and Ely (Fluid Phase Equil., 1992, 80, 45-46) is proposed for estn. of the viscosity of mixts.; this modification eliminates the possibility of discontinuities at the crit. point, ensures that the pure component viscosity is provided in the limit of a component mole fraction approaching 1, and improves the overall accuracy of the method. The method was applied to 12 pure refrigerants including three hydrocarbons and mixts. The av. abs. deviations between the calcd. and exptl. viscosity values are within 4% for all of the pure fluids and most of the mixts. investigated.
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  Yang, X.; Yang, F.; Yang, F. Thermo-economic performance limit analysis of combined heat and power systems for optimal working fluid selections. Energy 2023, 272, 127041 DOI: 10.1016/j.energy.2023.127041
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  Yang, 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, 18736– 18749, DOI: 10.1021/acs.iecr.3c02474
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  Bell, I. H.; Delage-Santacreu, S.; Hoang, H.; Galliero, G. Dynamic crossover in fluids: from hard spheres to molecules. J. Phys. Chem. Lett. 2021, 12, 6411– 6417, DOI: 10.1021/acs.jpclett.1c01594
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  Dynamic Crossover in Fluids: From Hard Spheres to Molecules
  Bell, Ian H.; Delage-Santacreu, Stephanie; Hoang, Hai; Galliero, Guillaume
  Journal of Physical Chemistry Letters (2021), 12 (27), 6411-6417CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
  We propose a simple and generic definition of a demarcation reconciling structural and dynamic frameworks when combined with the entropy scaling framework. This crossover line between gas- and liq.-like behaviors is defined as the curve for which an individual property, the contribution to viscosity due to mols.' translation, is exactly equal to a collective property, the contribution to viscosity due to mol. interactions. Such a definition is shown to be consistent with the one based on the min. of the kinematic viscosity. For the hard sphere, this is shown to be an exact soln. For Lennard-Jones spheres and dimers and for some simple real fluids, this relation holds very well. This crossover line passes nearby the crit. point, and for all studied fluids, it is well captured by the crit. excess entropy curve for at. fluids, emphasizing the link between transport properties and local structure.
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  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, 081703 DOI: 10.1063/5.0164037
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Supporting Information
Supporting Information
The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jced.4c00451.
- main.py (PY): implementation of the core of the RES model; Dilute_gas_viscosity.txt (TXT): parameters for the calculation of the dilute gas viscosity; RES_Parameter.txt (TXT): parameters for the models; Samples_* (TXT): all files beginning with “Samples_” are sample calculations that may be used to verify the model; Data_evaluation_REF_15.txt (TXT): various statistics concerned with the data used for the pure fluid calculations; Data_evaluation_mix.txt (TXT): various statistics concerned with the data used for the mixtures calculations; Table_multi.txt (TXT): information about the experimental data of mixtures; Table_pure_REF_15.txt (TXT): various statistics of the model qualities for the pure fluids; Fluid_Constants.txt (TXT): fluid constants used; pure-fluid data and literature.docx (DOCX): detailed information on pure fluid data and the literature; figure_pure_devs (folder/*PNG): relative deviation for all used data points for the RES model and REFPROP models for all substances; figure_pure_groups (folder/*PNG): η_res⁺ + 1 as a function of $s^{+} / ξ$ for one group each; mix_dev_exp_res_ecs (folder/*PNG): relative deviations for all mixtures for the RES model and the REFPROP models individually, as well as their data sources; mix_s_eta_all_data (folder/*PNG): η_res⁺ + 1 as a function of $s^{+} / ξ$ for each mixture individually for all data, as well as the data sources; mix_s_eta_select_data (folder/*PNG): η_res⁺ + 1 as a function of $s^{+} / ξ$ for each mixtures individually for the filtered data, as well as the data sources; pure_dev_exp_res_ecs (folder/*PNG): relative deviations for all pure fluids for the RES model and the REFPROP models individually, as well as the data sources; pure_s_eta_all_data (folder/*PNG): η_res⁺ + 1 as a function of $s^{+} / ξ$ for each pure fluid individually for all data, as well as the data sources; pure_s_eta_fitted_data (folder/*PNG): η_res⁺ + 1 as a function of $s^{+} / ξ$ for each pure fluid individually for the filtered data, as well as the data sources (ZIP)
- je4c00451_si_001.zip (111.11 MB)
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Entropy Scaling of Viscosity IV─Application to 124 Industrially Important FluidsClick to copy article linkArticle link copied!

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1. Introduction

2. Computational Methods

2.1. Fundamentals

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2.2. Equation Design, Predictions, and Parameter Identification

3. Results and Discussion

3.1. New RES Model

3.2. Details for Pure-Fluid Correlation

3.3. Prediction for Mixtures

4. Conclusions

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Appendix: Fluid Name Glossary

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Entropy Scaling of Viscosity IV─Application to 124 Industrially Important Fluids
Click to copy article linkArticle link copied!