Viscosity and Density of n-Alcohols at Temperatures between (298.15

Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Viscosity and Density of n‑Alcohols at Temperatures between (298.15 and 323.15) K and Pressures up to 30 MPa Alfredo Pimentel-Rodas, Luis A. Galicia-Luna,* and Jose ́ J. Castro-Arellano

J. Chem. Eng. Data Downloaded from pubs.acs.org by IMPERIAL COLLEGE LONDON on 12/08/18. For personal use only.

Laboratorio de Termodinámica, S.E.P.I.-E.S.I.Q.I.E. Instituto Politécnico Nacional, UPALM, Edif. Z, Secc. 6, 1ER piso, Lindavista C.P., Ciudad de México, 07738, México

ABSTRACT: Experimental data of dynamic viscosity (η) and density (ρ) of pure alcohols (1-butanol, 1-pentanol, 1-heptanol, 1-octanol and 1-nonanol) are presented in the temperature range from (293.15 to 323.15) K and pressures up to 30 MPa. The data were obtained simultaneously, a capillary tube viscometer was used to measure the dynamic viscosity coupled with a vibrating tube densimeter where density is obtained. The expanded uncertainties (k = 2) of the reported data were estimated considering the impurities of the samples and are 0.90% and 0.10% for the dynamic viscosity and density measurements, respectively. Also, the dynamic viscosity and density data obtained in this study were modeled successfully as a function of pressure and temperature, through empirical equations previously published in literature. Finally, isothermal compressibilities and thermal isobaric expansivities were obtained using the density data set obtained. out,7,8,22−29 without considering the conditions to which viscosity data are available. Several experimental methods have been proposed for measuring the viscosity and density of liquids at high pressures, in which the capillary flow technique and vibrating tube densimetry stand out. Owing to the lack of high-pressure viscosity and density data of alcohols, an extensive experimental study has been initiated. Recently,21,30 we have reported the experimental viscosity and density data as well as excess thermodynamic properties of pure liquids (alkanes and some alcohols) in a wide range of temperature and pressure. Continuing our analysis, we now report simultaneous measurements of viscosity and density of 1butanol, 1-pentanol, 1-heptanol, 1-octanol and 1-nonanol at temperatures from (293.15 to 323.15) K and pressures up to 30 MPa. The experimental uncertainty was estimated using the NIST technical note and considering the impurities of the compounds.31−38 The expanded relative uncertainty is 0.90% and 0.10% for viscosity and density, respectively.

1. INTRODUCTION Viscosity is an important property for different applications in chemical engineering especially where the movement of the fluids controls the process.1−3 Also, density, one of the most relevant properties in the industry, is required to develop and test equations of state, and especially in mass and moment balances.4−6 In particular, dynamic viscosity and the density data of alcohols are of great importance in many industrial applications, such as cryogenic power generation systems, additives to gasoline, solvent in paints or pharmaceuticals, or even the determination of fundamental properties such as the coefficient of isothermal compressibility and the coefficient of isobaric thermal expansion.7,8 Accurate knowledge of these properties is required to ensure a better understanding and design of technical processes. However, reliable experimental data of liquid viscosities of alcohols under high pressures are quite limited, especially if it involves simultaneous measurements of density.9−12 Among the lack of information on the viscosity data of alcohols at high pressures available in the literature, mainly ethanol, 1-propanol, 1-butanol, and 1-hexanol have been studied.9,11,13−19 Experimental viscosity determinations of 1-pentanol, 1-heptanol, 1octanol, and 1-nonanol have been less commonly performed,11,14,20,21 although, experimental determinations of density of alcohols at high pressure have been widely carried © XXXX American Chemical Society

Received: September 11, 2018 Accepted: November 22, 2018

A

DOI: 10.1021/acs.jced.8b00812 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

where ρF(P, T) is the density of the fluid in study, ρH2O(P,T) and ρN2(P, T) are the densities of water and nitrogen, respectively (calculated using the equations of state developed by Wagner and Pruβ,40 and Span et al.,41 respectively), τF (P, T) is the vibration period for each fluid in study at the same conditions of temperature and pressure within experimental uncertainty. In our previous work,21 the development for the estimation of the combined uncertainty in density was shown as a function of water and nitrogen periods, water and nitrogen densities, and the studied fluid period. Also, the effect of the impurities of the samples on the experimental uncertainty was considered according to the literature.32−34 For details about the procedure and equations used the reader is referred to the previous work.21 For density measurements, the estimated relative expanded uncertainty is 0.10%, considering the effect of the impurities of the samples. Viscosity Measurements. Viscosity experimental measurements were performed using a capillary tube viscometer. The length and diameter of the capillary tube are 12.50 × 10−1 m (standard uncertainty of 1 × 10−5 m) and 2.518 × 10−4 m (standard uncertainty of 9 × 10−8 m), respectively. As in the DTV, the temperature in the capillary tube is regulated by a thermostatic bath with a stability of 0.005 K and monitored by a platinum resistance probe, which measures the temperature with a combined uncertainty of 0.008 K. The pressure is recorded with two pressure transducers located in both ends of the capillary tube, which allows the measurement of pressure drop and system pressure with a combined uncertainty of 0.002 MPa. The flow rate across the capillary is regulated by a syringe pump with an uncertainty of 1 × 10−4 cm−3·min. Experimental viscosity data were obtained according to the following equation:

2. EXPERIMENTAL SECTION Materials. Nitrogen (99.995% in mass fraction) is from Infra México. Water (99.95% in mass fraction), 1-butanol (99.8% in mass fraction), 1-pentanol (99.6% in mass fraction), 1-heptanol (98.9% in mass fraction), 1-octanol (99.7% in mass fraction) and 1-nonanol (98.6% in mass fraction) are from Sigma-Aldrich. The purity of each sample were taken from the certificate of analysis provided by the supplier (checked by GC). All liquid substances are carefully degassed by agitation under vacuum prior to injection into the system and were used as received from the manufacturer. The water content for all alcohols was determining using a Karl Fischer coulometer (Metrohm, 831) and the results are 1-butanol, 5.03 × 10−4 mass fraction; 1pentanol, 5.12 × 10−4 mass fraction; 1-heptanol, 6.02 × 10−4 mass fraction; 1-octanol, 5.11 × 10−4 mass fraction; and 1nonanol, 6.06 × 10−4 mass fraction. The standard uncertainty of content of water is 0.40 × 10−4 mass fraction. Table 1 shows the name of the substance used, source, CAS number, and purity in mass fraction. Table 1. Chemical Information compound N2 water 1-butanol 1-pentanol 1-hexanol 1-heptanol 1-octanol 1-nonanol

source

CASRN

Infra Air Products Sigma-Aldrich Sigma-Aldrich Sigma-Aldrich Sigma-Aldrich Sigma-Aldrich Sigma-Aldrich Sigma-Aldrich

7732-18-5 71-36-3 71-41-0 111-27-3 111-70-6 111-87-5 143-08-8

mass fraction puritya

purification method

0.99995

none

0.9995 0.998 0.996 0.997 0.989 0.997 0.986

none none none none none none none

a

Analysis method: gas chromatography.

η=

ρF (P , T ) = ρH O (P , T ) 2

+

T ) − τH22O(P , T )][ρH O (P , T ) − ρN (P , T )] 2

(2)

where m and n are constants and their values are 1.12 ± 0.06 and 0.69 ± 0.04, according to Kestin et al.42 for Reynolds numbers of 50 or less (in this work the Reynolds numbers were less than 30), L and a are the length and radius of the capillary tube, respectively, and ρ is the density of the fluid obtained experimentally by VTD. The combined uncertainty was estimated according to NIST Technical Note 1297.31 In our previous work,21 we analyzed and showed that the combined uncertainty for the viscosity is a function of the pressure drop through the tube, the density of the fluid under study and the internal radius of the capillary tube, as well the impurities of the sample.33−38 For details about the procedure and equations used the reader is referred to the previous work.21 The estimated relative expanded uncertainty in the viscosity measurements are 0.90%, considering the effect of the impurities of the samples. The system variables (P, T, ΔP, ρF, Q) described above are visualized and recorded by an electronic acquisition data, which allows obtaining the statistics of the variables involved in the measurement. The measurements that are carried out with the equipment previously described are performed simultaneously. The complete instrument, as well as its operation and description of each of its parts, has been discussed and presented in previous works.21,30

Density Measurements. Experimental density measurements were performed using a vibrating tube densimeter (DMA HPM, mPDS 2000 with CPU and transducer board, Anton Paar). This instrument is located at the end of the capillary tube and has appeared and was discussed previously.21,30 The vibrating tube densimeter (VTD) contains a platinum resistance probe calibrated in this work with an Automatic System Laboratories F300 using a 25 Ω reference probe (Rosemount 162CE). The temperature inside the VTD is regulated by a thermostatic bath with a stability of 0.005 K. The temperature measurement was carried out with an estimated combined uncertainty of 0.008 K. Also, a pressure transducer calibrated against a dead-weight balance (Desgranges & Huot, model 5304), which measures the pressure inside the equipment, is located in the VTD supply. The combined uncertainty for the pressure measurement was estimated to be 0.002 MPa. The densimeter was calibrated using the method described by Galicia-Luna et al.39 with water HPLC grade and N2 as fluids of reference. Experimental density data were obtained according to the following equation:

[τF2(P ,

mρ Q πa 4ΔP − 8Q (L + na) 8π (L + na)

3. RESULTS AND DISCUSSION Before carrying out the experimental measurements of the fluids under study, the methods used were validated through the

2

τH22O(P , T ) − τN22(P , T ) (1) B



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Figure 1. Relative deviations of the measured viscosity of water from the model of Huber et al.43 (■) T = 298.15 K; (●) T = 303.15 K; (▲) T = 313.15 K; (▼) T = 323.15 K.

Figure 2. Relative deviations of the measured density of water from the model of Wagner and Pruβ.40 (■) T = 298.15 K; (●) T = 303.15 K; (▲) T = 313.15 K; (▼) T = 323.15 K.

these results, the methods used in the simultaneous determination of density and viscosity were validated. On the other hand, the viscosities and densities of 1-butanol were determined at four temperatures (298.15 K, 303.15 K, 313.15 K, and 323.15) and pressures up to 30 MPa. Figures 3 and 4 show the experimental data of viscosity and density, respectively, with those in the literature.16,18,19,22,25 As can be observed, the behavior of the viscosity and density data obtained in this work are similar to those reported in the literature. The experimental data of dynamic viscosity and density of 1-butanol are shown in Table 2. Simultaneous Measurements of Viscosity and Density. We have measured the densities and viscosities of 1alcohols (1-pentanol, 1-heptanol, 1-octanol and 1-nonanol) at temperatures between (298.15 and 323.15) K and up to 30 MPa. Experimental data of 1-pentanol and 1-heptanol have been measured previously (298.15 and 323.15 K and up to 25 MPa)

experimental determination of viscosity and density of a compound widely studied in the literature, in order to compare the results. Because water is considered a standard in viscosity and density, experimental measurements of viscosity and density of this fluid were carried out at four temperatures (298.15, 303.15, 313.15, and 323.15 K) and pressures up to 30 MPa. The data obtained were compared against calculated values of the viscosity and density resulting from the equations of Huber et al.43 (relative expanded uncertainty of 1%) and Wagner and Pruβ (relative standard uncertainty between 0.001% and 0.003%),40 respectively. Hence, Figures 1 and 2 show the deviations obtained between the measured data and the aforementioned equations for viscosity and density, respectively. Our experimental viscosities and densities agree with the literature viscosity and density values within a maximum deviation less than ±0.4% and ±0.03%, respectively. With C



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Figure 3. Experimental viscosity data of 1-butanol as a function of temperature and pressure compared with literature data. (■) This work at T = 298.15 K; (×) Assael and Polimatidou at T = 298.15 K;16 (□) Papaioannou et al. at T = 298.15 K;18 (+) Zambrano et al. at T = 298.15 K;19 (●) This work at T = 303.15 K; (▲) This work at T = 313.16 K; (△) Zambrano et al. at T = 313.15 K;19 (▼) This work at T = 323.14 K; (▽) Assael and Polimatidou at T = 323.15 K;16 (◇) Zambrano et al. at T = 323.15 K;19 () solid lines represent the model used.

Figure 4. Experimental density data of 1-butanol as a function of temperature and pressure compared with literature data. (■) This work at T = 298.15 K; (×) Assael and Polimatidou at T = 298.15 K;16 (□) Papaioannou et al. at T = 298.15 K;18 (●) This work at T = 303.15 K; (○) Alaoui et al. at T = 303.15 K;22 (▲) This work at T = 313.16 K; (△) Alaoui et al. at T = 313.15 K;22 (◇) Zúñiga-Moreno et al. at T = 313.10 K;25 (▼) This work at T = 323.14 K; (▽) Alaoui et al. at T = 323.15 K;22 (⧫) Assael and Polimatidou at T = 323.15 K;16 (+) Zuñiga-Moreno et al. at T = 323.08 K;25 () solid lines represent the model used.

According to the expected, for all the measured fluids, the dynamic viscosity and density increase when the pressure of the system increases (at fixed temperature), showing a directly proportional behavior. On the contrary, at constant pressure,

by this research group;21 however, these data were not included in this work. Moreover, the new experimental data were compared against the previously measured data, resulting in a maximum deviation of less than 0.7%. D



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while the temperature increases the viscosity and density decreases. Also, it can be seen that as the number of carbons increases, the difference in viscosity between the minimum and maximum pressure increases, which results in the linear behavior at high pressures disappearing for alcohols of higher molecular weight, which confirms the importance of the experimental data. Figure 5 shows the dynamic viscosity data of 1-nonanol obtained in this work as a function of temperature and pressure. As expected, the viscosity data of this compound are higher than any other compound measured here (the highest is 12513 μPa· s) at the same temperature and pressure conditions within the experimental uncertainty. In addition, the density behavior of 1nonanol is shown in Figure 6, as a function of temperature and pressure. Like the behavior in viscosity, the data of greater density are those of this compound (the highest is 841.1 kg·m−3) with respect to the other fluids measured here under the same conditions within the experimental uncertainty. The data of dynamic viscosity and density at high pressures obtained in this work for 1-pentanol, 1-heptanol, 1-octanol, and 1-nonanol are shown in Tables 3 to 6, respectively. To know the behavior of the viscosity with respect to the increase in the number of carbons, the experimental data at 298.15 K of 1-butanol, 1-pentanol, 1-heptanol, 1-octanol, and 1nonanol are shown in Figure 7. To have a longer observation range, the pressure was increased up to 60 MPa using an empirical equation which is described later. As can be seen, as the number of carbons increases, the difference between the value of the viscosity at low and high pressure increases significantly. This effect can be explained if the behavior of the viscosity at high pressures showed exponential curvature, as demonstrated by Matsuo and Makita in their experimental measurements up to 200 MPa.11 However, this effect is not demonstrated in this work due to the limitations of the experimental equipment, but experimental viscosity measurements at pressures greater than those presented here are necessary to demonstrate this effect. Viscosity Modeling. Recently in our previous research,30 we developed the Pimentel-Galicia equation in order to correlate the dynamic viscosity of pure nonpolar liquids (alkanes) as a function of temperature and pressure within the experimental uncertainty. Due to the good results that this model shows for these fluids and with the objective of knowing the viability of the correlation for polar substances (alcohols) we decided to use it, hence the viscosity data obtained in this work are represented as follows:

Table 2. Experimental Data of Dynamic Viscosity (ηexp) and Density (ρexp), and Calculated Data of Isothermal Compressibility (KT) and Isobaric Thermal Expansivity (αP) at Temperature (T) and Pressure (P) of 1-Butanola T

P

ρexp −3

ηexp

KT·104 −1

K

MPa

kg·m

μPa·s

MPa

298.12 298.12 298.12 298.12 298.12 298.13 298.12 298.12 298.12 298.12 298.12 298.12 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.16 303.15 303.15 303.15 303.15 313.16 313.16 313.16 313.16 313.15 313.15 313.16 313.16 313.15 313.15 313.16 313.16 323.14 323.14 323.14 323.14 323.14 323.14 323.14 323.14 323.14 323.14 323.14 323.14

2.01 3.91 6.02 8.03 9.91 13.01 16.02 19.03 22.00 25.02 28.00 30.01 2.01 4.00 5.98 8.01 9.99 12.99 15.99 19.00 22.01 25.01 27.97 29.99 1.99 3.98 5.99 7.98 10.02 12.98 15.98 19.01 22.02 25.01 27.99 29.99 2.00 3.92 6.03 8.00 10.02 13.04 16.05 19.00 21.99 24.97 28.00 29.97

806.8 808.2 809.8 811.2 812.5 814.6 816.6 818.5 820.4 822.3 824.0 825.1 803.3 804.8 806.3 807.8 809.2 811.3 813.3 815.3 817.3 819.1 820.9 822.1 795.5 797.1 798.7 800.2 801.8 803.9 806.1 808.2 810.2 812.2 814.1 815.3 787.9 789.6 791.3 792.9 794.5 796.9 799.2 801.3 803.4 805.5 807.5 808.8

2608.0 2657.3 2707.7 2752.2 2796.7 2866.5 2940.4 3018.4 3092.2 3166.0 3236.6 3287.1 2351.0 2393.4 2435.9 2479.4 2521.8 2585.9 2650.2 2714.5 2779.2 2843.3 2911.6 2957.0 1831.9 1868.2 1901.7 1935.0 1969.3 2018.7 2072.8 2125.4 2181.8 2236.9 2291.6 2329.1 1420.5 1445.8 1473.4 1499.0 1525.1 1564.5 1603.4 1646.0 1684.4 1722.9 1759.4 1784.9

9.37 9.16 8.94 8.73 8.55 8.26 7.99 7.73 7.49 7.26 7.04 6.90 9.66 9.44 9.22 9.01 8.81 8.52 8.24 7.98 7.72 7.48 7.26 7.11 10.27 10.03 9.80 9.58 9.36 9.05 8.75 8.47 8.20 7.95 7.70 7.55 10.90 10.65 10.39 10.16 9.92 9.59 9.27 8.98 8.70 8.42 8.16 8.00

αP·104 K−1 9.13 9.02 8.91 8.80 8.70 8.54 8.38 8.24 8.10 7.97 7.84 7.75 9.29 9.18 9.06 8.95 8.84 8.68 8.53 8.38 8.24 8.10 7.97 7.88 9.57 9.45 9.33 9.21 9.10 8.94 8.78 8.62 8.47 8.33 8.19 8.10 9.81 9.69 9.56 9.44 9.32 9.15 8.98 8.83 8.67 8.53 8.38 8.29

ηcal =

a1 + a 2P a3 − a4T + a5T 3 + P

(3)

where ηcal is the calculated data for viscosity in μPa·s, T and P are the temperature (in K) and pressure (in MPa) of the system, respectively, and a1 to a5 are fixed coefficients. This equation was found to give a good representation of the present viscosity data. Figure 8 shows the percentage deviation between the calculated data (empirical model) and the viscosity data obtained from 1butanol. Table 7 presents the coefficients for eq 3 for all the measured compounds together with the average absolute percentage deviation (AAPD),

a Combined uncertainties uc are uc(P) = 0.002 MPa, uc(T) = 0.008 K; relative combined uncertainty for isothermal compressibility, urc(KT) = 0.014 and for isobaric thermal expansivity urc(αP) = 0.008; the relative combined expanded uncertainty with a 0.95 level of confidence (k = 2) for the density, Urc(ρexp) = 0.001 and for dynamic viscosity, Urc(ηexp) = 0.009.

E



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Figure 5. Experimental viscosity data of 1-nonanol at high pressures: (■) T = 298.15 K; (●) T = 303.15 K; (▲) T = 313.15 K; (▼) T = 323.15 K; () solid lines represent the correlation used.

Figure 6. Experimental density data of 1-nonanol at high pressures: (■) T = 298.15 K; (●) T = 303.15 K; (▲) T = 313.15 K; (▼) T = 323.15 K; () solid lines represent the correlation used. N

100 ∑i = 1 AAPD =

ÄÅ ÅÅ ηexp − ηcal Å MAPD = maxÅÅÅÅ100 ÅÅ ηexp ÅÅÇ

ηexp − ηcal ηexp

N

(4)

ÉÑ ÑÑ ÑÑ ÑÑ ÑÑ ÑÑ ÑÖ

(5)

Density Representation. The experimental density data were successfully modeled using an empirical model (similar to the one used in the previous work)30 as follows:

and the maximum absolute percentage deviation (MAPD), F



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Table 3. Experimental Data of Dynamic Viscosity (ηexp) and Density (ρexp), and Calculated Data of Isothermal Compressibility (KT) and Isobaric Thermal Expansivity (αP) at Temperature (T) and Pressure (P) of 1-Pentanola T

P

ρexp −3

ηexp

KT·104 −1

K

MPa

kg·m

μPa·s

MPa

298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 303.16 303.16 303.16 303.16 303.16 303.16 303.16 303.15 303.16 303.16 303.15 303.16 313.15 313.15 313.15 313.15 313.15 313.15 313.16 313.15 313.15 313.16 313.16 313.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15

2.00 4.00 6.00 8.01 10.00 13.00 16.00 19.01 22.00 25.00 27.99 29.98 1.98 3.98 6.01 8.02 10.03 12.99 15.98 19.00 22.01 25.00 27.98 29.99 1.99 4.00 5.98 7.98 10.02 13.01 15.98 19.02 21.98 24.99 28.00 30.02 2.00 4.00 6.00 8.00 10.00 13.00 16.00 19.00 22.00 25.00 27.99 29.99

813.0 814.4 815.8 817.1 818.5 820.4 822.3 824.1 825.9 827.6 829.4 830.4 808.8 810.2 811.7 813.0 814.4 816.4 818.4 820.3 822.1 823.9 825.6 826.7 800.6 802.2 803.7 805.1 806.6 808.7 810.8 812.8 814.7 816.6 818.4 819.6 793.5 795.0 796.7 798.2 799.6 801.9 804.0 806.1 808.2 810.2 812.1 813.4

3590.1 3659.9 3732.5 3796.1 3869.5 3975.3 4081.1 4192.0 4298.8 4408.7 4506.6 4576.6 3218.7 3282.0 3346.3 3409.7 3473.5 3566.8 3661.7 3757.3 3852.1 3946.8 4041.1 4104.6 2437.6 2485.5 2532.9 2580.9 2629.5 2701.2 2772.1 2845.0 2915.7 2987.7 3059.8 3108.5 1832.9 1866.0 1900.8 1935.1 1969.3 2022.5 2077.9 2133.1 2189.2 2244.4 2299.1 2335.1

8.75 8.56 8.38 8.20 8.03 7.79 7.55 7.33 7.11 6.91 6.71 6.59 9.06 8.87 8.68 8.49 8.32 8.06 7.82 7.59 7.36 7.15 6.95 6.82 9.65 9.44 9.24 9.05 8.86 8.58 8.32 8.07 7.84 7.61 7.39 7.25 10.20 9.98 9.76 9.56 9.35 9.06 8.79 8.52 8.27 8.03 7.80 7.65

Table 4. Experimental Data of Dynamic Viscosity (ηexp) and Density (ρexp), and Calculated Data of Isothermal Compressibility (KT) and Isobaric Thermal Expansivity (αP) at Temperature (T) and Pressure (P) of 1-Heptanola

αP·104 K

T

−1

10.88 10.75 10.63 10.51 10.39 10.22 10.05 9.89 9.73 9.58 9.43 9.34 10.40 10.28 10.16 10.04 9.93 9.76 9.60 9.45 9.30 9.15 9.01 8.92 9.51 9.39 9.28 9.18 9.07 8.92 8.77 8.63 8.49 8.36 8.23 8.14 8.69 8.59 8.49 8.39 8.29 8.15 8.01 7.88 7.76 7.63 7.51 7.44


P

ρexp −3

ηexp

K

MPa

kg·m

μPa·s

298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 303.16 303.16 303.16 303.16 303.16 303.16 303.16 303.16 303.16 303.16 303.16 303.16 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15

2.00 4.02 6.01 8.00 10.00 13.00 16.00 19.00 22.00 25.00 28.00 29.99 2.03 4.03 6.04 7.98 9.99 12.99 16.02 19.02 22.00 24.98 27.98 30.01 2.00 4.00 5.98 7.98 9.97 13.03 16.02 19.00 22.02 25.01 27.98 30.01 1.99 4.01 5.99 8.01 10.01 13.00 16.00 18.99 22.00 25.00 28.00 30.00

820.2 821.4 822.8 824.0 825.3 827.1 828.9 830.7 832.5 834.2 835.9 836.9 816.5 817.9 819.3 820.5 821.8 823.6 825.5 827.3 829.2 830.9 832.5 833.7 809.2 810.6 811.9 813.3 814.6 816.5 818.4 820.4 822.2 824.0 825.7 826.9 802.1 803.4 804.8 806.2 807.6 809.7 811.8 813.7 815.6 817.4 819.3 820.5

5971.2 6099.6 6229.5 6363.7 6484.2 6686.1 6880.6 7084.5 7293.0 7516.5 7720.4 7864.1 5185.6 5302.4 5420.2 5533.8 5650.9 5826.1 6003.8 6179.0 6352.9 6526.8 6702.7 6821.6 3762.9 3847.6 3932.0 4016.8 4100.9 4230.7 4357.6 4484.2 4612.6 4739.4 4865.1 4951.5 2748.5 2812.4 2875.9 2940.0 2997.4 3087.7 3178.8 3266.5 3358.0 3451.3 3542.5 3607.1

KT·104 −1

MPa

8.05 7.92 7.80 7.68 7.56 7.39 7.23 7.07 6.91 6.76 6.62 6.53 8.24 8.11 7.99 7.87 7.75 7.57 7.40 7.24 7.08 6.93 6.78 6.68 8.64 8.50 8.37 8.24 8.12 7.93 7.75 7.58 7.41 7.25 7.10 6.99 9.04 8.89 8.75 8.62 8.48 8.29 8.10 7.92 7.75 7.58 7.41 7.31

αP·104 K−1 9.04 8.96 8.88 8.81 8.73 8.62 8.52 8.41 8.31 8.21 8.12 8.06 9.01 8.93 8.85 8.78 8.71 8.60 8.49 8.39 8.29 8.19 8.09 8.03 8.95 8.87 8.80 8.72 8.65 8.54 8.43 8.33 8.22 8.13 8.03 7.97 8.89 8.81 8.73 8.65 8.58 8.47 8.36 8.26 8.16 8.06 7.96 7.90


G



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Table 5. Experimental Data of Dynamic Viscosity (ηexp) and Density (ρexp), and Calculated Data of Isothermal Compressibility (KT) and Isobaric Thermal Expansivity (αP) at Temperature (T) and Pressure (P) of 1-Octanola T

P

ρexp −3

ηexp

K

MPa

kg·m

μPa·s

298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 303.15 303.15 303.15 303.16 303.15 303.16 303.15 303.15 303.16 303.15 303.16 303.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15

2.00 4.01 6.00 8.00 10.00 13.01 16.01 18.99 22.01 25.01 28.01 30.01 1.99 3.99 5.98 7.98 10.01 13.00 16.02 19.03 22.01 25.00 28.00 29.98 1.97 4.00 6.01 8.00 10.01 13.03 15.98 18.99 21.99 25.00 27.98 29.99 6.01 8.00 10.01 13.02 16.02 19.01 22.00 25.01 28.01 30.02

823.6 824.8 826.0 827.2 828.4 830.1 831.8 833.4 835.0 836.6 838.3 839.3 819.4 820.6 821.9 823.1 824.4 826.2 827.9 829.7 831.3 833.0 834.6 835.6 812.3 813.6 815.0 816.3 817.5 819.4 821.2 823.0 824.8 826.5 828.2 829.3 808.4 809.7 811.1 813.0 814.9 816.8 818.6 820.4 822.1 823.3

7363.2 7541.9 7701.6 7864.6 8031.1 8299.5 8568.1 8825.1 9111.8 9397.5 9667.6 9865.9 6327.5 6480.6 6632.3 6785.0 6941.0 7168.6 7400.4 7630.3 7857.9 8087.5 8316.0 8468.0 4516.4 4627.4 4737.3 4845.6 4955.3 5120.4 5281.5 5445.6 5609.7 5773.9 5937.0 6046.6 3427.2 3499.4 3572.6 3688.4 3796.6 3910.1 4030.1 4148.5 4264.4 4343.4

KT·104 MPa

−1

7.64 7.51 7.38 7.25 7.12 6.94 6.76 6.60 6.43 6.28 6.12 6.03 7.88 7.74 7.60 7.47 7.34 7.15 6.97 6.79 6.63 6.46 6.31 6.21 8.32 8.17 8.02 7.88 7.74 7.54 7.35 7.17 6.99 6.82 6.66 6.55 8.41 8.26 8.12 7.91 7.71 7.51 7.33 7.15 6.97 6.86

Table 6. Experimental Data of Dynamic Viscosity (ηexp) and Density (ρexp), and Calculated Data of Isothermal Compressibility (KT) and Isobaric Thermal Expansivity (αP) at Temperature (T) and Pressure (P) of 1-Nonanola

αP·104

T

−1

K

9.78 9.68 9.59 9.50 9.41 9.28 9.15 9.03 8.90 8.79 8.67 8.60 9.34 9.24 9.16 9.07 8.98 8.86 8.73 8.61 8.50 8.39 8.28 8.21 8.52 8.43 8.35 8.27 8.19 8.07 7.96 7.85 7.75 7.64 7.54 7.48 7.62 7.54 7.47 7.36 7.26 7.16 7.06 6.97 6.88 6.82


P

ρexp −3

K

MPa

kg·m

298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.14 303.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15

1.99 3.99 6.00 8.01 10.01 13.00 16.00 19.01 21.99 25.00 28.02 30.02 2.01 4.01 6.02 8.03 9.99 12.98 15.97 19.02 22.01 25.00 27.98 30.00 2.00 3.97 6.02 7.99 10.02 13.00 16.00 18.98 22.00 25.00 28.01 29.99 2.01 4.02 6.02 8.01 10.01 13.01 16.01 19.00 22.01 25.00 28.00 30.00

825.5 826.7 828.0 829.2 830.5 832.2 833.9 835.5 837.1 838.7 840.2 841.1 822.0 823.2 824.5 825.7 826.9 828.7 830.4 832.1 833.8 835.4 836.9 837.9 814.9 816.3 817.6 818.9 820.2 822.0 823.8 825.6 827.3 829.0 830.6 831.7 808.3 809.7 811.0 812.3 813.7 815.7 817.5 819.3 821.1 822.9 824.6 825.7

ηexp μPa·s 9284.8 9510.7 9746.4 9958.1 10174 10505 10846 11197 11557 11928 12279 12513 8424.3 8632.6 8842.7 9052.6 9256.8 9568.2 9879.8 10199 10510 10822 11134 11343 6381.0 6536.4 6698.8 6854.2 7014.9 7250.1 7486.7 7722.8 7961.1 8197.9 8436.1 8592.1 4745.1 4858.8 4976.3 5089.5 5202.4 5376.2 5539.1 5716.0 5892.2 6069.5 6247.2 6372.7

KT·104 −1

MPa

7.58 7.44 7.30 7.17 7.03 6.84 6.66 6.48 6.32 6.15 6.00 5.89 7.81 7.66 7.52 7.38 7.24 7.05 6.86 6.68 6.50 6.33 6.17 6.07 8.26 8.10 7.95 7.80 7.65 7.45 7.25 7.05 6.87 6.69 6.52 6.41 8.69 8.53 8.36 8.21 8.06 7.83 7.62 7.42 7.22 7.04 6.86 6.74

αP·104 K−1 8.86 8.77 8.68 8.59 8.51 8.38 8.26 8.15 8.03 7.92 7.81 7.74 8.71 8.62 8.53 8.44 8.36 8.24 8.12 8.00 7.89 7.78 7.67 7.60 8.41 8.32 8.24 8.15 8.07 7.95 7.83 7.72 7.61 7.50 7.40 7.33 8.13 8.04 7.96 7.88 7.80 7.68 7.57 7.46 7.35 7.25 7.15 7.08


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Figure 7. Experimental viscosity data at 298.15 K: (■) 1-butanol; (●) 1-pentanol; (▲) 1-heptanol; (▼) 1-octanol; (⧫) 1-nonanol; () solid lines represent the correlation used.

Figure 8. Deviations of experimental dynamic viscosity data of 1-butanol from the correlation used. (■) T = 298.15 K; (●) T = 303.15 K; (▲) T = 313.16 K; (▼) T = 323.15 K.

Table 7. Parameters of eq 3 for the Representation of Dynamic Viscosity Data fluid

a1/Pa2·s

1-butanol 1-pentanol 1-heptanol 1-octanol 1-nonanol

2064610 × 10 2.597487 × 109 6135.543 × 109 6923.858 × 109 8569.540 × 109

a2/μPa·s 9

a3/MPa

19602300 × 10 25.98973 × 106 70207.97 × 106 85099.62 × 106 108379.4 × 106

6

22256.5 × 10 0.026808 × 109 41.36561 × 109 41.35930 × 109 42.34456 × 109 9

b3 −

(

b4 T

+

b5 T1/2

)+P

a5/MPa·K−3

AAPD

MAPD

115763 × 10 0.138782 × 106 216.9288 × 106 217.0101 × 106 216.5141 × 106

492992 0.577523 919.2167 917.0972 873.6344

0.20 0.25 0.24 0.22 0.30

0.50 0.39 0.49 0.49 0.49

6

where v is the specific volume in m3·kg−1, P is the pressure of the system in MPa, T is the temperature of the system in K, and bi is the parameters fitted to experimental density data. The average absolute percentage deviation between the model used and the

b1 + b2P

v=

a4/MPa·K−1

(6)

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Article

Figure 9. Deviations of experimental density data of 1-butanol from the correlation used. (■) T = 298.15 K; (●) T = 303.15 K; (▲) T = 313.16 K; (▼) T = 323.15 K.

Table 8. Parameters of eq 6 for the Representation of Density Data of Alcohols fluid

b1/m3·kg−1 · MPa

b2/ m3·kg−1

b3/MPa

b4/MPa·K

b5/MPa·K1/2

AAPD

MAPD

1-butanol 1-pentanol 1-heptanol 1-octanol 1-nonanol

0.1922678 0.2067507 0.2782213 0.2462483 0.2321572

0.001057335 0.001047324 0.000993734 0.001024639 0.001033666

−127.4670 225.7768 −28.4341 267.5774 72.7878

58688.63 −50135.09 39475.73 −54946.97 4878.668

−8273.359 3904.718 −6710.935 4306.679 −2330.045

0.01 0.005 0.006 0.009 0.002

0.018 0.013 0.020 0.016 0.011

Figure 10. Isothermal compressibility (KT) of 1-nonanol over a wide range of pressures: (■) T = 298.15 K; (●) T = 303.15 K; (▲) T = 313.15 K; (▼) T = 323.15 K.

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Figure 11. Isobaric thermal expansivity (αP) of 1-nonanol over a wide range of pressures: (■) T = 298.15 K; (●) T = 303.15 K; (▲) T = 313.15 K; (▼) T = 323.15 K. b4

experimental data obtained for 1-butanol is shown in Figure 9. As can be seen, the deviation of the model from the experimental data is very small, average deviation is 0.01%, and the maximum absolute percentage deviation is 0.018%. The values of the fitted parameters of eq 6 are shown in Table 8 together with the AAPD and MAPD. As can be seen, the results obtained from the modeling of the alcohol density data are in good agreement with the experimental data. Derived Properties. From the experimental densities (ρ) values at different temperatures and pressures, we can also

(

1 ∂ρ ρ ∂P T

1 b3 −

b4 T

−

b5 T1/2

− +P

b2 b1 + b2P

−

b5 2T 3/2 b5 T1/2

+P

(8)

■

isothermal compressibility describe the effect of the pressure on the density at constant temperature and is calculated below (according with the density model used): KT =

+

Figure 11 shows the behavior of the isobaric thermal expansivity coefficient from the data of 1-nonanol. As can be observed, the behavior that was obtained for this fluid, as well as for the others studied in this work, is similar to that presented with the isothermal compressibility coefficient. For both derived properties, the uncertainty estimation was performed using the equations and procedure described in detail by Pimentel-Rodas et al.30 The relative combined uncertainty for isothermal compressibility, urc(KT), was estimated to be 0.014 and for isobaric thermal expansivity, urc(αP), was 0.008. The calculated values of isothermal compressibility and isobaric thermal expansivity coefficients are listed in Tables 2−6.

( ) ) and 1 ∂ρ expansivity (αP = − ρ ( ∂T ) ). The P

determine the isothermal compressibility KT = the isobaric thermal

αP =

T2 − b b3 − T4

CONCLUSIONS New experimental data of dynamic viscosity and density for 1butanol, 1-pentanol, 1-heptanol, 1-octanol, and 1-nonanol are presented at temperatures between (298.15 to 323.15) K and up to 30 MPa, using the capillary flow technique. The viability of the method used was validated determining simultaneously the dynamic viscosity and density of water and performed a comparison to the literature data. The experimental relative expanded uncertainty was estimated considering the purity of the samples used, obtaining 0.90% and 0.10% for dynamic viscosity and density, respectively. According to the results obtained in this work, the difference between the viscosity value at low and high pressure is higher in nonanol than in any other alcohol measured here, which means that as the number of carbons increases (higher molecular weight) the viscosity value increases significantly as the system pressure increases. From the results obtained in the modeling of viscosity and density data (MAPDη = 0.50 and MAPDρ = 0.020), it is shown

(7)

The behavior of isothermal compressibility from the data obtained for 1-nonanol is shown in Figure 10. As it is observed, the behavior for these fluids, as well as for the others studied in this work, is inversely proportional to the pressure increment, which means that, the coefficient of isothermal compressibility decreases while the pressure of the system increases (at fixed temperature). On the other hand, the isothermal compressibility coefficient increases when the system temperature increases (at fixed pressure). The isobaric thermal expansivity describes the effect of the temperature on the density at constant pressure and is defined as follows (according to the density model used): K



Article

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that both models used are valid to represent the thermophysical properties (η, ρ) of alcohols. Also, considering the results obtained in the previous work, it is observed that the model used is in good agreement with the experimental data of n-alkanes and n-alcohols.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Alfredo Pimentel-Rodas: 0000-0002-5379-003X Luis A. Galicia-Luna: 0000-0003-1862-8499 Funding

The authors would like to thank the Instituto Politécnico Nacional and CONACyT for the financial support of this research. Notes

The authors declare no competing financial interest.

■

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Viscosity and Density of n-Alcohols at Temperatures between (298.15

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