Thermophysical Properties of 1-Butanol at High Pressures

energies

Article † Thermophysical Properties of 1-Butanol at High Pressures

Marzena Dzida

Institute of Chemistry, University of Silesia in Katowice, Szkolna 9, 40-006 Katowice, Poland; [email protected]; Tel.: +48-323591643 In memoriam Michał Zor˛ebski,M.Sc. (1960–2020). † Received: 30 August 2020; Accepted: 21 September 2020; Published: 25 September 2020

Abstract: 1-Butanol can be considered as a good fuel additive, which can be used at high pressures. Therefore, the knowledge of high-pressure thermophysical properties is crucial for this application. In this paper, new experimental data on the speed of sound in 1-butanol in the temperature range from 293 to 318 K and at pressures up to 101 MPa are reported. The speed of sound at a frequency of 2 MHz was measured at atmospheric and high pressures using two measuring sets operating on the principle of the pulse–echo–overlap method. The measurement uncertainties were estimated to be better than 0.5 m s 1 and 1 m s 1 at atmospheric and high pressures, respectively. Additionally, the density ± · − ± · − was measured under atmospheric pressure in the temperature range from 293 to 318 K using a vibrating tube densimeter Anton Paar DMA 5000. Using the experimental results, the density and isobaric and isochoric heat capacities, isentropic and isothermal compressibilities, isobaric thermal expansion, and internal pressure were calculated at temperatures from 293 to 318 K and at pressures up to 100 MPa.

Keywords: 1-butanol; speed of sound; density; isobaric heat capacity; high pressure

1. Introduction 1-Butanol is an important chemical platform used as feedstock in the plastic industry, plasticizers, paints, binders and food extractant. However, much attention has been paid to the use of 1-butanol as a fuel. 1-Butanol can be used as an additive for gasoline, diesel, and kerosene or as an alternative fuel [1–4]. Studies show that the use of 1-butanol for this purpose is much more advantageous than the use of ethanol. 1-Butanol has higher energy density, lower than ethanol vapor pressure and improved miscibility with gasoline, lower solubility in water and it is less corrosive than ethanol [2,5,6]. Currently, 1-butanol is produced almost entirely from petroleum and the global demand for 1-butanol is about 2.8 metric tons per year [1]. The International Energy Agency forecasts that the demand for biofuels will be 690 million tons per year in 2050 [1]. The strong renewed interest in 1-butanol as a sustainable vehicle fuel has led to the development of improved biobutanol production processes including both biotechnological production processes as well as separation techniques [1,7–11]. Various species of the Clostridium bacteria such as C. acetobutylicum, C. beijerinckii, C. saccharoperbutylacetonicum and C. saccharobutylicum are mainly used for 1-butanol production [7]. However, Clostridium can be genetically modiﬁed in order to increase its ability to produce 1-butanol, and others have extracted enzymes from bacteria and incorporated them into other microbes such as yeast in order to turn them into 1-butanol production. Yeast (for example, Sacharomyces cerevisiae [8]) and Escherichia coli, one of the major bacteria in the human gut, are believed to be easily grown on an industrial scale [7]. The produced biobutanol can be separated by several methods including adsorption, gas stripping pervaporation, and liquid–liquid extraction using, for example, ionic liquids [6,8,11]. The next stage is the test of the properties of biobutanol in terms of its use in engines. In the injection systems used in automotive engines, the pressure can reach 250 MPa and the fuel injection takes place under

Energies 2020, 13, 5046; doi:10.3390/en13195046 www.mdpi.com/journal/energies Energies 2020, 13, 5046 2 of 21 adiabatic conditions [12]. Therefore, the petrochemical industry is interested in the thermodynamic and acoustic properties of fuel biocomponents under high pressures. Although 1-butanol has many important applications, especially as a fuel additive or intrinsic biofuel, the high-pressure speed of sound in this alcohol is still incomplete. There are only two available datasets. The speed of sound in primary alcohols under high pressures has been measured by Sysoev and Otpuschennikov and published in Nauchnye Trudy (Kurskiœi Gosudarstvennyœi Pedagogicheskiœi Institute) [13]. However, these data are not available. Khasanshin [14] published a correlation equation for the speed of sound in 1-alkanols with the carbon atoms in the chain ranging from 4 to 12 at pressures from (0.1 to 100) MPa and at six temperatures from (303.15 to 453.15) K determined at 20 K steps using the above-mentioned experimental data [13]. Plantier et al. [15] measured the speed of sound in 1-butanol at temperatures from (303.15 to 373.15) K at pressures up to 50 MPa. More literature data are available for the high-pressure density of 1-butanol. Recently, Safarov et al. [16] reported the experimental density of 1-butanol in the temperature range from (263.15 to 468.15) K and at pressures up to 140 MPa and they provided a careful literature search on experimental high-pressure density reported up to now. They also calculated the high-pressure speed of sound in 1-butanol using pressure dependence of density. Additionally, Dávila et al. [17] measured the density of 1-butanol over the temperature range from (278.15 to 358.15) K and at pressures up to 60 MPa. Khasanshin [18] published a correlation equation between the density and the number of carbon atoms ranging from 4 to 10 at pressures up to 50 MPa at 293.15 K and at 298.15 K. Cibulka and Ziková [19] also reported correlation equations of the Tait type based on the pρT data published by different authors before 1993. This work is the completion of systematic research on the high-pressure thermodynamic and acoustic properties of 1-akanols [20,21]. In this paper, new experimental speed of sound data are reported for 1-butanol in the temperature range from (293 to 318) K and at pressures up to 101 MPa. To the best of my knowledge, measurement of the speed of sound has never been conducted in this temperature and pressure range. Additionally, the density data under atmospheric pressure in the temperature range from (293 to 318) K are presented. Using the experimental results of speed of sound as a function of temperature and pressure, the temperature dependence of density under atmospheric pressure and the temperature dependence of isobaric heat capacity under atmospheric pressure reported by Zábranský et al. [22], the thermodynamic characteristics of compressed 1-butanol were obtained for temperatures from (293 to 318) K and for pressures from (0.1 to 100) MPa. The temperature and pressure dependence of density ρ(T, p), the temperature and pressure dependence of isobaric heat capacity Cp(T, p), and related quantities such as isentropic compressibility, κS, isobaric thermal expansion, αp, isothermal compressibility, κT, isochoric heat capacity, CV, and internal pressure, pint, were calculated. The method proposed by Davis and Gordon [23] with a numerical procedure described by Sun et al. [24] was applied for calculations. This study is aimed first to compare pressure dependence of density, isentropic compressibility and isobaric thermal expansion of 1-butanol with those of biocomponents or components of fuels such as ethanol, heptane, dodecane as well as biodiesel (fatty acid methyl esters of rapeseed oil, FAME) and low sulphur diesel oil (ekodiesel ultra), in the context of the use of 1-butanol as a fuel additive or alternative fuel. To the best of my knowledge, such analyses have never been performed to date. The second aim is to find whether the changes in properties of 1-butanol, caused by temperature and pressure, are reflected in the internal pressure.

2. Experimental Section

2.1. Chemical

The 1-butanol (0.998 mass fraction purity of C4H9OH) was purchased from Aldrich. Alcohol was dried over molecular sieves 0.3 nm. The mass fraction of water, determined by the Karl Fischer method, was less than 1 10 4. The purity of 1-butanol was tested by comparison of the measured · − speed of sound and density at 0.1 MPa with literature data (Table1). Additionally, the comparison of the results obtained of this work (yexp) and literature values (ylit) were presented as the relative Energies 2019, 12, x FOR PEER REVIEW 3 of 21

the results obtained of this work (yexp) and literature values (ylit) were presented as the relative deviation RD/% = 100·(yexp − ylit)/yexp. The relative deviations between the speed of sound at ambient pressure obtained of this work and literature values are in the range from −0.11% [15] to 0.013% [25] Energies 2020, 13, 5046 3 of 21 (Figure 1). The relative deviations between density at ambient pressure obtained of this work and literature values are in the range from −0.016% [16] to 0.018% [26] (Figure 2). deviation RD/% = 100 (yexp y )/yexp. The relative deviations between the speed of sound at ambient · − lit pressureTable obtained 1. Comparison of this work of the and speed literature of sound, values u, and are density, in therange ρ, at atmospheric from 0.11% pressure [15] to obtained 0.013% [in25 ] − (Figure1this). The work relative with those deviations reported betweenin the literature. density at ambient pressure obtained of this work and literature values are in the range from 0.016% [16] to 0.018% [26] (Figure2). This T (K) Literature− Work Table 1. Comparison of the speed of sound, u, and density, ρ, at atmospheric pressure obtained in this u (m·s−1) * 293.15 1256.33 1256.25 [25], 1256.8 [26], 1257.5 [27] work with those reported in the literature. 1239.2 [28], 1239.22 [25], 1239.29 [29] 1239.3 [27], 1239.39 [30,31], 298.15 1239.29 T (K)1239.8 This [26] Work Literature u (m s 1)* 293.151222.25 1256.33 [25],1222.36 1256.25 [14], 1222.4 [25], 1256.8 [27] [26], 1257.5 [27] · − 303.15 1222.36 1222.9 [26], 1223.6 [15]1239.2 [28], 1239.22 [25], 1239.29 [29] 1239.3 [27], 298.15 1239.29 308.15 1205.54 1205.53 [25], 1205.791239.39 [32], 1206.2 [30,31], [26] 1239.8 [26] 1222.25 [25],1222.36 [14], 1222.4 [27] 313.15303.15 1188.81 1188.65 1222.36 [25], 1189.6 [26], 1190.1 [15] 1222.9 [26], 1223.6 [15] 318.15308.15 1172.19 1173.0 1205.54 [26] 1205.53 [25], 1205.79 [32], 1206.2 [26] ρ (kg·m−3)** 293.15313.15 809.58 809.5 1188.81 [26], 809.60 [27], 1188.65 809.64 [25 [16]], 1189.6 [26], 1190.1 [15] 298.15318.15 805.79 805.7 1172.19 [26], 805.770 [30], 1173.0 805.77 [26] [16] 805.78 [27] ρ (kg m 3) ** 293.15 809.58 809.5 [26], 809.60 [27], 809.64 [16] · − 303.15 801.95 801.9 [26], 801.928 [30], 801.94 [27] 298.15 805.79 805.7 [26], 805.770 [30], 805.77 [16] 805.78 [27] 308.15303.15 798.10 798.0 801.95 [26], 798.054 [30] 801.9 [26], 801.928 [30], 801.94 [27] 313.15308.15 794.22 794.1 798.10 [26], 794.146 [30], 798.0 794.35 [26], 798.054 [16] [30] 318.15313.15 790.24 790.1 794.22 [26], 790.196 [30] 794.1 [26], 794.146 [30], 794.35 [16] 318.15* calculated 790.24 from Equation (1); 790.1 ** experimental [26], 790.196 data. [30] * calculated from Equation (1); ** experimental data.

FigureFigure 1. Comparison 1. Comparison of the of speed the ofspeed sound of in sound 1-butanol in as1-bu a functiontanol as of a temperature function of under temperature atmospheric under pressure obtained in this work (u ) with the literature values (u )[14,15,25–32] presented as atmospheric pressure obtainedthis in work this work (uthis work) with the literaturelit values (ulit) [14,15,25–32] relative deviations RDs (RD/% = 100 (u u )/u ). presented as relative deviations RD· sthis (RD work/%− = 100·(lit thisuthis work work−ulit)/uthis work).

Energies 2019, 12, x FOR PEER REVIEW 4 of 21 Energies 2020, 13, 5046 4 of 21

Figure 2. Comparison of the density of 1-butanol as a function of temperature under atmospheric Figure 2. Comparison of the density of 1-butanol as a function of temperature under atmospheric pressure obtained in this work (ρthis work) with the literature values (ρlit)[16,26,27,30] presented as pressure obtained in this work (ρthis work) with the literature values (ρlit) [16,26,27,30] presented as relative deviations RDs (RD/% = 100 (ρthis work ρlit)/ρthis work). relative deviations RDs (RD/% = 100·(· ρthis work−−ρlit)/ρthis work). 2.2. Speed of Sound Measurements 2.2. Speed of Sound Measurements The speed of sound measurements were conducted at ambient and high pressures using two measuringThe sets speed operate of sound based measurements on the pulse–echo–overlap were conduc methodted at ambient with measuring and high vessels pressures of the using same two acousticmeasuring path andsets constructed operate based by a on single the transmitting–receivingpulse–echo–overlap method ceramic with transducer measuring of 2 MHz vessels and of an the acousticsame mirror.acoustic The path pressure and constructed was measured by a using single a tr strainansmitting–receiving gauge measuring systemceramic (Hottinger transducer Baldwin of 2 MHz Systemand P3MD)an acoustic with mirror. accuracy The better pressure than 0.15%. was measured During measurements, using a strain the gauge pressure measuring stability system was 0.03(Hottinger MPa. The Baldwin temperature System was P3MD) measured with byaccuracy an Ertco better Hart 850than platinum 0.15%. During resistance measurements, thermometer the ± (NISTpressure certiﬁed) stability with was an uncertainty±0.03 MPa. ofThe 0.05temperature K and resolution was measured of 0.001 by K.an During Ertco Hart measurements, 850 platinum ± theresistance stability ofthermometer temperature (NIST was certified)0.005 K with at ambient an uncertainty pressure of and±0.05 K0.01 and K resolution at high pressures. of 0.001 K. ± ± TheDuring uncertainties measurements, of the speed the stability of sound of temperature measurements was under ±0.005 ambientK at ambient and highpressure pressures and ±0.01 were K at estimatedhigh pressures. to be better The thanuncertainties0.5 m sof1 theand speed1 m ofs sound1, respectively. measurements The detailsunder ambient concerning and the high ± · − ± · − constructionpressures ofwere a high-pressure estimated to device be better as well than as the ±0.5 method m·s− of1 and the speed±1 m·s of− sound1, respectively. measurements The anddetails calibrationconcerning can the be foundconstruction in the previousof a high-pressure paper [33]. device as well as the method of the speed of sound measurements and calibration can be found in the previous paper [33]. 2.3. Density Measurements 2.3.The Density density Measurements was measured at atmospheric pressure using a vibrating tube densimeter Anton Paar DMA 5000.The Thedensity calibration was measured was conducted at atmospheric using the pressure extended using procedure a vibrating with dry tube air densimeter and re-distilled Anton 3 water.Paar The DMA uncertainty 5000. The of calibration the density was measurements conducted was using estimated the extended to be 0.05procedure kg m− with. dry air and ± · re-distilled water. The uncertainty of the density measurements was estimated to be ±0.05 kg·m−3. 3. Results and Discussion 3. TheResults speed and of Discussion sound in 1-butanol was measured from (293 to 318) K in about 5 K steps and under the pressuresThe speed up to of 101.34 sound MPa. in 1-butanol The experimental was measured values from are (293 listed to in 318) Table K 2in. Theabout relative 5 K steps deviations and under RDsthebetween pressures the up high-pressure to 101.34 MPa. speed The experimental of sound obtained values of are this listed work in Table and literature 2. The relative values deviations are in the range from 0.12% [15] to 3.3% [16] (see Figure3). Additionally, the absolute average relative RDs between the high-pressure− speed of sound obtained of this work and literature values are in deviationsthe range (AARDs from 0.12%) between [15] resultsto −3.3% obtained [16] (see in thisFigure work 3). (Additionally,yexp) and the literaturethe absolute values average (ylit) wererelative Pn calculated as AARD = (100/N) (yexp, i y i)/yexp, i (where N is the number of data points). deviations (AARDs) between resultsi=1 obtained− lit, in this work (yexp) and the literature values (ylit) were The AARDs equal 0.03% [14=],() 0.08% [15],n and 1.1%− [16]. calculated as AARD 100/ N i=1 (yexp,i ylit,i ) / yexp,i (where N is the number of data points). The AARDs equal 0.03% [14], 0.08% [15], and 1.1% [16].

Energies 2019, 12, x FOR PEER REVIEW 5 of 21

Table 2. The experimental speed of sound, u, in 1-butanol measured at pressures up to 101.34 MPa Energies 2020within, 13 ,the 5046 temperature range from (293 to 318) K. 5 of 21 T p u T p u T p u Table 2. The experimental(K) (MPa) speed (m·s of sound,−1) (K)u, in(MPa) 1-butanol (m·s measured−1) (K) at pressures(MPa) (m·s up− to1) 101.34 MPa within the temperature292.65 range0.1 from1258.06 (293 to303.16 318) K. 0.1 1222.26 313.16 0.1 1188.85 292.86 15.2 1336.38 302.98 15.21 1304.62 313.10 15.21 1274.40 T p T p T p 292.85 30.39u 1406.63 302.97 30.39 1376.93u 313.13 30.39 1348.79 u (K) (MPa) (m s 1) (K) (MPa) (m s 1) (K) (MPa) (m s 1) 292.85 ·45.59− 1470.61 303.00 45.59 1442.45· − 313.12 45.59 1416.05 · − 292.65 0.1292.85 1258.06 60.80 1529.80 303.16 302.98 0.160.80 1502.93 1222.26 313.11 313.1660.79 1477.91 0.1 1188.85 292.86 15.2 1336.38 302.98 15.21 1304.62 313.10 15.21 1274.40 292.85 30.39292.87 1406.63 76.00 1583.46 302.97 303.05 30.3976.00 1557.55 1376.93 313.11 313.1376.01 1533.90 30.39 1348.79 292.85 45.59292.87 1470.61 91.19 1633.68 303.00 303.01 45.5991.19 1608.67 1442.45 313.03 313.1291.19 1585.65 45.59 1416.05 292.85 60.80292.83 1529.80 101.32 1665.21 302.98 302.98 60.80101.33 1640.91 1502.93 312.99 313.11101.33 1618.69 60.79 1477.91 292.87 76.00298.16 1583.46 0.1 1239.24 303.05 308.16 76.000.1 1205.55 1557.55 318.60 313.110.1 1170.66 76.01 1533.90 292.87 91.19298.00 1633.68 15.20 1319.99 303.01 308.00 91.19 15.2 1289.43 1608.67 318.52 313.0315.18 1257.86 91.19 1585.65 292.83 101.32 1665.21 302.98 101.33 1640.91 312.99 101.33 1618.69 298.16 0.1298.00 1239.24 30.40 1391.35 308.16 308.01 0.130.39 1362.92 1205.55 318.52 318.6030.39 1333.80 0.1 1170.66 298.00 15.20297.99 1319.99 45.59 1456.21 308.00 308.00 15.245.59 1429.35 1289.43 318.47 318.5245.60 1402.24 15.18 1257.86 298.00 30.40297.99 1391.35 60.79 1516.04 308.01 308.03 30.3960.79 1490.34 1362.92 318.46 318.5260.80 1464.54 30.39 1333.80 297.99 45.59298.00 1456.21 75.99 1570.22 308.00 307.99 45.5976.00 1545.86 1429.35 318.45 318.4776.01 1521.23 45.60 1402.24 297.99 60.79 1516.04 308.03 60.79 1490.34 318.46 60.80 1464.54 298.00 91.19 1620.86 307.99 91.19 1596.96 318.45 91.19 1573.46 298.00 75.99 1570.22 307.99 76.00 1545.86 318.45 76.01 1521.23 298.00 91.19297.99 1620.86 101.34 1652.77 307.99 308.02 91.19101.33 1629.34 1596.96 318.46 318.45101.34 1606.71 91.19 1573.46 297.99 101.34 1652.77 308.02 101.33 1629.34 318.46 101.34 1606.71

FigureFigure 3. 3.Comparison Comparison ofof thethe speedspeed of sound in 1-butanol 1-butanol as as aa function function of of pressure pressure obtained obtained in inthis this work (u ) with the literature values (u )[14–16] presented as relative deviations RDs work (uthis thiswork work) with the literature values (ulit) [14–16]lit presented as relative deviations RDs (RD/% = (RD/% = 100 (u u )/u ); * calculated from the pρT data [16]. 100·(uthis work· −thisulit)/ workuthis− worklit); * calculatedthis work from the pρT data [16]. The density of the alcohol under test was measured under atmospheric pressure within the The density of the alcohol under test was measured under atmospheric pressure within the temperature range from (293.15 to 318.15) K. The experimental values are collected in Table1. temperature range from (293.15 to 318.15) K. The experimental values are collected in Table 1. The dependence of the speed of sound and density on the temperature at atmospheric pressure The dependence of the speed of sound and density on the temperature at atmospheric pressure was approximated by the second-order polynomial: was approximated by the second-order polynomial: X2 2 = j j y =y bjbTjT,, (1)(1) = j=0j 0

where y is the speed of sound, u0, or density, ρ, at atmospheric pressure p0, b are the polynomial where y is the speed of sound, u0, or density, ρ, at atmospheric pressure p0, bj arej the polynomial = = ρ coecoefficientsfficients (b j (=bcj j forc j the for speed the ofspeed sound, of andsound,bj = andρj for b thej density)j for calculatedthe density) by thecalculated least-squares by the method. The backward stepwise rejection procedure was used to reduce the number of non-zero coe fficients. The coefficients and standard deviations from the regression lines are provided in Table3. Energies 2020, 13, 5046 6 of 21

Table 3. Coeﬃcients of polynomial (1) for the speed of sound and density.

3 a c0 c1 c2 10 δu0 · (m s 1) (m s 1 K 1) (m s 1 K 2) (m s 1) · − · − · − · − · − · − 2436.59 4.63487 2.07654 0.07 − 4 a ρ0 ρ1 ρ2 10 δρ · (kg m 3) (kg m 3 K 1) (kg m 3 K 2) (kg m 3) · − · − · − · − · − · − 964.750 0.304950 7.65424 0.01 − − a mean deviation from the regression line.

The speed of sound dependence on pressure and temperature was approximated using the equation proposed by Sun et al. [24]:

X3 X2 p p = a (u u )iT j, (2) − 0 ij − 0 i=1 j=0 where aij are the polynomial coefficients calculated by the least-squares method, u is the speed of sound at p > 0.1 MPa, u0 is the speed of sound at ambient pressure, calculated from Equation (1). The coefficients aij and the mean deviation from the regression line are provided in Table4. The stepwise rejection procedure was used to reduce the number of non-zero coefficients.

Table 4. Coeﬃcients of Equation (2).

a a1j a2j a3j δu (K j MPa s m 1) (K j MPa s2 m 2) (K j MPa s3 m 3) (m s 1) − · · · − − · · · − − · · · − · − j 0 0.282824 1.38485 10 4 1.37252 10 7 0.29 · − · − 1 - - - 2 1.20119 10 6 - 7.92802 10 13 − · − · − a mean deviation from the regression line.

The density and isobaric heat capacity of 1-butanol were determined for temperatures from (293 to 318) K and for pressures up to 100 MPa using the acoustic method. In the calculations, the experimental speed of sound data as a function of temperature and pressure were used, together with the temperature dependence of density and isobaric heat capacity at atmospheric pressure. The temperature dependence of the isobaric heat capacity reported by Zábranský et al. [22] was used. The applied acoustic method is based mainly on the thermodynamic relationship between isothermal compressibility κT and isentropic compressibility κS:

2 αp T κT = κS + · , (3) ρ cp · where cp is the speciﬁc isobaric heat capacity and αp is the isobaric thermal expansion deﬁned as:

1 αp ρ− (∂ρ/∂T) . (4) ≡ − · p The substitution the Laplace formula:

1 κS = , (5) ρu2 and deﬁnition of isothermal compressibility:

1 κT ρ− (∂ρ/∂p) , (6) ≡ · T Energies 2020, 13, 5046 7 of 21 into Equation (3) leads to the following relationship:

! 2 ∂ρ 1 Tαp = + . (7) 2 ∂p T u cp

The change of density, ∆ρ, caused by the change of pressure from p1 to p2 at constant temperature T can be approximated suﬃciently accurate as follows:

p2  p2 Z α2T Z α2T  1 p  1 p ∆ρ =  +  dp dp + ∆p, (8) u2 cp  ≈ u2 cp p1 p1 provided that ∆p = p2 – p1 is small. The initial values of u(T, p0 = 0.101325 MPa), ρ(T, p0 = 0.101325 MPa), and cp(T, p0 = 0.101325 MPa) were used in the Equation (8). The specific isobaric heat capacity at p2 is acquired by: 2 cp(p ) cp(p ) (T/ρ) α + (∂αp/∂T) ∆p, (9) 2 ≈ 1 − p p where cp(p1) is the specific isobaric heat capacity at p1. The uncertainties of the density and specific isobaric heat capacity estimated using the perturbation method are 0.02% and 0.3%, ± 4 ±3 respectively. The expanded uncertainties were estimated to be better than U(ρ) = 5 10− ρ kg m− and 2 1 1 · · · U(Cp)=1 10 Cp J mol K for density and molar isobaric heat capacity, respectively. The density · − · · − · − and molar isobaric heat capacity at high pressures are collected in Tables5 and6, respectively.

Table 5. The density, ρ, of 1-butanol at pressures up to 100 MPa and within the temperature range from (293 to 318) K.

ρ (kg m 3) p (MPa) · − T (K) 293.15 298.15 303.15 308.15 313.15 318.15 0.1 * 809.58 805.79 801.96 798.10 794.20 790.26 10 816.60 812.99 809.36 805.69 801.98 798.24 20 823.12 819.67 816.19 812.68 809.14 805.57 30 829.18 825.86 822.52 819.15 815.75 812.32 40 834.86 831.66 828.43 825.18 821.90 818.59 50 840.20 837.11 833.99 830.84 827.67 824.47 60 845.27 842.27 839.24 836.19 833.11 830.00 70 850.08 847.17 844.23 841.26 838.27 835.25 80 854.67 851.84 848.98 846.09 843.17 840.23 90 859.06 856.30 853.51 850.70 847.86 844.99 100 863.27 860.58 857.86 855.12 852.34 849.54 * calculated from Equation (1).

Table 6. The isobaric molar heat capacity, Cp, of 1-butanol at pressures up to 100 MPa and within the temperature range from (293 to 318) K.

1 1 Cp (J mol K ) p (MPa) · − · − T (K) 293.15 298.15 303.15 308.15 313.15 318.15 0.1 * 173.70 177.17 180.82 184.62 188.57 192.62 10 172.8 176.2 179.9 183.6 187.5 191.5 20 172.0 175.4 179.0 182.7 186.6 190.6 30 171.3 174.7 178.2 181.9 185.8 189.7 40 170.6 174.0 177.5 181.2 185.0 188.9 Energies 2019, 12, x FOR PEER REVIEW 8 of 21

Energies 2020, 13, 5046 8 of 21 40 170.6 174.0 177.5 181.2 185.0 188.9 50 170.0 173.4 176.9 180.5 184.3 188.2 60 169.4 172.7Table 6. 176.2Cont. 179.8 183.6 187.5 1 1 70 168.8 172.2 Cp175.6(J mol 179.2K ) 183.0 186.8 p (MPa) · − · − 80 168.3 171.6 175.0T (K) 178.6 182.3 186.2 5090 170.0 167.8 173.4 171.1 176.9174.5 178.0 180.5 181.7 184.3 185.6 188.2 60100 169.4 167.2 172.7 170.5 176.2173.9 177.5 179.8 181.2 183.6 185.0 187.5 70 168.8 172.2* values 175.6 from ref. [22]. 179.2 183.0 186.8 80 168.3 171.6 175.0 178.6 182.3 186.2 90 167.8 171.1 174.5 178.0 181.7 185.6 The density100 of 1-butanol 167.2 obtained 170.5 in this 173.9 work was 177.5 compared 181.2 with 185.0the experimental data reported by 1993, correlated by Cibulka* valuesand Ziková from ref. [[19].22]. The RDs are in the range from 0.02 to 0.09% (see Figure 4). The AARD was found to be 0.04%. Particularly, the attention has been paid to excellentThe agreement density of 1-butanol between obtained the raw in thisdensity work wasreported compared by Zúñiga–Moreno with the experimental et al. data [34] reported and density obtainedby 1993, correlatedin this work by Cibulka as follows: and Zikov 801.97á [ 19kg·m]. The−3 atRD 313.10s are in K, the 9.996 range MPa from [34] 0.02 toand 0.09% 801.98 (see kg·m Figure−34 ).at 313.15 AARD K,The 10 MPa aswas well found as 809.14 to be kg·m 0.04%.−3 at Particularly, 313.10 K, 20.015 the attention MPa [34] has beenand 809.14 paid to kg·m excellent−3 at 313.15 agreement K, 20 MPa. between the raw density reported by Zúñiga–Moreno et al. [34] and density obtained in this work as A good agreement was found also for data reported by Dávila et al. [17]. The RDs are in the range follows: 801.97 kg m 3 at 313.10 K, 9.996 MPa [34] and 801.98 kg m 3 at 313.15 K, 10 MPa as well as from −0.13% to −0.004%· − (see Figure 4), the AARD is 0.07%. The· − density obtained in this work is also 809.14 kg m 3 at 313.10 K, 20.015 MPa [34] and 809.14 kg m 3 at 313.15 K, 20 MPa. A good agreement · − · − inwas very found good also agreement for data reported with bythose Dávila reported et al. [17 by]. TheSafarovRDs are et inal. the [16], range the from RDs 0.13%are in to the0.004% range from − − −0.04(see Figureto 0.08%4), the (seeAARD Figureis 0.07%.4) and The AARD density equals obtained 0.04%. in this Thus, work again is also the in very density good calculated agreement by the indirect,with those acoustic reported method by Safarov is in et al.an[ 16excellent], the RD sagreement are in the range with from density0.04 measured to 0.08% (see by Figure high-pressure4) − vibratingand AARD tubeequals densimeter. 0.04%. Thus, On againthe other the density hand, calculatedthe speed by of the sound indirect, calculat acousticed methodfrom experimental is in ρ(anp,T excellent) data is agreementin worse agreement with density with measured experimental by high-pressure ones (see vibrating Figure 3). tube This densimeter. was discussed On the in detail inother the previous hand, the work speed [35]. of sound Using calculated both the from acoustic experimental methodρ (andp,T) densimetric data is in worse one, agreement the Cp(p, withT) data can experimental ones (see Figure3). This was discussed in detail in the previous work [ 35]. Using both be obtained by the same relationship (Equation (6)). The agreement between the Cp(p,T) data obtainedthe acoustic by the method acoustic and densimetricmethod (this one, work) the C pand(p,T )de datansimetric can be obtainedone (reported by the sameby Safarov relationship et al. [16]) is (Equation (6)). The agreement between the C (p,T) data obtained by the acoustic method (this work) excellent, the RDs are in the range from −0.67p to 0.17% and AARD is 0.22% (see Figure 5). and densimetric one (reported by Safarov et al. [16]) is excellent, the RDs are in the range from 0.67 to − 0.17% and AARD is 0.22% (see Figure5).

FigureFigure 4. 4. ComparisonComparison of of the the density density of of 1-butanol 1-butanol as a fu functionnction ofof pressurepressure obtainedobtained in in this this work work (ρthis work) with the literature values (ρlit)[16,17,19] presented as relative deviations RDs (ρthis work) with the literature values (ρlit) [16,17,19] presented as relative deviations RDs (RD/% = (RD/% = 100 (ρthis work ρlit)/ρthis work). 100·(ρthis work−·ρlit)/ρthis work− ).

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Figure 5. Comparison of the isobaric heat capacity of 1-butanol as a function of pressure obtained

Figurein this 5. work Comparison (Cp,this work of) the with isobaric the literature heat capacity values (C ofp,lit 1-)[butanol16] presented as a function as relative of deviationspressure obtainedRDs in this(RD work/% = (100Cp,this(Cp work, ) with theCp, literature)/Cp, values). (Cp,lit) [16] presented as relative deviations RDs (RD/% · this work − lit this work = 100·(Cp,this work − Cp,lit)/Cp,this work). The isentropic compressibility, κS, was determined from Equation (5) using the experimental speed of sound and determined density. The results are collected in Table7. The overall expanded The isentropic compressibility, κS, was determined from Equation (5) using the experimental uncertainty of κ was estimated to be U(κ ) = 1.5 10 3κ Pa 1. The isentropic compressibility calculated speed of sound andS determined density.S The· result− S s are− collected in Table 7. The overall expanded from the speed of sound and density reported by Plantier et al. [15] is in an excellent agreement with uncertainty of κS was estimated to be U(κS) = 1.5·10−3κS Pa−1. The isentropic compressibility calculated those reported in this work. The RDs are in the range from 0.31% to 0.16% (see Figure6), the AARD from the speed of sound and density reported by Plantier− et al. [15] is in an excellent agreement with is 0.16%. The RDs between κS obtained from pρT data reported by Safarov et al. [16] and obtained in thosethis reported work are inin thethis range work. from The 0.004%RDs are to in 6.3% the (see range Figure from6), the−0.31%AARD to 0.16%is 2.1%. (see Figure 6), the AARD − is 0.16%. The RDs between κS obtained from pρT data reported by Safarov et al. [16] and obtained in this workTable are 7. inThe the isentropic range from compressibility, −0.004% κtoS, of6.3% 1-butanol (see Figure at pressures 6), the up AARD to 100 MPa is 2.1%. and within the temperature range from (293 to 318) K.

Table 7. The isentropic compressibility, κS, of 1-butanol9 at 1pressures up to 100 MPa and within the κS 10 (Pa− ) temperaturep (MPa)range from (293 to 318) K. · T (K)

293.15 298.15 303.15κS ·109 (Pa 308.15−1) 313.15 318.15 p (MPa) 0.1 0.7826 0.8080 0.8345T (K) 0.8621 0.8909 0.9209 10 0.7150 0.7361 0.7579 0.7805 0.8038 0.8279 20 0.6586 293.15 0.6765 298.15 0.6949303.15 308.15 0.7138 313.15 0.7332 318.15 0.7532 300.1 0.6117 0.7826 0.6272 0.8080 0.64300.8345 0.8621 0.6592 0.8909 0.6757 0.9209 0.6926 4010 0.5720 0.7150 0.5855 0.7361 0.59940.7579 0.7805 0.6134 0.8038 0.6278 0.8279 0.6423 50 0.5379 0.5499 0.5622 0.5746 0.5872 0.5999 6020 0.5083 0.6586 0.5191 0.6765 0.53000.6949 0.7138 0.5411 0.7332 0.5523 0.7532 0.5636 7030 0.4823 0.6117 0.4920 0.6272 0.50190.6430 0.6592 0.5119 0.6757 0.5219 0.6926 0.5321 8040 0.4592 0.5720 0.4681 0.5855 0.47710.5994 0.6134 0.4861 0.6278 0.4952 0.6423 0.5044 90 0.4387 0.4468 0.4550 0.4633 0.4716 0.4799 10050 0.4202 0.5379 0.4277 0.5499 0.43530.5622 0.5746 0.4428 0.5872 0.4504 0.5999 0.4580 60 0.5083 0.5191 0.5300 0.5411 0.5523 0.5636 70 0.4823 0.4920 0.5019 0.5119 0.5219 0.5321 80 0.4592 0.4681 0.4771 0.4861 0.4952 0.5044 90 0.4387 0.4468 0.4550 0.4633 0.4716 0.4799 100 0.4202 0.4277 0.4353 0.4428 0.4504 0.4580

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FigureFigure 6. 6. Comparison of of the the isentropic isentropic compressibility compressibility of 1-butanol of 1-butanol as a function as of a pressure function obtained of pressure in this work (κS,this work) with the literature values (κS,lit)[15,16] presented as relative deviations RDs obtained in this work (κS,this work) with the literature values (κS,lit) [15,16] presented as relative (RD/% = 100 (κS,this work κS,lit)/κS,this work); * calculated from the pρT data [16]. deviations RD· s (RD/% = −100·(κS,this work − κS,lit)/κS,this work); * calculated from the pρT data [16]. Based on the temperature dependence of density, the isobaric thermal expansion was calculated usingBased a deﬁnition on the temperature (Equation (4)). dependence The obtained of results density, are the collected isobaric in Tablethermal8. The expansion overall expanded was calculated 2 1 usinguncertainty a definition of αp is(EquationU(αp) = 1 10(4)).α Thep K obtained. The agreement results with are collected literature datain Table is very 8. good, The overall the RDs expandedare · − − uncertaintyin the range of from αp is 1.9U(α top)0.17% = 1·10 [16−2α]p and K−1. from The agreement2.2 to 0.19% with [17] (see literature Figure7 ).data The isAARD very good,is 0.83% the [16 RDs] are − − in andthe 1.0%range [17 from]. −1.9 to 0.17% [16] and from −2.2 to 0.19% [17] (see Figure 7). The AARD is 0.83% [16] and 1.0% [17]. Table 8. The isobaric thermal expansion, αp, of 1-butanol at pressures up to 100 MPa and within the temperature range from (293 to 318) K. Table 8. The isobaric thermal expansion, αp, of 1-butanol at pressures up to 100 MPa and within the 3 1 temperature range from (293 to 318) K. αp 10 (K ) p (MPa) · − T (K) αp ·103 (K−1) p (MPa)293.15 298.15 303.15 308.15 313.15 318.15 0.1 0.931 0.945 0.959T (K) 0.973 0.988 1.002 10 0.879 293.15 0.891 298.15 0.903303.15 308.15 0.915 313.15 0.928 318.15 0.941 200.1 0.834 0.931 0.845 0.945 0.8560.959 0.973 0.868 0.988 0.879 1.002 0.890 30 0.796 0.806 0.817 0.827 0.837 0.848 4010 0.763 0.879 0.772 0.891 0.7820.903 0.915 0.792 0.928 0.802 0.941 0.812 5020 0.733 0.834 0.742 0.845 0.7520.856 0.868 0.761 0.879 0.770 0.890 0.780 6030 0.707 0.796 0.715 0.806 0.7240.817 0.827 0.733 0.837 0.742 0.848 0.751 70 0.682 0.691 0.699 0.708 0.717 0.726 8040 0.660 0.763 0.668 0.772 0.6770.782 0.792 0.686 0.802 0.694 0.812 0.703 9050 0.640 0.733 0.648 0.742 0.6560.752 0.761 0.665 0.770 0.673 0.780 0.682 10060 0.621 0.707 0.629 0.715 0.6370.724 0.733 0.646 0.742 0.654 0.751 0.663 70 0.682 0.691 0.699 0.708 0.717 0.726 80 0.660 0.668 0.677 0.686 0.694 0.703 90 0.640 0.648 0.656 0.665 0.673 0.682 100 0.621 0.629 0.637 0.646 0.654 0.663

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Figure 7. Comparison of the isobaric thermal expansion of 1-butanol as a function of pressure obtained

Figurein this 7. work Comparison (αp,this work )of with the the isobaric literature thermal values (αexpansionp,lit)[16,17 ]of presented 1-butanol as relative as a function deviations ofRD pressures obtained(RD/% = in100 this(αp , work (αpα,pthis, )work/αp), with ).the literature values (αp,lit) [16,17] presented as relative · this work − lit this work deviations RDs (RD/% = 100·(αp,this work − αp,lit)/αp,this work). For the comprehensive characterization of the tested liquid, the compressibility at a constant temperature,For the comprehensiveκT, is the next important characterization material constant. of the tested In this work,liquid,κT thewas compressibility calculated from κ Satusing a constant Eq. (3), the results are listed in Table9. The overall expanded uncertainty of κT was estimated to be temperature, κ3T, is the1 next important material constant. In this work, κT was calculated from κS U(κT) = 5 10− κT Pa− . In this work, the κT was obtained by the acoustic method based on integration using Eq. (3),· the results are listed in Table 9. The overall expanded uncertainty of κT was estimated procedures. On the other hand, the κT obtained by the densimetric method is based on diﬀerentiation −3 −1 to proceduresbe U(κT) = [ 165·10,17].κ TheT PaRD. sIn between this work, results the obtained κT was in thisobtained work usingby the the acoustic acoustic method andbased on integrationliterature dataprocedures. obtained On using the the other densimetric hand, the method κT obtained are in the by range the densimetric from 0.08 to method 5.2% [16 ]is and based on − differentiationfrom 3.5 to procedures1.5% [17] (see [16,17]. Figure 8The). The RDAARDs betweenis 1.6% results [16] and obtained 2.7% [17 in]. this work using the acoustic − − method and literature data obtained using the densimetric method are in the range from −0.08 to 5.2% [16]Table and 9. Thefrom isothermal −3.5 to − compressibility,1.5% [17] (seeκ TFigure, of 1-butanol 8). The at pressuresAARD is up 1.6% to 100 [16] MPa and and 2.7% within [17]. the temperature range from (293 to 318) K.

Table 9. The isothermal compressibility, κT, of 1-butanol9 at1 pressures up to 100 MPa and within the κT 10 (Pa ) p (MPa) · − temperature range from (293 to 318) K. T (K)

293.15 298.15 303.15κT·109 (Pa 308.15−1) 313.15 318.15 p (MPa) 0.1 0.917 0.946 0.977T (K)1.009 1.042 1.077 10 0.834 0.858 0.884 0.910 0.937 0.964 20 0.766 293.15 0.786 298.15 0.808303.15 308.15 0.830 313.15 0.852 318.150.875 300.1 0.709 0.917 0.727 0.946 0.7450.977 1.009 0.764 1.042 0.783 1.077 0.803 40 0.661 0.677 0.693 0.709 0.726 0.743 5010 0.620 0.834 0.634 0.858 0.6480.884 0.910 0.663 0.937 0.677 0.964 0.692 6020 0.584 0.766 0.597 0.786 0.6100.808 0.830 0.623 0.852 0.636 0.875 0.649 7030 0.553 0.709 0.564 0.727 0.5760.745 0.764 0.588 0.783 0.600 0.803 0.612 80 0.525 0.536 0.546 0.557 0.568 0.579 40 0.661 0.677 0.693 0.709 0.726 0.743 90 0.500 0.510 0.520 0.530 0.540 0.550 10050 0.478 0.620 0.487 0.634 0.4960.648 0.663 0.506 0.677 0.515 0.692 0.524 60 0.584 0.597 0.610 0.623 0.636 0.649 70 0.553 0.564 0.576 0.588 0.600 0.612 80 0.525 0.536 0.546 0.557 0.568 0.579 90 0.500 0.510 0.520 0.530 0.540 0.550 100 0.478 0.487 0.496 0.506 0.515 0.524

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Figure 8. Comparison of the isothermal compressibility of 1-butanol as a function of pressure obtained

Figurein this 8. work Comparison (κT,this work )of with the the isothermal literature values compressibility (κT,lit)[16,17 ]of presented 1-butanol as relativeas a function deviations ofRD pressures obtained(RD/% = in100 this(κ , work (κTκ,this, work)/κ ), with ).the literature values (κT,lit) [16,17] presented as relative · T this work − T lit T this work deviations RDs (RD/% = 100·(κT,this work − κT,lit)/κT,this work). The molar isochoric heat capacity, CV, was calculated using the experimental speed of sound as well as the determined density, molar isobaric heat capacity and isobaric thermal expansion: The molar isochoric heat capacity, CV, was calculated using the experimental speed of sound as well as the determined density, molar isobaric heat2 capacity and isobaric thermal expansion: αp T V C = C · · . (10) V p 2 2 − 1 α αp⋅T V⋅ + p · T· V = − ρ u2 Cp CV C p · 2 . 1 α ⋅T ⋅V (10) The C values obtained in this work are collected in+ Tablep 10. The overall expanded uncertainty V 2 2 ρ1⋅ 1 of C was estimated to be U(C ) = 2 10 C J mol Ku . The CC pvalues obtained in this work by the V V · − V · − · − V acoustic method and those obtained using the densimetric method by Safarov et al. [16] are in excellent Theagreement. CV values The obtainedRDs are in in this the work range fromare collected0.19 to 1.1%in Table [16] (see10. The Figure overall9) and expandedAARD is 0.35% uncertainty [16]. of CV − was estimated to be U(CV) = 2·10−2CV J·mol−1·K−1. The CV values obtained in this work by the acoustic methodTable and 10. thoseThe isochoric obtained molar using heat capacity, the densimetricCV, of 1-butanol method at pressures by Safarov up to 100 MPaet al. and [16] within are the in excellent agreement.temperature The RD ranges are from in (293the Krange to 318) from K. −0.19 to 1.1% [16] (see Figure 9) and AARD is 0.35% [16]. 1 1 CV (J mol K ) p (MPa) · − · − Table 10. The isochoric molar heat capacity, CV, of 1-butanol at pressures up to 100 MPa and within T (K) the temperature range from (293 K to 318) K. 293.15 298.15 303.15 308.15 313.15 318.15 0.1 148.3 151.3 154.4CV (J·mol− 157.81·K−1) 161.2 164.8 10p (MPa) 148.2 151.1 154.2 157.5 160.9 164.4 20 148.0 150.9 154.0T (K) 157.2 160.6 164.1 30 147.8 293.15 150.7 298.15 153.8303.15 308.15 157.0 313.15 160.3 318.15 163.7 400.1 147.7 148.3 150.6 151.3 153.6154.4 157.8 156.7 161.2 160.0 164.8 163.4 50 147.6 150.4 153.4 156.5 159.7 163.1 6010 147.4 148.2 150.2 151.1 153.2154.2 157.5 156.3 160.9 159.5 164.4 162.8 7020 147.3 148.0 150.1 150.9 153.0154.0 157.2 156.1 160.6 159.2 164.1 162.5 8030 147.2 147.8 150.0 150.7 152.8153.8 157.0 155.9 160.3 159.0 163.7 162.2 90 147.1 149.8 152.7 155.6 158.7 162.0 10040 147.0 147.7 149.7 150.6 152.5153.6 156.7 155.4 160.0 158.5 163.4 161.7 50 147.6 150.4 153.4 156.5 159.7 163.1 60 147.4 150.2 153.2 156.3 159.5 162.8 70 147.3 150.1 153.0 156.1 159.2 162.5 80 147.2 150.0 152.8 155.9 159.0 162.2 90 147.1 149.8 152.7 155.6 158.7 162.0 100 147.0 149.7 152.5 155.4 158.5 161.7

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Figure 9. Comparison of the isochoric heat capacity of 1-butanol as a function of pressure obtained

Figurein this 9. work Comparison (CV,this work of) the with isochoric the literature heat values capacity (CV ,oflit)[ 1-butanol16] presented as a as function relative deviationsof pressureRD obtaineds in (RDthis/% work= 100 ((CCV,this, work) withC ,the)/C literature, ). values (CV,lit) [16] presented as relative deviations RDs · V this work − V lit V this work (RD/% = 100·(CV,this work − CV,lit)/CV,this work). The internal pressure was calculated using the experimental speed of sound and determined density,The internal isobaric heatpressure capacity, was and calculated isobaric thermal using expansion:the experimental speed of sound and determined density, isobaric heat capacity, and isobaric thermal expansion:2  1 αp   1 αp T V −  p = T p = T α  + · ·   p. (11) int  p  2   −1 · κT −  · · ρ u Cp 2   −  α   · α ⋅T ⋅V   = ⋅ p − = ⋅α ⋅ 1 + p  − pint T   p T p  p . (11) The results are collected in κ Table 11. The overall expanded ρ ⋅ 2 uncertainty of p was estimated to  T    u C p  int be U(p ) = 1 10 2p Pa. The RDs for p obtained in this work by the acoustic method and those int · − int int obtained by the densimetric method are in the range from 6.3 to 0.36% [16] and from 0.21 to The results are collected in Table 11. The overall expanded− uncertainty− of pint was estimated− to be 3.0% [17] (see Figure 10). The AARD is 2.7% [16] and 1.7% [17]. U(pint) = 1·10−2pint Pa. The RDs for pint obtained in this work by the acoustic method and those obtained by the densimetric method are in the range from −6.3 to −0.36% [16] and from −0.21 to 3.0% Table 11. The internal pressure, pint, of 1-butanol at pressures up to 100 MPa and within the temperature [17] (seerange Figure from 10). (293 The to 318) AARD K. is 2.7% [16] and 1.7% [17].

6 pint 10 (Pa) Table 11. pThe(MPa) internal pressure, pint, of 1-butanol· at− pressures up to 100 MPa and within the temperature range from (293 to 318) K. T (K) 293.15 298.15 303.15 308.15 313.15 318.15 pint·10−6 (Pa) 0.1p (MPa) 297.9 297.4 297.2 296.9 296.5 295.9 10 299.1 299.4 299.7T (K) 300.0 300.2 300.5 20 299.6 300.5 301.4 302.2 303.0 303.7 30 299.4 293.15 300.8 298.15 302.2303.15 308.15 303.6 313.15 304.9 318.15 306.1 400.1 298.5 297.9 300.4 297.4 302.2297.2 296.9 304.0 296.5 305.8 295.9 307.6 5010 296.9 299.1 299.2 299.4 301.5299.7 300.0 303.8 300.2 306.0 300.5 308.3 60 294.6 297.4 300.1 302.8 305.5 308.3 7020 291.8 299.6 295.0 300.5 298.1301.4 302.2 301.3 303.0 304.4 303.7 307.6 8030 288.5 299.4 292.0 300.8 295.6302.2 303.6 299.2 304.9 302.8 306.1 306.4 9040 284.7 298.5 288.6 300.4 292.6302.2 304.0 296.6 305.8 300.6 307.6 304.7 10050 280.5 296.9 284.8 299.2 289.2301.5 303.8 293.6 306.0 298.0 308.3 302.5 60 294.6 297.4 300.1 302.8 305.5 308.3 70 291.8 295.0 298.1 301.3 304.4 307.6 80 288.5 292.0 295.6 299.2 302.8 306.4 90 284.7 288.6 292.6 296.6 300.6 304.7 100 280.5 284.8 289.2 293.6 298.0 302.5

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Figure 10. Comparison of the internal pressure of 1-butanol as a function of pressure obtained in

this work (pint,this work) with the literature values (pint,lit) [16,17] presented as relative deviations RDs Figure 10. Comparison of the internal pressure of 1-butanol as a function of pressure obtained in (RD/% = 100·(pint,this work − pint,lit)/pint,this work). Figurethis work 10. (Comparisonpint,this work) withof the the internal literature pressure values (p intof,lit 1-buta)[16,17nol] presented as a function as relative of pressure deviations obtainedRDs in this(RD work/% = 100(pint(,pthis work, ) with pthe, literature)/p , values). (pint,lit) [16,17] presented as relative deviations RDs The relative· deviationsint this work − RDint slit (Figureint this work 10) suggest that the pressure dependence of the internal (RD/% = 100·(pint,this work − pint,lit)/pint,this work). pressureThe of relative 1-butanol deviations is differentRDs (Figuredepend 10ing) suggest on the data that thesource pressure (see Figure dependence 11). of the internal pressureThe relative of 1-butanol deviations is diﬀerent RD dependings (Figure 10) on thesuggest data source that the (see pre Figuressure 11 ).dependence of the internal pressure of 1-butanol is different depending on the data source (see Figure 11).

Figure 11. Comparison of the internal pressure of 1-butanol as a function of pressure obtained in this Figurework with11. Comparison those obtained of from the theinternalpρT literature pressure data of [161-buta,17]. nol as a function of pressure obtained in this work with those obtained from the pρT literature data [16,17]. The density, isentropic compressibility and isobaric thermal expansion of 1-butanol were Figure 11. Comparison of the internal pressure of 1-butanol as a function of pressure obtained in comparedThe density, with density, isentropic isentropic compressibility compressibility and and isobaric thermalthermal expansion expansion of heptane of 1-butanol [36,37], were this work with those obtained from the pρT literature data [16,17]. comparedethanol [36 with,37], dodecanedensity, [38isentropic], diesel oil compressibili (ekodiesel ultra)ty [ 12and] and isobaric biodiesel [thermal12]. Heptane expansion and dodecane of heptane are components of the fuels [36–38]. The engine simulations were carried out ﬁrst using heptane and [36,37], ethanol [36,37], dodecane [38], diesel oil (ekodiesel ultra) [12] and biodiesel [12]. Heptane thenThe dodecane density, as aisentropic more suitable compressibility “low or no sulphur”, and isobaric “ideal” surrogatethermal componentexpansion forof petrodiesel1-butanol were and dodecane are components of the fuels [36–38]. The engine simulations were carried out first comparedfuels [39, 40with]. Moreover, density, the isentropic thermophysical compressibili propertiesty of dodecaneand isobaric are similar thermal to the expansion thermophysical of heptane [36,37],usingproperties heptane ethanol of aviation and[36,37], then kerosene dodecane dodecane [41]. [38], For as comparison, diesela more oil suitable(ekodiesel ethanol was“low ultra) also or chosen [12]no sulphur”,and as the biodiesel most “ideal” commonly [12]. surrogate Heptane andcomponent dodecane for arepetrodiesel components fuels of [3 the9,40]. fuels Moreover, [36–38]. the The thermophysical engine simulations properties were ofcarried dodecane out first are usingsimilar heptane to the thermophysical and then dodecane properties as aof moreaviati onsuitable kerosene “low [41]. or Forno comparison,sulphur”, “ideal” ethanol surrogate was also componentchosen as the for mostpetrodiesel commonly fuels [3used9,40]. bioalcohol. Moreover, A thedditionally, thermophysical the properti propertieses of of1-butanol dodecane were are similar to the thermophysical properties of aviation kerosene [41]. For comparison, ethanol was also chosen as the most commonly used bioalcohol. Additionally, the properties of 1-butanol were

Energies 2019, 12, x FOR PEER REVIEW 15 of 21 compared with those of petrodiesel oil with sulfur content < 10 mg/kg which fulfilled norm EN 590 [12] (named ekodiesel ultra) and biodiesel composed of fatty acid methyl esters from rapeseed oil, which fulfilled norm EN 14214 [12]. Among studied fuel components, the density of 1-butanol at Energies 2020, 13, 5046 15 of 21 288.15Energies K 2019is the, 12, xclosest FOR PEER to REVIEW norm EN 590 for diesel and the most similar to the density of15 ofdiesel 21 oil ekodiesel ultra (see Figure 12). Moreover, the differences between the density of 1-butanol and ekodieselusedcompared bioalcohol. ultra with decrease those Additionally, of withpetrodiesel increasing the properties oil with pressure sulfur of 1-butanol content from were 2.8%< 10 comparedmg/kg at 0.1 whichMPa with tofulfilled those 1.9% of atnorm petrodiesel 100 EN MPa 590 and at [12] (named ekodiesel ultra) and biodiesel composed of fatty acid methyl esters from rapeseed oil, 298.15oil with K (see sulfur Figure content 13).< 10 mg/kg which fulfilled norm EN 590 [12] (named ekodiesel ultra) and biodieselwhich fulfilled composed norm of EN fatty 14214 acid methyl[12]. Among esters fromstudie rapeseedd fuel components, oil, which fulfilled the density norm of EN 1-butanol 14214 [12 at]. Among288.15 K studied is the fuelclosest components, to norm EN the 590 density for diesel of 1-butanol and the at most 288.15 similar K is theto the closest density to norm of diesel EN 590 oil forekodiesel diesel andultra the (see most Figure similar 12). to Moreover, the density the of dieseldifferences oil ekodiesel between ultra the (seedensity Figure of 121-butanol). Moreover, and theekodiesel differences ultra between decrease the with density increasing of 1-butanol pressure and from ekodiesel 2.8% ultraat 0.1 decrease MPa to with1.9% increasing at 100 MPa pressure and at from298.15 2.8% K (see at 0.1 Figure MPa 13). to 1.9% at 100 MPa and at 298.15 K (see Figure 13).

Figure 12. Comparison of the density at 288.15 K of heptane [36,37], dodecane [38], ethanol [36,37], 1-butanol (this work), ekodiesel ultra [12], biodiesel [12] with norm EN 590 for diesel and EN 14214 forFigureFigure biodiesel. 12.12. ComparisonComparison ofof thethe densitydensity atat 288.15288.15 KK ofof heptaneheptane [[36,37],36,37], dodecanedodecane [[38],38], ethanolethanol [[36,37],36,37], 1-butanol1-butanol (this(this work),work), ekodieselekodiesel ultraultra [[12],12], biodieselbiodiesel [[12]12] withwith normnorm ENEN 590590 forfor dieseldiesel andand ENEN 1421414214 forfor biodiesel. biodiesel.

Figure 13. The pressure dependence of density of heptane and dodecane—fuel components, Figureethanol—theFigure 13. 13. The The most pressurepressure common dependence used bioalcohol, ofof density density low sulfurof ofheptane dieselheptane oiland (ekodieseland dodecane—fuel dodecane—fuel ultra) and components, biodiesel components, ethanol—the(FAME)ethanol—the at 298.15 most most K. commoncommon used bioalcohol,bioalcohol, low low sulf sulfur urdiesel diesel oil (ekodieseloil (ekodiesel ultra) ultra) and biodiesel and biodiesel (FAME)(FAME) at at 298.15 298.15 K. K.

Energies 2019, 12, x FOR PEER REVIEW 16 of 21 Energies 2020, 13, 5046 16 of 21 The 1-butanol is less compressible than heptane by 43 ÷ 20% in the pressure range of 0.1 ÷ 100 MPa,The and 1-butanol ethanol is lessby 21 compressible ÷ 12% in the than pressure heptane range by 43 of20% 0.1 in÷ 90 the MPa pressure at 298.15 range K. of 0.1The 1-butanol100 MPa, is ÷ ÷ andmore ethanol compressible by 21 12% than in diesel the pressure by 18 ÷ 12% range and of biodiesel 0.1 90 MPaby 28 at ÷ 298.1517% in K. the The pressure 1-butanol range is moreof 0.1 ÷ ÷ ÷ compressible100 MPa at than 298.15 diesel K. byOn 18the other12% and hand, biodiesel the compre by 28ssibility17% in of the 1-butanol pressure is range close of to 0.1 dodecane,100 MPa and ÷ ÷ ÷ atfurthermore, 298.15 K. On thethe other differences hand, the between compressibility compressibi of 1-butanollity of 1-butanol is close to and dodecane, dodecane and furthermore,decrease with theincreasing diﬀerences pressure between from compressibility 1.5% at 0.1 MPa of 1-butanol to 0.5% at and 100 dodecane MPa and decrease at 298.15 with K (Figure increasing 14). pressure from 1.5% at 0.1 MPa to 0.5% at 100 MPa and at 298.15 K (Figure 14).

Figure 14. The pressure dependence of isentropic compressibility of heptane and dodecane—fuel Figure 14. The pressure dependence of isentropic compressibility of heptane and dodecane—fuel components, ethanol—the most common used bioalcohol, low sulfur diesel oil (ekodiesel ultra) and biodieselcomponents, (FAME) ethanol—the at 298.15 K. most common used bioalcohol, low sulfur diesel oil (ekodiesel ultra) and biodiesel (FAME) at 298.15 K. As in the case of isentropic compressibility, the isobaric thermal expansion of 1-butanol is lower than thoseAs in of heptanethe case byof 32isentropic15% in compressibility, the pressure range the ofisobaric 0.1 100 thermal MPa, andexpansion ethanol of 15 1-butanol12% in is ÷ ÷ ÷ thelower pressure than range those of of 0.1 heptane90 MPa by 32 at ÷ 298.15 15% in K. the The pressure isobaric range thermal of expansion0.1 ÷ 100 MPa, of 1-butanol and ethanol is higher 15 ÷ 12% ÷ thanin the those pressure of diesel range by 10 of 0.17% ÷ and 90 MPa biodiesel at 298.15 by 12 K. The5% inisobaric the pressure thermal range expansion of 0.1 of100 1-butanol MPa at is ÷ ÷ ÷ 298.15higher K. Onthan the those other of hand, diesel isobaric by 10 ÷ thermal 7% and expansion biodiesel ofby 1-butanol12 ÷ 5% in is the mostpressure similar range to dodecaneof 0.1 ÷ 100 andMPa likewise, at 298.15 the K. pressure On the dependence other hand, of isobaric isobaric ther thermalmal expansion expansion of of 1-butanol 1-butanol is is the the most most similar similar to tododecane the pressure and dependence likewise, the of pressure isobaric thermaldependence expansion of isobaric of dodecane thermal (Figureexpansion 15). of The 1-butanol differences is the betweenmost similar the expansivity to the pressure of 1-butanol dependence and dodecane of isobaric slightly thermal decrease expansion with of increasing dodecane pressure(Figure 15). from The 3.3%differences at 0.1 MPa between to 2.9% the at 100expansivity MPa and atof 298.151-butanol K. and dodecane slightly decrease with increasing pressureThe internal from 3.3% pressure at 0.1 MPa is related to 2.9% to at the100 solubilityMPa and at parameter 298.15 K. [42–48] and cohesive energy density [43,46,49]. According to the definition, the internal pressure reflects molecular interactions which determine the change of internal energy that accompanying a very small isothermal expansion of 1 mole of liquid. Therefore, the internal pressure should be affected mainly by dispersion, repulsion, and weak dipole–dipole interactions. Kartsev et al. [50–53] pointed out that the temperature dependence of internal pressure is sensitive to the structural organization and reflects the character of the interactions of not hydrogen-bonded, hydrogen-bonded with the spatial net of H-bonds and associated liquids. They showed that, at atmospheric pressure, the sign reversal of the temperature coefficient of the internal pressure from (∂pint/∂T)p > 0 to (∂pint/∂T)p< 0 is characteristic for primary linear alkanols. Our group found that the pressure coefficient of internal pressure (∂pint/∂p)Tis also sensitive to the structural organization of the molecular liquids like alcohols [20,54,55] as well as ionic liquids [56] and reflects the character of the interactions. The temperature and pressure dependence of the internal pressure of 1-butanol found in this work confirms the results obtained previously for 1-alkanols [20,54,55]. In the temperature and pressure ranges under investigation, the maximum of the pressure dependence of the internal pressure of 1-butanol was observed for each isotherm

Energies 2020, 13, 5046 17 of 21

(see Figure 16). With increasing temperature, the maximum moves toward higher pressures. Thus, the internal pressure first increases with increasing pressure and then it decreases. This was also observed for ethanol and for other 1-alkanols from 1-pentanol to 1-decanol [20,54,55]. The internal pressure of 1-butanol obtained by Safarov et al. [16] decreases with increasing pressure ((∂pint/∂p)T < 0) in the pressure range under investigation and at temperatures as in this work. Meanwhile, the internal pressure of 1-butanol obtained by Dávila et al. [17] increases with increasing pressure ((∂pint/∂p)T > 0) in the pressure range under investigation and at temperatures as in this work. Moreover, the results obtained in this work shows that with the increasing pressure, the temperature dependence of the internal pressure of 1-butanol changes from (∂pint/∂T)p < 0 to (∂pnt/∂T)p > 0. This reflects the crossing point of the isotherms of the internal pressure, which was observed for ethanol and for other 1-alkanols from 1-pentanol to 1-decanol [20,54,55]. Dávila et al. [17] also found the crossing point of internal pressure isotherms of 1-butanol. On the other hand, Safarov et al. [16] did not observe this effect; (∂pint/∂T)p > 0 in the whole pressure range. The inspection of literature data shows better internal coherence of pint(p,T) dependence obtained by the acoustic method than obtained by the densimetric method. In the case of the densimetric method, isobaric thermal expansion and isothermal compressibility are obtained by differentiation using their definitions acquired by Equations (4) and (6), respectively. Meanwhile, in the acoustic method, differentiation is needed only for the determination of isobaric thermal expansion (Equation (4)). The crossing point of the internal pressure isotherms was also observed for 2-methyl-2-butanol and 3-pentanol [54,55]. For 3-pentanol, the crossing point of each two neighbor isotherms shifts toward higher pressure with increasing temperature [54,55]. For 2-methyl-2-butanol, the crossing point of each two neighbor isotherms appears at temperatures higher than 303.15 K and it moves toward higher pressure with increasing temperature as in the case of 3-pentanol [55]. On the other hand, for 2-methyl-1-butanol, the crossing point is not observed, and the internal pressure increases with increasing temperature over the whole investigated temperature and Energies 2019, 12, x FOR PEER REVIEW 17 of 21 pressure range. However, the temperature dependence of the internal pressure of 2-methyl-1-butanol under atmospheric pressure indicates that the crossing point could appear at higher temperatures [55].

Figure 15. The pressure dependence of isobaric thermal expansion of heptane and dodecane—fuel Figurecomponents, 15. The ethanol—the pressure dependence most common of usedisobaric bioalcohol, thermal low expansion sulfur diesel of heptane oil (ekodiesel and ultra)dodecane—fuel and components,biodiesel (FAME) ethanol—the at 298.15 K.most common used bioalcohol, low sulfur diesel oil (ekodiesel ultra) and biodiesel (FAME) at 298.15 K.

The internal pressure is related to the solubility parameter [42–48] and cohesive energy density [43,46,49]. According to the definition, the internal pressure reflects molecular interactions which determine the change of internal energy that accompanying a very small isothermal expansion of 1 mole of liquid. Therefore, the internal pressure should be affected mainly by dispersion, repulsion, and weak dipole–dipole interactions. Kartsev et al. [50–53] pointed out that the temperature dependence of internal pressure is sensitive to the structural organization and reflects the character of the interactions of not hydrogen-bonded, hydrogen-bonded with the spatial net of H-bonds and associated liquids. They showed that, at atmospheric pressure, the sign reversal of the temperature coefficient of the internal pressure from (∂pint/∂T)p > 0 to (∂pint/∂T)p < 0 is characteristic for primary linear alkanols. Our group found that the pressure coefficient of internal pressure (∂pint/∂p)T is also sensitive to the structural organization of the molecular liquids like alcohols [20,54,55] as well as ionic liquids [56] and reflects the character of the interactions. The temperature and pressure dependence of the internal pressure of 1-butanol found in this work confirms the results obtained previously for 1-alkanols [20,54,55]. In the temperature and pressure ranges under investigation, the maximum of the pressure dependence of the internal pressure of 1-butanol was observed for each isotherm (see Figure 16). With increasing temperature, the maximum moves toward higher pressures. Thus, the internal pressure first increases with increasing pressure and then it decreases. This was also observed for ethanol and for other 1-alkanols from 1-pentanol to 1-decanol [20,54,55]. The internal pressure of 1-butanol obtained by Safarov et al. [16] decreases with increasing pressure ((∂pint/∂p)T < 0) in the pressure range under investigation and at temperatures as in this work. Meanwhile, the internal pressure of 1-butanol obtained by Dávila et al. [17] increases with increasing pressure ((∂pint/∂p)T > 0) in the pressure range under investigation and at temperatures as in this work. Moreover, the results obtained in this work shows that with the increasing pressure, the temperature dependence of the internal pressure of 1-butanol changes from (∂pint/∂T)p < 0 to (∂pnt/∂T)p > 0. This reflects the crossing point of the isotherms of the internal pressure, which was observed for ethanol and for other 1-alkanols from 1-pentanol to 1-decanol [20,54,55]. Dávila et al. [17] also found the crossing point of internal pressure isotherms of 1-butanol. On the other hand, Safarov et al. [16] did not observe this effect; (∂pint/∂T)p > 0 in the whole pressure range. The inspection of literature data shows better internal coherence of pint(p,T) dependence obtained by the acoustic method than obtained by the densimetric method. In the case of the densimetric method, isobaric thermal expansion and isothermal compressibility are obtained by differentiation using their definitions

Energies 2019, 12, x FOR PEER REVIEW 18 of 21 acquired by Equations (4) and (6), respectively. Meanwhile, in the acoustic method, differentiation is needed only for the determination of isobaric thermal expansion (Equation (4)). The crossing point of the internal pressure isotherms was also observed for 2-methyl-2-butanol and 3-pentanol [54,55]. For 3-pentanol, the crossing point of each two neighbor isotherms shifts toward higher pressure with increasing temperature [54,55]. For 2-methyl-2-butanol, the crossing point of each two neighbor isotherms appears at temperatures higher than 303.15 K and it moves toward higher pressure with increasing temperature as in the case of 3-pentanol [55]. On the other hand, for 2-methyl-1-butanol, the crossing point is not observed, and the internal pressure increases with increasing temperature over the whole investigated temperature and pressure range. However, the temperature dependence of the internal pressure of 2-methyl-1-butanol under atmospheric pressure indicates that the crossing point could appear at higher temperatures [55]. Energies 2020, 13, 5046 18 of 21

Figure 16. The pressure dependence of internal pressure of 1-butanol obtained in this work. Figure 16. The pressure dependence of internal pressure of 1-butanol obtained in this work. 4. Summary 4. SummaryThe speed of sound in 1-butanol was conducted in the temperature range from (293 to 318) K and at pressures up to 101 MPa. The density of the liquid under test was measured within the temperatures The speed of sound in 1-butanol was conducted in the temperature range from (293 to 318) K from (293 to 318) K under atmospheric pressure. From the experimental results, the pressure and and at pressures up to 101 MPa. The density of the liquid under test was measured within the temperature dependence of the density, isobaric heat capacity and related thermodynamic properties temperaturessuch as isentropic from and (293 isothermal to 318) compressibilities, K under atmospheri the isobaricc pressure. thermal expansionFrom the andexperimental internal pressure results, the pressureas a function and of temperature temperature and dependence pressure were of determined the density, using theisobaric acoustic heat method. capacity The obtained and related thermodynamicresults show that properties the density such of 1-butanol as isentropic is close and to norm isothermal EN 590for compressibilities, diesel oil and, as athe consequence, isobaric thermal expansionis close to and the densityinternal of pressure ekodiesel as ultra. a function The isobaric of temperature expansivity and isentropicpressure compressibilitywere determined of using the1-butanol acoustic are method. close to The those obtained of dodecane—a results show surrogate that component the density for of petrodiesel 1-butanol fuelsis close and to aviation norm EN 590 forkerosene. diesel Theoil temperatureand, as a andconsequence, pressure dependence is close ofto the the internal density pressure, of ekodiesel obtained byultra. the acoustic The isobaric expansivitymethod, qualitatively and isentropic conﬁrms compressibility similarities and of dissimilarities 1-butanol are of 1-butanol,close to those other of 1-alkanols dodecane—a as well surrogate as component2-methyl-2-butanol for petrodiesel and 3-pentanol. fuels and Discrepancies aviation kero in thesene. sign The of (∂ ptemperatureint/∂T)p and (∂ andpint/ ∂pressurep)T were founddependence for 1-butanol obtained by the acoustic method and densimetric method. Thus, the determination of of the internal pressure, obtained by the acoustic method, qualitatively confirms similarities and internal pressure as a function of temperature and pressure is still an open, complex issue. dissimilarities of 1-butanol, other 1-alkanols as well as 2-methyl-2-butanol and 3-pentanol. DiscrepanciesAuthor Contributions: in the M.D.sign conceived of (∂pint and/∂T designed)p and the(∂p research,int/∂p)T conductedwere found the experimental for 1-buta research,nol obtained analyzed by the acousticthe data, method wrote the and manuscript. densimetric All authors method. have readThus, and the agreed determination to the published of versioninternal of thepressure manuscript. as a function ofFunding: temperatureThe work and was pressure ﬁnanced is by still a statutory an open, activity complex subsidy issue. from the Polish Ministry of Science and Higher Education for the Institute of Chemistry of University of Silesia in Katowice.

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