A new thermogravimetric application for determination of vapour pressure curve corresponding to average boiling points of oil fractions with narrow boiling ranges

Thermochimica Acta 683 (2020) 178468

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A new thermogravimetric application for determination of vapour pressure curve corresponding to average boiling points of oil fractions with narrow boiling ranges

T

Rivo Rannaveski, Vahur Oja* Department of Energy Technology, Tallinn University of Technology, Tallinn, 19086, Estonia

ARTICLE INFO

ABSTRACT

Keywords: Oil Narrow boiling range fraction Pseudocomponent Average boiling point Pressure dependence of the average boiling points

The average boiling point of oil fractions with narrow boiling ranges or pseudo-components is an important parameter in thermodynamic calculations in the fields of process design and environmental protection. The present work provides an experimental approach, involving a method based on the thermogravimetric analysis, for determination of the pressure dependence of average boiling points (or in other words for determination of “the vapour pressure curve corresponding to average boiling points”) of oil fractions with narrow boiling ranges, pre-prepared by distillation. This method can be used for determination of the atmospheric average boiling points (corresponding to atmospheric pressure) of thermally unstable fractions from the pressure dependence curves, obtained from the tests conducted at lower pressures. The method uses the principle of ASTM E1782 “Standard Test Method for Determining Vapor Pressure by Thermal Analysis”, where the material is vaporised at pre-determined pressure from a hermetically sealed capsule through a pinhole using a constant heating rate experiment. The accuracy of the method was evaluated on the basis of the average boiling point values of narrow boiling ranges fractions determined by rectification both at atmospheric pressure and in vacuum (determined as the arithmetic mean of the lower and upper temperature limits of the fraction). The pressure dependence curves of the average boiling points, formed here on the basis of average boiling points obtained in the pressure range from 5 kPa to atmospheric pressure, can be reliably described by the integrated Clausius-Clapeyron equation. To increase the accuracy in determining the atmospheric average boiling points of thermally unstable fractions, obtained in extrapolation from the Clausius-Clapeyron curve of the average boiling points in the tests conducted at lower pressures, a higher number of tests, on the basis of which to conduct the extrapolation, is desirable.

1. Introduction In the case of the next-generation oils, which become more complex, containing increasingly more heavy and polar compounds, including those having hydrogen bonding ability, the accuracy of application of the existing crude oil-based thermodynamic calculation models and correlations for process design and environmental protection is questionable without the test data-based checking [1–4]. Unlike pure substances or their well-defined mixtures, oils are complex mixtures of organic compounds with many different chemical structures and their molecular composition is quite complex [5,6]. In terms of thermodynamic calculations one way to simplify the calculations is to divide the oil into fractions with narrow boiling ranges (or pseudo-components) by distillation [3,7]. These pseudo-components can be described by mean parameters, such as molecular weight, density, the average

⁎

boiling point at atmospheric pressure [3,7–9]. Or in other words, the "pseudo" conception is a simplification on the assumption that a fraction with narrow boiling range behaves like a single substance characterized by mean parameters. Whereas, the average boiling point corresponding to atmospheric pressure is one of the most important parameters for calculating other thermodynamic and physical-chemical properties [3,7–9]. The average boiling point of continuous multicomponent mixture, such as oils or oil fractions, can be defined (formal definition) as n

Tb =

Tbi x i i=1

(1)

where Tb can be either a mass-averaged, volume-averaged or molaraveraged boiling point of the mixture, xi can be either a mass, a volume or a molar fraction of the component i in the mixture, respectively, and

Corresponding author. E-mail address: [email protected] (V. Oja).

https://doi.org/10.1016/j.tca.2019.178468 Received 14 August 2019; Received in revised form 21 November 2019; Accepted 22 November 2019 Available online 23 November 2019 0040-6031/ © 2019 Elsevier B.V. All rights reserved.

Thermochimica Acta 683 (2020) 178468

R. Rannaveski and V. Oja

Tbi is the boiling point of the component i. Depending on the parameters (thermodynamic properties) being calculated, different average boiling points (mass-averaged, volume-averaged, molar-averaged, etc.) are used for calculations [7,8,10]. In the case of mixtures with wide boiling ranges, the average boiling point is found from a classic distillation curve (where the mixture is conditionally divided into fractions with narrow boiling ranges or pseudo-components), and the volume-averaged boiling point is obtained. The obtained volume-averaged boiling point can be transformed into other types of average boiling points by means of empirical equations. In the case of fractions with narrow boiling ranges (or pseudo-components), on the assumption that the distribution of the boiling points of the components in the mixture is similar to the Gaussian distribution, the average boiling points of different types are practically equal [11]. The average boiling point of narrow boiling range fraction has been traditionally determined as the arithmetic mean of the initial and the final boiling points (more precisely, condensing temperature) of the fraction (distillation cuts) separated by distillation (derivable from the Eq. (1), provided that the fraction consists of two components which are in equal quantities). Historically, the most accurate method for determining the average boiling points has been the rectification according to the standard ASTM D2892. However, the full atmospheric rectification of thermally unstable samples is impossible due to their thermal decomposition, starting at a certain temperature. In order to avoid the thermal decomposition, the distillation can be carried out also in vacuum (ASTM D1160 or D5236). To obtain atmospheric boiling points, the results obtained at the sub-atmospheric pressure should be transformed into the results corresponding to atmospheric pressure. In principle, the relationship between the average boiling points at different pressures Tb = f(P), or the hypothetical vapour pressure curve P = f(Tb) is needed for this [7,12–15]. Although an average boiling point is not a “straightforward” physical property, but a definition based calculated thermodynamic parameter for applied purposes according to Eq. (1), still the average boiling point of the mixture depends on the components contained therein, on their boiling points affected by the mutual forces of the molecules. Thus, the relationships between the average boiling points at different pressures are different for oils with different compositions. As mentioned above, the next-generation oils from alternative sources become more complicated, containing increasingly more heavy compounds or more polar compounds, including those having hydrogen bonding ability [1–4]. While atmospheric average boiling points of the oil fractions with low boiling points are measurable (for example via rectification), the measurements of average boiling points of the oil fractions with high boiling points (more than 350−400 °C) have been limited by the constraints of analytical capability. The purpose of the present work was to develop a thermal analysis based experimental approach for determination of atmospheric average boiling points for pre-prepared narrow boiling range fractions, which are thermally unstable at their boiling point temperatures at atmospheric pressure (the fractions with high average boiling points, received by vacuum distillation). The hypothesis of the work was that the average boiling point corresponding to atmospheric pressure can be determined by extrapolation from the curves of average boiling points obtained from the tests at sub-atmospheric pressures. The development of the experimental approach for obtaining the curve corresponding to average boiling points at different pressures was based on two earlier works carried out in this laboratory: (1) “A new method for determining average boiling points of oils using a thermogravimetric analyzer” [16]; (2) “Extension of the DSC method to measuring of vapour pressures of narrow boiling range oil cuts” [17]. Both these works were based on the principle of ASTM E1782 “Standard Test Method for Determining Vapor Pressure by Thermal Analysis”. ASTM E1782 establishes a procedure for determination of the vapour pressure of pure substances by thermal analysis, which consist in vaporisation of the substance from a hermetically sealed crucible through a pinhole at constant heating rate and

at pre-determined pressure. The more detailed description of the standard can be found in [18]. Thus, the standardised method is for measuring the vapour pressure curves for pure substances [19]. The set of references for the use of the ASTM E 1782 method for the measurement of vapour pressure of pure compounds and binary systems (application not standardized) is as follows: until 2014 in the summary of article [17] and later articles [20–24]. Most of these articles use the differential scanning calorimeter (DSC) and only few are based on the thermogravimetric analyzer (TG) [25–27]. In the above mentioned earlier works of our laboratory we have demonstrated that this principle (vaporisation of the substance from a hermetically sealed crucible through a pinhole) can be also used for measuring the vaporisation parameters of oil fractions with narrow boiling ranges (the vapour pressure curve, but also the average atmospheric boiling point). The present work presents the further development of application of this principle, which should enable to determine the average boiling points of oil fractions with narrow boiling ranges (Tb) at different pressures (P) and from this to derive the relationship Tb = f(P), which is a conditional vapour pressure curve corresponding to average boiling points. The application benefit lies in the fact that the method would enable to measure the pressure dependence curve of average boiling points of the pre-prepared narrow boiling range fraction, using quite small quantities of substance (below 200 mg) and would be independent of the oil composition. 2. Materials and methods 2.1. Materials Oil fractions with narrow boiling ranges (or oil distillation cuts) obtained by distillation of oils were used in the experiments carried out in this work. Technical fractions produced from kukersite oil shale by the industrial Galoter process [28–30] (with indicative boiling ranges from 170 °C up to 465 °C) and winter diesel fuel were used as initial oils. Fractionation of the initial oils into fractions with narrow boiling ranges was carried out both by simple distillation in vacuum and by rectifications at atmospheric pressure, as well as in vacuum. The fractions were collected using the temperature collection intervals of up to 15 °C. Rectification at atmospheric pressure was carried out according to the standard ASTM D2892 [31]. Simple distillation was carried out in vacuum according to the standard ASTM D1160 [32]. The more detailed description of distillation equipment and procedures is presented in earlier articles [33,34]. All fractions were collected at condensing temperatures below 300 °C (experience-based temperature [35]) to avoid thermal decomposition of the samples affecting the measurements of this work (to influence the monotonic increase in condensing temperatures during fraction collection and thus the accuracy/reliability of the determination of the average boiling point by rectification). 2.2. Thermogravimetry for measuring the average boiling points Thermogravimetric measurements were performed with Du Pont Instruments 951 Thermogravimetric Analyzer, with the measurement sensitivity of 1 μg. The description of instruments and the descriptions of the test parameters and capsules are presented in [16]. In brief, hermetically sealable aluminium crucibles with the volume of 160 μl and with lids having apertures of 50 μm, were used in the tests. The quantity of samples varied between 5−20 mg, whereby smaller sample quantities were used at lower pressures than at higher pressures (similarly to DSC-based measurements of vapour pressures in [17,19,20]). The tests were carried out in the pressure ranges of 1 kPa to 100 kPa and the applied heating rate was 10 °C/min. A variable speed vacuum pump Vacuubrand PC3001 Vario and a secondary measuring instrument CVC 3000 were used to keep reduced pressure. The pressure was measured with Vacuubrand VSP 3000 pressure sensor (with the precision 0.1 kPa, checked by MKS Baratron Type 626B with the precision of 2

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R. Rannaveski and V. Oja

0.25 % of the reading). The vacuum system (the vacuum pump and the pressure sensor) was separated from TGA by a U-tube condenser at the temperature of −45 °C. The pressure loss, occurring with a 50 cm long piping, separating the vacuum sensor from the TGA, did not influence the accuracy of the pressure measurement. The temperature was measured with a K-type thermocouple at the distance of a couple of millimetres from the aluminium crucible, giving the accuracy of the temperature measurement better than ± 2 °C [16]. The temperature measurement system itself (the K-type thermocouple and the secondary measurement instrument) was calibrated with the accuracy of 0.2 °C using Omega Dry Block Calibrator CL-780A. The average boiling points of the fractions with narrow boiling ranges were calculated from the TGA measurements according to the procedure presented in the section "The methods of calculation of an average boiling point". Prior to the calculations, the shape of the differential thermogram was evaluated for experimental artefacts and signs of thermal degradation (signs of unusual shape or unexplained deviation). In case of further doubt, more precise, but time-consuming, approaches can be used to assess degradation effects by changing the test conditions [36]. For assessment of the method, the fractions prepared by means of rectification at the pre-determined pressure were measured by TGA at the same pressure (the preparation procedure is described in the following section), and then the average boiling points obtained were compared with the average boiling points, determined during the rectification (Tb,rect.).

point directly from the mass loss curve would give a value somewhere above 10 degrees of the actual value. In order to convert the vaporization temperature based curve to condensing temperature based curve at the same mass loss conditions the following simplified equation (performance verified with more than 20 narrow boiling range fractions) was used [16]: (2)

T = T1 x1 + T2 x2

where T is the measured temperature, the product T1x1 is the contribution of the vaporized part (consisting of the mass fraction x1 of the vaporized part on the total mass bases and the boiling point T1 of the vaporized part) and the product T2x2 is the contribution of the remaining part (consisting of the mass fraction x2 of the remaining part on the total mass bases and the boiling point T2 of remaining part, here the temperature measured at the next measuring point). The boiling point of the vaporized part T1 (corresponding to Tbi in the Eq. (1)) can then be calculated from this equation. By means of the obtained condensing temperatures (not including initial negative values, corresponding to the pre-boiling range with non-physical content) the weight-average boiling point (Tb) with the Eq. (1) can be calculated. 3. Results and discussion 3.1. Measuring the “vapour pressure curve”, corresponding to average boiling points (or the pressure dependence of the average boiling points) The present work was based on the hypothesis that the test methodology for determination of the average boiling points at atmospheric pressure (the tests are conducted at atmospheric pressure), described in an earlier article by our research team, can be used also for measurement of the average boiling points of pre-prepared fractions with narrow boiling ranges, corresponding to sub-atmospheric pressures. After that, the pressure dependence curve for the average boiling points can be constructed from the test data obtained at different pressures, similarly to the true vapour pressure curves for pure substances or the fractions themselves. The suitability of the methodology for the determination of atmospheric average boiling points was presented in earlier articles [16,34]. It was shown in the article [16] that the accuracy of the TGA method, using 20 oil fractions with narrow boiling ranges for determination of the mean boiling points at atmospheric pressure was of ± 1.9 °C (absolute average deviation). Table 1 illustrates the suitability of the method for measuring the average boiling points of the pre-prepared fractions with narrow boiling ranges, corresponding to sub-atmospheric pressures. Table 1 compares

2.3. The rectification procedure for obtaining reference data of the average boiling points The fractions with the average boiling points’ values corresponding to atmospheric pressure (103.0 ± 0.2 kPa) and sub-atmospheric pressures (39 ± 0.1 kPa and 69.2 ± 0.1 kPa) were collected by rectifications carried out at these pressures. Rectification at atmospheric pressure was carried out according to the standard ASTM D2892 [31]. The average boiling points corresponding to rectification pressures were calculated as arithmetic means of initial and final collecting temperatures of the fractions with narrow boiling ranges (as arithmetic means of temperatures measured in the condenser). A packed Vigreux column (4.2 theoretical plates) and the reflux ratio of at least 6:1 were used for rectification. An oil vacuum pump was used to get the vacuum. The pressure was measured with a MKS Baratron Type 626B with the precision of 0.25 % of the reading. The condensing temperature for the fractions was measured with a mercury thermometer (accuracy ± 0.5 °C). 2.4. The methodology for calculating the average boiling point

Table 1 The comparison between the average boiling points of the oil fractions, determined by vacuum rectification (Tb,rect) at the pressures of 39 and 69.2 kPa and the average boiling points, determined by the thermal analysis (Tb). Tinit and Tfin correspond to initial and the final boiling points (more precisely, condensing temperature) of the fraction (distillation cuts) separated by distillation.

The methodology for the measurement and calculation of the average boiling point on the basis of the results of thermogravimetric analysis carried out at atmospheric pressure was presented in the previous article of our research team [16]. In brief, under conditions when the vapour pressure of the mixture exiting the capsule is equal to the external pressure, the differential mass loss curve obtained from heating the sample (here the narrow boiling range fraction) corresponds to the curve of the boiling point (curve of the vaporisation temperatures) in regard to the progressively diminishing sample. This means that the mass loss measured by TGA occurs at a temperature equal to the boiling point of the remaining oil. At the same time the average boiling point for the fraction obtained by distillation is calculated on the basis of condensing temperatures of vaporized species (as the arithmetic mean of the initial and the final condensing temperatures of the fraction collected during the distillation – provided that the fraction consists of two components of the same amount, one having a boiling point equal to the initial temperature and the other having equal to the final temperature). Therefore, using the Eq. (1) to calculate the average boiling

Fraction

Rectification P, kPa

1 2 3 4 5 6 a b c

3

39 39.1 39 69.1 69.2 69.3

a

Tinit, oC 96 111 116 130 140 146

TGA b

Tfin, oC 111 116 121 140 146 150

Standard uncertainty of 0.1 kPa. Standard uncertainty of 0.5 °C. Standard uncertainty of 0.9 °C.

b

Trect -Tb c

Tb,rect, oC

Tb, oC

103.5 113.5 118.5 135 143 148

104 112 118.7 133.1 139.4 146.6 Abs. Av. Dev.

ΔT, oC −0.5 1.5 −0.2 1.9 3.6 1.4 1.5

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Table 2 The average boiling points determined by the thermal analysis based method in the pressure range from 1 kPa to atmospheric pressure. Fraction 13 P, kPa 103.6 50 35 27.5 20 15 10 7.5 5

a

Fraction 18

Fraction 19

Fraction 21

Tb, oCb

P, kPaa

Tb, oCb

P, kPaa

Tb, oCb

P, kPaa

Tb, oCb

237.0 207.2 195.5 166.8 177.0 159.6 156.9 152.5 138.1

103.5 50 35 27.5 20* 15 10 5 2.5 1

275.9 247.4 235.8 225.2 215.5 209.1 194.5 178.1 162.8 151.7

103.6 80 70 60 50 35 20 15 10** 9 8.5 8 7 6 5

285.2 271.6 268.4 262.4 252.4 241.1 221.2 214.9 200.4 198.6 195.8 196.6 190.9 191.0 182.4

103.5 50 35 27.5 20 17.5 15 12.5 10 7.5 5 2.5

291.6 262.5 248.2 238.7 230.5 226.1 222.2 215.3 211.5 202.2 192.0 180.7

Fig. 1. Distribution curves for boiling point of fractions 13, 18, 19 and 21, measured by thermogravimetry at atmospheric pressure. The thermograms are regarding the progressively diminishing sample in the aluminium crucible (normalized to the same height).

The atmospheric average boiling points obtained from the atmospheric rectification of these fractions are 239.5, 276.9, 285.0, 288.6 °C, respectively. * Average of 3 measurements. ** Average of 5 measurements. a Standard uncertainty of 0.1 kPa. b Standard uncertainty of 0.9 °C.

the average boiling points of the oil fractions with narrow boiling ranges (expressed as the arithmetic means of the initial and the final boiling points of the fractions, separated by distillation), determined during vacuum rectification (at the pressure of 39.0 ± 0.1 kPa and 69.2 ± 0.1 kPa), and the average boiling points, determined later using TGA method under the same pressure conditions. Diesel fuel was used as the initial oil, during the rectification of which 3 consecutive fractions with narrow boiling ranges were collected at each pressure. It is apparent from the Table 1 that the proposed TGA-based method can be used for determination of the boiling points of the pre-prepared narrow fractions also in the conditions of sub-atmospheric pressure with the accuracy of ± 2 °C. Slightly smaller sample weights were used for conducting the TGA tests at sub-atmospheric pressure (5−8 mg compared to 10−20 mg at atmospheric pressure). Note that such use of reduced sample weights at sub-atmospheric pressure can generally be seen at the practical applications of ASTM E1782 with lids having pinholes of 50 μm [17,19,20,33]. Table 2 presents the average boiling points measured at different pressures using the TGA method. The data are given for four fractions with narrow boiling ranges, pre-prepared during a rectification at atmospheric pressure (according to ASTM D2892). The middle oil technical fraction of the Kukersite shale oil was used to produce these narrow boiling range fractions. Fraction 13 has the rectification based average atmospheric boiling point of 239.5 °C (collected in the temperature range of 235.1–243.9 °C). Fractions 18 and 19 are consecutive fractions with the atmospheric average boiling points of 276.9 °C and 282.0 °C (collected in the temperature ranges of 274.1–279.7 °C and 297.7-284.3 °C, respectively). Fraction 21 is the next fraction after that one with the atmospheric average boiling point of 288.6 °C (collected in the temperature range of 287.0–290.2 °C). The comparative indicative distributions of the boiling ranges for these fractions (thermograms of this TGA method) are illustrated in Fig. 1. The Fig. 1 shows that although the average boiling points of nearby fractions at atmospheric pressure (peaks of the thermogram) are clearly distinctive from each other, the boiling ranges of these fractions are widely overlapping. Data of Table 2 (the average boiling points, measured in the pressure range of 1 kPa to 100 kPa by the TGA method) are illustrated graphically in Fig. 2 as a typical logarithmic curve for the vapour pressure. Fig. 2 shows that the conditional “vapour pressure curves”, corresponding to

Fig. 2. Pressure dependences of the average boiling points of the fractions 13, 18, 19 and 21 in the graph ln P vs 1/Tb. The lines are the integrated ClausiusClapeyron equation fits in the pressure range from 5 kPa to atmospheric pressure.

the average boiling points from Table 2, can be described by the integrated Clausius-Clapeyron equation:

ln P = A +

B T

(3)

where P is the vapour pressure in Pa (here the pressure P, at which the average boiling point was determined), T is the temperature in K (here the average boiling point Tb corresponding to the pressure P), R is the ideal gas constant, and A and B are the constants in the Clausius-Clapeyron equation (B is related to the conditional enthalpy of vaporisation corresponding to the pressure dependence of the average boiling point; A is related to the conditional entropy of vaporisation corresponding to the pressure dependence of the average boiling point). Note that like the vapour pressure of a pure component, also the vapour pressure of an oil fraction with a narrow boiling range, vary over a wide temperature range, and the temperature dependence of vapour pressure (P = f(T)) has an exponential form. While the measurement results for vapour pressures of pure substances are described by different empirical equations (from the simplest Clausius-Clapeyron equation with two constants to equations with three or more constants, depending on the width of the temperature range), then in the case of oil fractions mainly an application of Clausius-Clapeyron equation, to describe the vapour pressure curves, can be found [37–44]. It is apparent from Fig. 2 that the results of the fractions with narrow boiling ranges can be described by the integrated ClausiusClapeyron equation, or the relationship lnP vs 1/Tb is clearly with 4

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enthalpy of vaporisation, the coefficient A related to the entropy of vaporisation, the regression coefficient R2, the atmospheric average boiling point and its difference from the average boiling point determined by the atmospheric rectification), which are calculated from the measurements made above the 5 kPa of pressure value. The values in Table 4 show the following: (1) The regression coefficients R2 have high values (0.995-0.998), but somewhat poorer than the ones of the DCS-based typical measurements (extension of the ASTM E1782 to narrow boiling range cuts of oils) of vapour pressures for the oil fractions with narrow boiling ranges (R2 are better than 0.998) [17,33]. Note that while during the measurement of the vapour pressure in the case of ASTM E1782 the temperature is determined directly from the thermogram as the onset of the peak, then at determining the average boiling points, however, a recalculation of the thermogram peak is done according to the section “The procedure for calculating the average boiling point”. Such additional recalculation operation causes higher divergence of results. (2) The slope B (or the term corresponding to the enthalpy of vaporisation) increases together with the increase of the average boiling point, as could be assumed on the basis of the behavioural tendency of the enthalpy of vaporisation. Likewise, the terms corresponding to the enthalpy of vaporisation are clearly distinguishable in the case of close fractions 18 and 19. (3) The initial ordinate A (or the term corresponding to the entropy of vaporisation) also shows the expected behavioural tendency – increasing together with the mean boiling points. The slight deviation of fractions 18 and 19 from this general tendency (increase of the entropy of vaporisation together with the average boiling points) has no major significance, because the term of entropy is with higher divergence, as a rule, also in the case of measurements of vapour pressures of oil fractions.

Fig. 3. Pressure dependences of the average boiling points of the consecutive fractions 18 (solid points) and 19 (open points) in the graph ln P vs 1/Tb with expanded measurement uncertainties (fraction 18 – dashed lines; fraction 19 – dotted lines). Table 3 The results of repeated thermogravimetric measurements for the fractions 18 at pressure 20 kPa and the fraction 19 at pressure 10 kPa. Fraction 18 P, kPa

Fraction 19

a

o

a

T, oC

T, C

P, kPa

20 20 20

215.6 214.9 215.8

Average temperature, oC Standard deviation, oC

215.5 0.5

10 10 10 10 10 Average temperature, oC Standard deviation, oC

a

200.8 200.5 200.3 198.8 201.4 200.4 0.9

3.2. Applicability of the method for the determination of atmospheric average boiling points of thermally unstable fractions The practical purpose of the present work was to assess the applicability of the TGA method for the determination of the average boiling points of the thermally unstable fractions within the boiling ranges at atmospheric pressure from the results of the tests conducted at sub-atmospheric pressure (or from the curve based on the results). The hypothesis was that by using the curve, obtained at sub-atmospheric pressures, the average boiling point at atmospheric pressure could be determined by extrapolating from the range of measuring points. For assessment of the capability of extrapolation, the extrapolation was tested in the different pressure ranges, using the test data presented in Table 2. Table 5 aggregates the extrapolation data from four pressure ranges (5−15 kPa, 5−20 kPa, 5−35 kPa, 5–50 kPa). The selection of the pressure ranges was based on the consideration that the application scope would be to determine as precisely as possible the boiling points for the fractions, degrading in the boiling ranges at atmospheric pressure, or at the temperatures over 350 °C. Therefore, the lowest measurable pressure, 5 kPa was selected for the beginning of the pressure range being extrapolated. Table 5 shows that the values of the average boiling points at atmospheric pressure, extrapolated from the lower pressure range coincide well with the values of the actual average boiling points, determined by the results of rectification. The maximum difference between the extrapolated average boiling point and the

Standard deviation of 0.1 kPa.

linear dependence above 5 kPa. The mean boiling points obtained at lower pressures (about 5 kPa and below) do not fall on the straight line in the graph lnP vs 1/Tb under the current conditions of the test parameters. However, the studies of the measurements of the vapour pressures of pure substances according to ASTM E1782 give a reason to guess that the 5 kPa limit could be lowered by using different test parameters (heating rate, sample weight) or pans with wider opening (as recommended from 2014 in ASTM E1782-14, in the latest version of the standard). Another important information in Fig. 2 is that the close fractions 18 and 19 are clearly distinguishable. In order to bring it out better, the fractions 18 and 19 together with the measurement uncertainties are comparatively presented in Fig. 3. The measurement uncertainties shown in Fig. 3 (dotted lines), which are calculated on the basis of the results presented in Table 3 are obtained from the repeated measurements of the fraction 19 at the pressure of 10 kPa (rectification fraction with the mean boiling point Tb,rect of 282 °C). From five repeated measurement of the fraction 19 at the pressure of 10 kPa the standard deviation was 0.94 °C. Table 4 presents the Clausius-Clapeyron equation-based parameters of the fractions 13, 18, 19 and 21 (the coefficient B related to the

Table 4 The parameters based on the Clausius-Clapeyron equation for fractions 13, 18, 19 and 21. Fraction

A

13 18 19 21

17.577 18.394 18.290 19.208

B ± ± ± ±

0.318 0.342 0.208 0.225

6579.521 7534.139 7588.072 8169.933

± ± ± ±

143.361 167.987 102.005 113.105

5

R2

Tb, C

Tb,rect, oC

ΔT, oC

0.9976 0.9955 0.9969 0.9983

238.1 275.9 285.2 291.6

239.5 276.9 285.0 288.6

1.4 1 −0.2 −3

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Table 5 The comparison between the accuracies of atmospheric boiling points determined by rectification (Tb,rect) and those extrapolated (Tb,extr) from different under pressure ranges (data measured by the thermogravimetric method). Pressure range

5-50 kPa 5−35 kPa 5−20 kPa 5−15 kPa

Difference between Tb,rect and Tb,extr Fraction 13

Fraction 18

Fraction 19

Fraction 21

6.5 6.5 8.8 1.5

4.8 5.3 6.5 5

3.9 2.7 4.1 2.1

2.8 4.6 5.2 4.9

measured average boiling point is 8.8 °C and the average difference is 4.6 °C. In the case of the fraction 19 that had a great number of measurements done, the average difference was 3.2 °C and the maximum difference was 4.1 °C. In general the Tb,extr obtained by extrapolation is the more precise, the more points are used for the extrapolation, but also the more extensive (to higher pressure) range has been selected. As the behaviour of the vapour pressure for the given samples in the graph lnP = f(1/T) is relatively linear in the range from the under pressure to atmospheric pressure (Figs. 2 and 3), the selection of only lower pressure range points for extrapolation, the differences between the calculated and the test boiling points do not significantly differ from the results, obtained by extrapolation from the wider pressure range. The accuracy of the results is more influenced by the number of points used for the extrapolation. If a smaller number of test points are used for the extrapolation (irrespective of the width of the pressure range), then the accuracy of the measurement results will become essential. At the same time it is known that vapour pressure curves in the graph lnP = f(1/T) are generally somewhat non-linear in wide temperature ranges, therefore, the extrapolated results may be slightly lower than the actual average boiling point values (or the TGA-based measurements at atmospheric pressure) in Table 5. In Fig. 4 an illustrated example is given for extrapolation application for determining the average atmospheric boiling points of the narrow boiling range fraction with the high boiling point (Tb > 450 °C, at atmospheric pressure), received by vacuum distillation from the middle oil technical fraction of Kukersite shale oil. In Fig. 4 the average boiling point at atmospheric pressure, determined by the TGA method (the open point) at atmospheric pressure, is compared with the results of extrapolation (the solid rhomb) from measurements at the pressures of 5, 7.5, 10, 12.5 and 15 kPa (the solid circles). Fig. 5 shows the measurement thermograms at four pressures (atmospheric pressure, 5 kPa, 10 kPa and 15 kPa) for explanation. At atmospheric pressure, a strong deterioration of the sample can be observed (a gradual mass loss, where the mass loss

Fig. 5. Thermograms for the oil fraction with the high boiling point (normalized to the sample mass), pre-prepared by vacuum distillation, at four different pressures: 5 kPa, 10 kPa, 15 kPa and atmospheric pressure.

rate of the sample changes abruptly), and due to the deterioration, the distinctive peak of the differential curve disappears during the measurements. The differential mass loss curves of the same sample at subatmospheric pressure also show some deterioration of the sample at the temperatures over 300 °C, but its effect on the shape of the curve is significantly less and the received mass loss curve corresponds better to the expected distribution of the boiling point. It is apparent from Fig. 4 that the average boiling points, determined at sub-atmospheric pressures fall on the straight line (R2 = 0.9996) in the graph lnP = f(1/T), but the average boiling point determined at atmospheric pressure lies away from this straight line. As the compounds with higher boiling points decompose into the compounds with lower boiling points, it can be assumed that the average boiling point of the sample decreases during the deterioration. The previous tests with the fractions received by rectification (Figs. 2 and 3) showed that if practically no sample deterioration occurs during the measurements, the measurements done at atmospheric pressure will fall on the same line with the measurements, done at sub-atmospheric pressure. Thus, the experimental average boiling point, determined for the fraction, received at vacuum distillation using TGA at atmospheric pressure, is too low (the measured Tb at atmospheric pressure lies lower than the extrapolated curve Tb). The average boiling point, determined by extrapolation from the given pressure range (from 5 kPa to 15 kPa) was 454.5 °C, which is 28 °C higher than the one determined at atmospheric pressure. 4. Conclusions The application of the thermogravimetric method for determination of the average boiling points of the fractions with narrow boiling ranges, pre-prepared by distillation at different pressures, was studied in the framework of the present research. The purpose of application of the work was to develop a novel way for the determination of the average atmospheric boiling points for thermally unstable fractions, pre-prepared by vacuum distillation. The test results showed that the relationship between the pressures and the average boiling points corresponding to these pressures (the pressure dependence of the average boiling points) in the pressure ranges from 5 kPa to atmospheric pressure can be described by the ClausiusClapeyron equation, which expresses a linear dependence between the logarithm of vapour pressure and the reciprocal value of the temperature. The average boiling points obtained at lower pressures than 5 kPa deviated from the behaviour described by the Clausius-Clapeyron equation. Under different test conditions (capsules of different capacity, different size of opening in the lid, different heating rates) it may be possible to determine the average boiling points also below 5 kPa [17]. The analysis of the results showed that the average boiling point at atmospheric pressure for the fraction with a narrow boiling range can

Fig. 4. The average atmospheric boiling points for the oil fraction with the high boiling point (prepared by vacuum distillation) measured by the TGA method directly at atmospheric pressure (measured atmospheric Tb) and extrapolated from sub-atmospheric pressure boiling points (extrapolated atmospheric Tb). 6

Thermochimica Acta 683 (2020) 178468

R. Rannaveski and V. Oja

be determined by extrapolation of the average boiling points determined in vacuum, using the Clausius-Clapeyron equation. The present work compared the extrapolated average boiling points to the values determined during the rectification that resulted in the mean error of 4.6 °C and the maximum error of 8.8 °C. The accuracy depends on the number of test points and on the temperature/pressure ranges. As a result of the work, a novel approach was presented for the experimental determination of the pressure dependences of the average boiling points of pre-prepared oil fractions with narrow boiling ranges. This method can be applied for the oil fractions with narrow boiling ranges pre-prepared by distillation, which are thermally stable in the measuring range and are generating the vapour pressure starting from 5 kPa, irrespective of the oil type. Small quantities of material are used in the method, since a single average boiling point can be determined with up to 20 mg of a substance.

[17] [18] [19] [20] [21]

[22] [23]

CRediT authorship contribution statement [24]

Rivo Rannaveski: Investigation, Formal analysis, Methodology, Writing - original draft. Vahur Oja: Conceptualization, Formal analysis, Methodology, Writing - review & editing, Supervision, Project administration, Funding acquisition.

[25] [26]

Acknowledgements

[27]

The authors gratefully acknowledge financial support provided by Estonian Minister of Education and Research, under target financing SF0140022s10, by Estonian Science Foundation, under Grant G9297, and by the Estonian National R&D program Energy under project AR10129 “Examination of the Thermodynamic Properties of Relevance to the Future of the Oil Shale Industry”. The technical assistance by doctors Madis Listak and Oliver Järvik from Tallinn University of Technology is greatly appreciated.

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