Научная статья на тему 'DETERMINATION OF THE REAL CRITICAL DENSITY OF SUBSTANCES'

DETERMINATION OF THE REAL CRITICAL DENSITY OF SUBSTANCES Текст научной статьи по специальности «Физика»

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ВЕЩЕСТВО / ФАЗОВЫЙ ПЕРЕХОД / КРИВАЯ ТЕМПЕРАТУРЫ ПЛАВЛЕНИЯ / КРИТИЧЕСКИЕ ПАРАМЕТРЫ / АКСИОМАТИЧЕСКАЯ ГЕОМЕТРИЧЕСКАЯ СИСТЕМА / БЕНЗОЛ / БЕНЗОНИТРИЛ / ТОЛУИДИНЫ / ФАЗОВАЯ ДИАГРАММА

Аннотация научной статьи по физике, автор научной работы — Grigoryev B.A., Ibrahimoglu Beycan, Faruk Comert, Ibrahimoglu B.

Critical parameters such as temperature, pressure, volume and density are included in equations developed to characterize liquid phase of substances. The temperature indicating the disappearance of the difference between the liquid and gas phases located at the end point of the liquid-gas balance curve is known as critical temperature. The critical temperature of a substance is the temperature in which vapor of the substance cannot be liquefied even with the application of very high pressure. The critical density and critical pressure in the pressure-temperature phase diagram of pure substance represent only the pressure and density values corresponding to the critical temperature. Therefore, the critical pressure and critical density used in the equations do not correspond to the actual critical values of pressure and density. In this study, axiomatic geometry system was applied to experimental data of benzene, benzonitrile, middle-, para- and meta-tolouidines at high pressure and temperature to determine the real critical pressure and density values on the solid-liquid balance curve.

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Текст научной работы на тему «DETERMINATION OF THE REAL CRITICAL DENSITY OF SUBSTANCES»

UDC 536.4

Keywords:

substance, phase transition, melting curve, critical parameters, axiomatic geometry system, benzene, benzonitrile, middle-, para- and meta-tolouidines, solid-liquid balance curve.

Determination of the real critical density of substances

B.A. Grigoryev1, Beycan Ibrahimoglu2*, Faruk Comert3, Beycan Ibrahimoglu jun.4

1 Gazprom VNIIGAZ LLC, Bld. 1, Estate 15, Proyektiruemyy proezd no. 5537, Razvilka village, Leninskiy district, Moscow Region, 142717, Russian Federation

2 Ankara Science University, Qamlica Mah.Anadolu Bulvari No:16A/1 Yenimahalle, Ankara, Turkey

3 OSTIM Technical University, OSTiM, 06374 Ankara, Turkey

4 Anadolu Plazma Teknoloji Enerji Merkezi, Gazi Universitesi Yerlefkesi Golbafi Kampusu Teknoplaza Binasi C Blok Zemin Kat No:27 Golbafi Ankara, Turkey

* E-mail: beycanibrahimoglu@yahoo.com

Abstract. Critical parameters such as temperature, pressure, volume and density are included in equations developed to characterize liquid phase of substances. The temperature indicating the disappearance of the difference between the liquid and gas phases located at the end point of the liquid-gas balance curve is known as critical temperature. The critical temperature of a substance is the temperature in which vapor of the substance cannot be liquefied even with the application of very high pressure. The critical density and critical pressure in the pressure-temperature phase diagram of pure substance represent only the pressure and density values corresponding to the critical temperature. Therefore, the critical pressure and critical density used in the equations do not correspond to the actual critical values of pressure and density. In this study, axiomatic geometry system was applied to experimental data of benzene, benzonitrile, middle-, para-and meta-tolouidines at high pressure and temperature to determine the real critical pressure and density values on the solid-liquid balance curve.

For many years, critical parameters of substances (pressure, temperature, volume) have attracted and continue to attract great attention from scientists who do theoretical and experimental studies.

Many works devoted to melting are aimed at clarifying the nature of the melting curve, which is steel disputable now. The disagreement is whether the melting curve ends at the critical point. Simon and his co-workers carried out important work on the melting curves of certain constant gases at pressures (P) up to 6000 atm and proposed an analytical expression for the melting curve (namely log (a + P) = clog T +b, where p, T are pressure and temperature at the triple point and, a, b, c are constants without any physical meaning, obtained by experimental interpolation individually for each substance), which reproduced the melting curve over a wide range and became very significant. The form of the equation requires an infinite increase in pressure and temperature. Simon's point of view was that, nevertheless, the melting curve probably ends at a critical point [1, 2]. However, there is no experimental study (despite [3, 4]) showing that a critical point exists in the pressure and temperature values on the melting curve.

In our opinion, the main reason for this situation is that the results obtained in the experiments are erroneous especially in terms of melting curve and critical density [5-7]. To measure crystallization pressure up to 150 MPa, the confidence interval for the total error is ±5 %. In our opinion, it is impossible to determine critical parameters with this error.

In addition, many experimental facilities have been designed to study behavior of density near the critical point, and the Toppler optical method is considered to be the most effective of these. It was used to examine the critical density of heptane (C7H16), and the experimental results are presented in a thermogram.

Accordingly, we have designed a special experimental setup [8-11], and the melting curve was investigated by obtaining the metastable state of benzene at high pressures. Experimental results showed the presence of a critical point on benzene melting curve at P = 2200 atm and T = 356 K. In addition, the density and viscosity parameters ofbenzonitril and ortho-, meta- and para-tolouidines, which developed the combined experimental setup, were determined precisely [12-15]. The application of axiomatic geometry system to density test results constitutes the main line of this study.

Experimental results

Density (p) test results of benzonitrile (C7H5N) for high pressures and temperatures are given in table 1 and on the p - P&T = const diagrams (fig. 1).

By applying the spatial geometry system to the liquid phase of benzonitrile with P-p, T = const dependence, it was possible to determine the freezing temperature associated with pressure and the temperature of the triple point. In addition, the application of space geometry to P-p, T = const diagrams of benzonitrile, other than the p-P, T = const dependence, showed the presence of a new base point in the liquid phase of benzonitrile [10, 16].

Space geometry in conjunction with p-T, P = const diagram was applied for solid, liquid and gas phases of some organic and inorganic materials: oxygen (O2), nitrogen (N2), argon (Ar), ammonia (NH3), sodium (Na), potassium (K), benzene (C6H6), toluene (C7H8), medium-, meta-, para-toloudins (C7H9N), benzonitrile (C7H5N). Table 2 contains the pressure-related melting curve temperatures, K, and the critical pressures (Pc) determined on the melting curve.

When the graphical method was applied in the P-p, T = const diagram, it was observed that at high pressure for hydrocarbons, alkanes, nitric acids, paraffins and other liquids the isotherms are accumulated at a point. For example, P-p,

Table 1

Experimental density data of benzonitrile at high pressures and temperatures, kg/m3

P, MPa T, K

298 323 348 373 398 423 448 473 498 523

0,1 1001,2 980,1 957,5 935,8 911,8 885,1 859,8 832,6 - -

5 1004,2 982,8 962,1 940,9 917,4 893,8 866,8 842,3 816,5 791,2

10 1006,2 985,9 965,4 944,1 922,1 899,7 874,8 852,3 826,3 804,8

20 1010,8 990,9 969,9 949,8 927,6 907,1 884,8 862,2 839,6 818,2

30 1016,2 996,6 977,4 957,0 936,2 915,5 893,6 874,0 853,0 832,5

40 1020,2 1001,4 981,3 963,6 943,6 923,7 903,2 883,1 863,1 844,8

50 1022,6 1005,1 987,5 969,9 950,1 930,1 913,0 893,2 874,2 861,8

Table 2

Freezing temperatures of the substances and the critical point where all the isobars are gathered at high pressure (determined by the application of space geometry)

Substance T, K, at Pc, MPa

P = 0,1 MPa P = 50 MPa P = 75 MPa P = 100 MPa P = 150 MPa P = 175 MPa P = 200 MPa

Oxygen 56,6 62,8 65,5 67,8 72,2 74,5 76,5 180

Nitrogen 65,4 75,4 80,0 94,9 93,8 98,2 102,5 150

Ammonia 195,4 199,6 201,5 203,4 207,0 208,5 210,2 138

Benzen 279,0 293,4 300,2 306,7 319,5 325,6 331,3 210

Toluen 178,6 188,9 193,8 198,7 207,7 211,9 216,1 200

Benzonitril 256,6 270,7 276,1 281,4 292,2 297,1 301,9 270

T = const (fig. 2) and p-P, T = const (fig. 3) dependencies were applied to the liquid phase of benzonitrile at high pressure and temperature. In both diagrams, it was also observed that in the liquid phase of benzonitrile isotherms are collected at an unknown point (see figs 2, 3).

273

] 1000

M M

900-

800-

700-

600-

500

323

373

423

T, K 473

40 50 P, MPa

Fig. 1. Benzonitrile p-P, T = const & p-T, P = const diagrams at high pressures and temperatures

I 290 250 210 170 130 90 50

T, K:

10 800

vi

''//Hl

J / M ' ' / 1 ft

✓ 4: /7/7, II / /

✓ ✓ / ✓ / ✓ / / / / ! ' /'/! 'il ' ! 1

✓ ✓ / ✓ / / / / / / / / / ' / ' ' / п

// // ' /

M

850 900 950

1000 1050 1100

р, kg/m3

Fig. 2. Point where the isotherms of benzonitrile intersect at P-p, T = const dependency on the P axis (P = 270 MPa and p = 1100 kg/m3)

a 1100 1050 1000 950 900 850 800

w *

" / / / ' y . 's s Ш

T, K: — 298 — 323 — 348 - — 373 — 398 — 423 - — 448 — 473 — 498 — 523

, ^ / ' ✓ s * s ✓ / ' ' 'j // /

/у y s ' ✓ ✓ ' / ' ' / ' ✓ ' / / / /

'л ' ;, s / ' / • /

У

10 50 90 130 170 210

250 290 p, MPa

Fig. 3. Point where the isotherms of benzonitrile intersect at p-P, T = const dependency (P = 270 MPa, p = 1100 kg/m3)

In both diagrams (P-p, T = const and p-P, T = const) all isotherms in the liquid phase were gathered at a point where P = 270 MPa and p = 1100 kg/m3. We consider that this point represents an important critical point, exactly like absolute temperature, ionization temperature and critical temperature [10, 11, 17].

In our opinion, this point where isotherms are gathered in the liquid phase of benzonitrile is the critical pressure of benzonitrile, and the density

corresponding to this pressure is the critical density (fig. 4).

Furthermore, the critical pressure and critical density (pc) values obtained by the application of the graphic method to the liquid phases of some hydrocarbons, alkanes, nitrogen-containing compounds, paraffins and other substances are tabulated in table 3.

Fig. 4. P-T phase diagram of benzonitrile showing a real critical pressure:

TTRP - triple point temperature; Tc - critical temperature

Table 3

Critical pressure and critical density values of some substances

Substance Chemical formula Pc, MPa Pc, kg/m3

n-Decane c10h22 130 839

n-Nonane c9h20 150 826

m-Xylene c8h10 200 990

o-Xylene c8h10 205 1000

o-Toloudine c7h,n 150 1400

m-Toloudine c7h,n 140 1450

p-Toloudine c7h,n 200 1100

Benzonitrile c7h5n 270 1100

Benzene C6H6 210 1200

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Discussions

The habitual classical P-T phase diagram (fig. 5) shows the critical and triple points, three phases and boundary curves that separate these phases. Our studies have shown that at the critical point where the liquid-gas equilibrium curve ends, critical pressure and critical volume (Gc) are actually ordinary values corresponding to critical temperature and do not characterize a critical situation. The Pc does not characterize a critical situation, because the liquid phase is presented in the pressure values P1, Pc, P2 and P3, in other words, Pc is between P1 and P2 pressures. It clearly shows that it does not have a critical feature unlike temperature.

Gc depends on Pc and temperature, and it is impossible to determine precisely, because a very small change in Pc causes a very large change in volume. As a result Gc (pc) must be determined using reliable methods that are relatively easily applicable and accepted by science such as space geometry and graphical methods.

Application of the graphical methods on the graphs is an effective tool to solve problems. These applications visualise problems and help to approach it in different aspect. Therefore, this method was used to solve scientific problems

Fig. 5. The classical commonly used P-T phase diagram

in different fields. It was also applied to the physical diagrams of substances, with guidance of previous studies. Absolute zero was found when geometrical method was applied on a P-T, G = const diagram.

To prove it, P-p, T = const and p-P, T = const dependencies were applied to the liquid phase of benzonitrile at high pressure and temperature. In both diagrams, it was found that in the liquid phase of benzonitrile isotherms are collected at an unknown point. We suggest that this point where isotherms are gathered in the liquid phase of benzonitrile is the actual critical pressure of benzonitrile and the density corresponding to this pressure is the critical density as shown in fig. 6.

Finally, we have shown that it is possible to apply geometry on the physical diagrams of substances to determine important parameters such as freezing and boiling temperatures, actual critical pressure, critical density of a substance at high pressures and temperature without setting up experiments. This method provides fast, cheap and accurate solutions for problems about phase transitions where experimental and theoretical studies are not possible.

Fig. 6. P-T phase diagram which shows the actual critical pressure and critical density

References

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p. 309. ISSN 0044-2313. (Germ.).

2. BRIDGMAN, P.V. Recent work in the field of high pressures. Reviews of Modern Physics, 1946, vol. 18, no. 1. ISSN 0034-6861.

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of cyclohexane and benzene in the pressure range of 1-750 bar [Eksperimentalnoye issledovaniye liniy plavleniya tsiklogeksana i benzola v intervale davleniy 1-750 bar]. In: Questions of search, exploitation and processing in the oil industry. Grozny: Publishing house of the State Tax Inspection, 1974, pp. 66-67. (Russ.).

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of benzene in terms of low temperatures and high pressures [Fazovyye prevrashcheniya benzola v usloviyakh nizkikh temperature i vysokikh davleniy]. KimyaProblemhri, 2015, no. 4, p. 367-375. ISSN 2221-8668. (Russ.).

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i vyazkost benzonitrila, orta-, meta-, para-tolouidinov pri razlichnykh temperaturakh i davleniyakh]. Candidate's thesis (engineering). Azerbaijan Polytechnic University, 1983. (Russ.).

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Определение действительной критической плотности веществ

Б.А. Григорьев1, Б. Ибрагимоглы [Б.И. Фарзалиев]2*, Ф. Комерт3, Б. Ибрагимоглы мл.4

1 ООО «Газпром ВНИИГАЗ», Российская Федерация, 142717, Московская область, Ленинский район, пос. Развилка, Проектируемый проезд № 5537, вл. 15, стр. 1

2 Университет Анкары (Ankara Bilim Üniversitesi), Турция, Анкара, Çamlica Mah.Anadolu Bulvan No:16A/1 Yenimahalle

3 Университет Остим Текник (OSTÎM Teknik Üniversitesi) OSTÎM, 06374 Ankara, Türkiye

4 Энергетический центр «Анатолийские плазменные технологии» (Anadolu Plazma Teknoloji Enerji Merkezi), Турция, Анкара, Университет Гази, Yerle^kesi Gölba^i Kampüsü Teknoplaza Binasi C Blok Zemin Kat No:27 Gölba^i

* E-mail: beycanibrahimoglu@yahoo.com

Тезисы. В уравнения состояния, характеризующие жидкую фазу вещества, включены такие критические параметры, как температура, давление, объем и плотность. Температура, при которой жидкая и газовая фазы вещества находятся в равновесии и его невозможно перевести из газообразного состояния в жидкое даже под воздействием очень высокого давления, носит название критической температуры. Применительно к фазовым P-T-диаграммам чистых веществ критическая плотность и критическое давление представляют собой всего лишь некоторые значения одноименных величин, отвечающие критической температуре вещества, а не его реальные критические параметры. В статье изложены результаты аналитических исследований, в ходе которых действительные критические значения давления и плотности бензола, бензонитрила, а также орто-, мета- и пара-толуидинов моделировались на базе экспериментальных данных с использованием аксиоматической геометрической системы.

Ключевые слова: вещество, фазовый переход, кривая температуры плавления, критические параметры, аксиоматическая геометрическая система, бензол, бензонитрил, толуидины, фазовая диаграмма.

Список литературы

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2. Bridgman P. V. Recent work in the field of high pressures / P.V. Bridgman // Reviews of modern physics. -1946. - Т. 18. - № 1.

3. Murdaev R.M. Experimental study of the melting line of cyclohexane and benzene in the pressure range of 1-750 bar / R.M. Murdaev, D.S. Kurumov // Questions of search, exploitation and processing in the oil industry. - Grozny: Publishing house of the State Tax Inspection, 1974. - C. 66-67.

4. Григорьев Б.А. Экспериментальное исследование р,р,Т-зависимости н-гексана в паровой фазе / Б.А. Григорьев, Д.С. Курумов // ИФЖ. - 1981. - Т. 41. - № 2. - С. 343-344.

5. Анисимов М.А. Исследование критических явлений в жидкостях / М.А. Анисимов // Успехи физических наук. - 1974. - Т. 114. - Вып. 2. - С. 249-294.

6. Бриджмен П.В. Физика высоких давлений = The physics of high pressure / П.В. Бриджмен. - М.-Л.: ОНТИ, 1935.

7. Григорьев Б.А. Теплофизические свойства углеводородов нефти, газовых конденсатов, природного и сопутствующих газов / Б.А. Григорьев, А.А. Герасимов, И.С. Александров. - М.: МЭИ, 2019. - Т. 1.

8. Фарзалиев Б.И. Исследование фазовых переходов в жидкостях / Б.И. Фарзалиев, А. Рагимов // Известия Академии наук Азербайджанской ССР. - 1984. - Т. 12.

9. Фарзалиев Б.И. О бензольных фазовых переходах при высоких давлениях / Б.И. Фарзалиев, Н.Ф. Алиев // Термодинамические и переносные свойства веществ: c6. - Баку: Азерб. политехи. ин-т им. Ч. Ильдрыма, 1989. - С. 61-65.

10. Azreg-Aïnou M. Phase equilibrium and metastability of liquid benzene at high pressures / M. Azreg-Aïnou, A. Hüseynov, B. Ibrahimoglu // J. of Chemical Physics. - 2006. - Т. 124. - № 20. - Ст. 204505. -DOI: 10.1063/1.2198808.

11. Ибрагимоглы Б. Фазовые превращения бензола в условиях низких температур и высоких давлений / Б. Ибрагимоглы, Ч. Канбеш, И.М. Ахмедов // Kimya problemtari. - 2015. - № 4. - С. 367-375.

12. Фарзалиев Б.И. Термодинамические свойства и вязкость бензонитрила, орта-, мета-, пара-толуидинов при различных температурах и давлениях: дис. ... к.т.н. / Б.И. Фарзалиев. - Баку: Азербайджанский политехнический институт, 1983.

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