title: ÐÐ°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ ÑÐ°Ð·Ð¾Ð²Ð¾Ð³Ð¾ ÑÐ¾ÑÑÐ¾ÑÐ½Ð¸Ñ Ð¿ÑÐ¸ÑÐ¾Ð´Ð½Ð¾Ð³Ð¾ Ð³Ð°Ð·Ð°
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Mathematical modeling of the phase state of natural gas
Creators: name: ÐÑÐ¿Ð¾Ð²Ð°, ÐÐ°Ð»Ð¸Ð½Ð°
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2022
Subjects: ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ ÑÐ¾ÑÑÐ¾ÑÐ½Ð¸Ñ
Ð¿ÑÐ¸ÑÐ¾Ð´Ð½ÑÐ¹ Ð³Ð°Ð·
Ð¼Ð½Ð¾Ð³Ð¾ÐºÐ¾Ð¼Ð¿Ð¾Ð½ÐµÐ½ÑÐ½ÑÐµ ÑÐ¼ÐµÑÐ¸
ÑÐ°Ð·Ð¾Ð²Ð¾Ðµ ÑÐ°Ð²Ð½Ð¾Ð²ÐµÑÐ¸Ðµ
Ð¿Ð°ÑÐ¾Ð²Ð°Ñ Ð¸ Ð¶Ð¸Ð´ÐºÐ°Ñ ÑÐ°Ð·Ñ
equation of state
natural gas
multicomponent mixture
phase equilibrium
gas and liquid phases

description: Ð¢ÐµÐ¼Ð° Ð²ÑÐ¿ÑÑÐºÐ½Ð¾Ð¹ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÑ: Â«ÐÐ°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ ÑÐ°Ð·Ð¾Ð²Ð¾Ð³Ð¾ ÑÐ¾ÑÑÐ¾ÑÐ½Ð¸Ñ Ð¿ÑÐ¸ÑÐ¾Ð´Ð½Ð¾Ð³Ð¾ Ð³Ð°Ð·Ð°Â». ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð¿Ð°ÑÐ¾Ð¶Ð¸Ð´ÐºÐ¾ÑÑÐ½Ð¾Ð³Ð¾ ÑÐ°Ð²Ð½Ð¾Ð²ÐµÑÐ¸Ñ Ð¿ÑÐ¸ÑÐ¾Ð´Ð½Ð¾Ð³Ð¾ Ð³Ð°Ð·Ð°, Ð¸Ð·Ð²Ð»ÐµÐºÐ°ÐµÐ¼Ð¾Ð³Ð¾ Ð¸Ð· ÐÑÐ¸Ð¼Ð¾Ð²ÑÐºÐ¸Ñ Ð·Ð°Ð»ÐµÐ¶ÐµÐ¹ Ð£ÑÐµÐ½Ð³Ð¾Ð¹ÑÐºÐ¾Ð³Ð¾ Ð¼ÐµÑÑÐ¾ÑÐ¾Ð¶Ð´ÐµÐ½Ð¸Ñ. Ð¡Ð¾ÑÑÐ°Ð² Ð³Ð°Ð·Ð¾Ð²Ð¾Ð¹ ÑÐ¼ÐµÑÐ¸: CH4 (80.324%), C2H6 (6.024%), C3H8 (3.066%), nC5H12 (4.381%), nC7H16 (3.108%), nC10H22 (2.431%), N2 (0.0478%), CO2 (0.0188%). Ð¢ÐµÑÐ¼Ð¾Ð±Ð°ÑÐ¸ÑÐµÑÐºÐ¸Ðµ ÑÑÐ»Ð¾Ð²Ð¸Ñ Ð´Ð»Ñ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÑÐ¾Ð¾ÑÐ²ÐµÑÑÑÐ²Ð¾Ð²Ð°Ð»Ð¸ Ð¿ÑÐ¾ÑÐµÑÑÑ ÑÑÐ°Ð½ÑÐ¿Ð¾ÑÑÐ¸ÑÐ¾Ð²ÐºÐ¸ Ð³Ð°Ð·Ð°. ÐÐ°Ð´Ð°ÑÐ¸, ÐºÐ¾ÑÐ¾ÑÑÐµ ÑÐµÑÐ°Ð»Ð¸ÑÑ Ð² ÑÐ¾Ð´Ðµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ: ÐÐ·ÑÑÐ¸ÑÑ Ð¾ÑÐ½Ð¾Ð²Ð½ÑÐµ Ð²Ð¸Ð´Ñ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹, Ð¿Ð¾Ð·Ð²Ð¾Ð»ÑÑÑÐ¸Ðµ Ð¾Ð¿Ð¸ÑÑÐ²Ð°ÑÑ ÑÐ°Ð·Ð¾Ð²Ð¾Ðµ ÑÐ°Ð²Ð½Ð¾Ð²ÐµÑÐ¸Ðµ Ð¼Ð½Ð¾Ð³Ð¾ÐºÐ¾Ð¼Ð¿Ð¾Ð½ÐµÐ½ÑÐ½ÑÑ ÑÐ¼ÐµÑÐµÐ¹. ÐÑÐ¾Ð°Ð½Ð°Ð»Ð¸Ð·Ð¸ÑÐ¾Ð²Ð°ÑÑ Ð¸Ð¼ÐµÑÑÐ¸ÐµÑÑ ÑÐ°Ð±Ð¾ÑÑ Ð¿Ð¾ Ð´Ð°Ð½Ð½Ð¾Ð¹ ÑÐµÐ¼Ð°ÑÐ¸ÐºÐµ. ÐÑÐ±ÑÐ°ÑÑ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ ÑÐ¾ÑÑÐ¾ÑÐ½Ð¸Ñ, Ð¿Ð¾Ð´ÑÐ¾Ð´ÑÑÐ¸Ðµ Ð´Ð»Ñ Ð¾Ð¿Ð¸ÑÐ°Ð½Ð¸Ñ ÑÐ°Ð·Ð¾Ð²Ð¾Ð³Ð¾ ÑÐ°Ð²Ð½Ð¾Ð²ÐµÑÐ¸Ñ Ð³Ð°Ð·Ð¾Ð²Ð¾Ð¹ ÑÐ¼ÐµÑÐ¸, Ð¸ÑÑÐ»ÐµÐ´ÑÐµÐ¼Ð¾Ð¹ Ð² Ð´Ð°Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÐµ. Ð¡Ð¾Ð·Ð´Ð°ÑÑ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÑÑ Ð¼Ð¾Ð´ÐµÐ»Ñ Ð´Ð»Ñ ÑÐ°ÑÑÐµÑÐ° Ð´Ð²ÑÑÑÐ°Ð·Ð½Ð¾Ð³Ð¾ ÑÐ°Ð²Ð½Ð¾Ð²ÐµÑÐ¸Ñ ÑÐ¼ÐµÑÐ¸ Ð·Ð°Ð´Ð°Ð½Ð½Ð¾Ð³Ð¾ ÑÐ¾ÑÑÐ°Ð²Ð°. Ð¡Ð´ÐµÐ»Ð°ÑÑ Ð²ÐµÑÐ¸ÑÐ¸ÐºÐ°ÑÐ¸Ñ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½ÑÑ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² Ñ ÑÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½ÑÐ°Ð»ÑÐ½ÑÐ¼Ð¸ Ð´Ð°Ð½Ð½ÑÐ¼Ð¸. Ð ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ Ð¾Ð±Ð·Ð¾ÑÐ° Ð¸ Ð°Ð½Ð°Ð»Ð¸Ð·Ð° Ð±ÑÐ»Ð¸ Ð²ÑÐ±ÑÐ°Ð½Ñ ÐºÑÐ±Ð¸ÑÐµÑÐºÐ¸Ðµ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ ÑÐ¾ÑÑÐ¾ÑÐ½Ð¸Ñ: ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ Ð¡Ð¾Ð°Ð²Ðµ-Ð ÐµÐ´Ð»Ð¸ÑÐ°-ÐÐ²Ð¾Ð½Ð³Ð°, ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ ÐÐµÐ½Ð³Ð°-Ð Ð¾Ð±Ð¸Ð½ÑÐ¾Ð½Ð°, Ð¾Ð±Ð¾Ð±ÑÐµÐ½Ð½Ð¾Ðµ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ ÐÑÑÑÐ¸Ð»Ð¾Ð²ÑÐºÐ¾Ð³Ð¾ Ð. Ð. Ð ÐµÐ·ÑÐ»ÑÑÐ°ÑÑ ÑÐ°ÑÑÐµÑÐ¾Ð² ÐºÐ¾Ð¼Ð¿Ð¾Ð½ÐµÐ½ÑÐ½Ð¾Ð³Ð¾ ÑÐ¾ÑÑÐ°Ð²Ð° Ð³Ð°Ð·Ð° Ð¸ Ð¼Ð¾Ð»ÑÐ½ÑÑ Ð´Ð¾Ð»ÐµÐ¹ Ð¿Ð°ÑÐ¾Ð²Ð¾Ð¹ Ð¸ Ð¶Ð¸Ð´ÐºÐ¾Ð¹ ÑÐ°Ð· ÑÐ¾Ð¿Ð¾ÑÑÐ°Ð²Ð»ÐµÐ½Ñ Ñ ÑÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½ÑÐ°Ð»ÑÐ½ÑÐ¼Ð¸ Ð·Ð½Ð°ÑÐµÐ½Ð¸ÑÐ¼Ð¸. ÐÑÐ¸ Ð´Ð°Ð²Ð»ÐµÐ½Ð¸Ð¸ Ð¾Ñ 3ÐÐÐ° Ð´Ð¾ 7.5ÐÐÐ° Ð¸ ÑÐµÐ¼Ð¿ÐµÑÐ°ÑÑÑÐµ Ð¾Ñ 263Ð Ð´Ð¾ 283Ð Ð»ÑÑÑÐ¸Ðµ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÑ ÑÐ°ÑÑÐµÑÐ° Ð¿Ð¾ÐºÐ°Ð·Ð°Ð»Ð¾ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ Ð¡Ð¾Ð°Ð²Ðµ-Ð ÐµÐ´Ð»Ð¸ÑÐ°-ÐÐ²Ð¾Ð½Ð³Ð°.
description: The subject of the graduate qualification work is Â«Mathematical modeling of the phase state of natural gasÂ». The given work is devoted to the modeling of the vapor-liquid equilibrium of natural gas recovered from the Achimovsk accumulations of the Urengoy field. Gas mixture composition: methane (80.324%), ethane (6.024%), propane (3.066%), n-pentane (4.381%), n-heptane (3.108%), n-decane (2.431%), nitrogen (0.0478%), carbon dioxide (0.0188%). The thermobaric conditions for the simulation corresponded to the gas transportation process. The research sets the following goals: To investigate the main types of equations to describe the phase equilibrium of multicomponent mixtures. To analyze the available works on this topic. Selecting the equations of state most suitable for the gas composition and thermobaric conditions. Creating a mathematical model to calculate the two-phase equilibrium of a mixture of a given composition.Verification of the obtained results based on the comparison with the experimental data. Based on the literature review and analysis three cubic equations of state were chosen: Soave-Redlich-Kwong equation, Peng-Robinson equation, generalized equation of Brusilovsky A. I. The results of calculations of gas component composition and mole fractions of vapor and liquid phases have been compared with experimental values. At pressures from 3MPa to 7.5MPa and temperatures from 263K to 283K, the Soave-Redlich-Kwong equation showed the best calculation results.