Method for calculating saturated vapor pressure of liquid

Abstract

The invention discloses a method for calculating liquid saturated vapor pressure, and relates to the field of liquid physical property calculation. According to the method, non-dimensionalized pressure is used as a function, non-dimensionalized temperature is used as a variable, the liquid saturated vapor pressure is calculated by using an improved Antoine equation, and the problem that parameters of the Antoine equation are easy to confuse is solved. The method not only has the advantage that the Antoine equation is simple and easy to use, but also has wide applicability and high accuracy.

Description

Technical Field

[0001] The present invention relates to the field of calculating physical properties of liquids, and particularly to a method for calculating the saturated vapor pressure of liquids. Background Art

[0002] The saturated vapor pressure refers to the pressure generated by the vapor when a liquid reaches dynamic equilibrium with the vapor above it at a certain temperature. The saturated vapor pressure is an important physical property of liquids. Its magnitude determines the volatility of the liquid. The greater the saturated vapor pressure, the more volatile the liquid. It also determines the boiling point of the liquid. When the saturated vapor pressure is equal to the external pressure, the liquid boils. In addition, the saturated vapor pressure is the core parameter of the vapor-liquid phase equilibrium, affecting the separation of liquid mixtures. The saturated vapor pressure data of liquids plays a key role in the petroleum and chemical industries, directly affecting process design, safe operation, and product quality. This data can guide the setting of storage and transportation conditions for liquid materials to avoid risks of volatilization, leakage, or explosion due to excessive vapor pressure. In the process of chemical separation (such as distillation), it is the core parameter for optimizing operating temperature and pressure to ensure efficient separation. In addition, the management of volatile organic compound (VOCs) emissions also relies on this data to comply with environmental protection regulations and improve energy utilization efficiency, thereby ensuring production safety, economy, and environmental sustainability.

[0003] The most commonly used method for calculating the saturated vapor pressure of liquids is to use the Antoine equation, and the expression is:

[0004]

[0005] Or

[0006]

[0007] Where p s is the saturated vapor pressure of the liquid; T is the temperature of the liquid; A, B, and C are the Antoine parameters of the substance. The Antoine parameters of water are shown in Table 1.

[0008] Table 1

[0009]

[0010] As can be seen from Table 1, when the expressions of the Antoine equation are different, or the units of temperature and pressure are different, the values of A, B, and C are also different. This indicates that there are implicit constraints between the values of parameters A, B, and C and the units of temperature and pressure, which leads to the need to forcibly bind specific measurement units when using the Antoine equation and use the Antoine parameters corresponding one-to-one with the units. If the values of parameters A, B, and C are used incorrectly, the calculated saturated vapor pressure value will deviate significantly, which may lead to production accidents and even cause significant personnel and economic losses. Unfortunately, literature research shows that the incorrect use of Antoine parameters is still widespread. Summary of the Invention

[0011] The purpose of the present invention is to solve the above problems in the prior art, and provide a method for calculating the saturated vapor pressure of a liquid, which calculates the saturated vapor pressure of the liquid by using an improved Antoine equation.

[0012] To achieve the above purpose, the present invention adopts the following technical solutions:

[0013] A method for calculating the saturated vapor pressure of a liquid, comprising the following steps:

[0014] 1) Divide the saturated vapor pressure p s of the liquid by its critical pressure p c to obtain a dimensionless pressure p r ; divide the temperature T of the liquid by its critical temperature T c to obtain a dimensionless temperature T r ;

[0015] 2) Fit p r and T r with the following improved Antoine equation to obtain constants A, B, and C:

[0016]

[0017] 3) After obtaining the values of A, B, and C, calculate the saturated vapor pressure p s of the liquid at any temperature T with the following improved Antoine equation:

[0018]

[0019] In step 1), the units of the saturated vapor pressure p s and the critical pressure p c are the same, and can be any one of Pa, N / sqm, bar, atm, mmHg, mH2O, psi, and torr; the units of the temperature T and the critical temperature T c are K.

[0020] Compared with the prior art, the beneficial effects achieved by the technical solution of the present invention are as follows:

[0021] The present invention proposes a method for calculating the saturated vapor pressure of a liquid. This method takes the dimensionless pressure as a function and the dimensionless temperature as a variable, and uses an improved Antoine equation to calculate the saturated vapor pressure of the liquid, solving the problem that the parameters of the Antoine equation are easily confused. This method not only has the advantages of simplicity and ease of use of the Antoine equation, but also has wide applicability and high accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 is the p r ~ T r relationship diagram of water;

[0023] Figure 2 is the p r ~ T r relationship diagram of ethanol;

[0024] Figure 3 is the p r ~ T r relationship diagram of ethyl acetate;

[0025] Figure 4 is the p r ~ T r relationship diagram of methylcyclohexane. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0026] In order to make the technical problems, technical solutions and beneficial effects to be solved by the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0027] Embodiment 1

[0028] The saturated vapor pressure data of water is shown in Table 2, where the unit of pressure is Pa and the unit of temperature is K. The critical pressure of water is 2.2064×10 7 Pa, and the critical temperature is 647 K.

[0029] Table 2

[0030]

[0031] First, divide the saturated vapor pressure p s of water by its critical pressure p c to obtain the dimensionless pressure p r ; divide the temperature T of water by its critical temperature T c to obtain the dimensionless temperature T r ; use the least squares method to fit p rWith T r :

[0032]

[0033] The fitting results are as Figure 1 shown, obtaining the parameters A = 7.68917; B = -8.08866 and C = 0.05103. The saturated vapor pressure p of water at any temperature T is calculated using the following improved Antoine equation s :

[0034]

[0035] wherein, the saturated vapor pressure p s and the critical pressure p c have the same unit, which can be any one of Pa, N / sqm, bar, atm, mmHg, mH2O, psi, torr, etc.; the unit of temperature T is K. Between 273 and 643 K, the average prediction error of the present invention is 19 kPa, which is lower than the average prediction error of 2913 kPa of the Antoine equation.

[0036] Example 2

[0037] The saturated vapor pressure of ethanol is shown in Table 3, where the unit of pressure is bar and the unit of temperature is K. The critical pressure of ethanol is 61.37 bar and the critical temperature is 514 K.

[0038] Table 3

[0039]

[0040] First, divide the saturated vapor pressure p s of ethanol by its critical pressure p c to obtain the dimensionless pressure p r ; divide the temperature T of ethanol by its critical temperature T c to obtain the dimensionless temperature T r ; using the least squares method, fit p r with T r using the following improved Antoine equation

[0041]

[0042] The fitting results are as Figure 2 shown, obtaining the parameters A = 7.45013; B = -6.71819 and C = -0.09957. The saturated vapor pressure p of ethanol at any temperature T is calculated using the following improved Antoine equation s :

[0043]

[0044] Among them, the saturated vapor pressure p s and the critical pressure p c have the same unit, which can be any one of Pa, N / sqm, bar, atm, mmHg, mH2O, psi, torr, etc.; the unit of temperature T is K. Between 273 and 513 K, the average prediction error of the present invention is 12 kPa, which is lower than the average prediction error of the Antoine equation, 3637 kPa.

[0045] Example 3

[0046] The saturated vapor pressure of ethyl acetate is shown in Table 4, where the unit of pressure is bar and the unit of temperature is K. The critical pressure of ethyl acetate is 38.29 atm, and the critical temperature is 523.3 K.

[0047] Table 4

[0048]

[0049] First, divide the saturated vapor pressure p s of ethyl acetate by its critical pressure p c to obtain the dimensionless pressure p r ; divide the temperature T of ethyl acetate by its critical temperature T c to obtain the dimensionless temperature T r ; use the least squares method to fit p r and T r with the following modified Antoine equation:

[0050]

[0051] The fitting result is as shown in Figure 3 , and the parameters A = 7.57809; B = -7.83809 and C = 0.03268 are obtained. Calculate the saturated vapor pressure p s of ethyl acetate at any temperature T with the following modified Antoine equation:

[0052]

[0053] Among them, the saturated vapor pressure p s and the critical pressure p cThe units are the same and can be any one of Pa, N / sqm, bar, atm, mmHg, mH2O, psi, torr, etc.; the unit of temperature T is K. Between 273 and 513 K, the average prediction error of the present invention is 7.5 kPa, lower than the average prediction error of 13.0 kPa of the Antoine equation.

[0054] Example 4

[0055] The saturated vapor pressure of methylcyclohexane is shown in Table 5, where the unit of pressure is psi and the unit of temperature is K. The critical pressure of methylcyclohexane is 504.73 psi and the critical temperature is 572.1 K.

[0056] Table 5

[0057]

[0058] First, divide the saturated vapor pressure p s of methylcyclohexane by its critical pressure p c to obtain the dimensionless pressure p r ; divide the temperature T of methylcyclohexane by its critical temperature T c to obtain the dimensionless temperature T r ; use the least squares method to fit p r and T r with the following improved Antoine equation:

[0059]

[0060] The fitting results are as Figure 4 shown, and the parameters A = 5.5837; B = -5.06499 and C = -0.09913 are obtained. Calculate the saturated vapor pressure p s of methylcyclohexane at any temperature T with the following improved Antoine equation:

[0061]

[0062] where the units of the saturated vapor pressure p s and the critical pressure p c are the same and can be any one of Pa, N / sqm, bar, atm, mmHg, mH2O, psi, torr, etc.; the unit of temperature T is K. Between 273 and 503 K, the average prediction error of the present invention is 3.3 kPa, lower than the average prediction error of 14.5 kPa of the Antoine equation.

Claims

1. A method for calculating the saturated vapor pressure of a liquid, characterized in that, including the following steps: 1) Divide the saturated vapor pressure p of the liquid s by its critical pressure p c to obtain the dimensionless pressure p r ; divide the temperature T of the liquid by its critical temperature T c to obtain the dimensionless temperature T r ; 2) Fit p with the following improved Antoine equation r versus T r to obtain the constants A, B, and C: 3) After obtaining the values of A, B, and C, use the following improved Antoine equation to calculate the saturated vapor pressure p of the liquid at any temperature T s : 。 2. The method for calculating the saturation vapor pressure of a liquid according to claim 1, wherein: The saturated vapor pressure p s and the critical pressure p c have the same unit.

3. The method for calculating the saturated vapor pressure of a liquid according to claim 1, characterized in that: The saturated vapor pressure p s and the critical pressure p c have the same unit, which can be any one of Pa, N / sqm, bar, atm, mmHg, mH2O, psi, and torr.

4. A method for calculating the saturated vapor pressure of a liquid according to claim 1, characterized in that: The temperature T and the critical temperature T c are in the unit of K.

Images