A precise method for calculating the density of high-pressure pure gas

Abstract

A precise calculation method for the density of high-pressure pure gas, relating to the field of pressure vessel design technology, improves the van der Waals equation and includes the following steps: A1. Correction of the van der Waals equation formula; adding a gas molecule characteristic correction coefficient s to the second term of the van der Waals equation to correct the parameters a related to intermolecular attraction and b related to molecular volume, resulting in a precise calculation equation; performing a second-order Taylor expansion of the gas molecule characteristic correction coefficient s at the 0 point with respect to the physical property eccentricity factor parameter x; calculating multiple density parameters of the gas at the same temperature but different pressures by measurement and fitting the test data; A2. Precise density calculation; the calculation method of this invention, even at a pressure of 100 MPa, still maintains a deviation rate of less than 2% between the calculated density data and the measured value, effectively improving the accuracy of the calculation and providing precise guidance for the refined design of pressure vessels and the gas filling work of pressure vessels.

Description

Technical Field

[0001] This invention relates to the field of pressure vessel design technology, and in particular to a method for accurately calculating the density of high-pressure pure gas. Background Technology

[0002] As is well known, pressure vessels, as a special industry in China, have been widely used in the field of engineering technology. With the deepening of the market and the development of technology, contemporary pressure vessels have begun to gradually adopt miniaturization design ideas and concepts. To store the same gas while reducing the volume, higher gas pressure will be generated. As the gas pressure increases and the temperature decreases, the actual gas density differs significantly from the calculation results of the ideal gas law and van der Waals equation, which cannot accurately guide the fine design of pressure vessels and the gas filling work of pressure vessels.

[0003] Currently, in the design of pressure vessels both domestically and internationally, the calculation results for gas density are all based on the ideal gas law and the van der Waals equation; the ideal gas law... Where P is the gas pressure, T is the Kelvin temperature, R is the molar gas constant, and V m The equation, which uses molar volume as the reference value, is an ideal model that ignores the volume of the molecules themselves and the intermolecular forces. The equation only has a good fitting effect when the intermolecular distance is large, i.e., when the pressure is low and the temperature is high.

[0004] van der Waals equations Where a is the molecular attraction correction factor, b is the molecular volume correction factor, and T c P is the critical temperature. c The critical pressure is the equation. This equation is a modified equation derived from the ideal gas law, taking into account the volume of the molecules themselves and the intermolecular forces. The equation introduces two parameters, a and b, where parameter a is related to the intermolecular forces and parameter b is related to the molecular volume. The equation can reflect some properties of real gases to a certain extent, but there are still large deviations at higher pressures (close to the critical pressure) and lower temperatures (close to the critical temperature).

[0005] For example, when the pressure of nitrogen reaches 60 MPa or higher, the density calculation deviation rate is as high as 5%; when the pressure reaches 100 MPa or higher, the density calculation deviation rate is as high as 10%. Therefore, there is an urgent need for an accurate calculation method to improve the accuracy of density calculation for pure gases under high pressure. Summary of the Invention

[0006] To overcome the shortcomings of the prior art, the present invention discloses a method for accurately calculating the density of high-pressure pure gas.

[0007] To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0008] An accurate method for calculating the density of high-pressure pure gas, which improves the van der Waals equation, includes the following steps:

[0009] A1. Correction of the van der Waals equation: A gas molecule characteristic correction coefficient 's' is added to the second term of the van der Waals equation to correct the parameters 'a' (related to intermolecular attraction) and 'b' (related to molecular volume), resulting in the accurate calculation equation. R is the universal gas constant, R = 8.314 J·mol⁻¹ -1 ·K -1 ;

[0010] A second-order Taylor expansion of the gas molecule characteristic correction coefficient s at point 0 with respect to the property eccentricity factor parameter x yields the expansion formula s = k1x 2 +k2x+k3;

[0011] Find the critical temperature T of a gas. c Critical pressure P c The molar mass M and the eccentricity factor parameter x are used to calculate multiple actual density parameters of the gas at the same temperature but different pressures. The test data are then fitted to obtain the fitting parameters, s = k1x. 2 +k2x+k3,a s =k4a,b s =k5b, calculate k1 = -0.16, k2 = 1.55, k3 = 1.48, k4 = 1.01, k5 = 0.69;

[0012] A2. Precise density calculation; Look up the eccentricity factor parameter x of the gas whose density is to be calculated, and substitute it into s = k1x 2 Given k1 = -0.16, k2 = 1.55, and k3 = 1.48, find the value of s.

[0013] Query the van der Waals equation corrections 'a' and 'b' for the gas whose density needs to be calculated, and substitute them into 'a'. s =k4a,b s =k5b, where k4 = 1.01, k5 = 0.69, find a. s and b s The value;

[0014] Measure the temperature T and gas pressure P of the gas whose density needs to be calculated, where the temperature value is the Kelvin value in Kelvin (K) and the gas pressure value is in MPa; substitute these values ​​into the formula. In the middle, V is calculated. mThen the density value of the gas to be density calculated at temperature T and gas pressure P is ρ = M / V m .

[0015] By employing the technical solution described above, the present invention has the following beneficial effects:

[0016] This invention discloses a precise method for calculating the density of high-pressure pure gas. Based on accumulated data from actual production, the method shows that even at a pressure of 100 MPa, the deviation rate between the calculated density data and the measured value is still less than 2%, effectively improving the accuracy of the calculation. This method can accurately guide the refined design of pressure vessels and the gas filling process of pressure vessels. Attached Figure Description

[0017] Figure 1 A molecular model diagram of the van der Waals equation assumptions;

[0018] Figure 2 This is a partial measurement data using nitrogen as an example. Detailed Implementation

[0019] The present invention can be explained in detail through the following embodiments. The purpose of disclosing the present invention is to protect all technical improvements within the scope of the present invention. In the description of the present invention, it should be understood that if there are terms such as "upper", "lower", "front", "rear", "left", "right" indicating the orientation or positional relationship, they are only corresponding to the drawings of this application for the convenience of describing the present invention, and are not intended to indicate or imply that the device or element referred to must have a specific orientation.

[0020] Combined with appendix Figure 1 A precise method for calculating the density of high-pressure pure gas, which improves the van der Waals equation, includes the following steps:

[0021] A1. Correction of the van der Waals equation: A gas molecule characteristic correction coefficient 's' is added to the second term of the van der Waals equation to correct the parameters 'a' (related to intermolecular attraction) and 'b' (related to molecular volume), resulting in the accurate calculation equation. R is the universal gas constant, R = 8.314 J·mol⁻¹ -1 ·K -1 ;

[0022] A second-order Taylor expansion of the gas molecule characteristic correction coefficient s at point 0 with respect to the property eccentricity factor parameter x yields the expansion formula s = k1x 2+k2x+k3; Under higher pressure, the smaller the intermolecular distance, the more obvious the anisotropy of intermolecular forces. Therefore, a gas molecule characteristic correction coefficient s is added to the second term of the van der Waals equation. Since the anisotropy of intermolecular forces is related to the molecular eccentricity factor parameter, the coefficient s is expressed as a function of the eccentricity factor.

[0023] Find the critical temperature T of a gas. c Critical pressure P c The molar mass M and the eccentricity factor parameter x are used to calculate multiple actual density parameters of the gas at the same temperature but different pressures, and the test data are fitted to obtain the fitting parameters. Taking nitrogen as an example, the critical temperature T... c =126.2K; Critical pressure P c =3.4MPa; Molar mass M = 28.0135g / mol; Eccentricity factor parameter x = 0.03772; Take a pressure vessel with a certain volume V and mass m, and inject ultrapure nitrogen gas at a certain pressure P1 into the vessel. While keeping the temperature constant, weigh the gas after filling, m1. Calculate the weight difference Δm1, which is the weight of the nitrogen gas. Then, the corresponding gas density ρ1 = Δm1 / V, Vm1 = M / ρ1, thus determining a set of correspondences between P and Vm. Repeat the above steps to measure and calculate multiple sets of data, as shown in the attached figure. Figure 2 As shown, and by substituting the exact calculation equation... By fitting the data, the corresponding parameter values ​​in the formula can be obtained: s = k1x 2 +k2x+k3,a s =k4a,b s =k5b, where k1 = -0.16, k2 = 1.55, k3 = 1.48, k4 = 1.01, k5 = 0.69;

[0024] A2. Precise density calculation; Look up the eccentricity factor parameter x of the gas whose density is to be calculated, and substitute it into s = k1x 2 Given k1 = -0.16, k2 = 1.55, and k3 = 1.48, find the value of s.

[0025] Query the van der Waals equation corrections 'a' and 'b' for the gas whose density needs to be calculated, and substitute them into 'a'. s =k4a,b s =k5b, where k4 = 1.01, k5 = 0.69, find a. s and b s The value;

[0026] Measure the temperature T and gas pressure P of the gas whose density needs to be calculated, where the temperature value is the Kelvin value in Kelvin (K) and the gas pressure value is in MPa; substitute these values ​​into the formula. In the middle, V is calculated. m Then the density value of the gas to be density calculated at temperature T and gas pressure P is ρ = M / V m .

[0027] Example 1:

[0028] The nitrogen temperature inside a pressure vessel is 65℃, which corresponds to a Kelvin temperature of 338.15K and a gas pressure of 50MPa.

[0029] Find the nitrogen gas eccentricity factor parameter x = 0.03772, and substitute it into s = k1x 2 +k2x+k3, where k1=-0.16; k2=1.55; k3=1.48, we get s=1.5382;

[0030] According to the van der Waals equation, the nitrogen correction b = 38.6 J·MPa -1 ·mol -1 Substitute b s =k5b, where k5 = 0.69, and b is calculated. s =26.634 J·MPa -1 ·mol -1 ;

[0031] Substituting temperature T = 338.15 K and pressure P = 50 MPa into... in the formula;

[0032] V was calculated m =75.488 mL / mol;

[0033] The molar mass of nitrogen is M = 28.0135 g / mol;

[0034] The density of nitrogen gas at a Kelvin temperature of 338.15 K and a gas pressure of 50 MPa is ρ = M / V. m =0.3711 g / mL.

[0035] Example 2:

[0036] The oxygen temperature inside a pressure vessel is 35℃, which corresponds to a Kelvin temperature of 308.15K and a gas pressure of 70MPa.

[0037] Find the oxygen eccentricity factor parameter x = 0.022, and substitute it into s = k1x 2 +k2x+k3, where k1=-0.16; k2=1.55; k3=1.48, we get s=1.514;

[0038] According to the van der Waals equation, the oxygen correction factor a = 1.38 × 10⁻⁶. 5 J2 ·MPa -1 ·mol -2 Substitute a s =k4a, where k4 = 1.01, and a is calculated. s =1.3938×10 5 J 2 ·MPa -1 ·mol -2 ;

[0039] According to the van der Waals equation, the oxygen correction b = 31.9 J·MPa -1 ·mol -1 Substitute b s =k5b, where k5 = 0.69, and b is calculated. s =22.011 J·MPa -1 ·mol -1 ;

[0040] Substituting temperature T = 308.15 K and pressure P = 70 MPa into... in the formula;

[0041] V was calculated m = 49.086 mL / mol;

[0042] The molar mass of oxygen is M = 32.0 g / mol;

[0043] The density of oxygen at a Kelvin temperature of 308.15 K and a gas pressure of 70 MPa is ρ = M / V. m =0.6519 g / mL.

[0044] The parts of this invention not described in detail are prior art. It will be apparent to those skilled in the art that this invention is not limited to the details of the above exemplary embodiments, and that the invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments should be regarded as exemplary and non-limiting in all respects, and are intended to encompass all changes falling within the meaning and scope of equivalents within this invention.

Claims

1. A precise method for calculating the density of high-pressure pure gas, which improves the van der Waals equation, characterized by: including... The following steps: A1. Correction of the van der Waals equation: A gas molecule characteristic correction coefficient 's' is added to the second term of the van der Waals equation to correct the parameters 'a' (related to intermolecular attraction) and 'b' (related to molecular volume), resulting in the accurate calculation equation. R is the universal gas constant. ; A second-order Taylor expansion of the gas molecule characteristic correction coefficient s at point 0 with respect to the property eccentricity factor parameter x is given by the expansion formula as follows: ; Find the critical temperature T of a gas. c Critical pressure P c The molar mass M and the eccentricity factor parameter x were used to calculate multiple density parameters of the gas at the same temperature but different pressures, and the test data were fitted to obtain the fitted parameters. , , ,in , , , , ; A2. Precise density calculation; Query the eccentricity factor parameter x of the gas whose density needs to be calculated, and substitute it into... ,in , , Calculate the value of s; Query the van der Waals equation corrections 'a' and 'b' for the gas whose density needs to be calculated, and substitute them into the equation. , ,in , Find a s and b s The value; Measure the temperature T and gas pressure P of the gas whose density needs to be calculated, where the temperature value is the Kelvin value in Kelvin (K) and the gas pressure value is in MPa (MPa); substitute these values ​​into the formula. In the middle, V is calculated. m V m Given the molar volume, the density value of the gas to be density calculated is given at temperature T and gas pressure P. .

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