RU2478195C1 - Method of prompt determination of compressibility coefficient of gases and their mixtures - Google Patents

Abstract

FIELD: measurement equipment.

SUBSTANCE: method of prompt determination of compressibility coefficient involves a resonant chamber made from metal with low temperature expansion coefficient and with known proper frequency in vacuum ω₀. Then, the above resonant chamber is filled with gas at standard pressure and temperature, and resonant frequency value ω_c is measured. After that, it is filled with gas at working pressures P and temperature T and proper frequency value ω_p is measured. After that, compressibility coefficient K is calculated as per the following ratio:

EFFECT: possible prompt measurement of compressibility coefficient of gases and their mixtures; determination of a function with lower error and reduction of flow measurement error at use of flow metres on orifices.

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Description

The invention relates to measuring equipment and can be used on metering nodes of gas producing and gas transmission enterprises, when conducting studies of the physical properties of gases and their mixtures (in particular, natural fuel and associated petroleum) and in other cases where it is necessary to know the magnitude of the deviation of gas behavior from ideal .

One of the main indicators of the operation of a gas producing or gas transportation company is the amount of produced or transmitted gas per unit time - its volumetric flow rate Q ₀ .

The most common method for measuring volumetric flow, adopted today, is the method of determining the variable pressure drop on the constricting device (CS) - nozzle or diaphragm.

In this case, the main design relationships for determining the value of Q _o is the following [1-3]:

where ΔР is the pressure drop across the control system, ρ is the gas density under operating conditions (r.u.) (at pressure P and gas temperature in the pipeline 7), Q ₀ is the volumetric flow rate (in r.u.), A is the integral coefficient taking into account the shape of the control system (flow coefficient), the correction factor for gas expansion, the area of the minimum control passage opening, etc.

The gas density under operating conditions p is not measured at gas industry enterprises (due to the lack of reliable and relatively inexpensive measuring instruments). Typically, one of the following images comes in:

- either a representative gas sample is weighed in the laboratory in a special vessel of known volume (pycnometer) at room temperature, the density is determined, then the temperature and atmospheric pressure are measured, a correction is made for the difference between gas pressure and gas temperature from standard ones, i.e. the density is brought to standard conditions, in other words, its ρ _c value is obtained at a pressure P _c = 1.0131 · 10 ⁵ Pa and a temperature T _c = 293.15 K (the most common method);

either the component composition is determined on a chromatograph (with corresponding high accuracy) and, based on it, the value of ρ _{s is} calculated (a rarer method).

To calculate the state of real gases and their properties, semi-empirical formulas or equations are used that are based on processing real dependencies obtained from experiment [4]. In engineering calculations, they most often use the generalized Mendeleev-Clapeyron equation (2), into which a certain dimensionless coefficient Z, called the compressibility factor, is introduced; it takes into account the deviation of the behavior of real gas from ideal:

here P is the gas pressure, T is its temperature, V is the volume occupied by the gas, R is the universal gas constant, m is the mass of gas, M is its molar weight.

Knowing the temperature and pressure, from the equation of state (2) calculate the density ρ of the gas in both working and standard conditions:

далее находят ρ через ρ_с:and from the relation

then find ρ through ρ _with :

here Z _c and Z are the values of compressibility factors under standard (P _s , T _s ) and working (P, T) conditions. In this case, equation (1) takes the form

- отношение факторов сжимаемости получил название коэффициента сжимаемости.where is the coefficient

- the ratio of compressibility factors is called the compressibility factor.

As can be seen from (5), the compressibility coefficient is directly included in the formula by which the flow rate is calculated, and its error is included in the error in determining the flow rate.

The most accurate compressibility factors for any gases — pure associated petroleum or natural gases — are determined experimentally. On special physical equipment in the laboratory, in a certain range of temperatures and pressures, a set of experimental points [P _i , V _i , T _i , or [P _i , ρ _i , T _i ], or [Z _i , ρ _i , T _i ], where P _i , V _i , ρ _i , T _i , Z _i - respectively pressure, specific volume, density, temperature and compressibility factor at point i.

Processing this data, we obtain the dependences Z (P, T), by which it is possible to find the values of Z at intermediate points.

The technique for the experimental determination of the dependences Z (P, T) is quite complicated and cannot be reproduced today in the factory laboratory of a gas enterprise or in TsNIPRe. In addition, such measurements (essentially research) require considerable work and time. Therefore, in practice, use graphical and analytical methods for determining the coefficients Z and K.

GOST 30319.2-96 [4] recommends using one of the 4 calculation methods for determining Z and K, namely: NX19 mod., US GERG, US AGA8-92DC and US VNIC SMV. The initial data for the first two are pressure, temperature, density under standard conditions ρ _s and the molar fractions of nitrogen and carbon dioxide. For the last two methods, the initial ones are pressure, temperature and molar fractions of all natural gas components.

The error in calculating the value of Z-δZ depends on which calculation method is used, as well as on the accuracy of the measurement of the input data and thermobaric parameters (operating conditions). Indeed, referring to table 1 of GOST 30319.2-96, we see that for the NX19 method mod. at ρ _s > 0.75 kg / m ³ and P> 7 MPa, the calculation error is 1.09%, and the deviation from the experimental data is 1.65%.

For the GERG-91 method mod .: at ρ = 0.74-1.00 kg / m ² (mixture with H ₂ S) at Р - 0.1-11 MPa, the calculation error is 2.1% deviation from experimental data 3 ,one%.

For the AGA8-92DS method: at ρ = 0.74-1.00 (mixture with H ₂ S) and P = 0.1-11 MPa, the calculation error is 1.3%, the deviation of the experimental value is 1.88%, and t .d.

Further, we will take one of the methods as a prototype, for example, GERG-91 mod.

Thus, for natural gases, only calculation errors (in certain areas of the operating conditions) reach 2%. The experimental data, apparently, will give a discrepancy with the true ones even more. At the level of measurement errors of other flow parameters - temperature, pressure, pressure drop, lying in the range of 0.1 ... 0.5%, such large errors when determining the value of Z become decisive.

An important point is the fact that the calculated value of Z acts as the average for the period between measurements of the values included in the original calculation data when calculating the change in component composition during this period of time, an uncontrolled error may go beyond the error of the calculated value of Z.

является необходимость проведения предварительного хроматографического анализа с целью получения данных о компонентном составе и высокая погрешность расчетов величины К в отдельных термобарических областях. Кроме того, полученное значение коэффициента сжимаемости относится к определенному моменту времени - времени взятия пробы для анализа t_о, т.е. К=K(t_о). Невозможность непрерывного слежения за величиной К=K(t) является следующим недостатком способа определения К.Thus, the disadvantage of the existing method for determining the compressibility factor

There is a need for preliminary chromatographic analysis in order to obtain data on the component composition and a high error in calculating the K value in individual thermobaric regions. In addition, the obtained value of the compressibility coefficient refers to a certain point in time - the sampling time for analysis t _о , i.e. K = K (t _o ). The impossibility of continuously monitoring the value of K = K (t) is the next disadvantage of the method of determining K.

The technical result of the proposed method for determining the compressibility coefficient K is the ability to quickly measure this coefficient, i.e. to find the function K (t) with an error not higher than the measurement error of other physical quantities included in the flow formula (5) (P, ΔP, T, ρ _s ) in any range of thermobaric parameters and, as a result, a decrease in the error of flow measurement when using flowmeters on narrowing devices.

The technical result is achieved by the fact that in the method for quickly determining the compressibility coefficient, a volume resonator made of metal with a low coefficient of thermal expansion and with a known natural frequency in vacuum ω _{0 is used} , it is filled with gas at standard pressure and temperature, and the value of the resonant frequency ω _{s is} measured, then fill it with gas at operating pressures P and temperature T and measure the value of the natural frequency ω _p , after which the compressibility coefficient K is calculated by the ratio:

Figure 1 shows a diagram of a device that implements the proposed method. It includes a 3 cm microwave generator of the wavelength range on the Gunn 1 diode, two volume resonators made of metal with a low temperature expansion coefficient - measuring 2 and reference 3, detector of measuring channel 4, detector of reference channel 5.

The electronic part of the device consists of a control unit 8, a frequency measuring unit 9 and a stabilized power supply 10. The gas path includes a gas supply pipe 11, a reducer 12, an inlet 13 and an outlet 14 gas valves, a pressure gauge 15, a thermometer 16, a flow tube 17. A measuring resonator placed in thermostat 18.

The operation of the device is as follows.

In block 8, a sawtooth voltage is generated that controls the frequency of generator 1. More precisely, the “saw” consists of 256 steps, so that the step number (“code”) uniquely determines the voltage and, therefore, the generator frequency: thus, one-to-one correspondence between the code and frequency. The code corresponding to the resonant frequency of the resonator 2 is displayed on the front panel of the device.

The reference channel, based on the resonator 3 and the detector 5, serves to stabilize the initial frequency of the generator 1; the electronics of the control unit 8 is arranged in such a way that the resonant frequency of the resonator 3 always corresponds to the same code; in the event of a deviation from the set code value, a voltage is generated that is supplied to the Gunn diode, generator 1, which corrects the frequency drift.

The output parameter of the registration circuit is the resonant frequency of the resonator. In the absence of gas (in vacuum), the resonator frequency is equal to ω _о ; when the cavity is filled with gas with a dielectric constant ε, its frequency decreases and becomes equal to ω.

We use the relationship between the dielectric constant and gas density based on the Clausius-Mosotti relation, which connects the microscopic parameters of the gas substance — its polarizability α and molar mass M — with macroscopic, measured parameters — the density of the substance ρ and its relative dielectric constant (DP) ε [ 5-7]:

where N _A is the Avogadro number; ε _about = 8.854 · 10 ^-12 f / m is the electric constant.

Solving (5) with respect to ρ, we obtain:

Since for all gases at small and moderate pressures (P≤10 MPa) ε-1 << 1, we can put ε + 2 = 3. Then (6) can be rewritten as

The proportionality coefficient, as can be seen from (7), can be calculated from the values of M and α known for a given gas:

From expression (4) we find the compressibility coefficient

We find the density under standard conditions from (7)

where (ε - 1) s is the dielectric constant of a gas without unity under standard conditions. From (7), (9) and (10) we find:

where (ε-1) _p is the dielectric constant without unity under operating conditions.

The technical side of the procedure for measuring K is based on the following physical effect. If we take an empty metal cavity of simple geometric shape, for example a cylinder, and excite electromagnetic oscillations in it, then at some frequencies (ω ₀₁ , ω ₀₂ ...) there will be a sharp increase in their amplitude - resonance. In the absence of a substance in a cavity (in a vacuum), the values of resonant frequencies are determined only by the geometric dimensions and shape of the cavity (called a volume resonator).

When the cavity cavity is filled with gas, the speed of propagation of radio waves in it decreases, and the resonator eigenfrequencies shift ω ₀₁ → ω ₀₁ ^∗ = ω ₀₁ -Δω ₁ ; ω ₀₂ → ω ₀₂ ^∗ = ω ₀₂ -Δω ₂ etc. In this case, the relative frequency shift is determined by the dielectric constant of the gas [8; 9]:

where ω ₀ and ω ₁ are the natural frequencies of the resonator without gas and with gas, respectively.

In view of (12), expression (11) takes the form

The determination of the compressibility coefficient begins with measuring the frequency shift of the resonator under standard conditions. To do this, valve 13 and 14 are opened and the resonator 2 is purged with gas using a reducer 12 and then the volume of the resonator 2 is filled to a pressure just above P _s , after which the valves 13 and 14 are closed. After that, the temperature T _c = 293.15 K is set on the thermostat and, when the gas reaches this temperature, the valve 14 is opened and the pressure equal to the standard pressure is set on the pressure gauge 15: P _c = 1.013 · 10 ⁵ Pa, after which the valve 14 is closed. After that, using the frequency measuring unit 9, the frequency ω _s is measured. The initial frequency of the hollow resonator ω ₀ (i.e., in vacuum) at T = T _s is determined in advance and entered as a parameter in block 9.

Then the resonator 2 is again filled with gas, but at the operating pressure P and operating temperature T. To do this, fully open the gearbox 12 and valve 13, and set the temperature equal to the gas temperature in the pipeline on thermostat 18. After establishing the pressure and temperature of the gas to the workers, i.e. existing in the pipeline, and at time t = t ^∗ measure the frequency shift of the resonator ω _p .

Next, the compressibility coefficient is calculated by the formula (13); in this case, the quantity K (t) corresponding to the measurement time t = t ^∗ is obtained.

The process is easy to automate. To do this, it is enough to replace the valves 13 and 14 with electrically controlled ones, and force the temperature of the thermostat to follow the temperature of the gas in the gas pipeline.

Using the proposed method, measurements were made of the compressibility coefficient on carbon dioxide at operating pressures P = 26 ... 35 atm and temperatures T = 301-303 K.

The measurement results differed from the control data by 0.5 ... 1.0%, and the main source of error was gas temperature fluctuations, because the thermostat was absent in these measurements, and the volume resonators were made of brass, which had a rather high coefficient of thermal expansion.

Literature

1. Rules for measuring the flow of gases and liquids with standard narrowing devices RD50-213-80. M., Publishing House of Standards, 1982, 318 p.

2. GOST 8.563.2-97 GOS. Measurement of the flow rate of the amount of liquids and gases by the method of variable differential pressure.

3. Plotnikov V. M., Podreshetnikov V. A., Teterevyatnikov L. I. Instruments and means of accounting for natural gas and condensate. - L .: Nedra, 1989, 238 p.

4. GOST 30319.3-96 Natural gas. Methods for calculating physical properties.

5. Embroidered I. G., Moskalev I. N., Kostyukov V.E. and other NGZH. Density measurement of associated petroleum and natural gases based on the measurement of their dielectric constant, analysis of the problem. "Automation, telemechanization and communications in the oil industry." - M.: VNIIOENG, 2009, No. 10, 8-12 p.

6. Embroidered I. G., Moskalev I. N., Kostyukov V.E. and other NGZH. Dielcometric densitometry of oil and natural gases: fundamental difficulties. "Automation, telemechanization and communications in the oil industry." - M.: VNIIOENG, 2009, No. 11, 7-11 p.

7. Embroidered I. G., Moskalev I. N., Kostyukov V.E. and other NGZH. Experimental determination of the density of natural gas based on measurements of its dielectric constant. "Automation, telemechanization and communications in the oil industry." - M.: VNIIOENG, 2009, No. 12, 6-11 p.

8. Golant V.E. Microwave plasma research methods. - M .: Nauka, 1968, 326 p.

9. Moskalev I.N., Stefanovsky A.M. Diagnostics of plasma using open axisymmetric resonators. M .: Energoatomizdat. 1995, 145 p.

Claims (1)

A method for quickly determining the compressibility coefficient of gases and their mixtures, characterized in that the cavity resonator made of metal with a low temperature coefficient of expansion and with a known natural frequency in vacuum ω ₀ is filled with gas at standard pressure P _c and temperature T _c and the value of natural frequency ω _s , then fill it with gas at operating pressure P and temperature T and measure the value of the natural frequency ω _p , and the compressibility factor K is determined from the relation