RU2269113C1 - Method for determining physical property coefficients for natural gas and device for automatic realization of method - Google Patents

Abstract

FIELD: technology for automatic control of technological parameters and coefficients of physical properties of natural gas during its extraction, transportation, storage and distribution.

SUBSTANCE: method includes preparation of gas. Prepared controlled gas is let through serially positioned turbulent and lamellate throttle governors, absolute gas pressure is measured prior to turbulent throttle governor, in inter-throttle portion and after lamellate throttle governor. Gas temperature is measured before turbulent throttle governor and in inter-throttle portion and on basis of measured values of mentioned parameters coefficients of physical properties of natural gas (density, dynamic viscosity, compression coefficient, adiabatic curve coefficient, specific combustion heat level coefficient) are determined, while before turbulent throttling absolute pressure is maintained, providing lamellate gas flowing mode in lamellate throttle governor with maximum possible Reynolds coefficient. Device has controlled gas line with gas preparation block (filter) positioned thereon and computing device unit, to first output of which information display device is connected, turbulent and lamellate throttle governors, serially positioned on controlled gas line. Executive mechanism, for example, adjusting valve, is positioned on controlled gas line before turbulent throttle. Absolute pressure indicators are positioned before turbulent throttle governor, in inter-throttle portion and after lamellate throttle governor. Temperature indicators are positioned before turbulent throttle governor and inside the inter-throttle portion. Aforementioned indicators are connected to computing device unit, second output of which is connected to executive mechanism.

EFFECT: simplified procedure, increased speed of operation (execution in real time scale mode) for process of determining physical property coefficients of natural gas (density, dynamic viscosity, compression coefficient, adiabatic curve coefficient, specific combustion heat level coefficient.

2 cl, 1 dwg

Description

The invention relates to the field of automatic control of technological parameters and indicators of the physical properties of natural gas during its production, transport, storage and distribution. Natural gas is a (mainly) mixture of hydrocarbon gases. Indicators of the physical properties of natural gas are: its density under standard conditions, dynamic viscosity at a given pressure and temperature, compressibility coefficient at a given pressure and temperature, adiabatic index, specific heat of combustion (calorific value) of a gas. The listed indicators of the properties of natural gas (except for calorific value) are used when measuring gas flow by the method of variable pressure drop across a narrowing device (diaphragm, nozzle). The error in their determination has a noticeable effect on the error of cost-accounting measurement of gas consumption during its sale to consumers and, therefore, on the technical and economic performance indicators of both the consumer and the seller. The calorific value of gas is one of the main indicators of the quality of commercial gas. It, as well as other indicators, has a significant impact on the technical and economic indicators of consumer enterprises. This implies the importance and relevance of reliable and operational control of indicators of the physical properties of natural gas.

A known method of determining indicators of the physical properties of natural gas (density under standard conditions, dynamic viscosity and compressibility at given temperature and pressure, adiabatic exponent, specific heat of gas combustion) by the gas component composition (GOST 30319.1-96. Natural gas. Methods for calculating the properties of natural gas, its components and processed products). The method consists in preparing a controlled gas, determining the component composition, usually using a chromatograph, and calculating the above indicators of the physical properties of the gas using a computing device with software.

The disadvantage of this method is its complexity, determined by the complexity of determining the component composition of natural gas, and low efficiency.

A device for implementing this method consists of a gas preparation unit, a chromatograph, and a computing device with software. An information display device (display, printer) is connected to the output of the computing device. The known device operates as follows. The controlled gas through the preparation unit, with the help of which the reduction (lowering and maintaining a given pressure), purification from mechanical impurities and, if necessary, drying of the gas, is carried out on a chromatograph. The latter determines the component composition of the gas. Information on the percentage of each component in natural gas is input into a computing device, which, according to the appropriate program, determines (calculates) the physical properties of natural gas and displays their values on a display (or print).

A disadvantage of the known device is its complexity and low efficiency of obtaining the results of determining the indicators of the physical properties of natural gas.

The problem to which the invention is directed is to create such a technical solution that would simplify the procedure and increase the efficiency of determining the physical properties of natural gas.

To achieve the named technical result, the controlled gas is prepared, sequentially throttled through turbulent and laminar throttles; measure the absolute gas pressure in front of the turbulent throttle, in the inter-throttle portion and after the laminar throttle; measure the temperature of the gas in front of the turbulent throttle and in the inter-throttle section, and from the measured values of the parameters calculate the above indicators of the physical properties of the gas using a computing device with software, while the absolute pressure is maintained in front of the turbulent throttle, ensuring the laminar flow of gas in the laminar throttle at the maximum -possible Reynolds number (Re = 2300).

To achieve the named technical result, the known device for determining the physical properties of natural gas, comprising a line of controlled gas with a gas treatment unit (filter) installed on it, as well as a computing device, to the first output of which an information display device is connected, additionally contains: an actuator ( for example, control valve), turbulent and laminar throttles, sequentially installed on the line of the controlled gas; absolute pressure sensors installed in front of the turbulent throttle, in the inter-throttle section and after the laminar throttle; temperature sensors installed in front of the turbulent throttle and in the inter-throttle section; while the outputs of the above sensors are connected to the computing device, and an actuator is connected to its second output.

Determination of the physical properties of natural gas is that: the controlled gas after its preparation (filtration and, if necessary, drying) is passed through sequentially installed turbulent and laminar throttles; measure the absolute gas pressure in front of the turbulent throttle, in the inter-throttle portion and after the laminar throttle; measure the temperature of the gas in front of the turbulent throttle and in the inter-throttle section; the measured values of the listed parameters calculate the indicators of the physical properties of natural gas (gas density under standard conditions; compressibility coefficient and dynamic viscosity of gas at specified pressure and temperature values, adiabatic index, specific heat of gas combustion), while absolute pressure is maintained in front of the turbulent throttle, providing laminar gas flow in a laminar throttle at the highest possible Reynolds number (Re = 2300). The density of natural gas under standard conditions is calculated from the formula (the derivation of the formula is given in Appendix 1):

Where

ρ _st is the gas density under standard conditions, kg / m ³ ;

A is a constant coefficient determined by experimental data;

P ₁ - absolute gas pressure in front of the turbulent throttle, Pa;

P ₂ is the absolute gas pressure in the inter-throttle portion, Pa;

P ₃ is the absolute gas pressure in after the laminar throttle, Pa;

T ₁ - gas temperature in front of the turbulent throttle, K;

T ₂ - gas temperature in the inter-throttle section, K;

μ is the dynamic viscosity of the gas, Pa · s;

K _z1 = Z ₁ / Z _st is the compressibility coefficient of the gas in front of the turbulent throttle;

K _z2 = Z ₂ / Z _st is the gas compressibility coefficient in the inter-throttle section;

Z ₁ , Z ₂ , Z _st - gas compressibility factor, respectively, under working conditions and under standard conditions.

k is the adiabatic exponent.

The values of the compressibility coefficients K _z1 and K _{z2 are} determined according to the algorithm given in GOST 30319.2-96 (GOST 30319.2-96. Natural gas. Methods for calculating physical properties. Determination of the compressibility factor) depending on the gas density under standard conditions, absolute pressure and gas temperature , i.e.

The dynamic viscosity of natural gas is calculated according to the formula given in GOST 30319.1-96 (GOST 30319.1-96. Natural gas. Methods for calculating the properties of natural gas, its components and processed products) and having the form

where μ is the dynamic viscosity of the gas, μPa · s;

X _a is the volume fraction of nitrogen (N ₂ );

X _y is the volume fraction of carbon dioxide (CO ₂ ).

The value of the adiabatic exponent k is determined by the formula given in GOST 30319.1-96 and having the form

The values of the highest N _s.v. and lower _H.s.n. specific heat of combustion are determined by the formulas given in GOST 30319.1-96 and having the form

The values of X _a (volume fraction of nitrogen (N ₂ )) and X _y (volume fraction of carbon dioxide (CO ₂ )) are determined by the results of chromatographic analysis.

The value of the coefficient "A" is determined by experimental data before the implementation of the proposed method (the procedure is described in Appendix 1) from the formula

where ρ _st is the gas density measured by one of the known devices (for example, a pycnometer).

A device for implementing the proposed method is shown in the drawing.

The device consists of: a line of controlled gas, including an inlet section 1, an inter-throttle section 2 and an outlet section 3 connected by an input to a source of controlled gas (for example, a gas pipeline, separator, etc.), and an outlet to a gas recovery line 4; an actuator (control valve) 5 installed on the inlet section 1 of the line of controlled gas; filter 6; turbulent throttle 7; laminar throttle 8; absolute pressure sensors 9, 10, 11 installed on the line of the monitored gas, respectively, in front of the turbulent throttle 7, in the inter-throttle section, after the laminar throttle; temperature sensors 12, 13 installed in the inlet section in front of the turbulent throttle and in the inter-throttle section in front of the laminar throttle; a computing device 14, to the inputs of which the listed sensors are connected, and to the outputs - an actuator and an information display device (for example, a liquid crystal display) 15. The computing device contains a digital gas pressure regulator in front of the turbulent throttle 16, a program unit for calculating the Reynolds number 17, a program unit (digital controller) 18, software unit for calculating ρ _st , μ, K _z2 19.

The device operates as follows.

The controlled gas from, for example, the gas pipeline passes through an actuator (control valve) 5, a filter 6, a turbulent 7 and a laminar 8 throttles to the gas recovery line 4. Using the control valve 5 in the inlet section 1 is automatically maintained the required pressure. The filter 6 purifies the gas from mechanical impurities and liquids, which prevents clogging of the chokes. With the passage of gas through a turbulent throttle, the pressure P ₂ in the inter-throttle portion 2 decreases. The pressure P ₂ depends on the density ρ _{st of the} gas, as well as on the pressure P ₁ before the turbulent throttle, the pressure P ₃ after the laminar throttle, the temperature of the gas T ₁ , before the turbulent throttle, the temperature T _{2 of the} gas in the inter-throttle section 2, as well as the geometric the sizes of both throttles and the flow coefficient of the turbulent throttle. The influence of the geometric dimensions of the throttles and the flow coefficient of the turbulent throttle on the pressure value P ₂ is determined by the value of coefficient "A", which is included in the above equation for determining the gas density under standard conditions. The calculation formula for determining the coefficient "A" (for a conclusion, see Appendix 1) has the form

where ε is the flow coefficient of the turbulent throttle;

F is the flow area of the turbulent throttle, m ² ;

L is the length of the laminar throttle (capillary), m;

D _L - diameter of the passage channel of the laminar throttle, m

However, the value of coefficient "A" is determined by experimental data (as described in Appendix 1) and thereby eliminates the need to determine the geometric dimensions of both throttles and the flow coefficient of a turbulent throttle to determine the value of coefficient "A" by calculation. It is practically impossible to obtain high accuracy in determining the coefficient "A" by calculation due to the large errors in determining the geometric dimensions of both throttles and the flow coefficient of the turbulent throttle. Therefore, the value of the coefficient "A" is determined by the experimental data for each device. In other words, an individual identification of coefficient “A” is required for each device. This is inconvenient, but there is no other alternative.

The pressure P ₂ in the inter-throttle portion 2 is the main informative parameter, depending on the density of the gas. Other parameters (P ₁ , T ₁ , T ₂ , P ₃ ) do not depend on the gas density, but their neglect leads to unacceptable errors in determining the gas density. If these parameters (P ₁ , T ₁ , T ₂ , P ₃ ) were stabilized, then the gas density could be determined only by the pressure value P ₂ . However, stabilization of the parameters with high accuracy would complicate the device. It is easier to measure them and take the measurement results into account when determining the gas density. Therefore, in the proposed device, all parameters are measured using sensors 9, 10, 11, 12, 13 and the signals from these sensors are fed to the corresponding inputs of the computing device (controller) 14. The computing device 14 solves two problems.

First task. The computing device 14, based on the measured values of the parameters P ₁ , P ₂ , P ₃ , T ₁ , T ₂ and a pre-identified coefficient "A", calculates the density ρ _{st of the} gas under standard conditions and outputs it to the information display device 15 (for example, to a liquid crystal display). Knowing the density of the gas, the computing device also calculates other indicators of the physical properties of the gas. The calculation of the density and other above-mentioned indicators of the physical properties of the gas is carried out by the program unit 19 of the computing device 14. The calculation of the indicators of the physical properties of the gas is carried out from equations (1) - (7).

The second task. The computing device 14, together with the actuator (control valve) 5, implements the function of a cascade automatic system for controlling the Reynolds number for the laminar throttle. The function of the Reynolds number sensor is implemented by the program unit 17, which calculates the Reynolds number from the equation (for the conclusion, see Appendix 1, formula (A.18)).

In this case, the values of density ρ _st , dynamic viscosity μ ₂ and compressibility coefficient K _{z2 of the} gas are supplied to program unit 17 from program unit 19, and the values of P ₂ , P ₃ , T ₂ are input from sensors 10, 11 and 13, respectively. _L and L are entered manually. The calculated value of the Reynolds number is fed to the input of a digital controller (program block) 18 Reynolds number. The set value of the Reynolds number (Re _z = 2300) is entered into the input of this controller (by the user). The digital controller 18 of the Reynolds number together with the sensor 17 of the Reynolds number form the external circuit of a cascade automatic system for controlling the Reynolds number. The regulatory effect of this control loop is the set value of the gas pressure P _1z before the turbulent throttle 7. When the PID control law is implemented, the regulatory effect is calculated by the recurrence expression (see Appendix 1)

where εRe (i) = Re (i) -Re _z (i) is the error in the regulation of the Reynolds number at the ith step;

Re (i) - the current value of the Reynolds number at the i-th step;

Re _z (i) is the set value of the Reynolds number at the i-th step;

P _1z (i) - task pressure regulator at the i-th step (the regulatory effect of the regulator of the external control loop);

q ₀ , q ₁ , q ₂ - settings of the digital controller.

For small quantization clocks, the settings q ₀ , q ₁ , q ₂ can be calculated using the settings K, T ₁ and T _{D of the} analog PID controller, using the formulas:

q ₀ = K * (1 + T ₀ / (2 * T ₁ ) + T _D / T ₀ );

q ₁ = -K * (1 + 2 * T _D / T ₀ -T ₀ / (2 * T ₁ ));

q ₂ = K * T _D / T ₀ ;

where K is the transmission coefficient of the analog PID controller:

T ₁ - integration constant of the analog PID controller;

T _D - differentiation constant of the analog PID controller;

T ₀ - quantization cycle, s.

From the expression (11) it follows that to calculate the set pressure value at the ith step P _1z (i) in the memory of computing device 14 (more specifically, in program block 18), it is necessary to store the value of the set pressure value P _1z (i-1) for the previous step and the values of the regulation error in i-1 and i-2 steps.

The set value P _1z (i) at the i-th step is supplied to the input of the digital regulator (program unit) 16 of the gas pressure P ₁ . To the other input of this regulator is the current pressure value P ₁ from the pressure sensor 9. The digital controller (program unit) 16 together with the pressure sensor 10 and the actuator (control valve) 5 form the internal circuit of a cascade automatic Reynolds number control system. Digital controller 16 calculates the difference between the current and set pressure values P ₁ , i.e. regulation error, and depending on its size and sign acts on the actuator 5 until then, until the pressure P ₁ becomes equal to the specified.

The presence in the cascade system of automatic control of the internal pressure control loop P ₁ makes it possible to pre-suppress external disturbances, for example, arising from a change in gas pressure in the gas pipeline, and thereby improve the quality of the process of controlling the Reynolds number.

Using the proposed technical solution makes it possible to simplify the procedure and increase the efficiency (in real time) of determining indicators of the physical properties of natural gas.

Annex 1.

SUBSTANTIATION OF THE METHOD FOR DETERMINING INDICATORS OF PHYSICAL PROPERTIES OF NATURAL GAS BY EXHAUST PARAMETERS THROUGH TURBULENT AND LAMINARY THROTTLES

1. The relationship between flow parameters and gas density

Consider the process of flowing natural gas through successively installed turbulent and laminar throttles on a line of controlled gas. The purpose of the review is to obtain a dependence establishing a mathematical relationship between the gas density under standard conditions and gas flow parameters.

By the nature of the gas flow in the channels, the inductors are divided into laminar and turbulent ones [1]. Turbulent throttles are characterized by small ratios of the length of the throttle channel to its diameter and turbulent gas flow. Typically, in turbulent chokes, the ratio of the channel length to its diameter does not exceed 10. Since the channel is small and the flow velocity is high, the gas flowing through the throttle does not have time to exchange heat with the channel walls, and the thermodynamic process in this type of chokes is considered adiabatic [1 ].

The gas flow in turbulent chokes can occur both with subsonic (subcritical mode) and with sound speeds (supercritical mode). The flow regime through the turbulent throttle is determined by the ratio of the pressures P ₁ and P ₂ before and after it. The pressure ratio at which the transition from subsonic speed to sound occurs, is called critical and denote (P ₂ / P ₁ ) _cr . It is known [1] that

where k is the adiabatic exponent.

The pressure drop, and therefore the main losses in turbulent throttles, is due to compression of the flow at the inlet to the throttle and expansion at the outlet of it. Losses due to friction (along the length of the throttle) are small and neglected.

Consider the regime of subcritical gas flow through a turbulent throttle.

The mass flow rate G _{td of} gas (in kg / s) through a turbulent throttle is calculated by the formula [1]

Where

ε is the flow coefficient;

F - throttle bore area, m ² ;

P ₁ - absolute gas pressure in front of the throttle, Pa;

P ₂ - absolute gas pressure after the throttle, Pa;

R is the gas constant, J / (kg K);

T ₁ - gas temperature in front of the throttle, K;

K _z1 = Z ₁ / Z _st is the gas compressibility coefficient;

Z ₁ , Z _st - gas compressibility factor, respectively, under working conditions and under standard conditions;

k is the adiabatic exponent.

Dependencies for calculating compressibility factors Z = Z (ρ _st , P _st , T _st ) and adiabatic coefficient k = k (ρ _st , P _st , T _st ), where ρ _st (kg / m ³ ) is the gas density under standard conditions are given respectively in GOST 30319.2-96 [2] and GOST 30319.1-96 [3]. As we see, the compressibility coefficient and the adiabatic index depend on the gas density under standard conditions (P _st = 101325 Pa, T _st = 293.15 K, GOST 30319.0-96.

Formula (A.2) includes the gas constant, the value of which is calculated by the well-known expression

where R _u = 8314.31 J / (kg K) is the universal gas constant;

M is the relative molecular weight of the gas, kg / kmol.

Under standard conditions, the gas density (kg / m ³ ) is related to the relative molecular weight of the gas by a known ratio

where V _st = 24.0546 m ³ / kmol is the specific molar volume of gas under standard conditions.

From formulas (A.4) and (A.5) we obtain

where C _r = R _u / V _st = 345.64 J / (m ³ · K).

Substituting the expression (A.6) into the formula (A.2), we obtain the equation of the mass flow of gas through the turbulent throttle

where K _z1 = Kz (ρ _st , P ₁ , T ₁ ) and k = k (ρ _st , P ₁ , T ₁ ) are functions of the gas density under standard conditions, operating pressures, and gas temperature.

We proceed to consider the gas flow through the laminar throttle.

The mass flow rate G _{LD of} gas (in kg / s) through the laminar throttle (capillary) is determined by the Poiseuille formula [1, p. 37]

where π = 3.14;

D _L is the diameter of the passage section of the capillary, m;

P ₂ - absolute gas pressure in front of the laminar throttle, Pa;

P ₃ - absolute gas pressure after the laminar throttle, Pa;

μ - dynamic viscosity, Pa · s;

L is the length of the laminar throttle, m;

R is the gas constant, J / (kg · deg);

T ₂ - gas temperature, K;

To _z2 is the gas compressibility coefficient at P ₂ and T ₂ .

We substitute the expression (A.6) into (A.8). Get

or

We assume that the gas pressure after the turbulent throttle is equal to the pressure in front of the laminar throttle. In other words: we accept that there are no pressure losses in the inter-throttle section of the controlled gas line (or they can be neglected due to their vanishingly small value). In the steady state, the mass flow of gas through the turbulent throttle is equal to the mass flow of gas through the laminar throttle. Equating the left sides of equations (A.7) and (A.10), we obtain

Where

The values of compressibility coefficients K _z1 and K _{z2 are} determined according to the algorithm given in GOST 30319.2-96 [2], depending on the gas density under standard conditions, absolute pressure and gas temperature, i.e.

The value of the adiabatic exponent k is determined by the formula given in GOST 30319.1-96 [1] and having the form

The dynamic viscosity of natural gas and other gas mixtures, as shown in [3] and [5], clearly depends on the density of the gas under standard conditions. GOST 30319.1-96 [3] gives the dependence of the dynamic viscosity of natural gas on its density under standard conditions. With the above conventions, it has the form

where μ is the dynamic viscosity of the gas, μPa · s;

X _a is the volume fraction of nitrogen (N ₂ );

X _y is the volume fraction of carbon dioxide (CO ₂ ).

To convert the dynamic viscosity from μPa · s calculated according to equation (A.17) to Pa · s, it is necessary to divide its value by 10 ⁶ .

According to GOST 30319.1-96 [3], formula (A.17) is applicable at gas pressures up to 0.5 MPa and in the temperature range 240-360 K. The error in determining the gas viscosity in this range does not exceed 1.0% for methane. Natural gas, as a rule, contains mainly methane (95-100%). Therefore, GOST 30319.1-96 recommends the formula (A.17) for determining the dynamic viscosity of natural gas.

Equation (A1.11) establishes an unambiguous relationship between the density ρ _{st of the} gas under standard conditions and the gas flow parameters P ₁ , T ₁ , P ₂ , T ₂ , P ₃ . It is impossible to express explicitly the dependence of ρ _st on these parameters because of the complexity of the dependences of the compressibility coefficients, the adiabatic exponent, and the dynamic viscosity on the gas density ρ _st . However, it is possible to solve equation (A.11) with respect to ρ _st by a numerical method. To do this, you need to know the values of P ₁ , T ₁ , P ₂ , T ₂ , P ₃ and A.

The values of the parameters P ₁ , T ₁ , P ₂ , T ₂ and P ₃ can be measured by tools, and the value of the coefficient "A" (we will call this coefficient the constant of the device) can and must be determined from experimental data. To do this, conduct an experiment consisting in the fact that gas is passed through turbulent and laminar throttles in series, the parameters P ₁ , T ₁ , P ₂ , T ₂ , P ₃ are measured, the density ρ _{st of the} gas is determined under standard conditions (by a pycnometer or by component gas composition) and from equation (A.11) determine the value “A” of the device constant (for example, by a numerical method of half division, by a personal computer). The experiment is carried out several times and takes the average value of coefficient A. Calculation of the device constant by the formula (A1.12) leads to an unacceptable error due to the large error in determining ε, F, D _L , L.

From the above analysis, a method for determining gas density under standard conditions follows. It consists of the following. Controlled gas is passed through turbulent and laminar throttles installed in series on the controlled gas line; measure the absolute pressure P ₁ and the gas temperature T ₁ in front of the turbulent throttle, the absolute pressure P ₂ and the gas temperature T ₂ in the inter-throttle line, the absolute gas pressure P ₃ after the laminar throttle and calculate the gas density ρ _st under standard conditions from the equation ( A.11), using the value of the coefficient "A" obtained in advance.

2. Mathematical modeling of the process of gas outflow through turbulent and laminar throttles

The main informative parameter, depending on the gas density, is the pressure P ₂ in the inter-throttle section of the line of the controlled gas. The values of parameters such as pressure P ₁ in front of the turbulent throttle and pressure P ₃ after the laminar throttle are determined by the choice of the user and are not informative in the sense of their dependence on the gas density. These are disturbing parameters. Their values should be taken into account in the process of determining the gas density. The same applies to the temperatures T ₁ and T _{2 of the} gas. Their values are determined by the user's choice.

The purpose of the study is to determine the dependence of the gas pressure in the inter-throttle section of the line of the controlled gas on its density under standard conditions.

To achieve this goal, a mathematical model of the gas flow through two successively installed turbulent and laminar throttles and the ROTULA 1.BAS program, which calculates the dependence of the gas pressure in the inter-throttle chamber on the gas density, were developed. (The text of the program is attached, Appendix 2).

The program is written in the algorithmic language TURBOBASIC. A program consists of a main program and one subprogram. The main program implements an algorithm for interactive input of initial data and output of calculation results in one of three user-defined directions: to a monitor, to print, to a file. The main program translates the parameters into the required dimensions, calculates (in a cycle) the gas density values, the pressure values in the inter-throttle section of the monitored gas line, the gas mass flow rate and the Reynolds criterion for the laminar throttle. The subprogram calculates the values of the gas compressibility coefficient (according to the algorithm given in GOST 30319.1-96 [2], the adiabatic exponent and dynamic viscosity of the gas, as well as the specific heat of gas combustion.

As initial data, the values D _t , D _L , L, T ₁ , T ₂ , P ₁ , P _{3 are used} , as well as the initial value of the gas density ρ _n and the increment of the gas density dρ. Different values of ρ are formed in a cycle with a given increment of gas density. The initial data is entered into a personal computer in an interactive mode (at the request of a personal computer). As a result of the program, for each gas density value under standard conditions, the values of pressure Р ₂ , gas mass flow through turbulent and laminar throttles, dynamic viscosity, gas compressibility coefficients, adiabatic index and Reynolds number for the laminar throttle, and also the coefficient εf = ε × are calculated F, which is in the formula (A.7).

The Reynolds number (criterion) for a laminar throttle is determined by the formula

This formula is obtained as follows.

It is known [6] that

where v is the gas velocity, m / s;

d _L is the inner diameter of the capillary, m;

ρ is the gas density under operating conditions, kg / m ³ ;

μ ₂ is the dynamic viscosity of the gas, Pa · s.

Gas velocity in laminar throttle

where F = πd _L ^2/4;

Q is the volumetric gas flow through the laminar throttle, m ³ / s;

G _ld - mass gas flow through the laminar throttle, kg / s.

The gas density under operating conditions is determined by the formula

Substituting equations (A.8) and (A.21) into (A.20), we obtain

Substituting expressions (A.22) and (A.21) into equation (A.19), after simple transformations, we obtain the formula (A.18) for calculating the Reynolds criterion for the laminar throttle. When modeling took: Overpressure in front of the turbulent throttle P ₁ = 10000 mm century. (Absolute pressure was calculated in the program). Absolute pressure after a laminar throttle Р ₃ = 100000 Pa (barometric pressure).

The diameter of the turbulent D _t = 0.2 mm, the diameter of the laminar throttle D _L = 0.3 mm.

The length of the laminar throttle is L = 100 mm.

The initial gas density under standard conditions is ρ _n = 0.45 kg / m ³ .

The increase in gas density dρ = 0.05 kg / m ³ .

The number of steps in gas density N = 12.

The value of P _{1 was} varied. Printed: for each gas density value - pressure Р ₂ in the inter-throttle line, gas mass flow through turbulent and laminar throttles, Reynolds number for the laminar throttle.

The simulation results showed that the pressure P ₂ in the inter-throttle portion substantially depends on the gas density. Moreover, the greater the pressure P ₁ in front of the turbulent throttle, the greater the sensitivity. Figure 2 shows the dependence of the increment of the excess pressure dP ₂ on the gas density at various pressures in front of the turbulent throttle. By the pressure increment dP _{2 was} understood the difference between the pressure P ₂ at ρ = 0.5 kg / m ³ and the pressure P ₂ at ρ = 1.05 kg / m ³ . From figure 2 it follows that the dependence of the pressure increment P ₂ on the gas density in the general case is non-linear. When changing the gas density from 0.55 kg / m ³ to 1.05 kg / m ³ , i.e. by dρ = 0.55 kg / m ³ the pressure increment dP ₂ depends on the gas pressure P ₁ in front of the turbulent throttle. The values of dP ₂ for dρ = 0.55 kg / m ³ and various P ₁ are given in table 1. The sensitivity values are also given there, which means the ratio Kr = dP ₂ / dρ.

Table 1
The dependence of the sensitivity of Kr on the pressure P ₁ before the turbulent throttle P ₁ , mmHg 4000 6000 8000 10,000 dP ₂ , mm water column 767.3 1144.3 1493.6 1811.3 Kr, mm water.article / kg / m ³ 1395.1 2080.5 2715.6 3293.3

From table 1 it follows that to increase the sensitivity, and hence the accuracy of determining the gas density, the pressure in front of the turbulent throttle should be increased. However, the pressure increase P ₁ imposes restrictions associated with the need to provide a laminar regime of gas movement through the laminar throttle. Figure 3, built on the basis of the simulation results, shows the dependence of the Reynolds number on the gas density at various pressures P ₁ . As can be seen, the laminar regime (Re <= 2300) of the gas in the laminar throttle at P ₁ = 10000 mm water column can be provided only with a gas density of less than 0.62 kg / m ³ . At a pressure of P ₁ = 4000 mm water column the laminar regime of gas movement can be provided over the entire range of gas density changes (from 0.5 to 1.1 kg / m ³ ). However, when P ₁ = 4000 mm water column we have the lowest sensitivity. An important conclusion follows from this: in order to achieve maximum sensitivity for monitoring the gas density, the pressure in front of the turbulent throttle must be maintained such that the Reynolds number for the laminar throttle is Re = 2300.

Technically, this can be realized using an automatic control system (ACP) with feedback. In this case, two options are possible.

The first option: they implement a single-loop ASR with a virtual Reynolds number sensor, a PID controller and an actuator on the line of the monitored gas. A virtual Reynolds number sensor is a computing device (controller) that in real time calculates the Reynolds number from the measured parameters of the gas being monitored. The calculations are carried out according to equation (A.18), while using the appropriate sensors measure P ₂ , P ₃ and T ₂ , and ρ _st is determined by the proposed method. The output signal of the virtual Reynolds number sensor is introduced, for example, into the PID controller as an adjustable value. The set value of the Reynolds number (Re = 2300) is introduced into the regulator's input. The mismatch of these signals is converted according to the adopted law (for example, according to the PID law) into a regulatory effect on the actuator. As a result, the specified Reynolds number (Re = 2300) is automatically maintained. It is clear that the computational operations associated with the implementation of a virtual sensor of the Reynolds number and, for example, the PID control law, can be performed by one computing device (controller).

The second option: they implement a cascade ASR having internal and external control loops. The internal circuit is a conventional single-circuit pressure ASR P ₁ containing a gas pressure sensor (P ₁ ), an automatic controller (for example, a PID controller) and the aforementioned actuator on the monitored gas line. The task of this ACP (pressure setpoint P ₁ ) is entered by an external circuit containing a virtual Reynolds number sensor and, for example, a PID controller of the Reynolds number. The set value of the Reynolds number is entered by the user. When the current value of the Reynolds number deviates from the set value, the external circuit generates an output signal that is supplied as the set value to the input of the pressure regulator. The latter maintains a pressure P ₁ at which the current value of the Reynolds number is equal to the specified value (Re = 2300). The second version of the ACP provides the best quality regulation, because occurring pressure deviations P ₁ (from external disturbances) are eliminated in advance by the internal control loop.

The algorithm of the digital PID controller [7, p. 82] of the Reynolds number is

where εRe (i) = Re (i) -Rez (i) is the error in the regulation of the Reynolds number at the ith step;

Re (i) - the current value of the Reynolds number at the i-th step;

Rez (i) is the set value of the Reynolds number at the i-th step;

P ₁ z (i) - assignment to the pressure regulator at the i-th step (the regulating effect of the regulator of the external control loop).

For small quantization clocks, the settings q ₀ , q ₁ , q ₂ can be calculated using the settings K, T ₁ and T _{D of the} analog PID controller [7], according to the formulas

q ₀ = K * (1 + T ₀ / (2 * T ₁ ) + T _D / T ₀ );

q ₁ = -K * (1 + 2 * T _D / T ₀ -T ₀ / (2 * T ₁ ));

q ₂ = K * T _D / T ₀ ;

where K is the transmission coefficient of the analog PID controller:

T ₁ - integration constant of the analog PID controller;

T _D - differentiation constant of the analog PID controller;

T ₀ - quantization cycle, s.

Similarly, the operation algorithm of the digital PID pressure controller has the form

where U (i) is the regulatory effect of the pressure regulator at the i-th step;

εP ₁ (i) = P ₁ (i) -P ₁ z (i) - error of pressure regulation P ₁ at the i-th step;

P ₁ (i) is the current value of pressure P ₁ at the i-th step;

P ₁ z (i) is the set pressure value P ₁ at the i-th step.

3. Identification of the coefficient "A"

Identification of the coefficient "A" is carried out according to experimental data.

The technology of the experiment is described above. From equation (A.11) it follows that

The values of the compressibility coefficients K _z1 and K _{z2 are} determined by the algorithm given in GOST 30319.2-96 [2], depending on the gas density under standard conditions, absolute pressure and gas temperature.

The value of the adiabatic index k is determined by the formula given in GOST 30319.1-96 [1], depending on the density of the gas under standard conditions.

The dynamic viscosity of natural gas is determined by the formula given in GOST 30319.1-96 [1], depending on the density of the gas under standard conditions and gas temperature.

To calculate the coefficient "A" on the PC, the program ROTULA2.BAS was developed. The program is written in the algorithmic language TURBOBASIC. The text of the program is attached, Appendix 2. The program consists of a main program and a subprogram. The main program carries out: input of the initial data in an interactive mode, the choice of the direction of the output of the calculation results (on the display, on the printer or in the file), the printing of the initial data, the calculation of the absolute pressure from the overpressure, the calculation of the coefficient "A", the output of the coefficient "A" in one of the user-defined directions. The subprogram calculates: compressibility coefficients, adiabatic exponent, and dynamic viscosity of the gas.

The program was tested on specific data. Two examples are considered. In the first example, the initial data was taken: P ₁ = 4000 mm H ₂ O, P ₃ = 100,000 Pa, T ₁ = 300 K, T ₂ = 300 K, ε = 0.7, D _t = 0.20 mm, D _L = 0.3 mm, L = 100 mm, X _a = 0, X _y = 0. In the second: P ₁ = 4000 mm H ₂ O, P ₃ = 100,000 Pa, T ₁ = 300 K, T ₂ = 300 K, ε = 0.7, D _t = 0.20 mm, D _L = 0.3 mm, L = 100 mm , X _a = 0, X _y = 0.

In the first example, the gas density under standard conditions was ρ = 0.7 kg / m ³ , and the overpressure in the inter-throttle section was Р ₂ = 2505.9 mm water column, in the second example: ρ = 0.8 kg / m ³ , and Р ₂ = 3136.1 mm water column In the first example, the coefficient A = 0.5827 × 10 ^{9 is} obtained, in the second - A = 0.5816 × 10 ⁹ , i.e. almost the same values. The calculation of coefficient A by the formula (A.12), which was used to model the process of gas outflow, gave A = 0.5817 × 10 ⁹ . Thus, it can be argued that the coefficient identification program “A” gives good results.

4. Calculation of gas density under standard conditions for flow parameters

The calculation of the gas density under standard conditions, as indicated above, is carried out from the formula (A.11)

Where

In this case, coefficient A is determined from experimental data, as indicated in the previous section.

Manual calculation of ρ _st from formula (A.11) is practically impossible due to the cumbersome calculation of K _z1 , K _z2 , k, μ and P _ot . Therefore, the ROTULA3.BAS program was developed. The program is developed in the algorithmic language TURBOBASIC. The text of the program is attached, Appendix 2. The program consists of a main program and one subprogram. The main program implements: input and printing of input data in an interactive mode, selection of the direction of output of the values of the source data and calculation results (to a display, printer or file), recalculation of the input values of overpressure to absolute pressures, calculation and printing of gas density at standard conditions, Reynolds numbers and mass gas flow through the laminar throttle. The subprogram carries out: calculation of gas compressibility coefficients, gas viscosity in a laminar throttle, adiabatic index, higher and lower calorific value of gas. All these values are printed. The gas density under standard conditions is calculated by the method of successive approximations (half division method). The algorithm for calculating the gas density has the form

Ron = 0.2

Rok = 1.8

3 Ro = 0.5 * (Ron + Rok)

Call Zet (P1m, T1, Ro, Xa, Xy, Kz1, Mu1, Kad1, Hh1, Hl1)

Call Zet (P2m, T2, Ro, Xa, Xy, Kz2, Mu2, Kad2, Hh2, Hl2)

'Determination of the calculated coefficient Ar'

Pot = (P2a / P1a) ^ (2 / Kad1) - (P2a / P1a) ^ ((Kad1 + 1) / Kad1)

B1 = P1a * (Mu2 / 1,000,000) * Kz2 * T2 / ((P2a-P3) * (P2a + P3))

B2 = SQR (Kad1 * Pot / (Kz1 * (Kad1-1) * T1))

B3 = B1 * B2

Ar = SQR (Ro) / B3

EA = Ar-A

If Abs (EA) <0.001 * A then goto 1

End if

If EA <0 then

Ron = Ro goto 3 else Rok = Ro goto 3

End if

1 Further calculation and printout of calculation results.

The algorithm includes:

1. Calculation of the average (half) value of the gas density from the accepted initial Ron and final Rok density values. (Accepted: at the first step, Ron = 0.2, Rok = 1.8, which covers the possible range of changes in the density of natural gas).

2. Calculation of Kz1, Kz2, Mu2, k according to the subroutine.

3. The calculation of the coefficient Ar (The calculated value of the coefficient "A") according to the formula (A.28)

4. Determination of the residual of the calculated value of the coefficient Ar with the actual A value using the formula EA = Ar-A.

5. Verification of the condition: If the absolute value of the residual EA is less than 0.001 * A, then the gas density value calculated in paragraph 1 is taken as the solution to the problem. Otherwise, the residual sign is checked. If the discrepancy is negative, then they take Ron = Ro, otherwise - Rok = Ro, and return to item 1.

6. The calculation process is continued until the residual becomes less than 0.001 A. The accuracy of calculating the gas density Ro can be arbitrarily increased by taking the appropriate value of the permissible residual.

The ROTULA3.BAS program has been tested with two specific examples. In the first example, the initial values were taken for ρ = 0.7 kg / m ³ P ₁ = 4000 mm water column, P ₂ = 2505.9 mm water column, T ₁ = T ₂ = 300 K, D _L = 0.3 mm, L = 100 mm and barometric pressure Pb = 10125 Pa. Coefficient "A" was taken according to the identification results (see the previous section): A = 0.5817x10 ⁹ . As a result of the calculation, the gas density was ρ = 0.6984 kg / m ³ , versus 0.7 kg / m ³ , as it should be. This convergence of the result indicates a decent performance of the program. In addition to gas density, we calculated: dynamic viscosity μ = 0.1111 × 10 ² μPa · s of gas in the laminar throttle, the highest Hh = 38.55 MJ / m ³ and the lowest Hl = 34.77 MJ / m ³ calorific value, as well as adiabats Kad = 1.2937 and gas compressibility coefficients K _z1 = 1.0521, K _z2 = 1.0524.

In the second example, the following data were taken as initial data: P ₁ = 6000 mm H ₂ O, P2 = 3136 mm H ₂ O, P ₃ = 100000 Pa, T ₁ = T ₂ = 300 K, A = 0.5817 × 10 ⁹ , D _L = 0.30 mm, L = 100 mm for ρ = 0.8 kg / m ³ . As a result of solving the problem, we obtained ρ = 0.8 kg / m ³ , i.e. absolutely exact value. Thus, the developed program ROTULA3.BAS is efficient and can be used to calculate the gas density under standard conditions by the parameters of the gas flow through sequentially installed turbulent and laminar throttles.

5. The effect of nitrogen and carbon dioxide on the accuracy of determining the density of natural gas

The formulas for calculating the compressibility coefficient, adiabatic exponent, and dynamic viscosity of a gas include the values: nitrogen and carbon dioxide contents. Therefore, it should be expected that their neglect will lead to an error in determining the density of natural gas under standard conditions. However, it is unclear what their quantitative effect on the error in determining the gas density. In order to clarify this issue, mathematical modeling of the process of determining the gas density was carried out.

As an example, we considered the case of gas outflow through two throttles with the initial data: P ₁ = 6000 mm water column, P ₃ = 100,000 Pa, T ₁ = T ₂ = 300 K, A = 0.5817 × 10 ⁹ , D _L = 0.3 mm, L = 100 mm, Pb = 101325 Pa, X _a = X _y = 0%. In this case, the gas pressure in the inter-throttle section P ₂ = 3136.1 mm water column and gas density ρ _st = 0.8 kg / m ^{3 was} obtained. With the same initial data, the gas density was determined at different values of X _a and X _y . The results of solving the problem are shown in the table.

X _a ,% 0 2 four 6 8 X _y ,% 0 2 four 6 8 ρ _st , kg / m ³ 0.8000 0.8219 0.8438 0.8687 0.8922

As can be seen, the neglect of the content of nitrogen and carbon dioxide in determining the gas density can lead to a significant error. This error will appear in the case when the identification of the coefficient "A" was carried out on natural gas that did not contain nitrogen and carbon dioxide, and the density of the gas containing these components was determined. The rules follow from here: 1. Identification of coefficient "A" should be carried out on the gas whose density will be determined. 2. When determining the gas density, the values of X _a and X _y should be entered into the computing device based on the results of, for example, chromatographic analysis.

Information sources

1. Dmitriev V.N., Gradetsky V.G. Fundamentals of pneumatic automation. M.: Mechanical Engineering, 1973, 360 pp.

2. GOST 30319.2-96. Natural gas. Methods for calculating physical properties. Determination of compressibility factor.

3. GOST 30319.1-96. Natural gas. Methods for calculating the properties of natural gas, its components and processed products.

4. GOST 30319.0-96. Natural gas. Methods for calculating physical properties. General Provisions

5. Golubev I.F., Gnezdilov N.E. The viscosity of gas mixtures. M .: Publishing house "Standards". - 1971. 327 s.

6. Kremlin P.P. Flow meters and quantity counters. Vol. 3, rev. and add. L .: Engineering (Leningrad branch), 1975.776 p. with silt.

7. Iserman R. Digital control systems. Translated from English - M .: Mir, 1984. - 541 p., Ill.

Appendix 2

PROGRAMS:

1. ROTULA1.BAS: "CALCULATION OF GAS PRESSURE IN AN INTER-DOMESTIC CHAMBER DEPENDING ON THE DENSITY OF NATURAL GAS. THROTTLES: TURBULENT-LAMINAR"

2. ROTULA2.BAS: "IDENTIFICATION OF THE COEFFICIENT" A "BY THE PARAMETERS OF THE EXHAUST OF GAS THROUGH TURBULENT AND LAMINARY THROTTLES"

3. ROTULA3.BAS: "CALCULATION OF GAS DENSITY BY EXHAUST PARAMETERS THROUGH TURBULENT AND LAMINARY THROTTLES"

'PROGRAM ROTULA1.BAS'

'CALCULATION OF GAS PRESSURE IN THE INTERSIDER CHAMBER'

'DEPENDING ON NATURAL GAS DENSITY'

'THROTTLES: TURBULENT - LAMINAR'

DEFSNG P, T, E, V, R, D, G, Z, K, A, B, C, M, X

DEFINT i, j, n

77 cls

print "Enter gauge pressure"

print "in front of the turbulent throttle (mm water column)"

print "P1 =";

input P1

print "Enter the absolute pressure after lam.other (Pa)"

print "P3 =";

input P3

print "Enter the gas temperature in front of the turboswitch. (K)"

print "T1 =";

input T1

print "Enter the gas temperature in front of the lamin.ros. (K)"

print "T2 =";

input T2

print "Enter the diameter of the turbulent throttle (mm)"

print "Dt =";

input Dt

print "Enter the flow coefficient of the turbulent throttle (mm)"

print "E =";

input E

print "Enter the diameter of the laminar throttle (mm)"

print "DL =";

input DL

print "Enter the length of the laminar throttle (mm)"

print "L =";

input L

print "Enter initial gas density"

print "under standard conditions (kg / m3)"

print "Ron =";

input ron

print "Enter the gas density change step"

print "DRo =";

input DRo

print "Enter the number of steps to change the gas density"

print "N =";

input N

print "Enter the molar concentration of CO2 in the gas (%)"

print "xy =";

input Xy

print "Enter the molar concentration of nitrogen in the gas (%)"

print "Xa =";

input Xa

'SELECTION OF DIRECTION OF OUTPUT OF RESULTS'

print "Set the direction of output of calculation results"

print "1 - display"

print "2 - print"

print "3 - file REZTULA.TXT"

print "NAP =";

input nap

print "If you adjust the source data,"

print "set kor = 1, otherwise - kor = 0"

print "kor ⁼ ";

input kor

if kor = 0 goto 78

goto 77

78 if NAP = 1 then viw $ = "CON"

if NAP = 2 then viw $ = "PRN"

if NAP = 3 then viw $ = "REZTULA.TXT"

open viw $ for output as # 2

print # 2,

print # 2, "ROTULA 1.BAS PROGRAM"

print # 2,

print # 2, "CALCULATION OF GAS PRESSURE DEPENDENCE ON"

print # 2, "INTERSIDER CAMERA FROM ITS DENSITY"

print # 2, "(THROTTLES: TURBULENT - LAMINAR)"

print # 2,

print # 2, "BACKGROUND"

print # 2,

a1 $ = "P1 = ##### mm H2O P3 = ###### Pa T1 = ###. # K T2 = ###. # E == #. ##"

print # 2, using a1 $; P1, P3, T1, T2, E

a2 $ = "Dt = #. ## mm DL = #. ## mm L = ###. # mm Xa = #. #### mol.%"

print # 2, using a2 $; Dt, D1, L, Xa

a3 $ = "Ron = #. #### kg / m3 DRo = #. #### kg / m3 N = ## Xy = #. #### mol.%"

print # 2, using a3 $; Ron, DRo, N, Xy

print # 2,

print # 2, "CALCULATION RESULTS"

print # 2,

print # 2,

'Calculation of the coefficient of gas flow through the throttle'

Ef = E * 3.14 * (Dt * 0.001) ^ 2/4

P1 = P1 * 9.80665 'Conversion of mm H2O to Pa'

P1a = P1 + 101325

DL = 0.001 * DL 'Convert mm to m'

L = 0.001 * L 'Convert mm to m'

'Printing calculation results'

a4 $ = "Et = +. #### ^^^^

print # 2, using a4 $; Ef

print # 2,

print # 2, "i Ro P2 Gt GL Re " print # 2, "- kg / m3 mm H2O g / s g / s - "

print # 2,

P1m = P1a / (10 ^ 6) 'Conversion of Pa to MPa'

i = 0

17 i = i + 1

Ro = Ron + i * DRo

P2n = P1a

P2k = P3

1 P2 = 0.5 * (P2n + P2k)

P2m = P2 / (10 ^ 6) 'Conversion of Pa to MPa'

Call Zet (P1m, T1, Ro, Xa, Xy, Kz1, Mu1, Kad1, Hh1, Hl1)

Call Zet (P2m, T2, Ro, Xa, Xy, Kz2, Mu2, Kad2, Hh2, Hl2)

'Definition of the Reynolds criterion (laminar throttle)'

Re1 = DL ^ Ro * (P2 ^ 2-P3 ^ 2)

Re2 = 22121 * Kz2 * T2 * (Mu2 / 1,000,000 ^ 2 * L

Re = Re1 / Re2

'Determination of gas flow through a turbulent throttle'

Pot = (P2 / P1a) ^ (2 / Kad1) - (P2 / P1a) ^ ((Kad1 + 1) / Kad1)

B1 = SQR (2 * Kad1 * Ro * Pot / (345.64 * Kz1 * T1 * (Kad1-1)))

Gt = Ef * P1a * B1

'Determination of gas flow through the laminar throttle'

B5 = 3.14 * (DL ^ 4) * Ro * (P2 ^ 2-P3 ^ 2)

B6 = 88483 * Mu2 * L * Kz2 * T2 / 1,000,000

GL = B5 / B6

EpsG = Gt-GL

If Abs (EpsG) <0.00000001 then goto 5

else

goto 6

End if

6 If EpsG <0 then

P2n = P2 goto 1 else P2'k = P2 goto 1

End if

5 Gt = (10 ^ 3) Gt 'Convert kg / s to g / s'

GL = (10 ^ 3) * GL

P21 = (P2-101325) /9.80665 'Conversion of Pa in mm water column'

'Printing calculation results'

a5 $ = "## #. ### #####. # +. #### ^^^^ +. #### ^^^^ #####"

print # 2, using a5 $; i, Ro, P21, Gt, GL, Re

If i <N goto 17

12 print # 2,

print # 2, "Calculation is completed"

End

'GAS COMPRESSIBILITY COEFFICIENT CALCULATION PROGRAM'

'according to the modified equation of state of the GERG-91 mod,'

GOST 30319.2-96, as well as dynamic viscosity, '

'adiabatic index and calorific value of gas'

'according to GOST 30319.1-96'

Sub Zet (P, T, Ro, Xa, Xy, K, Mu, Kad, Hh, H1)

'Dimensions: R-MPa, T-grad. K, Ro-kg / m3, Ha, Hu-mol.%'

'Calculation of compressibility factor under standard conditions'

Zc = 1- (0.0741 * Ro-0.006 * Xa-0.0575 * Xy)

'Calculation of the molar fraction of equivalent hydrocarbon'

He = 1-Ha-Hu

'Calculation of the molar mass of equivalent hydrocarbon'

Me = (24.05525 * Zc * Ro-28.0135 * Xa-44.01 * Xy) / Xe

'Calculation of indicator H'

H = 128.64 + 47.479 * Me

'Calculation of the coefficients of the equation of state'

B11 = (8.77118 / 10 ^ -5.56281 * T / 10 ^ 6 + 8.8151 * T ^ 2/10 ^ 9) * Н B12 = (-

8.24747 / 10 ^ 7 + 4.31436 * T / 10 ^ 9-6.08319 * T ^ 2/10 ^ 12) * H ^ 2 B1 = -0.425468 + 2.865 * T / 10 ^ 3-4.62073 * T ^ 2/10 ^ 6 + B11 + B12

B2 = -0.1446 + 7.4091 * T / 10 ^ 4-9.1195 * T ^ 2/10 ^ 7 В23 = -0.339693 + 1.61176 * T / 10 ^ 3-2.04429 * T ^ 2/10 ^ 6 В3 = -0.86834 + 4.0376 * T / 10 ^ 3-5.1657 * T ^ 2/10 ^ 6

C11 = (6.46422 / 10 ^ 4-4.22876 * T / 10 ^ 6 + 6.88157 * T ^ 2/10 ^ 9) * H C12 = (-

3.32805 / 10 ^ 7 + 2.2316 * T / 10 ^ 9-3.67713 * T ^ 2/10 ^ 12) * H ^ 2 C1 = -0.302488 + 1.95861 * T / 10 ^ 3-3.16302 * T ^ 2/10 ^ 6 + C11 + C12

C2 = 7.8498 / 10 ^ 3-3.9895 * T / 10 ^ 5 + 6.1187 * T ^ 2/10 ^ 8 C3 = 2.0513 / 10 ^ 3 + 3.4888 * T / 10 ^ 5-8.3703 * T ^ 2/10 ^ 8 -C223 = 5.52066 / 10 ^ 3-1.68609 * T / 10 ^ 5 + 1.57169 * T ^ 2/10 ^ 8

C233 = 3.58783 / 10 ^ 3 + 8.06674 * T / 10 ^ 6-3.25798 * T ^ 2/10 ^ 8

Bz = 0.72 + 1.875 * (320-T) ^ 2/10 ^ 5

Cz = 0.92 + 0.0013 * (T-320)

Bm1 = Xe ^ 2 * B1 + Xe * Xa * Bz * (B1 + B2) -1.73 * Xe * Xy * (B1 * B3) ^ 0.5

Bm2 = Xa ^ 2 * B2 + 2 * Xa * Xy * B23 + Xy ^ 2 * B3

Bm = Bm1 + Bm2

Cm1 = Xe ^ 3 * C1 + 3 * Xe ^ 2 * Xa * Cz * (C1 ^ 2 * C2) ^ (1/3)

Cm2 = 2.76 * Xe ^ 2 * Xy * (C1 ^ 2 * C3) ^ (1/3) + 3 * Xe * Xa ^ 2 * Cz * (C1 * C2 ^ 2) ^ (1/3)

Cm3 = 6.6 * Xe * Xa * Xy * (C1 * C2 * C3) ^ (1/3) + 2.76 * Xe * Xy ^ 2 * (C1 * C3 ^) ^ (1/3)

Cm4 = Xa ^ 3 * C2 + 3 * Xa ^ 2 * Xy * C223 + 3 * Xa * Xy ^ 2 * C233 + Xy ^ 3 * C3

Cm = Cm1 + Cm2 + Cm3 + Cm4

'Calculation of the coefficients of the equation for calculating Z'

B = 1000 * P / (2.7715 * T)

C0 = B ^ 2 * Cm

B0 = B * Bm

A1 = 1 + B0

A0 = 1 + 1.5 * (B0 + C0)

A2 = (A0- (A0 ^ 2-A1 ^ 3) ^ 0.5) ^ 1/3)

'Compressibility factor calculation'

Z = (1 + A2 + A1 / A2) / 3

'Compressibility factor calculation'

K = Z / Zc

'Dynamic viscosity calculation'

'Calculation of pseudocritical pressure and temperature'

Ppk = 2.9585 * (1.608-0.05994 * Ro + Xy-0.392 * Xa) Tpk = 88.25 * (0.9915 + 1.759 * Ro-Xy-1.681 * Ha)

'Calculation of reduced pressure and temperature'

Ppr = p / ppk

Tpr = T / Tpk

'Calculation of dynamic viscosity at pressures up to 0.5 MPa'

Mu1 = T ^ 0.5 + 1.37-9.09 * Ro ^ 0.125

Mu2 = Ro ^ 0.5 + 2.08-1.5 * (Ha + Hu)

Mu = 3.24 * Mu1 / Mu2 'Dimension - μPa.s.'

'Calculation of dynamic viscosity at a pressure of 0.5 MPa and more'

If P> 0.5 then

Cmu = 1 + Ppr ^ 2/30 * (Tpr-1) goto 9

else

goto 2

End if

9 Mu = Cmu * Mu 'Dimension - μPa.s.'

'Calculation of specific volumetric heat of combustion' (calorific value) of natural gas'

'Dimension - MJ / cubic meter'

2 Hh = 92.819 * (0.51447 * Ro + 0.05603-0.65689 * Xa-Xy) 'highest'

H1 = 85.453 * (0.5219 * Ro + 0.04242-0.65197 * Xa-Xy) 'lowest'

'Calculation of the adiabatic index at T = 240-360 K and P up to 10 MPa'

Kad1 = 1.556 * (1 + 0.074 * Ha) -3.9 * T * (1-0.68 * Ha) /10^4-0.208*Ro

Kad2 = (p / T) ^ 1.43 * (384 * (1-Xa) * (p / T) ^ 0.8 + 26.4 * Xa)

Kad = Kad1 + Kad2

End sub

'PROGRAM ROTULA2.BAS'

'ID A OF THE COEFFICIENT "A" BY EXHAUST PARAMETERS'

'GAS THROUGH TURBULENT AND LAMINAR THROTTLES'

DEFSNG P, T, E, V, R, D, G, Z, K, A, B, C, M, X

DEFINT i, j, n

77 cls

print "Enter gauge pressure"

print "in front of the turbulent throttle (mm water column)"

print "P1 =":

input P1

print "Enter gauge pressure"

print "between inductors (mm water column)"

print "P2 =";

input P2

print "Enter the absolute pressure after the lam.dros. (Pa)"

print "P3 =":

input P3

print "Enter the barometric pressure (Pa)"

print "Pb =";

input pb

print "Enter the gas temperature in front of the turboswitch. (K)"

print "T1 =";

input T1

print "Enter the gas temperature in front of the lam.dros. (K)"

print "T2 =";

input T2

print "Enter the gas density under standard conditions Ro (kg / m3)"

print "Ro =";

input Ro

print "Enter the molar concentration of CO2 in the gas (%)"

print "xy =";

input Xy

print "Enter the molar concentration of nitrogen in the gas (%)"

print "Ha =";

input Xa

'SELECTION OF DIRECTION OF OUTPUT OF RESULTS'

print "Set the direction of output of calculation results"

print "1 - display"

print "2 - print"

print "3 - file REZTULA2.TXT"

print "NAP =";

input nap

print "If you adjust the source data,"

print "set kor = 1, otherwise - kor = 0"

print "kor =";

input kor

if kor = 0 goto 78

goto 77

78 if NAP = 1 then viw $ = "CON"

if NAP = 2 then viw $ = "PRN"

if NAP - 3 then viw $ = "REZTULA2.TXT"

open viw $ for output as # 2

print # 2,

print # 2, "PROGRAM ROTULA2.BAS"

print # 2,

print # 2, "IDENTIFICATION OF COEFFICIENT A BY PARAMETERS"

print # 2, "GAS FLOWS THROUGH TURBULENT AND LAMINARY THROTTLES"

print # 2,

print # 2, "BACKGROUND"

print # 2,

a1 $ = "P1 = #### mm H2O P2 = #### mm H2O P3 = ###### Pa T1 = ###. # K"

print # 2, using a1 $; P1, P2, P3, T1

a2 $ = "T2 = ###. # Xa = #. #### mol.% Hu = #. #### mol.%"

print # 2, using a2 $; T2, Xa, Xy

a3 $ = "Ro = #. #### Pb = ######. # Pa"

print # 2, using a3 $; Ro, Pb

print # 2,

print # 2, "CALCULATION RESULTS"

print # 2,

P2 = P2 * 9.80665 'Convert mm H2O to Pa'

P2a = P2 + Pb 'Absolute pressure calculation'

P1 = P1 * 9.80665 'Conversion of mm H2O to Pa'

P1a = P1 + Pb 'Absolute pressure calculation'

P1m = P1a / (10 ^ 6) 'Conversion of Pa to MPa'

P2m = P2a / (10 ^ 6)

Call Zet (P1m, T1, Ro, Xa, Xy, Kz1, Mu1, Kad1, Hh1, Hl1)

Call Zet (P2m, T2, Ro, Xa, Xy, Kz2, Mu2, Kad2, Hh2, Hl2)

'Determination of coefficient A'

Pot = (P2a / P1a) ^ (2 / Kad1) - (P2a / P1a) ^ ((Kad1 + 1) / Kad1)

B1 = P1a * (Mu2 / 1,000,000) * Kz2 * T2 / ((P2a-P3) * (P2a + P3))

B2 = SQR (Kad1 * Pot / (Kz1 * (Kad1-1) * T1))

B3 = B1 * B2

A = SQR (Ro) / B3

a5 $ = "Coefficient A = +. #### ^^^^"

print # 2, using a5 $; A

print # 2,

print # 2, "Calculation is completed"

End

'GAS COMPRESSIBILITY COEFFICIENT CALCULATION PROGRAM'

'according to the modified equation of state of the GERG-91 mod,'

'GOST 30319.2-96, as well as dynamic viscosity,'

'adiabatic index and calorific value of gas'

'according to GOST 30319.1-96'

Sub Zet (P, T, Ro, Xa, Xy, K, Mu, Kad, Hh, Hl)

'Dimensions: R-MPa, T-grad. K, Ro-kg / m3, Ha, Hu-mol.%'

'Calculation of compressibility factor under standard conditions'

Zc = 1- (0.0741 * Ro-0.006 * Xa-0.0575 * Xy)

'Calculation of the molar fraction of equivalent hydrocarbon'

He = 1-Ha-Hu

'Calculation of the molar mass of equivalent hydrocarbon'

Me = (24.05525 * Zc * Ro-28.0135 * Xa-44.01 * Xy) / Xe

'Calculation of indicator H'

H = 128.64 + 47.479 * Me

'Calculation of the coefficients of the equation of state'

B11 = (8.77118 / 10 ^ 4-5.56281 * T / 10 ^ 6 + 8.8151 * T ^ 2/10 ^ 9) * H

B12 = (- 8.24747 / 10 ^ 7 + 4.31436 * T / 10 ^ 9-6.08319 * T ^ 2/10 ^ 12) * H ^ 2

B1 = -0.425468 + 2.865 * T / 10 ^ 3-4.62073 * T ^ 2/10 ^ 6 + B11 + B12

B2 = -0.1446 + 7.4091 * T / 10 ^ 4-9.1195 * T ^ 2/10 ^ 7

B23 = -0.339693 + 1.61176 * T / 10 ^ 3-2.04429 * T ^ 2/10 ^ 6

B3 = -0.86834 + 4.0376 * T / 10 ^ 3-5.1657 * T ^ 2/10 ^ 6

C11 = (6.46422 / 10 ^ 4-4.22876 * T / 10 ^ 6 + 6.88157 * T ^ 2/10 ^ 9) * H

C12 = (- 3.32805 / 10 ^ 7 + 2.2316 * T / 10 ^ 9-3.67713 * T ^ 2/10 ^ 12) * H ^ 2

C1 = -0.302488 + 1.95861 * T / 10 ^ 3-3.16302 * T ^ 2/10 ^ 6 + C11 + C12

C2 = 7.8498 / 10 ^ 3-3.9895 * T / 10 ^ 5 + 6.1187 * T ^ 2/10 ^ 8

C3 = 2.0513 / 10 ^ 3 + 3.4888 * T / 10 ^ 5-8.3703 * T ^ 2/10 ^ 8

C223 = 5.52066 / 10 ^ 3-1.68609 * T / 10 ^ 5 + 1.57169 * T ^ 2/10 ^ 8

C233 = 3.58783 / 10 ^ 3 + 8.06674 * T / 10 ^ 6-3.25798 * T ^ 2/10 ^ 8

Bz = 0.72 + 1.875 * (320-T) ^ 2/10 ^ 5

Cz = 0.92 + 0.0013 * (T-320)

Bm1 = Xe ^ 2 * B1 + Xe * Xa * Bz * (B1 + B2) -1.73 * Xe * Xy * (B1 * B3) ^ 0.5

Bm2 = Xa ^ 2 * B2 + 2 * Xa * Xy * B23 + Xy ^ 2 * B3

Bm = Bm1 + Bm2

Cm1 = Xe ^ 3 * C1 + 3 * Xe ^ 2 * Xa * Cz * (C1 ^ 2 * C2) ^ (1/3)

Cm2 = 2.76 * Xe ^ 2 * Xy * (C1 ^ 2 * C3) ^ (1/3) + 3 * Xe * Xa ^ 2 * Cz * (C1 * C2 ^ 2) ^ (1/3)

Cm3 = 6.6 * Xe * Xa * Xy * (C1 * C2 * C3) ^ (1/3) + 2.76 * Xe * Xy ^ 2 * (C1 * C3 ^ 2) ^ (1/3)

Cm4 = Xa ^ 3 * C2 + 3 * Xa ^ 2 * Xy * C223 + 3 * Xa * Xy ^ 2 * C233 + Xy ^ 3 * C3

Cm = Cm1 + Cm2 + Cm3 + Cm4

'Calculation of the coefficients of the equation for computing Z'

B = 1000 * P / (2.7715 * T)

C0 = B ^ 2 * Cm

B0 = B * Bm

A1 = 1 + B0

A0 = 1 + 1.5 * (B0 + C0)

A2 = (A0- (A0 ^ 2-A1 ^ 3) ^ 0.5) ^ (1/3)

'Compressibility factor calculation'

Z = (1 + A2 + A1 / A2) / 3

'Compressibility factor calculation'

K = Z / Zc

'Dynamic viscosity calculation'

'Calculation of pseudocritical pressure and temperature'

Ppk = 2.9585 * (1.608-0.05994 * Ro + Xy-0.392 * Xa)

Tpk = 88.25 * (0.9915 + 1.759 * Ro-Xy-1.681 * Xa)

'Calculation of reduced pressure and temperature'

Ppr = p / ppk

Tpr = T / Tpk

'Calculation of dynamic viscosity at pressures up to 0.5 MPa'

Mu1 = T ^ 0.5 + 1.37-9.09 * Ro ^ 0.125

Mu2 = Ro ^ 0.5-2.08-1.5 * (Ha + Hu)

Mu = 3.24 * Mu1 / Mu2 'Dimension - μPa.s.'

'Calculation of dynamic viscosity at a pressure of 0.5 MPa and more'

If P> 0.5 then

Cmu = 1 + Ppr ^ 2/30 * (Tpr-1) goto 9

else

goto 2

End if

9 Mu = Cmu * Mu 'Dimension - μPa.s.'

'Calculation of specific volumetric heat of combustion'

'(calorific value) of natural gas'

'Dimension - MJ / cubic meter'

2 Hh = 92.819 * (0.51447 * Ro + 0.05603-0.65689 * Xa-Xy) 'highest'

Hl = 85.453 * (0.5219 * Ro + 0.04242-0.65197 * Xa-Xy) 'lowest'

'Calculation of the adiabatic index at T = 240-360 K and P up to 10 MPa'

Kad1 = 1.556 * (1 + 0.074 * Xa) -3.9 * T * (1-0.68 * Xa) /10^4-0.208*Ro

Kad2 = (p / T) ^ 1.43 * (384 * (1-Xa) * (p / T) ^ 0.8 + 26.4 * Xa)

Kad = Kad1 + Kad2

End sub

'PROGRAM ROTULA3.BAS'

'CALCULATION OF GAS DENSITY BY EXHAUST PARAMETERS'

'THROUGH TURBULENT AND LAMINAR THROTTLES'

DEFSNG P, T, E, V, R, D, G, Z, K, A, B, C, M, X

DEFINT i, j, n

77 cls

print "Enter gauge pressure"

print "in front of the turbulent throttle (mm water column)"

print "P1 =";

input P1

print "Enter gauge pressure"

print "between inductors (mm water column)"

print "P2 =";

input P2

print "Enter the absolute pressure after the lam.dros. (Pa)"

print "P3 =";

input P3

print "Enter the barometric pressure (Pa)"

print "Pb =";

input pb

print "Enter the gas temperature in front of the turboswitch. (K)"

print "T1 =":

input T1

print "Enter the gas temperature in front of the lam.dros. (K)"

print "T2 =":

input T2

print "Enter coefficient A"

print "A =";

input A

print "Enter the molar concentration of CO2 in the gas (%)"

print "xy =":

input Xy

print "Enter the molar concentration of nitrogen in the gas (%)"

print "Xa =":

input Xa

print "Enter the diameter of the laminar throttle (mm)"

print "DL =":

input DL

print "Enter the length of the laminar throttle (mm)"

print "L =";

input L

'SELECTION OF DIRECTION OF OUTPUT OF RESULTS'

print "Set the direction of output of calculation results"

print "1 - display"

print "2 - print"

print "3 - file REZTULA3.TXT"

print "NAP =";

input nap

print "If you adjust the source data,"

print "set kor = 1, otherwise - kor = 0"

print "kor =":

input kor

if kor = 0 goto 78

goto 77

78 if NAP = 1 then viw $ = "CON"

if NAP = 2 then viw $ = "PRN"

if NAP = 3 then viw $ = "REZTULA3.TXT"

open viw $ for output as # 2

print # 2,

print # 2, "PROGRAM ROTULA3.BAS"

print # 2,

print # 2, "CALCULATING GAS DENSITY BY EXHAUST PARAMETERS"

print # 2, "THROUGH TURBULENT AND LAMINARY THROTTLES"

print # 2,

print # 2, "BACKGROUND"

print # 2,

a1 $ = "P1 = #### mm H2O P2 = #### mm H2O P3 = ###### Pa T1 = ###. # K"

print # 2, using a1 $; P1, P2, P3, T1

a2 $ = "T2 = ###. # A = +. #### ^^^^ Xa = #. #### mol.% Hu = #. #### mol.%"

print # 2, using a2 $; T2, A, Xa, Xy

a3 $ = "DL = #. ### mm L = ###. ## mm Pb = ######. # Pa"

print # 2, using a3 $; DL, L, Pb

print # 2,

print # 2, "CALCULATION RESULTS"

print # 2,

P2 = P2 * 9.80665 'Convert mm H2O to Pa'

P2a = P2 + Pb 'Absolute pressure calculation'

P1 = P1 * 9.80665 'Conversion of mm H2O to Pa'

P1a = P1 + Pb 'Absolute pressure calculation'

P1m = P1a / (10 ^ 6) 'Conversion of Pa to MPa'

P2m = P2a / (10 ^ 6)

Ron = 0.2

Rok = 1.8

3 Ro = 0.5 * (Ron + Rok)

Call Zet (P1m, T1, Ro, Xa, Xy, Kz1, Mul, Kad1, Hh1, Hl1)

Call Zet (P2m, T2, Ro, Xa, Xy, Kz2, Mu2, Kad2, Hh2, Hl2)

'Determination of the calculated coefficient Ar'

Pot = (P2a / P1a) ^ (2 / Kad1) - (P2a / P1a) ^ ((Kad1 + 1) / Kad1)

B1 = P1a * (Mu2 / 1,000,000) * Kz2 * T2 / ((P2a-P3) * (P2a + P3))

B2 = SQR (Kad1 * Pot / (Kz1 * (Kad1-1) * T1))

B3 = B1 * B2

Ar = SQR (Ro) / B3

EA = Ar-A

If Abs (EA) <0.001 * A then goto 1

End if

If EA <0 then

Ron = Ro goto 3 else Rok = Ro goto 3

End if

'Definition of the Reynolds criterion (laminar throttle)'

1 DL = 0.001 * DL

L = 0.001 * L

Re1 = DL ^ 3 * (P2a ^ 2-P3 ^ 2) * Ro

Re2 = 22121 * Kz2 * T2 * (Mu2 / 1,000,000) ^ 2 * L

Re = Re1 / Re2

'Determination of gas flow through the laminar throttle'

B5 = 3.14 * (DL ^ 4) * Ro * (P2a ^ 2-P3 ^ 2)

B6 = 88,483.84 * Mu2 * L * Kz2 * T2 / 1,000,000

GL = B5 / B6

GL = 1000 * GL 'Convert kg / s to g / s'

a5 $ = "Gas density Ro = #. #### kg / m3 Re = ##### GL = +. #### ^^^^ g / s" print # 2, using a5 $; Ro, Re, GL

a8 $ = "Gas viscosity Mu = +. #### ^^^^ μPa · s"

print # 2, using a8 $; Mu2

a7 $ = "Calorific value of gas Hh = ###. ## H1 = ###. ## MJ / m3" print # 2, using a7 $; Hh1, hl2

a6 $ = "Kz1 = #. #### Kz2 = #. #### Kad = #. ####"

print # 2, using a6 $; Kz1, Kz2, Kad1

print # 2,

print # 2, "Calculation is completed"

End

'GAS COMPRESSIBILITY COEFFICIENT CALCULATION PROGRAM'

'according to the modified equation of state of the GERG-91 mod,'

'GOST 30319.2-96, as well as dynamic viscosity,'

'adiabatic index and calorific value of gas'

'according to GOST 30319.1-96'

Sub Zet (P, T, Ro, Xa, Xy, K, Mu, Kad, Hh, Hl)

'Dimensions: R-MPa, T-grad. K, Ro-kg / m3, Ha, Hu-mol.%'

'Calculation of compressibility factor under standard conditions'

Zc = 1- (0.0741 * Ro-0.006 * Xa-0.0575 * Xy)

'Calculation of the molar fraction of equivalent hydrocarbon'

He = 1-Ha-Hu

'Calculation of the molar mass of equivalent hydrocarbon'

Me = (24.05525 * Zc * Ro-28.0135 * Ha-44.01 * Hu) / He

'Calculation of the rocker N'

H = 128.64 + 47.479 * Me

'Calculation of the coefficients of the equation of state'

B11 = (8.771 18/10 ^ 4-5.56281 * T / 10 ^ 6 + 8.8151 * -T ^ 2/10 ^ 9) * H B12 = (-

8.24747 / 10 ^ + 4.31436 * T / 10 ^ 9-6.08319 * T ^ 2/10 ^ 12) * H ^ 2 B1 = -0.425468 + 2.865 * T / 10 ^ 3-

4.62073 * T ^ 2/10 ^ 6 + B11 + B12

B2 = -0.1446 + 7.4091 * T / 10 ^ 4-9.1195 * T ^ 2/10 ^ 7 В23 = -0.339693 + 1.61176 * T / 10 ^ 3-

2.04429 * T ^ 2/10 ^ 6 B3 = -0.86834 + 4.0376 ^ T / 10 ^ -5.1657 * T ^ 2/10 ^ 6

C11 = (6.46422 / 10 ^ 4-4.22876 * T / 10 ^ 6 + 6.88157 * T ^ 2/10 ^ 9) * H C12 = (-

3.32805 / 10 ^ 7 + 2.2316 * T / 10 ^ 9-3.67713 * 7 ^ 2/10 ^ 12) * H ^ 2 C1 = -0.302488 + 1.95861 * T / 10 ^ 3-

3.16302 * T ^ 2/10 ^ 6 + C11 + C12

C2 = 7.8498 / 10 ^ 3-3.9895 * T / 10 ^ 5 + 6.1187 * T ^ 2/10 ^ 8 C3 = 2.0513 / 10 ^ + 3.4888 * T / 10 ^ 5-

8.3703 * T ^ 2/10 ^ 8 C223 = 5.52066 / 10 ^ 3-1.68609 * T / 10 ^ 5 + 1.57169 * T ^ 2/10 ^ 8

C233 = 3.58783 / 10 ^ 3 + 8.06674 * T / 10 ^ 6-3.25798 * T ^ 2/10 ^ 8

Bz = 0.72 + 1.875 * (320-T) ^ 2/10 ^ 5

Cz = 0.92 + 0.0013 * (T-320)

Bm1 = Xe ^ 2 * B1 + Xe * Xa * Bz * (B1 + B2) -1.73 * Xe * Xy * (B1 * B3) ^ 0.5

Bm2 = Xa ^ 2 * B2 + 2 * Xa * Xy * B23 + Xy ^ 2 * B3

Bm = Bm1 + Bm2

Cm1 = Xe ^ 3 * C1 + 3 * Xe ^ 2 * Xa * Cz * (C1 ^ 2 * C2) ^ (1/3)

Cm2 = 2.76 * Xe ^ 2 * Xy * (C1 ^ 2 * C3) ^ (1/3) + 3 * Xe * Xa ^ 2 * Cz * (C1 * C2 ^ 2) ^ (1/3)

Cm3 = 6.6 * Xe * Xa * Xy * (C1 * C2 * C3) ^ (1/3) + 2.76 * Xe * Xy ^ 2 * (C1 * C3 ^ 2) ^ (1/3)

Cm4 = Xa ^ 3 * C2 + 3 * Xa ^ 2 * Xy * C223 + 3 * Xa * Xy ^ 2 * C233 + Xy ^ 3 * C3

Cm = Cm1 + Cm2 + Cm3 + Cm4

'Calculation of the coefficients of the equation for computing Z'

B = 1000 * P / (2.7715 * T)

C0 = B ^ 2 * Cm

B0 = B * Bm

A1 = 1 + B0

A0 = 1 + 1.5 * (B0 + C0)

A2 = (A0- (A0 ^ 2-A1 ^ 3) ^ 0.5) ^ 1/3)

'Compressibility factor calculation'

Z = (1 + A2 + A1 / A2) / 3

'Compressibility factor calculation'

K = Z / Zc

'Dynamic viscosity calculation'

'Calculation of pseudo-critical pressure and temperature'

Ppk = 2.9585 * (1.608-0.05994 * Ro + Xy-0.392 * Xa) Tpk = 88.25 * (0.9915 + 1.759 * Ro-Xy-1.681 * Ha)

'Calculation of reduced pressure and temperature'

Ppr = p / ppk

Tpr = T / Tpk

'Calculation of dynamic viscosity at pressures up to 0.5 MPa'

Mu1 = T ^ 0.5 + 1.37-9.09 * Ro ^ 0.125

Mu2 = Ro ^ 0.5 + 2.08-1.5 * (Ha + Hu)

Mu = 3.24 * Mu1 / Mu2 'Dimension - μPa.s.'

'Calculation of dynamic viscosity at a pressure of 0.5 MPa and more'

If P> 0.5 then

Cmu = 1 + Ppr ^ 2/30 * (Tpr-1) goto 9

else

goto 2

End if

9 Mu = Cmu * Mu 'Dimension - μPa.s.'

'Calculation of specific volumetric heat of combustion'

'(calorific value) of natural gas'

'Dimension - MJ / cubic meter'

2 Hh = 92.819 * (0.51447 * Ro + 0.05603-0.65689 * Xa-Xy) 'highest'

H1 = 85.453 * (0.5219 * Ro + 0.04242-0.65197 * Xa-Xy) 'lowest'

'Calculation of the adiabatic index at T = 240-360 K and P up to 10 MPa'

Kad1 = 1.556 * (1 + 0.074 * Ha) -3.9 * T * (1-0.68 * Ha) /10^4-0.208*Ro

Kad2 = (p / T) ^ 1.43 * (384 * (1-Xa) * (p / T) ^ 0.8 + 26.4 * Xa)

Kad ^ Kad1 + Kad2

End sub

Claims (3)

1. The method of determining indicators of the physical properties of natural gas (density, dynamic viscosity, compressibility coefficient, adiabatic index, specific heat of combustion), including the preparation of gas and the calculation of the above indicators of physical properties of the gas, characterized in that the prepared controlled gas is passed through successively installed turbulent and laminar throttles, measure the absolute gas pressure in front of the turbulent throttle, in the inter-throttle portion and after the laminar throttle, from eryayut turbulent gas temperature before the throttle portion and mezhdrosselnom and the measured values of these parameters determine the parameters of physical properties of natural gas. 2. The method according to claim 1, characterized in that before the turbulent throttling support absolute pressure, providing a laminar flow of gas in the laminar throttle at the maximum possible Reynolds number. 3. A device for automatically determining the physical properties of natural gas, comprising a controlled gas line with a gas preparation unit (filter) installed on it and a computing device, the first output of which is connected to an information display device, characterized in that it additionally contains turbulent and laminar chokes sequentially installed on a monitored gas line, an actuator (e.g. control valve) installed on a monitored gas line in front of the turbulent throttle, absolute pressure sensors installed in front of the turbulent throttle, in the inter-throttle section and after the laminar throttle; temperature sensors installed in front of the turbulent throttle and in the inter-throttle section; while the above sensors are connected to a computing device, the second output of which is connected to the actuator.

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