Experimental Studies for Determining Gas Flow Rate Accidental Release on Linear Part of Pipeline

Transcription

1 IOP Conference Series: Earth and Environmental Science PAPER OPEN ACCESS Experimental Studies for Determining Gas Flow Rate Accidental Release on Linear Part of Pipeline To cite this article: V G Fetisov et al 2017 IOP Conf. Ser.: Earth Environ. Sci View the article online for updates and enhancements. This content was downloaded from IP address on 18/10/2018 at 19:27

2 Experimental Studies for Determining Gas Flow Rate Accidental Release on Linear Part of Pipeline V G Fetisov, A K Nikolaev, Y V Lykov Saint Petersburg Mining University, 21 Line, No.2, , Saint Petersburg, Russian Federation v.fetisov80@gmail.com Abstract. The method of determining the flow rate of gas in the gas-dynamic resistance of a medium gas stream with high linear speed was studied. The reduction of the density of the gas is a result of its expansion. Multiple calculations of gas losses were evaluated. Calculation is set by loss of gas depending on the area of the pipeline damage. A comparative analysis was done. In order to establish a functional empirical dependence of the flow rate on the whole on the parameters of the leakage process, a series of experiments was conducted on a test bench and their processing was carried out. In experiments conducted, the effect of pressure and temperature in the receiver was evaluated, the physical properties of the gas and the diameter of the hole were predetermined by the limits of the amount of the whole flow rate in critical conditions, as well as the critical regime of gas leakage. 1. Purpose of study To determine the functional dependence of the empirical coefficient of discharge holes from the parameters of the flowing process, a series of tests has been carried out on the test bench and their processing was accomplished [1]. In a series of experiments conducted, the effect of pressure and temperature in the receiver, the physical properties of the gas, the diameter of the hole in the set limits of the amount of opening discharge coefficient in critical conditions and a critical mode of gas leakage were all evaluated. 2. Carrying out the research Among the independent factors affecting the value of the flow rate, the following parameters were selected: the absolute pressure of the gas in the receiver, Р 0 ; absolute temperature of the gas in the receiver, T 0 ; gas constant working medium R; hole diameter d; as-response option is selected aperture flow coefficient µ. Thus, the functional dependence on the reaction of the function-independent parameters was based on five levels to obtain a formula of this form: =,,,. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by Ltd 1

3 Conditions for carrying out a series of experiments are given in Tables 1-5. Numerical values of averaged-reaction function are in horizontal rows and vertical columns, by averaging the results of the graphs, which were processed by the method of least squares. As a result, each of the dependencies has been approximated by the formula. For the function of the pressure flow rate in the receiver, the formula of the law of normal distribution was chosen based on chart analysis: =. The remaining approximation depends on the degree of dependence: =. The general mathematical model for multi-function was the product of [3]:,,, =. As a result, empirical relationship has been obtained: =0.285,,, 0,0015. (1) where µ- holes flow coefficient; d - diameter of opening in mm; R - gas constant in J/kgK; T - the absolute temperature in K at the receiver; P - gas pressure in bars. The accuracy evaluation of calculations, made on the basis of the data, is given in Table 1. Table 1. Conditions for experiment in critical gas flow Options Function-feedback P 0 T 0. K R. J/kgK d. mm

4 P 0. T 0.K Table 2. Treatment parameters for research Р 0, Т 0! " F 1 (T 0 ) ! " F 2 (T 0 ) Table 3. Processing parameters for research К and d R. J/kgK. d.mm F 3 (d) ! " F 4 (R) The dependence obtained correlates well with the analytical expressions obtained on the basis of the implementation of the mathematical model to confirm the accuracy of the research. For this, the error was determined by the formula [4]: = # % & % " ; where n - number of experiments; X A, X i - the arithmetic mean and the current measured value. The width of the interval warranty is: %= () *;, - ;. /; student`s factor (criterion). Let us make a guarantee interval: (% & % % % & + %). The calculation results for different indicators depending on (1) are presented in Table 4. 3

5 Table 4. Value of guarantee intervals Index Guaranteed interval (0.275; 0.295) 2 (0.44; 0.46) 2 (0.031; 0.035) 2 (0.031; 0.035) (0.0012; ) As can be seen from Table 4, the indexes n 3 and n 2 provide the overlap intervals. This allows to replace the dimensional variables R and T of the derivatives. Then the empirical relationship (1) will have the form of =0.285,,, 0,0015. (2) It should be noted that the mathematical model is obtained and is valid only for the critical gas leakage mode conditions [5-7]. In this regard, calculations are made to determine the discharge hole coefficient for the conditions of the critical flow regime on the basis of the results of the experiments shown in Table 5. As a result, each of the approximate power dependences of the formula. Flow rate dependence of the hole diameter was not significant, therefore it is not taken into account. The remaining dependencies were sought in the form: =. The general mathematical model for multi-function has been as a product:,, =. The average rate has been the method of least squares data in Table 5. Table 5. Conditions for subcritical experiment in expiration gas Options Functionfeedback P 0. bar T 0. K R. J/kgK d. mm

6 As a result, authors have obtained empirical relationship: =0.582, -, (3) µ - holes flow coefficient; R - gas constant in J/kgK; T - the absolute temperature in K in the receiver; P - gas pressure in the receiver, bar. Significantly different results obtained for the region of subcritical and critical gas leakage mode have their own physical interpretations. Formula Saint-Venant-Wenzel, derived from the classical energy equation, is an expression of the general law of nature - the law of conservation of energy - derived strictly for critical gas leakage mode conditions. Treatment studies are conducted by a method based on the development of M.M. Protodjakonova and R.I. Teder [8]. It is based on the concept of embedded Raman square filling which are the results of experiments and can reduce the number of trials (with five levels of realization depending on each other) from 625 to 25. Assumption of Saint-Venant-Wenzel that the pressure in the outlet section of the nozzle could not fall below a critical and distribution of disturbances in the form of a reduction in ambient pressure could not cross the barrier of the speed of sound, it is lawful and confirmed by the practice. However, the critical gas outflow jet mode in the environment (in the nozzle) is experiencing rapid expansion [9]. Thus, one reason for the inadequacy of the mathematical model should be considered as neglected. The medium of gas-dynamic resistance to the movement of the gas jet with high linear speed grows and the density of the gas in the stream reduces as a result of its expansion. It should be noted that the model of Saint-Venant-Wenzel received for an ideal gas equation simplifies the gas state. The dependence of the density of the gas pressure and temperature gives an overestimate [10]. It is not considered on the compressibility of a real gas (compressibility factor for z <1). In the context of a critical mode of gas leakage as a result of low excess pressure, the state of a real gas, different from that of the real gas compressibility coefficient, can take z = Conclusions The assumption of no heat exchange with the environment and a zero value in the receiver gas velocity (at some distance from the orifice) also contribute an error to the determination of gas flow. The results, obtained by comparing theoretical studies, and actual amendments to claims Saint- Venant-Wenzel allow one to adapt the model to reality in terms of the critical regime of gas leakage. References [1] Abramovich G N 1991 Applied gas dynamics (Moscow: Nauka) p 106 [2] Cossack A S 1981 Calculation of temperature fields and hydraulic pipeline taking into account the variability of gases Gas industry 8(4) [3] Korn G 1970 Mathematical Handbook for Scientists and Engineers (Moscow: Nauka) p 720 [4] Protodyakonov M M and TederR I 1970 Methods Rational design of experiments (Moscow: Nauka) 5

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