Critical flow nozzle flowmeter for measuring respective flowrates of gas phase and liquid phase in multiphase fluid and measuring method thereof

Abstract

A method for measuring respective flowrates of gas phase and liquid phase in a multiphase fluid using a critical flow nozzle flowmeter. The critical flow nozzle flowmeter includes a throttling nozzle having an inlet, an outlet and a throat, and the throat has a smallest flow area for flowing fluid; a gamma ray detector, including a gamma ray emitter and a gamma ray receiver, arranged in a way allowing the gamma ray emitted by the gamma ray emitter to pass through a cross-section at the inlet of the throttling nozzle in a diametrical direction to reach the gamma ray receiver; pressure sensors respectively configured for measuring the pressure P.sub.1 at the inlet of the throttling zone and the pressure P.sub.2 at the outlet of the throttling nozzle; and a temperature sensor configured for measuring the temperature T.sub.1 at the inlet of the throttling nozzle.

Claims

1. A method for measuring respective flowrates of a gas phase and a liquid phase in a multiphase fluid using a critical flow nozzle flowmeter, wherein the critical flow nozzle flowmeter comprises: a throttling nozzle having an inlet, an outlet and a throat; wherein the throat has a smallest flow area for flowing fluid compared with the inlet and the outlet; and a cross-section area of the throat of the throttling nozzle is 1/10 to of a cross-section area of the inlet of the throttling nozzle; a gamma ray detector comprising a gamma ray emitter and a gamma ray receiver, and the gamma ray detector is arranged in a way allowing a gamma ray emitted by the gamma ray emitter to pass through a cross-section at the inlet of the throttling nozzle in a diametrical direction to reach at the gamma ray receiver; and the gamma ray detector is a single-energy gamma ray detector; pressure sensors respectively configured for measuring a pressure P.sub.1 at the inlet of the throttling nozzle and a pressure P.sub.2 at the outlet of the throttling nozzle; and a temperature sensor configured for measuring a temperature T.sub.1 at the inlet of the throttling nozzle; and the method comprises the following steps: a) measuring the pressure P.sub.1 at the inlet and the pressure P.sub.2 at the outlet of the throttling nozzle by using the pressure sensors, and measuring the temperature T.sub.1 at the inlet of the throttling nozzle by using the temperature sensor; b) flowing the multiphase fluid through the critical flow nozzle flowmeter in a critical flow manner, wherein judging whether the multiphase fluid has reached a critical flow state according to the following method: setting a symbol r as a ratio of the pressure P.sub.2 at the outlet to the pressure P.sub.1 at the inlet, and $r=\frac{p_2}{p_1};$ measuring the pressure P.sub.1 and the temperature T.sub.1 to determine a density .sub.g1 of the gas phase; measuring a mixed density m with the single-energy gamma ray detector to determine a gas mass fraction GMF according to a first equation: $\mathrm{GMF}=\frac{{}_l-{}_m}{{}_l-{}_{g1}},$ and further defining $a=\frac{1-\mathrm{GMF}}{\mathrm{GMF}}\frac{{}_{g1}}{{}_l};$ according to a characteristic, i.e., the gas phase flows in a sonic speed when the multiphase fluid reaches the critical flow state, defining a critical pressure ratio r.sub.c by a second equation $r_c={\left[\frac{a\left(1-r_c\right)+\frac{k}{k-1}}{\frac{k}{k-1}+\frac{k}{2}{\left(1+\right)}^2}\right]}^{\frac{k}{k-1}},$ and with the second equation, determining the critical pressure r.sub.c by iterative solution; when a measured pressure ratio r meets $r=\frac{p_2}{p_1}{r}_c,$ determining the multiphase fluid is a critical flow; in case of a critical flow, through a third equation $s=\sqrt{1+\frac{{}_l-{}_m}{{}_l-{}_{g1}}\left(\frac{{}_l}{{}_{g1}}-1\right)}\left(1+0.6e^{-5\mathrm{GMF}}\right),$ calculating a velocity slip ratio between the gas phase and the liquid phase; and c) respectively calculating a total mass flowrate Q.sub.m of the multiphase fluid, a gas phase mass flowrate Q.sub.m,g and a liquid phase mass flowrate Q.sub.m,l according to the following equations: the total mass flowrate: $Q_m=\sqrt{\frac{{\mathrm{CA}}^2{}_{g1}\left[\left(1-r\right)+\frac{k}{k-1}\left(1-r^{\frac{k-1}{k}}\right)\right]}{\mathrm{GMF}\left(r^{-\frac{1}{k}}+\right)\left[\mathrm{GMF}+\frac{1}{s}\left(1-\mathrm{GMF}\right)\right]}};$ the gas phase mass flowrate: Q.sub.m=Q.sub.mGMF; and the liquid phase mass flowrate: Q.sub.m,l=Q.sub.m(1GMF); wherein: Q.sub.m is the total mass flowrate, kg/s; .sub.g1 is a density of the gas phase at the inlet of the throttling nozzle, kg/m.sup.3; .sub.t is a density of the liquid phase, kg/m.sup.3; GMF is a gas mass fraction; A is the cross-section area of the throat of the throttling nozzle, m.sup.2; C is a flow coefficient of the throttling nozzle and is a constant; k is an adiabatic index of gas; r is a ratio of the pressure P.sub.2 at the nozzle outlet to the pressure P.sub.1 at the inlet, and $r=\frac{p_2}{p_1};$ and s is a velocity slip ratio between the gas phase and the liquid phase.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a schematic diagram of the critical flow nozzle flowmeter according to the invention. FIG. 2 is a flow chart of the method for measuring respective flowrates of a gas phase and a liquid phase in a multiphase fluid using the critical flow nozzle flowmeter.

(2) In the above FIGURE, the reference symbols have the following meanings:

(3) 1. Oil nozzle connection port; 2. Pressure and temperature composite sensor; 3. Gamma ray emitter; 4. Pressure sensor; 5. Gamma ray receiver; 6. Oil nozzle throat; 7. Oil nozzle outlet.

(4) The above FIGURE is only used for exemplarily describing the invention, but not restricting the invention in any manner.

DETAILED DESCRIPTION OF THE EMBODIMENTS

(5) As below described, there is a method of measuring the respectively flowrates of the gas phase and liquid phase in a multiphase fluid using the critical flow nozzle flowmeter according to the invention, comprising the following steps:

(6) a) measuring a pressure P.sub.1 at the inlet and a pressure P.sub.2 at the outlet of the throttling nozzle by using pressure sensors, and measuring a temperature T.sub.1 at the inlet of the throttling nozzle by using a temperature sensor;

(7) b) flowing the multiphase fluid through the critical flow nozzle flowmeter in a critical flow manner, wherein the multiphase fluid is judged to reach the critical flow state according to the following method: the symbol r is set as a ratio of the pressure at the nozzle outlet to the pressure at the nozzle outlet,

(8) $r=\frac{p_2}{p_1};$

(9) by measuring the pressure P.sub.1 and temperature T.sub.1, a density .sub.g1 of the gas phase is determined; by measuring a mixed density .sub.m with a single-energy gamma ray detector, a gas mass fraction GMF can be determined according to the equation:

(10) $\mathrm{GMF}=\frac{{}_l-{}_m}{{}_l-{}_{g1}},$
further to define

(11) $a=\frac{1-\mathrm{GMF}}{\mathrm{GMF}}\frac{{}_{g1}}{{}_l};$
according to the characteristic that the gas phase flows in a sonic speed when the multiphase fluid reaches a critical flow state, a critical pressure ratio r.sub.c can be defined by the equation

(12) $r_c={\left[\frac{a\left(1-r_c\right)+\frac{k}{k-1}}{\frac{k}{k-1}+\frac{k}{2}{\left(1+\right)}^2}\right]}^{\frac{k}{k-1}},$
and with the equation, the critical pressure r.sub.c can be determined by iterative solution; when a measured pressure ratio r meets

(13) $r=\frac{p_2}{p_1}{r}_c,$
the multiphase fluid is judged as a critical flow; in case of a critical flow, by the equations

(14) $=\sqrt{1+\frac{{}_l-{}_m}{{}_l-{}_{g1}}\left(\frac{{}_l}{{}_{g1}}-1\right)}\left(1+0.6e^{-5\mathrm{GMF}}\right),$
a velocity slip ratio between the gas phase and the liquid phase can be calculated;

(15) c) respectively calculating a total mass flowrate Q.sub.m of the multiphase fluid, a gas phase mass flowrate Q.sub.m,g and a liquid phase mass flowrate Q.sub.m,l according to the following equations:

(16) total mass flowrate:

(17) $Q_m=\sqrt{\frac{{\mathrm{CA}}^2{}_{g1}\left[\left(1-r\right)+\frac{k}{k-1}\left(1-r^{\frac{k-1}{k}}\right)\right]}{\mathrm{GMF}\left(r^{-\frac{1}{k}}+\right)\left[\mathrm{GMF}+\frac{1}{s}\left(1-\mathrm{GMF}\right)\right]}}$

(18) gas phase mass flowrate: Q.sub.m,g=Q.sub.mGMF

(19) liquid phase mass flowrate: Q.sub.m,l=Q.sub.m (1GMF)

(20) wherein:

(21) Q.sub.m is a total mass flowrate, kg/s

(22) .sub.g1 is a density of the gas phase at the inlet of the throttling nozzle, kg/m.sup.3

(23) .sub.l is a density of the liquid phase, kg/m.sup.3

(24) GMF is a gas mass fraction

(25) A is a cross-section area of the throat of the throttling nozzle, m.sup.2

(26) C is a flow coefficient of the throttling nozzle, being a constant

(27) k is an adiabatic index of gas

(28) r is a ratio of the pressure at the nozzle outlet to the pressure at the nozzle inlet,

(29) $r=\frac{p_2}{p_1}$

(30) s is a velocity slip ratio between the gas phase and the liquid phase,

(31) $s=\frac{u_g}{u_l}.$