Measurement of fluid properties of two-phase fluids using an ultrasonic meter

A method is disclosed for determining the composition of a two-phase fluid, such as saturated steam. In that method, the transit times of sound are measured within the two-phase fluid, the speed of sound of the two-phase fluid is calculated from the measured transit times, and the composition of the two-phase fluid is calculated from the calculated speed of sound. From the calculated linear velocity and the calculated composition, one can calculate at least one fluid property of the two-phase fluid, such as mass flow rate or energy flow rate. All of these calculations can be performed by a microprocessor.

The present invention relates to the measurement of fluid properties of 
two-phase fluids. 
BACKGROUND OF THE INVENTION 
Often, in the production of crude oil, steam needs to be injected into the 
petroleum reservoir because the crude oil is too viscous. Two parameters 
are usually required to describe a wet, saturated steam flow in a 
conduit--the total flow rate and the steam quality. The steam quality is 
defined as the mass fraction of the vapor phase in steam. Once the steam 
quality is known, properties such as specific volume and enthalpy can be 
calculated for a given saturation temperature or pressure. 
In the current practice of steam metering, two measuring devices are 
usually needed to obtain the flow rate and steam quality. For example, U.S 
Pat. No. 4,753,106 by Brenner et al. discloses using an orifice meter to 
measure the flow rate and a densitometer to measure the density, hence to 
deduce the quality. U.S. Pat. No. 4,681,466 by Chien et al. discloses a 
method using two flow meters, but that method is sometimes less than 
successful because it is based on empirical correlations of flow 
measurements. U.S. Pat. No. 4,712,006 by Zemel et al. and U.S. Pat. No. 
4,645,635 by Yuen et al. both disclose using radioactive elements to 
measure density, hence quality, but those methods are not easy to apply. 
Brenner et al., Chien et al., Zemel et al., and Yuen et al. are hereby 
incorporated by reference for all purposes. 
SUMMARY OF THE INVENTION 
The present invention is a method for determining the composition of a 
two-phase fluid, such as saturated steam, using only one meter. Since only 
one meter is used, this invention has advantages over the prior art, which 
usually require multiple devices. 
The present invention involves measuring transit times of sound within the 
two-phase fluid, calculating the speed of sound of the two-phase fluid 
from the measured transit times, and calculating the composition of the 
two-phase fluid from the calculated speed of sound. 
Fluid properties of a flowing two-phase fluid (such as mass flow rate and 
energy flow rate) can be determined by one embodiment of that invention. 
It involves measuring transit times of sound within the two-phase fluid, 
calculating both the speed of sound and the linear velocity of the 
two-phase fluid from the measured transit times, calculating the 
composition of the two-phase fluid from the calculated speed of sound, and 
calculating at least one fluid property of the two-phase fluid from the 
calculated linear velocity and the calculated composition. Preferably, the 
two-phase fluid is a homogeneous, saturated steam. All of those 
calculations can be performed by a microprocessor.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
In its broadest aspect, the present invention uses only one meter to obtain 
the needed information, resulting in less equipment and simpler operation. 
The composition of a two-phase fluid is determined by measuring transit 
times of sound within the two-phase fluid, calculating the speed of sound 
of the two-phase fluid from the measured transit times, and calculating 
the composition of the two-phase fluid from the calculated speed of sound. 
In one embodiment, an ultrasonic meter, suitably adapted to be operated in 
a high temperature (465.degree. F.) and high pressure (500 psia) 
environment, is installed in the steam line. The meter, with its 
electronic circuitry, measures a sonic velocity and bulk average velocity 
of the homogeneous wet steam flow using the transit-time principle. 
One particular advantage of the present invention is its ability to measure 
concurrently two properties of a wet steam flow: sonic velocity and 
average bulk velocity. The sonic velocity, being a thermodynamic property 
of the wet steam, depends on another thermodynamic property, the steam 
quality. Once the quality is calculated from the sonic velocity, all other 
parameters can be calculated by knowing the bulk velocity and other 
properties found in the Steam Table. 
The Two-Phase Fluid 
By "two-phase fluid," we mean a fluid that exists in two phases 
concurrently. For example, water can exist both in the gaseous and liquid 
phase at 500.degree. F. and 680 psia. The composition of the two-phase 
fluid (i.e., the fraction of each phase) at the saturation temperature and 
pressure can vary anywhere from 0 to 100% for one phase, with the balance 
in the other phase. 
While the methods and apparatuses of this invention can be used to 
determine the composition of a variety of two-phase fluids, they work 
especially well for the determination of the composition of steam. 
Preferably, the steam is saturated steam. More preferably, it is a 
homogeneous, saturated steam. 
The Measurement of Transit Times 
The first step of the present invention involves determining the 
composition of a two-phase fluid by measuring transit times of sound 
within the two-phase fluid. By "transit time of sound" we mean the time 
for a sonic pulse to travel in the fluid medium between a pair of acoustic 
transducers. The pulses travel at the speed of sound that is 
characteristic of the two-phase fluid at the measured temperature. If the 
fluid medium is not stationary, the sonic speed of the pulses will be 
either aided or retarded by the linear velocity of the fluid, depending 
upon the direction of the pulses relative to the direction of fluid 
movement. 
The transit times of sound can be measured using pairs of acoustic 
transducers that alternately act as transmitters and receivers in sending 
and receiving pulses. A typical frequency range of those pulses is from 50 
kilo hertz to 1 million hertz. 
A transit-time ultrasonic meter can measure two quantities when installed 
in a steam line: the average velocity, U, of the flow and the speed of 
sound, C, of the steam. From these two quantities, the flow rate, quality, 
and enthalpy of the steam stream can be deduced. 
Referring to FIG. 1, acoustic transducers A and B are placed diagonally 
across steam line 10 as steam passes through the line. The distance L 
between the two transducers is known. Also known is the horizontal 
component D of that distance. The transit times between these transducers 
are measured in both directions. 
The Calculation of Speed of Sound 
In the next step, the speed of sound of the two-phase fluid is calculated 
from the measured transit times. 
For a transit-time ultrasonic meter as set up in FIG. 1, U and C can be 
deduced by Equations 1 and 2: 
##EQU1## 
where T.sub.AB and T.sub.BA are the transit times for the sonic pulses to 
travel between transducers A and B. L and D are known dimensions in the 
meter setup. The travel times can be measured by the electronics in 
commercial ultrasonic meters currently on the market. 
The Calculation of Composition 
Then, the composition of the two-phase fluid is calculated from the 
calculated speed of sound. 
The quality, being a property of the steam at a saturation temperature or 
pressure, can be related to the speed of sound which is also a 
thermodynamic property of the steam. Michaelides and Zissis (1983) showed 
that the speed of sound of a homogeneous wet steam mixture can be 
calculated by Equation 3. 
##EQU2## 
where, except the steam quality x, all terms such as the specific volume 
v, enthalpy h, and saturation pressure P in the right-hand side of 
Equation 3 are either known values of thermodynamic properties of the 
steam in the Steam Tables or obtainable by correlations of those 
properties as a function of the saturation temperature T. Subscripts f and 
g denote liquid and vapor phase, respectively. Equation 3 can then be 
re-written to solve for x as shown in Equation 4. 
##EQU3## 
Thus, at a given saturation temperature T, all terms in Equation 4 
involving P, v, and h are either known from the Steam Table or can be 
computed from correlations based on the saturation temperature T. 
The quality, x, can be then calculated based on the measured speed of 
sound, C. Equation 4 is plotted in FIG. 2 where the quality, x, is shown 
as a function of the speed of sound measurement at various saturation 
temperature. Note that this scheme of computing steam quality based on the 
measured speed of sound is thermodynamically rigorous as compared to other 
acoustic schemes based on empiricism (e.g., U.S. Pat. No. 4,193,290 by 
Sustek, Jr. et al.) 
The Calculation of Fluid Property 
Once the quality is known, the enthalpy and any other thermodynamic 
properties of wet steam mixture can be calculated by the following 
formula: 
EQU h=h.sub.f (1-x)+h.sub.g x (5) 
For a homogeneous wet steam mixture, the flow rate, Q, is obtained simply 
by multiplying the measured average velocity and the cross sectional area, 
A, of the flowing tube as shown in Equation 6. 
EQU Q=U A (6) 
In one embodiment, at least one fluid property of a flowing two-phase fluid 
is determined by the four steps of: 
(a) measuring transit times of sound within the two-phase fluid, 
(b) calculating both the speed of sound and the linear velocity of the 
two-phase fluid from the measured transit times, 
(c) calculating the composition of the two-phase fluid from the calculated 
speed of sound, and 
(d) calculating at least one fluid property of the two-phase fluid from the 
calculated linear velocity and the calculated composition. 
Preferably, the fluid property that is determined is either mass flow rate 
or energy flow rate. All of these calculations can be performed by a 
microprocessor. The microprocessor can be a means for calculating both the 
speed of sound of the two-phase fluid from the measured transit times and 
the composition of the two-phase fluid from the calculated speed of sound. 
In one embodiment, the microcomputer is a calculating means for 
calculating: 
(1) the speed of sound and the linear velocity of the two-phase fluid from 
the measured transit times, 
(2) the composition of the two-phase fluid from the calculated speed of 
sound, and 
(3) at least one fluid property of the two-phase fluid from the calculated 
linear velocity and the calculated composition. 
While the present invention has been described with 5 reference to specific 
embodiments, this application is intended to cover those various changes 
and substitutions which may be made by those skilled in the art without 
departing from the spirit and scope of the appended claims.