Brian
Charles, Mark
Philip
Antony, Johnson
Mark
Wyatt, Sproston
John
Leslie
Brian
Charles, Mark
Philip
Antony, Johnson
Mark
Wyatt, Sproston
John
Leslie
| 1. | What is claimed is: A method of measuring the flow rate of a liquid in a two phase fluid and of determining the void fraction of a gaseous content of the fluid, including the steps of positioning a turbine flowmeter (16) in the flow and measuring the output frequency of the flowmeter (16) is characterised in that the output of the flowmeter is processed in terms of frequency and in terms of the Root Mean Square of the frequency and in that the processed results are compared with calibrations, the calibration process including the steps of; calibrating the flowmeter (16) in terms of liquid flow against the output of the flowmeter (16) to provide a first calibration and; calibrating the flowmeter (16) in terms of void fraction against a turbulence factor which is a function of the multiple of the frequency and the RMS of the inverse of the frequency to provide a second calibration. |
| 2. | A method as claimed in Claim 1 characterised in that the calibration in terms of void fraction is carried out in nondimensional terms by dividing the multiple of the frequency and the RMS of the inverse of the frequency by the void fraction to provide a nondimensionalised turbulence factor. |
| 3. | A method as claimed in Claim 2 characterised in that the calibration is carried out at a single void fraction. |
| 4. | A method as claimed in any one of Claims 1 to 3 characterised in that the output of the meter is compared with the first calibration. |
| 5. | A method as claimed in any one of Claims 1 to 4 characterised in that the output is processed to obtain the turbulence factor which is compared with the second calibration. |
| 6. | A method as claimed in any one of Claims 1 to 5 characterised in that the rotational frequency is measured by means whereby a sinusoidal voltage output from the flowmeter (16) is digitised and modified to a square wave, a machine code programme compares the digitised voltage with a threshold level set midway between the low and high square voltage levels, representing a point at which the programme recognises the start of a voltage pulse, after which the programme goes into a loop of a known duration which is continued until the threshold level is again crossed from below. |
| 7. | Apparatus for measuring the flow rate of a liquid in a two phase fluid and of determining the void fraction of a gaseous content of the fluid, including a turbine flowmeter (16) in a fluid flow pipe (54) providing an output signal in the form of rotational frequency and means (51, 52, 53) for processing the output signal, characterised in that the output of the flowmeter (16) is processed in terms of frequency and in terms of the Root Mean Square of the frequency and in that the processed results are compared with cali¬ brations, the calibration process having included the steps of; calibrating the flowmeter (16) in terms of liquid flow against the output of the flowmeter (16) to provide a first calibration and; calibrating the flowmeter (16) in terms of void fraction against a turbulence factor which is a function of the multiple of the frequency and the RMS of the inverse of the frequency to provide a second calibration. |
The present invention relates to the measurement of the flow rate of a fluid containing a liquid phase and a gas phase, henceforth referred to as a two-phase fluid.
Two-phase flow containing at least one liquid and at least one gas occurs either intentionally or unintentionally in many industrial situations, such as in the chemical process industry and in crude oil production. Frequently such flow occurs in situations where it is desired to measure the individual flow rates.
The conventional technique is to separate the two phases and then measure the flow rates of the liquid and gas phases separately using conven¬ tional metering equipment. The provision and operation of separating devices occupies valuable space and involves significant financial cost.
In other cases an operator might be satisfied with only a reasonable indication of liquid flow rate, and a notification that there is a gas phase present.
In the hope of solving the problems of measuring the flow rate of liquid in two-phase fluid flow some of the existing liquid flow meters have been tested to some degree in two-phase flows. It has been found that meters are either unsuitable for use in two-phase flow, or can produce repeatable results, but results which must be corrected in manner involving knowledge of the volumetic gas fraction (known as, and henceforth referred to as, void fraction) in order to correct the output.
The Applicant has discovered a method whereby meters producing repeatable results can be used to provide an indication of both liquid flow rate and void fraction in a two-phase flow.
Various suggestions have been made for measuring the liquid flow in two phase fluid flows where the gaseous flow is not of interest. For example in PCT WO 85/00881 an axially moveable turbine wheel in a vertically
extending flow passage has both its rotational speed and its vertical position measured. The combination of readings gives the liquid flow rate - presumably by comparison of the readings with calibration results, although no calibration process is discussed. Also in UK patent 1,471,450 a method of measuring liquid flow in a turbulent two-phase fluid flow is described where fluctuations in fluid pressure at frequencies above a predetermined level are measured and the Root Mean Square (RMS) of these fluctuations is integrated over a predetermined time period to give the liquid flow rate.
In UK Patent Application GB 2,057,134A a method is described for measur¬ ing both liquid and gaseous flow in a two phase fluid flow. In this the fluid is subjected to centripetal forces and the pressure difference between the maximum and minimum pressures measured. The average value of the pressure differential and the RMS value of pressure fluctuations are compared with a pre-determined calibration. The calibration is obtained by measuring both values during steadily increasing liquid flows with a plurality of gaseous contents. The means by which the various different fluid flows are prepared is not explained, but the calibration process is extensive and complicated.
The Applicant has discovered a method whereby meters producing repeatable results can be used to provide an indication of both liquid flow rate and void fraction with little more calibration than is required for calibrat¬ ing the meter for pure liquid flow.
According to the present invention, a method of measuring the flow rate of a/liquid in a two-phase fluid and of determining the void fraction of a gaseous content of the fluid, includes the steps of positioning a turbine flowmeter in the flow and measuring the output frequency of the flowmeter, characterised in that the output of the flowmeter is processed in terms of frequency and in terms of the Root Mean Square of the frequency and in that the processed results are compared with calibrations, the calibration process including the steps of; calibrating the flowmeter in terms of liquid flow against the output of the flowmeter to provide a first calibration and; calibration the flowmeter in terms of void fraction against a turbulence factor which is a function of the multiple of the frequency and the RMS of the inverse of the frequency to provide a second calibration.
The calibration in terms of void fraction is preferrably carried out in non-dimentional terms by dividing the multiple of the frequency and the RMS of the inverse of the frequency by the void fraction to provide a non- dim ensionalised turbulence factor. The calibration might be carried out at only one void fraction.
According to another aspect of the invention, apparatus for measuring the flow rate of a liquid in a two-phase fluid and of determining the void fraction of a gaseous content of the fluid includes a turbine flowmeter providing an output signal in the form of rotational frequency and means for processing the output signal, characterised in that the output of the flowmeter is processed in terms of frequency and in terms of the Root Mean Square of the frequency and in that the processed results are compared with calibrations, the calibration process having included the steps of; calibrating the flowmeter in terms of liquid flow against the output of the flowmeter to provide a first calibration and; calibrating the flowmeter in terms of void fraction against a turbulence factor which is a function of the multiple of the frequency and the RMS of the inverse of the frequency to provide a second calibration.
A turbine meter is calibrated by measuring the rotor frequency at various ' rates of liquid flow there-through. The rotor frequency is usually measured by means of magnetic inserts at the rotor blade tips. As these pass an external pick-up coil an AC voltage is generated. This method allows the rotor frequency to be measured without damaging the integrity of liquid (or fluid) flow pipes.
A test facility used in developing the method of the invention and results obtained therefrom, and an apparatus according to the invention, will now be described, by way of example only, with reference to the accompanying diagrammatic drawings, of which
Figure 1 is a schematic diagram of a test facility,
Figures 2 and 3 are graphs of time between pulses against pulse number during operation of a turbine meter in a fluid at two flow rates with identical void fractions,
Figures 4, 5 and 6 are graphs of signal turbulence against meter frequency at different void fractions for three turbine meters having rotors set at different degrees,
Figure 7 is a graph of non-dimensionalised turbulence against meter frequency for a turbine meter having a 30° rotor, for different void fractions,
Figure 8 is a graph of non-dimensionalised turbulence against reference o meter frequency for turbine meters having three different blade angles,
Figure 9 is a graph of void determination using a turbine meter in the method of the invention, and
5 Figure 10 is an apparatus according to the invention.
A test facility (Figure 1) has a working section 10 of 4" diameter plastic pipework, approximately 15 meters in length. Water is supplied to the working section 10 from a tank 11 supplying a nominally constant head which generates 0 a static pressure in the working section 10 of 3.5 bar. A calibrated reference turbine meter 12 is installed in the working section 10 upstream of an air injection point 13. An air flow measuring device 14 is installed in an air supply pipe 15 leading to the air injection point 13. A test turbine meter 16 and a pressure transducer 17 are installed in the working section 10 down- 5 stream of the air injection point 13. Readings from the reference turbine meter 12, air flow measuring means 14, pressure transducer 17 and test turbine meter 16 are fed to a computing facility 18. The turbine meters 12, 16 are of the type whose rotational speed is measured by means of magnetic inserts in turbine blade tips which generate an AC voltage in an external pick-up 0 coil. From the test turbine meter 16 the working section 10 leads to a diverter valve 19 one branch of which leads to a sump 20 and the other of which leads to a gravimetric facility 21 which feeds back into the sump 20. A return system 22 powered by a pump 23 leads from the sump 20 to the supply tank 11. 5
Tests carried out using this test facility will now be described. Water
was supplied from the supply tank 11 through the reference meter 12. After passage through the reference turbine meter 12 air was injected through the air injection point 13, the air flow rate being measured by the air flow measurement means 14 which supplied readings to the computer 18. By using the information from the reference turbine meter 12 and air flow meter 14 and the known physical characteristics of air and water the void fraction in the fluid flow downstream of the air injection point 13 could be determined. Readings from the test turbine meter 16 were also passed to the computer 18 and were treated as described below.
The fluctuating AC voltage from the test turbine meter 16 was amplified and digitised, the original sine wave being modified in the process to a square wave. A machine code programme compared the digitised voltage with a threshold level set midway between the low and high square wave voltage levels representing the point at which the programme recognised the start of a voltage pulse. Once this threshold level was crossed from below the programme went into a loop of known duration. The loop continued until the threshold level was again crossed from below indicating that the next voltage pulse had occurred. By counting the number of times the internal loop had run between pulses the duration between the two pulses was obtained.
This was the inverse of the instantaneous rotor frequency. The filtered signal was then processed to generate the average frequency and the root mean square value of the "peak to peak" times, that is the inverse of the rotor frequency. The root mean square value was multiplied by the average frequency to give a parameter representing the signal turbulence.
In the actual test apparatus used the air flow meter 14 consisted of a series of rotameters, readings from which were hand fed into the computer 18. These readings were corrected for rig conditions using the isothermal expansion procedure presented in an article "The performance of a turbine meter in gas/liquid flow with upstream mixing" by Millington, BC and King, N W at the International Conference on Flow Measurement in the Mid 80s, Glasgow 9-12 June 1986, using pressure information from the pressure transducer 17. A Butterworth Low Pass Filter was used to correct extraneous scatter in the readings caused by irregularities in the spacing of the magnetic inserts in the turbine blades, and the resolution of the pulse algorithm.
Tests were carried out using 3 test turbine meters, these differing in having blade angles respectively of 20, 30 and 40 degrees to the axis of rotation.
Tests were carried out over a water flow range of 5-60 litres per second with void fractions of up to 25%. Under these flow conditions the flow patterns were stratified slug flow, stratified bubbly flow and a transitional pattern exhibiting traits of the two main patterns. The flow patterns could be observed through transparent portions of the working section 10. As the flow rate changes so does the flow pattern. Using a 30° rotor at a flow rate of 12 litres per second and a void fraction of 5% stratified slug flow was observed.
A plot of the time between pulses verses pulse number is plotted in figure 2 and shows a series of quite sharp peaks 30 separated by relatively flat plateaux 31. The ascending face of the peaks represents increasing time between present rotor acceleration. It is believed that the peaks occur whilst the gas slug passes through the rotor. The presence of the gas slug reduces the driving torque generated by the rotor because of the low density of the gas phase. Since the rotor speed is proportional to driving torque, this results in the deceleration of the rotor. When the gas slug is replaced by the following liquid plug the rotor quickly accelerates back to its original speed. Whilst the rotor is influenced by the liquid plug the time between pulses remains constant, as shown by the plateaux 31.
As liquid flow rate increases the flow pattern tends towards bubbly stratified flow in which a mass of small gas bubbles is dispersed in the liquid phase, bouyancy effects resulting in the bubbles congregating at the top of the pipe 10. Since the flow is essentially steady a plot of time between pulses against pulse number does not show peaks and plateaux, as in figure 2, but a signal oscillatingabout a mean value as shown in Figure 3.
The time between pulses was processed to provide signals representing the average frequency and the root mean square of the "peak to peak" times, namely the root mean square of the inverse of the rotor frequency. These two parameters were multiplied to provide a parameter which represented the signal turbulence. This signal turbulence was plotted against meter frequency, for the 30° rotor, at void fractions as shown in Figure 4. Similar results were plotted for the 20° rotor in Figure 5 and for the 40° rotor (for
a single void fraction) in Figure 6. From these figures it can be seen that a unique turbulence characteristic is developed at each void fraction over the operating range of each meter. As the response is unique and repeatable this shows that providing a meter is calibrated over a range of two-phase flow conditions the turbulence signal can be used to indicate void fractions.
The meter will also, of course, have to be calibrated in the normal fashion for pure liquid flow, and the extra calibration for void fraction would signi¬ ficantly increase calibration times. As shown in Figures 4, 5 and 6 it is apparent that the form of the turbulence characteristic is similar in all cases. The turbulence rises quickly to a peak value and then gradually reduces with increasing meter frequency. As well as the form similarity the level of signal turbulence appears to be dependant upon void fraction, at any meter frequency.
For the 30° rotor the turbulence was non-dimensionalised by dividing by void fraction, and the non-dimensional turbulence (NDT) values plotted against meter frequency (Figure 7). This shows that the data collapses reasonably well onto a single curve where the NDT is a function solely of the meter frequency. This suggests, therefore, that a turbine meter calibration need only be carried out at one void fraction in order to determine the form of the turbulence characteristic, so reducing the calibration time to little more than taken at present for single-phase calibration.
Figure 8 shows a plot of non-dimensionalised data for the 20 and 40 degrees rotors as well as for the 30° rotor, plotted against the reference meter frequency. It can be seen that substantially a single curve is produced.
This suggests that the turbulence level in the "peak to peak" signal is purely a function of the flow pattern and phase distribution, and that the meter geometry has little if any influence.
To use a turbine meter according to the invention it is first calibrated in the normal fashion for liquid flow and also to determine the turbulence characteristic. When used in a fluid flow the "peak to peak" RMS signal is recorded for a short period, and multiplied by the average meter pulse frequency to give the measured turbulence. Using the average frequency in the NDT characteristic equation the NDT for that flow condition is given, and by dividing the measured turbulence by the NDT the void fraction is
obtained.
A programme was produced which generated the void fraction from the meter output signals. The equation fitted to the NDT characteristic was a fourth order polynomial with a correlation of 0.944 and a standard deviation error of 0.067. The performance of a meter in determining void fraction, against known void fraction, for a series of meter frequencies (that is flow rates) is shown in Figure 9. It can be seen that the agreement is good, particularly at low liquid flow rates, with rather high disagreement at the highest flow rates. It is thought that the reduction in accuracy is due to the different flow pattern existing at the higher flow rates.
An apparatus for carrying out the method of the invention (Figure 10) includes a flow meter 16 calibrated in terms of liquid flow rate against a standard parameter (for a turbine meter the rotor frequency) and of void fraction against a Turbulence parameter (for a turbine meter, the average rotor frequency multiplied by the root mean square of the inverse of the rotor frequency). An output (50) of the meter (16) is connected to a first processing means (51)and to a second processing means (52). The first processing means (51) is programmed " to process the output, signal in terms of the standard parameter and to compare this first processed output with the calibration to give a measurement of liquid flow. The second processing means 52 is programmed to process the output signal in terms of the Turbulence parameter and to compare this second processed output with the calibration to give a measurement of void fraction. The first and second processing means (51, 52) are connected to recording means (53) which may be a visual display, one of the well known data storage systems such as tape or disc, or any combination of these.
It will be reaslised, of course, that in practice the functions of the first
(51) and second (52) processing means will usually be carried out in the same equipment, such as a micro-computer.
In use the apparatus is positioned with a two-phase fluid flow pipe 54 connected to input and output ports of the fluid flow meter 16.
It will be realised that many alternative methods of achieving the method of the invention are possible. For example many alternative programmes for determining the time between pulses is possible, for example a method involving detection of actual peaks. Also alternative methods of processing the results to give a parameter corresponding to turbulence are possible.
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