Gas-Liquid Two-Phase Flow Rate Measurements by Flow Division and Separation Method

In this chapter we shall introduce a new and practical method for two-phase flow rate measurement, which is known as flow division and separation method. As its name suggested, a two-phase flow is measured by diverting a small fraction of the total stream to a division loop and metering it with the separation means. This method has been developed in Xi’an jiaotong university since the end of last century, and extensively studied in laboratory, some of the meters have been successfully applied in engineering. At first we briefly introduce the flow division technique in single phase flow, then we discuss how this method can be used in gas-liquid two-phase flow measurements, further more we shall give three detail examples of this kind of two-phase flow meters.


Introduction
In this chapter we shall introduce a new and practical method for two-phase flow rate measurement, which is known as flow division and separation method. As its name suggested, a two-phase flow is measured by diverting a small fraction of the total stream to a division loop and metering it with the separation means. This method has been developed in Xi'an jiaotong university since the end of last century, and extensively studied in laboratory, some of the meters have been successfully applied in engineering. At first we briefly introduce the flow division technique in single phase flow, then we discuss how this method can be used in gas-liquid two-phase flow measurements, further more we shall give three detail examples of this kind of two-phase flow meters.

Flow measurement by flow division technique
The rate of flow in a pipe can be measured by a flowmeter installed in the identical pipe, this kind of flowmeter is called the full bore flowmeter which has the same size of diameter as the flow tube. However as the flow tube becomes very large, the full bore flowmeter will be extremely expensive or even impossible to build. In this case, the flow division technique can be a very convenient choice. In addition to this, the flow division technique can also be used to solve the difficult problem of two-phase flow measurement.

Flow division technique in single phase flow
Flow division technique, also called flow ratio technique (DeCarlo, 1984), have been widely used in single phase flow measurements, whose main feature is to use a small size meter to measure a large volume flow in large lines. This kind of flow meter is usually called "bypass flow meter", or "shunt flow meter" or "proportional flow meter". As shown in Fig.1, a bypass flow meter consists of three major portions (Fenelon,1994), a main flow path, a bypass loop (flow division branch) and a restriction. The restrictive element is positioned in the main flow path and the bypass flow loop is arranged to cross the restrictive element, so that its inlet and outlet is located at the upstream and downstream of the restrictive element respectively. The function of the restrictive element is to create a pressure drop between the www.intechopen.com Flow Measurement 40 upstream and downstream of the restriction which will cause a portion of total flow to enter into the bypass loop. A small size flow meter is installed in the bypass flow loop to meter the flow quantity or flow rate passing through the bypass loop. The total flow quantity or flow rate can be inferred from the metered value since a definite ratio exists between the flow rate in bypass loop and the total flow rate.
From Fig.1 we can also see that the bypass loop and the main flow path have a common inlet and a common outlet i.e. they are in parallel to each other (Munson, 2002). In accordance with the nature of parallel loops, the pressure loss of these two loops must be equal (Munson,2002). The pressure loss in these two loops include friction and local resistance which can be express as Equation (4) clearly shows that the ratio of flow rate passing through the bypass loop to the total flow is dependent on the structure parameters of these two loops. By properly setting the resistance devices in these two loops, a constant ratio can be obtained. In practice the ratio should be calibrated by experiment, and a bypass flow meter will have an equivalent precision as the full bore meter.
The ratio of M 3 to M 1 can vary from 1 to 2.5×10 -4 , hence the flow meter in the bypass loop can be greatly reduced in size. We can use a small size flow meter or flow sensor to meter a large volume flow in a large pipe. Thus the capital cost and operation cost can be significantly reduced. This is the main advantage of a bypass flow meter.
The flow meter incorporated in bypass loop can be a flow quantity meter for measuring the quantity of flow (Hirst, 1951;Hodgson,1932;Kidder, 1934;Peranio, 1967;Thomson, 1895aThomson, , 1895b, or a flow rate meter for measuring the rate of flow. The flow rate meters used in the bypass loop can be any types, but we usually select the meters which have a relative large metering range, for example, it can be a rotameter (Rlkuta,1969;Stenberg,1962), a Coriolis mass flow meter (Kane, 1994;Kalotay,1994;Van Cleve,1999), or a thermal (calorimetric) mass flowmeter (Adams,1969;Baker,1969Baker, , 1971Baker, ,1977Hawk,1984;Kronberger,1952;Laub,1956;Sato,1983). Therefore a bypass flow meter will also have a large metering range. At the same time, the flow meter or a flow sensor will also have a higher sensitivity than the full bore flow meter because of its small size. For instance, a small size Coriolis effect flow sensor is more sensitive than a large one because of its thinner and more flexible flow tube which is more suitable for the generation of meaningful Coriolis forces (Kalotay,1994).
A bypass flow meter's metering range and precision can be further expanded and improved if a variable constriction is used. Fig.2 is an example of variable constriction flow meter (Bahrton,1996). The significant feature of the variable constriction in Fig.2 is that a moveable conical body is introduced in the orifice. When the total flow is very low, the conical body will be pressed to the left by the spring so as to decrease the flow area of the orifice or completely close the orifice, so that all of the flow, or at least a large part of the total flow will enter into the bypass loop and metered by the flowmeter. On the contrary, when the flow is large, the conical body will be forced to the right by the fluid so as to increase the flow area of the orifice, so that a smaller part of total flow will pass through the bypass loop. As a result the dynamics (the ratio of maximum flow rate to the minimum flow rate) of the bypass meter can be expanded to 2500:1 which is much larger than a full bore flow meter. It can also be seen from Fig.2 that in any case the flow passing through the bypass loop can always fall in the optimum measuring arrange of the flow meter by adjusting the restriction, and this will improve the precision of the flow meter. Similar structure can also be found in references (Connet,1928;Olin,1984  The restrictive element in a bypass flow meter can be also a Venturi tube (Van Cleve,1999), a nozzle (Baker,1971), a pitot tube (Baker,1977) or other resistance devices.

Recent development in two-phase flow measurement
Two-phase flow rate measurement is still a difficult problem in science and engineering. Traditional solution is to separate the two-phase mixture into single phase flows first, and then measure the flow rate of each phase with single-phase flow meters. In this method, usually a large separator vessel is required to complete the separation of two-phase flow, and both the capital and operating cost of equipments tend to be high. Also, in practice, the measurements derived from this process are subject to many errors Thorn et al ,1997 . During the last couple of decades, a number of techniques have been studied to measure the two-phase flow rate. Nearly all the conventional flow meters have been tried to meter the two-phase flow (Bates and Ayob ,1995;Cha et al ,2002;Chisholm ,1974;Jung et al ,2009;Kriiger et al,1996;Lin,1982;Murdock,1962;Skea and Hall,1999;Steven,2002;Steven and Hall,2009). Experiments show that the measurement errors will increase rapidly as the amount of second phase appeared in the flow increases. At the same time, the response of a single phase flowmeter to the two-phase flow depends on not only the flowrate but also on the phase fraction. For instance, under a certain flowrate, the higher the gas quality, the larger the differential pressure passing through an orifice. Therefore, a single phase flowmeter is not capable of measuring the flowrate and phase fraction simultaneously and a combination with other measuring devices is necessary. A lot of combined methods have been developed to measure the two-phase flowrate and phase fraction (Huang et al ,2005;Geng et al ,2007;Meng et al ,2010;Meribout et al ,2010;Oliveira et al ,2009;Reis and Jr ,2008;Sun ,2010;Zhang et al ,2010;Zheng et al ,2008).
These combined methods mentioned above can work well within their respective metering ranges, however, the measurement error would increase and the instruments may even fail to work once beyond their narrow rated ranges. One of the major reasons that cause the larger measuring error and the failure of measurement is that a two-phase flow is always in violent fluctuation. Fluctuation is an inherent feature of two-phase flow that makes the instruments unsteady and unreliable. Nevertheless some researchers consider it as useful information to determine the phase fraction or flowrate of a two-phase flow (Beg and Toral ,1993;Ferreira ,1997;Wang and Tong ,1995;Xu et al ,2003). A separation means for twophase flow measurement that does not employ large separator may be a good choice (Liou ,1995;Turkowski ,2004).

Two-phase flow measurement by flow division and separation method
From section 2.1 it has been known that the flow division technique is a reliable method for measuring the single phase flow rate. Its main advantage is to use a small size meter to measure the total flow in a large flow pipe. If this method can be used in gas-liquid twophase flow, then we can use a small size separator in the bypass loop to separate the twophase mixture passing through the bypass loop into single phase gas and liquid and consequently measuring them by conventional single phase flowmeters, thus the problem of two-phase flow rate measurement can simply be solved. However, there is a key problem which must be solved before this technique can be successfully used in two-phase flow, that is how to divert a portion of two-phase mixture, which will have the same components as the total flow and be proportional to the total flow, to the bypass loop. We can not simply place the inlet end opening of the bypass loop in the main flow as in the case of single phase flow, because a two-phase fluid is not a homogenous medium, on the contrary, it always presents different flow pattern at different flow conditions. Hence a special distributor must be employed between the main and bypass loop. Fig.3 shows a schematic representation of a flow division type two-phase flow measurement system (Wang & Lin, 2002). The measuring process is that, first, a small portion (1%-20%) of the total two-phase flow is extracted by a distributor, then it is separated by a small compact separator, after that the separated gas and liquid flows are metered by the single phase flowmeter respectively, in the end, the two metered flows are returned to the main stream. The total gas flow rate M G and total liquid flow rate M L are determined by the following equations Where M G3 and M L3 is the metered gas and liquid flow rate respectively, K G and K L represents the gas and liquid extraction ratio respectively. For an ideal distributor, K G and K L should be a constant so that the determinations of total flow rate of each phase would be much simpler. Apparently, it is difficult for a real distributor to keep the extraction ratio being constant in any condition. In fact, as long as K G and K L could be relatively stable within a quite wide range, the distributor could be used. From Fig.3 it can also been seen that the flow rate of the stream entering into the separator is only 1%-20% of the total www.intechopen.com Flow Measurement 44 flow, so the size of separator can be reduced at least 1%-20% times compared with the traditional separating method in which all the two-phase mixture is separated, and the size of a two-phase flow meter may nearly approach that of common single flow meter. In the following section we shall introduce three different distributors.  (Wang & Lin, 2002). The core part of a rotational drum distributor is the rotational drum. The outline of the drum is a cylinder, the inside space is equally segregated into a series of small flow channels which twisted around the drum axis. The outputs of the most channels are directed to the down stream part of the pipe, only a few channels, which are selected as the extraction channels, are connected to the separator (to the bypass loop).  As two-phase mixture passes through channels, the drum will be forced to run at a high speed around its axis by the fluid. With the running of the drum, the entrance of each channel will continuously scan over every point on the cross section in front of the drum. If each channel has the same characteristics of geometry, friction and output pressure, and the rotation speed is high enough, then the flow of fluid at any point on the cross section in front of the drum would not be influenced by the rotating of the rotational drum, and would have the same possibility to enter each channel. In other words, the flow would be considered as steady flow within a drum running period and the time duration Δt, during which the fluid at any point of the cross section in front of the drum flowing into a channel within a drum rotation period, will be equal, that is Where T is the drum rotation period; n is the total number of the channels inside the drum.
The amount of gas and liquid passing through each channel in a drum rotation period will be Where ΔM G and ΔM L is the amount of gas and liquid passing through each channel in a drum rotation period respectively; α i is the local void fraction and u Gi , u Li is the local gas and liquid velocity on the cross section in front of the drum respectively; ρ G and ρ L is the gas and liquid density respectively; A represents the cross section of the pipe in front of the drum. M G and M L is the total gas and liquid flow rate respectively.
Equation (8) and (9) also mean that ΔM G and ΔM L is equal to the amount of total flow of each phase passing through the cross section of the pipe in front of the drum within time Δt respectively. The drum distributor seemingly acts as a time controlled switch which equally directs the total flow into each channel. As long as the rotation period of drum is short enough, the accuracy of Equation (8) and (9) will be all right.
The average gas flow rate m G , and liquid flow rate m L passing through each channel will be GG GG If z channels are selected as the extraction channels, which are connected to the separator, then the sum of gas flow rate M G3 and liquid flow rate M L3 of the bypass stream is The gas extraction ratio K G , and liquid extraction K L is Equation (14) and (15) show that the extraction ratio of the rotational drum distributor is simply dependent upon the number of extraction channels and independent of the flow patterns. In the experiment of this study, n, the total number of channels, is 10, z, the number of extraction channels, is 2. According to Equation (14) and (15), the extraction ratio should be Equation (14)- (16) are obtained for a perfect rotational drum distributor. There are some factors which should be considered when use them to a real rotational drum distributor. These include the size of the gap between the drum and the shell, the rotating speed of the drum and the geometrical departure from the ideal shape during the manufacturing and the assembling process. All these effects on the extraction ratio will be determined by experiments.
Two different drums were used in the experiments in order to examine the effect of gap size between the shell and the drum on the extraction ratio. One drum has 0.75 mm gap size, and another one has 0.25 mm gap size. The experiments were carried out in an air-water twophase flow loop in Xi'an Jiaotong University as shown in Fig.5.

Fig. 5. The air-water two-phase flow experimental loop schematic
A gas rotameter was installed vertically upstream of the mixer for air flow rate adjustment, the precise gas flow rate was given by the vortex flow meter installed at the top of cyclone separator at the outlet end of the loop. The gas flow rate of the extracted (bypass) stream was also metered by a vortex flow meter. The water flow rates, both the total water flow rate and the extracted (bypass) water flow rate, were metered at the point of liquid output in the water leg of the cyclone separator and of the separator used in the bypass loop respectively by using the weight-time method. The duration of time during which water is collected was about 10-120 s, depending upon the flow rate of the water. An assessment was carried out on the uncertainty on each of the measured parameters. They were all within ±1.5%. From this the accuracy of the extraction ratio was determined and found to be ±1.5% for liquid extraction ratio K L , and ±2% for gas extraction ratio K G . The separator used in the bypass loop in this experiment was simply a vertically installed cylinder made from Plexiglas pipe, mounted internally with a multi-hole plate in the cross section of the cylinder just above the entrance of the bypass stream. The inner diameter and height of the separator were 70 and 350 mm respectively. The straight pipe between the mixer and the test section has 30 mm ID and 2400 mm total length, and is made from Plexiglas pipe through which the flow patterns can be observed.

Fig. 6. The rotation speed measuring circuit
In order to determine the effect of rotation speed of the drum on extraction ratio, a simple electrical circuit as shown in Fig. 6 was used to measure the rotation speed of the rotational drum. A short portion (about 3 mm wide) of the drum shaft was selected as one part of the circuit. Half of the outer surface of the shaft was coated with a thin layer of plastic to form the insulation surface, and the other half was a polished metal surface. An elastic beam made from thin copper-beryllium plate, is contacted to the shaft at one end, and is connected to the electrical resistance at the other end. With the running of the shaft, the elastic beam contacts alternatively with insulation surface and conductance surface. Thus, a square electric current pause is generated in the circuit for each cycle. The square wave signal can be seen on the screen of the data acquisition system, and the frequency of the square wave represents the drum rotation speed. If some water is appeared on the insulation surface, the amplitude of square wave signal will be reduced a little, but the shape and frequency of the square wave will not be changed any more, even the pipe is full of water.
Extraction ratio were measured in the following experiment range: gas superficial velocity varied between 4 and 40 m/s; water superficial velocity ranged from 0 to 0.28 m/s; flow patterns occurring during experiments included stratified flow, wave flow and annular flow. A typical experimental results of the extraction ratio are shown in Fig. 7, data symbol S, W and A represents the flow pattern of stratified, wave and annular flow respectively. These results were obtained with the drum having 0.25 mm gap size between the shell and the drum. From these results it is seen that both the gas extraction ratio and liquid extraction ratio are very close to the theoretical value-0.2 as the extracted (bypass) liquid flow rate is high, but as the extracted liquid flow rate is low, the liquid extraction ratio becomes higher than 0.2, while the gas extraction ratio becomes lower than 0.2. For the liquid extraction ratio, this phenomena could be explained by the fact that some of the liquid will preferentially leak into the separator through the gap between the shell and the drum, rather than through the flow channels in drum as two-phase flow passing through the distributor. Therefore the actual liquid flow rates extracted are a little more than the theoretical values (predicted with Eq. (13)). This liquid leakage is generally quite small compared to the total liquid flow rate extracted when the liquid flow rate is high, so the extraction ratio is close to 0.2; but when the liquid flow rate is low, the liquid leakage will not be a small value compared to the total liquid flow rate, and the liquid extraction ratio K L will be much higher than 0.2. The larger the gap is, the more apparent this tendency will be, as shown in Fig. 8, which was obtained with the drum having 0.75 mm gap size. Thus if the leakage could be effectively controlled by reducing the gap size between the drum and shell as far as possible or by other means, the stability of K L would be improved significantly. For the gas extraction ratio K G , the explanation is that the resistance to the air flow in the main flow loop is low compared to the bypass loop as the liquid flow rate is low, so some gas that should flow into the bypass loop will remain in the main loop, and the extraction ratio will be lower than 0.2; with the increase of the liquid flow rate, the resistance to the air flow in the main flow loop will increase, this make more gas flow into the bypass loop, and the gas extraction ratio increases gradually. Since the total resistance in main loop (and also bypass loop) comprises two parts: the resistances in drum and after the drum, it is easy to balance the first part of total resistance in main loop with that in bypass loop (as every flow channel of the drum nearly has the same geometry), and yet it is not easy to balance the second part in main loop with that in bypass loop, so it is the unbalance of the second part 49 of total resistance in main loop and in bypass loop that causes the variation of K G . If the second part of total resistance in both loops could be restricted within a very small fraction compared to the first part (or total resistance), the variation of K G would be reduced remarkably. From Fig. 7 and Fig. 8 it can also be seen that flow regime do not have significant effect on the extraction ratios in the experimental range. The effect of rotation speed of the drum on the extraction ratio is shown in Fig.9, where V SL represents superficial liquid velocity in the straight pipe. These data were obtained at arbitrary liquid and gas flow rates which cover the range of experiment. Although significant variations of extraction ratios can be seen in Fig. 9, any definite relationship between the variations and rotation speed of the drum can't be seen except the data of K L at low liquid superficial velocity V SL < 0.028 m/s. The extraction ratios, K G and K L , are only dependent upon the superficial liquid velocity. At the same nominal superficial liquid velocity, K G (or K L ) is nearly unchanged over the span of rotation speed. All the higher value points of K L and lower value points of K G occur at the condition of low superficial liquid velocity V SL < 0.028 m/s, the reason for this has been explained above. The value of K L at low superficial liquid velocity V SL < 0.028 m/s increases with increasing rotation speed, this can be further explained by the fact that the drum is driven by the fluid to be measured, so the rotation speed is nearly proportional to the gas flow rate at low superficial liquid velocity. Therefore, the increase in rotation speed means the increase in gas flow rate that will cause a higher pressure difference between the inlet and exit of the drum distributor, and of course a higher liquid leakage through the gap between the shell and the drum and finally a higher value of K L . It is the gas flow rate that affects the value of K L at low superficial liquid velocity. The rotation speed of drum does not have significant effect on the extraction ratios in the experimental range. Figs. 7 and 8 can also be considered as the extraction ratio calibration curves. By using these calibration values of K G and K L , the total gas flow rate and liquid flow rate can be determined according to Equation (5) and (6) respectively. The average error of flow rate measurement in the experiments were about ±6.2% and ±5.1% for gas and liquid respectively when the drum gap size was 0.75 mm; and ±5.6%, ±3.4% when the drum gap size was 0.25 mm.

The wheel -Fluid rooms distributor
Two type of wheel-fluid rooms distributors are schematically shown in Fig.10 and Fig.11 respectively (Wang et al, 2012).
www.intechopen.com  Fig.10 it can be seen that the main body of the distributor consists of two parts: a wheel and a number of fluid rooms (Fig.10B). The wheel is located at the center of the distributor, and the fluid rooms equally surround the wheel. These fluid rooms are divided into two groups, one is connected to the main flow loop through their bottom (Fig. 10A), which is named as main fluid rooms; the other is connected to the bypass loop through the header of bypass flow (Fig.10B,A), which is called bypass fluid rooms. In Fig.10 the number of bypass fluid rooms is 3 and they are arranged 120 degrees from one to another around the wheel (Fig. 10B). As shown in Fig. 10A, the wheel is vertically installed in the bracket with a shaft and two bearings. The planform of bracket is shown in Fig. 10D. The wheel can rotate about its center axis, and is flow driven. In Fig.10A, the cover of distributor is made from Plexiglas plate for an easy observation of the wheel rotation. The fluid entrance of the distributor is located at the center of the cover, from where a short tube, which is fixed into the cover is inserted into the wheel center. There are 3 flow paths that equally surround flow entrance extending to the edge of the wheel (Fig.10B). As two-phase mixture flow downwards into the center of wheel (Fig.10A), the fluids will pass through the 3 flow paths within the wheel (Fig. 10B) and form 3 jets at the exit of the path. A reaction force will act on the wheel when the jets leave, which has a component in the tangency direction of wheel and push the wheel to rotate around the shaft at a high speed. The velocity triangle of the jets is shown in Fig.10C, where w is the relative velocity of the fluids, U is the wheel linear velocity at the edge, and V is the absolute velocity of fluids. It can be seen that V is nearly in the radial direction of the wheel, which means that the fluids can flow directly into the fluid rooms without impacting with the side wall of fluid rooms, and this will reduce the pressure loss of the distributor. With the rotation of wheel, the total two-phase flow is conducted alternately into main flow loop and bypass loop through their corresponding fluid rooms.  Fig.10, only the wheel is driven by a motor and the rotation speed of the wheel is controlled by adjusting the electrical current to the motor. There are totally 4 bypass fluid rooms arranging 90 degrees from one to another around the wheel (Fig.11C). The number of flow paths within the wheel is 2 (Fig.11C). This distributor is designed for low velocity condition when the fluid can not drive the wheel steadily.
To be similar to a rotational drum, the wheel can evenly distributes the total flow to each fluid room during rotation, hence the relationship between M 1j and M 3j (where M is flowrate, j represents an arbitrary phase, gas or liquid, 1 presents total flow and 3 is the bypass flow) in the distributor mentioned above can be obtained based on the mass conservation within one period of rotation of the wheel.
where n is the total number of the fluid rooms, which is equal to 60 in Fig.10 and 72 in Fig.11; m is the number of bypass fluid rooms, which is 3 in Fig.10 and 4 in Fig.11 respectively; T represents the rotation period of the wheel.
Rearranging Equation (17), the extraction ratio will become Equation (18) shows that the extraction ratio depends only on the ratio of bypass fluid room number to the total fluid room number and is independent of the speed of rotation. The rotation period changes with the flow rate, while the extraction ratio will still remain constant. We can change the value of the extraction ratio by altering the value of m or n. In the present study, for the passive distributor of Fig.10, m=3, n=60, according to Equation (18), the theoretical value of extraction ratio K j is 0.05; and m=4, n=72 ,K j =0.0556 for the active distributor of Fig.11. It should be pointed out that Equation (17)-(18) are only correct under the isokinetic sampling condition, i.e. the flow to each fluid room (refer to Fig.10B or Fig.11C) must be equal (let it equal to q), hence the bypass flow rate should equal to mq, the main flow rate be (n-m)q and the total flow rate be nq. In order to meet this requirement, the resistance in bypass flow loop and main flow loop must be properly controlled. The pressure loss due to friction and local resistance in these two loops can be written as below based on homogeneous flow model (Butterworth et al, 1978) 2 Where △P is the pressure loss, Ψ is correction factor, is Darcy friction factor, l is tube length, D is tube inner diameter, ξ is local two phase flow loss factor, ρ L is the density of liquid phase, ρ G is the density of gas phase, M is mass flowrate, A is tube cross section area, and X is the gas quality; Symbol Σ represents summation; Subscript "2" represents the main flow loop and the subscript "3" represents the bypass flow loop. Although Equation (19) and (20) are derived from the homogeneous flow model, they have been corrected by experimental data and several correlations about Ψ and ξ have been established for engineering application, especially in China and Russia (Lin et al, 2003).
From Fig.3 it can be seen that the bypass flow loop and the main flow loop have a common inlet and a common outlet i.e. they are in parallel to each other (Munson 2002 ), in accordance with the nature of parallel loops, the pressure loss of these two loops must be equal (Munson 2002 ). In isokinetic sampling case, X 2 = X 3 =X 1 , where X 1 is gas quality of total flow, and the fluid densities are also equal. If we neglect the possible small difference of static head between two loops, the left hand sides of Equation (19) and (20) are equal. From Equation (18), (19) and (20), a relationship of resistances between two loops for isokinetic sampling can be obtained 3 32 3 33 3 23 Where M 3 is the mass flowrate of bypass flow, and M 2 is the mass flow flowrate of main flow. This means that the resistance in two loops should be adjusted according to Equation (21) once an expected extraction ratio is selected. To make this work become easier, a main throttle device and a smaller throttle device are installed in main loop and bypass loop respectively. These two devices produce the major pressure loss in the corresponding loop, and Equation (21) can be met by merely adjusting these two throttle devices. In this case the pressure loss due to friction and other local resistances can be neglected, Equation (21) Where ξ 3 and ξ 2 are the two-phase resistance factors of throttle devices in the bypass loop and main loop respectively. If both throttle devices belong to the same type (orifice or nozzle) then the value ofξ 3 /ξ 2 will only depend on the size of these two devices. It will be verified by experiments.
The distributor and measurement system (bypass flow loop) were vertically installed in the left leg of an inverted U-shape pipe, as show in Fig.12. The inner diameter of the pipe was 50 mm, and made from Plexiglas pipe for flow pattern observation purpose. The separator was a cyclone type with an inner diameter of 60 mm. And there was a layer of stainless steel mesh on the top of cyclone cylinder to further remove the small water particle mixed with the gas. The gas flowmeter in the bypass loop was a thermal mass flowmeter (Proline t-mass 65F) with an inner diameter of 15 mm, made by E+H instrument company. and with a measurement accuracy of ±1%. The liquid flow rate was measured with a YOKOGAWA electromagnetic flow meter (ADMAG AE) with an inside diameter of 5 mm and an accuracy of ±0.5% FS.
The two phase flow experimental loop is shown in Fig.13. There were 100 pipe diameters length of straight pipe section upstream of the test section. Air and tap water were used as the working fluids in the experiments. The total air flow rate was metered using a YOKOGAWA vortex flow meter (YF102) with a accuracy of ±1% FS. The total water flow rate was measured with two orifice flow meters with a accuracy of ±1% FS, for lower flow rates and higher flow rates respectively. Since the flow patterns in the inverted U tube were always under an unsteady condition and very difficult to define, we observed the flow regimes at the entrance of inverted U tube i.e. at the horizontal line. The flow pattern occurring during the experiments included stratified flow, stratified wave, slug flow and annular flow. Though the flow pattern observed in horizontal line were not exactly the flow regime in the inverted U tube before the distributor, it could reflect the effect of flow patterns on the measurement.  The electronic signals from instruments and transducers were connected to NI6023E data acquisition system and recorded by a computer. The acquisition frequency was 1kHz and the recording length was 120s. The average values were calculated after the recording. After that the air and water flowrates of total flow and bypass flow were able to be determined, and the real extraction ratio could also be calculated according to Equation (5) and (6). The uncertainty of extraction ratio was less than 1.4% according to the error theory (Taylor, 1982).
For the passive distributor of Fig.10, the wheel was driven by the two-phase flow, and the rotation speed was counted by a high speed video camera recording through the transparent cover of the distributor. Experiments showed that the rotation speed of the wheel was approximately proportional to the velocity of the two-phase mixture. The range of rotation speed of the wheel was 400 to 2000 r/min (T=0.15～0.03 s ) with the gas superficial velocity ranged from 8 m/s -22m/s, and the liquid superficial velocity ranged 55 from 0.02-0.2m/s. The wheel was not able to rotate steadily when the gas superficial velocity was below 7 m/s at the same time the flow pattern transforms to stratified flow and slug flow. The flow patterns appeared in this experiment was mainly annular flow. The maximum pressure loss of the distributor was less than 10kpa.
For the active distributor of Fig.11, the wheel was driven by a motor, and the rotation speed was controlled by adjusting the electrical current to the motor. The speed range was 100-700 r/min. The gas superficial velocity range was 1.5 m/s -8m/s, and the liquid superficial velocity was in the range of 0.02～0.45m/s. The flow patterns occurred in the experiment included stratified flow, slug flow and stratified wave. The maximum pressure loss of the distributor was less than 6kpa.
For the passive distributor of Fig.10, the theoretical value of extraction ratio was 0.05, hence the size of the throttle devices in the bypass loop and main loop should be determined by this value according to Equation (22). Both devices selected were orifice plates. In order to determine their size, we first set the diameter of main loop orifice to 20 mm, then determined the diameter of bypass loop orifice by a tentative method. As the diameter equaled to 4.1 mm, experimental data showed that Equation (22) was met, i.e. the real extraction ratio was nearly equal to 0.05 as shown in Fig.14. Where K L and K G are the liquid and gas extraction ratios determined by experiments, U SL is the superficial liquid velocity and U SG is the superficial gas velocity. It can be seen that K G and K L are very close to the theoretical value of 0.05 and independent of liquid and gas superficial velocity. The average value of K G was 0.0506, and the standard deviation was 0.00079; the average value of K L was 0.0498, and the standard deviation was 0.00166. The maximum difference between K G and the theoretical value was less than 4%, and the maximum difference between K L and the theoretical value was less than 6%.
For the active distributor of Fig.11, the theoretical value of extraction ratio was 0.0556, we determined the size of orifices with the same method mentioned above. The diameter of main loop orifice was 25 mm, and the diameter of sample loop orifice was 5 mm. the real extraction ratios are shown in Fig.15. It can be seen that when U SL is lager than about 0.1 m/s, K G and K L are very close to the theoretical value of 0.0556 and independent of gas and liquid superficial velocity. The average of K G was 0.0560, and the average of K L was 0.0559. But as U SL is less than about 0.1 m/s, both K G and K L will deviate below the theoretical value, and the lower the gas and liquid velocity, the smaller the K G and K L . This can be explained by the fact that as the superficial velocity of liquid and gas become lower, the dynamic pressure of the jets from the flow path of the wheel (refer to Fig.11C) will become smaller, at a certain point (critical value), the dynamic pressure is not high enough to overcome the resistance of fluid rooms to enable the jets to completely flow into the bypass flow header, and some fluid will preferentially flow back to the main flow loop. Fig.16 shows that this critical value is 400 Pa, and it can also be seen that nearly all points fall on the same line. Based on this critical value we can determine the lowest effective working point of the distributor. Fig.17 shows the effect of rotation speed on the extraction ratios. It can be seen that K G is not affected by the rotation speed, but K L increases with the rotation speed as U SL is less than about 0.1 m/s, due to centrifugal force.   Fig.11. In the experiments the most frequently occurred flow pattern was slug flow which is the most unsteady flow, from Fig.18 we can see that both K G and K L are very close to the theoretical value for all slug flow and some stratified wave data, however, K G and K L will drift below the theoretical value as the pattern is stratified flow and for partial stratified wave data. The reason is that in these two patterns both the gas and liquid superficial velocity are lower as compared with other patterns, the jet's dynamic pressure in the wheel is below the critical value of 400 Pa, so some fluids which should flow to bypass loop flow to the main loop. Therefore we can say that it is the jet's dynamic pressure or fluid velocities that affects the K G and K L .  Fig.14 and Fig.15 we have observed that both K G and K L are very close to the theoretical values, i.e. gas and liquid were drawn with the same proportion, so we certainly can expect that the bypass fluid will have the same components as the total flow, and this assumption was proved by the experiments. Comparisons of the gas quality of sample flow with that of total flow show that the gas quality of sample flow is very close to that of total flow in the experiments, the maximum difference between them is less than 1.3%. This demonstrates that the bypass fluid is an excellent representative of the total flow.
The calibrated values of K G and K L which are constants and independent of flowrates can be used to determine the total liquid and gas flow rates M 1L and M 1G according to Equation (5) and (6) after the bypass flow rate M 3L and M 3G have been metered. Fig.19 and Fig.20 present the measurement error of total gas and liquid flowrate of two-phase flow respectively. It can be seen that the total flow rates measurements error is less than ±5%，and the large errors occurred at low flowrates. Therefore we can conclude that this method is reliable.

Static distributor for high pressure steam-water two-phase flow
In high pressure steam-water flow condition, it is more suitable to use a static distributor that does not contain any moving parts. A distributor used in this study is shown in A-A section view of Fig.21 (Wang et al, 2011). 1. main pipe; 2,10.division holes; 3.collection ring; 4.separator; 5.steam meter; 6.water meter; 7.throttle device; 8.main loop throttle device; 9.pipe wall;11.the wall of collection ring;12.water film;13.water droplet;14.steam bubble The static distributor consists of 6 small division holes that are evenly spaced around the circumference of the main pipe and a collection ring surrounding the pipe wall. The inside diameter of the main pipe was 50 mm, and the thickness of the pipe wall was 3 mm. The inner diameter of the collection ring was 70 mm, and the diameter of the division hole was 3.5 mm. The separator is a cyclone type with inner diameter of 42 mm. Both the steam meter and water meter were venturi tubes with throat diameter of 7.4 mm and 4.4 mm respectively. The throttle device was a thick orifice plate with diameter of 3.5 mm. The restriction in main loop was a nozzle with diameter of 28 mm.
To be equivalent to equation (5) and (6), the total steam and water flow rates are determined by the following equations ss s s Where, M s is the total steam flow rate; M w is the total water flow rate; M ss is the bypass steam flow rate metered by steam meter; M sw is the bypass water flow rate metered by water meter; K s is the steam extraction ratio; K w is the water extraction ratio. Referring to Fig.21, we can also see that the fluid flowing to the division (bypass) loop comes from a region near the wall where the water proportion is higher, and therefore more water will enter the division loop, i.e. K w will be larger than K s , and it is beneficial to the measurement of water flow rate in the condition of flow with high steam volume fraction.
Equation (23) and (24) are only the definition of extraction ratios, the real values of K s and K w are dependent on the resistance relation between the division (bypass) loop and the main loop, and also on the distribution characteristic of the division loop. From Fig.21 we can see that the division (bypass) loop and the main loop have a common inlet and a common outlet, i.e. they are in parallel. In accordance with the nature of parallel loops (Munson, 2002), the pressure losses of both loops are equal Where,ΔP m is the pressure loss in the main loop;ΔP s is the pressure loss in the division (bypass) loop.
ΔP m andΔP s can be calculated based on the separated flow model (Lin, 1982) Where,ΔP ms andΔP mw are the pressure losses when steam phase and water phase flows in the main loop alone respectively;ΔP ss andΔP sw are the pressure losses when steam phase and water phase flows in the division loop alone respectively; θ is the correction factor which depends on the pressure (Lin, 1982).
In accordance with the single phase flow pressure loss calculation method (Munson, 2002 Where, λis the Darcy friction factor, l is the tube length, d is the tube inner diameter, ξ is the local loss factor, ρ w is the density of water, ρ s is the density of steam, M is the mass flowrate, A is the tube cross section area, the symbol Σ represents summation; subscript "m" represents the main loop and the subscript "s" represents the division loop. Let X m be the steam quality of the main loop, X s be the steam quality of division loop, and neglect the little difference between θ m and θ s i.e. θ m =θ s =θ, then substituting equations (23)- (24) and (26) Equation (34) is known as the resistance equilibrium equation because it is derived from the resistance relation, however, it alone cannot yet determine the values of K s and K w , therefore another additional equation must be developed, and equation (34) is the first equation for extraction ratios. Define K m as the mass extraction ratio ss sw m ss sw For a given structure of the main loop and the division loop, K m is usually a constant in the case of single phase flow, however in the condition of two phase flow, K m may vary with the flow rate and steam quality, therefore the value of K m /K 0 is the function of flow rate and steam quality The function F(M,X S ) reflects the distribution characteristic of division loop, and can only be determined by experiments.
Experiments were carried out in an once-through boiler for steam flooding in Keramay oilfield, Xinjiang China. Fig.22 is the schematic representation of the experimental systems. The experimental setup was horizontally installed at the test section. The length of the straight horizontal pipe between the sampler separator and test section was 3 meters, and the length of division steam pipe was 0.68 meters. All the pipe and test section were properly insulated with mineral fiber. The heat loss rate in the main pipe and division loop, based on a heat transfer calculation, were less than 0.15kw/m and 76w respectively, and the steam condensation due to heat loss were less than 0.41kg/(m‧h) and 0.13kg/h respectively, both were insignificant compared to the steam flow in the pipe.
The flow rate to the once-through boiler was adjusted by changing the rotation speed of the piston pump with a frequency converter, and metered by a calibrated orifice flow meter at the entrance of the boiler which has an accuracy of 1.3%. In accordance with the nature of once-through boiler, the flowrate throughout the boiler must keep a constant in the condition of steady state, because in the steady state the amounts of fluids (water and steam) within the boiler have reached their stable values, no additional fluid will accumulate or be removed from the boiler, i.e. the input must equal to the output. So the flowrate passing through the test section can be measured by the orifice flow meter at the entrance of the boiler under steady state.

Fig. 22. Schematic representation of the experimental setup
The output steam quality of the boiler was carefully controlled by adjusting the flow rate of natural gas entering the furnace. The value of steam quality at the boiler output was determined based on the fact that the salts dissolved in the softened water (Na 2 SO 4 , Na 2 SiO 3 , et al.) still remain in water after the evaporation process in boiler, hence, according the salts conservation, we can write down the following equations Where，S i is the salts concentration of softened water at the input of the boiler; S o is the salts concentration of condensed water at the output of the boiler, i.e. at the sampler separator. The sampler separator of Fig.22 is a small vessel connected to the steam pipe which is used to collect some water from the steam-water flow by gravitational effect, but not designed to separate the whole steam-water flow. A very small amount of water(less than 8kg/h) is drained from the sampler separator and then cooled by cooling water, this is the sampler of condensed water.It should be noted that equation (38) and equation (39) are correct only in the condition of steady state of the boiler operation. Due to this reason we had to wait for 2-3 hours after an adjustment of boiler parameters (flowrate or quality) to ensure that a steady state had been reached before the measurements of flowrate and steam quality were able to be taken.
Equation (39) is not convenient to use because it is not an easy task to measure the salts concentration directly in oilfield. The salts concentration measurements are usually replaced by that of electrical conductivity in oilfield based on the principle that in the case of low salts concentration (far below their solubility), the molar conductivity (the conductivity per unit of concentration) tends to be a constant (Aguado, 2006), hence the conductivity of water is proportional to the salts concentration, so Equation (39) can become as Where, C i is the softened water conductivity at the input of the boiler; C o is the condensed water conductivity at the output of the boiler, i.e. at the sampler separator.

Fig. 23. Experimental range
Equation (40) has been successfully used to measure steam quality in oilfield for many years.
During the experiments,both C i and C o were measured by a portable conductivity meter with an accuracy of 0.5%, according to error theory, the error of steam quality from Equation (40) is 0.6%. For the sake of boiler safety, the lowest steam quality allowed was 0.60, and the highest steam quality allowed was 0.82 and this range of steam quality is enough to cover the quality usually encountered in oilfield. The flow rate range was 2000kg/h to 8000kg/h, and pressure range was 7.6MPa to 16MPa. Fig.23 showed the experiments range in the Mandhane map (Collier,1981), where V s represents the superficial steam velocity, and V w the superficial water velocity. From Fig.22 we can see that the experiment points were mainly located on the borders of slug flow, annular flow and wavy flow which are the most frequently occurring regimes in the steam pipe line for the steam flooding and other industries.
The static pressure of the test section was measured by a Rosemount 3051 pressure transmitter, and both the steam venturi tube and water venture tube differential pressures in the division loop was measured by a Rosemount 3051 differential pressure transmitter respectively. These three transmitters' signals were connected to an industrial computer which automatically converts the signals to numerical data and calculate the bypass steam and water flow rates.
Before the normal two phase flow experiments, a single phase water flow experiment was conducted to determine the value of K 0 (the extraction ratio in single phase case), the result was K 0 =0.01350. During the two phase experiments, the pressure and bypass steam and water flow rates were automatically recorded by the computer, and the extraction ratios was able to be calculated according to equation (23) and (24) once the flow rate of the boiler and the steam quality were measured. The results of extraction ratios is shown in Fig. 24, where the horizontal axis represents the right term of equation (34), and the vertical axis represents the left term of equation (34). From Fig.24 it can be seen that a liner relationship exists between the ordinate and the abscissa, and all the experimental points fall on the same line, it means that the equation (34) is correct and independent of flow rate. From these data we can also obtain the value of θ=1.6259. showed the relationship between the mass extraction ratio K m and steam quality of bypass loop X s for various mass flow rates. It can be seen that a simple linear relation exists between them, and all the experimental data fall on the same line, this means that flow rate M has little effect on the F(M,X s ). From these data the actual form of F(M,X s ) in equation (37) can be determined Equation (42) is the second equation of extraction ratios and is called the distribution equation because it reflects the distribution nature of bypass loop.
The extraction ratios K s and K w can now be determined by solving equation (34) and (42), and then the total steam and water flow rate M s and M w ( or the total flow rate M and quality X) can be measured once the bypass steam and water flow rate M ss and M sw are metered, these works are automatically done by the computer which is connected to the pressure and different pressure transmitters. Table 1 give some measurement results, where the reference flowrates represent values metered by the orifice flowmeter at the entrance of the boiler, the reference mass quality is obtained by conductivity method. From Table 1 it can be seen that the maximum error of flow rate measurements is less than ±2.5%, and the maximum error of quality measurements is less than ±3.5%. The water extraction ratio K w is 3~5 times more than steam extraction ratio K s .

Conclusion
Flow division techniques have been widely used in single phase flow measurements, whose main feature is to utilize a small size meter to measure a large volume flow in large lines. In addition to this, a bypass flow meter usually has a much wider metering range, a better precision and a lower price. Further more, when we apply this technique in two-phase flow, an even more important advantage will appear: a small size separator can be used in the bypass loop to separate the two-phase mixture and consequently measuring them by conventional single phase meters, thus the problem of two-phase flow rate measurement can simply be solved. However a special distributor must be employed to ensure that the bypass flow will have the same components as the total flow and be proportional to the total flow. Three different kinds of distributors have been studied in this chapter.
The rotational drum is a flow driven distributor whose extraction ratio is equal to the ratio of extraction channel number to the total flow channel number and independent of flow patterns. The gap size between the drum and the shell has a significant effect on the real extraction ratios. When the gap size is equal to 0.25 mm, a much stable extraction ratio can be obtained. The measurements error of total flow is less than +5.6%. Experiments also showed that the drum rotation speed has no effect on the measurement.

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The wheel-fluid rooms distributor is much simpler in structure. The wheel can be driven either by the flow or by a motor and the rotation speed has no effect on the measurements. The extraction ratio can be as low as 0.05 (and 0.0556) and depends only on the ratio of bypass fluid room number to the total fluid room number. The superficial gas velocity can be as low as 1.5 m/s, and the measurement error of total flow rate is within ±5% in the above experimental ranges.
The static distributor was specially designed for the high pressure steam-water two-phase flow measurements where any moving parts in the apparatus may reduce the reliability of the meter. Although the static distributor can not keep the extraction ratio as a constant as the rotational drum or the wheel-fluid rooms distributor does, two independent equations about the extraction ratios have been derived from the resistance equilibrium relation between the main loop and bypass loop, and the distribution function respectively. Thus the extraction ratios can be determined by solving these two equations. The extraction ratios were as small as 0.007-0.05 which is very important to the development of high pressure two-phase flow meter. The experiment points were mainly located on the borders of slug flow, annular flow and wavy flow in the Mandhane map. The error of flow rate measurements is less than ±2.5%, and the error of quality measurements is less than ±3.5%.