Abstract:
Oil field management systems and methods for managing operation of one or more wells producing a high void fraction multiphase flow. The system includes a differential pressure flow meter which samples pressure readings at various points of interest throughout the system and uses pressure differentials derived from the pressure readings to determine gas and liquid phase mass flow rates of the high void fraction multiphase flow. One or both of the gas and liquid phase mass flow rates are then compared with predetermined criteria. In the event such mass flow rates satisfy the predetermined criteria, a well control system implements a correlating adjustment action respecting the multiphase flow. In this way, various parameters regarding the high void fraction multiphase flow are used as control inputs to the well control system and thus facilitate management of well operations.

Description:
RELATED APPLICATIONS 
     This application is a continuation of U.S. patent application Ser. No. 09/401,375, entitled IMPROVED METHOD AND SYSTEM FOR MEASURING MULTIPHASE FLOW USING MULTIPLE PRESSURE DIFFERENTIALS (which is a continuation-in-part of U.S. patent application Ser. No. 08/937,120 filed Sep. 24, 1997, now abandoned), filed Sep. 22, 1999, and incorporated herein in its entirety by this reference. 
    
    
     CONTRACTUAL ORIGIN OF THE INVENTION 
     This invention was made with United States Government support under Contract No. DE-AC07 94ID13223, now Contract No. DE-AC07-99ID13727 awarded by the United States Department of Energy. The United States Government has certain rights in the invention. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a flow meter for measuring the flow of very high void fraction multi-phase fluid streams. More particularly, the present invention relates to an apparatus and method in which multiple pressure differentials are used to determine flow rates of gas and liquid phases of a predominantly gas fluid stream to thereby determine the mass flow rate of each phase. 
     2. State of the Art 
     There are many situations where it is desirable to monitor multi-phase fluid streams prior to separation. For example, in oil well or gas well management, it is important to know the relative quantities of gas and liquid in a multi-phase fluid stream, to thereby enable determination of the amount of gas, etc. actually obtained. This is of critical importance in situations, such as off-shore drilling, in which it is common for the production lines of several different companies to be tied into a common distribution line to carry the fuel back to shore. While a common method for metering a gas is to separate out the liquid phase, such a system in not desirable for fiscal reasons. When multiple production lines feed into a common distribution line, it is important to know the flow rates from each production line to thereby provide an accurate accounting for the production facilities. 
     In recent years, the metering of multi-phase fluid streams prior to separation has achieved increased attention. Significant progress has been made in the metering of multi-phase fluids by first homogenizing the flow in a mixer then metering the pseudo single phase fluid in a venturi in concert with a gamma densitometer or similar device. This approach relies on the successful creation of a homogenous mixture with equal phase velocities, which behaves as if it were a single phase fluid with mixture density {overscore (ρ)}=αρ g +(1−α)ρ l  where α is the volume fraction of the gas phase, and ρ g  is the gas phase density and ρ 1  is the liquid phase density. This technique works well for flows which after homogenizing the continuous phase is a liquid phase. While the upper limit of applicability of this approach is ill defined, it is generally agreed that for void fractions greater than about ninety to ninety-five percent (90-95%) a homogenous mixture is difficult to create or sustain. The characteristic undisturbed flow regime in this void fraction range is that of an annular or ring shaped flow configuration. The gas phase flows in the center of the channel and the liquid phase adheres to and travels along the sidewall of the conduit as a thick film. Depending on the relative flow rates of each phase, significant amounts of the denser phase may also become entrained in the gas phase and be conveyed as dispersed droplets. Nonetheless, a liquid film is always present on the wall of the conduit. While the liquid generally occupies less than five percent (5%) of the cross-sectional volume of the flow channel, the mass flow rate of the liquid may be comparable to or even several times greater than that of the gas phase due to its greater density. 
     The fact that the phases are partially or fully separated, and consequently have phase velocities which are significantly different (slip), complicates the metering problem. The presence of the liquid phase distorts the gas mass flow rate measurements and causes conventional meters, such as orifice plates or venturi meters, to overestimate the flow rate of the gas phase. For example the gas mass flow can be estimated using the standard equation                m   g     =         A                   C   c        Y         1   -     β   4                  2        ρ   g        Δ                 P                 [   7   ]                                
     where m g  is the gas mass flow rate, A is the area of the throat, ΔP is the measured pressure differential, ρ g  the gas density at flow conditions, C c  the discharge coefficient, and Y is the expansion factor. In test samples using void fractions ranging from 0.997 to 0.95, the error in the measured gas mass flow rate ranges from 7% to 30%. It is important to note that the presence of the liquid phase increases the pressure drop in the venturi and results in over-predicting the true gas mass flow rate. The pressure drop is caused by the interaction between the gas and liquid phases. Liquid droplet acceleration by the gas, irreversible drag force work done by the gas phase in accelerating the liquid film and wall losses determine the magnitude of the observed pressure drop. In addition, the flow is complicated by the continuous entrainment of liquid into the gas, the redeposition of liquid from the gas into the liquid film along the venturi length, and also by the presence of surface waves on the surface of the annular or ringed liquid phase film. The surface waves on the liquid create a roughened surface over which the gas must flow increasing the momentum loss due to the addition of drag at the liquid/gas interface. 
     Other simple solutions have been proposed to solve the overestimation of gas mass flow rate under multi-phase conditions. For example, Murdock, ignores any interaction (momentum exchange) between the gas and liquid phases and proposed to calculate the gas mass flow if the ratio of gas to liquid mass flow is known in advance. See Murdock, J. W. (1962). Two Phase Flow Measurement with Orifices, ASME Journal of Basic Engineering, December, 419-433. Unfortunately this method still has up to a 20% error rate or more. 
     While past attempts at metering multi-phase fluid streams have produced acceptable results below the ninety to ninety five percent (90-95%) void fraction range, they have not provided satisfactory metering for the very high void multi-phase flows which have less than five to ten (5-10%) non-gas phase by volume. When discussing large amounts of natural gas or other fuel, even a few percent difference in the amount of non-gas phase can mean substantial differences in the value of a production facility. For example, if there are two wells which produce equal amounts of natural gas per day. The first well produces, by volume, 1% liquid and the second well produces 5% liquid. If a conventional mass flow rate meter is relied upon to determine the amount of gas produced, the second well will erroneously appear to produce as much as 20-30% more gas than the first well. Suppose further that the liquid produced is a light hydrocarbon liquid (e.g. a gas condensate such as butane or propane) which is valuable in addition to the natural gas produced. Conventional meters will provide no information about the amount of liquid produced. Then if the amount of liquid produced is equally divided between the two wells, the value of the production from the first well will be overestimated while the production from the second well will be underestimated. To properly value the gas and liquid production from both wells, a method of more accurately determining the mass flow rate of both the gas and liquid phases is required. 
     The prior art, however, has been generally incapable of accurately metering the very high void multi-phase fluid streams. In light of the problems of the prior art, there is a need for an apparatus and method that is less complex and provides increased accuracy for very high void multi-phase fluid streams. Such an apparatus and method should be physically rugged, simple to use, and less expensive than current technology. 
     SUMMARY OF THE INVENTION 
     It is an object of the present invention to provide an improved apparatus and method for metering very high void multi-phase fluid streams. 
     It is another object of the present invention to provide an apparatus and method which increases the accuracy of metering with respect to both the gas phase and the liquid phase when measuring very high void multi-phase fluid streams. 
     It is still another object of the present invention to provide such an apparatus and method which does not require homogenization or separation of the multi-phase fluid in order to determine flow rate for each of the phases. 
     The above and other objects of the invention are realized in a specific method for metering the phases of a multiple phase fluid. The flow meter includes a cross-sectional area change in the flow conduit such as a venturi with an elongate passage. Disposed along the elongate passage is a converging section, an extended throat section, and a diffuser. The flow meter also includes a plurality of pressure monitoring sites which are used to monitor pressure changes which occur as the multi-phase fluid passes through the elongate passage. These pressure changes, in turn, can be processed to provide information as to the respective flow rates of the phases of the multi-phase fluid. By determining the flow rates of the components of the multi-phase fluid, the amount of natural gas, etc., can be accurately determined and accounting improved. 
     In accordance with another aspect of the present invention a method for determining the mass flow of the high void fraction fluid flow and the gas flow includes a number of steps. The first step is calculating a gas density for the gas flow. The next two steps are finding the normalized gas mass flow rate through the venturi and then computing the actual gas mass flow rate. The following step is estimating the gas velocity in the venturi tube throat. The next step is calculating the additional pressure drop experienced by the gas phase due to work performed by the gas phase in accelerating the liquid phase between the upstream pressure measuring point and the pressure measuring point at the end of the venturi contraction or throat. Yet another step is estimating the liquid velocity in the venturi throat using the calculated pressure drop experienced by the gas-phase due to work performed by the gas phase. Then, the friction loss is computed between the liquid phase and the conduit wall in the venturi tube using the liquid velocity. Finally, the total mass flow rate based on measured pressure in the venturi throat is calculated, and the liquid mass flow rate is calculated by subtracting the total mass flow rate and the gas mass flow rate. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The above and other objects, features and advantages of the invention will become apparent from a consideration of the following detailed description presented in connection with the accompanying drawings in which: 
     FIG. 1 shows a side, cross-sectional view of a differential pressure flow meter with pressure measuring ports; 
     FIG. 2 is a flow chart showing the steps required to calculate the mass flow in a multiphase flow; 
     FIGS. 3-7 illustrate further operating steps according to the present invention; and 
     FIG. 8 schematically depicts additional equipment having utility for measuring or processing multiphase flow according to the present invention. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Reference will now be made to the drawings in which the various elements of the present invention will be given numeral designations and in which the invention will be discussed so as to enable one skilled in the art to make and use the invention. It is to be understood that the following description is only exemplary of the principles of the present invention, and should not be viewed as narrowing the pending claims. 
     Turning now to FIG. 1, there is shown another differential pressure flow meter, generally indicated at  110 . The differential pressure flow meter  110  includes a venturi  114  formed by a sidewall  118  which defines a fluid flow passage  122 . The fluid flow passage  122  is segmented into an inlet section  126 , a converging section  130 , an extended throat section  134 , a diffuser section  138  and an outlet section  140 . 
     The geometry and conduit diameter of the flow obstruction will vary depending on the particular application. The conduit may be larger or smaller depending on the specific flow rate, pressure, temperature and other similar factors. One important characteristic of the flow meter is that the preferred contraction ratio in the conduit should be between 0.4 and 0.75. The contraction ratio is defined as the ratio of the throat diameter  134  to the upstream conduit diameter  122 . It is also important that the length of the throat is at least ten times the diameter of the throat. Of course, other throat lengths may be used. 
     An example of one possible set of conduit measurements will now be given, but it should be realized that the actual geometry will depend on the volume and size of the specific application. In one embodiment of the invention, the inlet section  126  has a diameter of about 3.8 cm adjacent the opening  142  at the upstream, proximal end  114   a  of the venturi  114 . The converging section  130  tapers inwardly from the inlet section  126  at an angle of about ten degrees (10°) until it connects with the extended throat section  134 , which has a diameter of about 2.5 cm. The extended throat section  134  remains substantially the same diameter throughout its length and may be about 30 cm long to provide ample length to determine acceleration differences between the various phases. At the end of the extended throat section  134   b , the diffuser section  138  tapers outwardly at an angle of about three degrees (3°) until the diameter of the outlet section passage  140  is substantially the same as that at the inlet section  126  (i.e. 3 cm). It should be realized that many other specific geometric configurations could be defined which have characteristics similar to the example above. 
     In order to monitor the pressure differentials caused by the changes in fluid velocity, the differential pressure flow meter shown in FIG. 1 utilizes up to four different measurement points. Each pair of pressure measurement points defines a pressure differential. Only two pressure differential measurements are required to determine the gas and liquid flow rates. The preferred pressure differentials are ΔP 3  and ΔP 2 . Pressure differential number three (ΔP 3 ) is defined as the pressure change between points  150  and  154 . Pressure differential number two (ΔP 2 ) is between points  154  and  158 . It should also be apparent based on this disclosure, that pressure differentials ΔP 3  and ΔP 0  or ΔP 2  and ΔP 0  may be used instead. Each of these combinations work equally well, with the exception that the numerical constants in the algorithm change. It is also important that an absolute pressure and temperature measurement will be provided at the venturi inlet  142 . 
     Now the pressure ports will be described more specifically. A first pressure measuring port  150  is disposed to measure the pressure in the inlet section  142 . The first pressure measuring port  150  is connected to a pressure monitoring means, such as a pressure transducer  151 , to provide a pressure reading. 
     A second pressure measuring port  154  is provided at the entrance of the extended throat section  134 . The second pressure measuring port  154  is disposed adjacent the upstream, proximal end  134   a  of the extended throat section  134 . A pressure transducer  151  is also coupled to the second pressure measuring port  154 . 
     Distally from the second pressure measuring port  154 , but still within the extended throat section  134 , is a third pressure monitoring port  158 . Preferably, the third pressure monitoring port  158  is disposed adjacent the distal end  134   b  of the extended throat section  134 , and adjacent the beginning  138   a  of the diffuser section  138 . 
     The respective pressure measuring ports  150 ,  154 , and  158  are disposed in communication with a flow processor  153  or similar mechanism through the pressure monitoring means or pressure transducers  151 ,  155 , and  159 . The flow processor  153  enables the acquisition of the measured pressure differentials, and thus fluid flow rates in accordance with the present invention. Further, an accurate determination of the relative acceleration of the two phases can also be obtained by comparing the pressure drop between the inlet section  126  (through measuring port  150 ) and the distal end  134   b  of the extended throat section  134  (through measuring port  158 ), as indicated at ΔP 0 . 
     In an alternative embodiment of the invention, a fourth pressure measuring port  161  is disposed at the end of the extended throat  134   b . A fifth pressure measuring port  162  is disposed in the outlet section  140  adjacent to the distal end  138   b  of the diffuser section  138 . Both of these pressure measuring ports are coupled to pressure monitoring means or pressure transducer  163 . The fourth and fifth monitoring ports allow a pressure differential ΔP 1  to be measured. The pressure differential (ΔP 1 ) between the extended throat section  134  and the distal end  138   b  of the diffuser section  138  can also be analyzed. 
     It should also be realized that different angles and lengths can be used for the venturi constriction and the extended throat of the venturi tube. In fact, the converging section of the venturi is not required to gradually taper. Rather the converging section can be formed by an annular shoulder to reduce the cross-sectional area of the inlet section. The preferred size of the radius of curvature for an annular shoulder is about 0.652 cm. The converging section can also be formed by placing a solid object in the conduit which occupies part but not all of the conduit cross-section. 
     It is vital that the correct method be used in the current invention to estimate the gas and fluid mass flow. Otherwise errors in the range of 20% or more will be introduced into the measurements, as in the prior art. Reliable metering of high void fraction multi-phase flows over a wide range of conditions (liquid loading, pressure, temperature, and gas and liquid composition) without prior knowledge of the liquid and gas mass flow rates requires a different approach than the simple modification of the single phase meter readings as done in the prior art. Conceptually, the method of metering a fluid flow described here is to impose an acceleration or pressure drop on the flow field via a structure or venturi constriction and then observe the pressure response of the device across two pressure differentials as described above. Because the multi-phase pressure response differs significantly from that of a single-phase fluid, the measured pressure differentials are a unique function of the mass flow rates of each phase. 
     As described above, the gas and liquid phases are strongly coupled. When the gas phase accelerates in the converging section of the nozzle, the denser liquid phase velocity appreciably lags that of the lighter gas phase. In the extended throat region, the liquid phase continues to accelerate, ultimately approaching its equilibrium velocity with respect to the gas phase. Even at equilibrium, significant velocity differences or slip will exist between the gas and liquid phases. 
     A method for accurately calculating the gas and liquid mass flows in an extended venturi tube will now be described. (A derivation of the method is shown later.) This method uses the four values which are determined though testing. These values are: ΔP 3  which is the measured pressure differential across the venturi contraction, ΔP 2  which is the measured pressure differential across the extended venturi throat, P which is the absolute pressure upstream from the venturi (psi), and T which is the temperature of the upstream flow. These measured values are used with a number of predefined constants which will be defined as they are used. Alternatively, the pressure differentials ΔP 3  and ΔP 0,  or the pressure differentials ΔP 0  and ΔP 2  may be used. 
     First, the gas density for the gas flow must be calculated based on the current gas well pressure and temperature. This is done using the following equation which uses English units. Any other consistent set of units may also be used with appropriate modifications to the equations.                rho   gw     =         rho   g          (       P   +   14.7     14.7     )                       (       60   +   459.67       T   +   459.67       )               Equation  1                                
     where 
     rho g  is the density of natural gas (i.e. a mixture methane and other hydrocarbon and non-hydrocarbon gases) at standard temperature (60° F.) and pressure (1 atmosphere) for a specific well; 
     P is the pressure upstream from the venturi in pounds per square inch (psi); and 
     T is the temperature upstream from the venturi in degrees Fahrenheit. 
     The value of rho g  will be different for various natural gas compositions and must be supplied by the well operator. At the standard temperature (60° F.) and pressure (1 atmosphere) the value of rho g  for pure methane is 0.044 lb/ft 3 . 
     The second step is finding a normalized gas mass flow rate based on the square root of a pressure difference across the contraction multiplied by a first predetermined coefficient, and the square root of a measured pressure differential across a venturi throat. The normalized gas mass flow rate is found using the following equation: 
     
       
           mgm=A+B{square root over (ΔP 3 )}+   C{square root over (ΔP 2 )}   Equation 2 
       
     
     where 
     A, B, and C are experimentally determined constants required to calculate gas mass flow rate; 
     ΔP 3  is the measured pressure differential across a venturi contraction; and 
     ΔP 2  is the measured pressure differential across a venturi throat. The preferred values for the constants in the equation above are as follows: A is −0.0018104, B is 0.008104 and C is −0.0026832 when pressure is in pounds per square inch (psi), density in lbs/ft 3  and mass flow rate in thousands of mass lbs/minute. Of course, these numbers are determined experimentally and may change depending on the geometry of the venturi, the fluids used, and the system of units used. 
     Calculating the normalized gas mass flow rate is important because it allows the meter to be applied to the wells or situations where the pressure or meter diameter for the liquids present are different than the conditions under which the meter was originally calibrated. This means that the meter does not need to be calibrated under conditions identical to those present in a particular application and that the meter may be sized to match the production rate from a particular well. 
     The functional form of Equation 2 is arrived at by derivation from the conservation of mass and energy followed by a simplifying approximation. Other functional forms of Equation 2 can be used with equivalent results. The functional form of Equation 2 is consistent with the conservation laws and provides a good representation of the calibration data. 
     The third step is computing a gas mass flow rate using the normalized gas mass flow rate, the gas density, and a contraction ratio of the venturi tube. The equation for calculating the gas mass flow rate from these quantities is              mg   =     mgm   ·     A   t     ·         rho   gw           1   -     β   4                     Equation  3                                
     where 
     mgm is the normalized gas mass flow rate; 
     A t  is the venturi throat area; 
     β is the contraction ratio of the throat area; and 
     rho gw  is the gas density at current well conditions. 
     The fourth step is estimating the gas velocity in the venturi tube throat. The equation for estimating the gas velocity is:                u   g     =       m   g         rho   g     ·     A   t                 Equation  4                                
     where 
     m g  is the gas mass flow rate; 
     rho g  is the density of the gas phase for a specific well; and 
     A t  is the venturi throat area. 
     The fifth step is calculating the pressure drop experienced by the gas phase due to work performed by the gas phase in accelerating the liquid phase between an upstream pressure measuring point and a pressure measuring point in the distal end of the venturi throat. The pressure drop is calculated as follows:                Δ                   P   gl3       =       Δ                   P   3       -       1   2     ·     rho   gw     ·     u   g   2     ·     (     1   -     β   4       )                 Equation  5                                
     where 
     ΔP 3  is the measured pressure differential across a venturi contraction; 
     rho gw  is gas density at well conditions; 
     u g  is the gas velocity in the venturi throat; and 
     β is the contraction ratio of the throat area to the upstream area. 
     It is important to note that the calculations outlined in steps two and five are important because they allow for estimating the mass flow of each phase. 
     Step six is estimating the liquid velocity (u 1 ) in the venturi throat using the calculated pressure drop experienced by the gas phase due to work performed by the gas phase. This is performed as follows                u   l     =         2        (       Δ                   P   3       -     Δ                   P   gl3         )           rho   l     ·     [       (     1   +     β   4       )     +   gcfw     ]                   Equation  6                                
     where 
     ΔP 3  is the measured pressure differential across a venturi contraction; 
     ΔP gl3  is the pressure drop experienced by the gas-phase due to work performed by the gas phase on the liquid phase; 
     rho 1  is the liquid density; and 
     gcfw is a constant which characterizes wall friction. The preferred value for gcfw is defined as 0.062. This value may be adjusted depending on different venturi geometries or different fluids. 
     The seventh step is computing the friction between the liquid phase and a wall in the venturi which is performed:              f   =     gcfw   ·     1   2     ·     rho   l     ·     u   l   2               Equation  7                                
     where 
     gcfw is a constant which characterizes wall friction; 
     rho 1  is the liquid density; and 
     u 1  is the liquid velocity in the venturi throat. 
     The eighth step is calculating the total mass flow rate based on the measured pressure in the venturi throat, the calculated friction and the gas velocity. The equation for this is:                m   t     =         2        (       Δ                   P   3       -   f     )           (     1   -     β   4       )     ·     u   g         ·     A   t               Equation  8                                
     where 
     ΔP 3  is the measured pressure differential across a venturi contraction; 
     β is the contraction ratio of the throat diameter to the upstream diameter; and 
     u g  is the gas velocity in the venturi throat. 
     The liquid mass flow rate can now be calculated as the difference between the total and gas mass flow rates. 
     
       
           m   l =( m   t−m   g )  Equations 9 
       
     
     wherein 
     m t  is the total mass flow rate; and 
     m g  is the gas mass flow rate. 
     Calculating the gas mass flow rate, total mass flow rate, and liquid mass flow rate using the method outlined above is much more accurate than the prior art. The accuracy of method outlined above is within ±4% for the gas phase, ±5% for the liquid phase, and ±4% for the total mass flow. This accuracy can even be increased using measured calibrations for a specific installation to benchmark the readings. 
     FIG. 2 shows a summary of the method used to accurately calculate the mass flow through the elongated venturi. The method for determining the mass flow of the high void fraction fluid flow and the gas flow includes steps which were described with Equations 1-9. Referring to FIG. 2, the first step is calculating a gas density for the gas flow  210 . The next two steps are finding a normalized gas mass flow rate through the venturi  220  and computing a gas mass flow rate  230 . The following step is estimating the gas velocity in the venturi tube throat  240 . The next step is calculating the pressure drop experienced by the gas-phase due to work performed by the gas phase in accelerating the liquid phase between the upstream pressure measuring point and the pressure measuring point in the venturi throat  250 . Yet another step is estimating the liquid velocity  260  in the venturi throat using the calculated pressure drop experienced by the gas-phase due to work performed by the gas phase. Then the friction is computed  270  between the liquid phase and a wall in the venturi tube. Finally, the total mass flow rate based on measured pressure in the venturi throat is calculated  280  and the liquid mass flow rate is determined  290 . 
     Additional aspects of the present invention may enhance the method or portions of the method as outlined in FIG.  2 . For instance, adjustments may be performed based on a measurement of a mass flow rate of a multiphase flow. FIG. 3 shows a block diagram of such a configuration where a mass flow rate measurement is used to determine whether adjustment is required with respect to the multiphase flow  310 , and causing, as required, any adjustment action indicated by a mass flow rate of at least one phase of the multiphase flow  320 . Of course, a warning may be generated based on a mass flow rate of a phase within the multiphase flow as shown in FIG. 4 in  410 . Further, as shown in FIG. 5, it is contemplated by the present invention that the mass flow rate of one or more phases in a multiphase flow may be recorded over a time period  510  as well as summed over a time period to generate the total amount of a phase passing through the system  520 . In addition, as shown in FIG. 6, a molecular weight of at least one of the phases of the multiphase flow may be determined  610 . 
     The present invention may also be used with a multiphase flow that includes a liquid water fraction as well as another liquid phase, such as an oil producing operation, as shown in FIG.  7 . FIG. 7 shows a method of the present invention including determining a liquid water fraction  710 , measuring a plurality of pressure differentials of the multiphase flow  720 , determining a liquid water phase mass flow rate based upon said liquid water fraction and said plurality of pressure differentials  730 , determining a liquid phase mass flow rate based upon said plurality of presssure differentials  740 , determining by way of a mass flow rate of at least one of the phases of the multiphase flow whether adjustment is required with respect to the multiphase flow  750 , and causing, as required, any adjustment action indicated by the mass flow rate of at least one phase of the multiphase flow  760 . 
     Other aspects of the present invention may include addition equipment for measuring or processing the multiphase flow. For instance as shown in FIG. 8, a water cut meter  820 , a separator  830 , and/or a gas chromatograph  840  may be utilized as part of the present invention. FIG. 8 shows a multiphase flow  810  passing through one or more of a water cut meter  820 , a separator  830 , and/or a gas chromatograph  840  as well as the flow meter  110  show in FIG.  1 . Further, a gamma ray attenuation densitometer  860  or ultrasonic thickness measuring apparatus  850  may be used in conjunction with the flow meter  110  as shown in FIG  8 . Of course, FIG. 8 is merely illustrative, and the water cut meter  820 , a separator  830 , and/or a gas chromatograph  840 , ultrasonic thickness measuring apparatus  850 , and gamma ray attenuation densitometer  860  may be configured in serial or parallel arrangements and may be placed prior to or subsequent to the flow meter  110  in relation to the direction of the multiphase flow  810 . 
     Theoretical Gas Mass Flow Rate 
     Now a discussion of the theoretical derivations will be outlined which produced the method described above. The theoretical derivation is based on the physical laws describing the conservation of mass and energy for both the gas and liquid phases. The conservation of mass and energy equations for each phase are shown below where the subscript  1  denotes the upstream condition measured at  142  by pressure tap  150  in FIG. 1, and the subscript  2  denotes the venturi throat entrance measured at  134   a  by pressure tap  154 . ΔP gl3  is the pressure drop experienced by the gas phase due to work done by the gas phase in accelerating the liquid phase between the pressure measuring location at the beginning of the elongated throat and the pressure measuring location at the end of the throat. It is assumed that only the liquid phase is in contact with the wall, f w  is the wall friction coefficient and G c  is a geometry factor which accounts for the acceleration of the fluid in the venturi contraction and the surface area of the contraction. 
       m   g =α 1 ρ g1   u   g1   A   1 =α 2 ρ g   u   g2   A   2   
     
       
           m   l =(1−α 1 )ρ l   u   l1   A   1 =(1−α 2 )ρ l   u   l2   A   2   Equations 10 
       
     
     
       
         
           
             
               
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                   l2 
                   2 
                 
               
             
           
         
                 
         
             
         
      
     
     In Equations 10, α is void fraction, ρ g  is density of a gas at standard temperature, u g  is the gas velocity, A 1  is the conduit area upstream of the venturi, A 2  is the conduit area in the venturi throat, and P 1  and P 2  are the pressures at locations  142  (tap  150 ) and  134   a  (tap  154 ) in the conduit. 
     The gas phase energy equation can be rewritten using the equation for the gas phase mass flow rate, where D is the diameter of the upstream piping, d is the throat diameter, β=d/D is the contraction ratio, and ΔP 3 =P 2 −P 1  is the pressure drop across the contraction.                Δ                   P   3       =         1   2                       m   g   2         ρ   g          α   2   2          A   2   2              (     1   -         (       α   2       α   1       )     2          β   4         )       +     Δ                   P   gl3                 Equation  11                                
     With the approximation that α 1  and α 2 ≅1, the modified orifice equation results.                Δ                   P   3       ≈         1   2            m   g   2         ρ   g          A   2              (     1   -     β   4       )       +     Δ                   P     g   /   3                   Equation                 12                                
     For single-phase flow ΔP gl3  is equal to zero and the equation is solved directly for the mass flow rate m g . In practice, the single-phase result is modified by the addition of an empirical constant C c  which accounts for the true discharge characteristics (non-ideal one-dimensional behavior and friction losses) of the nozzle and Y which takes compressibility effects into account.                m     g                 1                 φ       =           C   c        AY         1   -       β                4                  2                   ρ   g        Δ                   P   3                   Equation                 13                                
     As shown in the introduction, if the Equation 13 above is used under multiphase conditions, the mass flow rate of the gas phase can be significantly overestimated. Under multiphase conditions the mass flow rate of the gas phase is given by:                m   g     =           C     2                 φ            α   2          A   2        Y         1   -         (       α   2       α   1       )     2          β   4                    2          ρ   g          (       Δ                   P   3       -     Δ                   P     g   /   3           )                     Equation                 14                                
     where α 2 A 2  represents the cross sectional area occupied by the gas phase. When ΔP 3  is large with respect to ΔP gl3  the quantity under the radical can be approximated by 
       {square root over (ΔP 3 −ΔP gl3 )}≈{square root over (Δ   P   3 )}−C gl3 ×{square root over (Δ P   gl3 )}  Equation 15 
     where C gl3  is a constant that is determined experimentally. Empirically it has been found that ΔP gl3  can be replaced by a function of ΔP 2 , the pressure drop in the extended throat, with appropriate choice of constants. The mass flow rate of gas under both single phase and multiphase conditions now becomes                m   g              C     2                 φ          AY         1   -     β   4                    2                   ρ   g              [         Δ                   P   3         -       C   2     ×       P   2           ]               Equation                 16                                
     where it has been assumed that α 2 ≈α 1 ≈1. The constants C 2φ  and C 2  have been determined empirically and the validity of the equation has been tested over a wide range of conditions. It is important to note that this method can be used not only with natural gas production but other gas and liquid phase compositions. In addition, it is also important to recognize that Equations 10-16 are used to derive calculation steps in the calculation method. 
     We have assumed that α 2 ≈α 1 ≈1, making Equation 16 above only approximate. The statistical fitting procedure used to determine the constants C 2φ  and C 2  implicitly determines a weighted mean value of α. Because α does not appear explicitly and is unknown, there is an uncertainty of ±1-2% over the void fraction range 0.95&lt;α&lt;1.0, implicit in the equation. If α or (1−α) is independently measured, the observed measurement uncertainties can be significantly reduced. The uncertainty can also be significantly reduced if, at installation, the actual flow rates are accurately known. If this measurement is available then the meter reading can be adjusted to reflect the true value and the uncertainty in the gas phase mass flow rate measurement can be reduced to less than 0.5% of reading if the gas and liquid flow rates change by less than 50% or so over time. The repeatability of the measurement is essentially the random uncertainty in the pressure measurements, less than about 0.5% of reading. 
     Total and Liquid Mass Flow Rate 
     If the ratio of liquid to gas flow rate is known a  priori  with certainty then the mass flow rate of the liquid phase can be directly obtained from m l =m g (m l /m g ) known . Note that because the liquid mass flow rate is only a fraction (0-30%) of the gas mass flow rate the uncertainty in the measurement is magnified. For instance, if m l /m g =0.01, a 1% error in m g  is magnified to become a 100% of reading error for the liquid phase. An additional fixed error of 1% in the ratio m l /m g  results in a 200% of reading total error for the liquid phase. This approach, of course, assumes that the m l /m g  ratio remains constant over time. 
     Unfortunately, without accurate independent knowledge of α or (1−α) the liquid mass flow rate cannot be obtained directly from one-dimensional theory. The velocity of the liquid phase can, however, be estimated directly as now described. Once the mass flow rate of the gas phase is determined the ΔP gl3  term can be estimated from the gas phase energy equation:                Δ                   P     g   /   3         ≈       Δ                   P   3       -       1   2            m   g   2         ρ   g          A   2              (     1   -     β   4       )                 Equation                 17                                
     Equation 17 allows us to derive Equation 5 in the calculation method. Rearranging the liquid phase energy equation yields                  Δ                   P   3       +     Δ                   P     g   /   3           =         1   2          ρ   l            u   l   2          (     1   -       u   l1   2       u   l2   2         )         +       G   c          f   w          1   2          ρ   l          u   l2   2                 Equation                 18                                
     and using the expression for the mass flow rate of liquid results in:                  Δ                   P   3       +     Δ                   P     g   /   3           =         1   2          ρ   l            u   l2   2          (     1   -           (     1   -     α   2       )     2         (     1   -     α   1       )     2            β   4         )         +       G   c          f   w          1   2          ρ   l          u   l1   2                 Equation                 19                                
     With the assumption that                (     1   -     α   2       )     2         (     1   -     α   1       )     2            β   4          1                          
     the liquid velocity u l2  can be estimated. If (1−α) is known then the liquid mass flow rate could be estimated directly from m l =(1−α 2 )ρu l2 A. Unfortunately, (1−α) cannot be accurately estimated directly from the differential pressure data; it must be independently measured to pursue this approach. 
     If we consider the gas and liquid phases together but allow their velocities to differ, the total mass flow rate can be written as:                m   t     =         m   g     +     m   l       =       (       α                   ρ   2       +         (     1   -   α     )     S          ρ   l         )          u   g        A               Equation                 20                                
     where the density term in brackets is the effective density, ρ slip  and S=u g /u l  which is ratio of the gas velocity to the liquid velocity or slip. Since m t  is constant throughout the venturi, it allows us to write the pressure drop ΔP 3  as                Δ                   P   3       =         1   2          (       αρ   g     +         (     1   -   α     )     S          ρ   l         )            u   g   2          (     1   -     β   4       )         +       G   c          f   w          1   2          ρ   l          u   l2   2                 Equation                 21                                
     The second term on the right hand side is the friction loss assuming that only the liquid phase is in contact with the wall. The equation can be rearranged to yield the total mass flow rate                      m   t     =       (       αρ   g     +         (     1   -   a     )     S          ρ   l         )          u   g        A                 =       2        (       Δ                   P   3       -       G   c          f   w          1   2          ρ   l          u   l2   2         )        A         (     1   -     β   4       )     ·     u   g                       Equation  22                                
     The total mass flow rate mt can then be obtained directly from ΔP 3  once u g  is estimated from the measured value of m g , u g =m g /ρ g A and the liquid velocity is calculated by solving equation 19 for u l2 . The total mass flow rate using this method is a measurement with an uncertainty of ±4% of the actual measured flow. In principle, (since the total mass flow rate is the sum of the gas and liquid mass flow rates) the liquid mass flow rate can now be obtained directly from m l   32  m t −m g . The liquid mass flow rate can then be obtained within ±5% of the total mass flow rate. 
     As previously noted in the discussion of the measurement of the gas mass flow rate, if the flow rates of each phase are accurately known at the time of installation, measurement performance over a reasonable range of mass flow rates can be significantly enhanced. The uncertainty in the gas mass flow rate measurement can be reduced to &lt;0.5% of reading by benchmarking even if the gas and/or liquid mass flow rates change by ±50%. Similarly, the uncertainty in the total mass flow rate can be reduced by &lt;2% of reading for the same ±50% changes in gas and/or liquid mass flow rates. The corresponding improvement in accuracy of the liquid phase measurement is also significant. Because the liquid mass flow rate measurement is dependent on both the gas phase and total mass flow rate measurements, the uncertainty is also sensitive to changes in both gas and liquid mass flow rate. If the liquid mass flow rate measurement is benchmarked at an initial value, the data indicate that the accuracy attainable is ±20% of reading for changes in gas mass flow rate in the range of ≦±15% and/or changes in liquid mass flow rate in the range of ≦±25%. The uncertainty in the liquid mass flow rate quoted in terms of percent of total mass flow rate becomes ±1%. 
     Measurement uncertainties can be significantly reduced if flow rates are accurately known at time of meter installation or periodically measured by separation and separate metering during the service life of the meter and the well. Because the liquid phase is generally only a small fraction of the total mass flow rate the uncertainty in its measurement is inherently high. If the void fraction α is accurately and independently measured, the liquid mass flow rate can be calculated directly from m l =(1−α)l l u l2 A where the u l2  the liquid velocity is obtained as described above from equation 19. The void fraction may be accurately and independently measured using a gamma ray attenuation densitometer or through ultrasonic film thickness measurements. This approach has been shown to significantly reduce the uncertainty in the liquid mass flow rate measurement.