# Patent

## Title
Apparatus and method for characterizing two phase fluid flow

## Abstract

An apparatus (and corresponding method) for characterizing the fluid properties of a two phase fluid includes a restriction element (e.g., orifice plate or nozzle) along the flow path of the two phase fluid. At least one temperature sensor measures temperature of the two phase fluid flowing through the restriction element. A pressure sensor measures the pressure downstream of the restriction element. Time-of-flight measurements of pulses passing through the two phase fluid are made. The speed of sound within the two phase fluid is calculated from the time-of-flight measurements. At least one fluid property (e.g., a vapor phase fraction) of the two phase fluid is calculated from the measured pressure, the measured temperature, and the calculated speed of sound.

## Background
CROSS-REFERENCE TO RELATED APPLICATION
This application is related to application Ser. No. 12/109,848 filed Apr. 25, 2008, entitled “Method, Apparatus and System for Characterizing Two Phase Fluid Flow in an Injection Well”.
BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates broadly to the analysis of two phase fluid flow.
2. Description of Related Art
There are many petroleum bearing formations from which oil cannot be recovered by conventional means because the oil is so viscous that it will not flow from the formation to a conventional oil well. Examples of such formations are the bitumen deposits in Canada and the United States and the heavy oil deposits in Canada, the United States, and Venezuela. In these deposits, the oil is so viscous under the temperatures and pressures prevailing within the formations that it flows very slowly (or not at all) in response to the force of gravity. Heavy oil is an asphaltic, dense (low API gravity), and viscous oil that is chemically characterized by its contents of asphaltenes. Most heavy oil is found at the margins of geological basins and is thought to be the residue of formerly light oil that has lost its light molecular weight components through degradation by bacteria, water-washing, and evaporation.
Heavy oil is typically recovered by injecting superheated steam into an oil reservoir, which reduces the oil's viscosity and increases the reservoir pressure through displacement and partial distillation of the oil. Steam may be injected continuously utilizing separate injection and production wells. Alternatively, the steam may be injected in cycles such that the well is used alternatively for injection and production (a “huff and puff” process).
A large percentage of heavy oil recovery methods use steam injection with different well arrangements, but fail to provide adequate support for monitoring the fluid flow into and through the injector well for control and optimization of the injection process.
BRIEF SUMMARY OF THE INVENTION
A method and corresponding system is provided for determining fluid properties of a two phase fluid flowing through various portions of a wellbore. Specifically, the method and corresponding system determines fluid properties (e.g., enthalpy flux via density, pressure, and temperature) of the two phase fluid flowing upstream of the injector portion of the wellbore (hereinafter ‘injector’) as well as fluid properties (e.g., mass flow rate and enthalpy flux via pressure and temperature) of the two phase fluid at various measurement locations along the injector.
The method and corresponding system of the present invention enable the properties of the two phase fluid flowing into and through the injector well to be monitored for better control and optimization of the injection process.
The fluid properties of the two phase fluid flowing upstream of the injector is determined by measuring temperature, pressure, and density of the two phase fluid upstream of the injector. These measurements are used to calculate the fluid's vapor phase fraction and homogeneous mass density. The homogeneous mass density is used in conjunction with energy and mass continuity equations to estimate the volume flow rate and mass flow rate for the vapor phase and liquid phase of the two phase fluid. The enthalpy flux of the two phase fluid is then calculated based on the mass flow rate of the vapor phase and liquid phase of the two phase fluid, as well as known enthalpy values for the vapor and liquid phases of the two phase fluid at the measured temperature and pressure.
The fluid properties of the two phase fluid along the injector are determined by measuring temperature, pressure, and velocity of the fluid at a plurality of measurement locations along the injector. A vapor phase fraction is estimated for each measurement location along the injector based on the measured temperature and pressure, and assuming phase equilibrium. The calculation of each vapor phase fraction is preferably based in part on the Clapeyron relationship, the equation of state for water vapor, and the ideal gas law. The calculated vapor phase fraction for each measurement location along the injector allows for fluid density corrections in the overall energy calculations. A mass balance equation is used in conjunction with the vapor phase fraction, and the measured temperature and pressure, to determine the mass flow rate and enthalpy flux of the two phase fluid at each measurement location.
In the preferred embodiment, measurements are taken along the injector with a tool that houses a temperature sensor, and a pressure sensor. The measurements taken by the tool are communicated to a surface-located data processing means for storage and processing. The tool is movable to the various measurement locations along the injector by a positioning means, which is preferably realized by coiled tubing that supports the tool at its downhole end. The coiled tubing and tool are conveyed downhole and deployed through a heel and injector portion of the wellbore. The coiled tubing may be pushed/pulled forward or backward in order to position the tool at various locations along the injector portion of the wellbore.
In another aspect of the invention, an apparatus (and corresponding method) for determining fluid properties of a two phase fluid includes a restriction element (e.g., orifice plate or nozzle) along the flow path of the two phase fluid. At least one temperature sensor measures temperature of the two phase fluid flowing through the restriction element. Pressure sensors measure the pressure drop across the restriction element. Time-of-flight measurements of sonic pulses passing through the two phase fluid are made. The speed of sound within the two phase fluid is calculated from the time-of-flight measurements. At least one fluid property (e.g., a vapor phase fraction and possibly other properties derived therefrom) of the two phase fluid is calculated from the measured pressure drop, the measured temperature, and the calculated speed of sound. The apparatus (and methodology) can be used to calculate fluid properties (e.g., vapor phase fraction and properties calculated therefrom) of a two phase fluid upstream of the injector as described herein.



BRIEF DESCRIPTION OF THE DRAWINGS
FIGS. 1A and 1B, collectively, is a flow chart outlining the methodology for determining fluid properties of a two phase fluid flowing through an injector well in accordance with the present invention.
FIG. 2 is a diagram illustrating a unit volume of a wellbore with a corresponding mass balance equation.
FIG. 3 is a schematic diagram of an illustrative embodiment of a system for determining the fluid properties of a two phase fluid flowing through an injector well in accordance with the present invention.
FIG. 4 is a schematic diagram of a metering device for determining fluid properties of a two phase fluid; the metering device can be used as part of the system of FIG. 3 to determine fluid properties of a two phase fluid upstream of the injector portion of the wellbore.



DETAILED DESCRIPTION OF THE INVENTION
Turning to FIGS. 1A and 1B there is shown a method for determining a number of fluid properties of a two phase fluid (e.g., steam and water) flowing upstream of an injector portion of a wellbore (FIG. 3) as well as a number of fluid properties of the two phase fluid along the injector portion of the wellbore.
The enthalpy (heat content) of the two phase fluid upstream of the injector portion the wellbore is given by the following equation:

ht=mvhv(T,P)+mlhl(T,P)  (1)

    
    
        where mv is the mass of the vapor phase of the two phase fluid.
        hv(T,P) is the enthalpy of the vapor phase of the two phase fluid at temperature T and pressure P.
        ml is the mass of the liquid phase of the two phase fluid, and
        hl(T,P) is the enthalpy of the liquid phase of the two phase fluid at temperature T and pressure P.

It is assumed that the vapor and liquid phases of the two phase fluid are in equilibrium along the wellbore, and thus that that their respective enthalpy values vary as a function of the pressure and temperature only.

    
    


The enthalpy flux is given by Equation 1 as follows:

{dot over (h)}l={dot over (m)}vhv(T,P)+{dot over (m)}lhl(T,P)  (2)

    
    
        where {dot over (m)}v is the mass flow rate of the vapor phase of the two phase fluid, and
        {dot over (m)}l is the mass flow rate of the liquid phase of the two phase fluid.
    
    


The methodology of FIGS. 1A and 1B begins in step 100 by measuring temperature and pressure of the two phase fluid upstream and downstream of a flow restrictor. Such temperature and pressure measurements may be carried out by any means known in the art, such as, for example, via a thermocouple or a resistance temperature detector (RTD) probe for temperature or a pressure transducer for pressure.
In step 150, the speed of sound in the two phase fluid is measured at the location where temperature and pressure are known.
In step 200, the vapor phase fraction is calculated from the temperature. pressure, and speed of sound. Vapor phase density estimates ρv and liquid phase density estimates ρl are then calculated upstream of the injector portion of the wellbore for the temperature and pressure measured in step 100. This calculation is made from known equations of state (e.g. steam tables).
In step 250, a homogeneous density estimate ρ is now calculated from the vapor phase fraction, α, and ρv, and ρl according to the relationship ρ=ρvα+ρl(1−α). A vapor phase fraction α of the two phase fluid is calculated by
measuring the time-of-flight of sound pulses traveling through the fluid as described below with respect to the metering device of FIG. 4. A homogeneous density estimate ρ1 upstream of the restriction element is derived from the vapor phase density estimate ρv and liquid phase density estimate ρl for the fluid upstream of the restriction element. A homogeneous density ρ2 at the vena contracta of the restriction element is derived from the vapor phase density estimate ρv and liquid phase density estimate ρl for the fluid at the vena contracta of the restriction element.
In step 300, the vapor phase fraction α generated in step 200 and the homogeneous density estimate ρ generated in step 250 are used to calculate a volume flow rate Ql of the two phase fluid upstream of the injector portion of the wellbore. In the preferred embodiment, the calculations of step 300 are derived from the energy and mass conservation equations representing the flow across the restriction element as follows:




  
    
      
        
          
            u
            2
            2
          
          -
          
            u
            1
            2
          
        
        =
        
          
            2
            ⁢
            
              (
              
                
                  h
                  1
                
                -
                
                  h
                  2
                
              
              )
            
          
          =
          
            2
            ⁢
            
              (
              
                
                  
                    e
                    1
                  
                  ⁡
                  
                    (
                    T
                    )
                  
                
                +
                
                  
                    p
                    1
                  
                  
                    ρ
                    1
                  
                
                -
                
                  
                    e
                    2
                  
                  ⁡
                  
                    (
                    T
                    )
                  
                
                -
                
                  
                    p
                    2
                  
                  
                    ρ
                    2
                  
                
              
              )
            
          
        
      
    
    
      
        (
        3
        )
      
    
  
  
    
      
        
          
            ρ
            1
          
          ⁢
          
            u
            1
          
          ⁢
          
            A
            1
          
        
        =
        
          
            ρ
            2
          
          ⁢
          
            u
            2
          
          ⁢
          
            A
            2
          
        
      
    
    
      
        (
        4
        )
      
    
  




where

    
    
        u1 is the homogeneous velocity of the two phase fluid upstream from the restriction element;
        u2 is the homogeneous velocity of the two phase fluid at the vena contracta of the restriction element;
        h1 is the enthalpy at the inlet of the restriction element;
        h2 is the enthalpy at the outlet of the restriction element;
        e1(T) is the internal energy of the flow (constant pressure) at the inlet of the restriction element;
        e2(T) is the internal energy of the flow (constant pressure) at the outlet of the restriction element;
        p1 is the pressure upstream of the restriction element;
        p2 is the pressure at the vena contracta of the restriction element;
        ρ1 is the homogeneous density upstream of the restriction element;
        ρ2 is the homogeneous density at the vena contracta of the restriction element:
        A1 is the cross sectional area of the two phase fluid flow upstream of the restriction element: and
        A2 is the cross-sectional area of the two phase fluid flow at the vena contracta of the restriction element.
    
    


Substituting Equation 4 into Equation 3 and solving for u2 yields:




  
    
      
        
          u
          2
        
        =
        
          
            C
            d
          
          ⁢
          
            
              
                2
                ⁢
                
                  (
                  
                    
                      h
                      1
                    
                    -
                    
                      h
                      2
                    
                  
                  )
                
              
              
                1
                -
                
                  
                    
                      ρ
                      2
                      2
                    
                    
                      ρ
                      1
                      2
                    
                  
                  ⁢
                  
                    
                      A
                      2
                      2
                    
                    
                      A
                      1
                      2
                    
                  
                
              
            
          
        
      
    
    
      
        (
        5
        )
      
    
  




where Cd is a discharge coefficient.

The volume flow rate Ql of the two phase fluid can calculated from Equation 5 as follows:

Ql=u2A2,  (6)

In step 400, the mass flow rates {dot over (m)}v, {dot over (m)}l for the vapor and liquid phases of the two phase fluid upstream of the injector portion of the wellbore are calculated as follows:

{dot over (m)}v=(αρv)2Ql  (7)

{dot over (m)}l=(ρl(1−α))2Ql.  (8)

In step 500, the mass flow rates {dot over (m)}v, {dot over (m)}l of step 400 along with the enthalpy of the vapor and liquid phases hv (T,P), hl (T,P) for the temperatures and pressures measured in step 100 are used to calculate the enthalpy flux {dot over (h)}l of the two phase fluid upstream of the injector portion of the wellbore in accordance with Equation 2 above.
In step 550, the temperature at the heel of the wellbore is measured.
In step 570, the volume fraction of the flow is estimated from the equation of state (e.g. Clausius-Clapeyron) and mass conservation, assuming local phase equilibrium.
In step 600, the temperature of the two phase fluid is measured at a plurality of locations along the injector portion of the wellbore.
In step 700, the temperature measurements of step 600 are used to derive vapor phase fractions, pressure, and local mass loss for each given location. In calculating the vapor phase fraction αi for the given location, it is assumed that the two phases of the fluid are in equilibrium. By combining the Clapeyron relationship and the equation of state for a two phase fluid, it can be shown that the change in volume of 1 mole of saturated vapor dv due to a change of temperature dT and pressure dp is:




  
    
      
        
          d
          v
        
        =
        
          
            1
            P
          
          ⁢
          
            (
            
              R
              -
              
                
                  L
                  v
                
                T
              
            
            )
          
          ⁢
          
            d
            T
          
        
      
    
    
      
        (
        9
        )
      
    
  




where Lv is the latent heat of vaporization and is a function of temperature

    
    
        T only:
        R is a known constant; and
        P and T are measured pressure and temperature values, respectively.

Therefore, if Vt is the volume occupied by one mole of liquid phase of the fluid at temperature T and pressure P, and if one mole of vapor occupies volume Vv at temperature T and pressure P, then it will occupy volume Vv+dv at pressure, P+dp, and temperature, T+dT. If the volume fraction of the mole of vapor phase of the two phase fluid at temperature T and pressure P is

    
    






  
    α
    1
  
  =
  
    
      V
      v
    
    
      
        V
        v
      
      +
      
        
          V
          I
        
        .
      
    
  




the volume fraction of the mole of vapor phase of the two phase fluid at temperature T+dT and pressure P+dp will be





  
    α
    2
  
  =
  
    
      
        
          V
          v
        
        +
        
          d
          ⁢
          
            
          
          ⁢
          v
        
      
      
        
          V
          v
        
        +
        dv
        +
        
          V
          I
        
      
    
    .
  




This estimation assumes that the change in volume of the liquid water is negligible, and that the vapor portion of the fluid behaves like an ideal gas. As the compressibility of the liquid phase is very small, the assumption is not a significant source of error. If desired, a more refined equation of state for the two phase fluid may be used to compute the compressibility factors of the liquid and vapor phases and thus the relative change in volume of the two phases.

In step 800, the vapor phase fractions generated in step 700 are used to calculate the changes in mass flow rate and enthalpy flux at the measurement locations along the injector portion of the wellbore. Consider the mass balance and the energy balance of a unit volume as shown in FIG. 2. The unit volume is modeled as a cylinder of radius r bounded by two opposing ends. One end of the cylinder (the entrance of the unit volume) lies at position x along the injector portion of the wellbore while the other end of the cylinder (the exit of the unit volume) lies at position x+dx along the injector portion of the wellbore. The length of the cylindrical unit volume is dx. The fluid arriving at the entrance of the unit volume includes two parts: one part flows through the cylindrical unit volume to the exit of the unit volume along the x direction, and the other part is injected radially through the annular sidewall of the cylinder of the unit volume into the formation.
Applying a mass balance to this unit volume produces the following equation:

((ρ(x+dx)ux(x+dx)−ρ(x)ux(x)·πr2)+((ρ(x)ur(x))·2πrdx)=0  (10)

    
    
        where ρ(x) is the homogeneous density of the two phase fluid at the entrance of the unit volume (at position x);
        ρ(x+dx) is the homogeneous density of the two phase fluid at the exit of the unit volume (at position x+dx);
        ux(x) is the homogeneous velocity of the two phase fluid along the x direction of the injector well at the entrance of the unit volume:
        ux(x+dx) is the homogeneous velocity of the two phase fluid along the x direction of the injector at the exit of the unit volume; and
        ur(x) is the uniform radial velocity of the two phase fluid along the unit volume of length dx.
    
    


Applying an energy balance on the unit volume yields the following equation:




  
    
      
        
          
            
              ρ
              ⁡
              
                (
                
                  x
                  +
                  dx
                
                )
              
            
            ⁢
            
              
                u
                x
              
              ⁡
              
                (
                
                  x
                  +
                  dx
                
                )
              
            
            ⁢
            
              h
              ⁡
              
                (
                
                  x
                  +
                  dx
                
                )
              
            
          
          -
          
            
              ρ
              ⁡
              
                (
                x
                )
              
            
            ⁢
            
              
                u
                x
              
              ⁢
              
                
              
              (
              x
              )
            
            ⁢
            
              h
              ⁡
              
                (
                x
                )
              
            
          
          +
          
            
              1
              2
            
            ⁢
            
              (
              
                
                  
                    ρ
                    ⁡
                    
                      (
                      
                        x
                        +
                        dx
                      
                      )
                    
                  
                  ⁢
                  
                    
                      (
                      
                        
                          u
                          x
                        
                        ⁡
                        
                          (
                          
                            x
                            +
                            dx
                          
                          )
                        
                      
                      )
                    
                    3
                  
                
                -
                
                  
                    ρ
                    ⁡
                    
                      (
                      x
                      )
                    
                  
                  ⁢
                  
                    
                      (
                      
                        
                          u
                          x
                        
                        ⁡
                        
                          (
                          x
                          )
                        
                      
                      )
                    
                    3
                  
                
              
              )
            
          
        
        =
        
          
            ρ
            ⁡
            
              (
              x
              )
            
          
          ⁢
          
            
              u
              x
            
            ⁡
            
              (
              x
              )
            
          
          ⁢
          
            
              h
              ⁡
              
                (
                x
                )
              
            
            ·
            2
          
          ⁢
          
            dx
            r
          
        
      
    
    
      
        (
        11
        )
      
    
  




    
    
        where h(x) is the total enthalpy of the two phase fluid at the entrance of the unit volume: and
        
            h(x+dx) is the total enthalpy of the two phase fluid at the exit of the unit volume.

This assumes that the void fraction (and enthalpy) of the fluid leaving the wellbore element is the same as the void fraction (and enthalpy) remaining in the wellbore element.

Equations 11 and 12 assume that the vapor and the liquid phases of the fluid travel across the unit volume with the same homogeneous velocity ux with no slip. Such assumptions are more accurate in the event that the two phases are mixed upstream of the unit volume. In the preferred embodiment, such mixing is accomplished by a static mixer disposed upstream of the unit volume.

        
        
    
    


Substituting Equation 10 into Equation 11 gives:




  
    
      
        
          
            
              ρ
              ⁡
              
                (
                
                  x
                  +
                  dx
                
                )
              
            
            
              ρ
              ⁡
              
                (
                x
                )
              
            
          
          ⁢
          
            
              u
              x
            
            ⁡
            
              (
              
                x
                +
                dx
              
              )
            
          
          ⁢
          
            (
            
              
                e
                ⁡
                
                  (
                  
                    x
                    +
                    dx
                  
                  )
                
              
              -
              
                
                  1
                  2
                
                ⁢
                
                  
                    
                      u
                      x
                    
                    ⁡
                    
                      (
                      
                        x
                        +
                        dx
                      
                      )
                    
                  
                  2
                
              
              -
              
                h
                ⁡
                
                  (
                  x
                  )
                
              
            
            )
          
        
        =
        
          
            
              1
              2
            
            ⁢
            
              
                
                  u
                  x
                
                ⁡
                
                  (
                  x
                  )
                
              
              3
            
          
          +
          
            
              
                ρ
                ⁡
                
                  (
                  
                    x
                    +
                    dx
                  
                  )
                
              
              
                ρ
                ⁡
                
                  (
                  x
                  )
                
              
            
            ⁢
            
              
                
                  u
                  x
                
                ⁡
                
                  (
                  
                    x
                    +
                    dx
                  
                  )
                
              
              .
            
          
        
      
    
    
      
        (
        12
        )
      
    
  




In Equation 12, the measured quantities are homogeneous velocity (at x and x+dx) and temperature (at x and x+dx): the inferred quantities are energy, enthalpy. and void fraction (density) at both end points of the wellbore element. Note that the measurements of homogeneous velocity ux along the injector portion of the wellbore can be carried out by a turbine flow meter or other instrument known in the art.
In step 900, the changes in mass flow rate and enthalpy flux calculations of step 800 along with the enthalpy flux of the two phase fluid upstream of the injector portion of the wellbore generated in step 500 are used to generate data that characterizes energy of the two phase fluid as it flows along the injector portion of the wellbore.
Turning to FIG. 3, there is shown a schematic diagram of an illustrative embodiment of a system 10 for determining fluid characteristics of a two phase fluid flowing through an injector wellbore in accordance with the present invention. The system includes a surface-located metering device 12 that is fluidly coupled between a source of two phase injection fluid (e.g., steam and water) and tubing 14 that extends downhole within an injector wellbore 16. The metering device 12 includes thermocouples (or temperature probes or other suitable sensors) for measuring temperatures of the two phase fluid before it enters the tubing 14, as well as pressure transducers for measuring pressures of the two phase fluid before it enters the tubing 14. The metering device 12 includes a data processing unit, which is preferably realized by a software programmed data processing system, that processes the temperature and pressure measurements provided by the temperature and pressure sensors of the metering device 12 (and possibly other input) to perform the calculations of steps 200 to 500 of FIG. 1 as described above in order to derive the enthalpy flux of the two phase fluid as it enters the tubing 14 for supply to the injector wellbore 16. It should be noted that the metering device 12 can be placed anywhere upstream of the wellhead, provided that local pressure and temperature are measured at the wellhead.
The system 10 also includes a tool 18 that houses a temperature sensor, a pressure sensor, and a flow rate meter (collectively referred to as the downstream measurement instruments) for measuring temperature, pressure and velocity, respectively, of the fluid at various measurement locations along the injector portion 24 of the wellbore 16. The tool 18 is conveyed to the various measurement locations along the wellbore 16 by positioning means, which is preferably realized by coiled tubing 20 that supports the tool 18 at or near its downhole end 26. The coiled tubing 20 and tool 18 are conveyed downhole through the tubing 14 and heel portion 22 of the wellbore 16 and into the injector portion 24 of the wellbore 16. The coiled tubing 20 comprises a continuous length of uniform outer diameter tubing (typically several hundred to several thousand feet), which is capable of being repeatedly coiled and uncoiled from a truckable spool, and which is capable of being repeatably inserted into and withdrawn from the wellbore 16 and thus allows the tool 18 to be moved and positioned along the injector portion 24 of the wellbore 16 as desired. The coiled tubing 20 is typically, although not necessarily, manufactured of steel having a longitudinally welded seam. Being flexible, the coiled tubing 20 is particularly useful for horizontal injection well applications as shown in FIG. 3. The coiled tubing 20 includes one or more electrical cables 28 operably disposed inside the coiled tubing 20 and extending from the surface to the downhole end 26 and tool 18. The electrical cable(s) 28 carry electrical power for supply to the electrical components of the tool 18. The data representing the measurements of the downhole measurement instruments of the tool 18 are preferably carried to a surface-located interface unit 30 by the electrical cable(s) 28 (for example, by modulating power supply current carried by the electrical cable(s) 28) or other suitable data telemetry means. The interface unit 30 provides the measurement data communicated thereto from the tool 18 to a data processor 32. The data processor 32 stores the measurement data communicated from the tool 18 and carries out the calculations of steps 700 to 900 of FIG. 1 as described above to derive data that characterizes energy along the injector portion of the wellbore 16. The data processor 32 interfaces to the metering device 12 to provide for communication of data therebetween as needed. Note that the data processor 32 and metering device 12 are shown as distributed systems for simplicity of description. It is contemplated that the data processing functionality of the metering device 12 and the data processor 32 can be realized by a common data processing platform or other suitable architectures.
In a preferred embodiment of the present invention, the method of FIG. 1 and/or the system of FIG. 3 are used in conjunction with steam injection processes for heavy oil recovery. In such processes, a pressurized two phase fluid (e.g., under saturated steam and water) is supplied to an injector well for injection into the formation surrounding a portion of the injector well. The escaping fluid heats oil situated within the earth in close proximity to the injector well. As the oil is heated, it becomes more viscous and falls via gravity to one or more production wells disposed nearby. In commercial applications where injection fluid is injected to numerous injector wells in close proximity to one another adjacent a heavy oil deposit (e.g., where there may be well-to-well cross-resistivity), information regarding the fluid properties of the injection fluid (e.g., energy) along the injector wells is useful for controlling and optimizing the injection process as it provides useful information regarding the injector wells, such as the health of the injector wells and whether the injection process should be modified. Such modifications can include modification(s) of the injection fluid distribution system, modification(s) at the head of a given injector well, and/or modifications along the injector portion of a given injector well.
FIG. 4 is a diagram of an illustrative embodiment of a metering device 12′ which can be used in the system of FIG. 3. The metering device 12′ includes a restriction element 51 (such as an orifice plate or a flow nozzle) for restricting the flow of a two phase fluid flowing through a tubular member 53 by decreasing the cross sectional area of the tubular member 53. When used as part of the system of FIG. 3, the tubular member 53 is fluidly coupled between a source of two phase fluid and the tubing 14 that extends down the injector well. A temperature sensor 55A mounted upstream of the restriction element 51 and a temperature sensor 55B, which is preferably mounted to the tubular member 53 downstream of the restriction element 51 after mixing of the two phase fluid as shown, measure the temperature of the two phase fluid flowing through the tubular member 53. Pressure transducers 57A and 57B, which are preferably mounted to the tubular member 53 on opposite sides of the restriction element 51, measure the pressure drop of the two phase fluid across the restriction element 51. Sonic transceivers 59A, 59B are supported by the tubular member 53 and spaced apart from one another along the length of the tubular member 53. The sonic transceivers 59A. 59B are preferably disposed downstream of the restriction element 51 where better mixing of the two phase fluid is achieved. The sonic transceivers 59A, 59B are coupled to a signal processor 61 that is adapted to derive time-of-flight measurements for sonic pulses in the two phase fluid flowing through the tubular member 53. More particularly, sonic transceiver 59A is controlled to emit a first sonic pulse train into the two phase fluid, which is received by sonic transceiver 59B. The first sonic pulse train propagates in the direction of flow for the two phase fluid in the tubular member 53. The signal processor 61 measures the time of flight (sometimes referred to as “transmit time”) of the pulses of the first sonic pulse train. Sonic transceiver 59B is controlled to emit a second sonic pulse train into the two phase fluid, which is received by sonic transceiver 59A. The second sonic pulse train propagates counter to the direction of flow for the two phase fluid in the tubular member 53. The signal processor 61 measures the time of flight of the pulses of the second sonic pulse train. The signal processor 61 digitizes the time of flight measurements for the first and second sonic pulse trains and communicates such measurements (in digital form) to the data processing unit 63, which stores the time-of-flight data for both the first and second sonic pulse trains. The data processing unit 63 also interfaces to the sensors 55A. 55B, 57A, 57B, and stores the temperature and pressure measured by the sensors 55A, 55B, 57A, 57B (in digital form). The data processing unit 63 is adapted to calculate speed of sound in the two phase fluid as well as a vapor phase fraction a for the two phase fluid utilizing the stored time of flight data and the temperature and pressure measured by the sensors 55B, 57A, 57B as follows.
The time-of-flight T1 of the pulses of the first sonic pulse train is given by the following equation:




  
    
      
        
          T
          1
        
        =
        
          L
          
            c
            +
            
              u
              x
            
          
        
      
    
    
      
        (
        13
        )
      
    
  




    
    
        where L is the distance between the transceivers 59A, 59B.
        
            c is the speed of sound in the two phase fluid, and
            ux is the homogeneous velocity of the two phase fluid.
        
        
    
    


The time-of-flight T2 for the pulses of the second sonic pulse train is given by the following:




  
    
      
        
          T
          2
        
        =
        
          
            L
            
              c
              -
              
                u
                x
              
            
          
          .
        
      
    
    
      
        (
        14
        )
      
    
  




Equation 13 may be combined with Equation 14 to cancel out the ux term and solve directly for c as follows:




  
    
      
        
          
            
              
                
                  1
                  T
                
                +
                
                  1
                  
                    T
                    2
                  
                
              
              =
              
                
                  2
                  ·
                  c
                
                L
              
            
          
        
        
          
            
              c
              =
              
                
                  L
                  2
                
                ⁢
                
                  
                    (
                    
                      
                        1
                        
                          T
                          1
                        
                      
                      +
                      
                        1
                        
                          T
                          2
                        
                      
                    
                    )
                  
                  .
                
              
            
          
        
      
    
    
      
        (
        15
        )
      
    
  




In this manner, the data processing unit 63 can calculate the speed of sound c in the two phase fluid from L (which is known) and the time of flight data T1, T2 for the first and second sonic pulse trains.

Finally, the speed of sound c is related to the vapor phase fractions of the two phase fluid according to the equation:




  
    
      
        
          c
          2
        
        ≈
        
          
            
              ρ
              v
            
            ⁢
            
              c
              v
              2
            
          
          
            
              α
              ⁡
              
                (
                
                  1
                  -
                  α
                
                )
              
            
            ⁢
            
              ρ
              l
            
          
        
      
    
    
      
        (
        16
        )
      
    
  




    
    
        where ρv is the vapor phase density estimate of the two phase fluid at the measured temperature and pressure (determined from the equation of state), the pressure being measured downstream of the flow restrictor, in the region where the speed of sound is being measured:
        
            ρl is the liquid phase density estimate of the two phase fluid at the measured temperature and pressure (determined from the equation of state), measured locally as above; and
            cv is the speed of sound in the vapor phase of the two phase fluid under isothermal conditions, which is calculated according to the equation
        
        
    
    






  
    c
    v
  
  =
  
    
      p
      
        ρ
        v
      
    
    .
  




where p is the local pressure.

In this manner, the data processing unit 63 can calculate the vapor phase fraction α of the two phase fluid from the calculated speed of sound c and the temperature and pressures measured by the sensors 55B, 57A, 57B.

The data processing unit 63 is preferably adapted to perform the following:

    
    
        the calculations of step 250 as described above to derive the homogeneous density estimate of the two phase fluid from the vapor phase fraction or:
        the calculations of step 300 as described above to derive the volume flow rate of the two phase fluid from the vapor phase fraction and the homogeneous density estimate:
        the calculations of step 400 as described above to derive the mass flow rates of the vapor and liquid phases of the two phase fluid; and
        the calculations of step 500 to derive the enthalpy flux of the two phase fluid.
    
    


It is noted that Equation 16 assumes that mechanical and thermal equilibrium conditions are met, namely, that the pressure pv of the vapor phase of the fluid equals the pressure pl of the liquid phase of the fluid and the temperature Tv of the vapor phase of the fluid equals the temperature Tl of the liquid phase of the fluid. Equation 16 also assumes that the wavelengths of the first and second sound waves are significantly longer than the dimensions of the two phase structures in the flow such as bubbles and slugs.
The first and second sonic pulse trains generated by the sonic transceivers 59A and 59B may be reflected by surface structures within the tubular member 53 (or by other structures in the two phase flow). These reflections can interfere with the time of flight measurements carried out by the transceivers 59A, 59B and the signal processor 61. Two Helmholtz resonators 65A, 65B can be supported by the tubular member 53 in order to minimize such interference. The Helmholtz resonators 65A, 65B are located opposite the sonic transceivers 59A, 59B and resonate at a frequency that matches the wavelength of the sonic pulse train emitted from the corresponding transceiver. At resonance, the Helmholtz resonator presents low acoustic impedance such that the incident sonic pulses experience a phase inversion of one hundred-eighty degrees. By locating the Helmholtz resonators 65A, 65B approximately one wavelength away from the corresponding sonic transceiver, the reflected sound waves generated by the Helmholtz resonators 65A, 65B will appear as phase inverted signals with a delay of approximately two wave cycles to the original signals. As the first two cycles of the first and second sonic pulse trains are not affected by such reflection, the signal processor 61 can employ a matched filter (or cross-correlator) that detects the arrival of the respective sonic pulse train based on the detected signal of the first two cycles. Note that Helmholtz resonators 65A, 65B are optional parts of the metering device 12′ when signal processing alone cannot remove the unwanted effects of reflected sound waves.
There have been described and illustrated herein several embodiments of a method, apparatus and system for determining the fluid properties of a two phase fluid. While particular embodiments of the invention have been described, it is not intended that the invention be limited thereto, as it is intended that the invention be as broad in scope as the art will allow and that the specification be read likewise. Thus, while particular steam injection applications have been disclosed, it will be appreciated that the present invention can be readily adapted for applications where monitoring and/or injection of a two phase fluid is required. It will therefore be appreciated by those skilled m the art that yet other modifications could be made to the provided invention without deviating from its scope as claimed.

## Claims

1. An apparatus for determining at least one fluid property of a two phase fluid, the apparatus comprising:
a conduit providing a fluid pathway for the two phase fluid;
a restriction element operably disposed inside said conduit for restricting flow of the two phase fluid therethrough;
means for measuring pressure of the two phase fluid downstream of the restriction element;
means for measuring temperature of the two phase fluid flowing through said conduit downstream of the restriction element;
means for measuring time of flight of sonic pulses within the two phase fluid flowing through said conduit downstream of the restriction element;
resonator means for presenting a low acoustic impedance such that incident sonic pulses experience a phase inversion of one hundred-eighty degrees;
means for calculating the speed of sound within the two phase fluid flowing through said conduit from the measured time of flight; and
means for calculating at least one fluid property of the two phase fluid from the measured pressure, the measured temperature, and the calculated speed of sound.

2. An apparatus according to claim 1, wherein said restriction element comprises one of an orifice plate and a nozzle.

3. An apparatus according to claim 1, wherein said means for measuring time of flight of sonic pulses within the two phase fluid flow comprises first and second sonic transceivers spaced apart from one another along said conduit, said first and second sonic transceivers acting as both transmitters and receivers of sonic pulses within the two phase fluid flow.

4. An apparatus according to claim 1, wherein:
said at least one fluid property is selected from the group including
i) a vapor phase fraction of the two phase fluid;
ii) a homogeneous density estimate of the two phase fluid;
iii) volume flow rate of the two phase fluid;
iv) mass flow rates of the vapor phase and liquid phase of the two phase fluid; and
v) enthalpy flux of the two phase fluid.

5. An apparatus according to claim 4, wherein:
said vapor phase fraction of the two phase fluid is derived in accordance with the equation





  
    
      c
      2
    
    ≈
    
      
        
          ρ
          v
        
        ⁢
        
          c
          v
          2
        
      
      
        
          α
          ⁡
          
            (
            
              1
              -
              α
            
            )
          
        
        ⁢
        
          ρ
          I
        
      
    
  
  ,




where α is the vapor phase fraction of the two phase fluid,
ρv is the vapor phase density estimate of the two phase fluid at the measured temperature and measured pressure,
ρl is a liquid phase density estimate of the two phase fluid at the measured temperature and measured pressure, and
cv is the speed of sound in the vapor phase of the two phase fluid.

6. An apparatus according to claim 5, wherein:
said homogeneous density estimate of the two phase fluid is derived in accordance with the equation


ρ=ρvα+ρl(1−α),

where ρ is said homogeneous density estimate of the two phase fluid.

7. An apparatus according to claim 6, wherein:
said volume flow rate Ql of the two phase fluid is derived in accordance with the following equations





  
    
      
        
          
            
              u
              2
              2
            
            -
            
              u
              1
              2
            
          
          =
          
            
              2
              ⁢
              
                (
                
                  
                    h
                    1
                  
                  -
                  
                    h
                    2
                  
                
                )
              
            
            =
            
              2
              ⁢
              
                (
                
                  
                    
                      e
                      1
                    
                    ⁡
                    
                      (
                      T
                      )
                    
                  
                  +
                  
                    
                      p
                      1
                    
                    
                      ρ
                      1
                    
                  
                  -
                  
                    
                      e
                      2
                    
                    ⁡
                    
                      (
                      T
                      )
                    
                  
                  -
                  
                    
                      p
                      2
                    
                    
                      ρ
                      2
                    
                  
                
                )
              
            
          
        
        ⁢
        
          
        
      
    
  
  
    
      
        
          and
          ⁢
          
            
          
          ⁢
          
            ρ
            1
          
          ⁢
          
            u
            1
          
          ⁢
          
            A
            1
          
        
        =
        
          
            ρ
            2
          
          ⁢
          
            u
            2
          
          ⁢
          
            A
            2
          
        
      
    
  




where
u1 is the homogeneous velocity of the two phase fluid upstream from the restriction element;
u2 is the homogeneous velocity of the two phase fluid at the vena contracta of the restriction element;
h1 is the enthalpy at the inlet of the restriction element;
h2 is the enthalpy at the outlet of the restriction element;
e1(T) is the internal energy of the flow (constant pressure) at the inlet of the restriction element;
e2(T) is the internal energy of the flow (constant pressure) at the outlet of the restriction element;
p1 is the pressure upstream of the restriction element;
p2 is the pressure at the vena contracta of the restriction element;
ρ1 is the homogeneous density upstream of the restriction element;
ρ2 is the homogeneous density at the vena contracta of the restriction element;
A1 is the cross sectional area of the two phase fluid flow upstream of the restriction element;
A2 is the cross-sectional area of the two phase fluid flow at the vena contracta of the restriction element; and







  
    
      
        
          u
          2
        
        =
        
          
            C
            d
          
          ⁢
          
            
              
                2
                ⁢
                
                  (
                  
                    
                      h
                      1
                    
                    -
                    
                      h
                      2
                    
                  
                  )
                
              
              
                1
                -
                
                  
                    
                      ρ
                      2
                      2
                    
                    
                      ρ
                      1
                      2
                    
                  
                  ⁢
                  
                    
                      A
                      2
                      2
                    
                    
                      A
                      1
                      2
                    
                  
                
              
            
          
        
      
    
    
      
        (
        5
        )
      
    
  




where Cd is a discharge coefficient; and


Ql=u2A2.

8. An apparatus according to claim 7, wherein:
said mass flow rates of the vapor and liquid phases of the two phase fluid are derived in accordance with the following equations


{dot over (m)}v=(αρv)2Ql 



{dot over (m)}l=(ρl(1−α))2Ql.

9. An apparatus according to claim 8, wherein said enthalpy flux of the two phase fluid is derived from said mass flow rates of the vapor and liquid phases of the two phase fluid and enthalpy of the two phases at the measured temperature and pressure.

10. An apparatus according to claim 1, wherein the two phase fluid comprises steam and water.

11. A method for determining at least one fluid property of a two phase fluid, the method comprising:
providing a device having a conduit providing a fluid pathway for the two phase fluid and a restriction element operably disposed inside said conduit for restricting flow of the two phase fluid therethrough;
integrating into said device an acoustic resonator adapted to provide low acoustic impedance such that incident sonic pulses experience a phase inversion of one hundred-eighty degrees;
measuring pressure of the two phase fluid downstream of the restriction element;
measuring temperature of the two phase fluid flowing through said conduit downstream of the restriction element;
measuring time of flight of sonic pulses within the two phase fluid flowing through said conduit downstream of the restriction element;
calculating the speed of sound within the two phase fluid flowing through said conduit from the measured time of flight; and
calculating at least one fluid property of the two phase fluid from the measured pressure, the measured temperature, and the calculated speed of sound.

12. A method according to claim 11, wherein said restriction element comprises one of an orifice plate and a nozzle.

13. A method according to claim 11, wherein:
said time of flight of sonic pulses is measured by first and second sonic transceivers spaced apart from one another along said conduit, said first and second sonic transceivers acting as both transmitters and receivers of sound waves within the two phase fluid flow.

14. A method according to claim 11, wherein:
said at least one fluid property is selected from the group including
i) a vapor phase fraction of the two phase fluid;
ii) a homogeneous density estimate of the two phase fluid;
iii) volume flow rate of the two phase fluid;
iv) mass flow rates of the vapor phase and liquid phase of the two phase fluid; and
v) enthalpy flux of the two phase fluid.

15. A method according to claim 14, wherein:
said vapor phase fraction of the two phase fluid is derived in accordance with the equation





  
    
      c
      2
    
    =
    
      
        
          ρ
          v
        
        ⁢
        
          c
          v
          2
        
      
      
        
          α
          ⁡
          
            (
            
              1
              -
              α
            
            )
          
        
        ⁢
        
          ρ
          I
        
      
    
  
  ,




where α is the vapor phase fraction of the two phase fluid,
ρv is the vapor phase density estimate of the two phase fluid at the measured temperature and measured pressure,
ρl is a liquid phase density estimate of the two phase fluid at the measured temperature and measured pressure, and
cv is the speed of sound in the vapor phase of the two phase fluid.

16. A method according to claim 15, wherein:
said homogeneous density estimate of the two phase fluid is derived in accordance with the equation


ρ=ρvα+ρl(1−α),

where ρ is said homogeneous density estimate of the two phase fluid.

17. A method according to claim 16, wherein:
said volume flow rate Ql of the two phase fluid is derived in accordance with the following equations





  
    
      
        
          
            
              u
              2
              2
            
            -
            
              u
              1
              2
            
          
          =
          
            
              2
              ⁢
              
                (
                
                  
                    h
                    1
                  
                  -
                  
                    h
                    2
                  
                
                )
              
            
            =
            
              2
              ⁢
              
                (
                
                  
                    
                      e
                      1
                    
                    ⁡
                    
                      (
                      T
                      )
                    
                  
                  +
                  
                    
                      p
                      1
                    
                    
                      ρ
                      1
                    
                  
                  -
                  
                    
                      e
                      2
                    
                    ⁡
                    
                      (
                      T
                      )
                    
                  
                  -
                  
                    
                      p
                      2
                    
                    
                      ρ
                      2
                    
                  
                
                )
              
            
          
        
        ⁢
        
          
        
      
    
  
  
    
      
        
          and
          ⁢
          
            
          
          ⁢
          
            ρ
            1
          
          ⁢
          
            u
            1
          
          ⁢
          
            A
            1
          
        
        =
        
          
            ρ
            2
          
          ⁢
          
            u
            2
          
          ⁢
          
            A
            2
          
        
      
    
  




where
u1 is the homogeneous velocity of the two phase fluid upstream from the restriction element;
u2 is the homogeneous velocity of the two phase fluid at the vena contracta of the restriction element;
h1 is the enthalpy at the inlet of the restriction element;
h2 is the enthalpy at the outlet of the restriction element;
e1(T) is the internal energy of the flow (constant pressure) at the inlet of the restriction element;
e2(T) is the internal energy of the flow (constant pressure) at the outlet of the restriction element;
p1 is the pressure upstream of the restriction element;
p2 is the pressure at the vena contracta of the restriction element;
ρ1 is the homogeneous density upstream of the restriction element;
ρ2 is the homogeneous density at the vena contracta of the restriction element;
A1 is the cross sectional area of the two phase fluid flow upstream of the restriction element;
A2 is the cross-sectional area of the two phase fluid flow at the vena contracta of the restriction element; and







  
    
      
        
          u
          2
        
        =
        
          
            C
            d
          
          ⁢
          
            
              
                2
                ⁢
                
                  (
                  
                    
                      h
                      1
                    
                    -
                    
                      h
                      2
                    
                  
                  )
                
              
              
                1
                -
                
                  
                    
                      ρ
                      2
                      2
                    
                    ⁢
                    
                      A
                      2
                      2
                    
                  
                  
                    
                      ρ
                      1
                      2
                    
                    ⁢
                    
                      A
                      1
                      2
                    
                  
                
              
            
          
        
      
    
    
      
        (
        5
        )
      
    
  




where Cd is a discharge coefficient; and


Ql=u2A2.

18. A method according to claim 17, wherein:
said mass flow rates of the vapor and liquid phases of the two phase fluid are derived in accordance with the following equations


{dot over (m)}v=(αρv)2Ql 



{dot over (m)}l=(ρl(1−α))2Ql.

19. A method according to claim 18, wherein said enthalpy flux of the two phase fluid is derived from said mass flow rates of the vapor and liquid phases of the two phase fluid and enthalpy of the two phases at the measured temperature and pressure.

20. A method according to claim 11, wherein the two phase fluid comprises steam and water.