Systems and methods for interpreting multi-phase fluid flow data

Abstract

Methods and systems are disclosed for interpreting multi-phase fluid flow in a conduit, such as a pipe in a wellbore. The method involves curve fitting holdup data sets and velocity data sets together wherein the second curve comprises a shape mutual to the first curve with an independent gain and an independent offset, and determining flow rates through the pipe.

What is claimed: 
     
         1 . A method, comprising:
 obtaining, from one or more holdup sensors, holdup measurements of a fluid flow in a conduit;   obtaining, from one or more flow velocity sensors, velocity measurements of the fluid flow in the conduit;   using one or more processors, fitting a first curve to a first set of the holdup measurements and a first set of the velocity measurements;   using one or more processors, fitting a second curve to a second set of the holdup measurements and a second set of the velocity measurements, wherein the second curve comprises a shape mutual to the first curve with an independent gain and an independent offset; and   determining a flow rate of the fluid flow based on the first and second curve.   
     
     
         2 . The method of  claim 1 ,
 wherein the first set is the set of holdup measurements and the second set is the set of velocity measurements; and   wherein the first curve is a holdup profile and the second curve is a velocity profile.   
     
     
         3 . The method of  claim 1 , wherein the first curve comprises one of a function with a linear fit to the measurements; a function with spline interpolations; and a function with spline interpolations and a constant projection. 
     
     
         4 . The method of  claim 1 , wherein the first curve comprises a hyperbolic tangent curve with at least two adjustable curve-fitting coefficients. 
     
     
         5 . The method of  claim 1 , further comprising:
 modifying one of the first and second curves that is fitted to the velocity measurements according to Prandtl's law at a wall of the conduit, wherein the modified curve comprises a velocity profile.   
     
     
         6 . The method of  claim 1 , further comprising:
 modifying one of the first and second curves that is fitted to the set of velocity measurements based on an averaging effect of the velocity measurements, wherein the modified curve is a modified velocity profile; and   generating a fluid flow rate with a holdup profile and the modified velocity profile.   
     
     
         7 . The method of  claim 1 , further comprising:
 generating a first curve-fitting error for the first curve;   generating a second curve-fitting error for the second curve;   generating a total curve-fitting error as a sum of the first and second curve-fitting errors; and   rejecting the set of holdup measurements and the set of velocity measurements when the total curve-fitting error is above a threshold.   
     
     
         8 . The method of  claim 7 , further comprising:
 validating the set of holdup measurements and the set of velocity measurements when the total curve-fitting error is equal to or below the threshold; and   adjusting at least one curve-fitting parameter of the first curve and the second curve to minimize the total curve-fitting error.   
     
     
         9 . The method of  claim 1 , wherein the fluid flow comprises a gas or a vapor. 
     
     
         10 . A method for interpreting measurements of a fluid flow in a conduit, comprising:
 obtaining at least one fluid holdup measurement from a holdup sensor;   obtaining at least one velocity measurement from a flow velocity sensor;   using one or more processors, fitting a first curve to one of the fluid holdup measurement and the velocity measurement;   using the first curve constrained by the other of the fluid holdup measurement and the velocity measurement to form a second curve, and   determining a flow rate of the fluid flow based on the first and second curves.   
     
     
         11 . The method of  claim 10 , wherein the fluid flow comprises a gas or a vapor. 
     
     
         12 . A system for interpreting measurements of a fluid flow in a conduit, comprising:
 a holdup sensor to obtain fluid holdup measurements;   a flow velocity sensor to obtain velocity measurements;   a processor in electronic communication with the holdup sensor and the flow velocity sensor, the processor fitting a first curve to a first set of fluid holdup measurements and a first set of velocity measurements and fitting a second curve to a second set of fluid holdup measurements and a second set of velocity measurements;   wherein the second curve is fitted using the first curve constrained by at least one of the second set of fluid holdup measurements or the second set of velocity measurements, and wherein the first curve and the second curve comprise a fluid holdup profile and a velocity profile.   
     
     
         13 . The system of  claim 12 , wherein the second curve has a same shape of the first curve with an independent gain and an independent offset and wherein the first curve and the second curve comprise a fluid holdup profile and a velocity profile. 
     
     
         14 . The system of  claim 12 , wherein the first curve is a hyperbolic tangent curve with two adjustable curve-fitting coefficients. 
     
     
         15 . The system of  claim 12 , wherein the fluid flow comprises a gas or a vapor. 
     
     
         16 . The system of  claim 12 , wherein the processor comprises a computer readable data storage in electronic communication with the processor that stores the set of fluid holdup measurements and the set of velocity measurements. 
     
     
         17 . The system of  claim 16 , wherein the computer readable data storage further comprises computer executable instructions that, when executed by the processor, causes the processor to compute a fluid flow rate in the conduit. 
     
     
         18 . The system of  claim 16 , wherein the computer readable data storage further comprises computer executable instructions that, when executed by the processor, causes the processor to constrain a fluid holdup profile by one measurement of the set of velocity measurements. 
     
     
         19 . The system of  claim 16 , wherein the computer readable data storage further comprises computer executable instructions that, when executed by the processor, cause the processor to constrain a velocity profile by one measurement of the set of fluid holdup measurements. 
     
     
         20 . The system of  claim 16 , wherein the computer readable data storage further comprises computer executable instructions that, when executed by the processor, cause the processor to:
 compute a total curve-fitting error as a function of a first curve-fitting error for the first curve and a second curve-fitting error for the second curve; and   reject the set of velocity measurements and the set of fluid holdup measurements when the total curve-fitting error exceeds a threshold.