System and method for modeling a transient fluid level of a well

Abstract

The disclosed embodiments include a method for determining fluid level drop and formation permeability during wellbore stimulation of a shut-in stage in real time. The method includes receiving an initial permeability value of a formation surrounding a wellbore. Further, the method includes performing, and if necessary repeating at a defined time interval, the following steps until a flowrate of stimulation fluid reaches zero or until a new pumping stage begins. The steps include solving for the flowrate of the stimulation fluid in the wellbore and computing hydrostatic pressure and a computed temperature in the wellbore. Further, the steps include updating a permeability calculation of the formation based on the flowrate of the stimulation fluid.

What is claimed is: 
     
         1 . A method for determining fluid level drop and formation permeability during wellbore stimulation of a shut-in stage in real time, comprising:
 receiving an initial permeability value of a formation surrounding a wellbore; and   performing, and if necessary repeating at a defined time interval, the following steps until a flowrate of stimulation fluid reaches zero or until a new pumping stage begins:
 solving for the flowrate of the stimulation fluid in the wellbore; 
 computing hydrostatic pressure and a computed temperature in the wellbore; and 
 updating a permeability calculation of the formation based on the flowrate of the stimulation fluid. 
   
     
     
         2 . The method of  claim 1 , comprising:
 receiving a measured temperature from a distributed temperature sensing (DTS) system; and   updating the flowrate based on a comparison of the computed temperature and the measured temperature when an accuracy of the flowrate is not acceptable.   
     
     
         3 . The method of  claim 2 , wherein updating the flowrate when the accuracy of the flowrate is not acceptable comprises:
 determining whether the computed temperature is greater than the measured temperature;   when the computed temperature is greater than the measured temperature, doubling the flowrate; and   when the computed temperature is less than the measured temperature, dividing the flowrate by 1.75.   
     
     
         4 . The method of  claim 2 , comprising:
 determining whether the accuracy of the flowrate is acceptable, wherein determining whether the accuracy of the flowrate is acceptable comprises:
 determining whether a difference between the computed temperature and the measured temperature exceeds a tolerance value. 
   
     
     
         5 . The method of  claim 1 , comprising:
 computing a fluid level drop within the wellbore based on the flowrate; and   updating stimulation fluid presence in divisions of the wellbore based on the fluid level drop.   
     
     
         6 . The method of  claim 1 , wherein the permeability calculation of the formation is determined based on Darcy's law. 
     
     
         7 . The method of  claim 1 , wherein solving for the flowrate of the stimulation fluid in the wellbore comprises:
 calculating an individual flow rate of each division of the wellbore; and   adding together the individual flow rates of each division of the wellbore.   
     
     
         8 . The method of  claim 1 , wherein the initial permeability value of the formation is based on logs produced from core samples of the formation. 
     
     
         9 . The method of  claim 1 , wherein the stimulation fluid comprises fracturing fluid or acidizing fluid. 
     
     
         10 . The method of  claim 1 , wherein the defined time steps comprise one second increments of time. 
     
     
         11 . A system for determining formation permeability during wellbore stimulation, comprising:
 a distributed temperature sensing (DTS) system comprising a fiber optic cable extending a length of a wellbore, wherein the DTS system is configured to provide a real-time measurement of a measured temperature of the wellbore;   a controller communicatively coupled to the DTS system, the controller comprising a processor and a memory, wherein the memory comprises instructions, that when executed, cause the processor to:
 receive an initial permeability value of a formation surrounding the wellbore; and 
 perform, and if necessary repeat at a defined time interval, the following instructions until a flowrate of stimulation fluid reaches zero or until a new pumping stage begins:
 solve for the flowrate of the stimulation fluid in the wellbore; 
 compute hydrostatic pressure and computed temperature in the wellbore; 
 compare the computed temperature to the measured temperature to determine accuracy of the flowrate; 
 update the flowrate when the accuracy of the flowrate is not acceptable; and 
 update a permeability calculation of the formation based on the flowrate of the stimulation fluid. 
 
   
     
     
         12 . The system of  claim 11 , wherein the stimulation fluid comprises acidizing fluid or fracturing fluid. 
     
     
         13 . The system of  claim 11 , wherein the initial permeability value of the formation is based on logs produced from core samples of the formation. 
     
     
         14 . The system of  claim 11 , wherein determining the accuracy of the flowrate comprises:
 determining whether a difference between the computed temperature and the measured temperature exceeds a tolerance value.   
     
     
         15 . The system of  claim 11 , wherein the instructions that cause the processor to solve for the flowrate of the stimulation fluid in the wellbore comprise instructions that cause the processor to:
 calculate an individual flow rate of each division of the wellbore; and   add together the individual flow rates of each division of the wellbore.   
     
     
         16 . The system of  claim 11 , wherein the instructions that cause the processor to update the flowrate when the accuracy of the flowrate is not acceptable comprise instructions that cause the processor to:
 determine whether the computed temperature is greater than the measured temperature;   when the computed temperature is greater than the measured temperature, double the flowrate; and   when the computed temperature is less than the measured temperature, divide the flowrate by 1.75.   
     
     
         17 . A non-transitory machine-readable medium comprising instructions stored therein, which when executed by one or more processors, causes the one or more processors to perform operations comprising:
 receiving an initial permeability value of a formation surrounding a wellbore; and   performing, and if necessary repeating at a defined time interval, the following operations until a flowrate of stimulation fluid reaches zero or until a new pumping stage begins:
 solving for the flowrate of the stimulation fluid in the wellbore; 
 computing hydrostatic pressure and computed temperature in the wellbore; 
 receiving a measured temperature of the wellbore; 
 comparing the computed temperature to the measured temperature to determine accuracy of the flowrate; 
 updating the flowrate when the accuracy of the flowrate is not acceptable; and 
 updating a permeability calculation of the formation based on the flowrate of the stimulation fluid. 
   
     
     
         18 . The medium of  claim 17 , wherein receiving the measured temperature of the wellbore comprises receiving the measured temperature in real-time from a distributed temperature sensing (DTS) system. 
     
     
         19 . The medium of  claim 17 , wherein updating the flowrate when the accuracy of the flowrate is not acceptable comprises:
 determining whether the computed temperature is greater than the measured temperature;   when the computed temperature is greater than the measured temperature, doubling the flowrate; and   when the computed temperature is less than the measured temperature, dividing the flowrate by 1.75.   
     
     
         20 . The medium of  claim 17 , comprising recording the permeability calculation in a memory at each time step.