Real-time well trajectory projection using stochastic processes

Abstract

Systems and methods for stochastically projecting a well trajectory of a bottom hole assembly in a subsurface formation, where the bottom hole assembly includes one or more transducers, a trajectory controller coupled to the bottom hole assembly, an information handling system coupled to the transducers, and the information system includes a processor, and a non-transitory computer readable medium for storing one or more instructions that, when executed, causes the processor to receive a first one or more system model parameters from a system model parameter probability distribution; receive a first one or more steering inputs; receive a first one or more values corresponding to the bottom hole assembly initial conditions from the one or more transducers at a first position within a subsurface formation; and stochastically project a trajectory of the bottom hole assembly from the first position within the subsurface formation to a second position within the subsurface formation.

What is claimed is: 
     
         1 . A method for stochastically projecting a well trajectory of a bottom hole assembly in a subsurface formation, the method comprising:
 receiving a first one or more system model parameters from a system model parameter probability distribution;   receiving a first one or more steering inputs;   receiving a first one or more values corresponding to the bottom hole assembly initial conditions at a first position within the subsurface formation; and   stochastically projecting a first one or more trajectories of the bottom hole assembly from the first position within the subsurface formation to a second position within the subsurface formation based at least in part on one or more of the first one or more system model parameters, the first one or more steering inputs, and the first one or more values corresponding to the bottom hole assembly initial conditions.   
     
     
         2 . The method of  claim 1  further comprising stochastically projecting the first confidence region between the first position and the second position based at least in part one or more of the first one or more stochastically projected trajectories, the first one or more system model parameters, the received one or more steering inputs, and the received one or more values corresponding to the bottom hole assembly initial conditions. 
     
     
         3 . The method of  claim 2  further comprising providing one or more of the first one or more stochastically projected trajectories and the first confidence region to one or more of a display and a trajectory controller. 
     
     
         4 . The method of  claim 2  further comprising discarding one or more outliers in the first one or more stochastically projected trajectories of the bottom hole assembly before stochastically projecting the first confidence region. 
     
     
         5 . The method of  claim 1  further comprising advancing the bottom hole assembly from the first position to the second position. 
     
     
         6 . The method of  claim 5  further comprising stochastically projecting a second one or more trajectories of the bottom hole assembly from the second position to a third position based at least in part on one or more of the first one or more system model parameters, the received one or more steering inputs, and the received one or more values corresponding to the bottom hole assembly initial conditions. 
     
     
         7 . The method of  claim 5  further comprising receiving a second one or more system model parameters from the system model parameter probability distribution, stochastically projecting a second one or more trajectories of the bottom hole assembly from the second position to a third position based at least in part on one or more of the second one or more system model parameters, the received one or more steering inputs, and the received one or more values corresponding to the bottom hole assembly initial conditions. 
     
     
         8 . The method of  claim 1 , wherein the first one or more system model parameters are randomly selected from the system model parameter probability distribution. 
     
     
         9 . The method of  claim 1 , further comprising generating a second one or more one or more steering inputs and stochastically projecting a second one or more trajectories of the bottom hole assembly from the second position to a third position based at least in part on one or more of the selected one or more system model parameters, the second one or more steering inputs, and the received one or more values corresponding to the bottom hole assembly initial conditions. 
     
     
         10 . The method of  claim 1 , wherein the stochastically projecting a first one or more trajectories of the bottom hole assembly occurs in real-time. 
     
     
         11 . The method of  claim 3  selecting a second one or more steering inputs based at least in part on one or more of the first one or more stochastically projected trajectories and the first confidence region to one or more of a display and a trajectory controller. 
     
     
         12 . The method of  claim 5  further comprising:
 receiving a second one or more system model parameters from the system model parameter probability distribution; 
 receiving a second one or more steering inputs; 
 receiving a second one or more values corresponding to the bottom hole assembly initial conditions at a second position within the subsurface formation; and 
 stochastically projecting a second one or more trajectories of the bottom hole assembly from the second position in the subsurface formation to a third position in the subsurface formation based at least in part on one or more of the second one or more system model parameters, the second one or more steering inputs, and the second one or more values corresponding to the bottom hole assembly initial conditions. 
 
     
     
         13 . A system for stochastically projecting a well trajectory of a bottom hole assembly, the system comprising:
 a bottom hole assembly comprising one or more transducers;   a trajectory controller coupled to the bottom hole assembly.   an information handling system coupled to the transducers, the information system comprising:
 a processor, and 
 a non-transitory computer readable medium for storing one or more instructions that, when executed, causes the processor to:
 receive a first one or more system model parameters from a system model parameter probability distribution; 
 receive a first one or more steering inputs; 
 receive a first one or more values corresponding to the bottom hole assembly initial conditions from the one or more transducers at a first position within a subsurface formation; and 
 stochastically project a first one or more trajectories of the bottom hole assembly from the first position within the subsurface formation to a second position within the subsurface formation based at least in part on one or more of the first one or more system model parameters, the first one or more steering inputs, and the first one or more values corresponding to the bottom hole assembly initial conditions. 
 
   
     
     
         14 . The system of  claim 13 , wherein the one or more instructions that, when executed, further causes the processor to stochastically project a confidence region for the projected trajectory of the bottom hole assembly between the first position within the subsurface formation to the second position within the subsurface formation. 
     
     
         15 . The system of  claim 14 , wherein the system further comprises a display and wherein the one or more instructions that, when executed, further causes the processor to provide one or more of the first one or more stochastically projected trajectories and the first confidence region to one or more of the display and the trajectory controller. 
     
     
         16 . The system of  claim 13 , wherein the one or more instructions that, when executed, further causes the processor to randomly select the first one or more system model parameters from the system model parameter probability distribution. 
     
     
         17 . The system of  claim 14 , wherein the one or more instructions that, when executed, further causes the processor to one or more of stochastically project the trajectory of the bottom hole assembly or stochastically project the confidence region for the projected trajectory of the bottom hole assembly in real time. 
     
     
         18 . The system of  claim 13 , wherein the one or more instructions that, when executed, further causes the processor to:
 receive a second one or more system model parameters from the system model parameter probability distribution;   receive a second one or more steering inputs; receive a second one or more values corresponding to the bottom hole assembly initial conditions at the second position within the subsurface formation; and   stochastically project a second one or more trajectories of the bottom hole assembly from the second position in the subsurface formation to a third position in the subsurface formation based at least in part on one or more of the second one or more system model parameters, the second one or more steering inputs, and the second one or more values corresponding to the bottom hole assembly initial conditions.   
     
     
         19 . A method for stochastically projecting a well trajectory of a bottom hole assembly in a subsurface formation in real time, the method comprising:
 receiving a first one or more system model parameters from a system model parameter probability distribution;   receiving a first one or more steering inputs;   receiving a first one or more values corresponding to the bottom hole assembly initial conditions at a first position within the subsurface formation;   stochastically projecting a first one or more trajectories of the bottom hole assembly from the first position within the subsurface formation to a second position within the subsurface formation;   advancing the bottom hole assembly from the first position to the second position;   receiving a second one or more system model parameters from the system model parameter probability distribution;   receiving a second one or more steering inputs;   receiving a second one or more values corresponding to the bottom hole assembly initial conditions at a second position within the subsurface formation; and   stochastically projecting a second one or more trajectories of the bottom hole assembly from the second position within the subsurface formation to a third position within the subsurface formation.   
     
     
         20 . The method of  claim 19 , further comprising stochastically projecting a first one or more confidence regions based on the stochastically projected first one or more trajectories of the bottom hole assembly between the first position within the subsurface formation and the second position within the subsurface formation and further comprising stochastically projecting a second one or more confidence regions based on the stochastically projected second one or more trajectories of the bottom hole assembly between the second position within the subsurface formation and the third position within the subsurface formation.