Wellbore Positioning System and Method

Abstract

A method and a system are provided for determining the relative positions of a wellbore and an object. The wellbore is represented by a first ellipse and the object is represented by a second ellipse. The first ellipse represents the positional uncertainty of the wellbore and the second ellipse represents the positional uncertainty of the object. The method includes receiving input data relating to a measured or estimated position of the wellbore and the object. In addition, the method includes calculating an expansion factor representing an amount by which one, or both, of the first ellipse and the second ellipse can be expanded with respect to one or both of respective first and second sets of elliptical parameters so that the first and second ellipses osculate. Further, the method includes determining, based on the calculated expansion factor, position data indicative of the relative positions of the wellbore and the object.

1 . A computer-implemented method for determining the relative positions of a wellbore and an object, the wellbore being represented by a first ellipse and the object being represented by a second ellipse, wherein the first ellipse represents a positional uncertainty of the wellbore and the second ellipse represents a positional uncertainty of the object, the method comprising the steps of:
 receiving input data relating to a measured or estimated position of the wellbore and the object, the position of the wellbore having a first set of parameters defining the first ellipse, and the position of the object having a second set of parameters defining the second ellipse;   calculating an expansion factor representing an amount by which one, or both, of the first ellipse and the second ellipse can be expanded with respect to one or both of respective first and second sets of elliptical parameters so that the first and second ellipses osculate, wherein calculating the expansion factor comprises determining and solving a quartic equation that is based on the geometry of the first and second ellipses; and   determining, based on the calculated expansion factor, position data indicative of the relative positions of the wellbore and the object.   
     
     
         2 . The method of  claim 1 , wherein the first and second ellipses are expanded equally, and wherein the calculation of the expansion factor further comprises:
 solving the quartic equation to determine a distance between a centre of the first ellipse and a centre of the second ellipse when the second ellipse is translated towards the first ellipse along a line joining the centres of the first and second ellipses so that the first and second ellipses osculate; and   calculating the expansion factor based on the determined distance and a scale factor.   
     
     
         3 . The method of  claim 1 , wherein either the first and second ellipses are expanded equally, or one of the first and second ellipses is expanded, so that the first and second ellipses osculate, and wherein the calculation of the expansion factor further comprises:
 applying the first and second sets of elliptical parameters to a polynomial equation, the solution of which represents a separation condition of the ellipses;   determining the quartic equation from the polynomial equation; and   solving the quartic equation to calculate the expansion factor.   
     
     
         4 . The method of  claim 3 , wherein the ellipses osculate when the polynomial equation has a double root. 
     
     
         5 . The method of  claim 1 , wherein the wellbore is a first planned or drilled wellbore, and the object is a second planned or drilled wellbore. 
     
     
         6 . The method of  claim 1 , wherein the object is a sub-surface hazard. 
     
     
         7 . The method of  claim 1 , wherein the first and second sets of elliptical parameters are derived from a measured or estimated position of the wellbore and the object. 
     
     
         8 . The method of  claim 1 , further comprising the step of determining a trajectory of the wellbore in a three-dimensional simulation. 
     
     
         9 . The method of  claim 1 , further comprising the step of optimising the position of the wellbore relative to the object. 
     
     
         10 . A computer-implemented method for determining one or more operating modes of a wellbore drilling system, the wellbore drilling system being arranged to drill a wellbore in a rock formation, the method comprising the steps of:
 receiving position data determined according to the method of  claim 1 ;   inputting said position data into a wellbore trajectory model;   operating the wellbore trajectory model so as to generate trajectory data indicative of a trajectory of the wellbore; and   determining, on the basis of the trajectory data, said one or more operating modes of the wellbore drilling system.   
     
     
         11 . The method of  claim 10 , further comprising the steps of:
 automatically configuring a controller of the wellbore drilling system with the one or more operating modes determined by the wellbore positioning system; and   applying the one or more operating modes.   
     
     
         12 . A wellbore positioning system arranged to determine the relative positions of a wellbore and an object, the wellbore being represented by a first ellipse and the object being represented by a second ellipse, wherein the first ellipse represents a positional uncertainty of the wellbore and the second ellipse represents a positional uncertainty of the object, the system comprising:
 data receiving means arranged to receive input data relating to a measured or estimated position of the wellbore and the object, the position of the wellbore having a first set of parameters defining the first ellipse, and the position of the object having a second set of parameters defining the second ellipse;   expansion factor calculation means arranged to calculate an expansion factor representing an amount by which one, or both, of the first ellipse and the second ellipse can be expanded with respect to one or both of respective first and second sets of elliptical parameters so that the first and second ellipses osculate, wherein calculating the expansion factor comprises determining and solving a quartic equation that is based on the geometry of the first and second ellipses; and   position determining means arranged to determine, based on the calculated expansion factor, position data indicative of the relative positions of the wellbore and the object.   
     
     
         13 . The wellbore positioning system of  claim 12 , further comprising operating mode determining means arranged to determine, on the basis of the position data, one or more operating modes of a wellbore drilling system. 
     
     
         14 . The wellbore positioning system of  claim 12 , the system being operatively connected to a controller of the wellbore drilling system such that the controller of the wellbore drilling system is automatically configured with the one or more operating modes determined by the wellbore positioning system, the controller being arranged to apply the one or more operating modes. 
     
     
         15 . A computer program product comprising a set of instructions which, when executed by a computing device, is configured to cause the computing device to carry out the method according to  claim 1 . 
     
     
         16 . The computer program product of  claim 15 , comprising a computer readable storage medium.