Wellbore Positioning System and Method
First Claim
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.
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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.
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Citations
16 Claims
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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:
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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. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 16)
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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:
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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. - View Dependent Claims (13, 14)
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Specification