Method and system for coordinate transformation to model radial flow near a singularity

1. A method of representing a physical fluid reservoir using a computational system, said method comprising:

providing a finite element representation of a feature of said physical fluid reservoir in a first coordinate system, said finite element representation associated with a fluid flow characteristic of fluid within said physical fluid reservoir;

applying a coordinate transformation to said finite element representation for transforming said finite element representation from said first coordinate system into a second coordinate system;

generating through finite element analysis a fluid flow representation in said second coordinate system based on said transformed finite element representation, said fluid flow representation providing a substantially linear representation of said fluid flow characteristic with respect to said second coordinate system; and

displaying said fluid flow representation in a graphical user interface of said computational system.

2. The method of claim 1 , wherein providing said finite element representation of said physical fluid reservoir comprises generating a finite element mesh representative of said physical fluid reservoir.

3. The method of claim 1 , wherein said first coordinate system is a Cartesian coordinate system.

4. The method of claim 1 , wherein said second coordinate system is a modified radial coordinate system.

5. The method of claim 4 , wherein said modified radial coordinate system comprises the coordinates (s, θ, z), wherein s=ln(r).

6. The method of claim 1 , wherein said feature of said physical fluid reservoir is a well bore.

7. The method of claim 1 , wherein said feature of said physical fluid reservoir is a singularity.

8. The method of claim 7 , wherein said singularity is a well bore.

9. The method of claim 1 , wherein said fluid flow characteristic is pressure.

10. The method of claim 1 , wherein said physical fluid reservoir comprises a fracture or fault.

11. The method of claim 1 , further comprising the steps of:

providing a second finite element representation in said first coordinate system to model a second feature of said physical fluid reservoir;

generating a second fluid flow representation in said first coordinate system;

transforming said fluid flow representation to said first coordinate system; and

combining said transformed fluid flow representation and said second fluid flow representation in said first coordinate system to obtain a combined representation.

12. The method of claim 1 , wherein transforming said fluid flow representation comprises mapping from said first coordinate system to said second coordinate system.

13. The method of claim 1 , wherein said fluid flow representation represents radial fluid flow near a singularity.

14. The method of claim 13 , wherein said singularity is a well bore in said physical fluid reservoir.

15. The method of claim 1 , wherein applying said coordinate transformation is performed via computer executable software instructions.

16. A computer-readable medium containing a plurality of instructions embodying a method of representing a physical fluid reservoir using a computational system, said method comprising:

providing a finite element representation of a feature of said physical fluid reservoir in a first coordinate system, said finite element representation associated with a fluid flow characteristic of fluid within said physical fluid reservoir;

applying a coordinate transformation to said finite element representation for transforming said finite element representation from said first coordinate system into a second coordinate system;

generating through finite element analysis a fluid flow representation in said second coordinate system based on said transformed finite element representation, said fluid flow representation providing a substantially linear representation of said fluid flow characteristic with respect to said second coordinate system; and

displaying said fluid flow representation in a user interface of said computational system.

17. The computer-readable medium of claim 16 , wherein providing said finite element representation of said physical fluid reservoir comprises generating a finite element mesh representative of said physical fluid reservoir.

18. The computer-readable medium of claim 16 , wherein said first coordinate system is a Cartesian coordinate system.

19. The computer-readable medium of claim 16 , wherein said second coordinate system is a modified radial coordinate system.

20. The computer-readable medium of claim 19 , wherein said modified radial system comprises the coordinates (s, θ, z), wherein s=ln(r).

21. The computer-readable medium of claim 16 , wherein said feature of said physical fluid reservoir is a well bore.

22. The computer-readable medium of claim 16 , wherein said feature of said physical fluid reservoir is a singularity.

23. The computer-readable medium of claim 22 , wherein said singularity is a well bore.

24. The computer-readable medium of claim 16 , wherein said fluid flow characteristic is pressure.

25. The computer-readable medium of claim 16 , wherein said physical fluid reservoir comprises a fracture or fault.

26. The computer-readable medium of claim 16 , wherein said method further comprises:

providing a second finite element representation in said first coordinate system to model a second feature of said physical fluid reservoir;

generating a second fluid flow representation in said first coordinate system;

transforming said fluid flow representation to said first coordinate system; and

combining said transformed fluid flow representation and said second fluid flow representation in said first coordinate system to obtain a combined representation.

27. The computer-readable medium of claim 16 , wherein transforming said fluid flow representation comprises mapping from said first coordinate system to said second coordinate system.

28. The computer-readable medium of claim 16 , wherein said fluid flow representation represents radial fluid flow near a singularity.

29. The computer-readable medium of claim 28 , wherein said singularity is a well bore in said physical fluid reservoir.

30. The computer-readable medium of claim 16 , wherein said method is implemented using a graphical user interface.

31. A method of representing a physical fluid reservoir using a computational system, the method comprising:

providing a first finite element representation of feature of said physical fluid reservoir in a first coordinate system, said first finite element representation associated with a fluid flow characteristic of fluid within said physical fluid reservoir;

mapping said first finite element representation for transforming said first finite element representation from said first coordinate system into a second coordinate system;

generating through finite element analysis a first fluid flow representation in said second coordinate system based on said transformed first finite element representation, said first fluid flow representation providing a substantially linear representation of said fluid flow characteristic with respect to said second coordinate system;

mapping said first fluid flow representation to said first coordinate system;

providing a second finite element representation of said physical fluid reservoir in said first coordinate system, said second finite element representation associated with a second feature of said physical fluid reservoir;

generating a second fluid flow representation in said first coordinate system based on said second finite element representation; and

combining said mapped first fluid flow representation and said second fluid flow representation in said first coordinate system to obtain a combined fluid flow representation; and

displaying said combined fluid flow representation in a user interface of said computational system.

32. The method of claim 31 , wherein providing said first finite element representation includes generating a finite element mesh of said physical fluid reservoir.

33. The method of claim 31 , wherein said first coordinate system is a Cartesian coordinate system.

34. The method of claim 31 , wherein said second coordinate system is a modified radial coordinate system.

35. The method of claim 34 , wherein said modified radial coordinate system comprises the coordinates (s, θ, z), wherein s=ln(r).

36. The method of claim 31 , wherein said feature is a well bore.

37. The method of claim 31 , wherein said feature is a singularity.

38. The method of claim 37 , wherein said singularity is a well bore.