Rapid Method for Reservoir Connectivity Analysis Using a Fast Marching Method

• US 20080154505A1
• Filed: 04/10/2006
• Published: 06/26/2008
• Est. Priority Date: 05/26/2005
• Status: Active Grant

• Current Assignee: Chul-Sung Kim, Mark Dobin
• Original Assignee: Chul-Sung Kim, Mark Dobin
• Inventors: Kim, Chul-Sung, Dobin, Mark
• Granted Patent: US 7,565,243 B2
• Time in Patent Office: Days
• US Class Current: 702/2
• CPC Class Codes: E21B 43/00 Methods or apparatus for obtaining oil, gas, water, soluble or meltable materials or a slurry of minerals from wells applicable only to water E03B
• CPC Class Codes: G01V 1/302 in 3D data cubes
• CPC Class Codes: G01V 20/00 Geomodelling in general
• CPC Class Codes: G01V 2210/641 Continuity of geobodies
• CPC Class Codes: G01V 2210/644 Connectivity, e.g. for fluid movement

Abstract

Methods for analyzing the connected quality of a hydrocarbon reservoir are disclosed. A model of a portion of the reservoir is divided into cells, each cell having a volume and some attributes, and wherein a speed function is assigned to a portion of the cells. A reference cell is chosen. A connectivity between cells in the reservoir is determined by solving an Eikonal equation that describes the travel time propagation, said propagating front progressing outward from a reference cell until an ending condition is met, said Eikonal equation being solved by a fast marching method with propagation velocity as a function of spatial position being provided by the speed function. Regions of the reservoir are characterized by their connective quality to the reference cell using the connectivity.

Claims

1. A method for analyzing the connected quality of a hydrocarbon reservoir, said method comprising:

(a) obtaining a model of a portion of the reservoir and dividing it into cells, each cell having a volume and some attributes;

(b) assigning a speed function to a portion of the cells;

(c) choosing a reference cell;

(d) determining a connectivity between cells in the reservoir by solving an Eikonal equation, describing a propagating front in a heterogeneous medium, said front progressing outward from a reference cell until an ending condition is met, said Eikonal equation being solved by a fast marching method with propagation velocity as a function of spatial position being provided by the speed function; and

(e) characterizing regions of the reservoir by their connective quality to the reference cell using the connectivity.

2. A method according to claim 1 wherein:

the ending condition is met when a preselected minimum connectivity is reached.

3. A method according to claim 1 wherein:

the ending condition is met when a preselected distance from the reference cell is reached.

4. A method according to claim 1 wherein:

the ending condition is met when the connectivity of a target object cell is determined.

5. A method according to claim 1 further comprising:

determining an optimum connected path from a reference cell to another cell in the reservoir by generating a gradient of the connectivity of the cells and backtracking from the other cell to the reference cell using the gradient.

6. A method according to claim 5 further comprising:

determining a cumulative attribute along the optimum connected path by totaling a desired attribute of cells along the path.

7. A method according to claim 5 further comprising:

determining the tortuosity of the optimum path by dividing the length of the path by the shortest line between the reference cell and the other cell.

8. A method according to claim 1 further comprising:

totaling desirable attributes of all cells with a connectivity greater than a preselected value.

9. A method according to claim 1 wherein step (c) comprises choosing multiple reference cells at different locations from each other in the reservoir the method further comprising:

performing step (d) and step (e) with respect to each reference cell chosen; and

individually totaling the connectivities for each cell in the reservoir with respect the reference cells chosen in step (c).

10. A method according to claim 9 wherein:

the ending condition is met when a preselected minimum connectivity is reached.

11. A method according to claim 9 wherein:

the ending condition is met when the connectivity of a target object cell is determined.

12. A method according to claim 9 wherein:

the ending condition is met when a preselected distance from the reference cell is reached.

13. A method according to claim 9 further comprising totaling desirable attributes of cells with a total connectivity greater than a preselected connectivity value.

14. A method according to claim 9 further comprising:

determining an optimal path between a first and a second reference cell by way of a desired cell by;

generating a gradient of connectivities with respect the first reference cell and backtracking from the desired cell to the first reference cell using the gradient; and

generating a gradient of connectivities with respect the second reference cell and backtracking from the desired cell to the second reference cell using the gradient.

15. A method according to claim 14 further comprising:

determining an nth optimal path between a first and a second reference cell by;

ranking the cells in the reservoir by the cells'"'"' total connectivity;

choosing the cell or cells with the nth ranked total connectivity as the desired cell.

16. A method of claim 1 wherein step (c) comprises choosing a portion of the cells in the reservoir as reference cells the method further comprising:

performing step (d) and step (e) with respect to each reference cell chosen; and

determining a total desirable attribute, V_boundary, for each reference cell by totaling desirable attributes of all the cells in the reservoir with a connectivity with respect to the reference cell greater than a preselected value.

17. A method according to claim 16 wherein:

the ending condition is met when the connectivity of a target object cell is determined.

18. A method according to claim 16 wherein the cells have corresponding cell indices wherein:

the portion of the cells chosen as reference cells comprises cells for which the total of the corresponding cell indices may be even the method further comprising;

determining a V_boundary for the cells in the reservoir not chosen as reference cells using an average of the V_boundary of neighboring cells that were chosen as reference cells.

19. A method according to claim 16 wherein the cells have corresponding cell indices wherein:

the portion of the cells chosen as reference cells comprises cells for which the corresponding cell indices are all even or all odd the method further comprising;

determining a V_boundary for the cells in the reservoir not chosen as reference cells using an average of the V_boundary of neighboring cells that were chosen as reference cells.

20. A method according to claim 1 wherein:

the speed function is determined using geological attributes.

21. A method according to claim 1 wherein:

the fast marching method is adapted to restrict front propagation to one or more specified directions.

22. A method according to claim 21 wherein:

the speed function is determined by a direction of front propagation of the fast marching method.

23. The method of claim 1 wherein:

the speed function is generated using porosity data.

24. The method of claim 23 wherein:

the speed function is a linear function.

25. The method of claim 23 wherein:

the speed function is a nonlinear function.

26. The method of claim 23 wherein:

the nonlinear function is a step function.