Rapid method for reservoir connectivity analysis using a fast marching method
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.
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, the speed function representing how hydrocarbons or other fluids flow through 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 the 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 the reference cell to another cell in the reservoir by generating a gradient of the connectivity of the cells and backtracking from said another 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 said another 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 to 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 to 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 to 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 evens 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 wave propagation to one or more specified directions.
22. A method according to claim 21 wherein:
the speed function is determined by a direction of wave 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 speed function is a step function.
27. The method of claim 1 , further comprising:
producing hydrocarbons from the characterized regions.