Method for determining a karstic region

1. A method for mapping a karstic region modified by karstification phenomena, comprising:

a/ creating a geological model of the karstic region comprising cells, the geological model is a gridded matrix of a subsoil area based on a plurality of subsoil measurements, said model comprising at least one seed zone comprising cells of the model, the seed zone including an area of the subsoil having an epikarst, a known fracture or a similar geological phenomenon, and at least one target zone comprising cells of the model, each cells of the model having coordinates;

b/ determining a seed cell in the cells of the at least one seed zone;

c/ determining a target cell in the cells of the at least one target zone;

d/ if a distance between the seed cell and the target cell is above a predetermined distance:

d1/ determining a bifurcation zone based at least on the coordinates of the seed cell, the coordinates of the target cell, a distance distribution, and an angular distribution,

d2/ determining a bifurcation cell in said bifurcation zone;

d3/ re-iterating step d/ with a cell based on said bifurcation cell as the seed cell;

e/ determining trajectory cells in the geological model based on the seed cell, the target cell and bifurcation cells determined in step d/;

f/ for each current cells in the trajectory cells,

f1/ determining conduits characteristics based on a predetermined conduit density distribution, a predetermined conduit aperture distribution and trajectory cells connected to said current cell;

f2/ determining cell characteristics based on the conduits characteristics of said current cell;

g/ determining a reservoir in said karstic region based on determined conduits characteristics and determined cell characteristics;

h/ displaying a revised geological model of the subsoil with the reservoir based on the determined conduit characteristics and determined cell characteristics; and

i/ drilling a well based on the display of the revised geological model.

2. A method according to claim 1 , wherein steps b/ to f/ are re-iterated a plurality of times with same seed zone and target zone.

3. A method according to claim 1 , wherein said model comprising a plurality of seed zones and a plurality of target zones, steps b/ to f/ are re-iterated a plurality of times with different combination of seed zone in the plurality of seed zones and target zone in the plurality of target zones.

4. A method according to claim 1 , wherein the seed cell is determined in step b/ according a stochastic process and according a predetermined distribution in the at least one seed zone.

5. A method according to claim 1 , wherein the target cell is determined in step c/ according a stochastic process and according a predetermined distribution in the at least one target zone.

6. A method according to claim 1 , wherein the cell based on said bifurcation cell is said bifurcation cell.

7. A method according to claim 1 , wherein the cell based on said bifurcation cell is a cell corresponding to a projection of the bifurcation cell on a line defined by the seed cell and the target cell.

8. A method according to claim 1 , wherein determining trajectory cells is performed by:

ordering the bifurcation cells according to an order of determination in step d/in a list of cells;

adding the seed cell at a first position in said list of cells;

adding the target cell at a last position in said list of cells;

determining segments in the model between two consecutive cells in the list of cells; and

determining cells of the model based on an approximation line algorithm.

9. A method according to claim 8 , wherein the approximation line algorithm is one algorithm in a group comprising the Bresenham algorithm, the DDA algorithm, and the Run-Slice computational algorithm.

10. A method according to claim 1 , wherein determining trajectory cells is performed by:

ordering the bifurcation cells according to an order of determination in step d/ in a list of cells;

adding the seed cell at a first position in said list of cells;

adding the target cell at a last position in said list of cells;

determining an interpolation curve fitting the list of cells in the model; and

determining cells of the model based on an approximation curve algorithm.

11. A method according to claim 1 , wherein, determining conduits characteristics comprises:

the cell being a 2D cell, for each direction of space perpendicular to at least one edge of the current cell, if an edge of said current cell perpendicular to said direction is shared with a trajectory cell connected to said current cell, determining at least one conduit in said current cell in said direction, a radius r c of said conduit is determined in said predetermined conduit aperture distribution, or

the cell being a 3D cell, for each direction of space perpendicular to at least one side of the current cell, if a side of said current cell perpendicular to said direction is shared with a trajectory cell connected to said current cell, determining at least one conduit in said current cell in said direction, a radius r c of said conduit is determined in said predetermined conduit aperture distribution.

12. A method according to claim 11 , wherein determining cell characteristics comprises:

receiving initial porosity characteristic ϕ m of the current cell;

setting the equivalent porosity ϕ eq to ϕ m ;

for at least one current conduit in the current cell in said direction,

computing a porosity ϕ temp of the current cell based on

ϕ

eq

(

1

-

S

c

S

)

+

S

c

S

 where S c being a section of the current conduit and S being a section of said edge or side of said current cell perpendicular to said direction and shared with a trajectory cell;

setting the equivalent porosity ϕ eq to ϕ temp .

13. A method according to claim 12 , wherein determining cell characteristics further comprises:

receiving initial permeability characteristic K m of the current cell;

setting the equivalent permeability K eq to K m ;

for at least one current conduit in the current cell in said direction,

computing the permeability K temp of the current cell based on

K

eq

(

1

-

S

c

S

)

+

K

c

⁢

S

c

S

 where S c being a section of the current conduit, S being a section of said edge or side of said current cell perpendicular to said direction and shared with a trajectory cell and where K c is the permeability of the current conduit;

setting the equivalent permeability K ee to K temp .

14. A method according to claim 13 , wherein permeability of the current conduit is computed based on

N

c

S

·

π

⁢

⁢

r

c

4

8

⁢

10

15

.

15. A method according to claim 1 , wherein determining conduits characteristics comprises:

the cell being a 2D cell, for each direction of space perpendicular to at least one edge of the current cell, if a edge of said current cell perpendicular to said direction is shared with a trajectory cell connected to said current cell,

determining a number N c of conduits to be determined based on said predetermined conduit density distribution;

determining N c conduits in said current cell in said direction; or

the cell being a 3D cell, for each direction of space perpendicular to at least one side of the current cell, if a side of said current cell perpendicular to said direction is shared with a trajectory cell connected to said current cell,

determining a number N c of conduits to be determined based on said predetermined conduit density distribution;

determining N c conduits in said current cell in said direction.

16. A method according to claim 15 , wherein determining cell characteristics comprises:

receiving initial porosity characteristic ϕ m of the current cell;

setting the equivalent porosity ϕ eq to ϕ m ;

for at least one current conduit in the current cell in said direction,

computing a porosity ϕ temp of the current cell based on

ϕ

eq

(

1

-

S

c

S

)

+

S

c

S

 where S c being a section of the current conduit and S being a section of said edge or side of said current cell perpendicular to said direction and shared with a trajectory cell;

setting the equivalent porosity ϕ eq to ϕ temp .

17. A method according to claim 16 , wherein determining cell characteristics further comprises:

receiving initial permeability characteristic K m of the current cell;

setting the equivalent permeability K eq to K m ;

for at least one current conduit in the current cell in said direction,

computing the permeability K temp of the current cell based on

K

eq

(

1

-

S

c

S

)

+

K

c

⁢

S

c

S

 where S c being a section of the current conduit, S being a section of said edge or side of said current cell perpendicular to said direction and shared with a trajectory cell and where K c is the permeability of the current conduit;

setting the equivalent permeability K eq to K temp .

18. A method according to claim 17 , wherein permeability of the current conduit is computed based on

N

c

S

·

π

⁢

⁢

r

c

4

8

⁢

10

15

.

19. A non-transitory computer readable storage medium, having stored thereon a computer program comprising program instructions, the computer program being loadable into a data-processing unit and adapted to cause the data-processing unit to carry out the steps of claim 1 when the computer program is run by the data-processing device.