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1. (WO2017003828) MODÉLISATION DE LA SATURATION ET DE LA PERMÉABILITÉ D'UN RÉSERVOIR DE CHAMP PÉTROLIFÈRE
Note: Texte fondé sur des processus automatiques de reconnaissance optique de caractères. Seule la version PDF a une valeur juridique

Claims

What is claimed is:

1. A method for modeling saturation in a reservoir, comprising:

obtaining capillary pressure data representing capillary pressure in the reservoir;

obtaining permeability data representing permeability in the reservoir;

determining a number of pore throats represented by the capillary pressure data;

creating hyperbolic tangents based on the capillary pressure data equal in number to the number of pore throats;

combining hyperbolic tangents to create a curve to fit the capillary pressure data and to define hyperbolic tangent parameters;

combining at least one of the hyperbolic tangent parameters with the permeability data to define a saturation height function;

modeling a saturation in the reservoir using the saturation height function; and displaying the saturation model based on the saturation height function,

wherein the determining the number of pore throats comprises creating an initial capillary pressure curve to identify the number of pore throats represented by the capillary pressure data.

2. The method of claim 1, wherein the determining the number of pore throats comprises: creating the initial capillary pressure curve using a predetermined number of multiple linked hyperbolic tangents;

determining a first derivative of the capillary pressure curve; and

determining a number of local minima in the capillary pressure curve,

wherein the number of pore throats represented by the capillary pressure data corresponds to the number of local minima.

3. The method of claim 2, wherein the predetermined number of hyperbolic tangents is equal or greater to the number of pore throats to be identified in the capillary pressure data.

4. The method of claim 1, wherein the at least one hyperbolic tangent parameter has a linear relationship with the logarithm of the obtained permeability data.

5. The method of claim 1, wherein each of the respective hyperbolic tangents is created for a unique one of the respective pore throats, such that no two of the hyperbolic tangents are created for the same one of the pore throats.

6. The method of claim 1, wherein the hyperbolic tangents are defined by the following equation:

/(Ρ5 }¾Λ) = i +
- an),tarih(wn.{P ~~ tn}) with constraints:

<r„. > 0, Vn€ [ N] n.. N e H

,i < %, [1, N ~~ 1] ft, i¥€

where P represents a logarithmic transform of a normalized capillary pressure and N represents the number of hyperbolic tangents.

7. The method of claim 6, wherein the hyperbolic tangent parameter tn has a linear relationship with the logarithm of the obtained permeability data as defined by the following equation:


where K represents the obtained permeability data.

8. The method of claim 7, wherein the saturation height function is defined by the following equation:

9. The method of claim 1, wherein combining of the hyperbolic tangents to create the curve to fit the capillary pressure data and to define the hyperbolic tangent parameters comprises using a non-linear least-square process.

10. A non-transitory computer-readable medium storing instructions that, when executed by one or more processors of a computing system, cause the computing system to perform operations, the operations comprising:

obtaining capillary pressure data representing capillary pressure in a reservoir;

obtaining permeability data representing permeability in the reservoir;

determining a number of pore throats represented by the capillary pressure data;

creating hyperbolic tangents based on the capillary pressure data equal in number to the number of pore throats;

combining hyperbolic tangents to create a curve to fit the capillary pressure data and to define hyperbolic tangent parameters;

combining at least one of the hyperbolic tangent parameters with the permeability data to define a saturation height function;

modeling a saturation in the reservoir using the saturation height function; and displaying the saturation model based on the saturation height function.

11. The non-transitory computer-readable medium of claim 10, wherein the predetermined number of hyperbolic tangents is equal or greater to the number of pore throats to be identified in the capillary pressure data.

12. The non-transitory computer-readable medium of claim 1 1, wherein the determining the number of pore throats comprises:

creating the initial capillary pressure curve using a predetermined number of multiple linked hyperbolic tangents;

determining a first derivative of the capillary pressure curve; and

determining a number of local minima in the capillary pressure curve,

wherein the number of pore throat represented by the capillary pressure data corresponds to the number of local minima, and

wherein the determining the number of pore throats comprises creating an initial capillary pressure curve to identify the number of pore throats represented by the capillary pressure data.

13. The non-transitory computer-readable medium of claim 10, wherein each of the respective hyperbolic tangents is created for a unique one of the respective pore throats, such that no two of the hyperbolic tangents are created for the same one of the pore throats.

14. The non-transitory computer-readable medium of claim 10, wherein the hyperbolic tangents are defined by the following equation:


%). anft.(%.{P - ½)) with constraints:

wn > 0, Vn€ [ N] n.. N e H


where P represents a logarithmic transform of a normalized capillary pressure and N represents the number of hyperbolic tangents.

15. A computing system, comprising:

one or more processors; and

a memory system comprising one or more non-transitory computer-readable media storing instructions that, when executed by one or more processors of a computing system, cause the computing system to perform operations, the operations comprising:

obtaining capillary pressure data representing capillary pressure in a reservoir; obtaining permeability data representing permeability in the reservoir;

determining a number of pore throats represented by the capillary pressure data; creating hyperbolic tangents based on the capillary pressure data equal in number to the number of pore throats;

combining hyperbolic tangents to create a curve to fit the capillary pressure data and to define hyperbolic tangent parameters;

combining at least one of the hyperbolic tangent parameters with the permeability data to define a saturation height function;

modeling a saturation in the reservoir using the saturation height function; and displaying the saturation model based on the saturation height function, wherein the determining the number of pore throats comprises creating an initial capillary pressure curve to identify the number of pore throats represented by the capillary pressure data.

16. The computer system of claim 15, wherein the determining the number of pore throats comprises:

creating the initial capillary pressure curve using a predetermined number of multiple linked hyperbolic tangents;

determining a first derivative of the capillary pressure curve; and

determining a number of local minima in the capillary pressure curve,

wherein the number of pore throat represented by the capillary pressure data corresponds to the number of local minima.

17. The computer system of claim 16, wherein the predetermined number of hyperbolic tangents is equal or greater to the number of pore throats identified in the capillary pressure data.

18. The computer system of claim 15, wherein the hyperbolic tangents are defined by the following equation:

j (P n , ¾½ , in) = (ii 4- ^x ($n+ 1 ~~ a^) nh(wn.{P ~~ tn ))

with constraints:

wn > 0, Vrc 6 [ N] n, N€ N

tt^i ¾ . Vn £ Ii. -N 11 ?L:N€ H

where P represents a logarithmic transform of a normalized capillary pressure and N represents the number of hyperbolic tangents.

19. The computer system of claim 18, wherein the hyperbolic tangent parameter tn has a linear relationship with the logarithm of the obtained permeability data as defined by the following equation:


where K represents the obtained permeability data.

20. The computer system of claim 19, wherein the saturation height function is defined by the following equation:

/ (P, if ? %.? wn , k.n) ~ ά| - α.ν -