Fractured reservoir simulation

1. A method for simulating fluid flow in a fractured reservoir comprising:

generating a hybrid grid model (HG model) by generating a grid for a fractured reservoir model comprising a fracture and a matrix to obtain a generated grid;

modifying the hybrid grid model to generate a hybrid grid cross flow equilibrium model (HG-CFE model), wherein modifying comprises:

selecting a volume expansion parameter for a plurality of cross flow equilibrium elements, wherein the volume expansion parameter comprises an amount the fracture is expanded to include surrounding matrix elements of the matrix;

generating the plurality of cross flow equilibrium elements based on the generated grid and the volume expansion parameter, the plurality of cross flow equilibrium elements comprising a plurality of physical properties,

wherein generating the plurality of cross flow equilibrium elements further comprises combining a portion of the fracture with a fraction of neighboring matrix blocks on either side of the fracture, within a volume defined by the volume expansion parameter, into larger cross flow equilibrium elements, and

wherein the plurality of cross flow equilibrium elements comprise the larger cross flow equilibrium elements;

executing a sensitivity analysis with respect to a volume of the plurality of cross flow equilibrium elements without re-gridding the fractured reservoir model by integrating flow equations in cross-flow equilibrium elements, of the plurality of cross flow equilibrium elements, related to fracture-fracture flow;

correcting inaccuracies by calibrating fluid saturations in the fracture by scaling a relative permeability in the fracture according to an oil saturation scaling factor; and

calculating, using the plurality of cross flow equilibrium elements, a plurality of pore volume and transmissibility multipliers;

simulating, using the HG-CFE model, a fluid flow in the fractured reservoir model by using the plurality of pore volume and transmissibility multipliers and a fracture relative permeability curve to obtain a result, wherein the fluid flow is calculated for the plurality of cross flow equilibrium elements; and

presenting the result.

2. The method of claim 1 , wherein the plurality of physical properties comprises a plurality of matrix and fracture properties of the fractured reservoir.

3. The method of claim 1 , wherein generating the grid comprises using at least one selected from a group consisting of a one dimensional fracture in a two dimensional fractured reservoir and a two dimensional fracture in a three dimensional fractured reservoir.

4. The method of claim 1 , wherein the volume expansion parameter is calculated as a ratio of a selected fracture aperture to a cross flow equilibrium expanded fracture.

5. The method of claim 1 , further comprising:

selecting the plurality of physical properties for cross flow equilibrium elements from a group consisting of volume, porosity, permeability, net-to-gross, and transmissibility.

6. The method of claim 1 , further comprising:

calculating a fracture to fracture transmissibility using a star-delta approach.

7. The method of claim 1 , further comprising:

calculating the fluid flow from the matrix to the fracture using the fracture relative permeability curve.

8. The method of claim 1 , further comprising:

scaling a relative permeability in the fracture with oil saturation.

9. The method of claim 1 ,

wherein executing the sensitivity analysis uses a fracture relative permeability curve.

10. A system comprising:

one or more processors;

a memory;

instructions stored in the memory and executable by at least one of the one or more processors to cause the system to:

generate a hybrid grid model (HG model) by generating a grid for a fractured reservoir model comprising a fracture and a matrix to obtain a generated grid;

modify the hybrid grid model to generate a hybrid grid cross flow equilibrium model (HG-CFE model), wherein modifying comprises:

selecting a volume expansion parameter for a plurality of cross flow equilibrium elements, wherein the volume expansion parameter comprises an amount the fracture is expanded to include surrounding matrix elements of the matrix;

generating the plurality of cross flow equilibrium elements based on the generated grid and the volume expansion parameter, the plurality of cross flow equilibrium elements comprising a plurality of physical properties,

wherein generating the plurality of cross flow equilibrium elements further comprises combining a portion of the fracture with a fraction of neighboring matrix blocks on either side of the fracture, within a volume defined by the volume expansion parameter, into larger cross flow equilibrium elements, and

wherein the plurality of cross flow equilibrium elements comprise the larger cross flow equilibrium elements; and

executing a sensitivity analysis with respect to a volume of the plurality of cross flow equilibrium elements without re-gridding the fractured reservoir model by integrating flow equations in cross-flow equilibrium elements, of the plurality of cross flow equilibrium elements, related to fracture-fracture flow;

correcting inaccuracies by calibrating fluid saturations in the fracture by scaling a relative permeability in the fracture according to an oil saturation scaling factor; and

calculating, using the plurality of cross flow equilibrium elements, a plurality of pore volume and transmissibility multipliers;

simulate, using the HG-CFE model, a fluid flow in the fractured reservoir model by using the plurality of pore volume and transmissibility multipliers and a fracture relative permeability curve to obtain a result, wherein the fluid flow is calculated for the plurality of cross flow equilibrium elements; and

present the result.

11. The system of claim 10 , wherein generating the grid comprises using at least one selected from a group consisting of a one dimensional fracture in a two dimensional fractured reservoir and a two dimensional fracture in a three dimensional fractured reservoir.

12. The system of claim 10 , wherein the volume expansion parameter is calculated as a ratio of a selected fracture aperture to a cross flow equilibrium expanded fracture.

13. The system of claim 10 , wherein the instructions further cause the system to:

select the plurality of physical properties for cross flow equilibrium elements from a group consisting of volume, porosity, permeability, net-to-gross, and transmissibility.

14. The system of claim 10 , wherein the instructions further cause the system to:

calculate a fracture to fracture transmissibility using a star-delta approach.

15. The system of claim 10 , wherein the instructions further cause the system to:

calculate the fluid flow from the matrix to the fracture using the fracture relative permeability curve.

16. The system of claim 10 , wherein the instructions further cause the system to:

scale a relative permeability in the fracture with oil saturation.

17. A computer program product comprising computer readable program code for causing a computing system to perform operations, the operations comprising:

generating a hybrid grid model (HG model) by generating a grid for a fractured reservoir model comprising a fracture and a matrix to obtain a generated grid;

modifying the hybrid grid model to generate a hybrid grid cross flow equilibrium model (HG-CFE model), wherein modifying comprises:

selecting a volume expansion parameter for a plurality of cross flow equilibrium elements, wherein the volume expansion parameter comprises an amount the fracture is expanded to include surrounding matrix elements of the matrix;

generating the plurality of cross flow equilibrium elements based on the generated grid and the volume expansion parameter, the plurality of cross flow equilibrium elements comprising a plurality of physical properties,

wherein generating the plurality of cross flow equilibrium elements further comprises combining a portion of the fracture with a fraction of neighboring matrix blocks on either side of the fracture, within a volume defined by the volume expansion parameter, into larger cross flow equilibrium elements, and

wherein the plurality of cross flow equilibrium elements comprise the larger cross flow equilibrium elements; and

executing a sensitivity analysis with respect to a volume of the plurality of cross flow equilibrium elements without re-gridding the fractured reservoir model by integrating flow equations in cross-flow equilibrium elements, of the plurality of cross flow equilibrium elements, related to fracture-fracture flow;

correcting inaccuracies by calibrating fluid saturations in the fracture by scaling a relative permeability in the fracture according to an oil saturation scaling factor; and

calculating, using the plurality of cross flow equilibrium elements, a plurality of pore volume and transmissibility multipliers;

simulating, using the HG-CFE model, a fluid flow in the fractured reservoir model by using the plurality of pore volume and transmissibility multipliers and a fracture relative permeability curve to obtain a result, wherein the fluid flow is calculated for the plurality of cross flow equilibrium elements; and

presenting the result.

18. The computer program product of claim 17 , wherein the plurality of physical properties comprises a plurality of matrix and fracture properties of the fractured reservoir model.

19. The computer program product of claim 17 , wherein generating the grid comprises using at least one selected from a group consisting of a one dimensional fracture in a two dimensional fractured reservoir and a two dimensional fracture in a three dimensional fractured reservoir.

20. The computer program product of claim 17 , wherein the volume expansion parameter is calculated as a ratio of a selected fracture aperture to a cross flow equilibrium expanded fracture.