Hydraulic fracture simulation with an extended finite element method

1. A computer-implemented method of modeling a hydraulically driven fracture comprising:

selecting an enrichment region for modeling a subject hydraulically driven fracture, the enrichment region representing a permeable medium, and the modeling resulting in a model of the subject hydraulically driven fracture;

defining respective positions of a first set of nodes and a second set of nodes in the enrichment region, wherein the second set of nodes are superposed on the first set of nodes;

performing a coupled pore fluid diffusion and stress analysis on the enrichment region at the first set of nodes;

determining whether the second set of nodes is activated as a result of the coupled pore fluid diffusion and stress analysis;

computing solutions to one or more equilibrium equations, the one or more equilibrium equations based on whether the second set of nodes is activated as a result of the coupled pore fluid diffusion and stress analysis, wherein the one or more equilibrium equations define tangential fluid flow and normal fluid flow in the model of the subject hydraulically driven fracture; and

visually outputting to a user a rendering of the model of the subject hydraulically driven fracture.

2. A computer-implemented method in accordance with claim 1 , further comprising defining the enrichment region.

3. A computer-implemented method in accordance with claim 1 , further comprising defining an initial crack using level node sets within the enrichment region.

4. A computer-implemented method in accordance with claim 1 , further comprising defining crack initiation criteria and crack propagation criteria within the enrichment region, wherein crack initiation refers to the beginning of degradation of the cohesive response at an enriched element.

5. A computer-implemented method in accordance with claim 1 , wherein determining whether the second set of nodes is activated comprises:

defining a fracture criterion based on properties of the enrichment region; and

determining whether the fracture criterion is satisfied as a result of the coupled pore fluid diffusion and stress analysis.

6. A computer-implemented method in accordance with claim 1 , further comprising defining respective positions of an additional set of nodes on edges of the subject hydraulically driven fracture, the additional set of nodes being used to compute the one or more equilibrium equations.

7. A computer of modeling a hydraulically driven fracture comprising:

a memory area configured to store:

an enrichment region for modeling a subject hydraulically driven fracture, the enrichment region representing a permeable medium, and the modeling resulting in a model of the subject hydraulically driven fracture;

respective positions of a first set of nodes and a second set of nodes in the enrichment region, wherein the second set of nodes are superposed on the first set of nodes; and

a processor coupled to said memory area, said processor configured to:

perform a coupled pore fluid diffusion and stress analysis on the enrichment region at the first set of nodes;

determine whether the second set of nodes is activated as a result of the coupled pore fluid diffusion and stress analysis;

compute solutions to one or more equilibrium equations, the one or more equilibrium equations based on whether the second set of nodes is activated as a result of the coupled pore fluid diffusion and stress analysis, wherein the one or more equilibrium equations define tangential fluid flow and normal fluid flow in the model of the subject hydraulically driven fracture; and

visually output to a user a rendering of the model of the subject hydraulically driven fracture.

8. A computer in accordance with claim 7 , wherein said processor is further configured to define the enrichment region.

9. A computer in accordance with claim 7 , wherein said processor is further configured to define an initial crack using level node sets within the enrichment region.

10. A computer in accordance with claim 7 , wherein said processor is further configured to define crack initiation criteria and crack propagation criteria within the enrichment region, wherein crack initiation refers to the beginning of degradation of the cohesive response at an enriched element.

11. A computer in accordance with claim 7 , wherein said processor is further configured to:

define a fracture criterion based on properties of the enrichment region; and

determine whether the fracture criterion is satisfied as a result of the coupled pore fluid diffusion and stress analysis.

12. A computer in accordance with claim 7 , wherein said processor is further configured to model discontinuities in a fluid pressure field and fluid flow within the enrichment region, wherein the fluid flow includes fluid leak-off.

13. A computer in accordance with claim 7 , wherein said processor is further configured to define respective positions of an additional set of nodes on edges of the subject hydraulically driven fracture, the additional set of nodes being used to compute the one or more equilibrium equations.

14. A computer program product for modeling a hydraulically driven fracture comprising:

one or more non-transitory computer-readable storage media having computer-executable components thereon, said computer-executable components comprising:

a selection component that when executed by a processor causes the processor to select an enrichment region for modeling a subject hydraulically driven fracture, the enrichment region representing a permeable medium, and the modeling resulting in a model of the subject hydraulically driven fracture;

a definition component that when executed by the processor causes the processor to define respective positions of a first set of nodes and a second set of nodes in the enrichment region, wherein the second set of nodes are superposed on the first set of nodes; and

an analysis component that when executed by a processor causes the processor to:

perform a coupled pore fluid diffusion and stress analysis on the enrichment region at the first set of nodes;

determine whether the second set of nodes is activated as a result of the coupled pore fluid diffusion and stress analysis;

compute solutions to one or more equilibrium equations, the one or more equilibrium equations based on whether the second set of nodes is activated as a result of the coupled pore fluid diffusion and stress analysis, wherein the one or more equilibrium equations define tangential fluid flow and normal fluid flow in the model of the subject hydraulically driven fracture; and

visually output to a user a rendering of the model of the subject hydraulically driven fracture to a user.

15. A computer program product in accordance with claim 14 , said definition component further causes the processor to define the enrichment region.

16. A computer program product in accordance with claim 14 , said definition component further causes the processor to define an initial crack using level node sets within the enrichment region.

17. A computer program product in accordance with claim 14 , said definition component further causes the processor to define crack initiation criteria and crack propagation criteria within the enrichment region, wherein crack initiation refers to the beginning of degradation of the cohesive response at an enriched element.

18. A computer program product in accordance with claim 14 , wherein said analysis component further causes the processor to:

define a fracture criterion based on properties of the enrichment region; and

determine whether the fracture criterion is satisfied as a result of the coupled pore fluid diffusion and stress analysis.

19. A computer program product in accordance with claim 14 , wherein said analysis component further causes the processor to model discontinuities in a fluid pressure field and fluid flow within the enrichment region, wherein the fluid flow includes fluid leak-off.

20. A computer program product in accordance with claim 14 , wherein said definition component further causes the processor to define respective positions of an additional set of nodes on edges of the subject hydraulically driven fracture, the additional set of nodes being used to compute the one or more equilibrium equations.