Nitsche continuity enforcement for non-conforming meshes

Patent metadata

Field	Value
Publication number	US-10920539-B2
Application number	US-201715832362-A
Country	US
Kind code	B2
Filing date	Dec 5, 2017
Priority date	Feb 24, 2017
Publication date	Feb 16, 2021
Grant date	Feb 16, 2021

Abstract

A method for modeling a subsurface reservoir system, the method including: generating, with a computer, a background mesh that does not honor at least one subsurface feature included in the subsurface reservoir system; splitting, with a computer, the background mesh along the subsurface feature included in the subsurface reservoir system such that a resulting mesh honors a geometry of the subsurface features; identifying, with a computer, element faces or edges where the resulting mesh is non-conforming and/or the element faces or edges lie on subsurface features; and performing a computer-based numerical simulation utilizing the resulting mesh to model at least one fluid-related or geomechanical reservoir response, wherein mass or traction balance is enforced on the identified element faces or edges.

First claim

What is claimed is:

1. A method for modeling a subsurface reservoir system, the method comprising:
generating, with a computer, a background mesh that does not honor at least one subsurface feature included in the subsurface reservoir system;
splitting, with a computer, the background mesh along the subsurface feature included in the subsurface reservoir system such that a resulting mesh honors a geometry of the subsurface features;
identifying, with a computer, element faces or edges where the resulting mesh is non-conforming and/or the element faces or edges lie on subsurface features; and
performing a computer-based numerical simulation utilizing the resulting mesh to model at least one fluid-related or geomechanical reservoir response, wherein mass or traction balance is enforced on the identified element faces or edges.

2. The method of claim 1 , wherein the non-conforming mesh is generated from the splitting of the background mesh.

3. The method of claim 1 , further comprising performing surface integration to ensure mass or traction balance on the identified element faces or edges, and the surface integration is performed by separating the surface integration of an interface between two sides of the identified element faces or edges into two parts, one for each side of the interface, and on each side of the interface, the surface integration follows its own discretization without any considerations for the other side's discretization.

4. The method of claim 3 , wherein the non-conforming mesh can include at least one hanging node on different sides of the interface, and at the identified element faces or edges the integration can be performed in order to account for a presence of the at least one hanging node.

5. The method of claim 1 , wherein after the splitting, inserting additional elements with different material properties between two sides of a split in the resulting mesh at a surface of the subsurface feature.

6. The method of claim 1 , wherein after the splitting, inserting additional elements with different material properties within the resulting mesh at a location of a one-dimensional subsurface feature.

7. The method of claim 6 , wherein the material properties are permeability and porosity for a fluid flow problem, and constitutive relations for a geomechanical problem.

8. The method of claim 1 , wherein the at least one fluid-related reservoir response is determination of fluid flow through a permeable rock formation.

9. The method of claim 1 , wherein the subsurface feature is at least one of a perforation from a wellbore, fracture wings of a fractured wellbore completion, or wormholes.

10. The method of claim 1 , wherein the subsurface feature is at least one of a fault, natural fractures, a thin reservoir layer, or formation stratification.

11. The method of claim 1 , wherein the simulation accounts for a discontinuity at the identified edges or faces with a Nitsche method.

12. The method of claim 1 , further comprising managing hydrocarbons based on a result of the simulation.

13. The method of claim 4 , wherein the interface is between high and low permeability regions of source rock.

14. The method of claim 1 , wherein the splitting is according to subsurface features.

15. The method of claim 1 , wherein the splitting is according to local grid refinement.

16. A non-transitory computer readable storage medium encoded with instructions, which when executed by a computer causes the computer to implement a method for modeling a subsurface reservoir system, the method comprising:
generating, with a computer, a background mesh that does not honor at least one subsurface feature included in the subsurface reservoir system;
splitting, with a computer, the background mesh along the subsurface feature included in the subsurface reservoir system such that a resulting mesh honors a geometry of the subsurface features;
identifying, with a computer, element faces or edges where the resulting mesh is non-conforming and/or the element faces or edges lie on subsurface features; and
performing a computer-based numerical simulation utilizing the resulting mesh to model at least one fluid-related or geomechanical reservoir response, wherein mass or traction balance is enforced on the identified element faces or edges.

Assignees

• Becker Gauthier D
• Huang Hao
• Sun Huafei
• Exxonmobil Upstream Res Co

Inventors

• Becker Gauthier D
• Huang Hao
• Sun Huafei

Classifications

• G06F30/28 Primary

  using fluid dynamics, e.g. using Navier-Stokes equations or computational fluid dynamics [CFD] · CPC title

• E21B41/00

  Equipment or details not covered by groups E21B15/00 - E21B40/00 · CPC title

• G06F30/23 Primary

  using finite element methods [FEM] or finite difference methods [FDM] · CPC title

• G06F2111/10

  Numerical modelling · CPC title

• E21B49/00

  Testing the nature of borehole walls; Formation testing; Methods or apparatus for obtaining samples of soil or well fluids, specially adapted to earth drilling or wells · CPC title