Method and system for finite volume simulation of flow

• US 9,134,454 B2
• Filed: 01/20/2011
• Issued: 09/15/2015
• Est. Priority Date: 04/30/2010
• Status: Active Grant

• Current Assignee: Exxonmobil Upstream Research Company (Exxon Mobil Corporation)
• Original Assignee: Exxonmobil Upstream Research Company (Exxon Mobil Corporation)
• Inventors: Mishev, Ilya D., Dubois, Olivier, Jiang, Lijian
• Primary Examiner(s): Shah, Kamini S
• Assistant Examiner(s): PIERRE LOUIS, ANDRE
• Application Number:
  US13/641,071
• Publication Number:
  US 20130035913A1
• Time in Patent Office: 1,699 Days
• Field of Search: 703/9, 703/10, 166/266
• US Class Current: 1/1
• CPC Class Codes: E21B 43/00 Methods or apparatus for obtaining oil, gas, water, soluble or meltable materials or a slurry of minerals from wells applicable only to water E03B
• CPC Class Codes: G01V 11/00 Prospecting or detecting by methods combining techniques covered by two or more of main groups G01V1/00 - G01V9/00
• CPC Class Codes: G06F 2111/10 Numerical modelling
• CPC Class Codes: G06F 30/23 using finite element methods [FEM] or finite difference methods [FDM]

Abstract

There is provided a method for modeling a hydrocarbon reservoir that includes deriving a computational mesh on a fine unstructured mesh using a multilevel mixed multiscale finite volume (MMMFV) method. Deriving the computational mesh includes computing a first algebraic multilevel basis function for a pressure, constructing an interaction region, and generating a primary mesh. A second algebraic multiscale basis function for a velocity approximation is computed and the primary mesh is discretized. The hydrocarbon reservoir is simulated using the computational mesh. A data representation of a physical hydrocarbon reservoir is generated in a non-transitory, computer-readable, medium based at least in part on the results of the simulation.

Claims

1. A method for modeling a hydrocarbon reservoir, comprising:

deriving a computational mesh from a fine unstructured mesh using a multilevel mixed multiscale finite volume (MMMFV) method, comprising;

constructing an interaction region;

generating a primary mesh;

computing a first algebraic multilevel basis function for a pressure, wherein the first algebraic multilevel basis function is based at least in part on a discrete harmonic function;

computing a second algebraic multiscale basis function for a velocity approximation, wherein the second algebraic multiscale basis function is solved to satisfy the following;

2. The method of claim 1, further comprising:

using global information in the construction of the second algebraic multiscale basis function by;

selecting an auxiliary mesh;

approximating a solution on the auxiliary mesh; and

calculating one or more velocity basis functions using the provided global information.

3. The method of claim 1, wherein, the second algebraic multiscale basis function is based at least in part on a discrete harmonic function.

4. The method of claim 1, wherein deriving the computational mesh comprises:

calculating a primary mesh and one or more interaction regions;

selecting approximation spaces, wherein the approximation spaces comprise pressure and velocity;

selecting test spaces, where the test spaces comprise a first test space and a second test space and; and

selecting discrete gradient and divergence operators.

5. The method of claim 1, wherein computing the first algebraic multilevel basis function comprises:

setting a plurality of boundary conditions to one at a center point of a coarse computational cell in the primary mesh;

setting the plurality of boundary conditions to zero at a boundary of the coarse computational cell in the primary mesh; and

solving a basis function using the plurality of boundary conditions.

6. The method of claim 1, wherein computing the first algebraic multilevel basis function comprises:

computing all coarse functions for a computational mesh simultaneously so as to minimize an energy of a computational mesh.

7. The method of claim 1, wherein computing the first algebraic multilevel basis function comprises:

selecting one or more coarse points;

selecting one or more fine points that belong to each coarse point;

computing a coarse basis; and

evaluating an approximation quality of the coarse basis.

8. The method of claim 7, further comprising:

iterating until the approximation quality is acceptable.

9. The method of claim 7, wherein computing the coarse basis comprises:

connecting two points, a_i and b, in a computational mesh Σ

_h with a straight line [a_i, b];

assigning a point in Σ

_h that is closest to the straight line [a_i, b] to be a_i+1;

generating a connecting line from a_i to a_i+1; and

if a_i+1≠

b, setting i=i +1,

selecting another connection and repeating.

10. The method of claim 7, wherein computing the coarse basis comprises:

selecting a center point of the interaction region;

selecting a center point of one or more edges of the interaction region;

connecting the center point of the interaction region to the center point of an edge; and

connecting the one or more edges to form faces of polygons.

11. The method of claim 1, wherein constructing the interaction region comprises:

constructing a triangulation of coarse points by;

constructing each edge of the triangulation by;

connecting two coarse points, a_i and b in a computational mesh Σ

_h with a straight line [a_i, b];

assigning a point in Σ

_h to be a_i+1, wherein the point is closest to the straight line [a_i, b];

generating a connecting line from a_i to a_i+1; and

if a_i+1≠

b, setting i=i+1, and repeating until a₁₊₁=b;

selecting another connection and repeating; and

constructing one or more faces of the triangulation by;

selecting a center point of an interaction region;

selecting a center point of one or more edges of the interaction region;

connecting the center point of the interaction region to the center point of an edge; and

connecting one or more faces of polygons.

12. The method of claim 1, further comprising:

managing a production of a hydrocarbon from the physical hydrocarbon reservoir based at least in part upon data representation.

13. The method of claim 12, wherein managing the production comprises one or more of:

converting injectors into producers;

converting producers into injectors;

changing production rates; and

drilling new wells to the reservoir.

14. The method of claim 1, wherein a quality of the velocity approximation is improved by:

calculating a special vector basis functions; and

solving a small local system for a coarse cell.

15. A method for producing a hydrocarbon from a hydrocarbon reservoir, comprising:

simulating the reservoir using a multilevel mixed multiscale finite volume method on an unstructured mesh, comprising;

constructing an interaction region;

generating a primary mesh;

computing a first algebraic multilevel basis function for a pressure, wherein the first algebraic multilevel basis function is based at least in part on a discrete harmonic function; and

computing a second algebraic multiscale basis function for a velocity approximation, wherein the basis function is solved to satisfy the following;

16. The method of claim 15, wherein producing the hydrocarbon comprises one or more of:

drilling one or more wells to the hydrocarbon reservoir, wherein the wells comprise production wells, injection wells, or both; and

setting production rates from the hydrocarbon reservoir.

17. A Mixed Multiscale Finite Volume Method for simulating flow in a porous media, comprising:

collecting global information about a hydrocarbon reservoir;

deriving an elliptic problem based on a saturation equation;

calculating a plurality of unstructured coarse meshes and a plurality of pressure basis functions corresponding to the plurality of unstructured coarse meshes, wherein the first algebraic multilevel basis function is based at least in part on a discrete harmonic function;

calculating a plurality of velocity basis functions corresponding to the plurality of unstructured coarse meshes to reconstruct a velocity vector field for each of the plurality of unstructured coarse meshes, wherein the basis function is solved to satisfy the following;

18. The Mixed Multiscale Finite Volume Method of claim 17, further comprising combining the phase velocity computed for each of the plurality of unstructured coarse meshes to obtain a phase velocity for the hydrocarbon reservoir.

19. The Mixed Multiscale Finite Volume Method of claim 17, further combining the component transport computed for each of the plurality of coarse meshes to obtain a phase velocity for the hydrocarbon reservoir.

20. A system for simulating a hydrocarbon reservoir, comprising:

a processor;

a non-transitory storage device, wherein the storage device comprises a data representation of the hydrocarbon reservoir, wherein the data representation is an unstructured computational mesh determined by a Mixed Multiscale Finite Volume method;

a memory device, wherein the memory device comprises code to direct the processor to;

construct an interaction region;

generate a primary mesh;

compute a first algebraic multilevel basis function for a pressure, wherein the first algebraic multilevel basis function is based at least in part on a discrete harmonic function;

compute a second algebraic multiscale basis function for a velocity approximation, wherein the basis function is solved to satisfy the following;

21. The system of claim 20, wherein the processor comprises a multi-processor cluster.