Adaptive multiscale multi-fidelity reservoir simulation

Patent metadata

Field	Value
Publication number	US-2016342718-A1
Application number	US-201615157172-A
Country	US
Kind code	A1
Filing date	May 17, 2016
Priority date	May 19, 2015
Publication date	Nov 24, 2016
Grant date	—

Abstract

Computer-implemented systems and methods for modeling behavior of at least one fluid in a reservoir are disclosed. The techniques can include obtaining measurements of physical parameters, including pressure, at locations within the reservoir, and discretizing, based on a three-dimensional fine grid, a system of partial differential mass balance equations that model, based on the measurements, at least the physical parameters at the locations within the reservoir, such that a system of nonlinear equations is produced. The techniques can include iterating from a current time step to a next time step, such that a solution to the system of nonlinear equations for a time interval that includes the current time step and the next time step is produced. The iterating can include an adaptive multi-fidelity multiscale technique that employs multiple restriction operators, prolongation operators, and coarse grids, to model various computationally challenging reservoir features, behaviors, or both.

First claim

What is claimed is:

1 . A computer-implemented method for modeling behavior of at least one fluid in a reservoir, the method comprising:
obtaining a plurality of measurements of a plurality of physical parameters at a plurality of locations within the reservoir, the plurality of physical parameters comprising at least pressure; discretizing, based on a three-dimensional fine grid, a system of partial differential mass balance equations that model, based on the plurality of measurements, at least the plurality of physical parameters at the plurality of locations within the reservoir, whereby a system of nonlinear equations is produced; iterating from a current time step to a next time step, whereby a solution to the system of nonlinear equations for a time interval that includes the current time step and the next time step is produced:
deriving a system of nonlinear pressure equations from the system of nonlinear equations;
linearizing the system of nonlinear pressure equations to obtain a system of linearized pressure equations;
selecting a plurality of three-dimensional coarse grids, wherein each coarse grid comprises a non-overlapping partition of the fine grid;
selecting a plurality of prolongation operators, each prolongation operator associated with a respective coarse grid;
selecting a plurality of restriction operators, each restriction operator associated with a respective coarse grid;
solving for pressure for the next time step at the plurality of locations within the reservoir based on a solution to the system of linearized pressure equations, wherein the solving comprises applying the plurality of prolongation operators and the plurality of restriction operators to the system of linearized pressure equations to generate a reduced-dimension system of linear pressure equations, wherein the reduced-dimension system of linear pressure equations has a lower dimensionality than a dimensionality of the system of linearized pressure equations; and
determining, based on the pressure for the next time step at the plurality of locations within the reservoir, physical parameters at the plurality of locations within the reservoir for the next time step; and
outputting the solution to the system of nonlinear equations for the time interval.

2 . The method of claim 1 , wherein the solving for pressure at the next time step at the plurality of locations within the reservoir based on a solution to the system of linearized pressure equations comprises iteratively:
applying at least one prolongation operator of the plurality of prolongation operators to a free variable representing a solution to the system of linearized pressure equations; and applying at least one restriction operator of the plurality of restriction operators to both sides of the system of linearized pressure equations, whereby the reduced-dimension system of linear pressure equations is produced.

3 . The method of claim 2 , wherein the solving for pressure at the next time step at the plurality of locations within the reservoir based on a solution to the system of linearized pressure equations further comprises iteratively applying a local linear solver for the linearized pressure equations to a prolongation of a solution to the reduced-dimension system of linear equations.

4 . The method of claim 1 , wherein:
each column of each prolongation operator of the plurality of prolongation operators has an associated support that is compact and includes a coarse grid block from a respective coarse grid; and each prolongation operator of the plurality of prolongation operators consists of a plurality of columns that form a partition of unity over the fine grid.

5 . The method of claim 4 , wherein each row of each prolongation operator of the plurality of prolongation operators sums to unity.

6 . The method of claim 1 , wherein the outputting comprises displaying a representation of a behavior of the at least one fluid in the reservoir.

7 . The method of claim 1 , further comprising:
predicting fluid behavior in the reservoir based on the solution to the system of nonlinear equations for the time interval; and extracting fluid from the reservoir based on the predicting.

8 . The method of claim 1 , wherein the iterating from the current time step to the next time step is performed in parallel by at least one hardware graphics processing unit.

9 . The method of claim 1 , wherein the physical parameters comprise pressure, flow rate, and composition.

10 . The method of claim 1 , wherein the system of partial differential mass balance equations that model at least the plurality of physical parameters at the plurality of locations within the reservoir further model a modification of the reservoir.

11 . A non-transitory computer-readable medium containing instructions which, when executed by at least one electronic processor, perform a method for modeling behavior of at least one fluid in a reservoir, the method comprising:
obtaining a plurality of measurements of a plurality of physical parameters at a plurality of locations within the reservoir, the plurality of physical parameters comprising at least pressure; discretizing, based on a three-dimensional fine grid, a system of partial differential mass balance equations that model, based on the plurality of measurements, at least the plurality of physical parameters at the plurality of locations within the reservoir, whereby a system of nonlinear equations is produced; iterating from a current time step to a next time step, whereby a solution to the system of nonlinear equations for a time interval that includes the current time step and the next time step is produced:
deriving a system of nonlinear pressure equations from the system of nonlinear equations;
linearizing the system of nonlinear pressure equations to obtain a system of linearized pressure equations;
selecting a plurality of three-dimensional coarse grids, wherein each coarse grid comprises a non-overlapping partition of the fine grid;
selecting a plurality of prolongation operators, each prolongation operator associated with a respective coarse grid;
selecting a plurality of restriction operators, each restriction operator associated with a respective coarse grid;
solving for pressure for the next time step at the plurality of locations within the reservoir based on a solution to the system of linearized pressure equations, wherein the solving comprises applying the plurality of prolongation operators and the plurality of restriction operators to the system of linearized pressure equations to generate a reduced-dimension system of linear pressure equations, wherein the reduced-dimension system of linear pressure equations has a lower dimensionality than a dimensionality of the system of linearized pressure equations; and
determining, based on the pressure for the next time step at the plurality of locations within the reservoir, physical parameters at the plurality of locations within the reservoir for the next time step; and
outputting the solution to the system of nonlinear equations for the time interval.

12 . The computer-readable medium of claim 11 , wherein the solving for pressure at the next time step at the plurality of locations within the reservoir based on a solution to the system of linearized pressure equations comprises iteratively:
applying at least one prolongation operator of the plurality of prolongation operators to a free variable representing a solution to the system of linearized pressure equations; and applying at least one restriction operator of the plurality of restriction operators to both sides of the system of linearized pressure

Assignees

• Schlumberger Technology Corp

Inventors

• Moyner Olav
• Lie Knut-Andreas
• Natvig Jostein

Classifications

• G06F30/23 Primary

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

• G01V11/00

  Prospecting or detecting by methods combining techniques covered by two or more of main groups G01V1/00 - G01V9/00 · CPC title

• G06F17/12

  Simultaneous equations {, e.g. systems of linear equations} · CPC title

• E21B47/06

  Measuring temperature or pressure · CPC title

• G06F17/5018 Primary

  Physics · mapped topic