Methods and systems for machine-learning based simulation of flow

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

generating a reservoir model comprising a plurality of sub regions, wherein each of the plurality of sub regions are associated with a different portion of a hydrocarbon reservoir and each of the sub regions comprise a plurality of cells;

selecting a sub region from the plurality of sub regions;

looking up a best-fit approximation model for a matrix equation solution surrogate for the sub region in a database of surrogate solutions based on a comparison of physical, geometrical, or numerical parameters of the sub region and the solution surrogate;

obtaining an approximate solution of the sub region when the best-fit approximation model exists in the database;

when the best-fit approximation model does not exist in the database:

simulating the sub region of the plurality of sub regions using a training simulation to obtain a set of training parameters comprising state variables and boundary conditions of the sub region; and

using a machine learning algorithm to approximate, based on the set of training parameters, an inverse operator of a matrix equation that provides a solution to fluid flow through a porous media;

simulating fluid flow for the plurality sub regions in the hydrocarbon reservoir to generate results, wherein the inverse operator approximated for the sub region represents fluid flow in the sub region; and

producing a hydrocarbon from the hydrocarbon reservoir based, at least in part, upon results of the simulation;

wherein the producing a hydrocarbon from a hydrocarbon reservoir based, at least in part, upon the results of the simulation, comprises at least one of:

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

setting production rates from the hydrocarbon reservoir.

2. The method of claim 1 , wherein producing the hydrocarbon comprises:

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

setting production rates from the hydrocarbon reservoir; or

any combinations thereof.

3. The method of claim 1 , wherein at least one of the plurality of sub regions comprises a well or a fault.

4. The method of claim 1 , wherein more than one of the plurality of sub regions comprises a well or a fault.

5. A system for producing a hydrocarbon from a hydrocarbon reservoir, comprising:

a processor;

a non-transitory machine readable medium comprising code configured to direct the processor to:

generate a reservoir model comprising a plurality of sub regions, wherein each of the plurality of sub regions are associated with a different portion of a hydrocarbon reservoir and each of the sub regions comprise a plurality of cells;

select a sub region from the plurality of sub regions;

look up a best-fit approximation model for a matrix equation solution surrogate for the sub region in a database of surrogate solutions based on a comparison of physical, geometrical, or numerical parameters of the sub region and the solution surrogate;

obtain an approximate solution of the sub region when the best-fit approximation model exists in the database;

when the best-fit approximation model does not exist in the database:

simulate the sub region of the plurality of sub regions using a training simulation to obtain a set of training parameters comprising state variables and boundary conditions of the sub region; and

use a machine learning algorithm to approximate, based on the set of training parameters, an inverse operator of a matrix equation that provides a solution to fluid flow through a porous media;

simulate fluid flow for the plurality sub regions in the reservoir, wherein the inverse operator approximated for the sub region represents fluid flow in the sub region; and

generate a data representation of a physical hydrocarbon reservoir in a non-transitory, computer-readable, medium based, at least in part, on results of the simulation; and

the hydrocarbon reservoir;

wherein producing a hydrocarbon from a hydrocarbon reservoir is based, at least in part, upon the results of the simulation; and

wherein the producing a hydrocarbon from a hydrocarbon reservoir based, at least in part, upon the results of the simulation, comprises at least one of:

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

setting production rates from the hydrocarbon reservoir.

6. The system for claim 5 , wherein the machine readable medium comprises code configured to direct the processor to receive a set of physical, geometrical, or numerical parameters of the at least one sub-region used for simulating the sub region using the training simulation, wherein the set of physical, geometrical, or numerical parameters comprises at least one of rock porosity, phase permeability, and geological characteristics.

7. The system for claim 5 , wherein the machine readable medium comprises code configured to direct the processor to store the inverse operator approximated for the sub region and physical, geometrical, or numerical parameters corresponding to the sub region to the database of surrogate solutions for use in subsequent reservoir simulations.

8. The system for claim 5 , wherein the machine readable medium comprises code configured to direct the processor to re-use the inverse operator approximated for the sub region for a second sub region based on a comparison of a set of physical, geometrical, or numerical parameters corresponding to the sub region and a new set of physical, geometrical, or numerical parameters that characterize the second sub region.

9. The system of claim 5 , comprising a neural net, wherein the machine readable medium comprises code configured to direct the processor to train the neural net using the training parameters, wherein the boundary conditions are used as input to the neural net and the state variables are used as the desired output.

10. The system of claim 5 , wherein the machine readable medium comprises code configured to direct the processor to receive a set of boundary condition types for each boundary of the sub region and generate a fine-gridded computational mesh of the sub region for simulating the sub region using the training simulation.

11. The system of claim 5 , wherein the machine readable medium comprises code configured to direct the processor to receive a set of boundary condition values for simulating the sub region using the training simulation, wherein the set of boundary condition values is based, at least in part, on physical characteristics of the reservoir.

12. The system of claim 5 , wherein at least one of the plurality of sub regions comprises a well or a fault.

13. The system of claim 5 , wherein more than one of the plurality of sub regions comprises a well or a fault.