Methods and systems for machine-learning based simulation of flow

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

• generating a reservoir model comprising a plurality of coarse grid cells;
• generating a plurality of fine grid models, each fine grid model corresponding to one of the plurality of coarse grid cells that surround a flux interface;
• simulating the plurality of fine grid models using a training simulation to obtain a set of training parameters comprising a potential at each coarse grid cell surrounding the flux interface and a flux across the flux interface;
• using a machine learning algorithm to generate a constitutive relationship that provides a solution to fluid flow through the flux interface;
• simulating the hydrocarbon reservoir using the constitutive relationship;
• and
• producing a hydrocarbon from the hydrocarbon reservoir based, at least in part, upon the results of the simulation, wherein using the machine learning algorithm to generate the constitutive relationship comprises training a neural net using the training parameters, wherein the potential at each coarse grid cell surrounding the flux interface is used as an input to the neural net and the flux across the flux interface is used as a desired output.

A system for modelling reservoir properties, 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 coarse grid cells;
• generate a plurality of fine grid models, each fine grid model corresponding to one of the plurality of coarse grid cells that surround a flux interface;
• simulate the plurality of fine grid models using a training simulation to obtain a set of training parameters comprising a potential at each coarse grid cell surrounding the flux interface and a flux across the flux interface;
• use a machine learning algorithm to generate a constitutive relationship that provides a solution to fluid flow through the flux interface;
• simulate the reservoir using the constitutive relationship, wherein the machine readable medium comprises code configured to direct the processor to re-use the constitutive relationship generate for the flux interface for a second flux interface based on a comparison of a set of phycsical, geometrical, or numerical parameters corresponding to the flux interface and a new set of physical, geometrical, or numerical parameters that characterize the second flux interface;
• and
• producing a hydrocarbon from the reservoir based, at least in part, upon the results of the simulation.

A system for modelling reservoir properties, 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 coarse grid cells;
• generate a plurality of fine grid models, each fine grid model corresponding to one of the plurality of coarse grid cells that surround a flux interface;
• simulate the plurality of fine grid models using a training simulation to obtain a set of training parameters comprising a potential at each coarse grid cell surrounding the flux interface and a flux across the flux interface;
• use a machine learning algorithm to generate a constitutive relationship that provides a solution to fluid flow through the flux interface;
• simulate the reservoir using the constitutive relationship;
• and
• 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 potential at each coarse gird cell surrounding the flux interface is used as an input to the neural net and the flux across the flux interface is used as a desired output;
• and
• producing a hydrocarbon from the reservoir based, at least in part, upon the results of the simulation.

A non-transitory, computer readable medium comprising code configured to direct a processor to:

• generate a reservoir model comprising a plurality of coarse grid cells;
• generate a plurality of fine grid models, each fine grid model corresponding to one of the plurality of coarse grid cells that surround a flux interface;
• simulate the plurality of fine grid models using a training simulation to obtain a set of training parameters comprising a potential at each coarse grid cell surrounding the flux interface and a flux across the flux interface;
• use a machine learning algorithm to generate a constitutive relationship that provides a solution to fluid flow through the flux interface;
• simulate the reservoir model using the constitutive relationship:
• and
• generate a neural net and train the neural net using the training parameters, wherein the potential at each coarse grid cell surrounding the flux interface is used as an input to the neural net and the flux across the flux interface is used as a desired output;
• and
• producing a hydrocarbon from the reservoir based, at least in part, upon the results of the simulation.