Exxonmobil Upstream Research Company

Rossen Parashkevov

Xiaohui Wu

Yahan Yang

Dachang Li

Adam Usadi

Sergey A Terekhov

Xiao-Hui Wu

Matt T Stone

Linfeng Bi

Weidong Guo

Adam K Usadi

There is provided a method for modeling a hydrocarbon reservoir that includes generating a reservoir model comprising a plurality of sub regions. At least one of the sub regions is simulated using a training simulation to obtain a set of training parameters comprising state variables and boundary conditions of the at least one sub region. A machine learning algorithm is used 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. The hydrocarbon reservoir can be simulated using the inverse operator approximated for the at least one sub region. The method also includes generating a data representation of a physical hydrocarbon reservoir can be generated in a non-transitory, computer-readable, medium based, at least in part, on the results of the simulation.

Methods and systems for machine-learning based simulation of flow

There is provided a method for modeling a hydrocarbon reservoir that includes generating a reservoir model that has a plurality of sub regions. A solution surrogate is obtained for a sub region by searching a database of existing solution surrogates to obtain an approximate solution surrogate based on a comparison of physical, geometrical, or numerical parameters of the sub region with physical, geometrical, or numerical parameters associated with the existing surrogate solutions in the database. If an approximate solution surrogate does not exist in the database, the sub region is simulated using a training simulation to obtain a set of training parameters comprising state variables and boundary conditions of the sub region. A machine learning algorithm is used to obtain a new solution surrogate based on the set of training parameters. The hydrocarbon reservoir can be simulated using the solution surrogate obtained for the at least one sub region.

Methods and systems for machine&#x2014;learning based simulation of flow

A variable discretization method for general multiphase flow simulation in a producing hydrocarbon reservoir. For subsurface regions for which a regular or Voronoi computational mesh is suitable, a finite difference/finite volume method ('FDM') is used to discretize numerical solution of the differential equations governing fluid flow (). For subsurface regions with more complex geometries, a finite element method ('FEM') is used. The invention combines FDM and FEM in a single computational framework (). Mathematical coupling at interfaces between different discretization regions is accomplished by decomposing individual phase velocity into an averaged component and a correction term. The averaged velocity component may be determined from pressure and averaged capillary pressure and other properties based on the discretization method employed, while the velocity correction term may be computed using a multipoint flux approximation type method, which may be reduced to two-point flux approximation for simple grid and permeability fields.

Variable discretization method for flow simulation on complex geological models

There is provided a method for modeling a hydrocarbon reservoir that includes generating a reservoir model that has a plurality of coarse grid cells. A plurality of fine grid models is generated, wherein each fine grid model corresponds to one of the plurality of coarse grid cells that surround a flux interface. The method also includes simulating the plurality of fine grid models using a training simulation to obtain a set of training parameters, including a potential at each coarse grid cell surrounding the flux interface and a flux across the flux interface. A machine learning algorithm is used to generate a constitutive relationship that provides a solution to fluid flow through the flux interface. The method also includes simulating the hydrocarbon reservoir using the constitutive relationship and generating a data representation of a physical hydrocarbon reservoir in a non-transitory, computer-readable medium based on the results of the simulation.

A method is presented for modeling reservoir properties. The method includes constructing a coarse computational mesh for the reservoir. The coarse computational mesh comprises a plurality of cells. The method further includes determining a plurality of flows for each of the plurality of cells based on Dirichlet boundary conditions. Additionally, the method includes determining a solution to a coarse pressure equation for the reservoir based on the plurality of flows.

Method and system for reservoir modeling

A method is provided for simulating a physical process such as fluid flow in porous media by performing a fine-grid calculation of the process in a medium and re-using the fine grid solution in subsequent coarse-grid calculations. For fluid flow in subsurface formations, the method may be applied to optimize upscaled calculation grids formed from geologic models. The method decreases the cost of optimizing a grid to simulate a physical process that is mathematically described by the diffusion equation.

Upscaling of reservoir models by reusing flow solutions from geologic models

A method for constructing a velocity vector field from a grid and a set of fluxes for each face of the grid cells. The cells are first subdivided and internal fluxes are calculated for each cell subject to the constraints of the flux for each cell and to achieve the minimum energy state for the each cell. The minimum energy state is computed efficiently using a divergence-free correction method without introducing a pressure variable. Then, the velocity vector field is constructed from the subcell fluxes using mixed finite element interpolation.

Computing a consistent velocity vector field from a set of fluxes

Method is provided for simulating a physical process such as fluid flow in porous media by performing a fine-grid calculation of the process in a medium and re-using the fine grid solution in subsequent coarse-grid calculations. For fluid flow in subsurface formations, the method may be applied to optimize upscaled calculation grids formed from geologic models. The method decreases the cost of optimizing a grid to simulate a physical process that is mathematically described by the diffusion equation.

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Houston, TX, United States of America

Rossen Parashkevov