Exxonmobil Upstream Research Company

Exxonmobil Technology and Engineering Company

Xiaohui Wu

Yahan Yang

Dachang Li

Rossen Parashkevov

Larisa V Branets

Adam Usadi

Linfeng Bi

Sergey A Terekhov

Thomas C Halsey

Tao Sun

Hao Bin Huang

John Van Wagoner

Dar-Lon Chang

Kaveh Ghayour

Gauthier D Becker

Sumeet Trehan

Weidong Guo

Valeriy Kubyak

Elena Kartasheva

Xiang Ma

Igor V Krasnogorov

Method for constructing a continuous design space for generating a physical property model in a faulted subsurface medium. The matching relationship of the fault traces on the two sides of each fault is used in a systematic way to determine the location of the fault traces in the design space. The location of any other point in the design space may then be determined by interpolation of the locations of fault traces. The fault traces are thus used as control points for the mapping. The method involves: (a) identifying the control points and determining their location in both physical and design space and (b) using selected control points, mapping any point from physical space to design space, preferably using the moving least squares method.

Methods to handle discontinuity in constructing design space using moving least squares

A method and system are described for hydrocarbon exploration, development and production. The method relates to performing regression and/or classification in subsurface models to support decision making for hydrocarbon operations. The evaluation may then be used in performing hydrocarbon operations, such as hydrocarbon exploration, hydrocarbon development and/or hydrocarbon production.

Method and system for regression and classification in subsurface models to support decision making for hydrocarbon operations

Method for mapping a 3D grid or mesh from a faulted subsurface domain to a continuous design domain, wherein the grid may be used to represent a discrete model of a subsurface material property (such as permeability) to use, for example, in a reservoir simulator. The mapping is geometry-based, not physics-based. The mapping is determined by an iterative optimization procedure designed to penalize deformation of tessellated mesh cells () in the design domain compared to their geometric quality in the faulted domain (), but subject to stitching constraints () appearing as a penalty term or Lagrange multiplier term in the optimization objective function to influence the final mesh to co-locate pairs of points identified on opposite sides of a fault as having been located together before the fault occurred.

Handling domain discontinuity with the help of grid optimization techniques

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

A method and system are described for generating a geologic model having material properties for a faulted subsurface region. The method and system involve parameterizing corresponding fault surfaces and solving an energy optimization equation and/or conservation law equation for the corresponding fault surfaces based on parameterized nodes on the fault surfaces to generate a displacement map. The displacement map is used to map a geologic model from the physical space to the design space, where it is populated with material properties. The resulting populated geologic model may be used for hydrocarbon operations associated with the subsurface region.

Managing discontinuities in geologic models

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 method is presented for modeling reservoir properties. The method includes an auxiliary time-stepping procedure of the reservoir between an old time and a new time, and calculating a plurality of masses explicitly. A plurality of phase component densities is updated linearly from the plurality of masses. A plurality of saturation changes is calculated based on the plurality of masses. A plurality of phase flow rates is updated based on the plurality of saturation changes, a plurality of phase flow rates at the old time, and a plurality of saturation derivatives of the phase flow rates at the old time. A plurality of component flow rates may be calculated based on the updated plurality of phase component densities and the plurality of phase flow rates. The method also includes a formulation method based on the auxiliary time stepping procedure.

Method and system for stabilizing formulation methods

A method and apparatus for generating a simulation grid for a reservoir model based on a geological model comprising horizons, constraints and multiple geological grid cells. A pre-image is generated corresponding to the geological grid cells, the pre-image comprising a surface and the modeling constraints being mapped onto the surface. A constrained two-dimensional grid is generated on the pre-image, the two-dimensional grid comprising multiple grid cells. Simulation layer boundaries are selected from the geological model and the constrained two-dimensional grid is projected onto the simulation layer boundaries. Prismatic cells are then generated to form the three-dimensional simulation grid. The method of generating a grid as herein described may be incorporated in existing reservoir simulators.

Method and apparatus for generating a three-dimensional simulation grid for a reservoir model

Method for transforming a discontinuous, faulted subsurface reservoir into a continuous, fault-free space where a complete geological model based on selected geological concepts can be built and updated efficiently. Faults are removed in reverse chronological order () to generate a pseudo-physical continuous layered model, which is populated with information according to the selected geological concept (). The fault removal is posed as an optimal control problem where unknown rigid body transformations and relative displacements on fault surfaces are found such that deformation of the bounding horizons and within the volume near the fault surface are minimized (). A boundary-element-method discretization in an infinite domain is used, with boundary data imposed only on fault surfaces. The data populated model may then be mapped back to the original faulted domain such that a one-to-one mapping between continuous and faulted spaces may be found to a desired tolerance ().

Fault removal in geological models

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 of generating a model of a turbidity current in a fluid is disclosed. A first flow layer in the turbidity current is defined. The method successively defines at least one more flow layer in the turbidity current. Each successive flow layer includes the previously defined flow layer. A set of depth-averaged flow variables for each flow layer is defined. A model is developed that describes the turbidity current. The model uses fluid flow equations and the set of depth-averaged flow variables for each flow layer to predict fluid flow in each flow layer. The model is then output.

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Sugar Land, TX, United States of America

Xiaohui Wu