Abstract: Geological stata can be modeled using weighted parameters. For example, geological data representative of strata in a subterranean formation can be received. A weight for a parameter usable to generate a geological model can be determined. Examples of the parameter can include (i) a first parameter for reducing a change in a thickness of a stratum, (ii) a second parameter for maintaining a minimum thickness of the stratum, (iii) a third parameter for maintaining a maximum thickness of the stratum, (iv) a fourth parameter for reducing a curvature in the thickness of the stratum, (v) a fifth parameter for a user-provided indication of a feature of the stratum, or (vi) any combination of these. The geological model can be generated by concurrently solving a system of equations using the weight and the geological data. The geological model can be displayed and can visually represent the cross-sectional shapes of the strata.

Abstract: The disclosed embodiments include a method, apparatus, and computer program product for generating multiple correlated meshes around complex and discrete fractures for the purpose of reservoir simulation. In an initial two-stage process, a 2.5-dimensional mesher algorithm, may be used in conjunction with an extended anisotropic geometry-adaptive refinement algorithm to produce, from a structured grid Earth Model, a refined reservoir model. Fractures may be modeled as a volumetric mesh that is independent of the refined reservoir model. Thereafter, the two independent, overlapping meshes are combined by forming matrix-matrix, fracture-fracture, and matrix-fracture connections to form a single model to allow rapid simulation of an extremely complex fracture network with sufficiently accurate results.

Abstract: A system and method inserts fracture networks into an existing Earth Model that exists as a structured grid and physical property values. The fracture network is in the form of a surface mesh (manifold or non-manifold) in a three-dimensional (“3D”) space. The structured grid of the Earth Model is then anisotropically refined to resolve the fractures and to provide appropriate cell grading in the near-fracture region. The generated Earth Model may be utilized in a variety of applications, including for example, a reservoir simulation.

Abstract: The disclosed embodiments include a method, apparatus, and computer program product for generating multiple correlated meshes around complex and discrete fractures for the purpose of reservoir simulation. In an initial two-stage process, a 2.5-dimensional mesher algorithm, may be used in conjunction with an extended anisotropic geometry-adaptive refinement algorithm to produce, from a structured grid Earth Model, a refined reservoir model. Fractures may be modeled as a volumetric mesh that is independent of the refined reservoir model. Thereafter, the two independent, overlapping meshes are combined by forming matrix-matrix, fracture-fracture, and matrix-fracture connections to form a single model to allow rapid simulation of an extremely complex fracture network with sufficiently accurate results.

Abstract: A system and method inserts fracture networks into an existing Earth Model that exists as a structured grid and physical property values. The fracture network is in the form of a surface mesh (manifold or non-manifold) in a three-dimensional (“3D”) space. The structured grid of the Earth Model is then anisotropically refined to resolve the fractures and to provide appropriate cell grading in the near-fracture region. The generated Earth Model may be utilized in a variety of applications, including for example, a reservoir simulation.

Abstract: A method and system for generating an unstructured automatic mesh and executing computational algorithms using a finite element numerical approach is disclosed. The method is to model a hydrocarbon reservoir, wells, and completions as a single system, accounting for static information and transient behavior of wells, hydraulic fractures and reservoirs in a single model.

Abstract: The disclosure is directed to a computer-implemented method of representing fluid flow in a physical fluid reservoir. The method includes generating a mesh representation of the physical fluid reservoir having a plurality of mesh elements. Each of the plurality of mesh elements is representative of a regional portion of the fluid reservoir. The method further includes generating a matrix-based representation of fluid flow comprising matrix elements associated with a mesh element and selectively weighting the matrix elements based on fluid flow direction in the regional portion of the fluid reservoir represented by the mesh element associated with the matrix element.

Abstract: A method and system for generating an unstructured automatic mesh and executing computational algorithms using a finite element numerical approach is disclosed. The method is to model a hydrocarbon reservoir, wells, and completions as a single system, accounting for static information and transient behavior of wells, hydraulic fractures and reservoirs in a single model.

Abstract: A method and system are disclosed for high-resolution modeling of a well bore in a reservoir. An embodiment of the present disclosure comprises the steps of constructing a first unstructured mesh having a plurality of n-dimensional simplices corresponding to a first modeled system (space), defining a surface bounding a second modeled space, identifying a subset of the plurality of n-dimensional simplices of the first mesh that are intersected by the surface, and modifying the subset of simplices so as to adapt the first mesh such that it comprises a second mesh and a third mesh, wherein the second mesh comprises a set of simplices located entirely interior to the surface and wherein the third mesh comprises another set of simplices located entirely exterior to said surface.

Abstract: Methods and systems for adapting an unstructured mesh to a modeled space. In one embodiment, a surface is defined in the modeled space, intersections of the surface with the elements of the mesh are determined, and new elements within the intersected elements are defined such that one or more of the faces of the new elements are substantially coincident with the surface. For each element which is intersected by the surface, a plurality of points at which the edges of the element are intersected is determined. For each point of intersection, a new node is located at that point and two new elements which incorporate the new node are created. This process is performed for each of the points of intersection so that the intersected element is subdivided into an new elements which include faces that lie substantially on the modeled surface.

Abstract: A method for simulating a physical system using finite element techniques, wherein two or more distinct models corresponding to distinct regions within the modeled system are solved, each with a corresponding evaluator. Nodes which lie on the boundaries between the models may have different values corresponding to the different models. When a particular model is solved, the evaluator for that model is used to obtain the appropriate values for each of these common nodes. In one embodiment, a first model is defined, then a region corresponding to a particular feature within the system is carved out of it. A finite element model corresponding to the feature is then inserted into the region. The finite elements may be adapted to share nodes on the boundaries between them.

Abstract: A method for solving space-time problems involving three-dimensional space wherein an unstructured four-dimensional finite element model is generated and solved to produce a four-dimensional solution. The four-dimensional mesh is generated from a three-dimensional mesh by extruding each of the simplices of the three-dimensional mesh in a time dimension. The four-dimensional prisms formed by extrusion of the three-dimensional simplices are divided into a plurality of four-dimensional simplices which form a four-dimensional finite element model. The elements of the four-dimensional model can be selectively refined to obtain a finer mesh in areas of greater interest, and a coarser mesh in areas which are of less interest. The mesh can be refined in the spatial dimensions and also in the temporal dimension.

Abstract: A method and system are disclosed for high-resolution modeling of a well bore in a reservoir. An embodiment of the present invention comprising the steps of constructing a first unstructured mesh, having a plurality of n-dimensional simplices, corresponding to a first modeled system (space), defining a surface bounding a second modeled space, identifying a subset of the plurality of n-dimensional simplices of the first mesh that are intersected by the surface, and modifying the subset of simplices so as to adapt the first mesh such that it comprises a second mesh and a third mesh, wherein the second mesh comprises a set of simplices located entirely interior to the surface and wherein the third mesh comprises another set of simplices located entirely exterior to said surface.

Abstract: A method for solving space-time problems involving three-dimensional space wherein an unstructured four-dimensional finite element model is generated and solved to produce a four-dimensional solution. The four-dimensional mesh is generated from a three-dimensional mesh by extruding each of the simplices of the three-dimensional mesh in a time dimension. The four-dimensional prisms formed by extrusion of the three-dimensional simplices are divided into a plurality of four-dimensional simplices which form a four-dimensional finite element model. The elements of the four-dimensional model can be selectively refined to obtain a finer mesh in areas of greater interest, and a coarser mesh in areas which are of less interest. The mesh can be refined in the spatial dimensions and also in the temporal dimension.

Abstract: Methods and systems for adapting an unstructured mesh to a modeled space. In one embodiment, a surface is defined in the modeled space, intersections of the surface with the elements of the mesh are determined, and new elements within the intersected elements are defined such that one or more of the faces of the new elements are substantially coincident with the surface. For each element which is intersected by the surface, a plurality of points at which the edges of the element are intersected is determined. For each point of intersection, a new node is located at that point and two new elements which incorporate the new node are created. This process is performed for each of the points of intersection so that the intersected element is subdivided into an new elements which include faces that lie substantially on the modeled surface.

Abstract: A method for simulating a physical system using finite element techniques, wherein two or more distinct models corresponding to distinct regions within the modeled system are solved, each with a corresponding evaluator. Nodes which lie on the boundaries between the models may have different values corresponding to the different models. When a particular model is solved, the evaluator for that model is used to obtain the appropriate values for each of these common nodes. In one embodiment, a first model is defined, then a region corresponding to a particular feature within the system is carved out of it. A finite element model corresponding to the feature is then inserted into the region. The finite elements may be adapted to share nodes on the boundaries between them.