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: Methods of modeling flow of gas within a reservoir are provided. A particular method includes generating a representation of a gas reservoir, where the gas reservoir includes at least two phases of matter. The representation of the gas reservoir models the gas reservoir as a single phase. The method also includes modeling flow of gas within the gas reservoir using the representation.

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: A method and system for predicting the behavior of a physical system are disclosed. One embodiment of the method of this invention comprises the steps of creating an equation in a first coordinate system to model an aspect of the physical system; applying a coordinate transformation to the equation to transform the equation from the first coordinate system into a second coordinate system more closely representative of an analytical solution to the equation; solving the equation in the second coordinate system to obtain a solution; transforming the solution back to the first coordinate system; creating a second equation in the first coordinate system to model a second aspect of the physical system; solving the second equation in the first coordinate system to obtain a solution to the second equation; and combining the mapped solution to the first equation and the solution to the second equation in the first coordinate system to obtain a combined solution.

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: Systems and methods for solving finite element models, wherein the matrix that governs the solution is modified by adjusting the weighting coefficients of the matrix so that the elements which lie on the diagonal of the matrix are non-negative and the elements which are off the diagonal are non-positive. In one embodiment, a system is discretized on a finite element mesh with the contribution of each node to the discretization being weighted based upon the direction of fluid flow across each element. The nodes which are upstream from the other nodes of the respective elements are weighted more heavily to cause the resulting matrix to be substantially diagonal. This matrix is solved using traditional techniques.

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 for predicting the behavior of a physical system are disclosed.

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: Systems and methods for solving finite element models, wherein the matrix that governs the solution is modified by adjusting the weighting coefficients of the matrix so that the elements which lie on the diagonal of the matrix are non-negative and the elements which are off the diagonal are non-positive. In one embodiment, a system is discretized on a finite element mesh with the contribution of each node to the discretization being weighted based upon the direction of fluid flow across each element. The nodes which are upstream from the other nodes of the respective elements are weighted more heavily to cause the resulting matrix to be substantially diagonal. This matrix is solved using traditional techniques.

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: 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.