Abstract: An illustrative hydraulic fracturing flow simulation system includes: a data acquisition module collecting measurements from a subterranean formation; a processing module implementing a hydraulic fracturing simulation; and a visualization module that displays a time-dependent spatial distribution. The implemented method includes: modeling a connected network of fractures; assigning an orientation to each fracture in the network to locate two different flow parameter types at each junction, thereby defining an arrangement of different flow parameter types spatially staggered along each fracture; capturing the arrangement as a set of linear equations for iteratively deriving a subsequent flow state from a current flow state; simulating flow through the network of fractures by repeatedly solving the set of linear equations; and determining the time-dependent spatial distribution of at least one flow component.

Abstract: An illustrative hydraulic fracturing flow simulation system includes: a data acquisition module collecting measurements from a subterranean formation; a processing module implementing a hydraulic fracturing simulation; and a visualization module that displays a time-dependent spatial distribution. The implemented method includes: modeling a connected network of fractures; assigning an orientation to each fracture in the network to locate two different flow parameter types at each junction, thereby defining an arrangement of different flow parameter types spatially staggered along each fracture; capturing the arrangement as a set of linear equations for iteratively deriving a subsequent flow state from a current flow state; simulating flow through the network of fractures by repeatedly solving the set of linear equations; and determining the time-dependent spatial distribution of at least one flow component.

Abstract: In a general aspect, a subterranean region is simulated using a finite element mesh and a boundary element mesh. In some aspects, a finite element mesh is generated over a domain representing a subterranean region. The finite element mesh defines elements that represent respective sub-regions of the subterranean region. The elements include a first element having a boundary defined by the finite element mesh, and at least a portion of the boundary of the first element represents a discontinuity in the subterranean region. A boundary element mesh is generated over the boundary of the first element, and the subterranean region is simulated using the finite element mesh and the boundary element mesh.

Abstract: The invention comprises a method of imaging a volume of the earth's subsurface. A selected volume of the earth's subsurface is divided into a three-dimensional grid of voxels. Seismic signals representing seismic energy emanating from the earth's subsurface and detected by sensors deployed in proximity to said selected subsurface volume and conducted to a recorder for recording. The recorded signals are transformed into a grid of discrete voxel signals representing energy emanating from voxels included in said three-dimensional grid of voxels in the earth's subsurface. A smooth analytic function is defined in three dimensional space based on the grid of discrete voxel signals; and fracture surfaces are derived from the smooth analytic function.

Abstract: In some aspects, a set of governing flow equations can be defined for a one-dimensional flow model representing well system fluid in a fractured subterranean region. A first subset of the governing flow equations can represent flow within a fracture, and a second subset of the governing flow equations can represent flow within a reservoir medium adjacent to the fracture. A reduced set of governing flow equations can be generated by eliminating the second subset from the set of governing flow equations based on fluid coupling between the fracture and the reservoir medium. Well system fluid flow in the fractured subterranean region can be simulated based on the reduced set of governing flow equations.

Abstract: In some aspects, techniques and systems for simulating well system fluid flow are described. Multiple subsystem models each include fluid flow variables and represent well system fluid dynamics associated with a sub-region in a subterranean region. The subsystem models are connected by one or more junction models. The junction models represent interactions among the subsystem models. For each of the subsystem models, an elimination of internal variables of the subsystem model is performed to express the internal variables in terms of junction variables of the junction models. The junction variables are solved based on the junction models. The internal variables of the subsystem model are solved based on the solved junction variables.

Abstract: In some aspects, techniques and systems for operating a subterranean region model are described. A global system model represents a subterranean region. A global coefficient matrix of the global system model can be identified. The global system includes preconditioned subsystem models. Each of the subsystem models represents a distinct subsystem within the subterranean region and is associated with a respective governing equation. Eigenvalues of the global coefficient matrix can be shifted by a regularization parameter. Shifting the eigenvalues of the global coefficient matrix generates a shifted global coefficient matrix. A solution to a shifted global system that includes the shifted global coefficient matrix can be obtained. The global system model can be solved based on the solution to the shifted global system.

Abstract: In some aspects, techniques and systems for operating a subterranean region model are described. A global system model represents a subterranean region. Subsystem models of the global system model are identified. Each of the subsystem models represents a distinct subsystem within the subterranean region and is associated with a respective governing equation. The subsystem models can be preconditioned based on the respective governing equations of the subsystem models. The global system model that includes the preconditioned subsystem models can be preconditioned. The preconditioned global system model can be operated.

Abstract: In some aspects, techniques and systems for simulating well system fluid flow are described. Multiple subsystem models each include fluid flow variables and represent well system fluid dynamics associated with a sub-region in a subterranean region. The subsystem models are connected by one or more junction models. The junction models represent interactions among the subsystem models. For each of the subsystem models, an elimination of internal variables of the subsystem model is performed to express the internal variables in terms of junction variables of the junction models. The junction variables are solved based on the junction models. The internal variables of the subsystem model are solved based on the solved junction variables.