Abstract: Higher order simulation of hydrocarbon flows associated with complex fractures produced in the hydraulic fracturing process in a well system may be used to obtain high fidelity results while minimizing a cost of computation. The higher order simulation of hydrocarbon flows may provide efficient and stable simulation algorithms that avoid any artificial boundary treatment inconsistent with the governing equations, while maintaining a uniform order of accuracy. In particular, a re-normalization technique implements higher-order finite difference/finite volume discretization near the boundary of the complex fractures. The simulation of hydrocarbon flows may be used to determine a production activity for the well system.

Abstract: In some aspects, a number of subsystem models is accessed by a computer system. Each subsystem model represents dynamic attributes of a distinct physical subsystem in a subterranean region. At least one of the number of subsystem models represents dynamic attributes of a mechanical subsystem in the subterranean region. A discrete fracture network (DFN) model representing a fracture network in the subterranean region is accessed at the computer system. The DFN model includes junction models. Each junction model represents interactions between a respective set of subsystem models associated with the junction model. Junction variables of the junction model can be defined based on dynamic attributes of the respective set of subsystem models associated with the junction model. A stimulation treatment for the subterranean region can be simulated by operating the DFN model including the junction variables.

Abstract: In some aspects, a flow model represents a flow path for well system fluid in a subterranean region. A first system of equations from a finite element (FE) discretization of a flow model is accessed by a computer system. A second system of equations that imposes a constraint on errors between an exact solution and an FE solution to the flow model is accessed by the computer system. The FE solution includes nodes representing locations along the flow path for well system fluid in the subterranean region. Locations of the nodes can be computed by operations of the computer system in an iterative manner by computing locations of new nodes based on locations of existing nodes and refining the locations of the new nodes and the locations of the existing nodes based on the first and second systems of equations.

Abstract: Systems, methods and software can be used for analyzing microseismic data from a subterranean zone. In some aspects, a plurality of basic planes are each defined from a subset of the microseismic data and each have an orientation relative to a common axis. Clusters of orientations of the basic planes are identified adaptively based on the extent of variation in the orientations. The number of orientations associated with each of the clusters is then identified.

Abstract: In some aspects, a one-dimensional flow model is generated. The one-dimensional flow model can represent flow of a first fluid and a second fluid in a flow path in a well system environment. The one-dimensional flow model comprises an effective diffusion coefficient model for a composite fluid volume comprising the first and second fluids. The effective diffusion coefficient model calculates an effective diffusion coefficient for the composite fluid volume based on a difference between the respective densities and viscosities of the first fluid and the second fluid.

Abstract: Systems, methods and software can be used for analyzing microseismic data collected from a fracturing treatment of a subterranean zone. In some aspects, a plurality of basic planes are each defined from a subset of the microseismic data and each have an orientation relative to a common axis. Clusters of orientations of the basic planes previously identified adaptively based on the extent of variation in the orientations can be updated with new data. The number of orientations associated with each of the clusters is then identified.

Abstract: Systems, methods, and software can be used to calculate fracture stratigraphy of a subterranean zone. In some aspects, microseismic event data associated with a fracture treatment of a subterranean zone are received, and the subterranean zone includes multiple subsurface layers. A filter is used to select a subset of the microseismic event data corresponding to fractures in a particular subsurface layer. Fracture stratigraphy is calculated for the particular subsurface layer from fracture planes associated with the selected subset of the microseismic event data.

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, a one-dimensional proppant transport flow model represents flow of a proppant-fluid mixture in a subterranean region. The one-dimensional proppant transport flow model includes a proppant momentum conservation model that balances axial proppant momentum in an axial flow direction of the proppant-fluid mixture against dynamic changes in transverse proppant momentum. In some instances, the proppant momentum conservation model can vary the axial proppant momentum, for example, to account for interphase momentum transfer between the proppant and the fluid.

Abstract: Systems, methods, and software can be used to analyze microseismic data from a fracture treatment. In some aspects, stored data associate a fracture plane with a first plurality of microseismic events from a fracture treatment of a subterranean region. Additional stored data indicate an ordering of a second, different plurality of microseismic events from the fracture treatment. One of the second plurality of microseismic events is selected based on the ordering, and the fracture plane is updated based on the selected microseismic event.

Abstract: Systems, methods, and software can be used to analyze microseismic data from a fracture treatment. In some aspects, fracture planes are identified based on microseismic event data from a fracture treatment of a subterranean zone. Each fracture plane is associated with a subset of the microseismic event data. Confidence level groups are identified from the fracture planes. Each confidence level group includes fracture planes that have an accuracy confidence value within a respective range. A graphical representation of the fracture planes is generated. The graphical representation includes a distinct plot for each confidence level group.

Abstract: In accordance with some embodiments of the present disclosure, a method of computational modeling for tracking ball scalers in a wellbore is disclosed. The method may include, for a time step, calculating a number of ball sealers to inject into a wellbore, injecting the ball sealers, determining a length of the wellbore occupied by a fluid, and computing a spacing between each ball sealer in the length of the wellbore occupied by the fluid. The method may include calculating a first position of a ball sealer, determining a velocity the ball sealer, and computing a second position of the ball sealer. The method may include recording a number of active ball sealers and open perforations in the wellbore, calculating a ball sealer skin per division, and determining a fluid flow rate. The method may include selecting parameters for a stimulation operation in the wellbore based on the fluid flow rate.

Abstract: Systems, methods, and software can be used to identify fracture planes in a subterranean zone. In some aspects, data representing locations of microseismic events associated with a subterranean zone are received. Fracture plane parameters are calculated from the locations of the microseismic events. The fracture plane parameters are calculated based on a sum of weighted terms, and each of the weighted terms includes a weighting factor that decreases with a distance between at least one of the microseismic events and a fracture plane defined by the fracture plane parameters.

Abstract: In some aspects, techniques and systems for operating a subterranean region model are described. A band matrix that represents well system fluid flow in a subterranean region is accessed. The band matrix includes flow variable coefficients based on governing flow equations for the well system fluid flow. A first elimination is performed on an upper part of the band matrix. The upper part of the band matrix includes a first subset of the flow variable coefficients corresponding to a first subset of flow variables. In parallel with the first elimination, a second elimination is performed on a lower part of the band matrix. The lower part of the band matrix includes a second subset of flow variable coefficients corresponding to a second subset of the flow variables. An intermediate part of the band matrix can be solved. The intermediate part of the band matrix includes other flow variable coefficients.

Abstract: In some aspects, techniques and systems for modeling fluid flow are described. A flow model represents intersecting flow paths for well system fluid. The flow paths intersect at a flow path intersection. A band matrix and an intersection table are generated based on the flow model. The band matrix represents fluid flow within the respective flow paths, and the intersection table represents fluid flow between the flow paths at the flow path intersection. The flow model can be operated using the band matrix and the intersection table, for example, to calculate fluid flow variables at various locations along the flow paths.

Abstract: Systems, methods, and software can be used to determine a confidence value for a fracture plane. In some aspects, a subset of microseismic events associated with a fracture treatment of a subterranean zone are selected. Confidence in associating the selected subset of microseismic events with a common fracture plane is determined. The confidence can be determined, for example, based on the number of microseismic events in the subset, a location uncertainty for each microseismic event in the subset, a moment magnitude for each microseismic event in the subset, a distance between each microseismic event and a fracture plane fitted to the microseismic events, an orientation of the fracture plane fitted to the microseismic events, or a combination of these and other factors.

Abstract: An injection treatment on a subterranean zone is simulated by modeling physically separate rock blocks of the subterranean zone by separate block models. The block model for each physically separate rock block represents intra-block mechanics of the rock block by finite element method. Condensation is performed in the finite element method to reduce nodal degrees of freedom operation on by the finite element method. Interactions between adjacent pairs of the rock blocks are modeled by separate joint models. The joint model for each adjacent pair of rock blocks represents inter-block mechanics between the adjacent rock blocks. The injection treatment of the subterranean zone is simulated with the block models and the joint models.

Abstract: In some aspects, techniques and systems for operating a subterranean region model are described. Sub-matrices and entries outside the sub-matrices in a first band matrix are identified. The first band matrix includes flow variable coefficients based on governing flow equations of a model representing well system fluid flow in a subterranean region. For each of the sub-matrices, a reduced-size matrix is generated based on the sub-matrix and a subset of the entries that are associated with the sub-matrix. A second band matrix is generated based on the reduced-size matrices. The model is operated based on the second band matrix.

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 block matrix is identified. The block matrix includes a banded portion and an augmented portion. The banded portion includes flow variable coefficients based on governing flow equations of a model representing well system fluid flow in a subterranean region. In a row of the block matrix, decomposition of a pivot element in the row is performed. Elements along the row are modified based on an inverse of the decomposition of the pivot element. A flow variable of the model is solved based on the block matrix that contains the modified elements.