Abstract: In accordance with embodiments of the present disclosure, a discretization technique may be used to solve for fluid and proppant flow through a fracture within a dynamic fracture network. The discretization technique may involve performing a spatial discretization of non-linear coupled equations by integrating the equations over staggered finite control volumes. For example, the spatial discretization may involve integrating a continuity equation representing fluid flowing through the fracture over a first control volume along the length of the fracture, integrating a momentum equation representing the fluid flowing through the fracture over a second control volume that is staggered with respect to the first control volume, and integrating a proppant equation representative of the proppant flowing with the fluid through the fracture over the first control volume. The discretized equations may be used to determine a linear system of equations to simulate proppant flow through the dynamic fracture network.

Abstract: In some aspects, locations for nodes are computed for a one-dimensional flow model that models well system fluid flow in a subterranean region. Truncation error threshold data indicate a truncation threshold value for each of the nodes. Discretization data indicate a lowest-order term truncated from a discretized governing flow equation for each of the nodes. The locations for the nodes can be computed based on a scalar cost function, such that each of the lowest order terms is less than or equal to the truncation error threshold value for the respective node.

Abstract: Present embodiments are directed to a method that includes receiving inputs indicative of a property of a fracture within a dynamic fracture network, assigning an orientation to each of the plurality of fractures, and assigning a plurality of fracture nodes and fracture cells encompassing each fracture node along the fracture. The method also includes receiving variables representative of apertures at a first fracture node and a second fracture node and determining fluid flow within the fracture cell based on Navier-Stokes equations with proppant transport, as a function of the conditions at the first fracture node and the second fracture node. The method further includes displaying a simulation representative of a flow of proppant through the fracture based on the junction conditions via a display coupled to the processing component.

Abstract: Present embodiments are directed to a method that includes receiving inputs indicative of a property of a fracture present within a dynamic fracture network, assigning an orientation to each of the plurality of fractures, and receiving variables representative of the endpoints of the fracture between a first junction and a second junction of the plurality of junctions. The method also includes determining a linear system representing fluid flow within the fracture based on Navier-Stokes equations, as a function of the variables at the first junction and the second junction. The method further includes displaying a simulation representative of a fluid flow through the fracture based on the junction conditions via a display coupled to the processing component.

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: 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: Systems, methods and software can be used for processing microseismic data from a subterranean region. In some aspects, groupings of data points are identified. The data points are based on microseismic data from a subterranean region. The identification of the groupings is constrained such that each grouping includes at least a minimum number of the data points, and such that the data points in each grouping have at most a maximum extent of variation. In some instances, a histogram of the data points is generated, and each of the identified groupings corresponds to a bin in the histogram.

Abstract: An illustrative hydraulic fracturing flow simulation method includes: identifying a network of fractures within a formation rock matrix; modeling each fracture in the network as fluid flow path having discrete points at which a fluid pressure is determined; representing the rock matrix with discrete nodes at which a fluid-solid interaction force is determined, each said discrete node being associated with multiple discrete points along a fluid flow path; deriving the fluid-solid interaction force for each node from the fluid pressure at the associated discrete points; estimating an extent of fracture propagation based in part on the fluid-solid interaction forces; and displaying a visual representation of the fracture propagation extent.

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 method; and a visualization module that displays the time-dependent spatial distribution. The simulation method includes: deriving from the measurements a network of fractures having junctions where two or more fractures intersect; ordering a set of corner points associated with each junction; calculating a junction area from each set of corner points; determining a current state that includes flow parameter values at discrete points arranged along the fractures in said network; constructing a set of linear equations for deriving a subsequent state from the current state while accounting for said junction areas; and repeatedly solving the set of linear equations to obtain a sequence of subsequent states, the sequence embodying a time-dependent spatial distribution of at least one flow parameter.

Abstract: An illustrative domain-adaptive hydraulic fracturing simulator includes: a data acquisition module, a simulator module, and a visualization module. The data acquisition module acquires measurements of a subterranean formation undergoing a hydraulic fracturing operation. The simulator module provides a series of states for a model of the subterranean formation by: (a) constructing said model from the measurements, the model representing said current state throughout a modeled domain; (b) determining a core domain of influence within the modeled domain by identifying active fractures; (c) generating a linear set of equations to derive the subsequent state from the current state, the linear set of equations including fluid flow equations for the core domain of influence and excluding fluid flow equations for a region of the modeled domain outside the core domain of influence; and (d) deriving the subsequent state from the linear set of equations. The visualization module displays the series of states.

Abstract: An illustrative domain-adaptive simulator includes: a data acquisition module, a simulator module, and a visualization module. The data acquisition module acquires measurements of a physical system. The simulator module provides a series of states for the physical system, the series including at least a current state and a subsequent state, wherein as part of said providing, the simulator module implements a method that includes: (a) constructing a modeled domain for the system; (b) determining a domain of influence within the modeled domain; (c) generating a linear set of equations to derive the subsequent state from the current state, the linear set of equations excluding a region of the modeled domain outside the domain of influence; and (d) deriving the subsequent state from the linear set of equations. The visualization module displays the series of states.

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 accordance with embodiments of the present disclosure, a discretization technique may be used to solve for fluid and proppant flow through a fracture within a dynamic fracture network. The discretization technique may involve performing a spatial discretization of non-linear coupled equations by integrating the equations over staggered finite control volumes. For example, the spatial discretization may involve integrating a continuity equation representing fluid flowing through the fracture over a first control volume along the length of the fracture, integrating a momentum equation representing the fluid flowing through the fracture over a second control volume that is staggered with respect to the first control volume, and integrating a proppant equation representative of the proppant flowing with the fluid through the fracture over the first control volume. The discretized equations may be used to determine a linear system of equations to simulate proppant flow through the dynamic fracture network.

Abstract: Present embodiments are directed to a method that includes receiving inputs indicative of a property of a fracture present within a dynamic fracture network, assigning an orientation to each of the plurality of fractures, and receiving variables representative of the endpoints of the fracture between a first junction and a second junction of the plurality of junctions. The method also includes determining a linear system representing fluid flow within the fracture based on Navier-Stokes equations, as a function of the variables at the first junction and the second junction. The method further includes displaying a simulation representative of a fluid flow through the fracture based on the junction conditions via a display coupled to the processing component.

Abstract: In accordance with embodiments of the present disclosure, a methodology may be used to computationally simulate a system of equations relating to the junction points of a dynamic fracture network (DFN). The simulation may utilize one or more efficient algorithms to perform a realistic, physically conservative, and stable coupled simulation of the DFN's complex flows. These algorithms may use assumptions based on the transient Navier-Stokes equations to perform the proppant laden flow simulation. As described in detail below, the algorithms may utilize a numerical methodology that accurately simulates a junction system of equations arising from solving the fluid and proppant flows inside individual fractures based on Navier-Stokes equations along with a proppant transport equation.

Abstract: Present embodiments are directed to a method that includes receiving inputs indicative of a property of a fracture within a dynamic fracture network, assigning an orientation to each of the plurality of fractures, and assigning a plurality of fracture nodes and fracture cells encompassing each fracture node along the fracture. The method also includes receiving variables representative of apertures at a first fracture node and a second fracture node and determining fluid flow within the fracture cell based on Navier-Stokes equations with proppant transport, as a function of the conditions at the first fracture node and the second fracture node. The method further includes displaying a simulation representative of a flow of proppant through the fracture based on the junction conditions via a display coupled to the processing component.

Abstract: Systems, methods and software can be used for processing microseismic data from a subterranean region. In some aspects, groupings of data points are identified. The data points are based on microseismic data from a subterranean region. The identification of the groupings is constrained such that each grouping includes at least a minimum number of the data points, and such that the data points in each grouping have at most a maximum extent of variation. In some instances, a histogram of the data points is generated, and each of the identified groupings corresponds to a bin in the histogram.

Abstract: In some aspects, a grid-point-spacing ratio is computed for a one-dimensional fluid flow model. The one-dimensional fluid flow model represents a flow path for well system fluid in a subterranean region, and the grid-point-spacing ratio is computed based on a parameter of the flow path. Grid points for the one-dimensional flow model are generated based on the grid-point-spacing ratio.

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.