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: A hydraulic fracturing flow simulation method includes identifying one or more reservoir layers contacted by a wellbore, the reservoir layers including a network of fractures. The method further includes determining a current network state that includes flow parameter values at discrete points arranged one-dimensionally along the wellbore and at discrete points arranged one-dimensionally along each fracture, the flow parameter values including concentrations of multiple proppant types or sizes. The method further includes constructing a set of linear equations for deriving a subsequent network state from the current network state while accounting for interaction and settling of the multiple proppant types or sizes. The method further includes repeatedly solving the set of linear equations to obtain a sequence of subsequent network states. The method further includes displaying the time-dependent spatial distribution.

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: A hydraulic fracturing flow simulation method includes identifying a discrete fracture network that partitions a reservoir into porous rock blocks. The method further includes determining a current network state that includes flow parameter values at discrete points arranged one-dimensionally along the fractures in said network. The method further includes constructing a set of linear equations for deriving a subsequent network state from the current state. The method further includes repeatedly solving the set of linear equations to obtain a sequence of subsequent network states, the sequence embodying a time-dependent spatial distribution of at least one flow parameter, said flow parameter comprising a proppant volume fraction. The method further includes displaying the time-dependent spatial distribution.

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 fluid momentum conservation model and a proppant bed momentum conservation model that account for viscoelastic effects of the proppant-fluid mixture. The one-dimensional proppant transport flow model may also include a proppant momentum conservation model. In some cases the one-dimensional proppant transport flow model may account for any of settling and resuspension of a proppant bed and interphase momentum transfer between the proppant, proppant bed, and the fluid.

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 hydraulic fracturing simulation method includes: creating an initial mesh representation of a subterranean formation, the mesh including mesh nodes; determining one or more fracture paths in the formation; for each of the one or more fracture paths, displacing a subset of the mesh nodes into alignment with the fracture path; interpolating from displacements of the aligned mesh nodes to obtain displacements for each non-aligned mesh node in the mesh, thereby obtaining a deformed mesh representation of the formation; using the deformed mesh to construct a linear set of equations representing fracture creation and propagation caused by injection of a hydraulic fracturing fluid; deriving one or more fracture path extensions from the linear set of equations; and displaying the one or more fracture paths with the one or more fracture path extensions accurately representing the fracture propagation path. The interpolation may be performed using radial basis functions.

Abstract: An illustrative monitoring system for a hydraulic fracturing operation includes: a data acquisition module collecting microseismic signals from a subterranean formation undergoing a hydraulic fracturing operation; a processing module implementing a monitoring method; and a visualization module that displays an estimate or prediction of fracture extent. The monitoring method implemented by the processing module includes: deriving microseismic event locations and times from the microseismic signals; fitting at least one fracture plane to the microseismic event locations; projecting each microseismic event location onto at least one fracture plane; determining a time-dependent distribution of the projected microseismic event locations; calculating one or more envelope parameters from the time-dependent distribution; and generating an estimate or prediction of fracture extent using the or more envelope parameters.

Abstract: An illustrative formation flow simulation method includes: measuring horizontal and vertical permeability of at least one bed in a formation penetrated by a vertical borehole; representing the borehole as a linear, discretized borehole flow path; representing the formation as a plurality of horizontal layers, each layer of the plurality of horizontal layers being represented as a linear, discretized layer flow path; constructing a current state vector having values of flow parameters for the discretized borehole flow path and each of the discretized layer flow paths; constructing a solution matrix embodying a set of flow equations that relate the current state vector to a subsequent state vector, the flow equations employing the measured horizontal permeability for flow along the discretized layer flow path for each layer and employing the measured vertical permeability for cross-flow to or from each layer, wherein the solution matrix, current state vector, and subsequent state vector form a linear system of

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 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: The disclosed embodiments include a method for determining fluid level drop and formation permeability during wellbore stimulation of a shut-in stage in real time. The method includes receiving an initial permeability value of a formation surrounding a wellbore. Further, the method includes performing, and if necessary repeating at a defined time interval, the following steps until a flowrate of stimulation fluid reaches zero or until a new pumping stage begins. The steps include solving for the flowrate of the stimulation fluid in the wellbore and computing hydrostatic pressure and a computed temperature in the wellbore. Further, the steps include updating a permeability calculation of the formation based on the flowrate of the stimulation fluid.

Abstract: A method for improved data-driven estimation of a stimulated reservoir volume may generate an optimized surface that encloses a set of data points including microseismic event data corresponding to a treatment of a subterranean formation. A Delaunay triangulation may be performed on the set of data points to generate a set of polytopes. A Voronoi polygon may be generated about each data point and used to obtain a local density measure that is locally and adaptively determined for each data point. Based on the local density measure, polytopes in the set of polytopes may be discriminated for inclusion in the optimized surface.

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 accordance with some embodiments of the present disclosure, a method of modeling a downhole drilling tool is disclosed. The method may include obtaining microseismic data corresponding to a treatment of a subterranean region, the microseismic data including a microseismic event time for each of a plurality of microseismic events, and a microseismic event location for each of the plurality of microseismic events. The method may additionally include calculating a plurality of fracture planes based upon the microseismic event times, and calculating a closed boundary enclosing a first subset of the plurality of fracture planes. The method may further include identifying a microseismic supported stimulated reservoir volume (?SRN) for the treatment based on the closed boundary.

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: In some aspects, a closed boundary is computed based on locations and location-uncertainty domains of microseismic events associated with a stimulation treatment of a subterranean region. The closed boundary encloses the locations and respective location-uncertainty domains of multiple microseismic event data points. An error bound of a stimulated reservoir volume (SRV) for the stimulation treatment is identified based on the closed boundary.

Abstract: In some aspects, reservoir characterizations of subterranean regions can be enhanced by using realtime fracture matching techniques for capturing the time dependent evolution of fracture parameters based on the occurrence of the time microseismic events generated by stimulation treatments. These microseismic events may further be used to determine hydraulic fracture planes, identify areas of concentration of high density microseismic events, identify and analyze complex fracture networks, and use these and other techniques to enhance the reservoir characterization.