Abstract: Methods and systems are presented in this disclosure for modeling fluid diversion in an integrated wellbore-reservoir system. A mathematical model for fluid diversion in a reservoir formation of the integrated wellbore-reservoir system is generated by capturing, within the model, combined effects of formation treatments by foaming agent and by a chemical agent (such as resin) that imposes skin effect and permeability reduction to the formation. The generated model can be employed to simulate treatment of the reservoir formation by the foamed resin system. Based on results of the simulated treatment, treatment of the reservoir formation by the foamed resin system can be initiated for fluid diversion among layers of different permeabilities in the reservoir formation.

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: 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: In some aspects, techniques and systems for modeling fluid flow are described. Pressure gradient values for respective nodes of a one-dimensional flow model are computed. The nodes represent locations of fluid flow along a flow path, and the pressure gradient values are computed based on an approximation of the flow velocity at a point on the flow path. A pressure drop between two opposite ends of the flow path is calculated based on the pressure gradient values. An improved approximation of the flow velocity for the point on the flow path is calculated based on a difference between the calculated pressure drop and a pressure drop boundary condition.

Abstract: Various embodiments disclosed relate to a fracture network model for simulating treatment of subterranean formations. In various embodiments, the present invention provides a method of simulating treatment of a subterranean formation. The method includes flowing a proppant slurry composition including proppant into each of one or more inlets of a fracture network model. The fracture network model includes a solid medium including a channel network, the one or more inlets, and one or more outlets. The channel network is free of fluidic connections leading outside of the solid medium other than the one or more inlets and the one or more outlets. The channel network includes a primary channel fluidly connected to each of the one or more inlets. The channel network also includes at least one secondary channel and fluidly connected to the primary channel, with the primary channel having a channel cross-section with a greater area than an area of a channel cross-section of the secondary channel.

Abstract: Computer-implemented methods for higher-order simulation, design and implementation of multi-phase, multi-fluid flows are disclosed. In one embodiment, a computer-implemented method is provided for a higher-order simulation, design and implementation of a strategy for injecting a plurality of stimulation fluids into a subterranean formation. In another embodiment, a computer-implemented method for higher-order simulation and enhancement of the flow of production fluids from a subterranean formation is disclosed. In a third embodiment, a computer-implemented higher-order simulation of the behavior of a plurality of fluids at an intersection of at least two geometrically discrete regions is disclosed.

Abstract: In some aspects, flow path connection conditions are generated for a flow path intersection in a one-dimensional fluid flow model. The one-dimensional fluid flow model represents a flow of well system fluid in a well system environment. The flow path connection conditions conserve fluid momentum among three or more flow path branches that meet at the flow path intersection. Fluid flow is simulated in the fracture network by operating the one-dimensional fluid flow model based on the connection condition.

Abstract: Various embodiments disclosed relate to a fracture network model for simulating treatment of subterranean formations. In various embodiments, the present invention provides a method of simulating treatment of a subterranean formation. The method includes flowing a proppant slurry composition including proppant into each of one or more inlets of a fracture network model. The fracture network model includes a solid medium including a channel network, the one or more inlets, and one or more outlets. The channel network is free of fluidic connections leading outside of the solid medium other than the one or more inlets and the one or more outlets. The channel network includes a primary channel fluidly connected to each of the one or more inlets. The channel network also includes at least one secondary channel and fluidly connected to the primary channel, with the primary channel having a channel cross-section with a greater area than an area of a channel cross-section of the secondary channel.

Abstract: In accordance with some embodiments of the present disclosure, a method of computational modeling for tracking ball sealers 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: Techniques for evaluating a fluid flow through a wellbore include identifying an input characterizing a fluid flow through a wellbore; identifying an input characterizing a geometry of the wellbore; generating a model of the wellbore based on the inputs characterizing the fluid flow and the geometry of the wellbore; simulating the fluid flow through the wellbore based on evaluating the model with a numerical method that determines fluid flow conditions at a first boundary location uphole and adjacent to a perforation of a plurality of perforations in the wellbore and at a second boundary location downhole and adjacent to the perforation; and preparing, based on the fluid flow conditions determined with the numerical method, an output associated with the simulated fluid flow through the wellbore for display to a user.

Abstract: In accordance with some embodiments of the present disclosure, a method of modeling for one-dimensional temperature distribution calculations in a wellbore is disclosed. The method may include estimating a pressure gradient of a fluid in a wellbore. The method may further include calculating a pressure of the fluid in the wellbore based on the pressure gradient of the fluid. Additionally, the method may include computing a velocity of the fluid in the wellbore. The method may also include determining a temperature of the fluid in the wellbore based on the pressure of the fluid in the wellbore and the velocity of the fluid in the wellbore. The method further includes using the temperature of the fluid to model a fluid property. The method includes selecting parameters for a stimulation operation based on the fluid property.

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 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: 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: 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: In some aspects, flow path connection conditions are generated for a flow path intersection in a one-dimensional fluid flow model. The one-dimensional fluid flow model represents a flow of well system fluid in a well system environment. The flow path connection conditions conserve fluid momentum among three or more flow path branches that meet at the flow path intersection. Fluid flow is simulated in the fracture network by operating the one-dimensional fluid flow model based on the connection condition.

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: 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: In some aspects, techniques and systems for modeling fluid flow are described. Pressure gradient values for respective nodes of a one-dimensional flow model are computed. The nodes represent locations of fluid flow along a flow path, and the pressure gradient values are computed based on an approximation of the flow velocity at a point on the flow path. A pressure drop between two opposite ends of the flow path is calculated based on the pressure gradient values. An improved approximation of the flow velocity for the point on the flow path is calculated based on a difference between the calculated pressure drop and a pressure drop boundary condition.

Abstract: Techniques for evaluating a fluid flow through a wellbore include identifying an input characterizing a fluid flow through a wellbore; identifying an input characterizing a geometry of the wellbore; generating a model of the wellbore based on the inputs characterizing the fluid flow and the geometry of the wellbore; simulating the fluid flow through the wellbore based on evaluating the model with a numerical method that determines fluid flow conditions at a first boundary location uphole and adjacent to a perforation of a plurality of perforations in the wellbore and at a second boundary location downhole and adjacent to the perforation; and preparing, based on the fluid flow conditions determined with the numerical method, an output associated with the simulated fluid flow through the wellbore for display to a user.