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Andrew P. Bunger - One of the best experts on this subject based on the ideXlab platform.
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numerical model for a penny shaped hydraulic fracture driven by laminar turbulent fluid in an Impermeable Rock
International Journal of Solids and Structures, 2019Co-Authors: Navid Zolfaghari, Andrew P. BungerAbstract:Abstract As hydraulic fracturing at high injection rates with low viscosity fluids grows in popularity, so also there is a growing need to include not only the more common laminar fluid flow, but also the turbulent and transition flow regimes in numerical simulators. One common scenario is embodied in the behavior of a radial (penny-shaped) hydraulic fracture where flow is turbulent near the inlet, laminar near the tip, and in transition somewhere between. The main goal of this paper is to investigate the impact of this transition on hydraulic fracture growth through development and use of a numerical simulator for penny-shaped hydraulic fractures using the so-called drag reduction method to estimate the friction factor inside the crack for all relevant flow regimes. Upon solving this problem numerically for the case of zero toughness, comparing the results with fully laminar and fully turbulent asymptotic solutions shows that the early time behavior of radial hydraulic fractures is predominantly turbulent while large time behavior if predominantly laminar. The time scale associated with this transition determines the relevance of either limiting regime to practical cases, i.e. when the transition takes place in a small fraction of the total treatment time it suffices to approximate growth using the laminar asymptotic solution and when the transition requires are large time compared to the treatment time it suffices to approximate growth using the turbulent asymptotic solution.
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Numerical model for a penny-shaped hydraulic fracture driven by laminar/turbulent fluid in an Impermeable Rock
International Journal of Solids and Structures, 2019Co-Authors: Navid Zolfaghari, Andrew P. BungerAbstract:Abstract As hydraulic fracturing at high injection rates with low viscosity fluids grows in popularity, so also there is a growing need to include not only the more common laminar fluid flow, but also the turbulent and transition flow regimes in numerical simulators. One common scenario is embodied in the behavior of a radial (penny-shaped) hydraulic fracture where flow is turbulent near the inlet, laminar near the tip, and in transition somewhere between. The main goal of this paper is to investigate the impact of this transition on hydraulic fracture growth through development and use of a numerical simulator for penny-shaped hydraulic fractures using the so-called drag reduction method to estimate the friction factor inside the crack for all relevant flow regimes. Upon solving this problem numerically for the case of zero toughness, comparing the results with fully laminar and fully turbulent asymptotic solutions shows that the early time behavior of radial hydraulic fractures is predominantly turbulent while large time behavior if predominantly laminar. The time scale associated with this transition determines the relevance of either limiting regime to practical cases, i.e. when the transition takes place in a small fraction of the total treatment time it suffices to approximate growth using the laminar asymptotic solution and when the transition requires are large time compared to the treatment time it suffices to approximate growth using the turbulent asymptotic solution.
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Approximate semi-analytical solution for a penny-shaped rough-walled hydraulic fracture driven by turbulent fluid in an Impermeable Rock
International Journal of Solids and Structures, 2018Co-Authors: Navid Zolfaghari, Andrew P. BungerAbstract:Abstract The popularity of high injection rate hydraulic fracturing treatments using low viscosity fluids is driving a need to consider the turbulent and laminar-turbulent transition regimes of fluid flow in hydraulic fracture simulators. The radial model is one of the most important geometries both for benchmarking and as a starter solution for 3D and Planar 3D models. Here we provide a semi-analytical, orthogonal polynomial series solution for a rough-walled radial (penny-shaped) hydraulic fracture driven by a fully turbulent fluid. Embedding the appropriate pressure singularities in a family of orthogonal polynomials used for derivation of the solution leads to very rapid convergence of the series, requiring just two terms for an accurate result. We conclude with an investigation of the occurrence of this limiting regime by comparison with numerical simulations, illustrating that the fully turbulent regime is typically not encountered for the radial geometry, although the present solution remains necessary as a starter solution and benchmark for the numerical simulators that are required to capture the laminar-turbulent transition. By comparison with numerical simulations that consider the laminar-turbulent transition, we find that such an estimate is expected to be sufficient for practical purposes when the inlet opening predicted by the turbulent solution exceeds the inlet opening predicted by the laminar solution.
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Blade-Shaped Hydraulic Fracture Driven by a Turbulent Fluid in an Impermeable Rock
Journal of Engineering Mechanics, 2017Co-Authors: Navid Zolfaghari, Colin R. Meyer, Andrew P. BungerAbstract:AbstractWater-driven hydraulic fractures with high flow rates are more common now than ever in the oil and gas industry. Although these fractures are small, the high injection rate and low viscosit...
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Blade-shaped (PKN) Hydraulic Fracture Driven By A Turbulent Fluid In An Impermeable Rock
arXiv: Geophysics, 2016Co-Authors: Navid Zolfaghari, Colin R. Meyer, Andrew P. BungerAbstract:High flow rate, water-driven hydraulic fractures are more common now than ever in the oil and gas industry. Although the fractures are small, the high injection rate and low viscosity of the water, lead to high Reynolds numbers and potentially turbulence in the fracture. Here we present a semi-analytical solution for a blade-shaped (PKN) geometry hydraulic fracture driven by a turbulent fluid in the limit of zero fluid leak-off to the formation. We model the turbulence in the PKN fracture using the Gaukler-Manning-Strickler parametrization, which relates the the flow rate of the water to the pressure gradient along the fracture. The key parameter in this relation is the Darcy-Weisbach friction factor for the roughness of the crack wall. Coupling this turbulence parametrization with conservation of mass allows us to write a nonlinear pde for the crack width as a function of space and time. By way of a similarity ansatz, we obtain a semi-analytical solution using an orthogonal polynomial series. Embedding the asymptotic behavior near the fracture tip into the polynomial series, we find very rapid convergence: a suitably accurate solution is obtained with two terms of the series. This closed-form solution facilitates clear comparisons between the results and parameters for laminar and turbulent hydraulic fractures. In particular, it resolves one of the well known problems whereby calibration of models to data has difficulty simultaneously matching the hydraulic fracture length and wellbore pressure.
Navid Zolfaghari - One of the best experts on this subject based on the ideXlab platform.
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numerical model for a penny shaped hydraulic fracture driven by laminar turbulent fluid in an Impermeable Rock
International Journal of Solids and Structures, 2019Co-Authors: Navid Zolfaghari, Andrew P. BungerAbstract:Abstract As hydraulic fracturing at high injection rates with low viscosity fluids grows in popularity, so also there is a growing need to include not only the more common laminar fluid flow, but also the turbulent and transition flow regimes in numerical simulators. One common scenario is embodied in the behavior of a radial (penny-shaped) hydraulic fracture where flow is turbulent near the inlet, laminar near the tip, and in transition somewhere between. The main goal of this paper is to investigate the impact of this transition on hydraulic fracture growth through development and use of a numerical simulator for penny-shaped hydraulic fractures using the so-called drag reduction method to estimate the friction factor inside the crack for all relevant flow regimes. Upon solving this problem numerically for the case of zero toughness, comparing the results with fully laminar and fully turbulent asymptotic solutions shows that the early time behavior of radial hydraulic fractures is predominantly turbulent while large time behavior if predominantly laminar. The time scale associated with this transition determines the relevance of either limiting regime to practical cases, i.e. when the transition takes place in a small fraction of the total treatment time it suffices to approximate growth using the laminar asymptotic solution and when the transition requires are large time compared to the treatment time it suffices to approximate growth using the turbulent asymptotic solution.
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Numerical model for a penny-shaped hydraulic fracture driven by laminar/turbulent fluid in an Impermeable Rock
International Journal of Solids and Structures, 2019Co-Authors: Navid Zolfaghari, Andrew P. BungerAbstract:Abstract As hydraulic fracturing at high injection rates with low viscosity fluids grows in popularity, so also there is a growing need to include not only the more common laminar fluid flow, but also the turbulent and transition flow regimes in numerical simulators. One common scenario is embodied in the behavior of a radial (penny-shaped) hydraulic fracture where flow is turbulent near the inlet, laminar near the tip, and in transition somewhere between. The main goal of this paper is to investigate the impact of this transition on hydraulic fracture growth through development and use of a numerical simulator for penny-shaped hydraulic fractures using the so-called drag reduction method to estimate the friction factor inside the crack for all relevant flow regimes. Upon solving this problem numerically for the case of zero toughness, comparing the results with fully laminar and fully turbulent asymptotic solutions shows that the early time behavior of radial hydraulic fractures is predominantly turbulent while large time behavior if predominantly laminar. The time scale associated with this transition determines the relevance of either limiting regime to practical cases, i.e. when the transition takes place in a small fraction of the total treatment time it suffices to approximate growth using the laminar asymptotic solution and when the transition requires are large time compared to the treatment time it suffices to approximate growth using the turbulent asymptotic solution.
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Approximate semi-analytical solution for a penny-shaped rough-walled hydraulic fracture driven by turbulent fluid in an Impermeable Rock
International Journal of Solids and Structures, 2018Co-Authors: Navid Zolfaghari, Andrew P. BungerAbstract:Abstract The popularity of high injection rate hydraulic fracturing treatments using low viscosity fluids is driving a need to consider the turbulent and laminar-turbulent transition regimes of fluid flow in hydraulic fracture simulators. The radial model is one of the most important geometries both for benchmarking and as a starter solution for 3D and Planar 3D models. Here we provide a semi-analytical, orthogonal polynomial series solution for a rough-walled radial (penny-shaped) hydraulic fracture driven by a fully turbulent fluid. Embedding the appropriate pressure singularities in a family of orthogonal polynomials used for derivation of the solution leads to very rapid convergence of the series, requiring just two terms for an accurate result. We conclude with an investigation of the occurrence of this limiting regime by comparison with numerical simulations, illustrating that the fully turbulent regime is typically not encountered for the radial geometry, although the present solution remains necessary as a starter solution and benchmark for the numerical simulators that are required to capture the laminar-turbulent transition. By comparison with numerical simulations that consider the laminar-turbulent transition, we find that such an estimate is expected to be sufficient for practical purposes when the inlet opening predicted by the turbulent solution exceeds the inlet opening predicted by the laminar solution.
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Blade-Shaped Hydraulic Fracture Driven by a Turbulent Fluid in an Impermeable Rock
Journal of Engineering Mechanics, 2017Co-Authors: Navid Zolfaghari, Colin R. Meyer, Andrew P. BungerAbstract:AbstractWater-driven hydraulic fractures with high flow rates are more common now than ever in the oil and gas industry. Although these fractures are small, the high injection rate and low viscosit...
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Blade-shaped (PKN) Hydraulic Fracture Driven By A Turbulent Fluid In An Impermeable Rock
arXiv: Geophysics, 2016Co-Authors: Navid Zolfaghari, Colin R. Meyer, Andrew P. BungerAbstract:High flow rate, water-driven hydraulic fractures are more common now than ever in the oil and gas industry. Although the fractures are small, the high injection rate and low viscosity of the water, lead to high Reynolds numbers and potentially turbulence in the fracture. Here we present a semi-analytical solution for a blade-shaped (PKN) geometry hydraulic fracture driven by a turbulent fluid in the limit of zero fluid leak-off to the formation. We model the turbulence in the PKN fracture using the Gaukler-Manning-Strickler parametrization, which relates the the flow rate of the water to the pressure gradient along the fracture. The key parameter in this relation is the Darcy-Weisbach friction factor for the roughness of the crack wall. Coupling this turbulence parametrization with conservation of mass allows us to write a nonlinear pde for the crack width as a function of space and time. By way of a similarity ansatz, we obtain a semi-analytical solution using an orthogonal polynomial series. Embedding the asymptotic behavior near the fracture tip into the polynomial series, we find very rapid convergence: a suitably accurate solution is obtained with two terms of the series. This closed-form solution facilitates clear comparisons between the results and parameters for laminar and turbulent hydraulic fractures. In particular, it resolves one of the well known problems whereby calibration of models to data has difficulty simultaneously matching the hydraulic fracture length and wellbore pressure.
Sayantan Ganguly - One of the best experts on this subject based on the ideXlab platform.
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Numerical Investigation of Temperature Distribution in a Confined Heterogeneous Geothermal Reservoir Due to Injection-production ☆
Energy Procedia, 2017Co-Authors: Sayantan Ganguly, Abhijit Date, Mandalagiri Subbarayappa Mohan KumarAbstract:The present study deals with the modeling of transient temperature distribution in a heterogeneous geothermal reservoir in response to the injection-production process. The heterogeneous geothermal aquifer considered here is a confined aquifer with homogeneous layers of finite length and overlain and underlain by Impermeable Rock media. The heat transport modes considered are advection, conduction in the geothermal reservoir and heat transfer to the confining Rock media. Results show that heterogeneity plays a very significant role in determining the transient temperature distribution and controlling the advancement of the thermal front in the reservoir. A one-dimensional (1D) analytical model for temperature distribution in the geothermal reservoir is also derived in this study. Results from a simpler version of the numerical model are compared with the results from the analytical solution which are in good agreement with each other. (C) 2017 The Authors. Published by Elsevier Ltd.
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Numerical investigation of temperature distribution in a confined heterogeneous geothermal reservoir due to injection-production
Energy Procedia, 2017Co-Authors: Sayantan Ganguly, Abhijit Date, Lippong Tan, M KumarAbstract:The present study deals with the modeling of transient temperature distribution in a heterogeneous geothermal reservoir in response to the injection-production process. The heterogeneous geothermal aquifer considered here is a confined aquifer with homogeneous layers of finite length and overlain and underlain by Impermeable Rock media. The heat transport modes considered are advection, conduction in the geothermal reservoir and heat transfer to the confining Rock media. Results show that heterogeneity plays a very significant role in determining the transient temperature distribution and controlling the advancement of the thermal front in the reservoir. A one-dimensional (1D) analytical model for temperature distribution in the geothermal reservoir is also derived in this study. Results from a simpler version of the numerical model are compared with the results from the analytical solution which are in good agreement with each other. (C) 2017 The Authors. Published by Elsevier Ltd.
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A numerical model for transient temperature distribution in an aquifer thermal energy storage system with multiple wells
Lowland Technology International, 2015Co-Authors: Sayantan Ganguly, M. S. Mohan KumarAbstract:The present study is concerned about developing a coupled thermo-hydrogeological numerical model for an Aquifer Thermal Energy Storage (ATES) system consisting of a confined porous aquifer underlain and overlain by Impermeable Rock media with different thermo-hydrogeological properties. Hot water is injected through injection well(s) into the porous medium which is at subsurface temperature. The main motive of the study is to model the movement of the thermal-front which is generated in the aquifer due to hot water injection. First the numerical model is developed for an ATES system with single production well and multiple injection wells and then for a system with multiple production wells and a single injection well, as both the scenario occur in field. Influence of a few parameters involved in the subsurface heat transport process is determined. Parameters of injection rate, permeability of the aquifer and the confining Rocks are proved to be very important. A simplified version of the model has been validated using an analytical model developed by the authors. Modeling the movement of the thermal-front is important in designing an injection-production well scheme to avoid thermal-breakthrough which severely affects efficiency of an ATES system.
M Kumar - One of the best experts on this subject based on the ideXlab platform.
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Numerical investigation of temperature distribution in a confined heterogeneous geothermal reservoir due to injection-production
Energy Procedia, 2017Co-Authors: Sayantan Ganguly, Abhijit Date, Lippong Tan, M KumarAbstract:The present study deals with the modeling of transient temperature distribution in a heterogeneous geothermal reservoir in response to the injection-production process. The heterogeneous geothermal aquifer considered here is a confined aquifer with homogeneous layers of finite length and overlain and underlain by Impermeable Rock media. The heat transport modes considered are advection, conduction in the geothermal reservoir and heat transfer to the confining Rock media. Results show that heterogeneity plays a very significant role in determining the transient temperature distribution and controlling the advancement of the thermal front in the reservoir. A one-dimensional (1D) analytical model for temperature distribution in the geothermal reservoir is also derived in this study. Results from a simpler version of the numerical model are compared with the results from the analytical solution which are in good agreement with each other. (C) 2017 The Authors. Published by Elsevier Ltd.
Mandalagiri Subbarayappa Mohan Kumar - One of the best experts on this subject based on the ideXlab platform.
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Numerical Investigation of Temperature Distribution in a Confined Heterogeneous Geothermal Reservoir Due to Injection-production ☆
Energy Procedia, 2017Co-Authors: Sayantan Ganguly, Abhijit Date, Mandalagiri Subbarayappa Mohan KumarAbstract:The present study deals with the modeling of transient temperature distribution in a heterogeneous geothermal reservoir in response to the injection-production process. The heterogeneous geothermal aquifer considered here is a confined aquifer with homogeneous layers of finite length and overlain and underlain by Impermeable Rock media. The heat transport modes considered are advection, conduction in the geothermal reservoir and heat transfer to the confining Rock media. Results show that heterogeneity plays a very significant role in determining the transient temperature distribution and controlling the advancement of the thermal front in the reservoir. A one-dimensional (1D) analytical model for temperature distribution in the geothermal reservoir is also derived in this study. Results from a simpler version of the numerical model are compared with the results from the analytical solution which are in good agreement with each other. (C) 2017 The Authors. Published by Elsevier Ltd.
