The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
E V Dontsov - One of the best experts on this subject based on the ideXlab platform.
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a semi infinite Hydraulic Fracture with leak off driven by a power law fluid
Journal of Fluid Mechanics, 2018Co-Authors: E V Dontsov, O KresseAbstract:This study investigates the problem of a semi-infinite Hydraulic Fracture that propagates steadily in a permeable formation. The fracturing fluid rheology is assumed to follow a power-law behaviour, while the leak-off is modelled by Carter’s model. A non-singular formulation is employed to effectively analyse the problem and to construct a numerical solution. The problem under consideration features three limiting analytic solutions that are associated with dominance of either toughness, leak-off or viscosity. Transitions between all the limiting cases are analysed and the boundaries of applicability of all these limiting solutions are quantified. These bounds allow us to determine the regions in the parametric space, in which these limiting solutions can be used. The problem of a semi-infinite Fracture, which is considered in this study, provides the solution for the tip region of a Hydraulic Fracture and can be used in Hydraulic fracturing simulators to facilitate solving the moving Fracture boundary problem. To cater for such applications, for which rapid evaluation of the solution is necessary, the last part of this paper constructs an approximate closed form solution for the problem and evaluates its accuracy against the numerical solution inside the parametric space.
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an approximate solution for a plane strain Hydraulic Fracture that accounts for Fracture toughness fluid viscosity and leak off
International Journal of Fracture, 2017Co-Authors: E V DontsovAbstract:The goal of this paper is to develop an approximate solution for a propagating plane strain Hydraulic Fracture, whose behavior is determined by a combined interplay of fluid viscosity, Fracture toughness, and fluid leak-off. The approximation is constructed by assuming that the Fracture behavior is primarily determined by the three-process (viscosity, toughness, and leak-off) multiscale tip asymptotics and the global fluid volume balance. First, the limiting regimes of propagation of the solution are considered, that can be reduced to an explicit form. Thereafter, applicability regions of the limiting solutions are investigated and transitions from one limiting solution to another are analyzed. To quantify the error of the constructed approximate solution, its predictions are compared to a reference numerical solution. Results indicate that the approximation is able to predict Hydraulic Fracture parameters for all limiting and transition regimes with an error of under one percent. Consequently, this development can be used to obtain a rapid solution for a plane strain Hydraulic Fracture with leak-off, which can be used for quick estimations of Fracture geometry or as a reference solution to evaluate accuracy of more advanced Hydraulic Fracture simulators.
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an approximate solution for a penny shaped Hydraulic Fracture that accounts for Fracture toughness fluid viscosity and leak off
Royal Society Open Science, 2016Co-Authors: E V DontsovAbstract:This paper develops a closed-form approximate solution for a penny-shaped Hydraulic Fracture whose behaviour is determined by an interplay of three competing physical processes that are associated with fluid viscosity, Fracture toughness and fluid leak-off. The primary assumption that permits one to construct the solution is that the Fracture behaviour is mainly determined by the three-process multiscale tip asymptotics and the global fluid volume balance. First, the developed approximation is compared with the existing solutions for all limiting regimes of propagation. Then, a solution map, which indicates applicability regions of the limiting solutions, is constructed. It is also shown that the constructed approximation accurately captures the scaling that is associated with the transition from any one limiting solution to another. The developed approximation is tested against a reference numerical solution, showing that accuracy of the Fracture width and radius predictions lie within a fraction of a per cent for a wide range of parameters. As a result, the constructed approximation provides a rapid solution for a penny-shaped Hydraulic Fracture, which can be used for quick Fracture design calculations or as a reference solution to evaluate accuracy of various Hydraulic Fracture simulators.
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tip region of a Hydraulic Fracture driven by a laminar to turbulent fluid flow
Journal of Fluid Mechanics, 2016Co-Authors: E V DontsovAbstract:The focus of this study is to analyse the tip region of a Hydraulic Fracture, for which a fluid flow inside the crack transitions from the laminar to the turbulent regime away from the tip. To tackle the problem, a phenomenological formula for flow in pipes has been adapted to describe flow in a Fracture through the concept of a Hydraulic diameter. The selected model is able to capture laminar, turbulent and transition regimes of the flow. The near-tip region of a Hydraulic Fracture is analysed by focusing on steady propagation of a semi-infinite Hydraulic Fracture with leak-off, for which the aforementioned phenomenological formula for the fluid flow is utilized. First, the distance from the tip within which a laminar solution applies is estimated. Then, expressions for asymptotic solutions that are associated with fully developed turbulent flow inside the semi-infinite Hydraulic Fracture are derived. Finally, the laminar zone size and the asymptotic solutions are compared with the numerical solution, where the latter captures all regimes of the fluid flow.
Yu Zhao - One of the best experts on this subject based on the ideXlab platform.
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a new criterion for a toughness dominated Hydraulic Fracture crossing a natural frictional interface
Rock Mechanics and Rock Engineering, 2019Co-Authors: Yu Zhao, Yongfa Zhang, Chaolin WangAbstract:Hydraulic fracturing is a powerful technology, especially in stimulating fluid production from reservoirs. However, the problem of the intersection between Hydraulic Fractures and natural Fractures is inevitable in engineering practice due to naturally Fractured formations. This paper presents a new criterion for a toughness-dominated Hydraulic Fracture crossing a natural frictional interface through coupling the fluid flow and elastic deformation of the Hydraulic Fracture prior to intersecting with the natural frictional interface. The critical condition for the Hydraulic Fracture crossing the natural frictional interface is that the total superimposed stress does not satisfy the failure condition of the Mohr–Coulomb criterion. Simultaneously, the new criterion considers nonorthogonal intersection angles and six independent parameters relating to fluid flow (Hydraulic Fracture half-length, approaching distance and injection rate), rock mechanic properties (rock Fracture toughness and Young’s modulus) and in situ stress. The prediction outcomes show good agreement with laboratory experiments as well as sufficient advantages compared with the analytical criteria of Blanton, extended Renshaw-Pollard and Llanos. Parameter sensitivity analysis is conducted using the control variable method. The parametric analysis results reveal that the influence sphere of different parameters is limited to a certain extent by the variations in the intersection angle except for Young’s modulus and the injection rate, which show slight effects on the intersection behaviors.
Brice Lecampion - One of the best experts on this subject based on the ideXlab platform.
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Impact of the anisotropy of Fracture toughness on the propagation of planar 3D Hydraulic Fracture
International Journal of Fracture, 2018Co-Authors: Haseeb Zia, Brice Lecampion, Weihan ZhangAbstract:Sedimentary rocks often exhibit a transverse isotropy due to fine scale layering. We investigate the effect of the anisotropy of Fracture toughness on the propagation of a planar 3D Hydraulic Fracture perpendicular to the isotropy plane: a configuration commonly encountered in sedimentary basins. We extend a fully implicit level set scheme for the simulation of Hydraulic Fracture growth to the case of anisotropic Fracture toughness. We derive an analytical solution for the propagation of an elliptical Hydraulic Fracture in the toughness dominated regime—a shape which results from a particular form of toughness anisotropy. The developed numerical solver closely matches this solution as well as classical benchmarks for Hydraulic Fracture growth with isotropic toughness. We then quantify numerically the transition between the viscosity dominated propagation regime at early time—where the Fracture grows radially—to the toughness dominated regime at large time where the Fracture reaches an elliptical shape in the case of an elliptical anisotropy. The time scale at which the Fracture starts to deviate from the radial shape and gets more elongated in the direction of lower toughness is in accordance with the viscosity to toughness transition time-scale for a radial Fracture defined with the largest value of Fracture toughness. Similarly, the toughness dominated regime is fully reached along the whole Fracture front when the time gets significantly larger than the same transition time-scale defined with the lowest value of toughness. Using different toughness anisotropy functions, we also illustrate how the details of the complete variation of Fracture toughness with propagation direction governs the final Hydraulic Fracture shape at large time. Our results highlight toughness anisotropy as a possible Hydraulic Fracture height containment mechanism as well as the need for its careful characterization beyond measurements in the sole material axes (divider and arrester) directions.
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Numerical methods for Hydraulic Fracture propagation: a review of recent trends
Journal of Natural Gas Science and Engineering, 2018Co-Authors: Brice LecampionAbstract:Development of numerical methods for Hydraulic Fracture simulation has accelerated in the past two decades. Recent advances in Hydraulic Fracture modeling and simulation are driven by increased industry and research activity in oil and gas, a drive toward consideration of more complex behaviors associated with layered and naturally-Fractured rock formations, and a deepening understanding of the underlying mathematical model and its intrinsic challenges. Here we review the basic approaches being employed. Some of these comprise enhancements of classical methods, while others are imported from other fields of mechanics but are completely new in their application to Hydraulic fracturing. After a description of the intrinsic challenges associated with the mechanics of fluid-driven Fractures, we discuss both continuum and meso-scales numerical methods as well as engineering models which typically make use of additional assumptions to reduce computational cost. We pay particular attention to the verification and validation of numerical models, which is increasingly enabled by an ever-expanding library of laboratory experiments and analytical solutions for simple geometries in a number of different propagation regimes. A number of challenges remain and are amplified with a drive toward fully-coupled, three-dimensional Hydraulic Fracture modeling that accounts for host-rock heterogeneity. In the context of such a drive to complex models, we argue that the importance of best-practice development that includes careful verification and validation is vital to ensure progress is constrained by the appropriate underlying physics and mathematics with a constant attention to identifying conditions under which simpler models suffice for the intended modeling purposes.
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initiation and breakdown of an axisymmetric Hydraulic Fracture transverse to a horizontal wellbore
ISRM International Conference for Effective and Sustainable Hydraulic Fracturing, 2013Co-Authors: Safdar Abbas, Brice LecampionAbstract:We investigate the initiation and early-stage propagation of an axi-symmetric Hydraulic Fracture from a wellbore drilled in the direction of the minimum principal stress in an elastic and impermeable formation. Such a configuration is akin to the case of a horizontal well and a Hydraulic Fracture transverse to the well axis in an open hole completion. In addition to the effect of the wellbore on the elasticity equation, the effect of the injection system compressi‐ bility is also taken into account. The formulation accounts for the strong coupling between the elasticity equation, the flow of the injected fluid within the newly created crack and the Fracture propagation condition. Dimensional analysis of the problem reveals that three di‐ mensionless parameters control the entire problem: the ratio of the initial defect length over the wellbore radius, the ratio between the wellbore radius and a length-scale associated with the fluid stored by compressibility in the injection system during the well pressurization, and finally the ratio of the time-scale of transition from viscosity to toughness dominated propagation to the time-scale associated with compressibility effects. A fully coupled nu‐ merical solver is presented, and validated against solutions for a radial Hydraulic Fracture propagating in an infinite medium. The influence of the different parameters on the transi‐ tion from the near-wellbore to the case of a Hydraulic Fracture propagating in an infinite me‐ dium is fully discussed.
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the impact of the near tip logic on the accuracy and convergence rate of Hydraulic Fracture simulators compared to reference solutions
ISRM International Conference for Effective and Sustainable Hydraulic Fracturing 2013, 2013Co-Authors: Brice Lecampion, Andrew P Bunger, Zuorong Chen, Xi Zhang, Emmanuel M Detournay, Safdar Abbas, A P Peirce, Christine Detournay, J A L Napier, Dmitry I GaragashAbstract:We benchmark a series of simulators against available reference solutions for propagating plane-strain and radial Hydraulic Fractures. In particular, we focus on the accuracy and convergence of the numerical solutions in the important practical case of viscosity dominated propagation. The simulators are based on different propagation criteria: linear elastic Fracture mechanics (LEFM), cohesive zone models/tensile strength criteria, and algorithms accounting for the multi-scale nature of Hydraulic Fracture propagation in the near-tip region. All the simulators tested here are able to capture the analytical solutions of the different configurations tested, but at vastly different computational costs. Algorithms based on the classical LEFM propagation condition require a fine mesh in order to capture viscosity dominated Hydraulic Fracture evolution. Cohesive zone models, which model the Fracture process zone, require even finer meshes to obtain the same accuracy. By contrast, when the algorithms use the appropriate multi-scale Hydraulic Fracture asymptote in the near-tip region, the exact solution can be matched accurately with a very coarse mesh. The different analytical reference solutions used in this paper provide a crucial series of benchmark tests that any successful Hydraulic fracturing simulator should pass.
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an extended finite element method for Hydraulic Fracture problems
Communications in Numerical Methods in Engineering, 2009Co-Authors: Brice LecampionAbstract:In this paper, the extended finite element method (X-FEM) is investigated for the solution of Hydraulic Fracture problems. The presence of an internal pressure inside the crack is taken into account. Special tip functions encapsulating tip asymptotics typically encountered in Hydraulic Fractures are introduced. We are especially interested in the two limiting tip behaviour for the impermeable case: the classical LEFM square root asymptote in Fracture width for the toughness-dominated regime of propagation and the so-called ⅔ asymptote in Fracture width for the viscosity-dominated regime. Different variants of the X-FEM are tested for the case of a plane-strain Hydraulic Fracture propagation in both the toughness and the viscosity dominated regimes. Fracture opening and fluid pressure are compared at each nodes with analytical solutions available in the literature. The results demonstrate the importance of correcting for the loss of partition of unity in the transition zone between the enriched part and the rest of the mesh. A point-wise matching scheme appears sufficient to obtain accurate results. Proper integration of the singular terms introduced by the enrichment functions is also critical for good performance. Copyright © 2008 John Wiley & Sons, Ltd.
Diguang Gong - One of the best experts on this subject based on the ideXlab platform.
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numerical simulation of directional propagation of Hydraulic Fracture guided by vertical multi radial boreholes
Journal of Natural Gas Science and Engineering, 2016Co-Authors: Zhan-qing Qu, Diguang GongAbstract:Abstract The conventional Hydraulic fracturing is not effective in the target oil development zone (remaining oil or gas, trap reservoir, etc.) with available wellbores located in the azimuth of non-maximum horizontal in-situ stress. The technology of directional propagation of Hydraulic Fracture guided by vertical multi-radial boreholes was innovatively developed. In order to verify the technology, a 3D extended finite element numerical model of Hydraulic fracturing promoted by vertical multi-radial boreholes was established using Abaqus Software, and the influence of horizontal in-situ stress differences, azimuth, diameters, spacing, and lengths of radial boreholes, rates and viscosities of fracturing fluids, Young modulus and Poisson's ratio of rock, and reservoir permeability on propagation of Hydraulic Fracture guided by radial borehole row were comprehensively analyzed. Moreover, the term ‘Guidance factor (G)’ was introduced for the first time to effectively quantify guidance of radial borehole row. Finally, the guidance of the above ten factors is comprehensively evaluated through gray correlation analysis. The results showed that the directional propagation of Hydraulic Fracture is realized through scientifically arranged vertical radial borehole row, and ‘G’ reflects the real guidance strength of radial borehole row to Hydraulic Fracture. The azimuth of radial borehole row increases by 75°, G increases by 18 times. Horizontal in-situ stress difference increases by 9 MPa, G increases by 95%. The borehole diameter increases by 4 cm, G decreases by 54%. The borehole spacing increases by 0.5 m, G increases by 18%. The borehole length increases by 10 m, G decreases by 40%. Young's modulus of reservoir rock increases by 20 GPa, G decreases by 23%. Poisson's ratio increases by 0.1, G increases by 57%. Permeability of reservoir increases by 100 times, G increases by 3.3 times. Injection rate increases by 9 m3/min, G decreases by 63%. Both excessively high and low viscosities are adverse to guidance of radial borehole to Hydraulic Fracture, and 50 mPa s fracturing fluid creates best guidance to propagation of Hydraulic Fracture. The gray correlation analysis showed that the influences (from strong to weak) of the above factors on guidance of radial borehole were listed as follows: azimuth of radial borehole > injection rate of fracturing fluid > horizontal in-situ stress differences > Young's modulus of rock > viscosity of fracturing fluid > borehole diameter of radial borehole > radial borehole spacing > reservoir permeability > length of radial borehole > Poisson's ratio. This study provided theoretical evidence for directional propagation of Hydraulic Fracture promoted by radial borehole, and it predicted the guidance of radial borehole to Hydraulic Fracture in a certain extent, which is helpful for planning well-completion and fracturing operation in technology of Hydraulic fracturing promoted by radial borehole.
Chaolin Wang - One of the best experts on this subject based on the ideXlab platform.
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a new criterion for a toughness dominated Hydraulic Fracture crossing a natural frictional interface
Rock Mechanics and Rock Engineering, 2019Co-Authors: Yu Zhao, Yongfa Zhang, Chaolin WangAbstract:Hydraulic fracturing is a powerful technology, especially in stimulating fluid production from reservoirs. However, the problem of the intersection between Hydraulic Fractures and natural Fractures is inevitable in engineering practice due to naturally Fractured formations. This paper presents a new criterion for a toughness-dominated Hydraulic Fracture crossing a natural frictional interface through coupling the fluid flow and elastic deformation of the Hydraulic Fracture prior to intersecting with the natural frictional interface. The critical condition for the Hydraulic Fracture crossing the natural frictional interface is that the total superimposed stress does not satisfy the failure condition of the Mohr–Coulomb criterion. Simultaneously, the new criterion considers nonorthogonal intersection angles and six independent parameters relating to fluid flow (Hydraulic Fracture half-length, approaching distance and injection rate), rock mechanic properties (rock Fracture toughness and Young’s modulus) and in situ stress. The prediction outcomes show good agreement with laboratory experiments as well as sufficient advantages compared with the analytical criteria of Blanton, extended Renshaw-Pollard and Llanos. Parameter sensitivity analysis is conducted using the control variable method. The parametric analysis results reveal that the influence sphere of different parameters is limited to a certain extent by the variations in the intersection angle except for Young’s modulus and the injection rate, which show slight effects on the intersection behaviors.
