The Experts below are selected from a list of 1485 Experts worldwide ranked by ideXlab platform
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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Analytical criterion predicting the impact of natural Fracture strength, height and cemented portion on Hydraulic Fracture Growth
Engineering Fracture Mechanics, 2018Co-Authors: Alexei A. Savitski, Andrew P BungerAbstract:Abstract Natural Fractures (NFs) are commonly encountered in unconventional reservoirs, sometimes strongly impacting Hydraulic Fracture (HF) propagation. The HF-NF interaction has been studied extensively as a 2D problem. However, outcrop and core observations indicate that many NFs are fully or partially cemented. The NF height also is variable relative to the full height of the reservoir layers(s). These features of NFs – including the proportion of the cemented region(s), cementation strength, and NF height – may lead to distinctive interaction behaviors that can only be understood in a 3D setting. This paper presents a new analytical crossing criterion, and its laboratory verification, for predicting the outcome when a HF impinges orthogonally on a NF. Consistent with laboratory results, this criterion captures the dependence of crossing/no crossing behaviors on the proportion of cemented region(s), cementation strength, and the NF height relative to the total reservoir/HF height. Crossing of the NF is shown to be promoted by stronger cementation, larger cemented region, and/or shorter NF height. While these observations are not surprising, quantifying the dependencies using an analytical model that can be deployed within the framework of HF simulators is an unresolved challenge. Here an analytical criterion has been developed based on linear elastic Fracture mechanics to quantitatively assess the influence of NF heterogeneity on the HF’s crossing/no crossing behaviors. The criterion shows good agreement with Hydraulic fracturing experiments. It is therefore shown to be capable of predicting the 3D interaction behaviors of HFs intersecting partially/fully cemented NFs.
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Laboratory measurement of tip and global behavior for zero-toughness Hydraulic Fractures with circular and blade-shaped (PKN) geometry
Journal of the Mechanics and Physics of Solids, 2017Co-Authors: Pengju Xing, Keita Yoshioka, Jose Adachi, Amr El-fayoumi, Andrew P BungerAbstract:Abstract The tip behavior of Hydraulic Fractures is characterized by a rich nesting of asymptotic solutions, comprising a formidable challenge for the development of efficient and accurate numerical simulators. We present experimental validation of several theoretically-predicted asymptotic behaviors, namely for Hydraulic Fracture Growth under conditions of negligible Fracture toughness, with Growth progressing from early-time radial geometry to large-time blade-like (PKN) geometry. Our experimental results demonstrate: 1) existence of a asymptotic solution of the form w ∼ s 3/2 (LEFM) in the near tip region, where w is the crack opening and s is the distance from the crack tip, 2) transition to an asymptotic solution of the form w ∼ s 2/3 away from the near-tip region, with the transition length scale also consistent with theory, 3) transition to an asymptotic solution of the form w ∼ s 1/3 after the Fracture attains blade-like (PKN) geometry, and 4) existence of a region near the tip of a blade-like (PKN) Hydraulic Fracture in which plane strain conditions persist, with the thickness of this region of the same order as the crack height.
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Modeling initiation and propagation of a Hydraulic Fracture under subcritical conditions
Computer Methods in Applied Mechanics and Engineering, 2017Co-Authors: Elizaveta Gordeliy, Romain Prioul, Andrew P BungerAbstract:Abstract A numerical model has been developed for simulating the initiation and propagation of a plane strain or axisymmetric Hydraulic Fracture from an openhole wellbore in an impermeable homogeneous rock formation. The main novelty is inclusion of a subcritical Growth law, thereby allowing consideration of Hydraulic Fracture Growth when the wellbore pressure is otherwise considered insufficient to initiate fracturing. To enable tracking the moving crack front in the simulations, we develop a new tip asymptotics based on a subcritical crack Growth law. The results are first validated against available analytical solutions for plane strain and axisymmetric Hydraulic Fractures. A comparison is presented between the solutions of the subcritical Growth model and a conventional Hydraulic Fracture model in which Fracture Growth is not allowed until the stress intensity factor equals the Fracture toughness of the rock. This comparison, as well as a study of the influence of the relevant parameters appearing in the subcritical Growth law, indicates significant influence of subcritical Growth on the evolution of the crack length and the wellbore pressure. Notably, this model provides the capability to simulate delayed Growth of Hydraulic Fractures under pressures that are insufficient to generate instantaneous Growth, which is a behavior observed in experiments but not considered by conventional Hydraulic fracturing models.
Xi Zhang - One of the best experts on this subject based on the ideXlab platform.
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A fractal approach for surface roughness analysis of laboratory Hydraulic Fracture
Journal of Natural Gas Science and Engineering, 2021Co-Authors: Abbas Movassagh, Xi Zhang, Manouchehr Haghighi, Dane Kasperczyk, Mohammad SayyafzadehAbstract:Abstract Hydraulic fracturing treatment in rocks creates surfaces that are not smooth but rough in general. Accurate characterization of surface roughness is necessary to relate Fracture deformation to fluid flow. In this study, we analyze the surface of an experimentally generated Hydraulic Fracture using a practical fractal approach which is capable of modeling applications. The Hydraulic fracturing test is conducted using a nearly homogeneous siltstone cube in a true triaxial cell, and a Fracture is created showing a perfectly radial pattern. To evaluate roughness, each surface profile is decomposed into large-scale Fracture waviness and localized surface roughness considering various length scales. Despite the waviness, estimated roughness amplitudes follow a power-law relation up to a length-scale, showing a fractal nature. Unlike ideal brittle materials with an exponent of 0.5, the roughness exponent is found to vary in a narrow range of 0.1 but exceeds 0.5. The fractal dimension (box dimension) of the Hydraulic Fracture surface is estimated to be 1.4 showing a good match with roughness exponents. An increase in roughness exponent may indicate an increasing difficulty in Fracture propagation and fluid and proppant transport along the Fracture. As such, the topology of a Hydraulic Fracture surface is essential to Hydraulic Fracture Growth to assess fracturing performance.
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An explicit algorithm for modeling planar 3D Hydraulic Fracture Growth based on a super-time-stepping method
International Journal of Solids and Structures, 2020Co-Authors: Ming Chen, Xi Zhang, Shicheng Zhang, Yushi ZouAbstract:Abstract Hydraulic Fracture propagation is a coupled solid-fluid problem involving moving boundaries. The boundary element method is an efficient way to model it in elastic media; however, the computational efficiency is still not promising because in most models the time-consuming implicit approach is used for iteratively solving the stiff equation of the targeted problem. In this paper, we present an explicit super-time-stepping algorithm based on the Runge–Kutta–Legendre method, to simulate a planar 3D Hydraulic Fracture propagation through the intermediately previous solutions. Each super-time-step covers s stages of single explicit time-step and the results generated can be around s2 times more stable than that using a single explicit time-step. Moreover, an adaptive super-time-step scheme is proposed to capture the marching Fracture fronts based on the Fracture Growth rate. The modeling results are validated against analytical solutions for a penny-shaped Hydraulic Fracture and experimental results considering stress contrasts. Compared to the implicit iteration approach for the stiff equation, the explicit super-time-stepping algorithm can be up to 30 times faster because of no iteration and super-time-step. Finally, numerical examples are examined for Fracture Growth in rock formations with stress contrasts and anisotropic toughness, and all the results indicate that the explicit super-time-stepping algorithm can be a promising alternative to the implicit method.
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Mechanics of Hydraulic-Fracture Growth from a Wellbore Intersecting Natural Fractures
SPE Journal, 2019Co-Authors: Yang Liu, Xi Zhang, Ping Chen, Robert G JeffreyAbstract:Summary The creation and propagation of Hydraulic Fractures (HFs) emanating from a well in a naturally Fractured rock is important not only to the success of fracturing treatments, but also for interpretation of the data from diagnostic Fracture injection tests (DFITs). In this paper, we consider the reservoir rock to consist of an impermeable rock matrix and a system of discrete natural Fractures (NFs) that are permeable. The well is assumed to intersect two sets of NFs at their midpoints, and injection into the wellbore might open the NFs and/or create new Fractures that extend along the maximum-principal-stress direction. Both new Fractures and pre-existing NFs can act as either a main HF or a fluid-loss path. In this near-well transient-Fracture analysis, the NFs are short segments characterized by size, orientation, and aperture. A fully coupled HF model is used to investigate the interaction between the Fractures to determine how the fluid injected is distributed to the Fractures for a range of stress, fluid-injection-rate, and NF-geometry conditions. We find that a more-isotropic stress condition and a lower value of the fluid-viscosity/injection-rate product favor propagation of NFs. These conditions cause the NFs to accept more fluid, and, as a result, the Growth of new Fractures is suppressed. The post-shut-in pressure responses for the cases with propagating new Fractures and nonpropagating NFs are studied.
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A model for Hydraulic Fracture Growth across multiple elastic layers
Journal of Petroleum Science and Engineering, 2018Co-Authors: Xi Zhang, Luke D. Connell, Yanhui Han, Robert G JeffreyAbstract:Abstract Typical stress conditions in gas reservoirs consisting of multiple thin coal seams interlayed with shales, tuffs and sandstones, often lead to generation of a planar vertical Hydraulic Fracture. A pseudo-3D model, in which the Growth of the planar Hydraulic Fracture occurs through multiple horizontal layers with different elastic properties, is developed to account for the effects of modulus contrasts on Fracture shapes. In this model, plane strain deformation is assumed for pseudo-3D cells that have uniform cross-sectional pressure distribution, and the horizontal fluid flow is simplified to be one dimensional. The vertical and horizontal Fracture Growth are controlled in the model by two failure criteria, respectively. Viscous fluid friction effects are included for vertical Growth and a correction factor is applied to the horizontal failure criterion to adjust the propagation speeds. The numerical results for different values of the correction factor are presented for a vertically planar Fracture propagating in a homogeneous rock subject to stress contrasts. Fitting the pseudo-3D results to fully-3D results provides a means to determine the correlation factor that is found to be a function of material constants and cell length. The correlation factor obtained is then extended to Hydraulic Fracture propagation in a layered rock mass. There are two options in choosing material constants for the correlation factor and their results are examined. Both choices demonstrate the same varying trends for Fracture height and propagation speed. The existence of softer coal seams retards upward Fracture Growth, with a stepwise injection pressure associated with the discontinuous upward Growth.
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Hydraulic Fracture Propagation Through an Orthogonal Discontinuity: A Laboratory, Analytical and Numerical Study
Rock Mechanics and Rock Engineering, 2017Co-Authors: Ella María Llanos, Robert G Jeffrey, Richard Hillis, Xi ZhangAbstract:Rocks are naturally Fractured, and lack of knowledge of Hydraulic Fracture Growth through the pre-existing discontinuities in rocks has impeded enhancing hydrocarbon extraction. This paper presents experimental results from uniaxial and biaxial tests, combined with numerical and analytical modelling results to develop a criterion for predicting whether a Hydraulic Fracture will cross a discontinuity, represented at the laboratory by unbonded machined frictional interfaces. The experimental results provide the first evidence for the impact of viscous fluid flow on the orthogonal Fracture crossing. The Fracture elliptical footprint also reflects the importance of both the applied loading stress and the viscosity in Fracture propagation. The Hydraulic Fractures extend both in the direction of maximum compressive stress and in the direction with discontinuities that are arranged to be normal to the maximum compressive stress. The modelling results of Fracture Growth across discontinuities are obtained for the locations of slip starting points in initiating Fracture crossing. Our analysis, in contrast to previous work on the prediction of frictional crossing, includes the non-singular stresses generated by the finite pressurised Hydraulic Fracture. Experimental and theoretical outcomes herein suggest that Hydraulic Fracture Growth through an orthogonal discontinuity does not depend primarily on the interface friction coefficient.
Lecampion Brice - One of the best experts on this subject based on the ideXlab platform.
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Reply to comments on "Explicit versus implicit front advancing schemes for the simulation of Hydraulic Fracture Growth" (Int. J. Numer. Anal. Methods Geomech., 2019, 43 (6), 1300-1315)" by Prof. Linkov
'Wiley', 2020Co-Authors: Zia Haseeb, Lecampion BriceAbstract:We reply to Prof. Linkov comments on our article entitled "Explicit versus implicit front advancing schemes for the simulation of Hydraulic Fracture Growth" (Int. J. Numer. Anal. Methods Geomech., 2019, 43 (6), 1300-1315). We present additional results indicating that both the implicit and explicit front advancement schemes are robust even in the case of a large stress contrast
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Laboratory studies of Hydraulic Fracture Growth in quasi-brittle rocks with different grain sizes
2020Co-Authors: Liu Dong, Lecampion BriceAbstract:Well completion for oil and gas, geothermal energy as well as CO2 storage sometimes require stimulation to achieve economical fluid flow rates (for both injector and producer wells). Predicting the Growth of fluid-driven Fractures in geological systems is essential for the sustainable and efficient engineering of those reservoirs. The quasi-brittle nature of rocks complexifies the coupling between fluid flow and Fracture Growth – especially in the Fracture process zone. To better understand the impact of the non-linear Fracture in such materials, we perform different laboratory Hydraulic fracturing experiments under controlled stresses and fluid injection conditions in a cubic block of 250*250*250 millimeter in size. We choose two different rocks (marble and gabbro) with an order of difference in grain sizes (and as a result most likely different process zone size) but both with very low permeability. We report a series of experiments performed under different regimes of propagation (lag-viscosity as well as toughness dominated) in these two rocks under different levels of confining stress. We use active acoustic monitoring to reconstruct the evolution of the Fracture front with time with a spatial resolution of a few millimeters every 4 seconds in time (see Liu et al. (2020) for details). We show that the Fracture Growth is also consistent with other measurements such as fluid injection pressure and displacement measured. Attenuation of the transmitted acoustic energy also indicates the existence of a damage zone (often denoted as a process zone) ahead of the Fracture. This process zone grows differently inside these two rocks during Fracture propagation. Its final size appears limited by the specimen dimensions with a decrease of the Fracture apparent toughness at later time
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Planar Hydraulic Fracture Growth perpendicular to the isotropy plane in a transversely isotropic material
'Elsevier BV', 2020Co-Authors: Moukhtari Fatima-ezzahra, Lecampion Brice, Zia HaseebAbstract:The configuration of a Hydraulic Fracture (HF) propagating perpendicular to the isotropy plane of a transversely isotropic (TI) material is encountered in most sedimentary basins. We account for both elastic and Fracture toughness anisotropy, and investigate Fracture Growth driven by the injection of a Newtonian fluid at a constant rate from a point source. In addition to the usual dimensionless parameters governing HF Growth in isotropy, four dimensionless elastic parameters enter the problem for a TI material: the ratio β of elastic plane-strain modulus in the two orthogonal directions of the material frame, two Thomsen parameters ϵ, δ and the stiffness ratio C13/C11. Moreover, the ratio κ of Fracture toughness in the two orthogonal directions as well as the details of the toughness anisotropy also plays a role on the development of the Fracture geometry. We quantify HF Growth numerically without any a-priori assumptions on the Fracture shape. In doing so, we derive the exact expression for the near-tip elastic modulus as a function of propagation direction and extend to TI an implicit level set algorithm coupling a finite discretization with the near-tip solution for a steadily moving HF. A solution for a toughness dominated elliptical HF in a TI material is derived and used to verify our numerical solver. Importantly, the Fracture shape is strictly elliptical only for a very peculiar form of toughness anisotropy. The evolution of the HF from the viscosity dominated regime (early time) to the toughness dominated regime (late time) results in an increase of the Fracture elongation. The elongation of the Fracture in the viscosity dominated regime scales as and increases as the propagation transition to the toughness dominated regime. We confirm the expressions for the transition time-scales in the two orthogonal directions of the material frame obtained from scaling considerations. The exact form of the toughness anisotropy plays a crucial role on the final Fracture elongation in the toughness regime, which scales as for the case of an isotropic toughness, for an isotropic Fracture energy and as (κ/β)2 for the peculiar case of an ’elliptical’ Fracture anisotropy. Our results also indicate that i) simplified approximations for the near-tip modulus previously derived are only valid for weak anisotropy (β
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PyFrac: A planar 3D Hydraulic Fracture simulator
'Elsevier BV', 2020Co-Authors: Zia Haseeb, Lecampion BriceAbstract:Fluid driven Fractures propagate in the upper earth crust either naturally or in response to engineered fluid injections. The quantitative prediction of their evolution is critical in order to better understand their dynamics as well as to optimize their creation. We present a Python implementation of an open-source Hydraulic Fracture propagation simulator based on the implicit level set algorithm originally developed by Peirce & Detournay (2008) -- "An implicit level set method for modeling Hydraulically driven Fractures". Comp. Meth. Appl. Mech. Engng, (33-40):2858--2885. This algorithm couples a finite discretization of the Fracture with the use of the near tip asymptotic solutions of a steadily propagating semi-infinite Hydraulic Fracture. This allows to resolve the multi-scale processes governing Hydraulic Fracture Growth accurately, even with relatively coarse meshes. We present an overview of the mathematical formulation, the numerical scheme and the details of our implementation. A series of problems including a radial Hydraulic Fracture verification benchmark, the propagation of a height contained Hydraulic Fracture, the lateral spreading of a magmatic dyke and the handling of Fracture closure are presented to demonstrate the capabilities, accuracy and robustness of the implemented algorithm
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Hydraulic Fracture Growth in transversely isotropic rocks
2019Co-Authors: Lecampion BriceAbstract:scales, sedimentary rocks exhibit a transverse isotropy associated with beddings. In this talk, I will discuss the impact of such type of anisotropy on the Growth of fluid-driven Fractures in the case of normal and strike-slip in-situ stress regimes where the Fractures grow vertical perpendicular to the horizontal layering.\ We will discuss the effect of both elastic properties and Fracture energy on the development of Hydraulic Fracture from a wellbore under constant injection rate – assuming the rock to be impermeable for simplicity.\ A detailed presentation of the extension to transverse isotropy of numerical methods for the simulation of Hydraulic Fracture Growth based on a level set description will be given. A number of verifications of the proposed numerical scheme will be presented against Growth solutions in the toughness dominated regime for a specific type of Fracture energy anisotropy leading to elliptical Fractures.\ I will also highlight important gaps in our knowledge of anisotropic rock Fracture properties, and especially how the detailed evolution of Fracture energy between the so-called divider and arrester directions strongly impact the ultimate shape of Hydraulic Fractures. Typical transverse isotropy encountered in practice leads to significant horizontal elongation and is thus an intrinsic mechanism for the height containment of Hydraulic Fractures in the absence of in-situ stress contrast – possibly explaining why stronger height containment is observed compared to the predictions of isotropic models in practice. H. Zia, B. Lecampion, and W. Zhang. Impact of the anisotropy of Fracture toughness on the propagation of planar 3D Hydraulic Fracture. International Journal of Fracture, 211(1-2):103–123, 2018. F. E. Moukhtari, B. Lecampion, and H. Zia. Propagation of a planar Hydraulic Fracture in a transversely isotropic materials perpendicular to the isotropy plane.\ In preparation (2018
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.
Robert G Jeffrey - One of the best experts on this subject based on the ideXlab platform.
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Mechanics of Hydraulic-Fracture Growth from a Wellbore Intersecting Natural Fractures
SPE Journal, 2019Co-Authors: Yang Liu, Xi Zhang, Ping Chen, Robert G JeffreyAbstract:Summary The creation and propagation of Hydraulic Fractures (HFs) emanating from a well in a naturally Fractured rock is important not only to the success of fracturing treatments, but also for interpretation of the data from diagnostic Fracture injection tests (DFITs). In this paper, we consider the reservoir rock to consist of an impermeable rock matrix and a system of discrete natural Fractures (NFs) that are permeable. The well is assumed to intersect two sets of NFs at their midpoints, and injection into the wellbore might open the NFs and/or create new Fractures that extend along the maximum-principal-stress direction. Both new Fractures and pre-existing NFs can act as either a main HF or a fluid-loss path. In this near-well transient-Fracture analysis, the NFs are short segments characterized by size, orientation, and aperture. A fully coupled HF model is used to investigate the interaction between the Fractures to determine how the fluid injected is distributed to the Fractures for a range of stress, fluid-injection-rate, and NF-geometry conditions. We find that a more-isotropic stress condition and a lower value of the fluid-viscosity/injection-rate product favor propagation of NFs. These conditions cause the NFs to accept more fluid, and, as a result, the Growth of new Fractures is suppressed. The post-shut-in pressure responses for the cases with propagating new Fractures and nonpropagating NFs are studied.
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A model for Hydraulic Fracture Growth across multiple elastic layers
Journal of Petroleum Science and Engineering, 2018Co-Authors: Xi Zhang, Luke D. Connell, Yanhui Han, Robert G JeffreyAbstract:Abstract Typical stress conditions in gas reservoirs consisting of multiple thin coal seams interlayed with shales, tuffs and sandstones, often lead to generation of a planar vertical Hydraulic Fracture. A pseudo-3D model, in which the Growth of the planar Hydraulic Fracture occurs through multiple horizontal layers with different elastic properties, is developed to account for the effects of modulus contrasts on Fracture shapes. In this model, plane strain deformation is assumed for pseudo-3D cells that have uniform cross-sectional pressure distribution, and the horizontal fluid flow is simplified to be one dimensional. The vertical and horizontal Fracture Growth are controlled in the model by two failure criteria, respectively. Viscous fluid friction effects are included for vertical Growth and a correction factor is applied to the horizontal failure criterion to adjust the propagation speeds. The numerical results for different values of the correction factor are presented for a vertically planar Fracture propagating in a homogeneous rock subject to stress contrasts. Fitting the pseudo-3D results to fully-3D results provides a means to determine the correlation factor that is found to be a function of material constants and cell length. The correlation factor obtained is then extended to Hydraulic Fracture propagation in a layered rock mass. There are two options in choosing material constants for the correlation factor and their results are examined. Both choices demonstrate the same varying trends for Fracture height and propagation speed. The existence of softer coal seams retards upward Fracture Growth, with a stepwise injection pressure associated with the discontinuous upward Growth.
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Hydraulic Fracture Propagation Through an Orthogonal Discontinuity: A Laboratory, Analytical and Numerical Study
Rock Mechanics and Rock Engineering, 2017Co-Authors: Ella María Llanos, Robert G Jeffrey, Richard Hillis, Xi ZhangAbstract:Rocks are naturally Fractured, and lack of knowledge of Hydraulic Fracture Growth through the pre-existing discontinuities in rocks has impeded enhancing hydrocarbon extraction. This paper presents experimental results from uniaxial and biaxial tests, combined with numerical and analytical modelling results to develop a criterion for predicting whether a Hydraulic Fracture will cross a discontinuity, represented at the laboratory by unbonded machined frictional interfaces. The experimental results provide the first evidence for the impact of viscous fluid flow on the orthogonal Fracture crossing. The Fracture elliptical footprint also reflects the importance of both the applied loading stress and the viscosity in Fracture propagation. The Hydraulic Fractures extend both in the direction of maximum compressive stress and in the direction with discontinuities that are arranged to be normal to the maximum compressive stress. The modelling results of Fracture Growth across discontinuities are obtained for the locations of slip starting points in initiating Fracture crossing. Our analysis, in contrast to previous work on the prediction of frictional crossing, includes the non-singular stresses generated by the finite pressurised Hydraulic Fracture. Experimental and theoretical outcomes herein suggest that Hydraulic Fracture Growth through an orthogonal discontinuity does not depend primarily on the interface friction coefficient.
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A pseudo-3D model for Hydraulic Fracture Growth in a layered rock
International Journal of Solids and Structures, 2017Co-Authors: Xi Zhang, Robert G Jeffrey, Luke D. Connell, Guangqing ZhangAbstract:Abstract This paper presents a new pseudo-3D (P3D) model for a Hydraulic Fracture growing in a layered rock with contrasts in both material properties and in situ stresses. In the model, the vertically planar Fracture is divided along the lateral direction into cells. Within each cell, the cross-sectional deformation is plane strain, and the fluid pressure is allowed to vary vertically. The cells are discretized by displacement discontinuity elements that are formulated to include the elastic layered effect. The fluid flow in the cell is in two directions. Along the central part, which is of uniform pressure, the fluid flow is lateral, corresponding to the main component of fluid transport. Near the vertical Fracture edge of a cell, the flow can be vertical and is generated by the vertical pressure gradient. This part of the cell is called the filling part. When the pressure in the filling part reaches the level equal to that in the central part, the flow direction switches from vertical to lateral. The filling and central parts both contribute to Fracture height Growth. The proposed P3D problem is solved in a coupled manner that accounts for the two-directional flow and cross-sectional deformation through a two-loop iterative method. In the outer loop, the fluid storage of the central part is updated by satisfying mass conservation in the lateral direction, and in the inner loop, the cross-sectional elastic deformation and the influxes to the filling parts are found by satisfying energy minimization subject to an equality constraint on the central-part volume of a cell. The results of pressure ad Fracture width at a given elapsed time are thus obtained. After that, Fracture Growth in both lateral and vertical directions is controlled by the Fracture toughness criterion based on linear elasticity. In describing the P3D model, the governing equations are provided and their dimensionless forms are derived. The numerical algorithm used for solving the P3D problem is also described. Numerical examples are presented, including a constant-height Fracture, a radial one and asymmetric Fractures in three-layered rocks. Comparisons of our results are made with other published results and good agreements between them are found.
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Hydraulic Fracture Growth in naturally Fractured rock
Porous Rock Fracture Mechanics, 2017Co-Authors: Robert G Jeffrey, Xi Zhang, Zuorong ChenAbstract:Abstract Volcanic dikes and sills, sometimes exposed in outcrops, are examples of natural Hydraulic Fractures that interact with faults and natural Fractures. The industrial use of Hydraulic fracturing for stimulation of naturally Fractured reservoirs and to modify rock strength for mining has motivated study of Hydraulic Fracture Growth in naturally Fractured rock in the petroleum, geothermal, and mining industries. Predicting the path and overall geometry of a Hydraulic Fracture growing through a naturally Fractured rock has proven to be difficult. A range of experimental, theoretical, and numerical studies are available in the literature that address the need for an accurate model to predict the outcome of Hydraulic Fracture interaction with natural Fractures. However, consensus regarding Hydraulic Fracture Growth in the presence of natural Fractures has yet to be reached. This chapter provides a review of recent progress in this area and presents current thinking on this important topic.
