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Abstract In this paper, we investigate the effects of poroelastic properties and permeability on hydraulic fracturing in an anisotropic medium. A hybrid approach combining the EDFM (embedded discrete fracture model) and XFEM (extended finite element method) is proposed. Fractures are embedded into a nonconforming grid used to determine the fluid flow in a porous matrix by the mimetic finite difference method, accounting for an anisotropic permeability tensor. The stress-strain problem is solved by the extended finite element method with the same grid. The fluid flow and rock deformation as well as the fracture propagation are iteratively coupled. The proposed approach is validated against the analytical solutions for Mandel's problem and the KDG model. A series of calculations are performed, and the obtained results are analyzed to investigate the effects of the anisotropy of permeability, that of the elastic modulus and Biot's coefficient on the hydraulic fracturing process. It is found that the anisotropy of permeability has a significant influence on the geometrical parameter of a fracture, while the anisotropy of the elastic modulus has a dominating influence on the propagation direction of a fracture. Biot's coefficient also has an influence on the fracture propagation kinetics. [ABSTRACT FROM AUTHOR]

The objective of this study is to investigate the effect of rock anisotropy on hydraulic fracture propagation. The coupled model of rock deformation and fluid flow is established to study hydraulic fracturing of orthotropic formation. Stress field is solved by using the extended finite element method with special tip enrichment functions for orthotropic formation. The coupling between stress field and pressure field is treated by Picard iterative procedure. The modified circumferential tensile stress criterion is used to determine fracture propagation, in which stress intensity factors are determined by an interaction integral method. Numerical results show that when fracture doesn't initiate from the direction of material axis with larger modulus, the fracture propagation direction would change and divert to the direction of material axis with larger modulus. And as Young's modulus ratio between two material axes increases, the phenomenon becomes more obvious. Moreover, shear modulus also enhances the diversion phenomenon of fracture propagation direction. However, the in-situ stress difference could weaken the effect of rock anisotropy. The results indicate that the propagation process of hydraulic fracture is influenced by comprehensive factors including material axis angle, Young’ modulus ratio, shear modulus and in-situ stress difference. [ABSTRACT FROM AUTHOR]

In this paper, a hydro-mechanical model for non-planar hydraulic fracture propagation in ductile formations is developed based on the Drucker-Prager plasticity theory, Biot's theory and cohesive zone model (CZM). A hybrid extended finite element method (XFEM)-finite volume method (FVM)-embedded discrete fracture model (EDFM) method is proposed for numerical implementation. The XFEM and return-mapping method are used to simulate the deformation of inelastic media with strong discontinuities. The discontinuous pressure field is modelled by the EDFM and FVM. In addition, a dual-layer iterative algorithm is proposed to solve the strong nonlinear systems by a combination of the fixed-stress iteration, Picard iteration and Newton-Raphson iterative method. Then, the accuracy and ability of the proposed model are demonstrated through several reference cases. Finally, the proposed model are applied to two numerical cases and the influences of the plastic deformation on the simultaneous propagation of multi-fractures are investigated. • A poro-elasto-plastic model for non-planar hydraulic fracture propagation in ductile formations was developed. • A hybrid XFEM-FVM-EDFM method was proposed to conduct numerical implementation. • A dual-layer iterative algorithm was constructed to solve the strong nonlinear equation systems. • The effects of rock plasticity on multi-fractures propagation in the ductile formations were investigated. [ABSTRACT FROM AUTHOR]

The multiphase flow processes during water injection and flowback in shales are largely affected by its multiscale pore structure, different pore types and complex fluid transport mechanisms. At present, it is difficult to measure shale multiphase flow properties in laboratory. This study presents an upscaling model to derive core-scale relative permeability from pore-scale multiphase simulation using organic matter (OM)/inorganic matter (IOM) pore network models. Gas and water absolute permeabilities on OM/IOM pore network models are determined, and gas-water two-phase imbibition (during water injection) and drainage (during flowback) processes in the IOM pore network model are conducted using the invasion percolation theory. A core-scale model is generated with stochastically distributed IOM/OM patches. The upscaled relative permeabilities are derived by assembling gas-water transport properties in the IOM/OM based on the corresponding pore network simulation results. The upscaling method is validated by comparison with an analytical model during water injection and flowback processes. Furthermore, the impacts of total organic carbon (TOC) content and intrinsic permeability ratio of OM to IOM on the upscaled relative permeabilities are analyzed. The critical TOC content and intrinsic permeability ratio at which OM influences the upscaled relative permeabilities are determined. This study provides an effective upscaling workflow to obtain core-scale gas-water relative permeabilities based on pore-scale modeling considering multiple gas/water transport mechanisms in different pore systems. • Relative permeabilities upscaling model is built with multiple transport mechanisms. • Upscaled relative permeabilities largely rely on multiphase flow properties in IOM. • The impact of OM on upscaled relative permeabilities can be ignored at TOC <4%. • Intrinsic permeability ratio (γ) of OM to IOM is in effect at γ < 0.3. [ABSTRACT FROM AUTHOR]

In this study, we present an efficient numerical solution for studying hydraulic fracturing under coupled thermal–hydraulic conditions in an elastic–plastic porous medium. The propagation of macroscopic fracture is described by using an extended finite element method. Both the fluid flow through the porous medium and the exchange between the medium and fracture are taken into account. It is the same for the heat transfer. An efficient iterative scheme is then proposed to deal with the coupling between material deformation with fracture growth, fluid flow and heat transfer. The proposed method is assessed through comparisons with analytical solutions for a number of well-established problems. A series of numerical calculations are further performed in order to investigate the effect of plastic deformation and temperature change on the process of hydraulic fracture propagation. [ABSTRACT FROM AUTHOR]

Proppants are used to resist fracture closure during hydraulic fracking treatments. Understand the proppant transport and distribution characteristics in fracture and fracture network become a meaningful topic for its effects on the conductivities of fractures. Since experiments are expensive, and it is also difficult to consider various conditions and detect the movement of particles during experiments, numerical simulation methods are often applied. In this work, the coupled Computational Fluid Dynamics-Discrete Element Method (CFD-DEM) was implemented to investigate the factors affecting proppant distribution in fracture and fracture networks. First, the CFD-DEM model was built for proppant flow and settlement. We validated the model by comparing with the published numerical simulation result. After that, we designed a series of cases to investigate the effects of fracture closure, injection velocity and no-uniform opening of the inlet on proppant distribution in a single fracture. Then, the effects of proppant diameter, density and perforation height differences on proppant sorting were studied. Next, we computed the proppant transport in fracture networks considering the aperture difference, the orientation of branch fractures and leak-off in fracture tips. The simulation results in this paper can help engineers to understand the transport and distribution of proppants visually in the fracture and fracture networks in unconventional reservoirs. • We have built a model to investigate the proppant distribution in fractures and fracture networks. • Particle diameter difference results in the proppants sorting and perforation height impacts the mixture degree. • Fracture closure results in a reduction in layers of proppant dune and increases the profile area of proppant dune. • The small angle between MF and BF and the big branch aperture are advantageous to the proppant particles into the branches. [ABSTRACT FROM AUTHOR]

Geologic storage of CO 2 in shale formation not only enhances natural gas recovery, but also sequestrates CO 2 effectively. According to this technology, a multi-continuum quadruple porosity binary component gas model is developed to investigate carbon dioxide storage capacity and CO 2 enhanced shale gas recovery, which is based on multiple flow mechanisms, including dissolution, adsorption/desorption, viscous flow, diffusion, slip flow and stress sensitivity of hydraulic fractures. This fully coupled model is divided into quadruple media, including organic matters, organic pore system, matrix system and natural fracture system. The matrix-fracture transfer flow is simulated by modified multiple interacting continua (MINC) method. Embedded discreate fracture model (EDFM) is introduced to describe the gas flow in hydraulic fractures and the transfer flow between hydraulic fractures and natural fractures. Finite difference method (FDM) and quasi-Newton iterative method are applied to solve this model. The reliability and practicability of this model is validated by matching the production history of a fractured horizontal well in shale gas reservoir. The effects of relevant parameters on production curves are analyzed, including adsorption parameters, dissolution parameters, well production pressure, injection pressure, volumetric fraction of kerogen and injection opportunity. The result shows that the model in this work is reliable and practicable, and the model presented here can be used to investigate the injectivity of CO 2 and CO 2 enhanced shale gas recovery. • Developing a multi-continuum quadruple porosity binary component gas model. • Considering multiple flow mechanisms for binary component gas. • Solving this model by finite difference method and quasi-Newton iterative method. • Estimating CO 2 storage capacity and CO 2 enhanced shale gas recovery. • Simulating fracture-matrix transfer flow by modified multiple interacting continua method. [ABSTRACT FROM AUTHOR]

Abstract With the increasing demand of oil and gas resource, the development of deep reservoir has become an inevitable trend. To investigate the coupled effects of rock elasto-plastic deformation, fluid flow and heat transfer in the process of hydraulic fracturing of deep reservoir, the mathematical model of elasto-plastic hydraulic fracture propagation is established based on cohesive zone model (CZM) and embedded discrete fracture model (EDFM). The constitutive equation incorporating thermal stress is derived by using Drucker-Prager yield condition and the associated flow law. Fluid flow in the fracture is modeled with lubrication theory. The thermal non-equilibrium theory is employed to describe the heat exchange between rock matrix and fluid in the fracture based on EDFM. The CZM is used as fracture propagation criterion. The rock deformation equation is solved by finite element method. The temperature field and fluid flow in the fracture are discretized by finite volume method. Due to the non-linearity of flow equation, the iterative method is used to solve the coupled problem of stress, pressure and temperature fields. A Triangular-PEBI (Perpendicular Bisector) dual mesh system is presented for numerical implementation. The numerical model is validated against with analytical solution and other methods in the literature. The results show the significance of accounting for elasto-plastic deformation and heat transfer when simulating hydraulic fracture propagation in deep reservoir. Highlights • Developed model involves plastic deformation, fluid flow and temperature field. • Heat exchange between matrix and fracturing fluid is modeled based on EDFM. • A Triangle-PEBI dual mesh system is presented for numerical implementation. • An efficient algorithm for thermal-elasto-plastic fracture propagating is proposed. • Result shows that plastic zone moves forward and expands during propagating. [ABSTRACT FROM AUTHOR]

In this study, an efficient hydro-mechanical model of hydraulic fracture propagation is proposed using the embedded discrete fracture model in conjunction with the extended finite element method. Fracture is embedded into a common computational grid for both stress and pressure fields. A hybrid scheme of fixed stress split and Picard iterative method is presented to deal with the hydro-mechanical coupling and fracture propagation. The model is verified against other numerical solution of hydro-mechanical coupling problem and analytical solution of fracture propagation available from literature. Numerical results show that as matrix permeability increases, more fracturing fluid is required to get a desired length of fracture. The effect of Biot's coefficient is similar to that of matrix permeability. Finally, the model is extended to simulate simultaneous propagation of multiple hydraulic fractures. It's interesting to find that the effect of stress shadowing could be weakened by the poroelastic stress when accounting for hydro-mechanical coupling. The study indicates that the hydro-mechanical coupling could have significant influence on hydraulic fracturing, especially for multi-cluster fracturing of horizontal wells. [ABSTRACT FROM AUTHOR]

The composite shale gas reservoir consists of an inner and an outer region. Inner region is stimulated reservoir volume (SRV) and contains shale matrix and natural fractures. Outer region represents un-stimulated reservoir volume (USRV) and contains shale matrix only. The interface boundary between SRV and USRV is often arbitrarily shaped rather than the regular, which can be derived from micro-seismic events of shale gas reservoirs with multiple fractured horizontal well (MFHW) Considering arbitrary interface boundary between SRV and USRV and outer boundary, a composite model is presented for MFHW in composite shale gas reservoirs, which based on multiple mechanisms, including adsorption/desorption, viscous flow, diffusive flow and stress sensitivity of natural fractures. Boundary element method (BEM) is introduced to solve the pressure response of MFHW in composite shale gas reservoirs. The accuracy of this model is validated by comparing its pressure response solution with the result derived from an analytical and a numerical method, respectively. According to pressure performance analysis of MFHW in composite shale gas reservoirs, eight flow regimes are identified: the early linear flow, the early radial flow, the second linear flow, the second radial flow, inter-porosity flow from shale matrix to natural fractures, the transition flow, diffusive flow and the third radial flow. The effects of relevant parameters on pressure response are analyzed, including mobility ratio, storability ratio, inter-porosity coefficient, diffusion coefficient, adsorption index and the shape of interface boundary. The result shows that BEM can be perfectly used to analyze the pressure performance of MFHW of composite shale gas reservoirs with arbitrary shaped interface boundary and outer boundary; the presented model can be used to interpret pressure data more accurately for shale gas reservoirs and provide more accurate dynamic parameters which are important for efficient reservoir development. [ABSTRACT FROM AUTHOR]

Naturally fractured carbonate reservoirs have been discovered in many oilfields around the world and are characteristic of a complex, heterogeneous porosity system. The presence of large-scale cavities will have a noticeable effect on the transient pressure behavior, especially, when a well is drilled through them. The cavities are usually filled with loose materials, such as gravel, sand, and mud, due to the physical or chemical processes. Therefore fluid flow in a filled cavity may range from low-velocity Darcy flow to high-velocity non-Darcy flow. It is necessary to incorporate cavity filling effect in the type curve matching for flow behavior in fractured carbonate reservoirs. The objective of this work is to develop an efficient well testing model to analyze and interpret the transient pressure responses observed in a naturally fractured carbonate reservoir, in which a well is drilled through a filled cavity. To this end, a radial composite reservoir model including the inner and outer regions with different characteristics is proposed. The inner region is a filled cavity with a well drilled into. The outer region, a naturally fractured reservoir, is considered as a dual-porosity model in this work. The Barree-Conway model, initially proposed for a proppant-packed fracture, is applied to simulate the non-Darcy flow in the inner region. The corresponding mathematical model is developed, and a numerical solution is then obtained based on the finite difference method, which is further verified by the analytical solution under simplified flow condition. Several standard log-log type curves are provided to reveal the flow characteristics. The flow process is shown to have six flow stages in general. Subsequently, sensitivity analyses of the type curves are carried out. The calculated results show that the characteristics of the well testing type curves are influenced significantly by non-Darcy coefficients, the size of the filled cavity, and the petrophysic property ratio between inner and outer areas. Finally, the proposed model is applied to analyze and interpret two field testing examples. [ABSTRACT FROM AUTHOR]

• A 3D hydro-mechanical coupled model is presented to study hydraulic fracturing interaction with bedding planes. • Cohesive zone method is employed to represent the bedding planes explicitly. • Fracture propagation behaviors are analyzed under different patterns. Bedding planes are abundant in the continental shale oil reservoirs, but their impact on hydraulic fracturing is still not fully understood. To investigate the effects of stress condition, bedding plane's properties and layer lithology on hydraulic fracture propagation in layered formation, a 3D hydro-mechanical coupled model is presented. The bedding planes are explicitly represented by cohesive elements with degraded properties compared to the rock. The results show that increasing the stress difference ratio of the vertical principal stress to horizontal principal stress promotes the hydraulic fracture propagating across bedding planes, and the critical value of vertical principal stress required for hydraulic fracture crossing rises with the decrease of bedding plane's critical traction. Furthermore, when the critical traction ratio of bedding plane to rock drops below 0.7, the fracture propagation pattern changes from crossing to deflecting. Additionally, the extension pressure increases slightly, the fracture length decreases and the area of opening bedding planes rises. As the permeability of bedding plane increases, the fracture cannot cross the bedding planes and even stops extension. The layer lithology contrast also affects fracture propagation patterns. This study examines the fracture propagation behaviors under different patterns, including the opening morphology of bedding plane and the evolution of injection pressure and strain energy. The simulation results may provide useful insights for hydraulic fracturing design in layered formations. [ABSTRACT FROM AUTHOR]

As an effective enhanced oil recovery (EOR) technique in tight reservoirs, cyclic water injection has been extensively studied recently. However, very few studies have considered the impacts of loading-path dependent fracture deformation, i.e. deformation hysteresis. In this study, an efficient coupled two-phase flow and geomechanics model is developed to simulate cyclic water injection in a tight oil reservoir with the consideration of fracture deformation hysteresis. The embedded discrete fracture model (EDFM) is applied to handle complex fracture geometries. Different loading-path dependent constitutive models are used to describe the deformations of hydraulic fractures and natural fractures, respectively. Then simulation studies are performed to demonstrate the impacts of deformation hysteresis of hydraulic fractures and natural fractures on EOR performance. The sensitivities to injection rate, depletion pressure and soaking time are examined. The results show that the deformation hysteresis of hydraulic fracture has significant effect on oil production, while that of natural fracture has negligible impact. The effects of fracture deformation hysteresis are more pronounced under high injection rate and depletion pressure, but less sensitive to soaking time. [ABSTRACT FROM AUTHOR]

Fracture penetration or deflection may occur when the hydraulic fracture approaches weak interface in multi-layered formation. However, the intrinsic mechanism of fracture propagation pattern remains unclear. A model was presented to investigate hydraulic fracture propagation in multi-layered formation via the phase field method. The interface is explicitly represented by a weak thin layer. Fluid flow in the fractured media was modeled by using the indicator function of phase field. The iterative algorithm was described and validated against the benchmark cases. Simulation results show that the evolution of injection pressure is more complex when the fracture deflects than that when the fracture penetrates the interface. The fracture is prone to penetrate the softer layer the perforated layer while deflects to the interface if the adjacent layer is stiffer. Decreasing the modulus ratio of interface to layers promotes the fracture deflecting to the interface, while increasing the stress ratio contributes to the fracture penetrating the interface. The stacking mode of layers greatly affects the fracture propagation morphology in three or more layered formations. Rock heterogeneity doesn't alter the fracture propagation pattern as a whole, but it affects the local fracture morphology. The results provide a cloud chart of the relationship between fracture propagation pattern and controlling factors for the potential of field application. [ABSTRACT FROM AUTHOR]

The Enhanced Geothermal System (EGS) creates an artificial geothermal reservoir by hydraulic fracturing which allows heat transmission through the fractures by the circulating fluids as they extract heat from Hot Dry Rock (HDR). The technique involves complex thermal–hydraulic–mechanical (THM) coupling process. A numerical approach is presented in this paper to simulate and analyze the heat extraction process in EGS. The reservoir is regarded as fractured porous media consisting of rock matrix blocks and discrete fracture networks. Based on thermal non-equilibrium theory, the mathematical model of THM coupling process in fractured rock mass is used. The proposed model is validated by comparing it with several analytical solutions. An EGS case from Cooper Basin, Australia is simulated with 2D stochastically generated fracture model to study the characteristics of fluid flow, heat transfer and mechanical response in geothermal reservoir. The main parameters controlling the outlet temperature of EGS are also studied by sensitivity analysis. The results shows the significance of taking into account the THM coupling effects when investigating the efficiency and performance of EGS. [ABSTRACT FROM AUTHOR]

• An improved thermo-hydro-mechanical coupling model is developed. • Effects of shear dilation and thermal stress on heat extraction are investigated. • Effects of fracture properties and deviatoric stress on THM processes are studied. • Practically useful guidelines for developing sustainable EGSs are proposed. Shear dilation of fractures has been recognized as a main mechanism of permeability enhancement by hydraulic stimulation in Enhanced Geothermal Systems (EGSs); however, the interactive role of fracture shear dilation and thermo-hydro-mechanical (THM) coupling processes in long-term heat extraction performance of EGSs remains unclear. In this study, we develop a novel THM coupling model based on the discrete fracture network approach, which can realistically capture important processes including hybrid normal-shear deformation of fractures, thermal expansion of rocks, fluid flow in both fractures and rocks, and heat convection/conduction as well as local thermal non-equilibrium effect and changes in physical parameters of fluid. We quantitatively investigate the effects of fracture network geometries and geomechanical boundary constraints on fracture shear dilatancy, and the resulting heat transfer characteristics of EGSs. Numerical results reveal that shear dilation of fractures can be triggered by transient pore pressurization and thermal stress under anisotropic in-situ stress condition, and would severely engender flow channeling as well as anisotropic heat transfer, which strongly impact the heat extraction performance. The production temperature tends to be overestimated while the thermal production rate may be underestimated, if the shear dilatational behavior is not incorporated. Increased in-situ stress ratio and injection/production pressure would magnify the effects of shear dilation, and lead to considerable enhancement of fracture permeability, eventually resulting in much earlier and quicker temperature drop. Excessive increase of fracture density and the location of injection-production wells parallel to potential channelized flow paths, formed by intersected fractures preferentially oriented for shear sliding, tend to form short circulating flow paths and reduce the heat extraction performance. Our study demonstrates the importance of considering fracture shear dilation and fully-coupled THM behaviors when evaluating the long-term performance and efficiency of heat extraction in EGSs. [ABSTRACT FROM AUTHOR]

Shale oil flow is commonly affected by the confined phase behavior, complex fracture geometries, and geomechanical effect, which are not fully considered in the conventional compositional simulators. In this study, a coupled compositional flow and geomechanics model is presented to incorporate these effects for more accurate prediction on shale oil production performance. The compositional model considering the confined phase behavior is used to model the multiphase flow in shale formations, in which the capillary pressure is introduced into the workflows of phase stability test and flash calculation. The embedded discrete fracture model (EDFM) is adopted to explicitly describe the complex fracture geometries. The deformations of hydraulic fractures and natural fractures are handled by different constitutive models. A mixed finite-volume and finite-element (FVM-FEM) scheme is used to discretize the flow and geomechanics equations, and the coupled problem is iteratively solved by the fixed-stress splitting method. Based on the proposed model, simulations are conducted on a multi-stage fractured shale reservoir to evaluate the effects of confined phase behavior, hydraulic fracture deformation, and natural fracture network on the production performance. Results show that the bubble point pressure is suppressed by the confined phase behavior effect, which leads to higher oil production. The hydraulic fracture deformation takes effect only when the hydraulic fractures cannot be treated as infinite-conductivity under poorly-propped condition. The oil production is greatly promoted with the increase of natural fracture density due to the increase of interface area between matrix and fractures. • A coupled compositional flow and geomechanics model with confined phase behavior is developed for shale oil reservoirs. • EDFM coupled with different constitutive models are used to describe the hydro-mechanical behaviors of complex fractures. • Effects of confined phase behavior, hydraulic fracture deformation, and natural fractures on oil production are investigated. [ABSTRACT FROM AUTHOR]