Non-planar Hydraulic Fractures Research Articles

Numerical analysis of 3D nonplanar hydraulic fracture propagation in fractured-vuggy formations using a hydromechanical coupled XFEM approach

In this paper, a hydromechanical coupled XFEM approach is developed for simulating 3D nonplanar hydraulic fracturing, fracture–vug interactions and natural crack intersection problems. The extended finite element method associated with a high-order tip enrichment function is used for describing rock deformation, and the finite element method is chosen for discretizing fluid flow at the fracture surface. Rock deformation and fluid flow are coupled and solved by the Picard iteration method. The hybrid explicit–implicit representation method is adopted to represent 3D nonplanar fracture surfaces, and the displacement correlation method is chosen for extracting the mixed-mode stress intensity factor. A new mixed-mode failure criterion is introduced for determining 3D nonplanar fracture growth. Analytical solutions and experimental investigations are employed to verify the validity and effectiveness of our model. The simulations of fracture–vug interactions show that fracture surface growth on the side without vugs is constrained, while vugs can aggravate the tortuousness of the fracture surface on the side with vugs. In addition, four new intersection patterns (penetration, partial arrest, partial diversion, full arrest, and vertical propagation) are found in the 3D nonplanar fracture intersection simulations. The numerical examples highlight the considerable impacts of vertical growth and the mixed-mode effect on hydraulic fracturing.

An improved dual-porosity dual-permeability modeling workflow for representing nonplanar hydraulic fractures

The Dual-Porosity Dual-Permeability (DPDK) model is commonly used for upscaling and simulating fractured reservoirs. However, many common upscaling approaches lead to disconnected fracture, particularly when simulating Discrete Fracture Networks (DFN) and nonplanar hydraulic fractures that are not aligned with the axes of corner-point grids supported by most reservoir simulation packages using the Two-Point Flux Approximation (TPFA) technique for flow and mass transfer calculations. This misalignment could result in inaccurate computed fluxes when fractures are disconnected in the upscaling process. Our previous works attempted to address this problem in DFNs by detecting misalignments and adjusting DPDK fracture parameters locally. However, such methods required explicit knowledge of the fracture coordinates. This paper introduces a novel approach based on area interpolation, which identifies disconnected fractures from fracture images without extracting fracture coordinates, significantly improving detection efficiency. This study primarily focuses on nonplanar fractures, aiming to simulate them using the DPDK model accurately. The simulations are compared with those obtained using the Embedded Discrete Fracture Model (EDFM). This work illustrates how nonplanar hydraulic fractures can be effectively simulated in a DPDK model. Our results demonstrate that the adjusted/corrected DPDK model can offer superior or comparable performance to an EDFM for simulating nonplanar fractures. The proposed method is flexible and readily applied in commercial simulation software.

Effects of rock ductility on the fracability of ductile reservoirs: An experimental evaluation

Deep hydrocarbon resources below 4000 m are an important replacement for shallow-depth resources; however, as depth increases, the difficulty and cost of development increase sharply. One of the possible reasons is that deep reservoir rocks exhibit strong ductility, which causes difficulties to stimulate a well-developed fracture network in rocks. To date, the mechanism by which rock ductility affects reservoir fracturing remains unclear, and there is a lack of quantitative evaluation models for reservoir fracability. To overcome the problems, in this study, artificial rock specimens with different ductility were fabricated using similar materials based on the geological data and petrophysical properties of the target deep reservoir; the specimens were classified using the proposed ductility index BIf. The hydrofracturing and CT scanning experiments of the artificial specimens with different BIf values under various horizontal stress differences Kh were conducted. The spatial fractal index Df was proposed to characterize the three-dimensional morphology and development of the fracturing network. The fracability evaluation function of ductile rock correlating the indices BIf and Kh was established. It was shown that ductile rocks tended to form non-planar hydraulic fractures with obvious tortuosity and the degree of fracture network development was lower than that of brittle rocks. The maximum breakdown pressure was approximately twice that of the brittle specimen, while the corresponding injection energy was approximately 5–10 times and the energy dissipation of fracture propagation was approximately 4–6 times those of the brittle rock. When Kh ≥ 0.3 the maximum horizontal principal stress played a major role in controlling the hydraulic fracture propagation in ductile rocks. If Kh < 0.3, the fracture propagation in rocks was mainly governed by material ductility rather than the maximum horizontal principal stress. This study provides a new way to explore and quantify the effect of rock ductility on the fracability of deep reservoirs.

Modeling fracture transient flow using the Embedded Discrete Fracture Model with nested local grid refinement

Transient flow around hydraulic fractures is an important topic in the study of tight reservoirs. In this work, the Embedded Discrete Fracture Model (EDFM) is combined with nested local grid refinement (LGR) to improve its accuracy for simulating near-fracture transient flow. An automatic grid refinement procedure is developed to iteratively conduct LGR around complex fractures. In each iteration, the cells intersected by or close to fractures are selected and refined. The size of the refinement region and the level of refinement can be adjusted. Through this process, the cell size in the near-fracture region is reduced rapidly, while the total cell count remains at a relatively low level. An analysis of the optimal refinement ratio for regular Cartesian grids is also conducted. Furthermore, the EDFM is implemented in grids with nested LGR, and connections between the matrix and fractures are properly determined to compute the transmissibility factors as input for reservoir simulators.The developed methodology is first verified against a logarithmic LGR model for different fracture orientations, and the results show that different flow regimes can be reliably simulated. Subsequently, the flow regimes for non-orthogonal, non-parallel, and nonplanar hydraulic fractures are studied with this approach to illustrate the unique patterns of transient flow around complex fractures. This work provides a general and convenient method to perform transient analysis for reservoirs with complex fracture geometries.

3D unrestricted fluid-driven fracture propagation based on coupled hydromechanical interface elements

Exploring unconventional reservoirs has raised several engineering challenges to improve oil/gas recovery. In the Brazilian pre-salt fields, highly heterogeneous carbonate formations compose these reservoirs containing fractures in multiple scales. The extracted carbon dioxide is reinjected in the reservoirs to increase oil recovery and reduce greenhouse gas emissions. For that reason, it is essential to develop robust numerical methods capable of simulating fracture propagation in naturally fractured porous media. This paper presents a new 3D mesh fragmentation technique to simulate non-planar hydraulic fracture propagation, considering its interaction with natural fractures. This method is based on discrete fracture representation through hydromechanical interface elements with a cohesive zone model to simulate fluid-driven fracture propagation. The proposed 3D mesh fragmentation algorithm inserts triple noded-interface elements into the continuum finite element faces, ensuring continuity of the fluid pressure field. The approach is successfully validated against experimental fracturing tests and analytical models. Also, by applying the proposed fragmentation technique, we study the influence of pre-existing oriented fractures on hydraulic fracture propagation in different scenarios. The results provide insight into the complex hydraulic fracturing process in naturally fractured formations. Finally, this approach is an attractive alternative to simulate multi-staged fracturing into 3D multilayered fractured rock formations.

Enhanced Pseudo-Three-Dimensional Model for Multiple Hydraulic Fractures

Abstract Modeling the propagation of hydraulic fractures is a complex problem that involves solving the equations that describe the intimate coupling between the cracked and porous solid phase and the fracturing fluid that drives the process according to established crack extension criteria. Most of the existing computational techniques become prohibitively expensive if applied to three-dimensional configurations, especially those involving multiple fractures because their accuracy relies on extremely fine discretizations of the geometry. These include the standard finite element method and standard displacement discontinuity method, which require substantial mesh densities in the vicinity of the crack front to capture the complex nature of the singular fields associated with fluid-driven cracks. Models have recently been proposed that offer sufficient accuracy and a significant increase in computational efficiency. These include the enhanced pseudo-3D model that explicitly incorporates a non-local elasticity relation and known crack-front asymptotic solutions that capture the multiscale near-front behavior. Here, we present an enhanced pseudo-3D model for simulating the propagation of multiple planar and nonplanar hydraulic fractures in a linear elastic medium. The algorithm is built on a fixed mesh with an adaptive tip element, and it incorporates leak-off, as well as stress interaction between the fractures. The model is validated against reference solutions of plane strain, radial, and multi-planar fracture geometries, for various sets of parameters that cover the majority of the problem parametric space.

A parametric study of hydraulic fracturing interference between fracture clusters and stages based on numerical modeling

Shale oil reservoirs are usually developed by horizontal wells completed with multi-stage hydraulic fractures. The fracture interference between clusters in a single stage and between consecutive stages has an impact on the stimulation quality in terms of fracture geometries and fracture widths. This study introduces a non-planar hydraulic fracture model based on the extended finite element method and its use in quantifying the effects of relevant parameters on multi-stage fracture quality in a realistic shale oil scenario. The numerical model is validated with field diagnostics based on vertical seismic profiling. Relevant parameters including stress contrast, fracturing fluid viscosity, cluster density, and fracturing in consecutive stages are quantitatively analyzed in the numerical study. Results show that effects of stress contrast on fracture quality are greater than those of fracturing fluid viscosity, while the effects are more significant in outer fractures instead of the inner fracture. Denser cluster design leads to greater inhibition for the growth of inner fractures which eventually divert them transversely. In fracturing for consecutive stages, the opening of fractures in the subsequent stages is inhibited and the fracture geometries are also altered by the inter-stage interference caused by the previous stage. Based on field data and numerical modeling, this study identifies key parameters and quantifies their effects on inter-fracture and inter-stage interference in multi-stage hydraulic fracturing in horizontal wells.

A numerical hybrid model for non-planar hydraulic fracture propagation in ductile formations

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.

Using Deep Learning to Predict Fracture Patterns in Crystalline Solids

Summary Fracture is a catastrophic process whose understanding is critical for evaluating the integrity and sustainability of engineering materials. Here, we present a machine-learning approach to predict fracture processes connecting molecular simulation into a physics-based data-driven multiscale model. Based on atomistic modeling and a novel image-processing approach, we compile a comprehensive training dataset featuring fracture patterns and toughness values for different crystal orientations. Assessments of the predictive power of the machine-learning model shows excellent agreement not only regarding the computed fracture patterns but also the fracture toughness values and is examined for both mode I and mode II loading conditions. We further examine the ability of predicting fracture patterns in bicrystalline materials and material with gradients of microstructural crystal orientation. These results further underscore the excellent predictive power of our model. Potential applications of this model could be widely applied in material design.

Pressure transient analysis in the child well with complex fracture geometries and fracture hits by a semi-analytical model

Recently, the model development of pressure transient analysis in wells with large-scale fracturing treatments has attracted more and more attention. However, a little work has involved the complex fracture networks with fracture hits. In this study, the transient pressure behaviors of a child well with complex fracture geometries and fracture hits are studied, using an efficient semi-analytical model. The semi-analytical model has the capability to simulate shale well performance by considering complex non-planar hydraulic fractures and fracture hits.The pressure transient solution of the semi-analytical model is obtained by the incorporation of nodal analysis and Laplace transforms. After the numerical verification of the proposed semi-analytical model, we apply it to analyze the pressure testing data of a child well and a parent well. Through conducting a series of history matching, the most likely fracture parameters of the child well is determined. Results show that the flow regimes of complex fracture geometries with fracture hits include wellbore storage, skin effect, fracture bilinear flow, “fluid feed”, pseudo-boundary dominated flow, unconnected fracture (UF) impact, and pseudo radial flow. During the flow regime of UF impact, the pressure derivative curves exist a second “V-shape”, as the UF improve the matrix permeability and the pressure depletion will be reduce once the flow reaches the UF. A case study in the Lucaogou shale oil reservoir from the Junggar Basin show that complex fracture geometries is developed along the child wellbore. After estimation, the fracture hits between the parent well and child well may via five hitting fractures. The length and conductivity of the hitting fractures are evaluated as 20 m and 120 mD∙m, respectively. This work could be beneficial to performance forecast and well spacing optimization in unconventional reservoirs.

Exploration of non-planar hydraulic fracture propagation behaviors influenced by pre-existing fractured and unfractured wells

Hydraulic fracturing plays significant role in enhancing production performance of low-porosity and low-permeability reservoirs because the created hydraulic fracture (HF) can improve the communication between formation and wellbore. Therefore, understanding propagation behaviors of HF is critically important for the design of hydraulic fracturing treatment. Normally, HF tends to take a straight path in a symmetrical stress field when rockmass is homogeneous and isotropic. However, as a result of fluid injection or production through pre-existing wells, non-uniform stress field can be encountered during the fracturing treatment in which case HF will be deviated along the perturbed principal stress field in the formation. In this work, to investigate the effects of adjacent fractured and unfractured wells on HF propagation, a new numerical model is developed within the framework of extended finite element method (XFEM) and cohesive zone method (CZM). The model can simultaneously capture HF initiation, propagation and re-orientation, fracturing fluid flow and leakoff, formation fluid flow and rock deformation. The results indicate that HF is attracted towards pre-existing injection well with deviation angle being larger when the injection well is fractured, whereas HF tends to deviate away from offset production well with deviation angle being larger around fractured production well. Meanwhile, the pre-existence of injection well makes the HF wider, and longer HF can be created near the production well. The results also demonstrate that both breakdown pressure (BDP) and fracture propagation pressure (FPP) are increased around the pre-existing injection well while BDP and FPP are decreased near the offset production well. The obtained conclusions provide new insights for understanding the HF propagation problem in the field scale.

Stimulated reservoir volume estimation for shale gas fracturing: Mechanism and modeling approach

Multi-stage fracturing, following horizontal well drilling, is the key technology in shale gas reservoir development to enhance the recovery from such tight formations for economic production. The stimulated reservoir volume (SRV), which correlates closely to fracturing performance, is a quantitative measure for both pre-fracturing design and post-fracturing evaluation. However, an accurate estimation of the SRV is a long-standing challenge, because it requires a great knowledge of various parameters and complex mechanisms.In this study, we developed a mathematical model to estimate the SRV through simulating the main process during shale fracturing—multiple simultaneous hydraulic fractures propagate, perturbing the formation stress and raising the reservoir pressure; meanwhile, the stress change and pressure rise may jointly make natural fractures occur failure, and the SRV is estimated based on the volume of the naturally fractured zone that experiences tensile or shear failure.Hybrid numerical methods have been employed in this study. It applies displacement discontinuity method (DDM) to simulate non-planar hydraulic fractures propagation and represent the induced stress triggered by hydraulic fractures. The reservoir pressure is calculated by finite difference method (FDM). The failure state of natural fractures is predicted by the tensor equations deduced from Warpinski's failure theory. The model considers complex but important physical mechanisms that involved in the shale fracturing, including unequal flow-rate distribution among each hydraulic fracture, non-planar hydraulic fractures propagation under stress interference, reservoir permeability increase with SRV extending (pressure & stress-depend), different failure states of natural fractures, etc.We validated our model by comparing its simulation results with analytical solution, published papers and on-site microseismic monitoring data. A field case study was performed to show the dynamic processes of hydraulic fractures propagation, reservoir permeability increase, and the SRV expansion during shale gas fracturing. Sensitivity analysis was conducted to investigate the influence of geological condition and fracturing parameters on SRV.

A Numerical Model for Simulating Pressure Response of Well Interference and Well Performance in Tight Oil Reservoirs With Complex–Fracture Geometries Using the Fast Embedded–Discrete–Fracture–Model Method

Summary The effect of well interference through fracture hits in shale reservoirs needs to be investigated because hydraulic fracturing is abundantly used in the development of unconventional oil and gas resources. Although numerous pressure tests have proved the existence of well interference, relatively few physical models exist to quantitatively simulate the pressure response of well interference. The objective of the present study is to develop a numerical compositional model in combination with a fast embedded-discrete-fracture-model (EDFM) method to simulate well interference. Through nonneighboring connections (NNCs), the fast EDFM method can easily and properly handle complex-fracture geometries, such as nonplanar hydraulic fractures and a large amount of natural fractures. Using public data for Eagle Ford tight oil, we build a reservoir model including up to three horizontal wells and five fluid pseudocomponents. The simulation results show that the connecting hydraulic fractures play a more-important role than natural fractures in declining bottomhole pressure (BHP) of the shut-in well. Matrix permeability has a relatively minor effect on pressure drawdown, and well productivity remains only slightly affected by the overall low permeability used. The BHP pressure-decline profiles change from convex to concave when the conductivity of the connecting fractures increases. At early times, the BHP of the shut-in well decreases when the number of natural fractures increases. At later times, the natural-fracture density has a lesser effect on the pressure response and no clear trend. The opening order of neighboring wells affects the well-interference intensity between the target shut-in well and the surrounding wells. After a systematic investigation of pressure drawdown in the reservoir, we formulate practical conclusions for improved production performance.

Coupled hydromechanical‐fracture simulations of nonplanar three‐dimensional hydraulic fracture propagation

SummaryThis paper presents an algorithm and a fully coupled hydromechanical‐fracture formulation for the simulation of three‐dimensional nonplanar hydraulic fracture propagation. The propagation algorithm automatically estimates the magnitude of time steps such that a regularized form of Irwin's criterion is satisfied along the predicted 3‐D fracture front at every fracture propagation step.A generalized finite element method is used for the discretization of elasticity equations governing the deformation of the rock, and a finite element method is adopted for the solution of the fluid flow equation on the basis of Poiseuille's cubic law. Adaptive mesh refinement is used for discretization error control, leading to significantly fewer degrees of freedom than available nonadaptive methods. An efficient computational scheme to handle nonlinear time‐dependent problems with adaptive mesh refinement is presented. Explicit fracture surface representations are used to avoid mapping of 3‐D solutions between generalized finite element method meshes. Examples demonstrating the accuracy, robustness, and computational efficiency of the proposed formulation, regularized Irwin's criterion, and propagation algorithm are presented.

Numerical simulation of MZF design with non-planar hydraulic fracturing from multi-lateral horizontal wells

In recent years, developments in the oil and gas industry have evolved significantly in advancing the mechanical systems technology to perform hydraulic fracturing. However, further developments will require an in-depth understanding of the impacts of fracture spacing, stress anisotropy, and reservoir characterization. In order to develop a comprehensive and robust completion design for hydraulic fracturing from multi-lateral wellbores with closely spaced fractures, it is important to consider stress shadowing effects. In this work the Cohesive Segments Method is combined with the Phantom Node Method, a combination termed CPNM. This is capable of not only simulating non-planar hydraulic fracture propagation with an unpredictable path, but also simulating the emergence of multiple cohesive cracks within a porous medium. This paper focuses on the “Modified Zipper-Frac” (MZF) design, which has been introduced to design the clusters from multi-lateral wells with the aim of increasing the fracture complexity. Validation of the numerical technique has been performed by comparing the solution for an individual hydraulic fracture with a Khristianovic-Geertsma-de Klerk (KGD) solution. In addition, a study of the development of double fractures has been conducted in the presence of stress shadowing to verify the simulation results. Taking the stress shadowing effects into account, a large number of numerical simulations are conducted using CPNM to investigate the stress anisotropy as well as the in-plane shear stress in the area between the two wells. The main contribution of this work is the detailed investigation of the effects of stress shadowing as a function of the fracture spacing on the horizontal stress contrast, direction of maximum local stress, leak-off flow rate, in-plane shear stress, and pore pressure of the formation.

A Comprehensive Numerical Model for Simulating Fluid Transport in Nanopores

Since a large amount of nanopores exist in tight oil reservoirs, fluid transport in nanopores is complex due to large capillary pressure. Recent studies only focus on the effect of nanopore confinement on single-well performance with simple planar fractures in tight oil reservoirs. Its impacts on multi-well performance with complex fracture geometries have not been reported. In this study, a numerical model was developed to investigate the effect of confined phase behavior on cumulative oil and gas production of four horizontal wells with different fracture geometries. Its pore sizes were divided into five regions based on nanopore size distribution. Then, fluid properties were evaluated under different levels of capillary pressure using Peng-Robinson equation of state. Afterwards, an efficient approach of Embedded Discrete Fracture Model (EDFM) was applied to explicitly model hydraulic and natural fractures in the reservoirs. Finally, three fracture geometries, i.e. non-planar hydraulic fractures, non-planar hydraulic fractures with one set natural fractures, and non-planar hydraulic fractures with two sets natural fractures, are evaluated. The multi-well performance with confined phase behavior is analyzed with permeabilities of 0.01 md and 0.1 md. This work improves the analysis of capillarity effect on multi-well performance with complex fracture geometries in tight oil reservoirs.

Discrete-Fracture Modeling of Complex Hydraulic-Fracture Geometries in Reservoir Simulators

Summary Hydraulic fracturing is a dominant technology in unconventional resources development. Recent advances in fracture-diagnostic tools and fracture-propagation models make it necessary to model fractures with complex geometries in reservoir-simulation studies. In this paper, we present an efficient method to model fractures with complex geometries with reservoir simulators. Through nonneighboring connections (NNCs), an embedded discrete-fracture modeling (EDFM) formulation is applied to reservoir simulators to properly model fractures with complex geometries such as fracture networks and nonplanar hydraulic fractures. We demonstrate the accuracy of the approach by performing a series of case studies with two commercial reservoir simulators and comparing the results with local-grid-refinement (LGR) models and a semianalytical solution. The limitations of the model are also discussed. In addition, the results show its computational efficiency as the complexity of fractures increases. We also present two numerical case studies to demonstrate the applicability of our method in naturally fractured reservoirs. The nonintrusive application of the EDFM allows insertion of the discrete fractures into the computational domain and the use of original functionalities of the simulators without having access to the source code of the simulators. It may be easily integrated into existing frameworks for unconventional reservoirs to perform sensitivity analysis, history matching, and production forecasting.

Numerical modeling of non-planar hydraulic fracture propagation in brittle and ductile rocks using XFEM with cohesive zone method

In this study, we present a fully coupled non-planar hydraulic fracture propagation model in permeable medium based on the Extended Finite Element Method (XFEM), and the arbitrary solution-dependent fracture path cam be determined by solving a set of discontinuity equations. The Cohesive Zone Method (CZM), which is able to model crack initiation and growth by considering process zone effects, is implemented at the crack tip to enable the modeling of fracture propagation in both brittle and ductile formations. The method represents a useful step towards the prediction of non-planar, complex hydraulic fractures and can provide us a better guidance of design wells and hydraulic fractures that will better drain reservoir volume in formation with complex stress conditions and heterogeneous properties.

Shear-Type Borehole Wall Shifts Induced During Lost Circulations

Summary Borehole wall shifts during lost circulations are studied and parameter studies are conducted for evaluating the magnitude of the shifts under the following typical drilling conditions. slant-crack induced around vertical wells during lost circulations borehole wall shifts induced during the drilling of normal, thrust, and strike-slip fault areas borehole wall shifts induced for an inclined well because of a fracture induced perpendicular to the minimum in-situ stress Parameters varied are the frac size/wellbore size, frac angle, borehole pressure, and σh1,σH2,σv ratio. These analyses are significant for the following reasons: A new fracture model from a borehole is coded using a 3D-dual-boundary element method. This method allows different displacement and stress traction at the two fracture surfaces along a fracture plane around a borehole. Note that other boundary element methods for 3D nonplanar hydraulic fracture problems have been developed by another group, but these methods did not include a borehole (Yamamoto et al. 1999). Minor borehole wall shifts occur with small-scale fluid losses as observed with borehole imagers (Maury and Zurdo 1996). Although these minor shifts do not create drilling problems, the in-situ stresses may be evaluated from the borehole wall shift if the fractured area is identified by acoustic devices. The current model quantifies the relation between these shifts and other parameters (such as the geological properties and frac size and angle). Significant borehole wall shifts occur if a lost circulation is significant and the leakoff plane is inclined with respect to the principal in-situ stress direction. Some stuck pipe problems may be caused by shear type borehole wall shifts rather than by borehole breakouts or differential sticking problems.