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Optimized three-dimensional (3D) fracture networks are crucial for multistage hydrofracturing. To better understand the mechanisms controlling potential disasters as well as to predict them in 3D multistage hydrofracturing, some governing factors, such as fluid injection-induced stratal movement, compression between multiple hydraulic fractures, fracturing fluid flow, fracturing-induced microseismic damaged and contact slip events, must be properly simulated via numerical models. This study aims to analyze the stratal movement and microseismic behaviours induced by multistage propagation of 3D multiple hydraulic fractures.

Adaptive finite element–discrete element method was used to overcome the limitations of conventional finite element methods in simulating 3D fracture propagation. This new approach uses a local remeshing and coarsening strategy to ensure the accuracy of solutions, reliability of fracture propagation path and computational efficiency. Engineering-scale numerical models were proposed that account for the hydro-mechanical coupling and fracturing fluid leak-off, to simulate multistage propagation of 3D multiple hydraulic fractures, by which the evolution of the displacement, porosity and fracture fields, as well as the fracturing-induced microseismic events were computed.

Stratal movement and compression between 3D multiple hydraulic fractures intensify with increasing proximity to the propagating fractures. When the perforation cluster spaces are very narrow, alternate fracturing can improve fracturing effects over those achieved via sequential or simultaneous fracturing. Furthermore, the number and magnitude of microseismic events are directly proportional to the stratal movement and compression induced by multistage propagation of fracturing fracture networks.

Microseismic events induced by multistage propagation of 3D multiple hydraulic fractures and perforation cluster spaces and fracturing scenarios that impact the deformation and compression among fractures in porous rock matrices are well predicted and analyzed.

The unstable dynamic propagation of multistage hydrofracturing fractures leads to uneven development of the fracture network and research on the mechanism controlling this phenomenon indicates that the stress shadow effects around the fractures are the main mechanism causing this behaviour. Further studies and simulations of the stress shadow effects are necessary to understand the controlling mechanism and evaluate the fracturing effect.

In the process of stress-dependent unstable dynamic propagation of fractures, there are both continuous stress fields and discontinuous fractures; therefore, in order to study the stress-dependent unstable dynamic propagation of multistage fracture networks, a series of continuum-discontinuum numerical methods and models are reviewed, including the well-developed extended finite element method, displacement discontinuity method, boundary element method and finite element-discrete element method.

The superposition of the surrounding stress field during fracture propagation causes different degrees of stress shadow effects between fractures and the main controlling factors of stress shadow effects are fracture initiation sequence, perforation cluster spacing and well spacing. The perforation cluster spacing varies with the initiation sequence, resulting in different stress shadow effects between fractures; for example, the smaller the perforation cluster spacing and well spacing are, the stronger the stress shadow effects are and the more seriously the fracture propagation inhibition arises. Moreover, as the spacing of perforation clusters and well spacing increases, the stress shadow effects decrease and the fracture propagation follows an almost straight pattern. In addition, the computed results of the dynamic distribution of stress-dependent unstable dynamic propagation of fractures under different stress fields are summarised.

A state-of-art review of stress shadow effects and continuum-discontinuum methods for stress-dependent unstable dynamic propagation of multiple hydraulic fractures are well summarized and analysed. This paper can provide a reference for those engaged in the research of unstable dynamic propagation of multiple hydraulic structures and have a comprehensive grasp of the research in this field.

The purpose of this study is to investigate the unstable propagation of parallel hydraulic fractures induced by interferences of adjacent perforation clusters and thermal diffusion. Fracture propagation in the process of multistage fracturing of a rock mass is deflected owing to various factors. Hydrofracturing of rock masses in deep tight reservoirs involves thermal diffusion, fluid flow and deformation of rock between the rock matrix and fluid in pores and fractures.

To study the unstable propagation behaviours of three-dimensional (3D) parallel hydraulic fractures induced by the interferences of adjacent perforation clusters and thermal diffusion, a 3D engineering-scale numerical model is established under different fracturing scenarios (sequential, simultaneous and alternate fracturing) and different perforation cluster spacings while considering the thermal-hydro-mechanical coupling effect. Stress disturbance region caused by fracture propagation in a deep tight rock mass is superimposed and overlaid with multiple fractures, resulting in a stress shadow effect and fracture deflection.

The results show that the size of the stress shadow areas and the interaction between fractures increase with decreasing multiple perforation cluster spacing in horizontal wells. Alternate fracturing can produce more fracture areas and improve the fracturing effect compared with those of sequential and simultaneous fracturing. The larger the temperature gradient between the fracturing fluid and rock matrix, the stronger the thermal diffusion effect, and the effect of thermal diffusion on the fracture propagation is significant.

This study focuses on the behaviours of the unstable dynamic propagation of 3D parallel hydraulic fractures induced by the interferences of adjacent perforation clusters and thermal diffusion. Further, the temperature field affects the fracture deflection requires could be investigated from the mechanisms; this paper is to study the unstable propagation of fractures in single horizontal well, which can provide a basis for fracture propagation and stress field disturbance in multiple horizontal wells.

This research study aims to develop regular cylindrical pore network models (RCPNMs) to calculate topology and geometry properties of explosively created fractures along with their resulting hydraulic permeability. The focus of the investigation is to define a method that generates a valid geometric and topologic representation from a computational modelling point of view for explosion-generated fractures in rocks. In particular, extraction of geometries from experimentally validated Eulerian smoothed particle hydrodynamics (ESPH) approach, to avoid restrictions for image-based computational methods.

Three-dimensional stabilized ESPH solution is required to model explosively created fracture networks, and the accuracy of developed ESPH is qualitatively and quantitatively examined against experimental observations for both peak detonation pressures and crack density estimations. SPH simulation domain is segmented to void and solid spaces using a graphical user interface, and the void space of blasted rocks is represented by a regular lattice of spherical pores connected by cylindrical throats. Results produced by the RCPNMs are compared to three pore network extraction algorithms. Thereby, once the accuracy of RCPNMs is confirmed, the absolute permeability of fracture networks is calculated.

The results obtained with RCPNMs method were compared with three pore network extraction algorithms and computational fluid dynamics method, achieving a more computational efficiency regarding to CPU cost and a better geometry and topology relationship identification, in all the cases studied. Furthermore, a reliable topology data that does not have image-based pore network limitations, and the effect of topological disorder on the computed absolute permeability is minor. However, further research is necessary to improve the interpretation of real pore systems for explosively created fracture networks.

Although only laboratory cylindrical rock specimens were tested in the computational examples, the developed approaches are applicable for field scale and complex pore network grids with arbitrary shapes.

It is often desirable to develop an integrated computational method for hydraulic conductivity of explosively created fracture networks which segmentation of fracture networks is not restricted to X-ray images, particularly when topologic and geometric modellings are the crucial parts. This research study provides insight to the reliable computational methods and pore network extraction algorithm selection processes, as well as defining a practical framework for generating reliable topological and geometrical data in a Eulerian SPH setting.

The purpose of this paper is to systematically investigate the fluid lag phenomena and its influence in the hydraulic fracturing process, including all stages of fluid-lag evolution, the transition between different stages and their coupling with dynamic fracture propagation under common conditions.

A plane 2D model is developed to simulate the complex evolution of fluid lag during the propagation of a hydraulic fracture driven by an impressible Newtonian fluid. Based on the finite element method, a fully implicit solution scheme is proposed to solve the strongly coupled rock deformation, fluid flow and fracture propagation. Using the proposed model, comprehensive parametric studies are performed to examine the evolution of fluid lag in various geological and operational conditions.

The numerical simulations predict that the lag ratio is around 5% or even lower at the beginning stage of hydraulic fracture under practical geological conditions. With the fracture propagation, the lag ratio keeps decreasing and can be ignored in the late stage of hydraulic fracturing for typical parameter combinations. On the numerical aspect, whether the fluid lag can be ignored depends not only on the lag ratio but also on the minimum mesh size used for fluid flow. In addition, an overall mixed-mode fracture propagation factor is proposed to describe the relationship between diverse parameters and fracture curvature.

In this study, relatively simple physical models such as linear elasticity for solid, Newtonian model for fluid and linear elasticity fracture mechanics for fracture are used. The current model does not account for such effects like leak off, poroelasticity and softening of rock formations, which may also visibly affect the fluid lag depending on specific reservoir conditions.

This study helps to understand the effect of fluid lag during hydraulic fracturing processes and provides numerical experience in dealing with the fluid lag with finite element simulation.

Multi-well hydrofracturing is an important technology to create new fractures and expand existing fractures to increase reservoir permeability. The propagation morphology of the fracture network is affected by the disturbance between the fractures initiation sequences and spacings between adjacent wells. However, it remains unclear how well spacing and initiation sequences lead to fracture propagation, deflection and connection.

In this study, the thermal-hydro-mechanical coupling effect in the hydrofracturing process was considered, to establish a finite element-discrete element model of multistage hydrofracturing in a horizontal well. Using typical cases, the unstable propagation of hydraulic fractures in multiple horizontal wells was investigated under varying well spacing and initiation sequences. Combined with the shear stress shadow caused by in situ stress disturbed by fracture tip propagation, the quantitative indexes of fracture propagation such as length, volume, displacement vector, deflection and unstable propagation behavior of the hydrofracturing fracture network were analyzed.

The results show that the shear stress disturbance caused by multiple hydraulic fractures is a significant factor in multi-well hydrofracturing. Reducing the spacing between multiple wells increases the stress shadow area and aggravates the mutual disturbance and deflection between the fractures. The quantitative analysis results show that a decrease of well spacing reduces the total length of hydraulic fractures but increases the total volume of the fracture; compared with sequential and simultaneous fracturing, alternate fracturing can effectively reduce stress shadow area, alleviate fracture disturbance and generate larger fracture propagation length and volume.

The numerical models and results of the unstable propagation and stress evolution of the hydraulic fracture network under thermal-hydro-mechanical coupling obtained in this study can provide useful guidance for the evaluation and design of rock mass fracture networks in deep unconventional oil and gas reservoirs.

The interaction between hydraulic fracture (HF) and natural fracture (NF) in naturally fractured rocks is critical for hydraulic fracturing. This paper aims to focus on investigating the development of tensile and shear debonding zone on the NF caused by the stresses produced by HF, and the influence of NF’s debonding behavior on the interaction between HF and NF.

Theoretically, tensile and shear debonding modes of NF are considered, two dimensionless parameters are proposed to characterize the difficulty of tensile and shear failure of NF, respectively. Numerically, a finite element model combining the extended finite element method and cohesive zone method (CZM) is proposed to study NF’s debonding behavior and its influence on the interaction between HF and NF.

Both theoretical analysis and numerical simulation show the existence of two debonding modes. The numerical results also show that the HF can cross, offset or propagate along the NFs depending on the parameters’ value, resulting in different fracture network and stimulated reservoir volume. When they are large, the NF’s debonding area is small, HF tends to cross the NF and the fracture network is simple; when they are small, the NF’s debonding area is large, HF will propagate along the NF. In addition, HF is easier to propagate along with NF under tensile debonding mode while it is easier to pass through NF under shear debonding mode.

The theoretical and numerical considerations are taken into account in the influence of the debonding of NFs on the interaction between HFs and NFs and the influence on the formation of the fracture network.

This paper aims to employ a multivariate nonlinear regression analysis to establish a predictive model for the final fracture area, while accounting for the impact of individual parameters.

This analysis is based on the numerical simulation data obtained, using the hybrid finite element–discrete element (FE–DE) method. The forecasting model was compared with the numerical results and the accuracy of the model was evaluated by the root mean square (RMS) and the RMS error, the mean absolute error and the mean absolute percentage error.

The multivariate nonlinear regression model can accurately predict the nonlinear relationships between injection rate, leakoff coefficient, elastic modulus, permeability, Poisson’s ratio, pore pressure and final fracture area. The regression equations obtained from the Newton iteration of the least squares method are strong in terms of the fit to the six sensitive parameters, and the model follow essentially the same trend with the numerical simulation data, with no systematic divergence detected. Least absolutely deviation has a significantly weaker performance than the least squares method. The percentage contribution of sensitive parameters to the final fracture area is available from the simulation results and forecast model. Injection rate, leakoff coefficient, permeability, elastic modulus, pore pressure and Poisson’s ratio contribute 43.4%, −19.4%, 24.8%, −19.2%, −21.3% and 10.1% to the final fracture area, respectively, as they increased gradually. In summary, (1) the fluid injection rate has the greatest influence on the final fracture area. (2)The multivariate nonlinear regression equation was optimally obtained after 59 iterations of the least squares-based Newton method and 27 derivative evaluations, with a decidability coefficient R2 = 0.711 representing the model reliability and the regression equations fit the four parameters of leakoff coefficient, permeability, elastic modulus and pore pressure very satisfactorily. The models follow essentially the identical trend with the numerical simulation data and there is no systematic divergence. The least absolute deviation has a significantly weaker fit than the least squares method. (3)The nonlinear forecasting model of physical parameters of hydraulic fracturing established in this paper can be applied as a standard for optimizing the fracturing strategy and predicting the fracturing efficiency in situ field and numerical simulation. Its effectiveness can be trained and optimized by experimental and simulation data, and taking into account more basic data and establishing regression equations, containing more fracturing parameters will be the further research interests.

The nonlinear forecasting model of physical parameters of hydraulic fracturing established in this paper can be applied as a standard for optimizing the fracturing strategy and predicting the fracturing efficiency in situ field and numerical simulation. Its effectiveness can be trained and optimized by experimental and simulation data, and taking into account more basic data and establishing regression equations, containing more fracturing parameters will be the further research interests.

This study aims to develop an efficient algorithm for generation of conforming mesh for seepage analysis through 3D discrete fracture networks (DFN).

The algorithm is developed based on a refined conforming Delaunay triangulation scheme, which is then validated using analytical solutions. The algorithm is well able to meet the challenge of meshing complex geometry of DFNs.

A series of sensitivity analysis have been performed to evaluate the effect of meshing parameters on steady state solution of Darcy flow using a finite element scheme. The results show that an optimized minimum internal angle of meshing elements should be predetermined to guarantee termination of the algorithm.

The developed algorithm is computationally efficient, fast and is of low cost. Furthermore, it never changes the geometrical structure and connectivity pattern of the DFN.

With the development of fracturing technology, the research of multi-well hydrofracturing becomes the key issue. Frac-hits in multi-well hydrofracturing has an important effect on fracture propagation and final production of fractured well; in the process of hydrofracturing, there are many implement parameters that can affect frac-hits, and previous studies in this area have not systematically targeted the influence of a single parameter on multi-well hydrofracturing. Therefore, it is of great significance to study the occurrence rule and influence of frac-hits for optimizing the design of fracturing wells.

Based on the proposed numerical models, the effects of different fracturing implement parameters (perforation cluster spacing, well spacing and injection rate) on frac-hits are compared in numerical cases. Through the analysis of fracture network, stress field and microseismic, the effects of different fracturing implement parameters on frac-hits and connections are compared.

The simulation results show that the effect of perforation cluster spacing and well spacing on frac-hits is greater than that of injection rate. Smaller well spacing makes it easier for fractures between adjacent wells to interact with each other, which increases the risk of frac-hits and reduces the risk of fracture connections. Smaller perforation cluster spacing results in larger individual fracture lengths and greater deflection angles, which makes the possibility of frac-hits and connections greater. The lower the injection rate, the lower the probability of frac-hits.

In this study, the influence of different fracturing implement parameters on frac-hits and connections in multi-well hydrofracturing is studied, and the mechanism of frac-hits and connections is analyzed through fracture network, stress field and microseismic analysis. Different simulation results are compared to optimize fracturing well parameter design and provide reference for engineering application.