Propagation Of Multiple Fractures Research Articles

Research on the Interaction Mechanism of Multi-Fracture Propagation in Hydraulic Fracturing

During the hydraulic-fracturing process, stress interference occurs among multiple wells and fractures, potentially affecting the trajectory of hydraulic fracture propagation. Previous studies have largely overlooked the influence of proppant support stresses on the trajectories of fracture propagation. This paper establishes a mathematical model, grounded in the boundary element method, designed to compute the propagation of multiple fractures, considering both proppant support on the fracture surface and dynamic perturbations within the local stress field. The findings of this research reveal that the stress field induced by hydraulic fracturing exhibits dynamic evolution characteristics, necessitating a comprehensive study of the fracture initiation and extension across the entire fracturing time domain. The effect of the residual fracture width under proppant action on the in situ stress field cannot be ignored. During simultaneous fracturing, hydraulic fractures are inclined to propagate in the direction of the maximum horizontal principal stress, particularly as the in situ differential stress escalates. Staggered fracturing between wells has been proven to be more effective than head-to-head fracturing. Simply increasing the well spacing cannot solve the problem of inter-well fracture interference. In zipper fracturing, adjusting the fracturing sequence can inhibit the fracture intersections between wells, thereby controlling the trajectory of fracture propagation. The aforementioned research has considerable significance in guiding the control of fracture morphology during hydraulic-fracturing processes.

Study on the Influence of Perforating Parameters on the Flow Rate and Stress Distribution of Multi-Fracture Competitive Propagation

It is of great significance to investigate the flow rate and stress distribution of multi-fracture propagation for the optimization of perforation parameters and fracture parameters. Considering the coupling of rock deformation, fracture direction and fluid flow in multi-fracture scenarios, a mathematical model and solution program for the flow and stress distribution of multiple fractures are established, and the analytical model is used for comparison and verification. The effects of perforation cluster number, cluster spacing, perforation diameter on fracture extension trajectory, fracture width, flow rate of each fracture and stress field are studied by the model. The results show that, as the number of perforating clusters increases, the inner fracture is inhibited more severely with less width, length and flow distribution, as well as lower bottom hole pressure. With the increase in cluster spacing, the stress interference between whole fractures is weakened and the flow distribution of the inner fracture is increased with lower bottom hole pressure. With the decrease in perforation diameter, the inhibition effect of inside fractures is weakened, while the inhibition effect of outside fractures, the flow distribution of inside fractures and the bottom hole pressure are increased. The uniform propagation of multiple fractures can be promoted by decreasing the perforation clusters’ number and perforation diameter or increasing fracture spacing.

Simulation and optimization of unstable dynamic propagation of multiple fractures in the shale formation

Multi-cluster hydraulic fracturing of horizontal wells is a well-adopted technique with high efficiency to increase the production of tight and shale formations. However, the stress shadows among clusters pose challenges to the synchronous propagation of hydraulic fractures during multi-cluster fracturing. In order to explore the fracture propagation mechanism and characteristics under the influence of stress shadow in low-spacing staged multi-cluster fracturing, a three-dimensional hydraulic fracturing model was generated using a lattice-based method. This model considered the impact of geological and engineering parameters on the propagation behavior of multiple fractures in shale formation. A variable pumping approach is adopted, where the fracturing fluid is initially injected at a high rate and then transitioned to a lower rate. Afterward, a method was proposed to quantitatively assess the extent of fracturing in a specific area (i.e., the stimulated area), considering the impact of stress shadow within a single stage. The simulation results demonstrated significant differences in the fracture stimulation area due to the influence of each parameter in the case of uncontrollable geological factors and controllable engineering factors. An increase in both Young’s modulus and stress anisotropy of the reservoir results led to a corresponding increase in the total fracture stimulation area. As the principal stress orientation increased, the fracture stimulation area gradually decreased. In terms of operational parameters, the stimulated area of hydraulic fractures gradually decreased as the fracture spacing increased. With increasing injection rate, the stimulated area initially expanded and then decreased, peaking at an injection rate of 0.04 m3/s. These findings can provide valuable insights into the propagation behavior of multi-cluster hydraulic fractures under uncertain parameters, with significant implications for future engineering applications.

Numerical simulation of the simultaneous propagation of multiple hydraulic fractures based on expanded finite element method

Hydraulic fracturing technology with horizontal wells is a highly efficient approach to stimulate the unconventional reservoir by creating lots of fractures to increase the oil and gas recovery rate. However, some field monitoring data indicate that multiple fractures could not propagate uniformly due to stress interference, which leads to a lower stimulation volume and production capacity. Therefore, investigating the stress interference mechanism between multiple fractures is important to obtain a higher production capacity for unconventional reservoirs. In this study, a two-dimensional XFEM (expanded finite element method) model was established to investigate the influence of stress interference on the fracture propagation of multiple fractures in horizontal wells. The different injection parameters, completion parameters, and fracturing patterns were investigated by sixteen simulation cases. The results show that first the influencing degree of stress interference from different parameters is fracture spacing, injection flow rate, number of fractures, and fluid viscosity, respectively. Second, compared to the simultaneous fracturing and sequential fracturing, the zip fracturing pattern (sides fractures created first and then mid-fracture) could create more uniform fractures in the reservoir. Third, a small fracture spacing and a higher injection flow rate could lead to a faster stress interference, but the fluid viscosity and the number of fractures have little effect on the occur timing of stress interference. This study could provide some meaningful perspective on the field fracturing design in horizontal wells.

Experimental study of hydraulic fracture propagation with multi-cluster in-plane perforations in a horizontal well

Tri-axial fracturing studies were carried out to understand the impact of lateral mechanical parameters on fracture propagation from multiple in-plane perforations in horizontal wells. Additionally, the discussion covered the effects of geology, treatment, and perforation characteristics on the non-planar propagation behavior. According to experimental findings, two parallel transverse fractures can be successfully initiated from in-plane perforation clusters in the horizontal well because of the in-plane perforation, the guide nonuniform fishbone structure fracture propagation still can be exhibited. The emergence of transverse fractures and axial fractures combined as complex fractures under low horizontal principal stress difference and large pump rate conditions. The injection pressure was also investigated, and the largest breakdown pressure can be also found for samples under these conditions. The increase in perforation number or decrease in the cluster spacing could provide more chances to increase the complexity of the target stimulated zone, thus affecting the pressure fluctuation. In a contrast, the increase in fracturing fluid viscosity can reduce the multiple fracture complexity. The fracture propagation is significantly affected by the change in the rock mechanical properties. The fracture geometry in the high brittle zone seems to be complicated and tends to induce fracture reorientation from the weak-brittle zone. The stress shadow effect can be used to explain the fracture attraction, branch, connection, and repulsion in the multiple perforation clusters for the horizontal well. The increase in the rock heterogeneity can enhance the stress shadow effect, resulting in more complex fracture geometry. In addition, the variable density perforation and temporary plugging fracturing were also conducted, demonstrating higher likelihood for non-uniform multiple fracture propagation. Thus, to increase the perforation efficiency along the horizontal well, it is necessary to consider the lateral fracability of the horizontal well on target formation.

Numerical study of multiple hydraulic fractures propagation in poroelastic media based on energy decomposition phase field methods

This paper proposes a novel phase-filed model for simulating hydraulic fracturing in poroelastic media under complex stress conditions. The main theoretical contribution lies in the fact that a generalized strain energy density decomposition is incorporated to hydraulic fracturing phase field model, which unifies hydrostatic-deviatoric and spectral decompositions and predicts material failure through classical Mohr-Coulomb failure criterion. Based on Biot’s poroelastic theory, an indicator function is used to distinguish between fluid flow in fractures and in pores. The fully coupled equations are solved by combining staggered schemes with Newton-Raphson methods. The proposed model is validated by comparing laboratory experimental results with numerical results. In order to demonstrate the influence of introducing hydrostatic-deviatoric and spectral energy decompositions, we simulated propagation of multiple hydraulic fractures and coalescence of hydraulic fractures with natural fractures. Finally, the effects of stress ratios (σx/σy) on multiple hydraulic fractures are analysed. It is found that when the stress ratio is 2, a more complex hydraulic fracture network is formed in the porous media.

Numerical Simulation of the Simultaneous Development of Multiple Fractures in Horizontal Wells Based on the Extended Finite Element Method

Simultaneous multiple-fracture treatments in horizontal wellbores have become an essential technology for the economic development of shale gas reservoirs. During hydraulic fracturing, fracture initiation and propagation always induce additional stresses on the surrounding rock. When multiple fractures develop simultaneously, the development of some fractures is limited due to the stress-shadow effect. An in-depth understanding of the multiple-fracture propagation mechanism as reflected by fracture morphology and flow rate distribution can help to set reasonable operation parameters for improving the uniformity of multiple fractures and forming a complex fracture network according to the different in situ stress conditions in a reservoir to increase the shale gas recovery and reduce the cost. In this study, a two-dimensional (2D) fracture propagation model was developed based on the extended finite element method (XFEM). Then, the influences of various factors, including geological and operational factors, on the development of multiple fractures were studied. The results of numerical simulations showed that increasing the cluster spacing or injecting fracturing fluid with lower viscosity can help reduce the stress-shadow effect. In the case of smaller in situ stress differences, the deflection of the fractures was larger due to the stress-shadow effect. As the stress difference increased, the direction of the propagation of the fracture was gradually biased towards the direction of maximum horizontal stress. In addition, the injection rate had some effects on the fracture morphology and flow rate distribution. However, as the injection rate increased, the dominant fracture developed rapidly, and the fracture length significantly increased.

Promoting the uniform propagation of multi-fracture through adjusting the injection rate and perforation parameter: A numerical study

The strong stress interference and fluid competitive distribution result in the non-uniform propagation of multiple fractures during horizontal well multi-stage hydraulic fracturing (HWMHF). The uniform stimulation effect can be effectively improved by adjusting the injection rate and perforation scheme. In this work, a two-dimensional fluid–solid fully coupled multi-fracture propagation model is established to investigate the pattern of multi-fracture propagation and the flow distribution. The considering factors include the fluid injection rate, the perforation parameters, and the reservoir heterogeneity. The pipe element is developed to realize the free fluid distribution among multiple fractures. The results show that multiple fractures are more likely to initiate simultaneously and propagate uniformly with a higher fluid injection rate. The stress interference among multiple fractures can be balanced and the equilibrium propagation degree of multiple fractures can be greatly improved by reducing the perforation number. In the homogeneous reservoir, when the fluid injection rate is 12 m3/min and the perforation number per cluster is reduced to 10, the difference coefficient of fluid distribution can be reduced to 3.31%. In the heterogeneous reservoir, multiple perforation clusters with different tensile strengths can generate nearly uniform fractures by increasing the fluid injection rate and reducing the perforation number. When the fluid injection rate is 12 m3/min and the perforation number per cluster is 6, the difference coefficient of fluid distribution can be reduced to 3.26%. This work is of great significance in clarifying the propagation pattern and optimizing the fluid injection rate and the perforation number to improve the uniform propagation degree of multiple fractures.

The intelligent optimization of perforation cluster locations incorporating the fiber optics monitoring results

During horizontal well multi-stage fracturing (HWMF), superfractures are often identified. To promote the uniform propagation of multiple fractures, it is necessary to finely optimize the perforation cluster locations based on the geological and engineering parameters. This work proposes an efficient method to design the perforation cluster locations in consideration of the geoengineering sweet spots with similar mechanical properties. Well log data and the precise fiber optics (FO) monitoring results are combined to find the main influencing factors. The principal component is conducted by introducing correlation analysis and Random Forest. Moreover, the K-means++ clustering method is used to evaluate reservoir quality. The fracturing sweet index (FSI) is proposed to measure the fracturing performance of each category quantitatively. The proposed workflow is effectively validated by two production scenarios. Moreover, the workflow can automatically evaluate reservoir quality based on intelligent clustering methods. Compared with the original design, the updated design lowers the gap among multiple fractures within one stage and increases the well production by 20%–50%. This work is beneficial for the on-site treatment of its feasibility and generalizability.

Investigation into the Perforation Optimization in Conglomerate Reservoir Based on a Field Test

The Mahu conglomerate reservoir is characterized by strong heterogeneity and the uneven stimulation of the horizontal lateral during hydraulic fracturing. The optimization of the perforation number per cluster is of great value for horizontal well multi-stage fracturing (HWMF) because the suitable perforation number not only promotes the uniform propagation of multiple fractures but also prevents excessive perforation erosion. In this work, a typical well in the Mahu conglomerate reservoir was selected, and a field test of optimizing the perforation number was carried out. The perforation schemes of three, five, and eight perforations per cluster were designed in nine fracturing stages, respectively. The wellhead pressure under different perforation schemes was compared and analyzed with the step-down flow rate test, and the optimal perforation number per cluster in the Mahu conglomerate reservoir was selected as eight. The theoretical calculation results show that eight perforations per cluster can generate the perforation friction of 5 MPa, sufficient to overcome the mechanical property differences among multiple clusters within one stage. The downhole video technology shows that the perforation erosion area is the most uniform with the case of eight perforations per cluster. Moreover, the optical fiber monitoring results show that the perforation number of eight per cluster can realize the simultaneous initiation and uniform propagation of six fractures or five fractures within one stage. This work is of great significance for the efficient development of the Mahu conglomerate reservoir through HWMF.

Induced hydraulic fractures in underground block caving mines using an extended finite element method

Block caving has become an attractive underground rock mining method that requires effective preconditioning of the orebody to initiate the progressive rock collapse by its weight. Hydraulic fracturing is commonly used in cave mining as a preconditioning method to induce artificial fractures in the orebody rock mass. This paper presents the numerical model of hydraulic fracture propagation in underground caving mines. An extended finite element method based on phantom nodes is adopted to simulate the propagation of multiple fractures along arbitrary paths. A poroelastic constitutive model governs the behavior of orebody rock mass, while a cohesive zone model controls the hydraulic fracture propagation. The adopted method is validated against analytical solutions for penny-shaped hydraulic fracture. The stress shadowing effect on hydraulic fracturing is investigated using representative rock properties from the “El Teniente mine”, obtained by calibrating a hydraulic fracturing field test. Several analyses of multiple hydraulic fractures considering a sequential fracturing scheme are simulated to investigate the influence of in-situ stresses, fracture spacing, injection flow rate, and Young's modulus and permeability of the matrix. The numerical results show that small fracture spacing, in-situ stress, and rock permeability locally change the principal stress magnitude, resulting in a more extensive fracture propagation. Also, the injection of new fractures induces stress shadows that reinitiate the propagation of the previous ones. This behavior is reduced by increasing the fracture spacing and rock permeability. Finally, this paper provides insights into the main parameters that affect fracture extension, which can be used to optimize the preconditioning process of underground block caving mines.

Stress interference and interaction between two fractures during their propagation: insights from SCDA test and XFEM simulation

Understanding and predicting the propagation and disturbance of multiple fractures is the key to the successful implementation of hydraulic fracturing. In this study, the two-hole fracturing tests are carried out on granite samples by using soundless cracking demolition agent (SCDA). Combined with the extended finite element method (XFEM) simulation and the induced stress analysis, the interaction and stress interference during the propagation of two fractures are systematically investigated. The relative position of two holes determines whether attraction or repulsion effect occurs between adjacent fractures, the pattern of which can be classified into three modes: the fracture collinear, staggered propagation and parallel propagation. The fractures in collinear pattern are prone to coalescence, the staggered fractures are easy to attract each other and the parallel fractures tend to propagate independently, which ultimately lead to the formation of single, spiral and multiple main fractures, respectively. The stress near the fracture tip controls the possibility and direction of fracture propagation. The superposition of tensile stress is prone to promote fracture propagation, and the stress interference tends to make fractures deflection and mutual exclusion. The fracturing results are quantitatively evaluated by using fractal dimension and fracture surface characteristics. It is found that increasing perforation spacing makes the degree of internal rupture of the sample increase first and then decrease, and the fracturing scheme is optimal when the perforations are arranged perpendicular to the direction of maximum horizontal principal stress.

Numerical simulation of proppant migration in horizontal wells with multi-fracture fracturing

For horizontal wells fracturing in unconventional reservoirs, the fracture morphology and proppant migration are severely affected by the interfering effects among multiple fractures propagation. Current numerical simulation for proppant migration did not reveal the interrelation among flow distribution, fracture length and sandbank shape during multiple fractures propagation. In this study, a proppant migration model is proposed by combining the displacement discontinuity method (DDM) and the Eulerian-Lagrangian method (E-L M), which implement dynamic multiple fractures propagation simulation as well as the changing state of flow distribution for each fracture. The accuracy of the numerical model is verified by laboratory experiments. The sensitivity parameters of proppant settlement are analyzed, and two dimensionless parameters, height ratio γ and area ratio η are proposed for proppant migration evaluation. The results show that with a lower fracturing fluid flow rate, fluid viscosity, the height ratio γ is lower, and the area ratio η is higher, which also results in the proppant being more likely to accumulate at the fracture entrance. As the proppant particle size increases from 100 μm to 500 μm, the dimensionless height ratio γ and the dimensionless area ratio η decrease significantly. Increase in fracture spacing during horizontal well multi-cluster fracturing results in a limited improvement for proppant settlement. Formation elastic modulus has an appreciable impact on proppant migration in multi-fracture propagation, high elastic modulus formation leads to an ununiform proppant placement over long distances.

Formulation optimization of materials used in temporary plugging diversion between fracture front end and cluster in shale gas: From laboratory research to field application

The staged and multi-cluster fracturing of horizontal wells is the main fracturing technology used for shale gas reservoir development. Temporary plugging diversion (TPD) is an important technical means to realize a uniform propagation of hydraulic fractures and avoid problems such as frac hits (i.e., well-to-well interference). Although this technology has been extensively used worldwide, field monitoring results have shown that temporary plugging cannot effectively improve the nonuniform propagation of multiple fractures. The fundamental reason is the lack of an organic combination of laboratory research and field application. To solve this problem, this study investigated the reservoir adaptability and plugging performance of three types of temporary plugging agent (TPAs), namely, powder, particle, and fiber, used in the fracturing of wells in the Weiyuan (WY) shale gas field, Sichuan, China, using a pressure-bearing capacity test device for three dimensional (3D)-printing-simulated TPA. A calculation method for the plugging efficiency of the TPA was established, and the ratio and concentration of the TPA were optimized under different fracture widths. The similarity criterion was used to calculate the amount of TPA required for different fracture widths. A field application chart of the TPA was formulated, and a method that connects laboratory research and field application was established. The results showed that the three TPAs have good reservoir adaptability and degradation performance. It is recommended to use 200–400 mesh powder + 6 mm fiber with different concentrations and dosages when performing temporary plugging and fracturing at the front end of 1–3 mm fractures. In the case of inter-cluster TPD for a fracture width of 4–6 mm, a combination of 20 mesh powder + 6 mm fiber + 1–3 mm particles is recommended. The field application results showed that the pressure increased significantly at the front end of the fractures and during inter-cluster temporary plugging when the plugging agent was in place, and there were no frac hits in the adjacent wells. This paper provides a practical research method for hydraulic fracturing involving temporary plugging, from laboratory research to engineering application.

Numerical Study on Simultaneous Propagation of Multiple Fractures: A Method to Design Nonuniform Perforation and In-Stage Diversion

Summary The uneven propagation of multifractures is a key factor restricting production growth due to stress shadow and heterogeneity. To date, limited-entry fracturing techniques, nonuniform perforation, and in-stage diversion have been commonly used to promote even multifracture growth. In this study, a fully coupled multiple pseudo-3D (P3D) fracture simulator has been developed to examine the competitive propagation of multifractures during multicluster fracturing in a horizontal well. The present model considers stress interaction among multiple fractures, perforation erosion, fluid distribution among clusters, and in-stage diversion. The results of the model are validated against the reference data. Using the model, a series of numerical simulations are performed to investigate multifracture propagation with nonuniform perforation and in-stage diversion fracturing. We estimate the value of stress interaction for different fractures and time based on the approximate solution of Perkins-Kern-Nordgren (PKN) fracture in the viscosity-dominated regime and improve the dimensionless parameter that characterizes the competition between stress interaction and perforation friction. The fluid distributes evenly when the dimensionless parameter is less than unity (perforation friction is larger than stress interference). Based on this dimensionless parameter, a method to design nonuniform perforation and in-stage diversion is proposed. Results show that in the case of homogeneous in-stage stress, the perforation parameters should be selected under the condition that the dimensionless parameter is less than unity. In the case of heterogeneous in-stage stress and based on the perforation parameters selected under homogeneous stress conditions, the perforation holes in the high-stress cluster should be increased, making the reduction of perforation friction equal to the value of the in-stage stress heterogeneity. The stress heterogeneity can be balanced by decreasing the perforation friction of the high-stress clusters. In this way, nonuniform perforation under heterogeneous in-stage stress conditions can be designed quantitatively without numerical simulation. For in-stage diversion treatment, a method to design the number of ball sealers is proposed based on the results of nonuniform perforation, and only several or even zero groups of simulation are necessary to find the optimal number of ball sealers. A series of numerical simulations shows that the proposed design method is reliable and achieves a satisfactory result in an actual field case. The results can be helpful for nonuniform perforation and in-stage diversion design for multicluster fracturing in a horizontal well.

A hydro‐mechanically‐coupled XFEM model for the injection‐induced evolution of multiple fractures

AbstractIn this paper, a two‐dimensional eXtended Finite Element Method (XFEM) solution is presented for the hydro‐mechanically coupled hydro‐frac‐induced propagation of multiple fractures in rocks. Fractures are considered one‐dimensional objects, and the rock matrix is regarded as a two‐dimensional medium. Rules for improving the accuracy of the solution are included to deal with the transfer of variables between fractures and matrix in the coupling process. The main variables include fluid pressure and fracture aperture. The following assumptions are made: (1) the fluid pressure inside a fracture is applied as a net pressure; (2) fluid leak‐off is ignored; (3) the fluid front is regarded as a fracture front provided that the area of fluid lag has a small effect on fracture propagation compared to the area at which the fluid pressure is applied. The fluid flow is governed by the lubrication equation, while the XFEM is used to describe the behaviour of the elastic medium. The simulation results are compared with analytical solutions for a single hydraulic fracture model to verify and validate the proposed algorithm. A simulation with multiple hydraulic fractures is also performed to investigate the interference effect of multiple fractures and fracture propagation. The shadow effect caused by multiple fractures is analysed to manifest the stress variation along the propagation path.

Adaptive multiscale extended finite element method (MS-XFEM) for the simulation of multiple fractures propagation in geological formations

In fractured geological formations, as a result of the in-situ stress changes, fractures can propagate or slide. This phenomenon can be efficiently modeled by the extended finite element method (XFEM) when there are only a few fractures present. However, geological reservoirs contain many fractures which can also cross and are densely populated. Therefore, the classical XFEM is too expensive to be applied for the simulation of propagating fractures in geological formations. To reduce the costs, typically, homogenization or upscaling is used. However, they result in inaccurate solutions, since no separation of scales exists in this process. To resolve this challenge, in this work, a multiscale XFEM (MS-XFEM) for propagating fractures is developed and presented. In each time step, given the current geometries of the fractures, local XFEM-based basis functions are constructed or adaptively updated. The adaptive update takes place in certain regions where fracture geometries are changed due to propagation. Using these basis functions, a very efficient FEM-based coarse-scale system is developed since it has no extra degrees of freedom (DOFs). Once the coarse-scale system is solved, its solution is prolonged to the fine-scale original resolution using the basis functions. This approximate fine-scale solution is then used to estimate the group of growing fractures tips and their growing angles. This allows for exploiting the locality of the propagation process fully while solving a global system. To control the error, an iterative procedure is also developed. Proof-of-concept test cases are presented to study the developed MS-XFEM algorithm. It is shown that MS-XFEM results are capable of predicting the propagating paths for complicated fracture patterns. As such, MS-XFEM casts a promising method for field-scale applications.

Phase Field Modeling of Multiple Fracture Growth in Natural Fractured Reservoirs

In recent years, hydraulic fracturing techniques have been widely used in extracting unconventional reservoir resources. During multicluster fracturing process, the stress shadowing effect can lead to a nonuniform distribution of fracturing fluid. In this paper, a two-dimensional multiple fracture propagation model is developed based on phase field method considering the distribution of fracturing fluid within each fracture during fracturing process. The distribution of fracturing fluid injected into each fracture is calculated through solving governing equations of perforation friction as well as wellbore friction. Numerical results demonstrate that the natural fractures in the reservoir have a significant influence on the distribution of injected fluid and the morphology of fracture network. In addition, higher injection rates and higher fluid viscosity stimulations are in favor of inducing uniform distribution of injected fluid into each cluster. The presented numerical model provides an effective tool to extend our understandings in generating fracture networks.

Modeling method for rock heterogeneities and multiple hydraulic fractures propagation based on homogenization approach and PHF-LSM

Hydraulic fracturing is an important technique to enhance the production rate of oil and gas. We extend the functions of Permeability-based Hydraulic Fracture, Level Set Method (PHF-LSM) by including homogenization approaches to take into account the influence of the heterogeneities of rock media at both mesoscale and macroscale during hydraulic fracture propagation. The center position pattern of mesoscale heterogeneities is generated by introducing the Fast Poisson Disk (FPD) approach with an inherent parameter controlling the randomly distributed inclusions, and we developed an algorithm to detect inclusion collision by binary image matrix calculation. The level set function is used to describe the distributed joints at the macroscale. Both numerical and theoretical homogenization approaches are applied to study the characteristics of the material properties of rock matrices with randomly distributed hard inclusions at the mesoscale. Based on these results, we adopt the Mori–Tanaka (MT) and the Halpin–Tsai (HT) methods to homogenize the elasticity parameters (elastic modulus and Poisson’s ratio) and the hydraulic conductivity of the rock material, respectively. The Voigt upper bound is applied to estimate the tensile strength of the rock material at the integration points. A series of numerical simulations first indicated that the proposed method can model multi-scale heterogeneous rock that contains both the influences of macro-heterogeneities, e.g., distributed joints, and meso-heterogeneities, e.g., randomly distributed inclusions. Second, the development of pore pressure and stress path varied at the injection point, on the fracture path and on a joint. Finally, both the macro- and meso- heterogeneities influenced the propagation of multiple hydraulic fractures with joints significantly influenced the propagation path of the fractures, and increased injection number Np enhanced the height of the equivalent fracture zone when Np<5.

Investigating the simultaneous fracture propagation from multiple perforation clusters in horizontal wells using 3D block discrete element method

Multi-cluster horizontal well fracturing is one of the key technologies to develop the unconventional reservoirs such as shales. However, the field data shows that some perforation clusters have little production contribution. In this study, a three-dimensional (3D) numerical model for simulating the multiple fracture propagation based on 3D block discrete element method was established, and this model considers the stress interference, perforation friction and fluid-mechanical coupling effect. In order to determine the most appropriate measures to improve the uniformity of multiple fracture propagation, the effect of the geologic and engineering parameters on the multiple fracture propagation in shale reservoirs is investigated. The modeling results show that the geometry of each fracture within a stage is different, and the outer fractures generally receive more fracturing fluid than the interior fractures. The vertical stress almost has no effect on the geometries of multiple fractures. However, higher horizontal stress difference, larger cluster spacing, smaller perforation number, higher injection rate, and smaller fracturing fluid viscosity are conducive to promote the uniform propagation of multiple fractures. The existence of bedding planes will increase the fluid filtration, resulting in a reduction in fracture length. The middle two fractures receive less fluid and the width of them is smaller. Through analyzing the numerical results, a large amount of fracturing fluid should be injected and the proppant with smaller size is suggested to be used to effectively prop the bedding planes. Cluster spacing and perforation number should be controlled in an appropriate range according to reservoir properties. Increasing the injection rate and reducing the viscosity of fracturing fluid are important means to improve the geometry of each fracture.