Flow-stress-damage Research Articles

Numerical Investigation of Hydraulic Fracture Propagation Morphology in the Conglomerate Reservoir

The random distribution of gravels makes the conglomerate reservoir highly heterogeneous. A stress concentration occurs at the gravel-matrix interfaces owing to the embedded gravel and affects the local mechanical response significantly, making it difficult to control and predict hydraulic fracture (HF) propagation. The mechanism of HF propagation in conglomerate reservoirs remains unclear; thus, it is difficult to effectively design and treat hydraulic fracturing. Based on the global pore-pressure cohesive zone element (GPPCZ) model method, a two-dimensional (2D) fracture propagation model with flow-stress-damage (FSD) coupling was established to investigate HF nucleation, propagation, and coalescence in conglomerate reservoirs. This model was experimentally verified, and fractal theory was introduced to quantify the complexity of fracture morphology. The microscale interactions of the gravel, matrix, and interface have been taken into consideration during simulating HF propagation accurately in macroscale. The influence of the mechanical properties of gravel, matrix, matrix-gravel interface, and reservoir stress distribution state, on HF morphology (HF length, stimulated reservoir square, and HF complexity morphology), was investigated. Finally, the main factors affecting fracture propagation were analyzed. It was revealed that the difference between the mechanical properties of the gravel and the matrix in the conglomerate rock will affect the geometry of HF to varying degrees. The local behavior of fracture propagation is obviously dominated by the elastic modulus, tensile strength, and the strength for the matrix-gravel interface. However, the propagation of HF at the whole scale is mainly dominated by the horizontal stress state, including the minimum horizontal stress and horizontal stress difference. In addition, the difference in horizontal stress significantly affects the fracturing patterns (deflection, bifurcation, and penetration) when HF encounters gravel. In this study, a simulation method of HF propagation in conglomerate reservoirs is introduced, and the results provide theoretical support for the prediction of HF propagation morphology and plan design of hydraulic fracturing in conglomerate reservoirs.

Numerical simulation and multi-factor optimization of hydraulic fracturing in deep naturally fractured sandstones based on response surface method

Hydraulic fracturing is an effective stimulation technology for enhancing recovery in deep reservoirs. Multi-factor analysis and fracturing design optimization are essential for the efficient development of deep naturally fractured sandstones. A three-dimensional flow-stress-damage (FSD) coupled model was presented to simulate the hydraulic fracture (HF) propagation and stimulated reservoir volume (SRV). The numerical model was validated with experimental results of the HF-natural fracture (NF) intersection. The sensitivity analysis is conducted to screen the significant factors affecting HF geometry and SRV. The response surface method was employed to investigate the coupling effects of multiple geomechanical and hydraulic factors on SRV by integrating Box-Behnken design and numerical modeling. Subsequently, the SRV was optimized by identifying the optimum combinations of uncertain parameters based on the established response surface model (RSM). The results indicated that the injection rate, NF density, fluid viscosity, and horizontal stress difference are the key factors controlling SRV. It is more difficult to improve SRV by increasing injection rate at higher horizontal stress difference than at lower horizontal stress difference. The proposed method is effective for enhancing the artificial ability to optimize the HF geometry and SRV. The results can provide insight into the fracture geometry control mechanism in deep naturally fractured sandstones, and offer a guideline for treatment design and optimization of well performance.

Study on the Rock Fracture during Fluid Injection Using a Coupled Flow‐Stress‐Damage (FSD) Model: Insight into the Stress Shadow Effect

In order to investigate the influence of pore pressure on hydraulic fracturing behavior in the local and whole model, the coupled flow‐stress‐damage (FSD) analysis system RFPA‐Flow was used to study the influence of rock heterogeneity, natural stress ratio, double‐hole spacing, and water pressure gradient on the stress shadow effect. The numerical results show that the tensile crack induced by pore water pressure is significantly affected by the pore water pressure and water pressure gradient. The larger the pore pressure gradient is, the more asymmetrical the crack development pattern and the smaller the instability pressure of the model. In addition, the shape of hydraulic fracture becomes much more irregular with the increase in rock heterogeneity. The number and shape of tip microcracks under the influence of local water pressure are closely related to the homogeneity of rock. Moreover, when the natural stress difference is large, the hydraulic fracture propagates parallel to the maximum principal stress; when the stress field is close and the spacing between two holes is less than 5 times the diameter, the propagation direction of hydraulic fractures between holes is perpendicular to the maximum principal stress. It is found that no hydraulic fractures occur between the two holes when the distance between holes is greater than 5 times the diameter.

Study on Propagation Behaviors of Hydraulic Fracture Network in Tight Sandstone Formation with Closed Cemented Natural Fractures

Natural fractures in tight sandstone formation play a significant role in fracture network generation during hydraulic fracturing. This work presents an experimental model of tight sandstone with closed cemented preexisting fractures. The influence of closed cemented fractures’ (CCF) directions on the propagation behavior of hydraulic fracture (HF) is studied based on the hydraulic fracturing experiment. A field-scaled numerical model used to simulate the propagation of HF is established based on the flow-stress-damage (FSD) coupled method. This model contains the discrete fracture network (DFN) generated by the Monte-Carlo method and is used to investigate the effects of CCFs’ distribution, CCFs’ strength, and in-situ stress anisotropy, injection rate, and fluid viscosity on the propagation behavior of fracture network. The results show that the distribution direction of CCFs is critical for the formation of complex HFs. When the angle between the horizontal maximum principal stress direction and the CCFs is in the range of 30° to 60°, the HF network is the most complex. There are many kinds of compound fracture propagation patterns, such as crossing, branching, and deflection. The increase of CCFs’ strength is not conducive to the generation of branched and deflected fractures. When the in-situ stress difference ranges from 3 MPa to 6 MPa, the HF network’s complexity and propagation range can be guaranteed simultaneously. The increase in the injection rate will promote the formation of the complex HF network. The proper increase of fracturing fluid viscosity can promote HF’s propagation. However, when the viscosity is too high, the complex HFs only appear around the wellbore. The research results can provide new insights for the hydraulic fracturing optimization design of naturally fractured tight sandstone formation.

Numerical Investigation to Influence of Perforation Angle on Hydraulic Fracturing Process

Considering the heterogeneous characteristics of rock in a meso-scale, a flow–stress–damage coupling model was created based on the finite element method firstly. Then the hydraulic fracturing process of the heterogeneity rockmass under different perforation angles were investigated by the RFPA2D-flow software. The numerical simulation results show that the maximum principle stress controls the fracture propagation direction no matter how perforation angle changes. With the increase of the perforation angle, a turning fracture becomes more obvious and the turning distance bigger. The best perforation angle area is from 0° to 30°. Above results are of some significance to hydraulic fracturing tests and engineering practice.

Influence of gravel on the propagation pattern of hydraulic fracture in the glutenite reservoir

The clear mechanism of hydraulic fracture propagation in glutenite reservoirs with high heterogeneity is still not obtained, thus it is difficult to carry out the design of fracturing plan effectively. Based on the characteristics of the glutenite reservoirs, a coupled flow-stress-damage (FSD) model of hydraulic fracture propagation with gravels is established. This model is experimentally verified and the research on the influence of rock physical parameters and gravel property on the hydraulic fracture propagation is conducted. It is shown that as the gravel tensile strength increases, the hydraulic fracture is prone to propagate around the gravel, where the fracture deflection always occurs; as the gravel Young's modulus increases, there is high probability that hydraulic fracture propagates around the gravel, with more obvious fracture deflection; the matrix permeability influences fracture propagating morphology when encountering gravel and total fracture length; the horizontal geostress difference seriously impacts the fracture deflection; as the fracturing fluids injection displacement increases, the fracture is prone to deflect when encountering gravel; the low viscosity fracturing fluids result in the shorter fracture; the larger gravel increases the possibility of fracture deflection; in case of smaller gravel sizes, the increasing gravel content has a big influence on fracture deflection, and the increasing content of large gravel complicates the fracture morphology, resulting in the fine branched fractures; for the well rounded gravel, the fracture propagation around the gravel is prone to occur, and the fracture is not prone to deflect. Compared with the conventional sandstone reservoir, the glutenite reservoirs have higher breakdown and extension pressures, which fluctuate due to the gravel; the larger gravel size results in higher extension pressure. In this paper, a simulation method of hydraulic fracture propagation in the glutenite reservoirs is introduced, and the result provides the theoretical support for prediction of fracture propagation morphology and plan design of hydraulic fracturing in the glutenite reservoirs.

Numerical simulation of horizontal well network fracturing in glutenite reservoir

Hydraulic fracturing is an economically effective technology developing the glutenite reservoirs, which have far stronger heterogeneity than the conventional sandstone reservoir. According to the field production experience of Shengli Oilfield, horizontal-well fracturing is more likely to develop a complex fractured network, which improves the stimulated volume of reservoir effectively. But the clear mechanism of horizontal-well hydraulic fracture propagation in the glutenite reservoirs is still not obtained, thus it is difficult to effectively carry out the design of fracturing plan. Based on the characteristics of the glutenite reservoirs, a coupled Flow-Stress-Damage (FSD) model of hydraulic fracture propagation is established. The numerical simulation of fracturing expansion in the horizontal well of the glutenite reservoir is conducted. It is shown that a square mesh-like fracture network is developed near the horizontal well in the reservoir with lower stress difference, in which fracture is more prone to propagate along the direction of the minimum principal stress as well. High fracturing fluids injection displacement and high fracturing fluid viscosity lead to the rise of static pressure of the fracture, which results in the rise of fracture complexity, and greater probability to deflect when encountering gravels. As the perforation density increases, the micro-fractures generated at each perforation gather together faster, and the range of the stimulated reservoir is also relatively large. For reservoirs with high gravel content, the complexity of fracture network and the effect of fracture communication are obviously increased, and the range of fracture deflection is relatively large. In the case of the same gravel distribution, the higher the tensile strength of the gravel, the greater fracture tortuosity and diversion was observed. In this paper, a simulation method of horizontal well fracture network propagation in the reservoirs is introduced, and the result provides the theoretical support for fracture network morphology prediction and plan design of hydraulic fracturing in the glutenite reservoir.

Experimental and Numerical Investigation of Permeability Evolution with Damage of Sandstone Under Triaxial Compression

A series of triaxial compression tests with permeability measurements was carried out under different confining pressure and pore pressure difference coupling conditions to investigate some mechanical properties and permeability evolution with damage of sandstone. It is found that the shapes of stress–strain curves, permeability evolution curves, and failure patterns are significantly affected by the confining pressure but are only slightly affected by the pore pressure difference. In addition, the corresponding numerical simulations of the experiments were then implemented based on the two-dimensional Realistic Failure Process Analysis-Flow (RFPA2D-Flow) code. In this simulator, the heterogeneity of rock is considered by assuming the material properties of the mesoscopic elements conform to a Weibull distribution and a statistical damage constitutive model based on elastic damage mechanics and the flow–stress–damage (FSD) coupling model. The numerical simulations reproduced the failure processes and failure patterns in detail, and the numerical results about permeability–strain qualitatively agree with the experimental results by assigning different parameters in the FSD model. Finally, the experimental results about relationship between permeability evolution and volumetric strain are discussed.

Numerical Modeling of Variable Fluid Injection-Rate Modes on Fracturing Network Evolution in Naturally Fractured Formations

In this study, variable injection-rate technology was numerically investigated in a pre-existing discrete fracture network (DFN) formation, the Tarim Basin in China. A flow-stress-damage (FSD) coupling model has been used in an initial attempt towards how reservoir response to variable injection-rates at different hydraulic fracturing stages. The established numerical model simultaneously considered the macroscopic and microscopic heterogeneity characteristics. Eight numerical cases were studied. Four cases were used to study the variable injection-rate technology, and the other four cases were applied for a constant injection-rate in order to compare with the variable injection-rate technology. The simulation results show that the variable injection-rate technology is a potentially good method to a form complex fracturing networks. The hydraulic fracturing effectiveness when increasing the injection-rate at each stage is the best, also, the total injected fluid is at a minimum. At the initial stage, many under-fracturing points appear around the wellbore with a relatively low injection-rate; the sudden increase of injection rate drives the dynamic propagation of hydraulic fractures along many branching fracturing points. However, the case with decreasing injection rate is the worst. By comparing with constant injection-rate cases, the hydraulic fracturing effectiveness with variable flow rate technology is generally better than those with constant injection-rate technology. This work strongly links the production technology and hydraulic fracturing effectiveness evaluation and aids in the understanding and optimization of hydraulic fracturing simulations in naturally fractured reservoirs.

Effect of injection rate on hydraulic fracturing in naturally fractured shale formations: a numerical study

This paper studies the effect of fluid injection rate on hydraulic fracturing in pre-existing discrete fracture network (DFN) formations. A flow–stress–damage coupling approach has been used in an initial attempt toward how reservoir responses to injection rate under different DFN connected configuration states. The simulation results show that injection rate has an significant influence on the hydraulic fractures (HF) and DFN interaction and hydraulic fracturing effectiveness, which can be characterized by the total interaction area, stimulated DFN length, stimulated HF length and leak-off ratio. For the sparse DFN model, stimulated HF length increases with increasing injection rate and the stimulated DFN length decreases with the increasing injection rate. For the medium DFN model, stimulated HF and DFN length both increase with increasing of injection rate. For the dense DFN model, length of stimulated HF deceases with increasing injection rate; however, the stimulated DFN length increases with the increasing injection rate. The effect of injection rate on hydraulic fracturing is closely related to formation characteristics, which are strongly affected by the DFN connected configuration. For the studied fracture network, the sparse DFN model gets the optimal hydraulic fracturing effectiveness with lower injection rate; however, the dense DFN model has the best hydraulic fracturing effectiveness with higher injection rate. This work strongly links the production technology and hydraulic fracturing effectiveness evaluation and aids in the understanding and optimization of hydraulic fracturing simulations in naturally fractured reservoirs.

Numerical Evaluation and Optimization of Multiple Hydraulically Fractured Parameters Using a Flow-Stress-Damage Coupled Approach

Multiple-factor analysis and optimization play a critical role in the the ability to maximizethe stimulated reservoir volume (SRV) and the success of economic shale gas production. In this paper, taking the typical continental naturally fractured silty laminae shale in China as anexample, response surface methodology (RSM) was employed to optimize multiple hydraulic fracturing parameters to maximize the stimulated area in combination with numerical modeling based on the coupled flow-stress-damage (FSD) approach. This paper demonstrates hydraulic fracturing effectiveness by defining two indicesnamelythe stimulated reservoir area (SRA) and stimulated silty laminae area (SLA). Seven uncertain parameters, such as laminae thickness, spacing, dip angle, cohesion, internal friction angle (IFA), in situ stress difference (SD), and an operational parameter-injection rate (IR) with a reasonable range based on silty Laminae Shale, Southeastern Ordos Basin, are used to fit a response of SRA and SLA as the objective function, and finally identity the optimum design under the parameters based on simultaneously maximizingSRA and SLA. In addition, asensitivity analysis of the influential factors is conducted for SRA and SLA. The aim of the study is to improve the artificial ability to control the fracturing network by means of multi-parameteroptimization. This work promises to provide insights into the effective exploitation of unconventional shale gas reservoirs via optimization of the fracturing design for continental shale, Southeastern Ordos Basin, China.

Coupled flow-stress-damage simulation of deviated-wellbore fracturing in hard-rock

In this study, the evolution of hydraulic fractures and micro-annuluses around wellbores was simulated using zero-thickness Pore Pressure Cohesive Elements (PPCE). A coupled flow-stress-damage (FSD) nonlinear finite element model which consists of deviated wellbore, perforation hole, micro-annulus, cement sheath and casing was established. The viscoelastic continuum damage induced by hydraulic fracturing is governed by the traction-separation law. Mohr-Coulomb law is used to determine the elastic and plastic behaviors of the cement sheath and surrounding rock. Numerical results show that micro-annulus propagates around the wellbore firstly, then it would gradually close. In addition, the sensitivities of rock parameters and in-situ stresses were also analyzed. It is found that, in the strike-slip stress regime, the width of fracture increases with the increasing deviated angle of wellbore. The fracture length increases with the increasing deviated angle of wellbore if the angle is smaller than 45°. However, if the deviated angle is above 45°, the fracture length decreases when the angle increases. When the bulk modulus is greater than 90 GPa, the fracture geometry keeps nearly unchanged. A higher Poisson's ratio increases the fracture propagation pressure and the in-situ stress differences can not effectively restrict the fracture height growth in hard formation.

Three-Dimensional Micro Flow-Stress-Damage (FSD) Model and Application in Hydraulic Fracturing in Brittle and Heterogeneous Rocks

In order to investigate the hydraylic fracture development of the specimens and simulate the cracks drived by fluid flow in rocks, a flow-stress-damage (FSD) model, implemented with parallel Rock Failure Process Analysis code (parallel -RFPA3D), is presented. The numerical code is based on linear elastic damage mechanics on mesoscopic scale and FEM. For simulating the complete progressive 3D failure and macroscopic mechanical behaviors of rock materials, rock properties such as elastic constants, peak strength, and poisson ratio are randomly distributed to reflect the initial random distributed weakness in mesoscopic scale. The FSD model is used to represent the permeability variation at the two stages, that is stress-dependent permeability for pre-failure and deformation-dependent permeability for post-peak stage of rock at the elemental scale. The results of the simulation with 680,000-element cylindrical rock specimen coincide well with reported experimental results and the process of crack from initiation to the instability extensions is captured vividly. The results and the process indicate that the FSD model works well and parallel-RFPA3D incorporated with FSD model is a valid tool of understanding the physical essence of the evolution of fracture with large-scale elements and fluid flows in rocks.

Application of an Improved Flow-Stress-Damage Model to the Criticality Assessment of Water Inrush in a Mine: a Case Study

This paper presents a case study of water inrush on a mine working face from roof strata. The flow-rock failure process analysis (F-RFPA2D) code with an improved flow-stress-damage (FSD) model was adopted to perform the failure and coupling analysis. The improved FSD model was used to represent the permeability variation at the four stages (elastic, damaged, cracked, and crack closure) of the rock failure process. The fracture initiation, propagation, and coalescence in the stressed strata and the seepage field evolution in the stress field are represented visually during the whole process of water inrush. The failure zone with high permeability induced by mining disturbance becomes the water-conducting zone after full excavation of the coal seam. The height of the water-conducting zone obtained in this study is in reasonable accordance with that predicted by an empirical formula. It is definitely clarified that the water inrush from the roof strata is induced by the failure zone full of vertical coalesced mine fractures. It is unlikely that roof accidents resulting in water inrush would occur if the water-conducting zone does not grow upwards into the aquifer. The main task for mine extraction under a confined aquifer is to locate the aquifer and find the maximum height of the water-conducting zone, which is very important for mine construction and support design.

Fracture Behavior and Water Migration in Heterogeneous and Porous Rocks

Based on the heterogeneous and porous characteristics of rock materials, a flow-stressdamage (FSD) model, implemented with the Rock Failure Process Analysis code (RFPA2D), is used to investigate the behavior of fluid flow and damage evolution, and their coupling action in rock sample that are subjected to both hydraulic and uniaxial compressive loading. A highly heterogeneous sample, containing grains, grain boundaries and weak zones, is employed in the numerical simulation. The simulation results provide a deep insight in the physical essence of the evolutionary nature of fracture phenomena as well as the fluid flow in heterogeneous materials, especially when they are highly stressed. The simulation result suggests that the nature of fluid flow and strength character in rocks strongly depends upon the heterogeneity of the rocks.