Semianalytical modeling on 3D stress redistribution during hydraulic fracturing stimulation and its effects on natural fracture reactivation

The hydraulic fracturing technique has been widely applied in many fields, such as the enhanced geothermal systems (EGS), the improvement of injection rates for geologic sequestration of CO₂, and for the stimulations of oil and gas reservoirs. The key points for the success of hydraulic fracturing operations in unconventional resources are to accurately estimate the redistribution of pore pressure and stresses around the induced fracture and predict the reactivations of preexisting natural fractures. The pore pressure and stress regime around hydraulic fracture are affected by poroelastic and thermoelastic phenomena as well as by fracture opening compression. In this work, a comprehensive semi-analytical model is used to estimate the stress and pore pressure distribution around an injection-induced fracture from a single well in an infinite reservoir. The model allows the leak-off distribution in the formation to be three-dimensional with the pressure transient moving ellipsoidically outward into the reservoir from the fracture surface. The pore pressure and the stress changes in three dimensions at any point around the fracture caused by poroelasticity, thermoelasticity, and fracture compression are investigated. With Mohr-Coulomb failure criterion, we calculate the natural fracture reactivations in the reservoir. Then, two case studies of constant water injection into a hydraulic fracture are presented. This work is of interest in the interpretation of microseismicity in hydraulic fracturing and in the estimation of the fracture spacing for hydraulic fracturing operations. In addition, the results from this study can be very helpful for the selection of stimulated wells and further design of the refracturing operations.     

Thermomechanical effects of a rapid depressurization in a gas cavern

Rapid gas depressurization leads to gas cooling followed by slow gas warming when the cavern is kept idle. Gas temperature drop depends upon withdrawal rate and cavern size. Thermal tensile stresses, resulting from gas cooling, may generate fractures at the wall and roof of a salt cavern. However, in most cases, the depth of penetration of these fractures is small. These fractures are perpendicular to the cavern wall. The distance between two parallel fractures becomes larger when fractures penetrate deeper in the rock mass, as some fractures do not keep growing. These conclusions can be supported by numerical computations based on fracture mechanics. Salt slabs are created. However, these slabs remain strongly bounded to the rock mass and it is believed that in many cases their weight is not large enough to allow them to break off the cavern wall. Depth of penetration of the fractures must be computed to prove that they cannot be a concern from the point of view of cavern tightness.     

Analysis of refracturing in horizontal wells: Insights from the poroelastic displacement discontinuity method

In this paper, a fully coupled 2‐dimensional poroelastic displacement discontinuity method is used to investigate the refracturing process in horizontal wells. One of the objectives of refracturing is to access new reserves by adding new hydraulic fractures in zones that were bypassed in the initial fracturing attempt. Pore pressure depletion in the vicinity of old fractures directly affects the state of stress and eventually the propagation of newly created hydraulic fractures. Thus, a poroelastic analysis is required to identify guidelines for the refracturing process, in particular to understand the extension of the pore pressure depletion, and eventually, the orientation of new as well as old fractures. We propose a fully coupled approach to model the whole process of child fracture propagation in a depleted area between 2 parent fractures in the same wellbore. This approach omits the need of using multistep workflow that is regularly used to model the process. The maximum tensile stress criterion (σ criterion) is used for hydraulic fracture propagation. The proposed method is verified using available analytical solutions for total stress and pore pressure loading modes on a line fracture in drained and undrained conditions. Then, test cases of multifractured horizontal wells are studied to calculate the time evolution of the stress and pore pressure fields around old fractures and to understand the effect of these fields on the propagation path of newly created fractures. Finally, the effect of the pore pressure depletion on the propagation path of the newly created fractures in the bypassed area of the same wellbore is studied. The results show that the depleted areas around old fractures are highly affected by the extent and severity of the stress redistribution and pore pressure depletion. It is observed that a successful creation of new fractures may only happen in certain time frames. The results of this study provide new insights on the behavior of newly created fractures in depleted zones. They also clarify the relationship between stress change and pore pressure depletion in horizontal wells.     

预制横缝条件下水力裂缝的起裂和扩展

针对高角度天然裂缝发育地层中的水平井水力压裂问题,开展了水力裂缝自天然裂缝处起裂扩展的理论和试验研究。尝试将天然裂缝简化为与井筒轴线垂直的横向裂缝,基于线弹性断裂力学理论和最大拉应力准则,给出了水力裂缝起裂压力和扩展过程中应力强度因子的计算方法。利用预制横缝模拟高角度天然裂缝,开展了室内水力压裂试验,对水力裂缝的扩展形态和起裂压力进行了研究。理论计算表明,（1）水力裂缝自预制横缝端部起裂后,扩展距离超过1倍的预制横缝端部半径时可将预制横缝和水力裂缝合并起来,整体视作一条横向裂缝来计算应力强度因子;（2）水力裂缝尖端距井壁处的距离大于4倍的井筒半径时,应力强度因子的计算可忽略井筒的影响,近似采用硬币形裂缝的计算公式。试验研究发现,（1）水力裂缝在预制横缝端部起裂并扩展,形成与井筒轴线垂直的横向裂缝,裂缝的扩展呈现出Ⅰ型断裂的特点,形态近似呈圆形,未发现与井筒轴线平行的纵向裂缝的起裂和扩展;（2）排量对破裂净压力和起裂净压力有重要影响,大排量会导致较高的破裂净压力和起裂净压力,在大、小两种排量下起裂净压力的离散性均较小,计算得到的KⅠ临界断裂值的离散性也较小。研究结果可为改善裂缝发育储层的近井裂缝形态提供指导,也可为煤矿开采中预制横向切槽的水力压裂设计提供参考。     

断层影响下的页岩气储层水力压裂模拟研究

断层对页岩气储层压裂改造有重要影响,甚至诱发深部地震事件和近地表环境问题.本文采用多物理场耦合方法,基于渗流和应力耦合理论,研究储层水力压裂过程中断层以及封闭顶板中水力破坏区域的产生与演化机理,并分析讨论流体沿高渗通道运移扩散机理,研究结果表明:(1)断层改变储层水力破坏区域形态并且扩展了水力压裂破坏空间.较高注水压力...     

Rock Cavern Stability Analysis Under Different Hydro-Geological Conditions Using the Coupled Hydro-Mechanical Model

Rock cavern stability has a close relationship with the uncertain geological parameters, such as the in situ stress, the joint configurations, and the joint mechanical properties. Therefore, the stability of the rock cavern should be studied with variable geological conditions. In this paper, the coupled hydro-mechanical model, which is under the framework of the discontinuous deformation analysis, is developed to study the underground cavern stability when considering the hydraulic pressure after excavation. Variable geological conditions are taken into account to study their impacts on the seepage rate and the cavern stability, including the in situ stress ratio, joint spacing, and joint dip angle. In addition, the two cases with static hydraulic pressure and without hydraulic pressure are also considered for the comparison. The numerical simulations demonstrate that the coupled approach can capture the cavern behavior better than the other two approaches without the coupling effects.     

Analysis of rock drainage and cooling experiments for underground cryogenic LNG storage

Hydrogeological monitoring was conducted around a pilot cavern for underground cryogenic LNG (Liquefied Natural Gas) storage. The monitoring was mainly focused on the operation of a drainage and recharge system. After the operation of the drainage system commenced, the drainage rate decreased rapidly in the initial stages and then decreased gradually. Hydrogeological monitoring revealed that the rock drainage system operated effectively. During drainage, the water table was maintained below the cavern roof. The recharge for ice-ring formation was performed in two phases. The first phase involved the cessation of pumping in downward-drainage holes and the second involved the closure of upward boreholes. Since the water table was maintained below the cavern roof, artificial recharge was planned at first. However, it was not implemented due to heavy rainfall in the recharge stage. On the basis of hydrogeological monitoring and hydraulic tests, it was found that the fractures above the roof and on the right wall of the pilot cavern mainly affected seepage into the cavern and thermal variation due to the storage of liquid nitrogen. Thermal variation was examined by the thermometers installed around the pilot cavern. The cooling and thawing processes reveal the characteristics of thermal distribution in the rock and the 0 °C isotherm. The cooling phase lasted for six months, and the 0 °C isotherm progressed in time after the injection of liquid nitrogen into the cavern. The isotherm propagated up to about 4 m from the floor and the sidewall of the cavern and about 3 m from the cavern roof. The cooling rate of the rock mass above the cavern roof was lower than that of the other cavern sides due to the gaseous space in the upper part of the containment. The fractures were analyzed and considered for thermal modeling. A two-dimensional finite element analysis was performed to compare the field monitoring at the pilot cavern. The numerical modeling shows the distance between the ice ring and heat transfer pattern of the fractures around the pilot cavern. The propagation of the measured and calculated 0 °C isotherm reveals that the water-conveying joint on the right wall might affect thermal propagation through a thermal pipe.     

Similarity solutions for wedge-shaped hydraulic fractures driven into a permeable medium by a constant inlet pressure

Similarity solutions are derived for wedge-shaped hydraulic fractures driven by a constant inlet pressure P₀ into a permeable medium under a uniform confining stress σ. These results describe the seepage-dominated regime in which most of the injected fluid is lost into the permeable walls of the fracture; they complement previous results for the capacitance-dominated regime in which seepage is negligible. Fracture propagation velocity is obtained as an analytical function of fracture length, driving pressure, confining stress, material properties and a single separation constant or eigenvalue which is determined numerically. Self-similar profiles of pressure, opening displacement and fluid velocity along the fracture are presented, together with the self-similar isobars of the two-dimensional pressure field within the permeable medium. Comprehensive results are reported for laminar or turbulent flow of a constant-compressibility liquid or an ideal gas driven by overpressures (P₀?σ)/σ ranging from 10^?2 to 10².     

Prediction and analysis of the stimulated reservoir volume for shale gas reservoirs based on rock failure mechanism

The ultra-low-permeability shale gas reservoir has a lot of well-developed natural fractures. It has been proven that hydraulic fracture growth pattern is usually a complex network fracture rather than conventional single planar fractures by micro-seismic monitoring, which can be explained as the shear and tensile failure of natural fractures or creation of new cracks due to the increase in reservoir pore pressure caused by fluid injection during the process of hydraulic fracturing. In order to simulate the network fracture growth, a mathematical model was established based on full tensor permeability, continuum method and fluid mass conservation equation. Firstly, the governing equation of fluid diffusivity based on permeability tensor was solved to obtain the reservoir pressure distribution. Then Mohr–Coulomb shear failure criterion and tensile failure criterion were used to decide whether the rock failed or not in any block on the basis of the calculated reservoir pressure. The grid-block permeability was modified according to the change of fracture aperture once any type of rock failure criterion was met within a grid block. Finally, the stimulated reservoir volume (SRV) zone was represented by an enhancement permeability zone. After calibrating the numerical solution of the model with the field micro-seismic information, a sensitivity study was performed to analyze the effects of some factors including initial reservoir pressure, injection fluid volume, natural fracture azimuth angle and horizontal stress difference on the SRV (shape, size, bandwidth and length). The results show that the SRV size increases with the increasing initial pore reservoir and injection fluid volume, but decreases with the increase in the horizontal principal stress difference and natural fracture azimuth angle. The SRV shape is always similar for different initial pore reservoir and injection fluid volume. The SRV is observed to become shorter in length and wider in bandwidth with the decrease in natural fracture azimuth angle and horizontal principal stress difference.     

A semi‐analytical approach for modelling heat transfer during salt‐cavern leaching process

The use of gas‐storage caverns in salt formations is a growing industry that continues to gain momentum because it allows gas to be injected and withdrawn at high rates compared with other underground gas‐storage systems such as porous rock systems. In order to predict cavern production performances, cavern thermodynamics behaviour must be studied by higher accuracy approaches. This behaviour is extremely related to the temperature distribution in the surrounding formations. During the leaching process, the thermal equilibrium of the rock salt surrounding the cavern is extensively disrupted. The purpose of this paper is to study the heat transfer problem during the leaching process and to develop a thermal model that can be easily used in field applications. The results of this work will be the input data for the prediction of the gas temperature and pressure during cavern gas‐storage operation phase. Moreover, the developed model can find its use in the design of salt caverns since it can be coupled with geometrical modelling of salt dissolution codes. Copyright © 2008 John Wiley & Sons, Ltd.     

Simulation of non‐planar three‐dimensional hydraulic fracture propagation

Hydraulic fracturing is the method of choice to enhance reservoir permeability and well efficiency for extraction of shale gas. Multi‐stranded non‐planar hydraulic fractures are often observed in stimulation sites. Non‐planar fractures propagating from wellbores inclined from the direction of maximum horizontal stress have also been reported. The pressure required to propagate non‐planar fractures is in general higher than in the case of planar fractures. Current computational methods for the simulation of hydraulic fractures generally assume single, symmetric, and planar crack geometries. In order to better understand hydraulic fracturing in complex‐layered naturally fractured reservoirs, fully 3D models need to be developed. In this paper, we present simulations of 3D non‐planar fracture propagation using an adaptive generalized FEM. This method greatly facilitates the discretization of complex 3D fractures, as finite element faces are not required to fit the crack surfaces. A solution strategy for fully automatic propagation of arbitrary 3D cracks is presented. The fracture surface on which pressure is applied is also automatically updated at each step. An efficient technique to numerically integrate boundary conditions on crack surfaces is also proposed and implemented. Strongly graded localized refinement and analytical asymptotic expansions are used as enrichment functions in the neighborhood of fracture fronts to increase the computational accuracy and efficiency of the method. Stress intensity factors with pressure on crack faces are extracted using the contour integral method. Various non‐planar crack geometries are investigated to demonstrate the robustness and flexibility of the proposed simulation methodology. Copyright © 2014 John Wiley & Sons, Ltd.     

Interaction between groundwater quality and hydraulic head in an area around an underground LPG storage cavern,Korea

The interactive influence between groundwater flow and salinization that occurs in an underground LPG cavern site in Korea was investigated using chemical analysis data and cross-correlation analysis between hydraulic head and operating pressure data. The concentration of the major cations and anions showed a large difference between rainy and dry seasons due to the seasonal intrusion of highly saline water into the cavern area. However, the Cl/Br ratio and '¹⁸O-Cl relationship showed that two types of saline water (seawater and halite-dissolved solution) influenced the groundwater salinization of the study area. The cross-correlation results revealed that a positive relationship between hydraulic head and cavern operating pressure was far more conspicuous in the propane cavern area (89-91% of correlation coefficients), and tidal change influenced the head variation in the butane cavern area. That is, continuous intrusion of seawater near the South Sea could bring about a high concentration of major cations and anions in the butane seepage waters and groundwaters near the coastal area, and seasonal variation in the operating pressure at the propane cavern played an important driving force in fast infiltration of halite-dissolved solution from surface halite stock and a subsequent increase in Na and Cl concentration during the dry season.     

Geometric nature of hydraulic fracture propagation in naturally-fractured reservoirs

The geometry of hydraulic fracture propagation in the absence and presence of natural fractures in reservoirs was studied. The results revealed a marked influence of natural fractures on the symmetry of fracture propagation observed for rock free of natural fractures. Natural fracture properties such as stiffness and approaching angle, and the distance from wellbore to the natural fracture were found to influence the hydraulic fracture geometry. Furthermore, the location of the wellbore with respect to the natural fractures in a reservoir having a system of natural fractures displayed a significant influence on the resulting geometry of hydraulic fracture propagation.     

Linear Elastic and Cohesive Fracture Analysis to Model Hydraulic Fracture in Brittle and Ductile Rocks

Hydraulic fracturing technology is being widely used within the oil and gas industry for both waste injection and unconventional gas production wells. It is essential to predict the behavior of hydraulic fractures accurately based on understanding the fundamental mechanism(s). The prevailing approach for hydraulic fracture modeling continues to rely on computational methods based on Linear Elastic Fracture Mechanics (LEFM). Generally, these methods give reasonable predictions for hard rock hydraulic fracture processes, but still have inherent limitations, especially when fluid injection is performed in soft rock/sand or other non-conventional formations. These methods typically give very conservative predictions on fracture geometry and inaccurate estimation of required fracture pressure. One of the reasons the LEFM-based methods fail to give accurate predictions for these materials is that the fracture process zone ahead of the crack tip and softening effect should not be neglected in ductile rock fracture analysis. A 3D pore pressure cohesive zone model has been developed and applied to predict hydraulic fracturing under fluid injection. The cohesive zone method is a numerical tool developed to model crack initiation and growth in quasi-brittle materials considering the material softening effect. The pore pressure cohesive zone model has been applied to investigate the hydraulic fracture with different rock properties. The hydraulic fracture predictions of a three-layer water injection case have been compared using the pore pressure cohesive zone model with revised parameters, LEFM-based pseudo 3D model, a Perkins-Kern–Nordgren (PKN) model, and an analytical solution. Based on the size of the fracture process zone and its effect on crack extension in ductile rock, the fundamental mechanical difference of LEFM and cohesive fracture mechanics-based methods is discussed. An effective fracture toughness method has been proposed to consider the fracture process zone effect on the ductile rock fracture.     

Cluster spacing optimization of multi-stage fracturing in horizontal shale gas wells based on stimulated reservoir volume evaluation

The multi-stage fracturing in horizontal well is a common technique for shale gas reservoir exploitation, in which cluster spacing governs the fracturing performance. Undersized cluster spacing might make the stimulated reservoir volume (SRV), activated by the respective hydraulic fracture, excessively overlap with each other, while oversized cluster spacing might leave a large unstimulated volume between neighboring hydraulic fractures; in either case, fracturing would be inefficient. Previous design of cluster spacing has failed to maximize the SRV due to the absence of a dynamic SRV evaluation model. A numerical model of SRV evaluation in shale reservoir was established by integrating four main modules, including fracture propagation, reservoir pressure distribution, formation stress distribution, and natural fracture failure criterion. Then, a method to optimize cluster spacing was developed with the goal of maximizing SRV. In order to validate this method, it was applied in Fuling shale gas reservoir in Southwest China to determine the optimal cluster spacing. The sensitivity of key parameters on the optimal cluster spacing has been analyzed. This research proposed a compelling cluster spacing optimization method, which could reduce the uncertainty in cluster spacing design, and provides some new insights on the optimal design of multi-stage fracturing in horizontal shale gas well.     

Experimental investigation into the sealing capability of naturally fractured shale caprocks to supercritical carbon dioxide flow

Geological storage of CO₂ is considered a solution for reducing the excess CO₂ released into the atmosphere. Low permeability caprocks physically trap CO₂ injected into underlying porous reservoirs. Injection leads to increasing pore pressure and reduced effective stress, increasing the likelihood of exceeding the capillary entry pressure of the caprocks and of caprock fracturing. Assessing on how the different phases of CO₂ flow through caprock matrix and fractures is important for assessing CO₂ storage security. Fractures are considered to represent preferential flow paths in the caprock for the escape of CO₂. Here we present a new experimental rig which allows 38 mm diameter fractured caprock samples recovered from depths of up to 4 km to be exposed to supercritical CO₂ (scCO₂) under in situ conditions of pressure, temperature and geochemistry. In contrast to expectations, the results indicate that scCO₂ will not flow through tight natural caprock fractures, even with a differential pressure across the fractured sample in excess of 51 MPa. However, below the critical point where CO₂ enters its gas phase, the CO₂ flows readily through the caprock fractures. This indicates the possibility of a critical threshold of fracture aperture size which controls CO₂ flow along the fracture.     

页岩水平井多段分簇压裂起裂压力数值模拟

页岩储层孔隙度和渗透率极低,天然裂缝和水平层理发育,常规压裂增产措施无法满足页岩气的开发要求,水平井多段分簇压裂是页岩气开发的关键技术之一,该技术能够大幅度提升压裂改造的体积、产气量和最终采收率。为确定页岩储层水平井多段分簇射孔压裂的起裂点和起裂压力,采用有限元方法建立了水平井套管完井（考虑水泥环和套管的存在）多段分簇射孔的全三维起裂模型。数值模型的起裂压力与室内试验结果吻合较好,证明了数值模型的准确性和可靠性。利用数值模型研究了页岩水平井多段分簇射孔压裂的起裂点和起裂压力的影响因素,研究发现：射孔孔眼附近无天然裂缝或水平层理影响,起裂点发生在射孔簇孔眼的根部;射孔簇间距越小,中间射孔簇的干扰越大,可能造成中间的射孔簇无法起裂;射孔密度和孔眼长度增大,起裂压力降低;天然裂缝的存在,在某些情况能够降低起裂压力且改变起裂位置,主要与天然裂缝的分布方位及水平主应力差有关;水平层理可能会降低起裂压力,但与垂向主应力与水平最小主应力的差值有关。获得的起裂压力变化规律,可作为进一步研究水平井多段分簇射孔条件下的裂缝扩展规律的基础,可以为压裂设计和施工的射孔参数确定及优化给出具体建议。     

A New Elasto-Viscoplastic Damage Model Combined with the Generalized Hoek–Brown Failure Criterion for Bedded Rock Salt and its Application

According to the requirement of the West–East Gas Transmission Project in China, the solution-mined cavities located in the Jintan bedded salt formation of Jiangsu province will be utilized for natural gas storage. This task is more challenging than conventional salt dome cavern construction and operation due to the heterogeneous bedding layers of the bedded salt formation. A three-dimensional creep damage constitutive model combined with the generalized Hoek–Brown model is exclusively formulated and validated with a series of strength and creep tests for the bedded rock salt. The viscoplastic model, which takes the coupled creep damage and the failure behavior under various stress states into account, enables both the three creep phases and the deformation induced by vicious damage and plastic flow to be calculated. A further geomechanical analysis of the rapid gas withdrawal for the thin-bedded salt cavern was performed by implementing the proposed model in the finite difference software FLAC^3D. The volume convergence, the damage and failure propagation of the cavern, as well as the strain rate of the salt around the cavern, were evaluated and discussed in detail. Finally, based on the simulation study, a 7-MPa minimum internal pressure is suggested to ensure the structural stability of the Jintan bedded salt cavern. The results obtained from these investigations provide the necessary input for the design and construction of the cavern project.     

基于离散元法的水力压裂数值模拟

不同条件下水压裂隙的发展特性对有效开采页岩气具有重要的指导作用。针对岩体在微观上为颗粒和孔隙的结构系统,提出离散元水力压裂数值模拟方法,离散元能量转化和能量守恒计算方法,建立了相应的三维离散元模型。采用自主研发的三维离散元模拟软件Mat DEM3D,通过控制模型的竖向应变与颗粒直径,来模拟地层中的应力与压裂速率的变化。模拟结果表明:(1)水力压裂产生裂隙的数量和方向受岩石的各向异性,压力状态和变化速率所影响。(2)裂隙在压缩波传播时发展,当水压力高速增加时,诱发的裂隙数量增多,并且有效能量(断裂热)百分比也随之增加,压裂作用也变得更明显。(3)当竖向应变为零时,50%的裂隙呈垂直状态,当竖向应变为-1×10-4时,裂隙趋于沿着最大压力方向发展,竖向裂隙的百分率增大。数值模拟和能量分析为定量地研究岩石水力压裂过程提供了一个新的方法。