在非常规油气开采中，由于储层岩石的低渗透性，需要水力压裂技术在储层中压出体积缝网，为油气采出开辟渗流通道。以往压裂施工中，以压出长直水力裂缝为目的。然而由于储层地质构造及油气分布的非均质性，这种长直扩展的水力裂缝不利于油气高效开采。为了解决和避免水力裂缝进入含水区、过早沟通近井裂缝带、井间裂缝窜通等实际问题，需要在水力压裂中构造倾斜、弯曲等依据储层实际情况展布的水力裂缝。目前针对该思路下的裂缝轨迹机理研究尚未见报道。

本文以储层水力裂缝为研究对象，以揭示水力裂缝轨迹形成机理和探讨其可调控性为研究目标，采用理论分析、数值模拟、实验验证相结合的方法，围绕水力裂缝转向及分岔、地层实地应力场变化时的裂缝扩展、水力裂缝和天然裂缝互作用及缝网演化、裂缝扩展轨迹调控方法四个方面，建立裂缝扩展数学模型，通过Matlab自主开发数值计算程序，进行水力压裂裂缝扩展轨迹数值模拟研究。本文主要研究成果如下：

（1）水力裂缝转向和分岔机理及数学模型。依据裂缝面摩尔库伦定律和位移梯度法建立了裂缝转向和分岔的数学模型，通过裂缝面受力计算分岔点位置和起裂角，解决了以往在连续介质模型水力裂缝扩展模拟过程中，难以处理转向水力裂缝分岔的问题。模拟了单簇水力裂缝转向过程中的三维扭转形态；研究了缝内压力、水平主应力差、射孔角、岩石力学性质、压裂液粘度对裂缝偏转轨迹的影响。研究表明：影响系数越大，裂缝越容易偏转。得到水力裂缝在转向过程中具有趋于中心对称扩展的特征以及“尺寸效应”的新认识，为压裂施工时裂缝轨迹调控提供了新思路。通过数值模拟揭示了水力裂缝面分岔的力学机理，指出地应力场产生的裂缝面切向滑移对分岔具有促进作用，缝内压力对裂缝面分岔具有抑制作用。

（2）实地应力场变化的裂缝扩展轨迹及数学模型。分别针对水力裂缝同时开裂和次序开裂，建立了考虑支撑剂支撑刚度、水力裂缝变形、局部地应力场变化的裂缝扩展数学模型和数值计算程序。解决了对历史压裂施工造成局部地应力场改变后新老水力裂缝轨迹干扰问题的模拟。研究了单井多簇压裂、多井同步压裂、拉链式压裂和加密井压裂过程中的裂缝轨迹。研究表明：多簇压裂时外侧裂缝转向后在三维空间内呈现贝壳状曲面，通过构造簇间应力场，可调控中间簇裂缝扩展轨迹；多井多裂缝压裂时交错布缝方式优于对顶布缝方式；加密井压裂中老井中间压新井的压裂顺序可降低水平井套管损伤风险。提出对于水力裂缝扩展轨迹，应统筹储层诱导应力场的时空演化特征进行分析，基于此有望在储层同一位置制造不同的裂缝轨迹。

（3）缝网演化机理及数学模型。耦合水力裂缝和天然裂缝变形计算模型、裂缝面支撑刚度计算模型、裂缝面摩尔库伦定律、最大周向应力准则，建立了可模拟水力裂缝-天然裂缝轨迹相互干扰和缝网演化的数学模型及模拟计算程序。该模型考虑了水力裂缝和天然裂缝非相交时，相互间的诱导起裂和轨迹干扰问题。首先变化水平主应力、天然裂缝倾角、水力裂缝逼近距离、簇间距，研究了水力裂缝和天然裂缝相交时的扩展轨迹；其次从天然裂缝尖端起裂扩展和沟通、周围局部应力场变化、对水力裂缝轨迹引导三个方面分析了其与水力裂缝非相交时的互作用机理；通过以上两方面揭示了复杂缝网形成机理。研究表明：水力裂缝逼近天然裂缝时，天然裂缝倾斜角越大，储层岩石抗拉强度越大，最小水平主应力越大，水力裂缝越不容易穿透天然裂缝扩展，同时越趋于形成单一主缝的轨迹形态。平行分布的大尺寸天然裂缝会放大水力裂缝的缝间干扰作用，导致水力裂缝在纵深方向上扩展轨迹的非对称分布。提出天然裂缝对诱导应力存在遮挡和传递效应，引起诱导应力锥进和天然裂缝沟通。水力裂缝可诱使与其非相交的天然裂缝发生失稳扩展。天然裂缝会诱使水力裂缝扩展轨迹发生偏移。

（4）裂缝扩展轨迹调控方法。基于裂缝扩展轨迹相关机理研究，提出可通过排量（压力）、射孔角、射孔位置、压裂次序等施工措施调控水力裂缝的起裂和止裂、转向扩展、直线扩展。首次基于比例积分微分控制方法建立了裂缝转向自动控制系统，可自动调整缝内压力以使裂缝在极小的偏转角度下冲过异常应力区，有利于实现以相对小的压裂液注入量获得最佳裂缝扩展轨迹的目的。

上述研究成果揭示了水力压裂储层改造过程中的裂缝扩展轨迹机理，建立了针对实际问题的裂缝轨迹调控方法。研究成果可以为压裂施工布井位置、射孔位置及射孔角度、压裂顺序、缝内压力等的设计，以及水力裂缝扩展形态刻画和预测、调控水力裂缝轨迹、制造体积缝网提供理论基础和指导。

In unconventional oil and gas exploitation, due to the low permeability of reservoir rocks, hydraulic fracturing technology is required to prduce the fracture network in the reservoir to open up flow channels for oil and gas exploitation. In the past fracturing construction, the purpose was to produce long and straight hydraulic fractures. However, due to the heterogeneity of reservoir geological structure and oil distribution, such long, straight hydraulic fractures are not effective in improving the efficiency of oil and gas production. In order to solve and avoid following practical problems, such as hydraulic fractures propagate into water-bearing areas, connect with natural fractures near the wellboll, and hydraulic fractures communicate with each other. At this point, it is considered necessary to artificially construct curved and inclined fracture trajectories according to the actual conditions of the reservoir. At present, there is no report on the study of fracture trajectory mechanism under this idea.

This paper takes tight sandstone as the research object and aims to reveal the formation mechanism of hydraulic fracture trajectory and explore its controllability. Theoretical analysis, numerical simulation and experimental verification are adopted. A mathematical model of fracture propagation was established based on four aspects, including hydraulic fracture deflection and bifurcation, fracture propagation trajectory when the in-situ stress changes, the interaction between hydraulic fracture and natural fracture and the evolution of fracture network, and the control method of fracture propagation trajectory. The mathematical model and calculation program of fracture propagation are independently developed through the software of Matlab to conduct numerical simulation research. The main research results of this paper are as follows:

(1) The mechanism and its mathematical model about the deflection and bifurcation of hydraulic fracture. The mathematical calculation model of fracture deflection and bifurcation is established based on Mohr Coulomb's law and displacement gradient method, which solves the problem that it is difficult to deal with the bifurcation of fracture surface in the process of simulation of hydraulic fracture propagation in continuous media. Simulated the 3D torsional pattern of single cluster hydraulic fracture in deflecting process. The effects of fracture pressure, horizontal principal stress difference, perforation angle, rock mechanical properties and fracturing fluid viscosity on fracture deflection and bifurcation are studied. The research shows that the larger the influence coefficient is, the easier the fracture is to deflect. Pointed out the new understanding of "size effect" and symmetrical propagation characteristic in the process of hydraulic fracture deflection, which provides a new idea for the control of fracture trajectory during fracturing construction. The mechanical mechanism of fracture plane bifurcation is revealed by numerical simulation. It is pointed out that the tangential slip of fracture surface caused by geostress field can promote the bifurcation, and the pressure inside the fracture can inhibit the bifurcation of fracture surface.

(2) Fracture propagation trajectory and mathematical model with in-situ stress field variation. The mathematical model and numerical calculation program of fracture propagation considering the propping stiffness of proppant, hydraulic fracture deformation and local in-situ stress change are established respectively for simultaneous fracturing and sequential fracturing. The problem of simulating the interference between new and old hydraulic fracture tracks after local stress field changes caused by historical fracturing operation is solved. Fracture trajectories of single well multi cluster fracturing, multi well synchronous fracturing, zipper fracturing and infill well fracturing are studied. The research results show that the outer fracture turns to be a shell shaped curved surface in three-dimensional space after multi cluster fracturing. By adjusting the cluster spacing to construct the stress field between clusters, and the propagation trajectory of the middle cluster fracture can be controlled by constructing the stress field between clusters. The staggered joint arrangement is better than the top joint arrangement in multi well and multi fracture fracturing. In infill well fracturing, fracturing a new well between two old Wells reduces the risk of casing damage in horizontal Wells. It is proposed that the spatio-temporal evolution characteristics of induced stress field of reservoir should be considered to analyze the trajectory of hydraulic fracture, based on which it is expected to create different fracture tracks at the same location of reservoir.

(3) Evolution mechanism and mathematical model of fracture network. Coupled with hydraulic fracture and natural fracture deformation calculation model, the stiffness calculation model in fracture surface support, the Mohr Coulomb criterion in fracture surface, the maximum circumferential stress criterion, a mathematical model and simulation calculation program that can simulate the interaction between hydraulic fracture and natural fracture trajectory and the evolution of fracture network are established. The model considers the interaction between hydraulic fractures and natural fractures when they do not intersect. Firstly, the interaction mechanism between hydraulic fractures and natural fractures is studied by changing the horizontal principal stress, the natural fracture inclination, the approach distance of fractures, and the cluster spacing. Secondly, the interaction mechanism of the disjoint fractures is studied from three aspects: the initiation, propagation and communication of the natural fractures, the change of local stress field around the natural fractures, and the guidance of the natural fractures to the trajectory of the hydraulic fractures. Finally, the formation mechanism of complex fracture network is revealed through the above two aspects. The results show that when hydraulic fractures approach natural fractures, the greater the inclination Angle of natural fractures, the greater the tensile strength of reservoir rock and the greater the minimum horizontal principal stress, the more difficult it is for hydraulic fractures to penetrate the natural fractures, and the more easier it is to form a single main fracture trajectory. The long natural fractures with parallel distribution will amplify the interfracture interference and lead to the asymmetric distribution of the propagation trajectory of hydraulic fractures in the perforation direction. It proposed that natural fractures have shielding and transmission effects on induced stress, causing induced stress coning to communicate with natural fractures. Hydraulic fractures can induce the natural fractures that do not intersect with hydraulic fractures to propagate the natural fracture will induce the migration of hydraulic fracture propagation path, and at the same time, natural fractures will deflect the trajectory of hydraulic fracture propagation.

(4) Control method of fracture propagation trajectory. Based on fracture propagation trajectory mechanism, it is pointed out that the initiation and arrest of hydraulic fractures, the deflecting and linear propagation of hydraulic fractures can be controlled by such construction measures as displacement pressure, perforation angle, perforation position and fracturing sequence. An automatic fracture deflection control system based on the proportional integral differential control method was established for the first time, which can automatically adjust the pressure in the fracture and make the fracture rush through the abnormal stress zone with a small deflection Angle, which is conducive to the optimal fracture propagation trajectory under the condition that the injection amount of fracturing fluid is relatively small.

The above research results reveal the mechanism of fracture propagation trajectory in the process of hydraulic fracturing reservoir reconstruction, and establish a fracture trajectory control method for practical problems. The research results can provide theoretical basis and guidance for the design of well layout position, perforation position and angle, fracturing sequence, and fracture pressure, as well as the characterization and prediction of hydraulic fracture propagation morphology, control of hydraulic fracture trajectory, and optimization of volume fracture network.

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