| Hydraulic fracturing is one of the primary technologies used for reservoir production enhancement. For different formation conditions, the hydraulic fracture shape may be horizontal or vertical. For vertical fracture, engineers pay close attention to the three dimensional fracture configurations, especially to the fracture height and the crossing layer situation. In this dissertation, the finite element software ABAQUS is used as a platform to simulate the hydraulic fracturing processes. The key point is to study the effect of various parameters on fracture configuration and fracture height control. The results are valuable for hydraulic treatment design and practice.First, the concept and function of hydraulic fracturing is introduced. The processes of hydraulic fracturing technology development and application at home and abroad are briefly reviewed. Different hydraulic fracturing models are summarized. Hydraulic fracturing related rock mechanics and other concerned problems (near wellbore effect, proppant choosing, volume fracturing in shale-gas reservoirs and so on) are expounded. Through the explanation of the importance of the fracture height control and the current results from other researchers, the contents and significance of this dissertation are presented.Usually the reservoir is a kind of porous media, and it is regarded as a structure constructed by solid framework and pore. The Terzaghi effective stress principle is adopted to couple the solid deformation and seepage flow. The basic equations and boundary conditions as well as the corresponding incremental finite element solution formulae are summarized. The formulae are the math foundation of this dissertation. Cohesive elements with pore pressure freedom are used to simulate the fracture behavior. The fracture initiation and propagation laws are explained. The dimensionless scalar-damage factor is introduced to characterize the damage situation of the elements (the stiffness of the damaged elements may decrease). The fluid flow in the fracture is assumed to be linear. The tangential flow rate is proportional to the pressure gradient in the fracture, and the normal flow rate is proportional to the pressure difference between the fracture center and the fracture top/bottom surface. The basic theories of linear elastic and viscolinear elastic are stated, and the constitutive relation of a typical viscoelastic model-standard linear model is introduced. The ways of dealing with proppant concentration are presented, and the influence of proppant concentration distribution on hydraulic fracturing is represented by the fracturing fluid viscocity vatiation.Two-dimensional plane strain model is established to simulate the vertical growth of hydraulic fracture. The advantages of two dimensional model are the small computational overburden and save of time. A hydraulic fracturing process of a well in Daqing Oilfield is simulated. Combing the obtained bottomhole pressure and the frictions based on the empirical formulae, the surface pressure can be derived. The surface pressure curve from the simulation is consistent with field-measured data, and thus the feasibility of the two-dimensional model is approved. For the three layered formation (one pay layer sandwiched between two barrier layers), the effect of lithological parameters on fracture height is investigated. The results indicate that larger in-situ stress, smaller elastic modulus and larger tensile strength in barrier layers could make the fracture height smaller, and the crossing layer status is restricted.Fully three-dimensional model is established to study various factors which may influence the three-dimensional fracture configuration and fracture height. Main results are summarized below.(1) Hydraulic fracturing process in multi-layered reservoir. A typical hydraulic fracturing process of a well in Oilfield is simulated. The bottomhole pressure curve obtained from the simulation is compared with field-measured data, and the three-dimensional model is validated. Then hydraulic fracturing processes in multi-layered reservoir are simulated. The results show that larger in-situ stress and tensile strength, as well as smaller elastic modulus in barrier layers could make the fracture to be lower and longer. The reason is that in-situ stress and tensile strength hinder the fracture from opening; larger elastic modulus will make the fracture to be narrower, which has larger resistance to fluid flow, leading to the enlarged bottomhole pressure and fracture height. Since the pay layers and the barrier layers are interlinked by turns, the fracture cross-section is wave-shape.(2) Effect of rock porosity and clay content on hydraulic fracturing. According to the relation between linear elastic wave velocity and elastic parameters, as well as several empirical formulae based on the laboratory test and well logging data, porosity and clay content are connected to elastic modulus, Poisson’s ratio, tensile strength and permeability. Numerical results indicate that larger porosity and clay content could confine the fracture height. Larger porosity will make the permeability increase, and more fracturing fluid may leak off into the reservoir. Larger clay content will make the elastic modulus decrease and tensile strength enlarge, and therefore the formation will become harder to be damaged. All these factors will lead the fracture height smaller.(3) Effect of orthotropic permeability on hydraulic fracturing. The influence of orthotropic permeability components on fracture configuration and bottomhole pressure is discussed. The conclusion is that as the permeability component along the fracture width direction increase, the fracture length, fracture height and bottomhole pressure may decrease. The influence of the permeability components along the fracture length and height directions on hydraulic fracturing is not evident. This may be interpreted with the direction of fluid leaking off. The fluid leaking off is mainly governed by the permeability component along the fracture width direction. The other two permeability components have little influence on fluid leaking off.(4) Simulation of hydraulic fracture propagating in the formation with viscoelastic property. Standard linear solid model is used to characterize the constitutive relation of formation. Numerical results indicate that as the viscosity and the shear modulus of Kelvin body in the standard linear solid decrease, the fracture height decreases. When any of the two parameters decreases, the relaxation modulus decreases, leading to stress relaxation and bottomhole pressure drop. As a result, the fracture height will be reduced. The fracture height predicted by viscoelastic model is smaller than that predicted by the corresponding linear elastic model.(5) Effect of proppant setting on hydraulic fracturing. The proppant setting model is proposed and its application in hydraulic fracturing modeling is discussed. The results demonstrate that duo to proppant settling, the fracture cross-section shape should be asymmetric, i.e. the lower half part of the fracture cross-section is wider than the upper half part. Compared to the proppant uniform distribution model, the fracture cross-section area obtained from the proppant settling model is larger. This is caused by neglecting the influence of fluid leaking off on proppant concentration in uniform distribution model. The influence of fluid leaking off is the increase of proppant concentration, and then the viscosity of fluid will be larger. As a result, the fluid leaking off is restrained. A hydraulic fracturing process of a well in Oilfield is simulated, and the bottomhole pressure curve obtained from the proppant settling model is closer to the field-measured data than that obtained from uniform distribution model.(6) Effect of interface shear failure on hydraulic fracturing. The influence of shear strength of interface between barrier layer and pay layer on fracture configuration is investigated. The results demonstrate that when the shear strength of interface is lower than a critical value, the interface will be damaged so that serious slippage along the interface will occur and the facture tip becomes blunted. The fracture height is confined and the fracture length will increase. On the contrary, when the shear strength of interface is large enough, the interface will not be damaged and there is no slippage along the interface. The fracture vertical growth cannot be stopped and it may penetrate into barrier layer.The present dissertation explores the key factors influencing fracture height. The obtained results are valuable for design and engineering practice of hydraulic fracturing. |
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