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Title:Simulating and diagnosing three-dimensional multistage hydraulic fracturing with the generalized finite element method
Author(s):Shauer, Nathan
Director of Research:Duarte, Carlos Armando
Doctoral Committee Chair(s):Duarte, Carlos Armando
Doctoral Committee Member(s):Lopez-Pamies, Oscar; Makhnenko, Roman; Gordon, Peter A
Department / Program:Civil & Environmental Eng
Discipline:Civil Engineering
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):Extended FEM
Generalized FEM
Fracture propagation
Hydraulic fracture
Krauklis waves
Stoneley guided waves
Fluid-filled fracture
Abstract:Hydraulic fracturing is the process in which a fracture propagates through the injection of pressurized fluid in its cavity. This technique allows one to considerably enlarge the accessible reservoir volume by the injection of fluid along with the isolated segments of the wellbore into the formation. In order to reduce operational costs, hydraulic fractures are usually created in stages (or clusters) where multiple fractures are propagated at the same time. It is estimated, however, that the majority of the production comes from only 20 to 30% of these clusters. It is known that tortuosity of the fractures may cause the failure of the hydraulic fracturing treatment. Thus, a possible explanation for this low production is the complex three-dimensional behavior of the simultaneous propagation of hydraulic fractures at the early stages. However, quantitative predictions of three-dimensional hydraulic fracturing geometry near a wellbore and its impact on fracturing pressures remain an open problem. In this work, a Generalized Finite Element Method (GFEM) is proposed for the simulation of the hydraulic fracturing process. A distinctive feature of the method is the fact that the mesh does not need to conform to the fracture geometry. Instead, the fracture is defined based on discontinuous and singular shape functions. This feature makes the method very attractive for the simulation of the complex fractures geometries that happen in the early propagation stages of hydraulic fracturing. The method assumes a 3D isotropic elastic material for the rock and Reynolds lubrication theory for the fluid inside the fracture. The fluid partition between fractures is estimated by coupling with the wellbore, which is modeled using Hagen–Poiseuille relation. The pressure losses between wellbore and hydraulic fractures are modeled with the sharp-edged orifice equation and the use of 1D connecting elements. A propagation criterion based on regularization of Irwin’s criterion is adopted and the time step that leads to propagation of the fractures is automatically calculated assuming a linear variation of the quantities. Some of the main features of the numerical method are the use of a quadratic basis, mesh adaptivity, geometrical enrichments around the fracture front, and a fully coupled monolithic system. A precise estimate of the fracture geometry created during hydraulic stimulation operations is believed to be key to maximizing the extraction of hydrocarbons from unconventional resource plays. However, due to uncertainties in the subsurface particularly related to heterogeneities in the earth, the predictions based on a computational tool may diverge from the real fracture geometries. A promising technique for inferring fracture geometry involves monitoring pressure transients in the wellbore. The transient response may be generated from a controlled source input such as in hydraulic impedance testing, or may be the by-product of a water hammer generated in the wellbore when pumping operations are rapidly shut down. The pressure pulse so created travels down the wellbore and back multiple times, and the interaction with open fractures connected to the wellbore influences the frequency and attenuation of this traveling wave. It is believed that the hydraulic connection between the wellbore and the fracture geometry can potentially be inferred by calculating the system’s resonance frequencies. Also in this work, a GFEM to estimate these resonance frequencies is proposed based on the simulation of waves in fluid-filled fractures. These guided waves are known as Krauklis waves and are characterized by a high degree of dispersion and by considerably low wave speeds due to coupling with the deformable rock. Differently from the classical Reynolds lubrication equations used for hydraulic fracture propagation, the fluid is considered nearly incompressible and inertial effects are not neglected. The rock is assumed as a 3-D isotropic elastic medium and the effects of considering inertial effects are shown to be negligible if the frequency of the excitation is low. A quadratic GFEM is used to model the fractured rock and a quadratic FEM is used for the governing equations of the fluid. The final system of equations is symmetric and is solved monolithically with a sparse solver. It is shown that the computational time can be strongly decreased since, in the majority of problems, the stiffness matrix only needs to be assembled and factorized once. Several examples - with verification and validation - are presented for both the simulation of hydraulic fractures propagation and the simulation of waves in fluid-filled fractures.
Issue Date:2021-02-24
Rights Information:Copyright 2021 Nathan Shauer
Date Available in IDEALS:2021-09-17
Date Deposited:2021-05

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