Simulation of Hydraulic Stimulation: Acoustic Wave Emission in Fractured Porous Media Using Local and Global Partition-of-Unity Finite Element

Generalized Finite Element Method;Hydraulic Fracturing;Acoustic Emission

Komijani, Mohammadadvisor:Gracie, Robert ; affiliation1:Faculty of Engineering ; Gracie, Robert ;

University of Waterloo

关键词: Acoustic Emission;    Generalized Finite Element Method;    Doctoral Thesis;    Hydraulic Fracturing;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/13927/3/Komijani_Mohammad.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

Hydraulic Fracturing (HF) is an effective stimulation process for extracting oil and gas fromunconventional low-permeable reservoirs. The process is conducted by injecting high-pressure fluids into the ground to generate fracture networks in rock masses and stimulate natural fracturesto increase the permeability of formation and extract oil and gas. Due to the multiple andcoupled-physics involved, hydraulic fracturing is a complex engineering process.The extent of the induced fractures and stimulated volume and reactivation of natural faultsand fractures are some of the practical issues associated with hydraulic fracturing. AcousticEmission (AE) monitoring and analysis are used to probe the behaviour of solid materials insuch applications. The process of elastic wave propagation induced by an abrupt local releaseof stored strain energy is known as acoustic, microseismic, and seismic emission (depending onthe context and the magnitude of the event). These emissions can be triggered by materialbifurcation-instabilities like slope slipping, fault-reactivation, pore collapsing, and cracking -processes that are all categorized as localization phenomena.The microseismic monitoring industry attempts to relate acoustic emissions measured bygeophones to the nature of the stimulated volume created during hydraulic fracturing. Thisprocess is full of uncertainties and researchers have not yet focused on both explicitly modelingthe process of fracture reactivation and the accurate simulation of acoustic wave propagationsresulting from the localization. The biggest gap in the modeling literature is that most of theprevious works fail to accurately simulate the process of transient acoustic wave propagationthrough the fractured porous media following the elastic energy release. Instead of explicitly modeling fracturing and acoustic emission, most previous studies have aimed to relate energyrelease to seismic moment.To overcome some of the existing shortcomings in the numerical modeling of the coupledproblem of interface localization-acoustic emission, this thesis is focused on developing new computationalmethods and programs for the simulation of microseismic wave emissions induced byinterface slip instability in fractured porous media. As a coupled nonlinear mixed multi-physicsproblem, simulation of hydraulic stimulation involves several mathematical and computationalcomplexities and difficulties in terms of modeling, stability, and convergence, such as the inf-supstability problems that arise from mixed formulations due to the hydro-mechanical couplingsand contact conditions. In AE modeling, due to the high-frequency transient nature of theproblem, additional numerical problems emerging from the Gibbs phenomenon and artificial period elongation and amplitude decay are also involved.The thesis has three main objectives. Thefirst objective is to develop a numerical modelfor simulation of wave propagation in discontinuous media, which is fulfilled in Chapter 2 ofthe thesis. In this chapter a new enriched finite element method is developed for simulationof wave propagation in fractured media. The method combines the advantages of the globalPartition-of-Unity Method (PUM) with harmonic enrichment functions via the Generalized FiniteElement Method (GFEM) with the local PUM via the Phantom Node Method (PNM).The GFEM enrichments suppress the spurious oscillations that can appear in regular FiniteElement Method (FEM) analysis of dynamic/wave propagations due to numerical dispersions and Gibbs phenomenon. The PNM models arbitrary fractures independently of the originalmesh. Through several numerical examples it has been demonstrated that the spurious oscillationsthat appear in propagation pattern of high-frequency waves in PNM simulations canbe effectively suppressed by employing the enriched model. This is observed to be especiallyimportant in fractured media where both primary waves and the secondary reflected waves arepresent.The second objective of the thesis is to develop a mixed numerical model for simulationof wave propagation in discontinuous porous media and interface modeling. This objectiveis realized in Chapter 3 of the thesis. In this chapter, a new enriched mixedfinite elementmodel is introduced for simulation of wave propagation in fractured porous media, based onan extension of the developed numerical method in Chapter 2. Moreover, frictional contact atinterfaces is modeled and realized using an augmented Lagrange multiplier scheme. Throughvarious numerical examples, the effectiveness of the developed enriched FE model over conventionalapproaches is demonstrated. Moreover, it is shown that the most accurate wave resultswith the least amount of spurious oscillations are achieved when both the displacement andpore pressurefields are enriched with appropriate trigonometric functions.The third objective of the thesis is to develop computational models for the simulation ofacoustic emissions induced by fracture reactivation and shear slip. This objective is realized inChapter 4 of the thesis. In this chapter, an enriched mixedfinite element model (introducedin Chapter 3) is developed to simulate the interface slip instability and the associated inducedacoustic wave propagation processes, concurrently. Acoustic events are triggered through asudden release of strain energy at the fracture interfaces due to shear slip instability. Theshear slip is induced via hydraulic stimulation that switches the interface behaviour from astick to slip condition. The superior capability of the proposed enriched mixedfinite elementmodel (i.e., PNM-GFEM-M) in comparison with regularfinite element models in inhibitingthe spurious oscillations and numerical dispersions of acoustic signals in both velocity andpore pressurefields is demonstrated through several numerical studies. Moreover, the effects of different characteristics of the system, such as permeability, viscous damping, and frictioncoefficientat the interface are investigated in various examples.