Application of the Finite Element Method to Solve Coupled Multiphysics Problems for Subsurface Energy Extraction

Fractures are a source of extra compliance in the rock mass. Fracture compliance can estimate the fracture roughness and the type of fluid filling the fracture. The focus of this research study in chapter 2 is to illustrate how the compliance ratio of rough fractures can diverge from the compliance ratio of smooth fractures. The imperfect interface of the fracture is modeled with saw-tooth-like structures. The defined saw-tooth-like structures of contact asperities impose an in-plane asymmetry in the shear direction. The compliance ratio of the rough fracture is larger than the compliance ratio of the smooth fracture. Interlocking and riding up effects may explain our findings in chapter 2. Recovered core samples and extensive outcrops studies have proved the existence of natural fractures in many tight formations. These natural fractures are likely filled with digenetic materials such as clays, quartz or calcite. In chapter 3, this study suggests that small cemented natural fractures can be opened by the induced tensile stress due to the temperature difference between the cold fracturing fluid and hot formation. Cohesive zone model (CZM) is utilized here to simulate these natural fractures. Contribution of these micro natural fractures to cumulative gas production from a shale reservoir is investigated by modifying the transmissibility coefficient. Reservoir simulation results in chapter 3 suggest that reactivated natural fractures in the tight formations at early stages can improve gas production up to 25\%; however, their effect significantly reduces to 3\% in long term. Geothermal systems are identified as either open-loop systems (OLGS) or closed-loop systems (CLGS). The loss of working fluid, surface subsidence, formation compaction, and induced seismicity are major challenges in OLGS. To address the indicated challenges, CLGS can be considered as an alternative option. To improve the heat extraction from closed-loop wells, this research study in chapter 4 suggests highly conductive hydraulic fractures for CLGS to improve heat extraction rate. The results suggest that fractures significantly improve thermal power and cumulative extracted heat in CLGS. Thermal conductivity of the proppants is the key parameter enhancing heat extraction

Simulation of fracture slip and propagation in hydraulic stimulation of geothermal reservoirs

Rollen til hydraulisk stimulering i å øke produksjonen fra geotermiske reservoarer, og muliggjøre kommersiell utnyttelse av et større spekter av geotermiske ressurser, har fått økt oppmerksomhet de siste tiårene. Under stimulering kan eksisterende sprekker sideforskyves, forplante seg og koble seg til andre sprekker og der igjennom øke permeabiliteten i reservoaret. Prosessene er preget av sterke hydromekaniske interaksjoner, som vi har begrensede muligheter til å overvåke. Numeriske simuleringer er derfor et viktig verktøy for å hjelpe oss til å bedre forstå mekanismene som er i spill. Avhandlingen tar sikte på å utvikle en omfattende matematisk modell og en numerisk tilnærming for å analysere bruddmekanismer og undersøke koblede hydromekaniske prosesser som forekommer i oppsprukne porøse medier. Den foreslåtte modellen benytter en blandet-dimensjonal konseptuell modell, som inkluderer porelastisitet i det porøse mediet og kontaktmekanikk for sprekkene. Modellen tillater også forplantning og koalescens av eksisterende sprekker. Et nytt diskretiseringsskjema for å løse den foreslåtte matematiske modellen presenteres. Den foreslåtte metoden bruker en to-nivå simuleringstilnærming, kategorisert i grove og fine nivåer, for å redusere beregningskostnader og sikre nøyaktighet. En endelig volummetode kombineres med en aktiv-sett løsningsstrategi for å diskretisere porelastisitet og bruddkontaktmekanikk på det grove nivået. Sprekkeforplantning betraktes på et fint nivå, der en endelig elementmetode kombineres med kollapsede kvartpunktselementer for å approksimere singulariteten i spenningen ved enden av sprekkene. Adaptiv gitring basert på en feilestimator og Laplace-glatting av gitteret introduseres på begge nivåer for effektivt å håndtere sprekkepropagering og koalescens. Simuleringene utført i denne avhandlingen forbedrer vår forståelse av hydraulisk stimulering og dens effekt på forbedring av sprekkepermeabilitet og konnektivitet i geotermiske reservoarer.The role of hydraulic stimulation in enhancing geothermal reservoir production and allowing for commercial exploitation of a larger range of geothermal resources has attracted attention from researchers in recent decades. During stimulation, preexisting fractures may slip, propagate, and connect to other fractures to enhance permeability. The processes are characterized by strong hydromechanical interactions, which have limited monitoring opportunities. Therefore, numerical simulations provide a powerful tool to help us better understand the mechanisms. This thesis aims to develop a comprehensive mathematical model and a numerical approach to analyze fracture mechanisms, and to investigate the coupled hydromechanical processes occurring in fractured porous media. The proposed model will employ a mixed-dimensional conceptual model, incorporating the concepts of poroelasticity and fracture contact mechanics. The model will also allow for the growth and coalescence of preexisting fractures. A novel discretization scheme for solving the proposed mathematical model is presented. The proposed scheme employs a two-level simulation approach, categorized into coarse and fine levels, to reduce the computational costs and ensure accuracy. A finite volume method is combined with an active set strategy to discretize poroelasticity and fracture contact mechanics on the coarse level. Fracture propagation is considered on a fine level, in which a finite element method is combined with collapsed quarter-point elements to capture the stress singularity at the fracture tips. Adaptive remeshing based on an error estimator and Laplacian smoothing is introduced on both levels to effectively capture fracture propagation and coalescence in the computational grid. The simulations conducted in this thesis improve our understanding of hydraulic stimulation and its effect on enhancing fracture permeability and connectivity in geothermal reservoirs.Doktorgradsavhandlin

Modelling Fracture Propagation in Shale Cap Rocks Cooled by CO2 Injection

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Thermomechanical analysis of rock asperity in fractures of enhanced geothermal systems

Enhanced Geothermal Systems (EGS) offer great potential for dramatically expanding the use of geothermal energy and become a promising supplement for fossil energy. The EGS is to extract heat by creating a subsurface system to which cold water can be added through injection wells. Injected water is heated by contact with rock and returns to the surface through production well. Fracture provides the primary conduit for fluid flow and heat transfer in natural rock. Fracture is propped by fracture roughness with varying heights which is called asperity. The stability of asperity determines fracture aperture and hence imposes substantial effect on hydraulic conductivity and heat transfer efficiency in EGS. Firstly, two rough fracture surfaces are characterized by statistical method and fractal analysis. The asperity heights and enclosed aperture heights are described by probability density function before cold water is pumped into fracture. Secondly, when water injection and induced cooling occurs, the thermomechanical analysis of single asperity is studied by establishing an un-symmetric damage mechanics model. The deformation curve of asperity under thermal stress is determined. Thirdly, deformation of fracture with various asperities on it in response to thermal stress is analyzed by a new stratified continuum percolation model. This model incorporates the fracture surface characteristics and preceding deformation curve of asperity. The fracture closure and fracture stiffness can be accurately quantified by this model. In addition, the scaling invariance and multifractal parameters in this process are identified and validated with Monte Carlo simulation --Abstract, page iii

Fluid pressure drops during stimulation of segmented faults in deep geothermal reservoirs

Hydraulic stimulation treatments required to produce deep geothermal reservoirs present the risk of generating induced seismicity. Understanding the processes that operate during the stimulation phase is critical for minimising and preventing the uncertainties associated with the exploitation of these reservoirs. It is especially important to understand how the phenomenon of induced seismicity is related to the pressurisation of networks of discrete fractures. In this study, we use the numerical simulator CFRAC to analyse pressure drops commonly observed during stimulation of deep geothermal wells. We develop a conceptual model of a fractured geothermal reservoir to analyse the conditions required to produce pressure drops and their consequences on the evolution of seismicity, fluid pressure, and fracture permeability throughout the system. For this, we combine two fracture sets, one able to be stimulated by shear-mode fracturing and another one able to be stimulated by opening-mode fracturing. With this combination, the pressure drop can be triggered by a seismic event in the shear-stimulated fracture that is hydraulically connected with an opening-mode fracture. Our results indicate that pressure drops are not produced by the new volume created by shear dilatancy, but by the opening of the conjugated tensile fractures. Finally, our results reveal that natural fracture/splay fracture interaction can potentially explain the observed pressure drops at the Rittershoffen geothermal site

3-D Stress Redistribution During Hydraulic Fracturing Stimulation And Its Interaction With Natural Fractures In Shale Reservoirs

The hydraulic fracturing (also called fracturing, or fracking) 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, especially for unconventional reservoirs with extremely low permeability. The key point for the success of hydraulic fracturing operations in unconventional resources is to connect and reactivate natural fractures and create the effective fracture network for fluid flow from pores into the production wells. To understand hydraulic fracturing technology, we must to understand some other affecting factors, e.g. in-situ stress conditions, reservoir mechanical properties, natural fracture distribution, and redistribution of the stress regime around the hydraulic fracture. Therefore, an accurate estimation of the redistribution of pore pressure and stresses around the hydraulic fracture is necessary, and it is very important to find out the reactivations of pre-existing natural fractures during the hydraulic fracturing process. Generally, fracture extension as well as its surround pore pressure and stress regime are affected by: poro- and thermoelastic phenomena as well as by fracture opening under the combined action of applied pressure and in-situ stresses. In this thesis, the previous studies on the hydraulic fracturing modeling and simulations were reviewed; a comprehensive semi-analytical model was constructed to estimate the pore pressure and stress distribution around an injection induced fracture from a single well in an infinite reservoir. With Mohr-Coulomb failure criterion, the natural fracture reactivation potential around the hydraulic fracture were studied. Then, a few case studies were presented, especially with the application in unconventional natural fractured shale reservoirs. This work is of interest in interpretation of micro-seismicity in hydraulic fracturing and in assessing permeability variation around a stimulation zone, as well as in estimation of the fracture spacing during hydraulic fracturing operations. In addition, the results from this study can be very helpful for selection of stimulated wells and further design of the re-fracturing operations

Fluid pressure drops during stimulation of segmented faults in deep geothermal reservoirs

Acknowledgements The Institut Cartogràfic i Geològic de Catalunya is acknowledged for their support in our investigation of Geothermal resources. G. Piris was supported by an AGAUR grant of the Industrial Doctorate programme 2016-DI-031. EGR acknowledges the support of the Beatriu de Pinós programme of the Government of Catalonia’s Secretariat for Universities and Research of the Department of Economy and Knowledge (2016 BP 00208). The authors would like to thank three anonymous reviewers and the editors Dr. Carola Meller and Prof. Olaf Kolditz for their helpful comments that improved this manuscript.Peer reviewedPublisher PD