Publications
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Underlined names are links to current or past GEG members
REFEREED PUBLICATIONS IN JOURNALS
27.
Ezzat, M., J. Beorner, B. Kammermann, E. Rossi, B.M. Adams, V. Wittig, J. Biela, H-O. Schiegg, D. Vogler, and M.O. Saar, Impact of Temperature on the Performance of Plasma-Pulse Geo-Drilling (PPGD), Rock Mechanics and Rock Engineering, 2024. https://doi.org/10.1007/s00603-023-03736-y [Download] [View Abstract]Advanced Geothermal Systems (AGS) may in principle be able to satisfy the global energy demand using standard continental-crust geothermal temperature gradients of 25-35◦C/km. However, conventional mechanical rotary drilling is still too expensive to cost-competitively provide the required borehole depths and lengths for AGS. This highlights the need for a new, cheaper drilling technology, such as Plasma-Pulse Geo-Drilling (PPGD), to improve the economic feasibility of AGS. PPGD is a rather new drilling method and is based on nanoseconds-long, high-voltage pulses to fracture the rock without mechanical abrasion. The absence of mechanical abrasion prolongs the bit lifetime, thereby increasing the penetration rate. Laboratory experiments under ambient-air conditions and comparative analyses (which assume drilling at a depth between 3.5 km and 4.5 km) have shown that PPGD may reduce drilling costs by approximately 17-23%, compared to the costs of mechanical drilling, while further research and development are expected to reduce PPGD costs further. However, the performance of the PPGD process under deep wellbore conditions, i.e., at elevated temperatures as well as elevated lithostatic and hydrostatic pressures, has yet to be systematically tested. In this paper, we introduce a standard experiment parameter to examine the impact of deep wellbore conditions on drilling performance, namely the productivity (the excavated rock volume per pulse) and the specific energy, the latter being the amount of energy required to drill a unit volume of rock.
We employ these parameters to investigate the effect of temperature on PPGD performance, with temperatures increasing up to 80◦C, corresponding to a drilling depth of up to approximately 3 km.
26.
Li, Z., X. Ma, X.-Z. Kong, M.O. Saar, and D. Vogler, Permeability evolution during pressure-controlled shear slip in saw-cut and natural granite fractures, Rock Mechanics Bulletin, 2023. https://doi.org/10.1016/j.rockmb.2022.100027 [Download] [View Abstract]Fluid injection into rock masses is involved during various subsurface engineering applications. However, elevated fluid pressure, induced by injection, can trigger shear slip(s) of pre-existing natural fractures, resulting in changes of the rock mass permeability and thus injectivity. However, the mechanism of slip-induced permeability variation, particularly when subjected to multiple slips, is still not fully understood. In this study, we performed laboratory experiments to investigate the fracture permeability evolution induced by shear slip in both saw-cut and natural fractures with rough surfaces. Our experiments show that compared to saw-cut fractures, natural fractures show much small effective stress when the slips induced by triggering fluid pressures, likely due to the much rougher surface of the natural fractures. For natural fractures, we observed that a critical shear displacement value in the relationship between permeability and accumulative shear displacement: the permeability of natural fractures initially increases, followed by a permeability decrease after the accumulative shear displacement reaches a critical shear displacement value. For the saw-cut fractures, there is no consistent change in the measured permeability versus the accumulative shear displacement, but the first slip event often induces the largest shear displacement and associated permeability changes. The produced gouge material suggests that rock surface damage occurs during multiple slips, although, unfortunately, our experiments did not allow quantitatively continuous monitoring of fracture surface property changes. Thus, we attribute the slip-induced permeability evolution to the interplay between permeability reductions, due to damages of fracture asperities, and permeability enhancements, caused by shear dilation, depending on the scale of the shear displacement.
25.
Javanmard, H., M. O. Saar, and D. Vogler, On the applicability of connectivity metrics to rough fractures under normal stress, Advances in Water Resources, 161/104122, 2022. https://doi.org/10.1016/j.advwatres.2022.104122 [Download] [View Abstract]Rough rock fractures have complex geometries which result in highly heterogeneous aperture fields.
To accurately estimate the permeability of such fractures, heterogeneity of the aperture fields must be quantified.
In this study heterogeneity of single rough rock fractures is for the first time parametrized by connectivity metrics, which quantify how connected the bounds of a heterogeneous field are.
We use 3000 individual realizations of synthetic aperture fields with different statistical parameters and compute three connectivity metrics based on percolation theory for each realization.
The sensitivity of the connectivity metrics with respect to the determining parameter, i.e the cutoff threshold, is studied and the correlation between permeability of the fractures and the computed connectivity metrics is presented.
The results show that the $Theta$ connectivity metric predicts the permeability with higher accuracy.
All three studied connectivity metrics provide better permeability estimations when a larger aperture value is chosen as the cutoff threshold.
Overall, this study elucidates that using connectivity metrics provides a less expensive alternative to fluid flow simulations when an estimation of fracture permeability is desired.
24.
Ezzat, M., B. M. Adams, M.O. Saar, and D. Vogler, Numerical Modeling of the Effects of Pore Characteristics on the Electric Breakdown of Rock for Plasma Pulse Geo Drilling, Energies, 15/1, 2022. https://doi.org/10.3390/en15010250 [Download] [View Abstract]Drilling costs can be 80% of geothermal project investment, so decreasing these deep drilling costs substantially reduces overall project costs, contributing to less expensive geothermal electricity or heat generation. Plasma Pulse Geo Drilling (PPGD) is a contactless drilling technique that uses high-voltage pulses to fracture the rock without mechanical abrasion, which may reduce drilling costs by up to 90% of conventional mechanical rotary drilling costs. However, further development of PPGD requires a better understanding of the underlying fundamental physics, specifically the dielectric breakdown of rocks with pore fluids subjected to high-voltage pulses. This paper presents a numerical model to investigate the effects of the pore characteristics (i.e., pore fluid, shape, size, and pressure) on the occurrence of the local electric breakdown (i.e., plasma formation in the pore fluid) inside the granite pores and thus on PPGD efficiency. Investigated are: (i) two pore fluids, consisting of air (gas) or liquid water; (ii) three pore shapes, i.e., ellipses, circles, and squares; (iii) pore sizes ranging from 10 to 150 μm; (iv) pore pressures ranging from 0.1 to 2.5 MPa. The study shows how the investigated pore characteristics affect the local electric breakdown and, consequently, the PPGD process.
23.
Ezzat, M., D. Vogler, M. O. Saar, and B. M. Adams, Simulating Plasma Formation in Pores under Short Electric Pulses for Plasma Pulse Geo Drilling (PPGD), Energies, 14/16, 2021. https://doi.org/10.3390/en14164717 [Download] [View Abstract]
Plasma Pulse Geo Drilling (PPGD) is a contact-less drilling technique, where an electric discharge across a rock sample causes the rock to fracture.
Experimental results have shown PPGD drilling operations are successful if certain electrode spacings, pulse voltages, and pulse rise times are given.
However, the underlying physics of the electric breakdown within the rock, which cause damage in the process, are still poorly understood.
This study presents a novel methodology to numerically study plasma generation for electric pulses between 200 to 500 kV in rock pores with a width between 10 and 100 \(\mu\)m.
We further investigate whether the pressure increase, induced by the plasma generation, is sufficient to cause rock fracturing, which is indicative of the onset of drilling success.
We find that rock fracturing occurs in simulations with a 100 \(\mu\)m. pore size and an imposed pulse voltage of approximately 400 kV.
Furthermore, pulses with voltages lower than 400 kV induce damage near the electrodes, which expands from pulse to pulse, and eventually, rock fracturing occurs.
Additionally, we find that the likelihood for fracturing increases with increasing pore voltage drop, which increases with pore size, electric pulse voltage, and rock effective relative permittivity while being inversely proportional to the rock porosity and pulse rise time.
22.
Deb, P., S. Salimzadeh, D. Vogler, S. Düber, C. Clauser, and R. R. Settgast, Verification of coupled hydraulic fracturing simulators using laboratory-scale experiments, Rock Mechanics and Rock Engineering, 54, pp. 2881-2902, 2021. https://doi.org/10.1007/s00603-021-02425-y [Download] [View Abstract]In this work, we aim to verify the predictions of the numerical simulators, which are used for designing field-scale hydraulic stimulation experiments. Although a strong theoretical understanding of this process has been gained over the past few decades, numerical predictions of fracture propagation in low-permeability rocks still remains a challenge. Against this background, we performed controlled laboratory-scale hydraulic fracturing experiments in granite samples, which not only provides high-quality experimental data but also a well-characterized experimental set-up. Using the experimental pressure responses and the final fracture sizes as benchmark, we compared the numerical predictions of two coupled hydraulic fracturing simulators—CSMP and GEOS. Both the simulators reproduced the experimental pressure behavior by implementing the physics of Linear Elastic Fracture Mechanics (LEFM) and lubrication theory within a reasonable degree of accuracy. The simulation results indicate that even in the very low-porosity (1–2%) and low-permeability ($10^{-18} m^2 - 10^{-19} m^2$) crystalline rocks, which are usually the target of EGS, fluid-loss into the matrix and unsaturated flow impacts the formation breakdown pressure and the post-breakdown pressure trends. Therefore, underestimation of such parameters in numerical modeling can lead to significant underestimation of breakdown pressure. The simulation results also indicate the importance of implementing wellbore solvers for considering the effect of system compressibility and pressure drop due to friction in the injection line. The varying injection rate as a result of decompression at the instant of fracture initiation affects the fracture size, while the entry friction at the connection between the well and the initial notch may cause an increase in the measured breakdown pressure.
21.
Lima, M., H. Javanmard, D. Vogler, M.O. Saar, and X.-Z. Kong, Flow-through Drying during CO2 Injection into Brine-filled Natural Fractures: A Tale of Effective Normal Stress, International Journal of Greenhouse Gas Control, 109, pp. 103378, 2021. https://doi.org/10.1016/j.ijggc.2021.103378 [Download] [View Abstract]Injecting supercritical CO2 (scCO2) into brine-filled fracture-dominated reservoirs causes brine displacement and possibly evaporite precipitations that alter the fracture space.
Here, we report on isothermal near-field experiments on scCO2-induced flow-through drying in a naturally fractured granodiorite specimen under effective normal stresses of 5-10 MPa, where two drying regimes are identified. A novel approach is developed to delineate the evolution of brine saturation and relative permeability from fluid production and differential pressure measurements. Under higher compressive stresses, the derived relative permeability curves indicate lower mobility of brine and higher mobility of the scCO2 phase. The derived fractional flow curves also suggest an increase in channelling and a decrease in brine displacement efficiencies under higher compressive stresses. Finally, lowering compressive stresses seems to hinder water evaporation. Our experimental results assist in understanding the behaviour of the injectivity of fractures and fracture networks during subsurface applications that involve scCO2 injection into saline formations.
20.
Javanmard, H., A. Ebigbo, S.D.C. Walsh, M.O. Saar, and D. Vogler, No-Flow Fraction (NFF) permeability model for rough fractures under normal stress, Water Resources Research, 57/3, 2021. https://doi.org/10.1029/2020WR029080 [Download] [View Abstract]Flow through rock fractures is frequently represented using models that correct the cubic law to account for the effects of roughness and contact area. However, the scope of such models is often restricted to relatively smooth aperture fields under small confining stresses. This work studies the link between fracture permeability and fracture geometry under normal loads. Numerical experiments are performed to deform synthesized aperture fields of various correlation lengths and roughness values under normal stress. The results demonstrate that aperture roughness can more than triple for applied stresses up to 50 MPa – exceeding the valid range for roughness in most previously published models. Investigating the relationship between permeability and contact area indicates that the increase in flow obstructions due to the development of new contact points strongly depends on the correlation length of the unloaded aperture field. This study eliminates these dependencies by employing a parameter known as the No-Flow Fraction (NFF) to capture the effect of stagnation zones. With this concept, a new Cubic-law-based permeability model is proposed that significantly improves the accuracy of permeability estimations, compared to previous models. For cases, where the NFF is difficult to obtain, we introduce an empirical relationship to estimate the parameter from the aperture roughness. The new models yield permeability estimates accurate to within a factor of two of the simulated permeability in over three quarters of the 3000 deformed fractures studied. This compares with typical deviations of at least one order of magnitude for previously published permeability models.
19.
Adams, B.M., D. Vogler, T.H. Kuehn, J.M. Bielicki, N. Garapati, and M.O. Saar, Heat Depletion in Sedimentary Basins and its Effect on the Design and Electric Power Output of CO2 Plume Geothermal (CPG) Systems, Renewable Energy, 172, pp. 1393-1403, 2021. https://doi.org/10.1016/j.renene.2020.11.145 [Download] [View Abstract]CO2 Plume Geothermal (CPG) energy systems circulate geologically stored CO2 to extract geothermal heat from naturally permeable sedimentary basins. CPG systems can generate more electricity than brine systems in geologic reservoirs with moderate temperature and permeability. Here, we numerically simulate the temperature depletion of a sedimentary basin and find the corresponding CPG electricity generation variation over time. We find that for a given reservoir depth, temperature, thickness, permeability, and well configuration, an optimal well spacing provides the largest average electric generation over the reservoir lifetime. If wells are spaced closer than optimal, higher peak electricity is generated, but the reservoir heat depletes more quickly. If wells are spaced greater than optimal, reservoirs maintain heat longer but have higher resistance to flow and thus lower peak electricity is generated. Additionally, spacing the wells 10% greater than optimal affects electricity generation less than spacing wells 10% closer than optimal. Our simulations also show that for a 300 m thick reservoir, a 707 m well spacing provides consistent electricity over 50 years, whereas a 300 m well spacing yields large heat and electricity reductions over time. Finally, increasing injection or production well pipe diameters does not necessarily increase average electric generation.
18.
Lima, M., P. Schädle, C. Green, D. Vogler, M.O. Saar, and X.-Z. Kong, Permeability Impairment and Salt Precipitation Patterns during CO2 Injection into Single Natural Brine-filled Fractures, Water Resources Research, 56/8, pp. e2020WR027213, 2020. https://doi.org/10.1029/2020WR027213 [Download] [View Abstract]Formation dry-out in fracture-dominated geological reservoirs may alter the fracture space, impair rock absolute permeability and cause a significant decrease in well injectivity. In this study, we numerically model the dry-out processes occurring during supercritical CO2 (scCO2) injection into single brine-filled fractures and evaluate the potential for salt precipitation under increasing effective normal stresses in the evaporative regime. We use an open-source, parallel finite-element framework to numerically model two-phase flow through 2-Dimensional fracture planes with aperture fields taken from naturally fractured granite cores at the Grimsel Test Site in Switzerland. Our results reveal a displacement front and a subsequent dry-out front in all simulated scenarios, where higher effective stresses caused more flow channeling, higher rates of water evaporation and larger volumes of salt precipitates. However, despite the larger salt volumes, the permeability impairment was lower at higher effective normal stresses. We conclude that the spatial distribution of the salt, precipitated in fractures with heterogeneous aperture fields, strongly affects the absolute permeability impairment caused by formation dry-out. The numerical simulations assist in understanding the behavior of the injectivity in fractures and fracture networks during subsurface applications that involve scCO2 injection into brine.
17.
Vogler, D., S.D.C. Walsh, and M.O. Saar, A Numerical Investigation into Key Factors Controlling Hard Rock Excavation via Electropulse Stimulation, Journal of Rock Mechanics and Geotechnical Engineering, 12/4, pp. 793-801, 2020. https://doi.org/10.1016/j.jrmge.2020.02.002 [Download] [View Abstract]Electropulse stimulation provides an energy-efficient means of excavating hard rocks through repeated application of high voltage pulses to the rock surface. As such, it has the potential to confer significant advantages to mining and drilling operations for mineral and energy resources. Nevertheless, before these benefits can be realized, a better understanding of these processes is required to improve their deployment in the field.
In this paper, we employ a recently developed model of the grain-scale processes involved in electropulse stimulation to examine excavation of hard rock under realistic operating conditions. To that end, we investigate the maximum applied voltage within ranges of 120~kV to 600~kV, to observe the onset of rock fragmentation. We further study the effect of grain size on rock breakage, by comparing fine and coarse grained rocks modeled after granodiorite and granite, respectively. Lastly, the pore fluid salinity is investigated, since the electric conductivity of the pore fluid is shown to be a governing factor for the electrical conductivity of the system. This study demonstrates that all investigated factors are crucial to the efficiency of rock fragmentation by electropulsing.
16.
Vogler, D., S.D.C. Walsh, Ph. Rudolf von Rohr, and M.O. Saar, Simulation of rock failure modes in thermal spallation drilling, Acta Geotechnica, 15/8, pp. 2327-2340, 2020. https://doi.org/10.1007/s11440-020-00927-7 [Download] [View Abstract]Thermal spallation drilling is a contact-less means of borehole excavation that works by exposing a rock surface to a high-temperature jet flame. In this study, we investigate crucial factors for the success of such thermal drilling operations using numerical simulations of the thermomechanical processes leading to rock failure at the borehole surface. To that end, we integrate a model developed for spalling failure with our thermomechanical simulations. In particular, we consider the role of material heterogeneities, maximum jet-flame temperature and maximum jet-flame temperature rise time on the onset of inelastic deformation and subsequent damage. We further investigate differences in energy consumption for the studied system configurations. The simulations highlight the importance of material composition, as thermal spallation is favored in fine-grained material with strong material heterogeneity. The model is used to test the relationship between the jet-flame temperature and the onset of thermal spallation.
15.
von Planta, C., D. Vogler, P. Zulian, M.O. Saar, and R. Krause, Contact between rough rock surfaces using a dual mortar method, International Journal of Rock Mechanics and Mining Sciences (IJRMMS), 133, pp. 104414, 2020. https://doi.org/10.1016/j.ijrmms.2020.104414 [Download] [View Abstract]The mechanical behavior of fractures in rocks has strong implications for reser- voir engineering applications. Deformations, and the corresponding change in contact area and aperture field, impact rock fracture stiffness and permeability, thus altering the reservoir properties significantly. Simulating contact between fractures is numerically difficult as the non-penetration constraints lead to a nonlinear problem and the surface meshes of the solid bodies on the opposing fracture sides may be non-matching. Furthermore, due to the complex geome- try, the non-penetration constraints must be updated throughout the solution procedure. Here we present a novel implementation of a dual mortar method for contact. It uses a non-smooth sequential quadratic programming method as solver, and is suitable for parallel computing. We apply it to a two body con- tact problem consisting of realistic rock fracture geometries from the Grimsel underground laboratory in Switzerland. The contributions of this article are: 1) a novel, parallel implementation of a dual mortar and non-smooth sequential quadratic programming method, 2) realistic rock geometries with rough sur- faces, and 3) numerical examples, which prove that the dual mortar method is capable of replicating the nonlinear closure behavior of fractures observed in laboratory experiments.
14.
von Planta, C., D. Vogler, X. Chen, M.G.C. Nestola, M.O. Saar, and R. Krause, Modelling of hydro-mechanical processes in heterogeneous fracture intersections using a fictitious domain method with variational transfer operators, Computational Geosciences, 2020. https://doi.org/10.1007/s10596-020-09936-7 [Download] [View Abstract]Fluid flow in rough fractures and the coupling with the mechanical behavior of the
fractures pose great difficulties for numerical modeling approaches, due to complex
fracture surface topographies, the non-linearity of hydromechanical processes and
their tightly coupled nature. To this end, we have adapted a fictitious domain method to
enable the simulation of hydromechanical processes in fracture-intersections. The
main characteristic of the method is the immersion of the fracture domain, modelled as
a linear elastic solid, in the surrounding fluid, modelled with the incompressible Navier
Stokes equations. The fluid and the solid problems are coupled with variational transfer
operators. Variational transfer operators are also used to solve contact within the
fracture using a mortar approach and to generate problem specific fluid grids. With
respect to our applications, the key features of the method are the usage of different
finite element discretizations for the solid and the fluid problem and the automatically
generated representation of the fluid-solid boundary.
We demonstrate that the presented methodology resolves small-scale roughness on
the fracture surface, while capturing fluid flow field changes during mechanical loading.
Starting with 2D/3D benchmark simulations of intersected fractures, we end with an
intersected fracture composed of complex fracture surface topographies, which are in
contact under increasing loads. The contributions of this article are: (1) the application
of the fictitious domain method to study flow in fractures with intersections, (2) a
mortar based contact solver for the solid problem, (3) generation of problem specific
grids using the geometry information from the variational transfer operators.
13.
Walsh, S.D.C., and D. Vogler, Simulating Electropulse Fracture of Granitic Rock, International Journal of Rock Mechanics and Mining Sciences, 128, pp. 104238, 2020. https://doi.org/10.1016/j.ijrmms.2020.104238 [Download] [View Abstract]Electropulse treatments employ a series of high-voltage discharges to break rock into small fragments. As these methods are particularly suited to fracturing hard brittle rocks, electropulse treatments can serve to enhance or substitute for more traditional mechanical approaches to drilling and processing of these materials. Nevertheless, while these treatments have the potential to improve hard-rock operations, the coupled electro-mechanical processes responsible for damaging the rock are poorly described. The lack of accurate models for these processes increases the difficulty of designing, controlling and optimizing tools that employ electropulse treatments and limits their range of application.
This paper describes a new modeling method for studying electropulse treatments in geotechnical operations. The multiphysics model simulates the passage of the pulse, electrical breakdown in the rock, and the mechanical response at the grain-scale. It also accounts for the contributions from different minerals and porosities, allowing the effect of material composition to be considered. In so doing, it provides a means to investigate the different physical and operational factors influencing electropulse treatments.
12.
Perras, M.A., and D. Vogler, Compressive and Tensile Behavior of 3D-Printed and Natural Sandstones, Transport in Porous Media, 129/2, pp. 559-581, 2019. https://doi.org/10.1007/s11242-018-1153-8 [Download] [View Abstract]The presented work compares the mechanical behavior from standard unconfined compressive strength and indirect tensile strength tests of natural sandstone and artificial sand-based specimens created by 3D additive manufacturing. Three natural sandstones of varying strength and stiffness were tested to capture a wide range of behavior for comparison with the 3D-printed specimens. Sand grains with furan and silicate binders, as well as, ceramic beads with silicate binder were 3D-printed by commercial suppliers.
The tensile and compressive strength, the stiffness, the crack initiation and the crack damage thresholds and the strain behavior were examined to determine if the mechanical behavior of the 3D-printed specimens is similar to natural sandstones. The Sand-Furan 3D-prints behaved the closest to the weak natural sandstone. The compressive strength to stiffness ratio, also known as the modulus ratio, and the compressive to tensile strength ratio of the 3D-printed Sand-Furan specimens were found to be similar to the natural sandstones tested in this study and literature values. The failed specimens composed of ceramic beads with silicate binder, both in compression and tension, showed fracture growth not commonly observed in natural specimens. The other 3D-printed specimens generally fractured in a similar manner to natural specimens, although several of the quartz sand with furan binder specimens showed fracturing behavior similar to high porosity natural specimens. Over all, using the commercially available quartz sand with furan binder 3D-print materials showed promise to be able to replicate natural rock specimen behavior.
11.
von Planta, C., D. Vogler, X. Chen, M.G.C. Nestola, M.O. Saar, and R. Krause, Simulation of hydro-mechanically coupled processes in rough rock fractures using an immersed boundary method and variational transfer operators, Computational Geosciences, 23/5, pp. 1125-1140, 2019. https://doi.org/10.1007/s10596-019-09873-0 [Download] [View Abstract]Hydro-mechanical processes in rough fractures are highly non-linear and govern productivity and associated risks in a wide range of reservoir engineering problems. To enable high-resolution simulations of hydro-mechanical processes in fractures, we present an adaptation of an immersed boundary method to compute fluid flow between rough fracture surfaces. The solid domain is immersed into the fluid domain and both domains are coupled by means of variational volumetric transfer operators. The transfer operators implicitly resolve the boundary between the solid and the fluid, which simplifies the setup of fracture simulations with complex surfaces. It is possible to choose different formulations and discretization schemes for each subproblem and it is not necessary to remesh the fluid grid. We use benchmark problems and real fracture geometries to demonstrate the following capabilities of the presented approach: (1) resolving the boundary of the rough fracture surface in the fluid; (2) capturing fluid flow field changes in a fracture which closes under increasing normal load; and (3) simulating the opening of a fracture due to increased fluid pressure.
10.
Lima, M.M., D. Vogler, L. Querci, C. Madonna, B. Hattendorf, M.O. Saar, and X.-Z. Kong, Thermally driven fracture aperture variation in naturally fractured granites, Geothermal Energy Journal, 7/1, pp. 1-23, 2019. https://doi.org/10.1186/s40517-019-0140-9 [Download] [View Abstract]Temperature variations often trigger coupled thermal, hydrological, mechanical, and chemical (THMC) processes that can significantly alter the permeability/impedance of fracture-dominated deep geological reservoirs. It is thus necessary to quantitatively explore the associated phenomena during fracture opening and closure as a result of temperature change. In this work, we report near-field experimental results of the effect of temperature on the hydraulic properties of natural fractures under stressed conditions (effective normal stresses of 5-25 MPa). Two specimens of naturally fractured granodiorite cores from the Grimsel Test Site in Switzerland were subjected to flow-through experiments with a temperature variation of 25-140 °C to characterize the evolution of fracture aperture/permeability. The fracture surfaces of the studied specimens were morphologically characterized using photogrammetry scanning. Periodic measurements of the efflux of dissolved minerals yield the net removal mass, which is correlated to the observed rates of fracture closure. Changes measured in hydraulic aperture are significant, exhibiting reductions of 20-75 % over the heating/cooling cycles. Under higher confining stresses, the effects in fracture permeability are irreversible and notably time-dependent. Thermally driven fracture aperture variation was more pronounced in the specimen with the largest mean aperture width and spatial correlation length. Gradual fracture compaction is likely controlled by thermal dilation, mechanical grinding, and pressure dissolution due to increased thermal stresses exerted over the contacting asperities, as confirmed by the analyses of hydraulic properties and efflux mass.
9.
Schädle, P., P. Zulian, D. Vogler, S. Bhopalam R., M.G.C. Nestola, A. Ebigbo, R. Krause, and M.O. Saar, 3D non-conforming mesh model for flow in fractured porous media using Lagrange multipliers, Computers & Geosciences, 132, pp. 42-55, 2019. https://doi.org/10.1016/j.cageo.2019.06.014 [Download] [View Abstract]This work presents a modeling approach for single-phase flow in 3D fractured porous media with non-conforming meshes. To this end, a Lagrange multiplier method is combined with a parallel variational transfer approach. This Lagrange multiplier method enables the use of non-conforming meshes and depicts the variable coupling between fracture and matrix domain. The variational transfer allows general, accurate, and parallel projection of variables between non-conforming meshes (i.e. between fracture and matrix domain). Comparisons of simulations with 2D benchmarks show good agreement, and the applied finite element Lagrange multiplier spaces show good performance. The method is further evaluated on 3D fracture networks by comparing it to results from conforming mesh simulations which were used as a reference. Application to realistic fracture networks with hundreds of fractures is demonstrated. Mesh size and mesh convergence are investigated for benchmark cases and 3D fracture network applications. Results demonstrate that the Lagrange multiplier method, in combination with the variational transfer approach, is capable of modeling single-phase flow through realistic 3D fracture networks.
8.
Dambly, M.L.T., M. Nejati, D. Vogler, and M.O. Saar, On the direct measurement of shear moduli in transversely isotropic rocks using the uniaxial compression test, International Journal of Rock Mechanics and Mining Sciences (IJRMMS), 113, pp. 220-240, 2019. https://doi.org/10.1016/j.ijrmms.2018.10.025 [Download] [View Abstract]This paper introduces a methodology for the direct determination of the shear moduli in transversely isotropic rocks, using a single test, where a cylindrical specimen is subjected to uniaxial compression. A method is also developed to determine the orientation of the isotropy plane as well as the dynamic elastic constants using ultrasonic measurements on a single cylindrical specimen. Explicit formulae are developed to calculate the shear moduli from strain gauge measurements at different polar angles. The calculation of shear moduli from these formulae requires no knowledge about Young's moduli or Poisson's ratios and depends only on the orientation of the isotropy plane. Several strain gauge setups are designed to obtain the shear moduli from different numbers and arrangements of strain gauges. We demonstrate, that the shear moduli can be determined accurately and efficiently with only three strain gauge measurements. The orientation of the isotropy plane is measured with different methods, including ultrasonic measurements. The results show, that the isotropy plane of the tested granitic samples slightly deviates from the foliation plane. However, the foliation plane can still determine the orientation of the isotropy plane with a good approximation.
7.
Vogler, D., S. Ostvar, R. Paustian, and B.D. Wood, A Hierarchy of Models for Simulating Experimental Results from a 3D Heterogeneous Porous Medium, Advances in Water Resources, 114, pp. 149-163, 2018. https://doi.org/10.1016/j.advwatres.2018.02.009 [Download] [View Abstract]In this work we examine the dispersion of conservative tracers (bromide and fluorescein) in an experimentally-constructed three-dimensional dual-porosity porous medium. The medium is highly heterogeneous ($\sigma_Y^2=5.7$), and consists of spherical, low-hydraulic-conductivity inclusions embedded in a high-hydraulic-conductivity matrix. The bi-modal medium was saturated with tracers, and then flushed with tracer-free fluid while the effluent breakthrough curves were measured. The focus for this work is to examine a hierarchy of four models (in the absence of adjustable parameters) with decreasing complexity to assess their ability to accurately represent the measured breakthrough curves. The most information-rich model was (1) a direct numerical simulation of the system in which the geometry, boundary and initial conditions, and medium properties were fully independently characterized experimentally with high fidelity. The reduced models included; (2) a simplified numerical model identical to the fully-resolved direct numerical simulation (DNS) model, but using a domain that was one-tenth the size; (3) an upscaled mobile-immobile model that allowed for a time-dependent mass-transfer coefficient; and, (4) an upscaled mobile-immobile model that assumed a space-time constant mass-transfer coefficient. The results illustrated that all four models provided accurate representations of the experimental breakthrough curves as measured by global RMS error. The primary component of error induced in the upscaled models appeared to arise from the neglect of convection within the inclusions. We discuss the necessity to assign value (via a utility function or other similar method) to outcomes if one is to further select from among model options. Interestingly, these results suggested that the conventional convection-dispersion equation, when applied in a way that resolves the heterogeneities, yields models with high fidelity without requiring the imposition of a more complex non-Fickian model.
6.
Vogler, D., R. R. Settgast, C. Annavarapu, C. Madonna, P. Bayer, and F. Amann, Experiments and Simulations of Fully Hydro-Mechanically coupled Response of Rough Fractures exposed to High Pressure Fluid Injection, Journal of Geophysical Research: Solid Earth, 123, pp. 1186-1200, 2018. https://doi.org/10.1002/2017JB015057 [Download] [View Abstract]In this work, we present the application of a fully-coupled hydro-mechanical method to investigate the effect of fracture heterogeneity on fluid flow through fractures at the laboratory scale. Experimental and numerical studies of fracture closure behavior in the presence of heterogeneous mechanical and hydraulic properties are presented. We compare the results of two sets of laboratory experiments on granodiorite specimens against numerical simulations in order to investigate the mechanical fracture closure and the hydro-mechanical effects, respectively.
The model captures fracture closure behavior and predicts a non-linear increase in fluid injection pressure with loading. Results from this study indicate that the heterogeneous aperture distributions measured for experiment specimens can be used as model input for a local cubic law model in a heterogeneous fracture to capture fracture closure behavior and corresponding fluid pressure response.
5.
Kling, T., D. Vogler, L. Pastewka, F. Amann, and P. Blum, Numerical simulations and validation of contact mechanics in a granodiorite fracture, Rock Mechanics and Rock Engineering, 51/9, pp. 2805-2824, 2018. https://doi.org/10.1007/s00603-018-1498-x [Download] [View Abstract]Numerous rock engineering applications require a reliable estimation of fracture permeabilities to predict fluid flow and transport processes. Since measurements of fracture properties at great depth are extremely elaborate, representative fracture geometries typically are obtained from outcrops or core drillings. Thus, physically valid numerical approaches are required to compute the actual fracture geometries under in situ stress conditions. Hence, the objective of this study is the validation of a fast Fourier transform (FFT)-based numerical approach for a circular granodiorite fracture considering stress-dependent normal closure. The numerical approach employs both purely elastic and elastic--plastic contact deformation models, which are based on high-resolution fracture scans and representative mechanical properties, which were measured in laboratory experiments. The numerical approaches are validated by comparing the simulated results with uniaxial laboratory tests. The normal stresses applied in the axial direction of the cylindrical specimen vary between 0.25 and 10 MPa. The simulations indicate the best performance for the elastic--plastic model, which fits well with experimentally derived normal closure data (root-mean-squared error $=9 \mu m$). The validity of the elastic--plastic model is emphasized by a more realistic reproduction of aperture distributions, local stresses and contact areas along the fracture. Although there are differences in simulated closure for the elastic and elastic--plastic models, only slight differences in the resulting aperture distributions are observed. In contrast to alternative interpenetration models or analytical models such as the Barton--Bandis models and the ''exponential repulsion model'', the numerical simulations reproduce heterogeneous local closure as well as low-contact areas (<2\%) even at high normal stresses (10 MPa), which coincides with findings of former experimental studies. Additionally, a relative hardness value of 0.14 for granitic rocks, which defines the general resistance to non-elastic deformation of the contacts, is introduced and successfully applied for the elastic--plastic model.
4.
Hobé, A., D. Vogler, M.P. Seybold, A. Ebigbo, R.R. Settgast, and M.O. Saar, Estimating Fluid Flow Rates through Fracture Networks using Combinatorial Optimization, Advances in Water Resources, 122, pp. 85-97, 2018. https://doi.org/10.1016/j.advwatres.2018.10.002 [Download] [View Abstract]To enable fast uncertainty quantification of fluid flow in a discrete fracture network (DFN), we present two approaches to quickly compute fluid flow in DFNs using combinatorial optimization algorithms. Specifically, the presented Hanan Shortest Path Maxflow (HSPM) and Intersection Shortest Path Maxflow (ISPM) methods translate DFN geometries and properties to a graph on which a max flow algorithm computes a combinatorial flow, from which an overall fluid flow rate is estimated using a shortest path decomposition of this flow. The two approaches are assessed by comparing their predictions with results from explicit numerical simulations of simple test cases as well as stochastic DFN realizations covering a range of fracture densities. Both methods have a high accuracy and very low computational cost, which can facilitate much-needed in-depth analyses of the propagation of uncertainty in fracture and fracture-network properties to fluid flow rates.
3.
Vogler, D., S.D.C. Walsh, E. Dombrovski, and M.A. Perras, A Comparison of Tensile Failure in 3D-Printed and Natural Sandstone, Engineering Geology, 226, pp. 221-235, 2017. https://doi.org/10.1016/j.enggeo.2017.06.011 [Download] [View Abstract]This work investigates the possibility of replication of natural rock specimens, which can be used to analyze rock mechanical behavior by subjecting a number of identical specimens to tensile tests and a variety of analysis methods. We compare the properties of fractures generated in artificial sandstone specimens to those generated in natural sandstone specimens. Artificial sandstone specimens, created using 3D additive manufacturing printing processes, were subject to tensile failure using the Brazilian test method and the results from these tests were compared to results from Brazilian tests conducted on natural sandstones. The specimens included two distinct types of synthetic rock, unaltered from the manufacturers typical process, and three natural sandstones. For each test, the loading history to failure of the specimens were recorded and the failure mode was confirmed using digital imaging techniques. In addition, three dimensional images were taken of the fracture surfaces, which were then used to compare the geometric characteristics of all materials tested. The indirect tensile strength of the artificial sandstone specimens ranged between 1.0 and 2.8 MPa. Natural sandstone specimens with a wide range of indirect tensile strengths were tested for comparison. These included a strong sandstone, an intermediate sandstone, and a weak sandstone; which were found to have indirect tensile strength ranges of 10.5-25.5 MPa, 4.4-6.4 MPa, and 0.9-1.1 MPa, respectively. Digital image correlation confirmed that the artificial specimens generally failed in a tensile (mode I) fracture, similar to the natural specimens. Likewise, fracture surface roughness measures showed no clear distinction between weak natural and artificial sandstones. This indicates that there are distinct similarities between the fractures generated in the natural and artificial sandstones of comparable indirect tensile strengths. The three dimensionally printed sandstone specimens are shown to exhibit indirect tensile strength, surface roughness and crack propagation behavior which resembles a weak natural sandstone.
2.
Vogler, D., S.D.C. Walsh, P. Bayer, and F. Amann, Comparison of Surface Properties in Natural and Artificially Generated Fractures in a Crystalline Rock, Rock Mechanics and Rock Engineering, 50/11, pp. 2891-2909, 2017. https://doi.org/10.1007/s00603-017-1281-4 [Download] [View Abstract]This work studies the roughness characteristics of fracture surfaces from a crystalline rock by analyzing differences in surface roughness between fractures of various types and sizes. We compare the surface properties of natural fractures sampled in situ and artificial (i.e., man-made) fractures created in the same source rock under laboratory conditions. The topography of the various fracture types is compared and characterized using a range of different measures of surface roughness. Both natural and artificial, and tensile and shear fractures are considered, along with the effects of specimen size on both the geometry of the fracture and its surface characterization. The analysis shows that fracture characteristics are substantially different between natural shear and artificial tensile fractures, while natural tensile fracture often spans the whole result domain of the two other fracture types. Specimen size effects are also evident, not only as scale sensitivity in the roughness metrics, but also as a by-product of the physical processes used to generate the fractures. Results from fractures generated with Brazilian tests show that fracture roughness at small scales differentiates fractures from different specimen sizes and stresses at failure.
1.
Vogler, D., F. Amann, P. Bayer, and D. Elsworth, Permeability Evolution in Natural Fractures Subject to Cyclic Loading and Gouge Formation, Rock Mechanics and Rock Engineering, 49/9, pp. 3463-3479, 2016. https://doi.org/10.1007/s00603-016-1022-0 [Download] [View Abstract]Increasing fracture aperture by lowering effective normal stress and by inducing dilatant shearing and thermo-elastic effects is essential for transmissivity increase in enhanced geothermal systems. This study investigates transmissivity evolution for fluid flow through natural fractures in granodiorite at the laboratory scale. Processes that influence transmissivity are changing normal loads, surface deformation, the formation of gouge and fracture offset. Normal loads were varied in cycles between 1 and 68 MPa and cause transmissivity changes of up to three orders of magnitude. Similarly, small offsets of fracture surfaces of the order of millimeters induced changes in transmissivity of up to three orders of magnitude. During normal load cycling, the fractures experienced significant surface deformation, which did not lead to increased matedness for most experiments, especially for offset fractures. The resulting gouge material production may have caused clogging of the main fluid flow channels with progressing loading cycles, resulting in reductions of transmissivity by up to one order of magnitude. During one load cycle, from low to high normal loads, the majority of tests show hysteretic behavior of the transmissivity. This effect is stronger for early load cycles, most likely when surface deformation occurs, and becomes less pronounced in later cycles when asperities with low asperity strength failed. The influence of repeated load cycling on surface deformation is investigated by scanning the specimen surfaces before and after testing. This allows one to study asperity height distribution and surface deformation by evaluating the changes of the standard deviation of the height, distribution of asperities and matedness of the fractures. Surface roughness, as expressed by the standard deviation of the asperity height distribution, increased during testing. Specimen surfaces that were tested in a mated configuration were better mated after testing, than specimens tested in shear offset configuration. The fracture surface deformation of specimen surfaces that were tested in an offset configuration was dominated by the breaking of individual asperities and grains, which did not result in better mated surfaces.
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PROCEEDINGS REFEREED
10.
Walsh, S.D.C., T. Czaszejko, and D. Vogler, Electropulse stimulation of rock: insights from grain-scale experimental studies and numerical models, ISRM International Symposium - EUROCK 2020, pp. 1-8, 2020. [Download PDF] [View Abstract]Electropulse stimulation provides a means to fracture hard rocks into small fragments with the use of high-voltage electric pulses. As these techniques offer a frictionless method to break rock in tension, they have the potential to improve drilling, processing and excavation by reducing energy requirements and decreasing equipment wear. However, to date, descriptions of the processes involved in hard-rock electropulse stimulation remain largely empirical in nature - concentrating on the macroscopic effects of the electrical discharges, rather than their underlying causes.
Results from a recent series of experimental studies and associated numerical models investigating the effects of electropulse stimulation on hard rock at the grain scale are outlined in this paper. The effects of the electric pulse treatments on the rock microstructure and the nature of the fragmented particles produced are also described. These results are compared with numerical simulations that track the path and effect of the voltage pulse on the rock mass. The implications of these results on the performance of electropulse methods are discussed for a range of operating conditions and rock-types.
9.
Rossi, E., B. Adams, D. Vogler, Ph. Rudolf von Rohr, B. Kammermann, and M.O. Saar, Advanced drilling technologies to improve the economics of deep geo-resource utilization, Proceedings of Applied Energy Symposium: MIT A+B, United States, 2020 , 8, pp. 1-6, 2020. https://doi.org/10.3929/ethz-b-000445213 [Download] [View Abstract]Access to deep energy resources (geothermal energy, hydrocarbons) from deep reservoirs will play a fundamental role over the next decades. However, drilling of deep wells to extract deep geo-resources is extremely expensive. As a fact, drilling deep wells into hard, crystalline rocks represents a major challenge for conventional rotary drilling systems, featuring high rates of drill bit wear and requiring frequent drill bit replacements, low penetration rates and poor process efficiency. Therefore, with the aim of improving the overall economics to access deep geo-resources in hard rocks, in this work, we focus on two novel drilling methods, namely: the Combined Thermo-Mechanical Drilling (CTMD) and the Plasma-Pulse Geo-Drilling (PPGD) technologies. The goal of this research and development project is the effective reduction of the costs of drilling in general and particularly regarding accessing and using deep geothermal energy, oil or gas resources. In this work, we present these two novel drilling technologies and focus on evaluating the process efficiency and the drilling performance of these methods, compared to conventional rotary drilling.
8.
Hassanjanikhoshkroud, N., M.G.C. Nestola, P. Zulian, C. von Planta, D. Vogler, H. Köstler, and R. Krause, Thermo-Fluid-Structure Interaction Based on the Fictitious Domain Method: Application to Dry Rock Simulations, PROCEEDINGS, 45th Workshop on Geothermal Reservoir Engineering, pp. 1-12, 2020. [View Abstract]Enhanced Geothermal Systems(EGS) generate geothermal energy without the need for natural convective hydrothermal resources by enhancing permeability through hydraulic fracturing. EGS involve complex and highly nonlinear multiphysics processes and face several technical challenges that govern productivity and associated risks in a wide range of reservoir engineering problems.Numericalsimulations offer a unique opportunity to improve the hydraulic stimulation design and investigate their long-term performance. In this work, we present a thermo-hydro–mechanical coupling based on the fictitious domain method. Fictitious domain methodsinclude nonconforming mesh approaches that rely on the use of different discretizationsfor the solid and the fluid domain. We consider the governing equations of linear thermo-elasticity to model the heat transfer in dry and hot rocks.Navier-Stokes equations and heat convection equationsare adopted for describingthe thermal flux in an incompressible fluidflow. The two problems are coupled in a staggered manner through the variational transfer. Indeed, the use of the variational transfer allows simplifying the setup of fracture simulations with complex surfaces embedded in the fluid domain, thus avoiding the inconvenient mesh generation required bythe boundary fitted methods. The presented computational framework is validated by comparing with analytical solutions of two-dimensional benchmarks. Finally, we show that our framework provides high flexibility and cansimulatethe thermo-hydro–mechanical coupling between fluid and idealized fracture asperities.
7.
Lima, M., P. Schädle, D. Vogler, M. Saar, and X.-Z. Kong, A Numerical Model for Formation Dry-out During CO2 Injection in Fractured Reservoirs Using the MOOSE Framework: Implications for CO2-based Geothermal Energy Extraction, Proceedings of the World Geothermal Congress 2020, Reykjavík, Iceland, (in press). [View Abstract]Injection of supercritical carbon dioxide (scCO2) into geological reservoirs is involved in Carbon Capture, Utilization, and Storage (CCUS), such as geological CO2 storage, and Enhanced Geothermal Systems (EGS). The potential physico-chemical interactions between the dry scCO2, the reservoir fluid, and rocks may cause formation dry-out, where mineral precipitates due to continuous evaporation of water into the scCO2 stream. This salt precipitation may impair the rock bulk permeability and cause a significant decrease in the well injectivity. Formation dry-out and the associated salt precipitation during scCO2 injection into porous media have been investigated in previous studies by means of numerical simulations and laboratory experiments. However, few studies have focused on the dry-out effects in fractured rocks in particular, where the mass transport is strongly influenced by the fracture aperture distribution. In this study, we numerically model the dry-out processes occurring during scCO2 injection into brine-saturated single fractures and evaluate the potential of salt precipitation. Fracture aperture fields are photogrammetrically determined with fracture geometries of naturally fractured granite cores from the Deep Underground Geothermal (DUG) Lab at the Grimsel Test Site (GTS), in Switzerland. We use an open-source, parallel finite element framework to numerically model two-phase flow through a 2D fracture plane. Under in-situ reservoir conditions, the brine is displaced by dry scCO2 and also evaporates into the CO2 stream. The fracture permeability is calculated with the local cubic law. Additionally, we extend the numerical model by the Young-Laplace equation to determine the aperture-based capillary pressure. Finally, as future work, the precipitation of salt will be modelled by employing a uniform mineral growth approach, where the local aperture uniformly decreases with the increase in precipitated mineral volume. The numerical simulations assist in understanding the long-term behaviour of reservoir injectivity during subsurface applications that involve scCO2 injection, including CO2-based geothermal energy extraction.
6.
Lima, M.M., P. Schädle, D. Vogler, M.O. Saar, and X.-Z. Kong, Impact of Effective Normal Stress on Capillary Pressure in a Single Natural
Fracture, European Geothermal Congress 2019, pp. 1-9, 2019. [View Abstract]Multiphase fluid flow through rock fractures occurs in many reservoir applications such as geological CO2 storage, Enhanced Geothermal Systems (EGS), nuclear waste disposal, and oil and gas production. However, constitutional relations of capillary pressure versus
fluid saturation, particularly considering the change of fracture aperture distributions under various stress conditions, are poorly understood. In this study, we use fracture geometries of naturally-fractured granodiorite cores as input for numerical simulations of two-phase brine displacement by super critical CO 2 under various effective normal stress conditions. The aperture fields are first mapped via photogrammetry, and the effective normal stresses are applied by means of a Fast Fourier Transform (FFT)-based convolution numerical method. Throughout the simulations, the capillary pressure is evaluated from the local aperture. Two approaches to obtain the capillary pressure are used for comparison: either directly using the Young-Laplace equation, or the van Genuchten equation fitted from capillary pressure-saturation relations generated using the pore-occupancy model. Analyses of the resulting CO2 injection patterns and the breakthrough times enable investigation of the relationships between the effective normal stress, flow channelling and aperture-based capillary pressures. The obtained results assist the evaluation of two-phase flow through fractures in the context of various subsurface applications.
5.
von Planta, C., D. Vogler, M. Nestola, P. Zulian, and R. Krause, Variational Parallel Information Transfer between Unstructured Grids in Geophysics -
Applications and Solution Methods, PROCEEDINGS, 43rd Workshop on Geothermal Reservoir Engineering, pp. 1-13, 2018. [View Abstract]State of the art simulations of enhanced geothermal systems are multi-physics simulations, where different physical properties are often being modeled on different geometries or grids. For example, for the simulation of fluids many prefer finite difference or volume formulations on structured grids, whereas in mechanics finite element formulations on unstructured grids are often preferred. To transfer information between these various geometries, we use a generic variational transfer operator, which has previously been introduced as pseudo-L2-projection. In this paper, we demonstrate that this transfer operator can be particularly useful for geophysics with three applications: First, in contact
simulations we often have non-matching surfaces at the contact boundary. Here, the transfer operator acts as a mortar projection and we show with high resolution rock fracture geometries from the Grimsel Test Site in Switzerland how the variational transfer operator is used to formulate the contact problem. Secondly, we present a three-dimensional fluid-structure simulation, computing water flow between two rock surfaces and simultaneous deformation with an immersed boundary approach. In this method the solid, which is formulated on an unstructured grid, interacts with the fluid, formulated on a structured grid, by means of weakly enforced velocity constraints at the interface between fluid and solid. And lastly, we show how the transfer operator can be used to effectively solve contact problem between rock bodies. Using our operator, we can generate nested multilevel hierarchies, enabling us to solve the problem with optimal complexity, thus extending the possible size of simulations immensely.
4.
von Planta, C., D. Vogler, X. Chen, M.G.C. Nestola, M.O. Saar, and R. Krause, Fluid-structure interaction with a parallel transfer operators to model hydro-mechanical processes in heterogeneous fractures, International Conference on Coupled Processes in Fractured Geological Media (CouFrac 2018), pp. 1-4, 2018. [View Abstract]Contact mechanics and fluid flow in rough fractures are actively researched topics in reservoir
engineering (e.g., enhanced geothermal systems, CO2 sequestration and oil- and gas-extraction) to
estimate reservoir productivity or leak-off. Mechanical and fluid flow processes in reservoirs are often
tightly coupled and exhibit a strongly non-linear behavior. Understanding hydro-mechanically
coupled behavior in fractures is complicated further by highly variable fracture geometries [3, 4]. We
present a simulation approach for hydro-mechanical processes in rough fracture geometries with
variational parallel transfer operators. The contact problem at the boundary between the two rough
fracture surfaces is solved using a finite element formulation of linear elasticity on an unstructured mesh. The contact formulation uses a mortar method with Lagrange multipliers and does not use a penalty parameter or other regularizations. For the Navier-Stokes formulation of the fluid we use a finite element formulation on a structured grid. Information between the meshes is transferred via the variational transfer operators, whereby the solid interacts with the fluid by enforcing velocity constraints at the solid-fluid interface and the fluid interacts with the solid by converting the fluid velocity into a pressure force acting on the solid.
3.
Deb, P., D. Vogler, S. Dueber, P. Siebert, S. Reiche, C. Clauser, R.R. Settgast, and K. Willbrand, Laboratory Fracking Experiments for Verifying Numerical Simulation Codes, 80th EAGE Conference and Exhibition, pp. 1-4, 2018. https://doi.org/10.3997/2214-4609.201801166 [Download] [View Abstract]Carefully designed and well monitored experiments are irreplaceable when it comes to producing reliable data sets for a detailed understanding of physical processes, such as hydraulic fracturing. While such experiments provide insight into the governing physical processes, numerical simulations provide additional information on system behaviour by enabling a straightforward study of parameter sensitivity. In this study, we focus on both these aspects. We report on results from (1) a benchmark experimental facility for performing hydraulic fracturing experiments on large rock samples in the laboratory under controlled conditions and (2) numerical simulations of these experiments using programs, which, in future, may be used for designing hydraulic stimulation layouts. We conduct series of experiments in order to ensure reproducibility and accuracy of the measurements. This experimental data set is then shared with several research institutes to be used for verifying their simulation software. Results from the simulation provide further insight regarding parameters, which contribute to uncertainties during measurements. Detailed study of the sensitive parameters help us to improve our experimental set up further and to perform future experiments under even better controlled conditions.
2.
Vogler, D., R.R. Settgast, C.S. Sherman, V.S. Gischig, R. Jalali, J.A. Doetsch, B. Valley, K.F. Evans, F. Amann, and M.O. Saar, Modeling the Hydraulic Fracture Stimulation performed for Reservoir Permeability Enhancement at the Grimsel Test Site, Switzerland, Proc. of the 42nd Workshop on Geothermal Reservoir Engineering, Stanford University Stanford, CA, USA, February 13-15, 2017, Proceedings of the 42nd Workshop on Geothermal Reservoir Engineering Stanford University, 2017. [Download PDF] [View Abstract]In-situ hydraulic fracturing has been performed on the decameter scale in the Deep Underground rock Laboratory (DUG Lab) at the Grimsel Test Site (GTS) in Switzerland in order to measure the minimum principal stress magnitude and orientation. Conducted tests were performed in a number of boreholes, with 3–4 packer intervals in each borehole subjected to repeated injection. During each test, fluid injection pressure, injection flow rate and microseismic events were recorded amongst others. Fully coupled 3D simulations have been performed with the LLNL's GEOS simulation framework. The methods applied in the simulation of the experiments address physical processes such as rock deformation/stress, LEFM fracture mechanics, fluid flow in the fracture and matrix, and the generation of micro-seismic events. This allows to estimate the distance of fracture penetration during the injection phase and correlate the simulated injection pressure with experimental data during injection, as well as post shut-in. Additionally, the extent of the fracture resulting from simulations of fracture propagation and microseismic events are compared with the spatial distribution of the microseismic events recorded in the experiment.
1.
Vogler, D., R. Settgast, C. Annavarapu, P. Bayer, and F. Amann, Hydro-Mechanically Coupled Flow through Heterogeneous Fractures, Proc. of the 41st Workshop on Geothermal Reservoir Engineering Stanford University pp. SGP-TR-209 Stanford, CA, USA, February 13-15, 2017, Proceedings of the 41st Workshop on Geothermal Reservoir Engineering Stanford University, pp. SGP-TR-209, 2016. [Download PDF] [View Abstract]Heterogeneous aperture distributions are an intrinsic characteristic of natural fractures. The presence of highly heterogeneous aperture distributions can lead to flow channeling, thus influencing the macroscopic behavior of the fluid flow. High-fidelity numerical simulation tools are needed for realistic simulation of fracture flow when such features are present. Here, focus is set on the role of mechanical fracture closure for fluid flow and appropriate simulation by a fully hydro-mechanically (HM) coupled numerical model. In a laboratory experiment, an artificial fracture in a granodiorite sample is created. During different sequential loading cycles, the development of fracture closure, contact area and contact stress are examined. Constant fluid flow rate injection into the center of the rough fracture is modelled to investigate the impact of fracture closure on the flow field and injection pressure. Results show that the numerical framework for heterogeneous fracture surfaces allows for reproducing experimental data of dry, mechanical tests at the laboratory scale, and it may offer advanced understanding and prediction of the behavior of reservoirs that are subject to high-pressure fluid injections.
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PROCEEDINGS NON-REFEREED
4.
Ezzat, M., J. Börner, D. Vogler, V. Wittig, B. Kammermann, J. Biela, and M. O. Saar, Lithostatic Pressure Effects on the Plasma-Pulse Geo-Drilling (PPGD), 48 EPS Conference on Plasma Physics , 2022. https://doi.org/10.3929/ethz-b-000568862 [Download] [View Abstract]Drilling cost is one of the main challenges facing the utilization of deep closed-loop geothermal systems, so-called Advanced Geothermal Systems (AGS). Plasma-Pulse GeoDrilling (PPGD) is a novel drilling technology that uses high-voltage electric pulses to damage the rock without mechanical abrasion. PPGD may reduce the drilling costs significantly compared to mechanical rotary drilling, according to a comparative analysis that assumes ambient operating conditions. However, the level of performance of PPGD under deep wellbore conditions of higher pressures and temperatures is still ambiguous. Therefore, this contribution presents preliminary experiment results from the laboratory that investigate the effect of high lithostatic pressures of up to 150 MPa, equivalent to a depth of ∼5.7 km, on the performance of PPGD.
3.
Lima, M.M.G., Ph. Schädle, D. Vogler, M.O. Saar, and X. Xiang-Zhao, Impact of Effective Normal Stress on Capillary Pressure in a Single Natural Fracture, European Geothermal Congress, The Hague, Netherlands, 11-14 June 2019, 2019.
2.
von Planta, C., D. Vogler, M. Nestola, P. Zulian, and R. Krause, Variational Parallel Information Transfer between Unstructured Grids in Geophysics - Applications and Solutions Methods, PROCEEDINGS, 43rd Workshop on Geothermal Reservoir Engineering Stanford University, Feb. 12-14, 2018, 2018. [View Abstract]State of the art simulations of enhanced geothermal systems are multi-physics simulations, where different physical properties are often being modeled on different geometries or grids. For example, for the simulation of fluids many prefer finite difference or volume formulations on structured grids, whereas in mechanics finite element formulations on unstructured grids are often preferred. To transfer information between these various geometries, we use a generic variational transfer operator, which has previously been introduced as pseudo-L2-projection. In this paper, we demonstrate that this transfer operator can be particularly useful for geophysics with three applications: First, in contact simulations we often have non-matching surfaces at the contact boundary. Here, the transfer operator acts as a mortar projection and we show with high resolution rock fracture geometries from the Grimsel Test Site in Switzerland how the variational transfer operator is used to formulate the contact problem. Secondly, we present a three-dimensional fluid-structure simulation, computing water flow between two rock surfaces and simultaneous deformation with an immersed boundary approach. In this method the solid, which is formulated on an unstructured grid, interacts with the fluid, formulated on a structured grid, by means of weakly enforced velocity constraints at the interface between fluid and solid. And lastly, we show how the transfer operator can be used to effectively solve contact problem between rock bodies. Using our operator, we can generate nested multilevel hierarchies, enabling us to solve the problem with optimal complexity, thus extending the possible size of simulations immensely.
1.
Vogler, D., R.R. Settgast, C.S. Sherman, V.S. Gischig, J.A. Doetsch, M.R. Jalali, B. Valley, K.F. Evans, M.O. Saar, and F. Amann, Comparing Simulations and Experiments for Hydraulic Fracture Stimulations Performed at the Grimsel Test Site, Switzerland, Proc. of the 42nd Stanford Geothermal Workshop Palo Alto, CA, USA, February 13-15, 2017, 2017.
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THESES
3.
Vogler, D., Hydro-mechanically coupled processes in heterogeneous fractures: experiments and numerical simulations, Dissertation, ETH Zurich, 169 pp., 2016. [Download PDF] [View Abstract]Enhanced Geothermal Systems (EGS), CO2-sequestration, oil- and gas reservoirs rely on an in-depth understanding of geomechanics and fluid flow in the subsurface to achieve production targets. In Switzerland, EGS are commonly targeted for deep basement formations of crystalline rock, as these are deep enough underground to provide high temperatures. In crystalline rock, fluid flow through fractures dominates transport processes, while mechanical behavior strongly depends on fracture topography and strength. This work focusses on fracture behavior in crystalline rock, such as granite and granodiorite, by investigating: (1) Differences in fracture topography linked to fracture size and nature; (2) Hydromechanically coupled processes in heterogeneous fractures in experiments on the laboratory scale; and (3) Hydro-mechanically coupled processes in heterogeneous fractures in simulations on the laboratory and field scale, supported by laboratory experiments. All rock specimens in this work are granite or granodiorite specimens obtained from the Grimsel Test Site (GTS), Switzerland. Fracture topography is studied by overcoring mode I and mode II fractures from core material and by subjecting intact specimens to Brazilian tests. This yields a range of fractures of various nature with sizes between 1 to 30 cm. Fracture topography is compared with the JRC, Z2 measure, fractal dimensions (Hausdorff and Box count dimension) and correlation functions (Two point correlation function and lineal path function) to quantify and compare roughness with a large range of parameters. Additionally, surface roughness is compared to specimen tensile strengths. Results show a clear distinction of natural shear and artificial tensile fractures, as measured with the Z2 measure. Fracture roughness appears to be linked to specimen size when comparing whole fracture sizes. Computing local roughness on small surface patches (e.g. 1 cm x 1 cm) yields smoother surfaces for large fractures, further indicating that fracture roughness is scale dependent and that this scale dependency can be traced down to scales significantly smaller than the whole fracture. The scale of the specimen has an influence on the probable fracture propagation path and therefore the tensile strength, which leads to different surface roughnesses of the induced tensile fracture. As specimen sizes increase, the tensile strength decreases and the fracture roughness increases. In summary, fractures of different nature and size can be distinguished by surface roughness measures, indicating that fracture origin has significant influence on surface topography. This is especially important, as fracture topography is linked to fracture conductivity and strength. Laboratory tests on granodiorite specimen were performed to investigate the relation of fluid flow rate, injection pressure, confining stress and fracture aperture during testing. Cylindrical specimen were overcored from natural tensile and shear fractures and subjected to a fluid pressure gradient across the fracture to sustain a constant flow rate. The specimens were tested in mated configuration and with shear offset in the fracture between 1 and 6 mm. Additionally, specimen fracture surfaces were scanned before and after testing to study the relationship of fracture transmissivity evolution during testing and surface deformation. Confining stress varied between 1 and 68 MPa for 5 to 10 cycles, yielding changes in transmissivity of up to three orders of magnitude. Shear offset of specimens lead to transmissivity increase of up to three orders of magnitude. Specimens experienced strongly damaged fracture surface and gouge production, which reduced transmissivity up to one order of magnitude for subsequent load cycles. While fracture surface roughness increased during testing, this effect was especially pronounced for specimens with shear offset. Almost all tests show hysteretic behavior during individual load cycles, indicating stress path dependent behavior of transmissivity. The experimental results qualitatively demonstrate and quantify mechanisms commonly encountered in EGS reservoir fractures. To further system understanding and predictive capabilities, a novel numerical model was tied into the GEOS framework to compute fully hydro-mechanically coupled processes in heterogeneous fractures. The model is compared against three experimental test sets investigating cylindrical granodiorite specimens with axial loads between 0.25 and 10 MPa for: (i) dry fracture closure; (ii) contact stress evolution in fractures during normal loading; and (iii) constant fluid flow rate injection into the fracture center. The non-linear behavior or fracture normal closure and fluid injection pressure increase with increasing axial load is replicated by the numerical model, by using the fracture aperture fields obtained from photogrammetry scans as model input. The numerical model captures contact stress evolution with axial load increase and shows a linear increase in contact area with axial load. Study of flow field simulations show an early onset of channeling, for axial loads as low as 2 MPa. Additionally, simulations of a field scale domain (100 m x 100 m x 40 m), with a 100 x 100 m fracture plane are performed. Pre-existing natural fractures were scanned, to use their aperture field to generate a synthetic aperture field for the fracture plane. In the next step, vertical stresses of 8.3 MPa, corresponding to the host rock of the fracture origin at the GTS are applied to the system. This yields the unique aperture field corresponding to the given stress state. Fluid is subsequently injected with constant pressure head into the fracture center with pressures between 0.01 and 8.7 MPa. While heterogeneous flow paths and pressure diffusion can be observed, the model additionally allows to observe heterogeneous fracture opening due to lowered effective normal stresses during injection. Further, the hydro-mechanically coupled analysis of the velocity and pressure field shows a deviation of the pressure distribution from linear diffusion for increased injection pressures, once hydro-mechanical contact between the fluid and the rock mass is established. Fluid pressure induced fracture opening is shown to strongly depend on aperture magnitude before injection and aperture magnitudes of the surrounding fracture region. Thereby, the model captures mechanical and hydraulic behavior of the laboratory tests, while providing unique insights for heterogeneous fracture behavior under compression and high pressure fluid injection. In summary, this work attempts to scrutinize heterogeneous fractures, and especially related hydro-mechanical processes. This is done by investigating possible bias by specimen fracture nature and size selection for testing. Hydro-mechanical processes are studied in experiments, which aim to replicate reservoir conditions, and showcase the impact of specific fractures, stress paths and gouge production. Finally, this work presents an approach to incorporate the observed phenomena in a numerical framework, which is tested against specifically designed laboratory tests. This work combines laboratory scale investigations by employing the framework to perform fully hydro-mechanically coupled simulations of a field scale fracture with heterogeneous aperture distribution, which yields quantitative results of fracture opening during high-pressure injection. The presented work thereby contributes to further understanding of fracture processes, which characterize behavior of Enhanced Geothermal Systems and other subsurface phenomena.
2.
Vogler, D., A comparison of different model reduction techniques for model calibration and risk assessment, MSc Thesis, University of Stuttgart, 62 pp., 2013. [Download PDF] [View Abstract]Many engineering systems represent challenging classes of complex dynamic systems. Lacking information about their systems properties leads to model uncertainties up to a level where quantification of uncertainties may become the dominant question in modeling, simulation andapplication tasks. Uncertainty quantification is the prerequisite for probabilistic risk assessment and related tasks. The current work will present recent approaches for these challenges based on response surface techniques, which reduce massively the initial complex model. The reduction is achieved by a regression-like analysis of model output with orthonormal polynomials that depend on the model input parameters. This way, the model response to changes in uncertain parameters, design or control variables is represented by polynomials for each model prediction of interest. This technique is known as polynomial chaos expansion (PCE) in the field of stochastic PDE solutions. The reduced model represented by the response surface is vastly faster than the original complex one, and thus provides a promising starting point for follow-up tasks: uncertainty quantification, model calibration and probabilistic risk assessment. Obviously, a response surface can be constructed in different ways. Methods for constructing the response surface can demand only a minimum number of model evaluations, but as well may ask for many model evaluations to achieve a better quality of the involved projection integrals. The scope of the current work is to test and compare different integration rules, i.e., methods to choose the sets of parameter values for which the model has to be evaluated. To test and compare the different methods, their accuracy in uncertainty quantification, model calibration and risk assessment will be measured against brute-force reference computations based on the original model. As illustrative example, we consider a study from the field of CO2 storage in the subsurface.
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Vogler, D., Investigation of transport phenomena in a highly heterogeneous porous medium, MSc Thesis, Oregon State University, 70 pp., 2012. [Download PDF] [View Abstract]This work focuses on solute mass transport in a highly heterogeneous two-region porous medium consisting of spherical low-hydraulic conductivity inclusions, embedded in a high-hydraulic conductivity matrix. The transport processes occuring in the system are described by three distinct time scales. The first time scale reflects the characteristic time for convective transport in the high-conductivity matrix. The second time scale reflects the characteristic time for diffusive transport in the low-conductivity inclusions. The third time scale reflects the characteristic time for convection within the inclusions. Two Péclet numbers can be defined that compare the time scales and provide qualitative insight into the net transport behavior in two-region media. To model this system, four different representations were developed: (1) a Darcy-scale model that involved direct microscale computation over the entire domain of the experimental system, (2) a direct microscale simulation computed on a simplified domain that had similar geometric parameters (e.g. volume fraction of inclusions) as the complete domain for the experimental system, (3) a volume averaged model (after Chastanet and Wood [2008]) which uses a constant mass transfer coefficient and (4) a volume averaged model which employs a time-dependent mass transfer coefficient. Two different experimental conditions were investigated: a high flow rate, and a low flow rate. Detailed understanding of the experimental system was developed, which led to accurate prediction of the system’s behavior for the higher flow rate. Accurate early time fit of the data was achieved for the experiment with the lower flow rate, while late time behavior between the models and experimental data diverged. Further investigations of the experimental system were conducted to examine possible sources of errors that could lead to an inaccurate description of the system’s properties. Additional mixing within the system, inhomogeneous distribution of the effective diffusion coefficient and imprecise initial estimates of the hydraulic parameters are all possible explanations for the inaccurate model representation of the system’s behavior for the lower flow rate case.