# Daniel Vogler Publications Content

## Publications

A complete overview can be found here

### REFEREED PUBLICATIONS IN JOURNALS

 9 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. AbstractThis 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. 8 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. AbstractIn 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. 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. AbstractIn 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 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. AbstractNumerous 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. 5 Perras, M.A., and D. Vogler Compressive and Tensile Behavior of 3D-Printed and Natural Sandstones, Transport in Porous Media, pp. 1-23, 2018. AbstractThe 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. 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. AbstractTo 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. AbstractThis 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. AbstractThis 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. AbstractIncreasing 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.

### PROCEEDINGS REFEREED

 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. AbstractCarefully 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, Proceedings of the 42nd Workshop on Geothermal Reservoir Engineering Stanford University, 2017. AbstractIn-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, Proceedings of the 41st Workshop on Geothermal Reservoir Engineering Stanford University, pp. SGP-TR-209, 2016. AbstractHeterogeneous 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.

### THESES

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### REFEREED PUBLICATIONS IN JOURNALS

 9 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. AbstractThis 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. 8 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. AbstractIn 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. 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. AbstractIn 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 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. AbstractNumerous 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. 5 Perras, M.A., and D. Vogler Compressive and Tensile Behavior of 3D-Printed and Natural Sandstones, Transport in Porous Media, pp. 1-23, 2018. AbstractThe 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. 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. AbstractTo 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. AbstractThis 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. AbstractThis 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. AbstractIncreasing 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.

### PROCEEDINGS REFEREED

 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. AbstractCarefully 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, Proceedings of the 42nd Workshop on Geothermal Reservoir Engineering Stanford University, 2017. AbstractIn-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, Proceedings of the 41st Workshop on Geothermal Reservoir Engineering Stanford University, pp. SGP-TR-209, 2016. AbstractHeterogeneous 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.