Daniel Vogler Publications Content

Publications

A complete overview can be found at https://www.researchgate.net/profile/Daniel_Vogler

REFEREED PUBLICATIONS IN JOURNALS

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. 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.
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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, pp. 1-19, 2017. 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.
/ Download
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. 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

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. / Download
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, (in press). / Download

THESES

3.  Vogler, D. Hydro-mechanically coupled processes in heterogeneous fractures: experiments and numerical simulations, Dissertation ETH Zurich, 169 pp., 2016. 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.
/ Download
2.  Vogler, D. A comparison of different model reduction techniques for model calibration and risk assessment, MSc Thesis University of Stuttgart, 62 pp., 2013. 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.
/ Download
1.  Vogler, D. Investigation of transport phenomena in a highly heterogeneous porous medium, MSc Thesis Oregon State University, 70 pp., 2012. 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.
/ Download

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REFEREED PUBLICATIONS IN JOURNALS

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. 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.
/ Download
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, pp. 1-19, 2017. 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.
/ Download
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. 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.
/ Download

PROCEEDINGS REFEREED

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. / Download
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, (in press). / Download

THESES

3.  Vogler, D. Hydro-mechanically coupled processes in heterogeneous fractures: experiments and numerical simulations, Dissertation ETH Zurich, 169 pp., 2016. 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.
/ Download
2.  Vogler, D. A comparison of different model reduction techniques for model calibration and risk assessment, MSc Thesis University of Stuttgart, 62 pp., 2013. 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.
/ Download
1.  Vogler, D. Investigation of transport phenomena in a highly heterogeneous porous medium, MSc Thesis Oregon State University, 70 pp., 2012. 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.
/ Download