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Calibrating the heterogeneous permeability distribution of hard-rock aquifers based on sparse data is challenging but crucial for obtaining meaningful groundwater flow models. This study demonstrates the applicability of stochastic sampling of the prior permeability distribution and Metropolis sampling of the posterior permeability distribution using typical production data and measurements available in the context of groundwater abstraction. The case study is the Hastenrather Graben groundwater abstraction site near Aachen, Germany. A three-dimensional numerical flow model for the Carboniferous hard-rock aquifer is presented. Monte Carlo simulations are performed, for generating 1,000 realizations of the heterogeneous hard-rock permeability field, applying Sequential Gaussian Simulation based on nine log-permeability values for the geostatistical simulation. Forward simulation of flow during a production test for each realization results in the prior ensemble of model states verified by observation data in four wells. The computationally expensive ensemble simulations were performed in parallel with the simulation code SHEMAT-Suite on the high-performance computer JURECA. Applying a Metropolis sampler based on the misfit between drawdown simulations and observations results in a posterior ensemble comprising 251 realizations. The posterior mean log-permeability is −11.67 with an uncertainty of 0.83. The corresponding average posterior uncertainty of the drawdown simulation is 1.1 m. Even though some sources of uncertainty (e.g. scenario uncertainty) remain unquantified, this study is an important step towards an entire uncertainty quantification for a sparsely sampled hard-rock aquifer. Further, it provides a real-case application of stochastic hydrogeological approaches demonstrating how to accomplish uncertainty quantification of subsurface flow models in practice., Helmholtz-Gemeinschaft http://dx.doi.org/10.13039/501100001656

The existence of submarine fresh groundwater has been recorded at continental shelves worldwide. The dynamic preservation and lifetime of fresh groundwater in the offshore environment remains an open hydrogeological problem. The mechanisms and time scales of fresh groundwater preservation are examined using numerical simulations based on a geologically representative model of the New Jersey shelf, USA. Utilizing two-dimensional depth-migrated seismic and well data, a detailed hydrogeological model is built, with a vertical resolution of 10 m. The model captures the highly heterogeneous shelf environment and accounts for porosity compaction trends derived from core data. The results show transient coupled simulations of groundwater flow and heat and salt transport from the late Pleistocene until present day and projected 18,000 years into the future. They reveal freshwater preservation patterns and yield simulated borehole salinity profiles broadly consistent with field observations. The simulations show that freshwater intervals of a thickness of 200–300 m and lateral extent of tens of kilometers may have been preserved from the Last Glacial Maximum until today. It was found that approximately 30–45% of the initial freshwater volume remains preserved after 12,000 years, depending on the recharge boundary condition. The preserved volume ranges between 15 and 30% after 30,000 years. These results improve the understanding of submarine preservation of fresh groundwater through an interdisciplinary approach which integrates seismic imaging, hydrogeological modeling and high-performance numerical simulation.

Upscaling permeability of grid blocks is crucial for groundwater models. A novel upscaling method for three-dimensional fractured porous rocks is presented. The objective of the study was to compare this method with the commonly used Oda upscaling method and the volume averaging method. First, the multiple boundary method and its computational framework were defined for three-dimensional stochastic fracture networks. Then, the different upscaling methods were compared for a set of rotated fractures, for tortuous fractures, and for two discrete fracture networks. The results computed by the multiple boundary method are comparable with those of the other two methods and fit best the analytical solution for a set of rotated fractures. The errors in flow rate of the equivalent fracture model decrease when using the multiple boundary method. Furthermore, the errors of the equivalent fracture models increase from well-connected fracture networks to poorly connected ones. Finally, the diagonal components of the equivalent permeability tensors tend to follow a normal or log-normal distribution for the well-connected fracture network model with infinite fracture size. By contrast, they exhibit a power-law distribution for the poorly connected fracture network with multiple scale fractures. The study demonstrates the accuracy and the flexibility of the multiple boundary upscaling concept. This makes it attractive for being incorporated into any existing flow-based upscaling procedures, which helps in reducing the uncertainty of groundwater models.

For a Bunter formation in the German Federal State of North Rhine Westphalia, we use numerical models to consider reactions between the supercritical, aqueous, and solid phases. These reactions may occur in a CO2-water system representing a saline aquifer CO2 storage scenario. Thus, the models are used for determining the extent of fluid–rock reactions during mineral dissolution or precipitation. In particular, we study the effect of temperature by comparing results for our system set at 100 °C and at 58 °C. Results show that the abundance of dissolved ions changes as a result of elevated temperature. For the entire 10,000-year simulation period, the overall geochemical behavior of the Bunter reservoir rock at the Minden site is explained in terms of different mineral transformations, although some of them are not changed significantly. This mainly comprises the alteration of carbonate minerals such as calcite, and aluminium silicates such as oligoclase, chlorite, illite, albite, kaolinite, and Na-smectite. Another chemical behavior derives from the generation and consumption of new secondary minerals such as dawsonite, pyrite, and Ca-smectite. In contrast to a system temperature of 58 °C, the mineralogical transformations of other minerals such as siderite, ankerite, dolomite, and magnesite are not observed at 100 °C. Also, the numerical simulation results show that at elevated temperature, the dominant role played by hydrodynamic mechanism dwarfs the role of other trapping mechanisms including dissolution and mineralization. Results also demonstrate how geological, petrophysical, and geochemical data can be integrated to estimate quantitatively the magnitude of the fluid–rock reactions. These reactions may entail new geotechnical problems, such as rock self-fracturing which ultimately decreases the CO2 sequestration projects security.

The possible effects of iron oxide coatings on the reactive surface area of calcite in column experiments have been studied and then modeled numerically. A column with six compartments separated by teflon filters was packed with Emscher Marl (essentially calcite). The marl was initially mixed with corundum as an internal standard. Hydrochloric acid with pH 3 was percolated through the column for a given period, after which the mineralogical changes were quantified by X-ray diffraction ex-situ. Then, the column compartments were re-filled and again percolated with HCl. This procedure was repeated five times. The losses and gains of calcite in the column compartments provided the data basis for modeling the entire experiment with the reactive transport code TOUGHREACT using a kinetic rate law. The experimental results showed that during the first period, loss of calcite in the first compartment is about 50 % less than that determined from the theoretical analysis. This showed the entrance of acid into the higher compartments through preferential flow paths (wormholes) which was observed at the boundary between sample and cell wall. This pattern could also be verified by the relatively high Peclet and low Damkohler numbers, showing a strongly advection-dominant system. Apart from calcite dissolution, structural Fe2+ released from calcite oxidized and formed iron hydroxide (FeOOH) coatings along preferential fluid pathways. Despite specific assumptions such as using pure calcite in the model, a comparison between modeling results and lab observations is instructive. The simulated calcite change patterns in the most compartments are consistent with the experiments. Some discrepancies are noted in the last compartment, which may bring the attention to a need for model improvements.

We study opportunities for CO2 sequestration in geological formations of the state North Rhine Westphalia in Germany. Simulations are performed for evaluating a potential site within the Bunter sandstone formation near the town of Minden in a depth of around 3,000 m using the numerical simulator TOUGHREACT. Our focus is on three CO2 storage mechanisms: (1) hydrodynamic trapping, (2) dissolution trapping, and (3) mineral trapping. The results show that due to buoyancy the injected CO2 phase initially migrates towards the top of the reservoir and is hydrodynamically trapped beneath the confining layer of the cap rock. Then, the CO2 spreads laterally and dissolves partially in the formation water. The dissolution of CO2 results in an increase of the density of the brine causing a downward migration until it settles after 10,000 years at the bottom of the reservoir. The simulations indicate that after 10,000 years, 15% (17 Mt) from a total of 114 Mt injected CO2 are trapped hydrodynamically, 20% (23 Mt) are trapped by dissolution, and 65% (74 Mt) are fixed in newly formed carbonates such as dawsonite, ankerite, and siderite. Within our study pressure increases near the injection well by a factor of 1.1 which is lower than the upper limit usually accepted in gas storage operations. The mineral reactions cause a net decrease of porosity and in turn a decrease of permeability down to 9% of the initial value in parts of the reservoir.

The groundwater flow regime at great depth within the Molasse Basin (SW Germany) was studied. Data relevant for a flow model at 600–1,600 m depth are sparse in the western part of the basin. However, temperature measurements are available covering much of the area at a wide range of depths. Therefore, a thermal 3D steady-state model was set up with the aim of comparing modeled with observed subsurface temperatures. Stratigraphic information from many boreholes was also available, but only a few values of rock thermal conductivity and heat-production rate could be obtained. Some strong thermal residual anomalies were identified with respect to the purely conductive model, especially along fault zones, and within stratigraphic layers with high hydraulic conductivity. These anomalies can be explained by various advective heat-transport mechanisms, yet most explanations can be eliminated. The most plausible constellation explaining the major positive thermal anomalies of 10 Kelvin and more is a fault zone of E–W strike, intersected by an aquifer with flow parallel to the fault zone. This concept was investigated by using a simplified type model. In spite of some shortcomings, the method presented here can be used to identify temperature anomalies, and to identify possible explanations.

Estimating permeability from NMR well logs or mobile NMR core scanner data is an attractive method as the measurements can be performed directly in the formation or on fresh cores right after drilling. Furthermore, the method is fast and non-destructive. Compared to T 1 relaxation times, commonly measured T 2 distributions are influenced by external and internal magnetic field gradients. We performed two-dimensional T 1 and T 2 relaxation experiments on samples of Rhaetian sandstone, a rock with low porosity and small pore radii, using a mobile NMR core scanner which operates within a nearly homogeneous static magnetic field. Because small pore sizes are associated with high internal magnetic field gradients, standard methods from NMR logging in the oil industry cannot be applied for accurate permeability prediction. Therefore, a new model theory was developed, which describes the pore radius dependence of the surface relaxivity p 2 by both an analytical and a more practical empirical equation. Using corrected p 2 values, permeability can be predicted accurately from the logarithmic mean of the T 2 distribution and the physically based Kozeny-Carman equation. Additional core plug measurements of structural parameters such as porosity, permeability, specific inner surface area and pore radius distributions supported the NMR results.

NMR relaxometry is a powerful tool for inferring porosity and permeability data. In practice, measured magnetization decay curves are inverted for relaxation time distributions. Subsequently, one presumes a linear relationship between the pore radius distribution and the T1 and T2 distribution, for longitudinal and transverse magnetization, respectively. The fundamental equations used are based on a pore model, in which pores are assumed to be isolated from each other with respect to the NMR process and have smooth walls. The present study is based on a geometrical pore space model with connected pores and structured pore walls. The physical processes of surface relaxation, irreversible dephasing of magnetic spins and diffusive proton exchange between pores, are described by a system of differential equations. The solution yields a set of exponential functions representing the relaxation time distribution. We describe the difference between the distributions obtained for diffusion coupling and for isolated pores. With diffusion coupling on, the spectral width of the T1 distribution is strongly reduced, which indicates that the influence of large and small radii according to the T1-pore radius relationship is mixed to some extent. For a fractal pore space structure, where large pores are surrounded by adjacent minor pores, the T1 distribution does not resolve these substructures. Nevertheless, permeability values calculated from the logarithmic mean relaxation time T1,LM are quite the same for diffusion coupling and for isolated pores. The T2 distribution for diffusion coupling is little constricted and gives a better resolution of the pore wall structures than the corresponding T1 distribution. The permeability values from T2 distributions agree with the values from longitudinal magnetization, provided that we use a corrected relaxation time T2,corr, accounting for the dependence of the surface relaxivity ρ2 on pore radius. The study shows that radius distributions calculated from a T1 and from a T2 distribution differ from one another and both present an altered image of the true pore radius distribution. In practice, this has no serious influence on estimating permeability of medium- to high-permeability sandstones with the currently applied methods. The presented methodology of calculating the NMR response of pore space models with diffusion coupling may facilitate understanding porosity-permeability relationships of different rock types such as carbonate rocks with micro-porosity.

Hydrothermal systems are characterised by complex interactions between heat transfer, fluid flow, deformation, species transport and chemical reactions. Numerical models can provide quantitatively constrained information in regions where acquisition of new data is difficult or expensive thus providing a means for reducing risks, costs, and effort during targeting, production, and management of resources linked to hydrothermal systems. Here we show how numerical simulations of hydrothermal processes can be used to better understand coupled reactive transport in modern geothermal systems and in ancient hydrothermal ore deposits. We give examples based on the Enhanced Geothermal System at Soultz-sous-Forets in France, hydrothermal mineralisation at Mount Isa in Australia, and the geothermal resource at Hamburg-Allermohe in Germany.

The heat of the Earth derives from internal and external sources. A heat balance shows that most of the heat provided by external sources is re-emitted by long-wavelength heat radiation and that the dominant internal sources are original heat and heat generated by decay of unstable radioactive isotopes. Understanding of the thermal regime of the Earth requires appreciation of properties and mechanisms for heat generation, storage, and transport. Both experimental and indirect methods are available for inferring the corresponding rock properties. Heat conduction is the dominant transport process in the Earth’s crust, except for settings where appreciable fluid flow provides a mechanism for heat advection. For most crustal and mantle rocks, heat radiation becomes significant only at temperatures above 1200°C.

We estimate the maximum geothermal potential in Germany available for exploitation by operated engineered geothermal systems (EGS). To this end, we assume that (a) capabilities for creating sufficient permeability in engineered deep heat exchange systems will become available in the future and (b) it will become possible to implement multiple wells in the reservoir for extending the rock volume accessible by water circulation for increasing the heat yield. While these assumptions may be challenged as far too optimistic, they allow for testing the potential of EGS, given the required properties, in countries lacking natural steam reservoirs. With this aim, we model numerically the thermal and electric energies which may be delivered by such systems by solving coupled partial differential equations governing fluid flow and heat transport in a porous medium. Thus, our model does not represent the engineered fractures in their proper physical dimension but rather distributes their flow volume in a small region of enhanced permeability around them. By varying parameters in the subsurface, such as flow rates and well separations, we analyze the long-term performance of this engineered reservoir. For estimating the maximum achievable potential for EGS in Germany, we assume the most optimistic conditions, realizing that these are unlikely to prevail. Considering the available crystalline landmass and accounting for the competing land uses, we evaluate the overall EGS potential and compare it with that of other renewables used in Germany. Under most optimistic assumptions, the land surface available for emplacing EGS would support a maximum of 13,450 EGS plants each comprising 18 wells and delivering an average electric power of 35.3 MW e . When operated at full capacity, these systems collectively may supply 4155 TWh of electric energy in 1 year which would be roughly seven times the electric energy produced in Germany in the year 2011. Thus, our study suggests that major scientific, engineering, and financial efforts are justified for developing the drilling and stimulation technologies required for creating the permeabilities required for successful EGS. Then, EGS will have great potential for contributing towards national power production in a future powered by sustainable, decentralized energy systems., Geothermal Energy, 3 (1), ISSN:2195-9706