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In its publication IEC 60287, the International Electrotechnical Commission recommends procedures for thermal analysis of power cables in the presence of a dry-out zone in the surrounding medium. It is well known, that the ampacity of cables depends strongly on the so-called critical temperature at which the surrounding medium dries out. However, research on how to estimate this critical temperature has been limited. In semi-arid Mediterranean climate regions, dry summers typically lead to a decrease of the critical temperature. In this paper, the critical temperature is calculated for a field in Riverside, California under various ambient conditions. This is done from the numerical solution of the differential equation for moisture content in the planar case of steady-state coupled heat and mass transfer in porous media. Finite-difference simulations of a system of two medium-voltage DC cables in this field are performed with SHEMAT-Suite (Simulator of HEat and MAss Transport) to compute the maximum temperature for daily cases of calculated critical temperature and compared to a prediction from IEC 60287. It is found that large day-to-day variations in field conditions in a semi-arid area may significantly affect the maximum allowable current. Our results emphasize the importance of ambient conditions for the cable performance.

We measured P-wave velocity, thermal conductivity and thermal diffusivity on 26 sandstone samples under dry and water-saturated conditions. Subsequently, we compared these measurements with predictions by frequently used models. Overall, these three properties decrease with porosity and increase with water saturation. Comparing data sets and models, we distinguish three main groups of sandstone samples: From the difference in the intrinsic elastic and thermal properties of the dominant mineral, two tendencies attributed to either quartz or another rock forming mineral are identified, which separate class 1 sandstone and samples from class 2 sandstones. Within class 1 clean sandstones, a sub-class ( sub-class 1a ) consists of similarly porous samples having different elastic and thermal properties. Based on elasticity, we attribute this effect to microcracks or grain contacts in the samples. While this feature does not affect the total porosity, it affects all of three physical properties strongly and in a similar way. Additionally, we define a second sub-class ( sub-class 1b ) for Fontainebleau sandstone with porosities above 13%. For these four samples, the effect of water saturation on the elastic and thermal properties is different.

Comparisons of fix and variable costs for converting different forms of primary into electric energy performed by national and international agencies as well as by a major German electrical utility consented in concluding: geothermal electricity produced from natural steam or permeable hot water reservoirs is among the cheapest renewable forms of electricity. However, in years to come, geothermal electricity may find itself restricted to the limited number of regions worldwide which feature these particularly favorable reservoirs. This would exclude most of the continental land mass of the earth which is hot but lacks natural steam or hot water reservoirs. This is due to the current lack of proven technology for engineering man-made geothermal reservoirs where natural ones do not exist. At the same time, proven technologies for generating wind and solar electricity are readily available. This may turn out to be a serious competitive disadvantage for geothermal energy as fossil primary energies are being replaced by renewables. Therefore, dedicated and proactive funding of geothermal technology development is required at much larger scale than previously for making geothermal electricity competitively available almost everywhere.

Reconstructing the thermal history in active volcanic complexes characterized by multiple magmatic events is challenging due to the limited knowledge of the nature and extent of the transient heat sources. Although understanding of the geometry and architecture of a magmatic system is of prime importance for accurate temperature assessments, it is still one of the most uncertain parameters in numerical models. In this work, we presented a methodology for thermal assessment in active volcanic systems, whereby field-based geological, geochemical and petrological data are integrated to define the transient heat sources of a magma plumbing system. This time-varying heat source conceptual model is applied in the Los Humeros Volcanic Complex, an active Quaternary caldera complex in the Trans Mexican Volcanic Belt, for evaluating the thermal footprint related to the major volcanic events. The site is characterized by two caldera-forming eruptions, the Los Humeros (164 000 years ago) and the Los Potreros (69 000 years ago) and numerous episodes of post-caldera bi-modal volcanism during Holocene period (8 000 – 3 000 years old). The transient nature of the heat sources is implemented as time-varying temperature boundary conditions and the complete temporal evolution for a period of 182 000 years is simulated in 13 modeling stages. The thermal impact due to the voluminous caldera-forming events and the later short-lived magma pockets of Holocene ages is simulated by emplacing heat sources in the numerical model distributed heterogeneously in space and active at different instants of time. The depth, volume and age of the magma pockets are constrained from geochemical, petrological, geochronological and thermo-barometric analysis of erupted material. The present temperature state obtained from this approach agrees well with the temperature data recorded in the geothermal wells. The thermal footprint of the individual volcanic events indicates that almost 80 % of the present-day thermal contribution results from the massive caldera-forming events. The post-caldera Holocene magma pockets had additionally increased temperatures locally by 10 % - 20 % depending on the volumes and ages of the magma pockets. The present-day thermal regime of the younger Holocene magma pockets suggests existence of super-hot resources at shallow depths in the southern part of the geothermal field, making it a potential site for future exploration activities.

We study the impact of spatially heterogeneous permeability on the formation and shape of hydrothermal porous flow convection in the Yarragadee Aquifer by modelling three simulation scenarios, each with differing permeability distributions. In all scenarios, the southern part of the model is characterised by convection rolls, while the north is dominated by a stable region of decreased temperatures at depth due to hydraulic interaction with shallower aquifers. This suggests that reservoir structure is a first-order controlling factor for the formation of the free convective system. The convective system adjusts to the spatially heterogeneous permeability distribution, yielding locally different convection patterns.

Modeling anisotropic flow in porous or fractured rock often assumes that the permeability tensor is diagonal, which means that its principle directions are always aligned with the coordinate axes. However, the permeability of a heterogeneous anisotropic medium usually is a full tensor. For overcoming this shortcoming, we use the mimetic finite difference method (mFD) for discretizing the flow equation in a hydrothermal reservoir simulation code, SHEMAT-Suite, which couples this equation with the heat transport equation. We verify SHEMAT-Suite-mFD against analytical solutions of pumping tests, using both diagonal and full permeability tensors. We compare results from three benchmarks for testing the capability of SHEMAT-Suite-mFD to handle anisotropic flow in porous and fractured media. The benchmarks include coupled flow and heat transport problems, three-dimensional problems and flow through a fractured porous medium with full equivalent permeability tensor. It shows firstly that the mimetic finite difference method can model anisotropic flow both in porous and in fractured media accurately and its results are better than those obtained by the multi-point flux approximation method in highly anisotropic models, secondly that the asymmetric permeability tensor can be included and leads to improved results compared the symmetric permeability tensor in the equivalent fracture models, and thirdly that the method can be easily implemented in existing finite volume or finite difference codes, which has been demonstrated successfully for SHEMAT-Suite.

SoftwareX 12, 100533 (2020). doi:10.1016/j.softx.2020.100533, Published by Elsevier, Amsterdam [u.a.]

We present a method to determine equivalent permeability of fractured porous media. Inspired by the previous flow-based upscaling methods, we use a multi-boundary integration approach to compute flow rates within fractures. We apply a recently developed multi-point flux approximation Finite Volume method for discrete fracture model simulation. The method is verified by upscaling an arbitrarily oriented fracture which is crossing a Cartesian grid. We demonstrate the method by applying it to a long fracture, a fracture network and the fracture network with different matrix permeabilities. The equivalent permeability tensors of a long fracture crossing Cartesian grids are symmetric, and have identical values. The application to the fracture network case with increasing matrix permeabilities shows that the matrix permeability influences more the diagonal terms of the equivalent permeability tensor than the off-diagonal terms, but the off-diagonal terms remain important to correctly assess the flow field.

We present a comprehensive statistical analysis of petrophysical properties of rocks of the northeastern Rhenish Massif and the Lower Rhine Embayment in Germany. Properties measured comprise thermal conductivity, specific heat capacity density, porosity, hydraulic permeability, and compressional wave velocity. This robust and statistically reliable data is generally useful for numerical modeling of heat transport processes and helps, in particular, reducing the risk of failure in projects of geothermal energy use. We measured the thermophysical properties of rocks from two geological settings: (1) predominantly little consolidated Tertiary rocks forming the young sedimentary cover of the Lower Rhine Embayment in the condition they arrived in the laboratory; (2) well consolidated Paleozoic rocks from the northeastern Rhenish Massif in both dry and saturated condition. We tested a total of 476 samples from different lithologies in both settings in a comprehensive laboratory program consisting of mineralogical analyses and various petro- and thermophysical measurements at ambient and elevated p-T-conditions. This yields relations between composition and thermophysical properties of different sedimentary rock types and allows distinguishing between effects due to rock matrix and structure. The results are used to prove petrophysical rock models and allow predicting thermal properties of distinct rock types for greater depth. The results show that the thermophysical properties of Paleozoic rocks are mainly controlled by their mineralogical compositions, while thermophysical characteristics of Tertiary rocks are the result of a superposition of properties of their mineral content and the water-filled pore volume.

We analyze the likelihood of success for heat production strategies in a sandstone reservoir in the north-eastern German basin in a depth of about 2 km by simulating both double and single well configurations. For this test case study we use an exploited oil and gas field. We combine seismic interpretation, numerical modeling, and stochastic estimation of rock properties to predict the transient temperature and pressure variations and their uncertainties in a geothermal reservoir. We demonstrate the essential necessity in geothermal reservoir modeling to account for heterogeneity of rock properties. We use 3D seismic data and stratigraphy data from about 100 wells at 1500 m – 2500 m depth for setting up a 3D stratigraphic model. Rock properties are assigned to this model by a Monte Carlo approach using Sequential Gaussian Simulation. Using 3D inversion of temperature data obtained in the wells we estimate a specific heat flow of 77.7 mW m −2 ± 1.2 mW m −2 at 6 km depth, in agreement with a temperature of 87.1 °C ± 1.8 K in the Rhaetian sandstone target layer at a depth of ∼2 km. For different types of potential geothermal well installations inside the Rhaetian sandstone layer the probability of success is just 1.6%.

Many popular groundwater modeling codes are based on the finite differences or finite volume method for orthogonal grids. In cases of complex subsurface geometries this type of grid either leads to coarse geometric representations or to extremely fine meshes. We use a coordinate transformation method (CTM) to circumvent this shortcoming. In computational fluid dynamics (CFD), this method has been applied successfully to the general Navier-Stokes equation. The method is based on tensor analysis and performs a transformation of a curvilinear into a rectangular unit grid, on which a modified formulation of the differential equations is applied. Therefore, it is not necessary to reformulate the code in total. We applied the CTM to an existing three-dimensional code (SHEMAT), a simulator for heat conduction and advection in porous media. The finite volume discretization scheme for the non-orthogonal, structured, hexahedral grid leads to a 19-point stencil and a correspondingly banded system matrix. The implementation is straightforward and it is possible to use some existing routines without modification. The accuracy of the modified code is demonstrated for single phase flow on a two-dimensional analytical solution for flow and heat transport. Additionally, a simple case of potential flow is shown for a two-dimensional grid which is increasingly deformed. The result reveals that the corresponding error increases only slightly. Finally, a thermal free-convection benchmark is discussed. The result shows, that the solution obtained with the new code is in good agreement with the ones obtained by other codes.

A lightweight Halbach magnet system for use in nuclear magnetic resonance (NMR) studies on drill cores was designed and built. It features an improved homogeneous magnetic field with a strength of 0.22 T and a maximum accessible sensitive volume. Additionally, it is furnished with a sliding table for automatic scans of cylindrical samples. This device is optimized for nondestructive online measurements of porosity and pore size distributions of water-saturated full cylindrical and split semicylindrical drill cores of different diameters. The porosity of core plugs with diameters from 20 to 80 mm can be measured routinely using exchangeable radiofrequency coils. Advanced NMR techniques that provide 2D T(1)-T(2) correlations with an average measurement time of 30 min and permeability estimates can be performed with a special insert suitable for small core plugs with diameter and length of 20 mm.

Transient thermal signals such as Pleistocene surface temperature variations or exhumation of great rock volumes are important for the current thermal regime of the Eastern Alpine crust. In this study transient 1-D forward simulations and an analytical approach were used to estimate the order of magnitude of these effects. A comparison with numerical forward simulations and inverse analyses of steady-state heat conduction yields the following main conclusions with respect to the thermal regime of the Eastern Alps along the TRANSALP profile: (1) The change of surface temperatures in the past affects mainly the uppermost part of the Eastern Alpine crust. It results in a maximum thermal signature of more than − 6 K at a depth of 2 km. The deviations from a steady-state temperature gradient and heat flow in the region of the Tauern Window range from 0.3–4 K km − 1 and 0–6 mW m − 2 , respectively, with maximum values at the surface. (2) Exhumation of the Eastern Alpine lithosphere may result in a thermal signature of up to 4 K at a depth of 1 km. The thermal signature increases further with depth to a maximum of approximately 80 K at a depth of 50 km. As the temperature gradient of the exhumation signal is almost zero at the base of the crust, Moho heat flow appears to be not critically perturbed. (3) The combined effect of exhumation and changing surface temperatures at the Tauern Window amounts to less than 15% of the steady-state temperatures at a depth of ∼ 8 km and to less than 10% at the base of Eastern Alpine root. The corresponding perturbation in heat flow is less than 20% at a depth of 4 km, approaching zero below 40 km.

In order to analyze local clogging phenomena due to the precipitation of anhydrite in the pore-space we performed a petrophysical study on cores and data from three boreholes probing the Rhaetian hydrothermal aquifer in northern Germany (Allermohe, Neuruppin 1/88, Neuruppin 2/87). The pore size geometry of sandstones was studied using, among other methods, pulsed field gradient-nuclear magnetic resonance (PFG-NMR). We found two facies types with clearly different diagenetic history: (1) a fine-grained sand with small pores, mechanically compacted during diagenesis into an average sandstone of fractal pore geometry; (2) a coarser sand with larger pores, almost completely cemented by anhydrite after compaction had reduced the pore-space to a porosity of 30%; thus no further mechanical compaction occurred and the pores remained smooth. In contrast, the fine-grained facies was not cemented, possibly because anhydrite crystal nuclei are unstable in pores of insufficient size. With regard of these two facies types we developed: (1) an approach for calculating vertical logs of anhydrite and permeability content from gamma density measurements in boreholes or on core; (2) a chemical reaction model to calculate the amount of precipitation and dissolution of each mineral species at high temperature and salinity. These petrophysical and geochemical models are integrated into the numerical simulation tool SHEMAT for simulating coupled flow, heat and species transport, and chemically induced permeability changes. A comparison of the diagenesis of the cemented and un-cemented facies types yields an improved understanding of the geological conditions required for anhydrite cementation. Specifically, with regard to the studied Rhaetian sandstones, numerical reactive flow simulations demonstrate that intense, local anhydrite cementation may occur when saline formation waters mix with hot brines ascending on faults.

We present new heat flow values and other geothermal data in the upper crystalline crust in the immediate vicinity of the 12.4-km deep Kola super-deep borehole, NW Russia. Our results show a systematic vertical increase in geothermal gradient and heat flow density as deep as we could measure (1.6 km). Our results confirm earlier results on vertical heat flow trends of in the uppermost part of the Kola super-deep hole, and imply that the thermal regime is not in steady-state conductive conditions. In an area of 3-km × 5-km measurements were performed in 1–2-km deep boreholes surrounding the Kola super-deep hole and on core samples from these holes. Temperature logs are available from 36 holes. Core data exists from 23 boreholes with a total length of 11.5 km at a vertical resolution of 10 m. We carried out a very detailed study on thermal conductivity with regard to anisotropy, inhomogeneity and temperature dependence. Tensor components of thermal conductivity were determined on 1375 core samples from 21 boreholes in 3400 measurements. Additionally, we measured specific heat capacity, heat generation rate, density, porosity, and permeability on selected subsets of core samples. Heat flow from 19 boreholes varies between 31 and 45 mW m−2 with an average value of 38 mW m−2. In most boreholes the vertical heat flow profiles show a considerable variation with depth. This is consistent with observations in the upper part of the Kola super-deep borehole. We conclude that this variation is not caused by technical operations but reflects a natural process. It is considered to be due to a combination of advective, structural and paleoclimatic effects. Preliminary 3-D numerical modeling of heat and flow in the study area provides an indication of relative contributions of each of these factors: advective heat transfer turns out to have a major influence on the vertical variation of heat flow, although transient changes in surface temperature may also cause a significant variation. Heterogeneity of the rocks in the study area is less important.

The thermal regime and the distribution of heat flow at the base of sedimentary basins is fundamental to the understanding of the process of basin evolution and the associated mobilization and migration of hydrocarbon and other fluids. For the Northeastern-German sedimentary basin, available information on structure, temperature, and thermal properties along a seismic DEKORP reflection profile allow high resolution 2-D forward and inverse simulations. This approach is attractive in situations where much information is available, if only with considerable uncertainty. In particular, this allows to introduce “soft” information into the analysis. In our case, forward simulations yield initial a priori estimates of the parameters while inversion calculations yield a posteriori estimates of the parameters and their uncertainty. The a priori parameters as well as their assumed uncertainty are input for a Bayesian parameter estimation scheme. In respect to the Northeastern-German sedimentary basin, the inverse analysis postulates a significant and characteristic a posteriori variation of thermal conductivity of the Zechstein unit along the entire profile as well as a generally large a posteriori thermal conductivity of the (pre-Permian) basement in the northern part of the basin. For inverse calculations, we used two alternative scenarios: One assumes the thermal conductivity of the Zechstein unit to be homogeneous along the profile while the other allows a lateral variation. A posteriori heat flow across the base of the model varies from 40 to 60 and 50 to 65 mW m−2 for models in which values for thermal conductivity and radiogenic heat generation rate were either based on literature values or direct measurements, respectively.

A combination of petrophysical measurements and inverse modeling is used to estimate the 2-D, steady-state conductive thermal regime in the crust and heat flow at the Moho along the N–S trending TRANSALP profile across the continental collision zone of the Eastern Alps. The uncertainty to which each parameter in the simulation is known beforehand is expressed in terms of its variance, entering a Bayesian parameter estimation scheme. This approach is particularly attractive for geological applications–– where often information is available, if only with large uncertainty––because it allows to introduce soft information into a quantitative approach. Our inversion studies show that while the large a priori standard deviation of particularly the heat production rate in the upper crust can be significantly reduced a posteriori, the variance of the middle crust heat production rate remains comparatively large. Using two extreme models with maximum and minimum heat production rates in the middle crust the range of Moho temperatures and heat flow can be estimated. Depending on different assumptions about the composition of the middle crust we obtain maximum temperatures of around 900 C � 30% in the lower most parts of the European crust. In the Alpine root and in the Southern Alps, maximum temperatures are 700–800 C � 10% and 600 C � 10%, respectively. Moho heat flow varies from 5–25 mW m � 2 and is

The German continental deep-drilling program (KTB) provided a unique opportunity for studying heat transfer processes in deep continental crust. We used an inversion technique based on the Bayesian parameter estimation to constrain parameters involved in crustal heat transfer at the KTB site and their standard deviations. Measurements in the two deep KTB boreholes and on rock material recovered from these holes were used to compile a set of a priori information for a 2-D cross-section of 40 km × 30 km. Thermal and hydraulic parameters were determined in a steady-state inverse finite-element model for a simplified geological structure. The inversion algorithm yielded a posteriori information for thermal conductivity, permeability, and heat production rate as well as for temperature and hydraulic head. Because of the large temperature range (up to 800°C), we introduced the variation of thermal conductivity with temperature into the numerical algorithm. While thermal conductivity could be well resolved, the distribution of heat production rate was relatively poorly resolved. The uncertainties for the parameters varied depending on the number of free parameters. If heat production rate was constrained tightly, the resolution of the thermal conductivity was improved. A zone of high heat production rate between 3.8 km and 10 km combined with a reduced thermal conductivity above it provided the best fit to the measured temperatures in the borehole. The steady-state inversion yielded a better solution when paleoclimatic temperature perturbations, such as those caused by the last ice age, were removed from the temperature data.

This study examines heat transfer during forced water circulation through fractured crystalline rock using a fully 3-D finite-element model. We propose an alternative to strongly simplified single or multiple parallel fracture models or porous media equivalents on the one hand, and to structurally complex stochastic fracture network models on the other hand. The applicability of this “deterministic fracture network approach” is demonstrated in an analysis of the 900-day circulation test for the Hot Dry Rock (HDR) site at Rosemanowes (U.K.). The model design with respect to structure, hydraulic and thermal behavior is strictly conditioned by measured data such as fracture network geometry, hydraulic and thermal boundary and initial conditions, hydraulic reservoir impedance, and thermal drawdown. Another novel feature of this model is that flow and heat transport in the fractured medium are simulated in a truly 3-D system of fully coupled discrete fractures and porous matrix. While an optimum model fit is not the prime target of this study, this approach permits one to make realistic long-term predictions of the thermal performance of HDR systems.

By the end of 1995 direct thermal use of geothermal energy in Germany amounted to an installed thermal power of roughly 323 MWt. Of this sum, 38.7 MW, are generated in 22 major centralized installations. Small, decentralized earth-coupled heat pumps and groundwater heat pumps are estimated to contribute an additional 95 and 190 MW, respectively. By the year 2000 an increase in total installed geothermal power of about 144 MWt is expected: 115 MWt from major central and 29 MWt from small, decentralized installations. This would bring direct thermal use in Germany close to an installed thermal power of 467 MWt. At present no electric power is produced from geothermal resources in Germany, whose annual final energy consumption now amounts to about 9000 PJ. This is equivalent to a total consumed power of 285,000 MW. Almost 60% of this energy is required as heat. The technical potential for direct thermal use of geothermal energy in Germany is estimated to be 1622 PJ yr−1 for hydrothermal applications and 960 PJ yr−1 for earth-coupled and groundwater heat pumps; this is equivalent to a thermal power generation of 51,400 and 30,420 MW, respectively. The total, 81,820 MWt, corresponds to about 29% of the country's annual final energy consumption, or roughly 49% of its demand for heat. However, at present only about 4% of the existing technical potential for direct thermal use of geothermal energy meets the demand for heat. If the vast potential of geothermal energy for direct thermal use was utilized to substitute fossil fuels, roughly 110 million tons less of CO2 would be released to the atmosphere annually, equivalent to about 12% of Germany's CO2 output in 1994.