Geothermal refraction problem for a 2-D body of polygonal cross-section buried in the two-layered earth
We present the exact boundary integral formulae for calculation of the geothermal anomaly due to a two dimensional body whose thermal conductivity is λT and its cross-section is bounded by the closed general polygonal contour. This body is buried in the superficial layer of conductivity λ1. The half-space z > h with the thermal conductivity λ2 is considered as a substratum of models. The boundary integral technique for the solution of this problem requires the application of logarithmic potential terms in infinite series. Numerical calculations based on derived formulae revealed that the surface anomaly heat flow reflects the "topography" mainly of the upper boundary of the perturbing body. The derived algorithm and the developed numerical program enable calculations for a number of interesting models: intrusions, protrusions of the substratum etc.
Refraction effect in geothermal heat flow due to a 3D prismoid, situated in the substratum of two-layer Earth
We present mathematical modelling of the stationary geothermal field for the two-layered Earth which includes a three-dimensional perturbing body below the first layer (in the substratum). The body is in the form of 3D prismoid with sloping side faces, while its upper and lower face are rectangles at the planes z = z1, z2. The theoretical formulae are based on the generalized theory of the double-layer potential and boundary integral equation (BIE). Special attention is paid to the quadrilateral prismoids bounded by planar skew faces. The numerical calculations were performed for the 3D prismoids (blocks) with thermal conductivity different to the ambient substratum, while the upper face of the prismoid may be in contact with the upper layer. Numerous graphs are shown for the disturbance of the heat flow on the surface of the Earth or inside the first layer.
Refraction of heat flow on subsurface contrast structures - the influence both on geothermal measurements and interpretation approaches
The paper deals with some problems of the heat flow refractions on the subsurface structures with contrasting thermal conductivities. The qualitative and quantitative analyses of these effects were made on the selected structure configurations. Analysed structures are important particularly for the study of temperature as well as heat flow density distributions influencing the Earth's heat flow measurements, the construction of terrestrial heat flow distribution maps and also for the interpretation of the heat flow density data. The related 2D and 3D mathematical problems were solved by means of the finite difference methods. The presented results have a great importance both for the solution of some problems of the applied geothermics (e.g. determination of the heat flow density values from measured data, their accuracy, eventual data corrections and relation of measured data to the surface heat flow density distributions) and also for the modelling of the thermal state of the lithosphere (e.g. determination of the boundary conditions and of the model check parameters, robustness of the modelling approaches, etc.).
Dušan Majcin, Miroslav Král, Dušan Bilčík, Martin Šujan and Andrea Vranovská
The contribution presents the results of geothermic interpretation approaches applied to measured geothermal data and is focused to determination of the thermal conditions both for application of classic hydrothermal sources exploitation and specialized EGS technologies for electricity production in the region of Slovakia and adjacent areas. Primarily, the heat flow density data and the temperature distribution measurements in boreholes were interpreted by classic 1D interpolation and extrapolation methods. New terrestrial heat flow density map for the studied area was constructed using the values determined in boreholes, their interpretations, the newest outcomes of geothermal modelling methods based both on steady-state and transient heat transfer approaches, and on other recently gained geoscientific knowledge. Thereafter, we constructed the maps of temperature field distribution for selected depth levels up to 6000 m below the surface and the final map of the isothermal surface depths for the reservoir temperature of 160 ◦ C. This final map serves for the appraisal of the effective application of the binary cycle power plant technology in Slovakia in terms of thermal conditions.
Dušan Majcin, Roman Kutas, Dušan Bilčík, Vladimír Bezák and Ignat Korchagin
The contribution presents the results acquired both by direct cognitive geothermic methods and by modelling approaches of the lithosphere thermal state in the region of the Transcarpathian depression and surrounding units. The activities were aimed at the determination of the temperature field distribution and heat flow density distribution in the upper parts of the Earth’s crust within the studied area. Primary new terrestrial heat flow density map was constructed from values determined for boreholes, from their interpretations and from newest outcomes of geothermal modelling methods based on steady-state and transient approaches, and also from other recently gained geophysical and geological knowledge. Thereafter we constructed the maps of temperature field distribution for selected depth levels of up to 5000 m below the surface. For the construction we have used measured borehole temperature data, the interpolation and extrapolation methods, and the modelling results of the refraction effects and of the influences of source type anomalies. New maps and other geothermic data served for the determination of depths with rock temperatures suitable for energy utilization namely production of electric energy minimally by the binary cycles. Consequently the thermal conditions were used to identify the most perspective areas for geothermal energy exploitation in the region under study.
The area of the Danube Basin is interesting in the light of the evaluation both of the lithosphere structure and of various theories of Carpathian-Pannonian region tectonic evolution. The aim of this paper is to analyse both the thermal conditions in the Danube Basin and the mutual relations to geological structure and tectonic development of the region under study. First the improved distributions of the terrestrial heat flow density and of the lithosphere thickness were constructed using recently gained geophysical and geological knowledge. Then the critical analysis of existing models of the tectonic development of the region under study was carried out. The tectono-thermal interpretation activities were accomplished by new geothermal modelling approach for transient regime which utilizes also the backstriped sedimentology data as a control parameter of model. Finally the McKenzie’s “pure-shear” model of the Danube basin was constructed as acceptable conception for used geothermal and tectonic data. The determined stretching parameter has an inhomogeneous horizontal distribution and the thinning factors express the depth dependency for separate lithospheric layers.
We present mathematical modelling of the stationary geothermal field for the three-layered earth which includes a three-dimensional perturbing body below the first layer (over the halfspace substratum). The unperturbed temperature field corresponds to the uniform vertical heat flux. The perturbing body is in the form of 3D prismoid with sloping side faces, while its upper and lower face are rectangles at the planes z = z1, z2. The theoretical formulae are based on the generalized theory of the double-layer potential and boundary integral equation (BIE). Special attention is paid to the quadrilateral prismoids bounded by planar skew faces. The numerical calculations were performed for the 3D prismoids (blocks), the thermal conductivity of which was greater than that in the ambient second layer, while the upper face of the prismoid may be in contact with the upper layer and the lower face may touch the bottom halfspace. Numerous graphs are shown for the disturbance of the temperature and heat flow distribution on the surface of the Earth or inside all three layers.
Our contribution presents the geological analysis results of the lithological composition for deep geothermal sources characterized by the thermal conditions suitable for application of classic hydrothermal sources exploitation and specialized EGS technologies for the electricity production in the territory of Slovakia. The results are presented in the form of lithological characterization for the isothermal surface depths with the reservoir temperature of 160 °C. The lithological conditions of geothermal source regions were constructed using available published and archive materials. From the point of view of technically utilized depths (up to 5000 m) there are two most perspective regions – Eastern Slovakia and Danube Basin with surrounding areas. We tried to characterize supposed lithological composition also in second category of geothermal sources between 5and 6km.
Vladimír Bezák, Josef Pek, Dušan Majcin, Jana Bučová, Tomáš Šoltis, Dušan Bilčík and Radek Klanica
In this paper we present a geological interpretation of magnetotelluric sounding along the southern part of the seismic 2T profile situated in the southern Central Slovakia. The complexes with higher conductivity are imaged in the shallow depths, formed by the Tertiary sediments and volcanics. In the northernmost part of the profile, the influence of non-conductive complexes composed of orthogneisses and overlying Mesozoic carbonates is significant. In the central part of the profile, the low conductive granitoid complexes are superposed over the metamorphic rocks with higher conductivity. This structure is a remnant of the Hercynian middle crust nappes. The most outstanding phenomenon of the profile is the sudden, almost step change in the conductivity parameters of the crust in the southern part. The significantly high conductivity of the crust in this area is most probably not related to its lithological composition, but by the abundant supply of fluids in the crust connected with the Neogene tectonic and volcanic processes.
Dušan Majcin, Dušan Bilčík, Roman Kutas, Petra Hlavňová, Vladimír Bezák and Ľudovít Kucharič
The locality of the northeastern most part of Slovakian Flysch belt belongs to interesting areas in terms of the interpretation of geothermal conditions in mutual relation with the lithosphere structure and their tectonic development. The evaluation of the geothermal energy sources parameters of this locality is likewise worthwhile. The region under study has the centre in position of the borehole Zboj ZB-1 and spreads out Slovakia also in Poland and Ukraine.
Our contribution provides the analyses of existing geothermal data enhanced by the construction of temperature field models corresponding to the global and local aspects that influence the temperature and heat flow density distributions. The analyses are related to the structures and effects of separate phenomena along as well as across the Carpathian arc. The model calculations were carried out both by analytical and numerical methods of solving the heat transfer equations including their steady state forms and transient cases too.
Besides the regional trend of thermal activity decrease in direction from East-Slovakian Basin to the outer Carpathian units the combined local influences are applied: subsurface thermophysical parameters of rock complexes distributions, non-stationary sources from supposed subvolcanic bodies in close surroundings of borehole Zboj ZB-1, and the effects of the hydrological factors. Considering the observed higher thermal activity in arched zone along the Carpathian structures we discussed the thermal effects of rock complexes supposed as a source of regional Carpathian Conductivity Anomaly and the transfer of heat from East-Slovakian Basin to Outer Carpathian Flysch units. The analysis and the modelling results suggest that the mentioned activity is caused by the influences of source type phenomena mainly related to deep fault systems at the margin of the European Platform. That means the anomalies in heat flow density distribution can reach the value 70 mW/m2 and more in the zone above the thermally active deep-fault system with the presence of volcanism and hydrothermal activities.