Development and validation of regression model via machine learning to estimate thermal conductivity and heat flow using igneous rocks from the Dikili-Bergama geothermal region, Western Anatolia

In western and southwestern Anatolia, the geothermal gradient cannot be accurately measured in many wells due to the complex horizontal water cycle. The aim of this study is to calculate the geothermal gradients by using a new approach for such wells. In this case, the first step is to calculate the geothermal gradients in order to estimate the heat flow values around the wells. Naturally, a direct heat flow estimate cannot be made for wells without a geothermal gradient. However, the heat flow values can be indirectly obtained by different methods. Curie point depth, silica geothermometer, and magnetotelluric conductive layer depth are some of these indirect methods. In this study, we used the heat flow data based on the Curie depth. In this approach, Curie temperature gradients are calculated using the Curie heat flow values and thermal conductivities for problematic wells. An empirical relationship between the Curie temperature gradient and the correctly measured temperature gradients in the region was established. With this relationship, it is possible to make an approach from the current Curie temperature gradient to the normal temperature gradient. In this way, heat flow can also be calculated for areas where no geothermal gradient can be obtained, and heat flow distribution over the whole area can be given. This proposed approximation, to obtain thermal gradient and heat flow, can also be extended to any other region.

Abstract: Geothermal gradients and present day heat flow values were evaluated for about seventy one wells in parts of the eastern Niger delta, using reservoir and corrected bottom – hole temperatures data and other data collected from the wells. The results showed that the geothermal gradients in the shallow/continental sections in the Niger delta vary between 10 - 18° C/km onshore, increasing to about 24° C/km seawards, southwards and eastwards. In the deeper (marine/paralic) section, geothermal gradients vary between 18 - 45° C/km. Heat flow values computed using Petromod 1–D modeling software and calibrated against corrected BHT and reservoir temperatures suggests that heat flow variations in this part of the Niger delta range from 29 – 55 mW/m2 (0.69 – 1.31 HFU) with an average value of 42.5 mW/m2 (1.00 HFU). Heat flow variations in the eastern Niger delta correspond closely to variations in geothermal gradients. Geothermal gradients increase eastwards, northwards and seawards from the coastal swamp. Vertically, thermal gradients in the Niger delta show a continuous and non-linear relationship with depth, increasing with diminishing sand percentages. As sand percentages decrease eastwards and seawards, thermal gradient increases. Lower heat flow values (< 40 mW/m2) occur in the western and north central parts of the study area. Higher heat flow values (40 - 55 mW/m2) occur in the eastern and northwestern parts of the study area. A significant regional trend of eastward increase in heat flow is observed in the area. Other regional heat flow trends includes; an eastwards and westwards increase in heat flow from the central parts of the central swamp and an increase in heat flow from the western parts of the coastal swamp to the shallow offshore. Vertical and lateral variations in thermal gradients and heat flow values in parts of the eastern Niger delta are influenced by certain mechanisms and geological factors which include lithological variations, variations in basement heat flow, temporal changes in thermal gradients and heat flow, related to thicker sedmentary sequence, prior to erosion and evidenced by unconformities, fluid redistribution by migration of fluids and different scales of fluid migration in the sub-surface and overpressures.

Basin and petroleum systems are routinely modelled to provide qualitative and quantitative assessments of a hydrocarbon play. The importance of the rock thermal properties and heat flow density in thermal modelling the history of a basin are well‐known, but little attention is paid to assumptions of the thermal conductivity, present‐day heat flow density and thermal history of basins. Assumed values are often far from measured values when data are available to check parameters, and effective thermal conductivity models prescribed in many basin simulators require improvement. The reconstructed thermal history is often justified by a successful calibration to present‐day temperature and vitrinite reflectance data. However, a successful calibration does not guarantee that the reconstruction history is correct. In this paper, we describe the pitfalls in setting the thermal conductivity and heat flow density in basin models and the typical uncertainties in these parameters, and we estimate the consequences by means of a one‐dimensional model of the super‐deep Tyumen SG‐6 well area that benefits from large amounts of reliable input and calibration data. The results show that the entire approach to present‐day heat flow evaluations needs to be reassessed. Unreliable heat flow density data along with a lack of measurements of rock thermal properties of cores can undermine the quality of basin and petroleum system modelling.

Gonghe Basin is the most critical distribution area of hot dry rock (HDR) geothermal resources in China. Geophysical results (resistivity, velocity, density, etc.) provide an indirect way to image the spatial distribution to understand its genesis, which has a multisolution problem. However, heat flow and thermal conductivity are the most direct and reliable evidence to reveal the distribution of geothermal resources. The conventional thermal conductivity and heat flow obtained based on geologic surveys and rock samples are highly accurate, but it is challenging to characterize the regional distribution characteristics. In this paper, we develop the heat transfer adaptive finite-element equation parameter inversion workflow to invert the thermal parameters and analyze the geothermal formation mechanisms in the Gonghe Basin. First, the synthetic model test verifies that our inversion process has reliable accuracy and strong antinoise ability. For the Gonghe Basin HDR geothermal example, we use high-precision aeromagnetic data to estimate the Curie depth using the improved Parker-Oldenburg method. Then, the regional conductivity thermal and temperature field can be established according to the empirical formula as the initial input model for the inversion procedure. In addition, we collect the temperature data of six HDR geothermal wells across the Gonghe-Guide Basin as a priori constraint information. Combined with the inverted thermal parameters (thermal conductivity, geothermal gradient, and heat flow), geologic structure, and geophysical result, we infer that the high thermal conductivity layer at a depth of 5–10 km provides the main deep heat source channel and the shallow low thermal conductivity fine sandstone layer of Neogene provides good caprock protection for forming a high-temperature geothermal reservoir.

A theoretical equation of the combined thermal conductive, convective, and radiative heat flow through heterogeneous multilayer fibrous materials is presented. Samples whose properties are analyzed by this equation were constructed from glass and ceramic webs and used in an earlier work to experimentally determine their thermal conductivities. In that experimental work, overall effective thermal conductivities were determined using a guarded hot plate instrument with temperatures ranging from 430 to 480°C. In the theoretical equation presented here, thermal convective heat flow is ignored because of fabric structural conditions, and the conduction component of the overall conductivity is determined by Fricke's equation. Furthermore, the results of Fricke's equation and the overall effective thermal conductivity are used to estimate the radiative thermal conduc tivity of the samples.

Derived values of the thickness of the effective elastic lithosphere on Mars are converted to estimates of lithospheric thermal gradients and surface heat flow by finding the thickness of the elastic‐plastic plate having the same bending moment and curvature, subject to assumed strain rates and temperature‐dependent flow laws for crustal and mantle material. Local thermal gradients and heat flow values so estimated were 10–14 K km−1 and 25–35 mW m−2, respectively, at the time of formation of flexurally induced graben surrounding the Tharsis Montes and Alba Patera, while gradients and heat flow values of less than 5–6 K km−1 and 17–24 mW m−2, respectively, characterized the lithosphere beneath the Isidis mascon and Olympus Mons at the time of emplacement of these loads. On the basis of the mean global thickness of the elastic lithosphere inferred to support the Tharsis rise and estimates of mantle heat production obtained from SNC meteorites, it is suggested that the present average global heat flux on Mars is in the range 15–25 mW m−2. Approximately 3–5% of this heat flux during the Amazonian epoch has been contributed by excess conducted heat in the central regions of major volcanic provinces. Most likely, this excess heat flux has been delivered to the base of the lithosphere by mantle plumes. The fractional mantle heat transport contributed by plumes during the last 2 b.y. on Mars is therefore similar to that at present on Earth.

The Curie point depth, or magnetic basal depth, of the Lesugolo geothermal area in Ende, Flores Island, East Nusa Tenggara, Indonesia was estimated by performing spectral analysis on spatial magnetic data and transforming it into the frequency domain, resulting in a link between the 2D spectrum of magnetic anomalies and the depths of the top and centroid of the magnetic sources. Shallow Curie point depths of 16 to 18 km were found in the north-northeast to southeast areas of Lesugolo, while deeper depths of 24 to 26 km were found in the southwest. The tectonic setting beneath the central part of Flores Island governs the distribution of the Curie point depths in the area. Shallow Curie point depth zones are associated with high thermal gradients (30 to 34 °C/km) and heat flow (80 to 100 mW/m2). Deep depths, on the other hand, correspond to zones of low thermal gradient (21 to 26 °C/km) and low heat flow (65 to 80 mW/m2). Both the derived thermal gradient and the heat flow maps contribute to a better understanding of the Lesugolo geothermal system’s configuration. This study suggests that the Lesugolo geothermal area’s prospect zone is located in the center of the investigated area, where the Lesugolo normal fault forms its southeastern boundary.

Results of geothermal studies carried out at 72 localities have been used in evaluation of temperature gradient and heat flow values of the upper crust in the state of Rio de Janeiro. The investigations included temperature logs in boreholes and wells, calculation of geothermal gradients, measurements of thermal conductivity and determination of heat flow density. In addition, estimates of temperature gradients and heat flow were also made for areas of thermo-mineral springs, based on the so-called geochemical methods. Analysis of these data sets, after incorporation of appropriate corrections (for the perturbing effects of drilling operations, topography and climate changes) has allowed for the first time a better understanding of the regional distribution of thermal gradients and heat flow within the study area. The results obtained indicate that geothermal gradient values are in the ranges of 14 to 26oC/km in Precambrian metamorphic terrain and 19 to 33oC/km in areas of Phanerozoic sedimentary basins. Most of the rock formations are characterized by thermal conductivity values varying from 2.2 to 3.6 Wm-1K-1. Consequently regionally averaged mean heat flow values are found to fall in the interval of 40 to 70 mW/m2. Computer generated contour maps reveal that geothermal gradients and heat flow are systematically high in the western compared to the eastern parts of the state of Rio de Janeiro. There are indications that this geothermal anomaly is probably associated with the belt of Tertiary alkaline intrusives, between Itatiaia and Cabo Frio. Residual heat of large scale magma intrusions in the later part of the Tertiary period may be one of the possible mechanisms responsible for this thermal anomaly.

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Surface heat flow and CO2 emissions within the Ohaaki hydrothermal field, Taupo Volcanic Zone, New Zealand

The subsurface temperature distribution of part of Chad sedimentary basin has been determined by applying analytical solution for multi-layer-model in solving the 1-D steady state conductive heat flow equation. Four-layer model was adopted because the Chad basin is made up of four lithostratigraphies. In this model, equilibrium geotherm of the four layers was computed by considering each layer separately while the temperature and heat flow are matched across the boundaries. The solution was used for generating temperature for each of the formation. Computed minimum, maximum and average thermal conductivity and surface heat flow of the basin were used as the input parameters for the analytical solution. The estimated temperatures increase with depth within the sedimentary column. The estimated temperatures were compared with measured bottom hole temperatures from four deep wells in the basin and the result shows very good match for the following different scenarios; (1) when maximum thermal conductivities of each formations are combined with the maximum heat flow of 100 mWm-2, (2) when the average thermal conductivities of each formation and the average heat flow of 85 mWm-2 are used as input for the model and (3) when the minimum thermal conductivities of each formation and the minimum heat flow of 65 mWm-2 are used as input for the model. The thermal structure of the sediment depends on its thermal conductivity, radiogenic heat sources, basal heat flow and surface temperature. The results of this research work have been used to effectively characterize the thermal structure of the study area.

Correlation analysis of geothermal data for the sedimentary basins of India

Simple shear and pure shear extension of the lithosphere produce very different patterns of heat flow and topography. These differences are investigated using a numerical technique which solves for two‐dimensional conductive and advective heat transport through time. Simple shear extension of the lithosphere is modeled as occurring along a straight shear zone. Two parameters define the simple shear model: the dip of the shear zone and its width. Likewise, the pure shear model is defined by two variables: the initial width of a vertical zone of pure shear extension and the rate of change of its width. These pairs of parameters are varied between calculations, as is the overall rate of extension. Each model results in distinct patterns of crustal thinning, lithospheric thermal structure, heat flow, thermal uplift, crustal subsidence, and topography. For the simple shear model, extension results in asymmetric uplift across the rift, while the total volume of uplift is limited by the total amount of extension. The peak heat flow and thermal uplift are centered over the intersection of the shear zone with the surface. Isostatic response to simple shear extension results in successive, formerly active shear zones being rotated into listric faults which sole into a subhorizontal detachment. The pure shear results show that the surface heat flow is greater for smaller widths of the zone of extension. For the same overall extension rate, a pure shear model with a narrow zone of extension can result in pressure release melting of the mantle long before low angle simple shear models. These results are compared with topographic and heat flow data from the northern Red Sea rift, a Neogene continental rift which is close to initiating seafloor spreading. The long wavelength topographic asymmetry across the Red Sea, which has been cited as evidence for simple shear extension of the lithosphere, is not matched by any of the models. The observed high heat flow anomalies in the Red Sea require a large component of pure shear lithospheric extension centered under the region of maximum crustal extension. In contrast, at the plate separation rate of the northern Red Sea, simple shear extension of the lithosphere along a shallow (<30°) dip detachment is ineffective in reproducing the observed heat flow anomalies. Only a narrowing region of pure shear extension can satisfy the width of the rift, and the peak heat flow values and generate pressure release melting.

___________________________________________________________ Temperature and heat-flow plays an important role in the field of Geodynamics, many other processes can be explained on the basis of these two properties since all mechanical properties of the lithosphere, like the rheology of a region, are dependent on the temperature and pressure conditions prevailing in lithosphere in that region. Heat flow from continental/shield and oceanic lithosphere is attributable to different processes, but it is found that the heat flow from oceanic lithosphere is greater than its continental counterpart. This poster mainly concentrates on the thermal distribution, heat flow and topography of the oceanic floor at creation point, i.e., mid-oceanic ridges. Topography/subsidence of the oceanic floor, which is calculated from the thermal distribution, is an important tool in reconstructing the tectonic history of the Earth where other parameters like magnetic anomalies fail to do so. In order to determine these basic properties we need to define a theoretical model. Two basic models are available to explain the heat flow i.e., the cooling model and the plate model. Earlier works (by various authors) show that the plate model explains the variation in depth and heat flow with increasing age of the oceanic floor, better at older ages. Variants of the plate model, like isothermal base, constant basal heat flow have been successful in explaining various anomalies, but the work presented here highlights the importance of small-scale convection at the base of the lithospheric plate. A plate model is considered with small-scale convection at the plate bottom boundary. Heat-flow and bathymetric results show that the small scale convection model explains the variation of these two properties for the oceanic lithosphere is way better than previous models for older ages (70-180 Ma). .

A model for thermal gradient and heat flow in central Chile: The role of thermal properties