A model for temperature variations in sedimentary basins due to random radiogenic heat sources

The thermal structure of a sedimentary basin is controlled by its thermal conductivity, its boundary conditions, water flow, rate of sedimentation and erosion and radiogenic heat sources. The radiogenic heat production in the sediments is known to vary over several orders of magnitude, with the lowest values in evaporites and carbonates and the highest values in black shales. Due to a paucity of information available on the existing heat sources, this parameter can be represented with a known mean value and a Gaussian correlation structure rather than a deterministic function. In this paper, the 1-D steady-state thermal structure in a sedimentary basin has been modelled in a stochastic framework with a random radiogenic heat source, and analytical expressions for the first two moments of the temperature field have been obtained. A synthetic example has been examined to quantify the error bounds on the temperature field due to uncertainties in the radiogenic heat sources.     

Joint three-dimensional inversion of coupled groundwater flow and heat transfer based on automatic differentiation: sensitivity calculation, verification, and synthetic examples

Inverse methods are useful tools not only for deriving estimates of unknown parameters of the subsurface, but also for appraisal of the thus obtained models. While not being neither the most general nor the most efficient methods, Bayesian inversion based on the calculation of the Jacobian of a given forward model can be used to evaluate many quantities useful in this process. The calculation of the Jacobian, however, is computationally expensive and, if done by divided differences, prone to truncation error. Here, automatic differentiation can be used to produce derivative code by source transformation of an existing forward model. We describe this process for a coupled fluid flow and heat transport finite difference code, which is used in a Bayesian inverse scheme to estimate thermal and hydraulic properties and boundary conditions form measured hydraulic potentials and temperatures. The resulting derivative code was validated by comparison to simple analytical solutions and divided differences. Synthetic examples from different flow regimes demonstrate the use of the inverse scheme, and its behaviour in different configurations.     

On the importance of rock thermal conductivity and heat flow density in basin and petroleum system modelling

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.     

Terrestrial heat flow and lithospheric thermal structure in the Chagan Depression of the Yingen-Ejinaqi Basin,north central China

The Chagan Depression in the Yingen-Ejinaqi Basin, located at the intersection of the Paleo-Asian Ocean and the Tethys Ocean domains is an important region to gain insights on terrestrial heat flow, lithospheric thermal structure and deep geodynamic processes. Here, we compute terrestrial heat flow values in the Chagan Depression using a large set of system steady-state temperature data from four representative wells and rock thermal conductivity. We also estimate the “thermal” lithospheric thickness, mantle heat flow, ratio of mantle heat flow to surface heat flow and Moho temperature to evaluate the regional tectonic framework and deep dynamics. The results show that the heat flow in the Chagan Depression ranges from 66.5 to 69.8 mW/m², with an average value of 68.3 ± 1.2 mW/m². The Chagan Depression is characterized by a thin “thermal” lithosphere, high mantle heat flow, and high Moho temperature, corresponding to the lithospheric thermal structure of “cold mantle and hot crust” type. We correlate the formation of the Yingen-Ejinaqi Basin to the Early Cretaceous and Cenozoic subduction of the western Pacific Plate and the Cenozoic multiple extrusions. Our results provide new insights into the thermal structure and dynamics of the lithospheric evolution in central China.     

Application of the boundary element method to a terrestrial heat flow problem

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In this paper, we apply the boundary element method (BEM) to the 2-D steady state heat flow problem of what would be the perturbation to the regional temperature gradient, and hence heat flow density, determined from temperatures measured in a borehole that passes close to, but does not penetrate, a body of anomalous thermal properties. This type of problem with an infinity boundary is particularly well suited to the BEM.
The results have been compared with those obtained from analytical solutions for bodies of simple shape; it is found that for the worst case of a close approach to a boundary of small radius of curvature, a numerical modelling error of less than 1 per cent can still be obtained provided the length of each element is less than the shortest distance between the calculation point and the object.     

Emplacement mechanism of gravity flows inferred from high resolution Lidar data: The 1944 Somma–Vesuvius lava flow (Italy)

A Digital Terrain Model derived from high resolution Lidar data allows the determination of the morphometric and physical parameters of a lava flow erupted from the Somma–Vesuvius volcano in 1944. The downstream variation of morphometric parameters including slope, aspect, relative relief, thickness, width, and cross sectional area is analyzed, and the changes in viscosity, velocity and flow rate are estimated. The aims of the analyses are to recognize different flow surfaces, to reconstruct the flow kinematics, and to obtain information on the mechanism of emplacement. The results indicate that the 1944 lava flow can be divided in three sectors: a near vent sector (NVS) characterized by a toe-like surface, an intermediate sector (IS) with an ‘a’ātype brittle surface, and a distal sector (DS) with a sheet-like ductile surface. Lateral leveés and channels do not occur in NVS, whereas they are well developed in IS. In DS, leveés increase with an increasing distance from the vent. Fold-like surfaces occur in NVS and DS, reflecting local shortening processes due to a decrease in the slope of the substratum and overflows from the main channel. IS and DS emplaced between March 18 and 21, 1944, whereas NVS emplaced on March 19 and partly covered IS. The morphometric and physical parameters indicate that IS moved in a ‘tube’-like regime, whereas DS emplaced in a 'mobile crust' regime. The IS to DS transition is marked by an increase in velocity and the flow rate, and by a decrease in thickness, width, cross sectional area, and viscosity. This transition is due to an abrupt increase in the slope of the substratum. The estimated velocity values are in good agreement with the measurements during the 1944 eruption. The analysis used here may be extended to other lava flows. Some gravity flows (debris/mud flows, floods, and avalanches) have rheological properties and shapes similar to those of lavas, and the same process-form relationships may apply to these flows. The approach used here may be therefore useful for evaluating hazards from various gravity currents.