scholarly journals Thermal conductivity of sandstones from Biot’s coefficient

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. D173-D185 ◽  
Author(s):  
Tobias Orlander ◽  
Eirini Adamopoulou ◽  
Janus Jerver Asmussen ◽  
Adam Andrzej Marczyński ◽  
Harald Milsch ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Flow ◽  
Cross Section ◽  
Geometric Mean ◽  
Well Log ◽  
Biot’S Coefficient ◽  
Model Predictions ◽  
The Cross ◽  
Rock Texture

Thermal conductivity of rocks is typically measured on core samples and cannot be directly measured from logs. We have developed a method to estimate thermal conductivity from logging data, where the key parameter is rock elasticity. This will be relevant for the subsurface industry. Present models for thermal conductivity are typically based primarily on porosity and are limited by inherent constraints and inadequate characterization of the rock texture and can therefore be inaccurate. Provided known or estimated mineralogy, we have developed a theoretical model for prediction of thermal conductivity with application to sandstones. Input parameters are derived from standard logging campaigns through conventional log interpretation. The model is formulated from a simplified rock cube enclosed in a unit volume, where a 1D heat flow passes through constituents in three parallel heat paths: solid, fluid, and solid-fluid in series. The cross section of each path perpendicular to the heat flow represents the rock texture: (1) The cross section with heat transfer through the solid alone is limited by grain contacts, and it is equal to the area governing the material stiffness and quantified through Biot’s coefficient. (2) The cross section with heat transfer through the fluid alone is equal to the area governing fluid flow in the same direction and quantified by a factor analogous to Kozeny’s factor for permeability. (3) The residual cross section involves the residual constituents in the solid-fluid heat path. By using laboratory data for outcrop sandstones and well-log data from a Triassic sandstone formation in Denmark, we compared measured thermal conductivity with our model predictions as well as to the more conventional porosity-based geometric mean. For outcrop material, we find good agreement with model predictions from our work and with the geometric mean, whereas when using well-log data, our model predictions indicate better agreement.

Convective Heat Transfer in Elliptical Microchannels Under Slip Flow Regime and H1 Boundary Conditions

2015 ◽  
Vol 138 (4) ◽  
Author(s):  
Pamela Vocale ◽  
Gian Luca Morini ◽  
Marco Spiga
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Aspect Ratio ◽  
Boundary Conditions ◽  
Convective Heat Transfer ◽  
Cross Section ◽  
Convective Heat ◽  
Slip Flow ◽  
The Cross ◽  
Cross Section Geometry

In this work, hydrodynamically and thermally fully developed gas flow through elliptical microchannels is numerically investigated. The Navier–Stokes and energy equations are solved by considering the first-order slip flow boundary conditions and by assuming that the wall heat flux is uniform in the axial direction, and the wall temperature is uniform in the peripheral direction (i.e., H1 boundary conditions). To take into account the microfabrication of the elliptical microchannels, different heated perimeter lengths are analyzed along the microchannel wetted perimeter. The influence of the cross section geometry on the convective heat transfer coefficient is also investigated by considering the most common values of the elliptic aspect ratio, from a practical point of view. The numerical results put in evidence that the Nusselt number is a decreasing function of the Knudsen number for all the considered configurations. On the contrary, the role of the cross section geometry in the convective heat transfer depends on the thermal boundary condition and on the rarefaction degree. With the aim to provide a useful tool for the designer, a correlation that allows evaluating the Nusselt number for any value of aspect ratio and for different working gases is proposed.

Charge transfer from rare gas atoms to Kr+

1982 ◽  
Vol 60 (7) ◽  
pp. 981-987 ◽  
Author(s):  
B. Hird ◽  
S. P. Ali
Keyword(s):  
Charge Transfer ◽  
Energy Dependence ◽  
Cross Section ◽  
Rare Gas ◽  
Zener Model ◽  
Energy Data ◽  
Model Predictions ◽  
Rare Gas Atoms ◽  
The Cross ◽  
Good Agreement

The cross section for electron capture by Kr+ ions from rare gas atoms between 30 and 120 keV is found to be in good agreement with previous measurements where these exist, except for neon. The Rapp–Francis model gives an acceptable fit to the energy dependence of these and higher energy data but is too large by a factor of about five. In contrast the Landau–Zener model predictions are too large for helium and neon and too small for the heavier targets unless metastable states of krypton with large polarizabilities dominate the cross section.

scholarly journals Numerical study on heat transfer and flow resistance characteristics of multi-head twisted spiral tube

2021 ◽  
pp. 206-206
Author(s):  
Zhiqun Zheng ◽  
Fayi Yan ◽  
Lei Shi
Keyword(s):  
Heat Transfer ◽  
Numerical Calculation ◽  
Cross Section ◽  
Heat Transfer Performance ◽  
Numerical Study ◽  
Smooth Tube ◽  
Transfer Performance ◽  
Spiral Tube ◽  
Inside Diameter ◽  
The Cross

A numerical calculation model of multihead twisted spiral tube (MTST) was established. In the range of Reynolds number from 5000 to 35000, the influence of different twisted structure on the flow and heat transfer characteristics of the MTST was studied by numerical calculation. Numerical calculation results indicate that the Nusselt number and friction coefficient increase with the increase in the ratio of outside and inside diameter of the cross-section, the increase in the number of twisted nodes, and the increase in the number of twisted spiral tube heads. Under the condition of the same spiral structure and the same hydraulic diameter, the heat transfer performance of the MTST is better than that of the spiral smooth tube. In addition, through artificial neural network (ANN) analysis, the ratio of outside and inside diameter of the cross-section, number of twisted nodes, and the number of twisted spiral tube heads were optimized to promote the comprehensive heat transfer performance. The performance evaluation criterion is the highest when the ratio of outside and inside diameter of the cross-section is 25/22.5, the number of twisted nodes is 3, and the number of twisted spiral tube heads is 3, which is 1.849 of the spiral smooth tube.

Modelling of Thermal Rectification in Si and Ge Thin Films

2013 ◽  
Author(s):  
E. Chávez-Ángel ◽  
C. M. Sotomayor Torres ◽  
F. Alzina
Keyword(s):  
Thin Films ◽  
Thermal Conductivity ◽  
Heat Flow ◽  
Temperature Dependence ◽  
Cross Section ◽  
Impurity Concentration ◽  
Boundary Scattering ◽  
Bulk Materials ◽  
Thermal Rectification ◽  
Scattering Effects

In the present work we have studied an extension of the classical thermal rectification, arising in certain cases from the contact of two dissimilar bulk materials with different temperature dependence of the thermal conductivity, to the Si-Ge system when boundary scattering effects are taken into account. Moreover, the directionality of the in-plane heat flow in a Si plate can be achieved by tuning the thickness and the impurity concentration along the cross section of the plate. We have designed several potential structures with this function in mind and discussed the physics behind.

Modeling the Phonon Transport in Nanowire with Different Cross-Section

2013 ◽  
Vol 401-403 ◽  
pp. 852-855
Author(s):  
Gao Hui Su ◽  
Zi Chun Yang ◽  
Feng Rui Sun
Keyword(s):  
Thermal Conductivity ◽  
Cross Section ◽  
Diffuse Reflection ◽  
Silicon Nanowire ◽  
Circular Cross Section ◽  
Phonon Transport ◽  
Reflection Mode ◽  
Section Shape ◽  
Section Size ◽  
The Cross

The phonon transport in silicon nanowire was simulated by Monte Carlo Method (MCM). The effect on the phonon transport of the boundary reflection mode, cross-section size and cross-section shape was studied. Analysis shows that diffuse reflection can result in phonon accumulation at the circumferential boundary. As the cross-section size decrease, the nonuniformity of the temperature distribution within the cross-section becomes more severe. When the area of the square cross-section silicon nanowire (SCSN) is equal to that of the circular cross-section silicon nanowire (CCSN), the thermal conductivity of them is more close to each other.

Heat production and thermal conductivity of rocks from the Pikwitonei–Sachigo continental cross section, central Manitoba: implications for the thermal structure of Archean crust

1987 ◽  
Vol 24 (8) ◽  
pp. 1583-1594 ◽  
Author(s):  
David M. Fountain ◽  
Matthew H. Salisbury ◽  
Kevin P. Furlong
Keyword(s):  
Thermal Conductivity ◽  
Heat Flow ◽  
Cross Section ◽  
Heat Production ◽  
Thermal Structure ◽  
Granulite Facies ◽  
Surface Heat ◽  
Gamma Ray Spectrometry ◽  
Surface Heat Flow ◽  
Greenstone Belts

The Pikwitonei and Sachigo subprovinces of central Manitoba provide a cross-sectional view of the Superior Province crust. In cross section, the upper to mid-level crust is composed of synformal greenstone belts surrounded by tonalitic gneisses, both of which are intruded by granitoid plutons. This crustal structure persists downward into the granulite facies, where keels of the greenstone belts can be found. To constrain thermal models of the crust, we measured heat production and thermal conductivity in 60 rocks from this terrain using standard gamma-ray spectrometry and divided bar techniques. Large vertical and lateral heterogeneities in heat production in the upper crust are evident; heat production is high in granites and metasedimentary rocks, intermediate in tonalite gneisses, and low in the portions of greenstone belts dominated by mafic meta-igneous rocks. In the deeper granulite facies rocks, heat production decreases by a factor of two in the tonalitic gneisses and remains low in the high-grade mafic rocks. When applied to the Pikwitonei–Sachigo crust cross section, the laboratory data here do not support step function or exponential models of the variation of heat production with depth. However, estimates of surface heat flow and surface heat production for various sites in the crustal model yield the well-known linear relationship between surface heat production and surface heat flow observed for heat-flow provinces for both one- and two-dimensional models. This demonstrates that determinations of heat production with depth based on inversion of the linear heat-production–heat-flow relationship are nonunique.

CFD Investigation of Heat Transfer in Supercritical Water-Cooled Flow Through 3×3 Fuel Rod Bundles

2008 ◽  
Author(s):  
Zhi Shang ◽  
Yufeng Yao
Keyword(s):  
Heat Transfer ◽  
Secondary Flow ◽  
Cross Section ◽  
Supercritical Water ◽  
Wall Temperature ◽  
Mass Flux ◽  
Rod Bundles ◽  
Fuel Rod ◽  
Channel Analysis ◽  
The Cross

CFD investigation of heat transfer in supercritical water-cooled flow through fuel rod bundles has been carried out, using commercial software STAR-CD 4.02 with specific ad hoc user routines for modeling physical property of supercritical water. The configuration considered is a typical core assembly of 3×3 fuel rod (round tube) bundles inside solid square box, as seen in the nuclear reactor. After priori mesh convergence studies, investigations are focused on key characteristics of flow and heat transfer performance, notably the wall temperature distributions, the mass flux and the secondary flow patterns in the cross-section. It is found that the rod wall temperature distributions exhibit highly non-uniform feature near the domain exit with very high wall temperatures: about 625°C observed on the corner rod and about 562.5°C on the border rod, respectively. It is believed that the appearance of the extremely wall temperature may be related to the non-uniform distributions of mass flux in the cross-section of the bundles as the low mass flux co-existing with the high wall temperature. Further analysis of the secondary flow in the cross-section reveals wider spectrum of vortex flow structures, more complicated than previously noted by the sub-channel analysis. To verify the influence of turbulence models on the secondary flow, both linear and non-linear k-ε models are applied and results are quite similar. This finding indicates that the cause of the secondary (cross) flow might not be solely due to the anisotropic property of turbulence as suggested by other researchers. The present 3D CFD study provides more complete database of 3×3 rod bundle flows and will be useful to improve the industry practice of applying the sub-channel analysis.

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