Thermal Conductivities of Porous Rocks Filled with Stagnant Fluid

1961 ◽  
Vol 1 (01) ◽  
pp. 37-42 ◽  
Author(s):  
D. Kunii ◽  
J.M. Smith
Keyword(s):  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Water Solution ◽  
Pure Water ◽  
General System ◽  
Practical Significance ◽  
Glycerol Water ◽  
Starting Point ◽  
Thermal Conductivities ◽  
Stagnant Fluid

Abstract Effective thermal conductivities of sandstones filled with stagnant fluids were measured using a steady-state technique. Data were obtained for seven sandstone samples, taken from four different locations and ranging in permeability from 18 to 590 md. The measurements with gases (helium, nitrogen, air and carbon dioxide) covered a pressure range from 0.039 psia to 400 psig. Data were taken for four liquids - n-heptane, methyl alcohol, 79.8 weight per cent glycerol-water solution and pure water at atmospheric pressure. The experimental results were used to evaluate the theoretical equations for predicting stagnant conductivities developed earlier. The low-pressure measurements permitted evaluation of the consolidation parameter hpDp/ks (necessary to utilize the theory) for the various types of sandstones. Using these characteristic values, the theoretical equations correlated well with the experimental conductivity data for the several fluids and rock samples. Introduction An aspect of heat transfer in solid-fluid systems of considerable current interest is the effective thermal conductivity of porous media. The stimulus for study of the subject arises from the need for sound procedures for designing thermal methods of petroleum production. The general system occurs when there exists a flow of fluid through the pores of the solid material. However, a logical starting point in developing a theory for predicting the effective thermal conductivity in the general system is to attack the special case when the porous solid is filled with stagnant fluid. Since the flow rates anticipated in thermal production processes are very low, such stagnant conductivities k are also of practical significance.

scholarly journals Investigation of Effective Thermal Conductivity for Ordered and Randomly Packed Bed with Thermal Resistance Network Method

Energies ◽  
2019 ◽  
Vol 12 (9) ◽  
pp. 1666 ◽  
Author(s):  
Jian Yang ◽  
Yingxue Hu ◽  
Qiuwang Wang
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Thermal Resistance ◽  
Effective Thermal Conductivity ◽  
Packed Bed ◽  
Random Packing ◽  
Packing Factor ◽  
Resistance Network ◽  
Network Method ◽  
Thermal Conductivities

In the present paper, the effective thermal conductivities of Li4SiO4-packed beds with both ordered and random packing structures were investigated using thermal resistance network methods based on both an Ohm’s law model and a Kirchhoff’s law model. The calculation results were also validated and compared with the numerical and experimental results. Firstly, it is proved that the thermal resistance network method based on the Kirchhoff’s law model proposed in the present study is reliable and accurate for prediction of effective thermal conductivities in a Li4SiO4-packed bed, while the results calculated with the Ohm’s law model underestimate both ordered and random packings. Therefore, when establishing a thermal resistance network, the thermal resistances should be connected along the main heat transfer direction and other heat transfer directions as well in the packing unit. Otherwise, both the total heat flux and effective thermal conductivity in the packing unit will be underestimated. Secondly, it is found that the effect of the packing factor is remarkable. The effective thermal conductivity of a packed bed would increase as the packing factor increases. Compared with random packing at similar packing factor, the effective thermal conductivity of packed bed would be further improved with an ordered packing method.

Numerical determination of pressure-dependent effective thermal conductivity in Berea sandstone

2021 ◽  
Author(s):  
Mirko Siegert ◽  
Marcel Gurris ◽  
Erik Hans Saenger
Keyword(s):  
Experimental Data ◽  
Thermal Conductivity ◽  
Numerical Model ◽  
Effective Thermal Conductivity ◽  
Rock Sample ◽  
Rock Physics ◽  
Contact Phase ◽  
Data Set ◽  
Computed Tomography Images ◽  
Thermal Conductivities

<p>Within the scope of the present work, the pressure-dependent effective thermal conductivity of rock samples is simulated. Our workflow can be assigned to the field of digital rock physics. In a first step, a 3D micro-CT scan of a rock sample is taken. Subsequently, the resulting greyscale images are analysed and segmented depending on the occurring phases. Based on this data set, a computational mesh is created and the corresponding thermal conductivities are assigned to each phase. Finally the numerical simulations can be carried out.<br>For the representation of the pressure dependency we use the approach proposed by Saenger [1]. By making use of the watershed algorithm, boundaries between the individual grains of the rock sample are detected and assigned to an artificial contact phase. In the course of several simulations, the thermal conductivity of the contact phase is continuously increased. Starting with the thermal conductivity of the pore phase and ending with the thermal conductivity of the grain phase. A linear correlation is used to match the thermal conductivity of the contact phase with the pressure of a given experimental data set. This enables a direct comparison between simulation and measurement.<br>In a further step, the numerical model is calibrated to optimise the agreement between experimental data and simulation results. In particular, starting from two calibration points of the experimental data set, an adjustment of the thermal conductivities in the numerical model is carried out. While the thermal conductivity of the pore phase is held constant during the whole calibration process, thermal conductivities of the grain and contact phase are adjusted.</p><p>References<br>[1] Saenger et al. 2016. Analysis of high-resolution X-ray computed tomography images of Bentheim sandstone under elevated confining pressures. Geophysical Prospecting, 64(4), 848–859.</p><p> </p>

Convective Heat Transfer for Water-Based Alumina Nanofluids in a Single 1.02-mm Tube

2009 ◽  
Vol 131 (11) ◽  
Author(s):  
W. Y. Lai ◽  
S. Vinod ◽  
P. E. Phelan ◽  
Ravi Prasher
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Convective Heat Transfer ◽  
Effective Thermal Conductivity ◽  
Convective Heat ◽  
Volume Fraction ◽  
Pure Water ◽  
Submicron Particles ◽  
Strong Temperature Dependence ◽  
Water Based

Nanofluids are colloidal solutions, which contain a small volume fraction of suspended submicron particles or fibers in heat transfer liquids such as water or glycol mixtures. Compared with the base fluid, numerous experiments have generally indicated an increase in effective thermal conductivity and a strong temperature dependence of the static effective thermal conductivity. However, in practical applications, a heat conduction mechanism may not be sufficient for cooling high heat dissipation devices such as microelectronics or powerful optical equipment. Thus, thermal performance under convective heat transfer conditions becomes of primary interest. We report here the heat transfer coefficient h in both developing and fully developed regions by using water-based alumina nanofluids. Our experimental test section consists of a single 1.02-mm diameter stainless steel tube, which is electrically heated to provide a constant wall heat flux. Both pressure drop and temperature differences are measured, but mostly here we report our h measurements under laminar flow conditions. An extensive characterization of the nanofluid samples, including pH, electrical conductivity, particle sizing, and zeta potential, is also documented. The measured h values for nanofluids are generally higher than those for pure water. In the developing region, this can be at least partially explained by Pr number effects.

Measurements of the Intrinsic Thermal Conductivity of Individual Multi-Wall Carbon Nanotubes

2011 ◽  
Author(s):  
Juekuan Yang ◽  
Scott W. Waltermire ◽  
Yang Yang ◽  
Deyu Li ◽  
Yunfei Chen
Keyword(s):  
Thermal Conductivity ◽  
Carbon Nanotubes ◽  
Heat Source ◽  
Thermal Resistance ◽  
Effective Thermal Conductivity ◽  
Experimental Studies ◽  
Contact Thermal Resistance ◽  
Multi Wall Carbon Nanotubes ◽  
The Past ◽  
Thermal Conductivities

Thermal transport through carbon nanotubes (CNTs) attracted a lot of attention over the past decade. Several experimental studies have been carried out to determine the thermal conductivities of CNTs [1–3]. However, the measurements are based on an individual CNT sample between two suspended membranes and the results actually include both the intrinsic thermal resistance of the CNT and the contact thermal resistance between the CNT and the two suspended membranes that serve as a heat source and a heat sink. Hence, the effective thermal conductivity extracted from these measurements should be lower than the intrinsic thermal conductivities of the CNTs measured. To minimize the contact thermal resistance, electron beam induce deposition (EBID) of different metals has been used to increase the contact area between the CNT and the heat source and sink [3,4]. However, it is still not clear how effective this treatment is and to what level the effective thermal conductivity obtained after the EBID treatment reflects the intrinsic one.

Curvature Effect on the Thermal Conductivity of Nanowires

2008 ◽  
Author(s):  
Liang-Chun Liu ◽  
Mei-Jiau Huang ◽  
Ronggui Yang
Keyword(s):  
Thermal Conductivity ◽  
Monte Carlo ◽  
Effective Thermal Conductivity ◽  
Silicon Nanowires ◽  
Phonon Transport ◽  
Curvature Effect ◽  
Transport Efficiency ◽  
Directional Preference ◽  
Monte Carlo Simulator ◽  
Thermal Conductivities

Directional preference of the ballistic phonon transport plays an important role in the effective thermal conductivity of nanostructures. Curved nanowires can have very different thermal conductivities from straight ones. In this work, a Monte-Carlo simulator is developed and used to investigate the curvature effect on the phonon transport in silicon nanowires. The results show that the curvature of geometry does not alter the phonon transport efficiency in large wires but decreases the effective thermal conductivity in their nano-sized counterparts.

An Experimental Evaluation of the Effective Thermal Conductivities of Packed Beds at High Temperatures

1994 ◽  
Vol 116 (4) ◽  
pp. 829-837 ◽  
Author(s):  
K. Nasr ◽  
R. Viskanta ◽  
S. Ramadhyani
Keyword(s):  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
High Temperatures ◽  
Radiation Heat Transfer ◽  
Particle Diameter ◽  
Spherical Particles ◽  
Packed Beds ◽  
Packing Materials ◽  
Bed Temperature ◽  
Thermal Conductivities

Combined conduction and radiation heat transfer in packed beds of spherical particles was investigated. Three different packing materials (alumina, aluminum, and glass) of various particle diameters (2.5 to 13.5 mm) were tested. Internal bed temperature profiles and corresponding effective thermal conductivities were measured under steady-state conditions for a temperature range between 350 K and 1300 K. The effects of particle diameter and local bed temperature were examined. It was found that higher effective thermal conductivities were obtained with larger particles and higher thermal conductivity packing materials. The measured values for the effective thermal conductivity were compared against the predictions of two commonly used models, the Kunii–Smith and the Zehner–Bauer–Schlu¨nder models. Both models performed well at high temperatures but were found to overpredict the effective thermal conductivity at low temperatures. An attempt was made to quantify the relative contributions of conduction and radiation. Applying the diffusion approximation, the radiative conductivity was formulated, normalized, and compared with the findings of other investigators.

In Situ Characterization of Coal Ash Thermal Conductivity Under Oxidizing and Reducing Conditions

2011 ◽  
Author(s):  
D. Cundick ◽  
D. Maynes ◽  
T. Moore ◽  
D. R. Tree ◽  
M. R. Jones ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Flow Reactor ◽  
Coal Ash ◽  
In Situ Measurements ◽  
Powder River Basin ◽  
Reducing Conditions ◽  
Bituminous Coals ◽  
Thermal Conductivities

This work presents in situ measurements of the effective thermal conductivity in particulate coal ash deposits under both reducing and oxidizing environments. Laboratory experiments generated deposits on an instrumented deposition probe of loosely-bound particulate ash from three coals generated in a down-fired flow reactor with optical access. An approach is presented for making in situ measurements of the temperature difference across the ash deposits, the thickness of the deposits, and the total heat transfer rate through the ash deposits. Using this approach, the effective thermal conductivity was determined for coal ash deposits formed under oxidizing and reducing conditions. Three coals were tested under oxidizing conditions: two bituminous coals derived from the Illinois #6 basin and a subbituminous Powder River Basin coal. The subbituminous coal exhibited the lowest range of effective thermal conductivities (0.05–0.18 W/m· K) while the Illinois #6 coals showed higher effective thermal conductivities (0.2–0.5 W/m· K). One of the bituminous coals and the subbituminous coal were also tested under reducing conditions. A comparison of the ash deposits from these two coals showed no discernible difference in the effective thermal conductivity based on stoichiometry. All experiments indicated an increase in effective thermal conductivity with deposit thickness, probably associated with deposit sintering.

Tomography-Based Determination of the Effective Thermal Conductivity of Fluid-Saturated Reticulate Porous Ceramics

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Jörg Petrasch ◽  
Birte Schrader ◽  
Peter Wyss ◽  
Aldo Steinfeld
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Solid Phase ◽  
Effective Conductivity ◽  
Porous Ceramics ◽  
Conduction Heat Transfer ◽  
Digital Resolution ◽  
Reticulate Structure ◽  
Thermal Conductivities

The effective thermal conductivity of reticulate porous ceramics (RPCs) is determined based on the 3D digital representation of their pore-level geometry obtained by high-resolution multiscale computer tomography. Separation of scales is identified by tomographic scans at 30μm digital resolution for the macroscopic reticulate structure and at 1μm digital resolution for the microscopic strut structure. Finite volume discretization and successive over-relaxation on increasingly refined grids are applied to solve numerically the pore-scale conduction heat transfer for several subsets of the tomographic data with a ratio of fluid-to-solid thermal conductivity ranging from 10−4 to 1. The effective thermal conductivities of the macroscopic reticulate structure and of the microscopic strut structure are then numerically calculated and compared with effective conductivity model predictions with optimized parameters. For the macroscale reticulate structure, the models by Dul’nev, Miller, Bhattachary and Boomsma and Poulikakos, yield satisfactory agreement. For the microscale strut structure, the classical porosity-based correlations such as Maxwell’s upper bound and Loeb’s models are suitable. Macroscopic and microscopic effective thermal conductivities are superimposed to yield the overall effective thermal conductivity of the composite RPC material. Results are limited to pure conduction and stagnant fluids or to situations where the solid phase dominates conduction heat transfer.

The Effective Thermal Conductivity (ETC) of Spherical Packed-Bed Porous Media for Modification of the Color Surface as Black Color

2018 ◽  
Vol 911 ◽  
pp. 100-104
Author(s):  
Bundit Krittacom ◽  
Pornsawan Tongbai
Keyword(s):  
Thermal Conductivity ◽  
Porous Media ◽  
Effective Thermal Conductivity ◽  
Average Diameter ◽  
Packed Bed ◽  
Worst Case ◽  
Original Surface ◽  
Black Surface ◽  
Black Color ◽  
Stagnant Fluid

The effective thermal conductivity (ETC) of the spherical packed-bed porous media in stagnant fluid case is estimated by modifying the color surface of the porous media as black surface. The Alumina-Cordierite (Al-Co) ceramic balls having average diameter (d) of 5.0 cm is constructed as the porous media and, then, a porosity (f) has 0.398. For development of the porous media as black surface, the Al-Co ceramic balls are painted by black color and then it is composed of 600 °C × 8 hr. The experimental procedure to evaluate the ECT is based on ASTM E1225. A higher temperature (TH) is investigated in the range of 400 to 800 K at the constant power of 350 W. The ETC of three surfaces of the Al-Co ceramics ball, i.e., original surface (λorg), combined black-painted and original surface (λcom) and black surface (λblk), are examined. From experiment, it is found that all ETC of three surfaces decrease with increasing TH. The value of three ETCs are in the range of 6.2 to 27.1 W/(m K). The lblk gives highest for the present research and, exactly, the worst case is obtained by λorg. Thus, the ETC of spherical packed-bed porous media with stagnant fluid can be improved by developing the color surface as black color.

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