Title of Thesis

Prediction of Effective Thermal Conductivity of Fluid Saturated Porous Media: in situ Thermo Physical Measurements

Author(s)

Aurang Zeb

Abstract
The density related properties of igneous (dunite and gabbro) and sedimentary (limestone) rocks are measured at room temperature and normal pressure, using ASTM Standards. Dunite samples are taken from Chillas near Gilgit and gabbro samples from Warsik near Peshawar, both of these places are located in north of Pakistan. The limestones are taken from Nammal Gorge sections, Western Salt Range, Pakistan.The thermal properties are determined using the well known transient plane source (TPS) technique. The thermal parameters of dunite are measured in temperature range from 83K to 483K, using air as saturant in pore spaces. The thermal properties of gabbro samples are reported using air as well as water as saturants in pore spaces at room temperature where as the thermal properties of limestones are measured in temperature range from 293K to 443K. All of the measurements on thermal parameters are carried out at normal pressure.
The density related properties of igneous (dunite and gabbro) and sedimentary (limestone) rocks are measured at room temperature and normal pressure, using ASTM Standards. Dunite samples are taken from Chillas near Gilgit and gabbro samples from Warsik near Peshawar, both of these places are located in north of Pakistan. The limestones are taken from Nammal Gorge sections, Western Salt Range, Pakistan. The thermal properties are determined using the well known transient plane source (TPS) technique. The thermal parameters of dunite are measured in temperature range from 83K to 483K, using air as saturant in pore spaces. The thermal properties of gabbro samples are reported using air as well as water as saturants in pore spaces at room temperature where as the thermal properties of limestones are measured in temperature range from 293K to 443K. All of the measurements on thermal parameters are carried out at normal pressure.
Where eλ is the effective thermal conductivity, fλ is the thermal conductivity of fluid in pore spaces,sλ is the thermal conductivity of solid phase, Φis the fractional porosity and m is the empirical coefficient whose value can be determined by the method of least squares.
The results of this proposal are compared with the existing models and the corresponding improvements are reported.
Using the concept that thermal resistivity ⎟⎠⎞⎜⎝⎛λ1 is a linear function of temperature, the above model is then extended to involve the effect of temperature, given as:
⎟⎟⎠⎞⎜⎜⎝⎛+=o11TTmΦfseλλλ,
where is certain reference temperature. oT
An exponential decay trial is also given for the prediction of effective thermal conductivity of porous media under ambient conditions, as:
fszΦseeλλλλ−=,
where z is the empirical coefficient. This formula is tested on gabbro samples with air and water as fluids in pore spaces. The results of this relation are again compared with the results obtained from the existing models and the corresponding variations are discussed.

1

1.1 Introduction to Samples
1.2 Rocks and Rock-Forming Minerals
1.3 The Rock Cycle
1.4 Igneous Rocks
1.5 Literature Survey
1.6 The Aim of Present Work
1.7 The Future Work
References

2.1 Density Related Properties of Rocks
2.2 Determination of Density Related Properties
2.3 Thermal Transport Properties of Rocks
References

3.1 Mechanisms of Heat Transfer
3.2 Theory of Thermal Conductivity
3.3 Heat Conduction Equations
References

4

4.1 The Transient Plane Source (TPS) Technique
4.2 Thin Section Technique

4.3 Error Analysis
4.4 Curve Fitting by the Principle of Least Squares
References

5

5.1 Prediction of Effective Thermal Conductivity under Ambient Conditions
5.2 Mixing Law Models
5.3 Bounds on Thermal Conductivity
5.4 Empirical Models
5.5 Determination of Thermal Conductivity of Solid Phase
5.6 Prediction of Effective Thermal Conductivity as a Function of Temperature
References

6

6.1 Density Related Properties
6.2 Thermal Transport Data under Ambient Conditions
6.3 Prediction of Thermal Conductivity under Ambient Conditions
6.4 Conclusions
References

7

7.1 Density Related Properties
7.2 Thermal Transport Properties
7.3 Exponential Decay Trial for Thermal Conductivity Prediction
7.4 Conclusions
References

8

8.1 Density Related Properties
8.2 Determination of Thermal Conductivity of Solid Phase
8.3 Thermal Properties at Elevated Temperatures
8.4 Prediction of Thermal Conductivity at Elevated Temperatures
8.5 Proposed Model
8.6 Conclusions
References

9

9.1 Different relations for Thermal Conductivity Prediction
9.2 Results and Discussion
9.3 Conclusions
References