**1. Introduction**

The conductivity of rocks, the constituents of oil and gas reservoirs, has not been a parameter investigated for a long time, because it was difficult to predict how fluids flowed and their temperature loss (heat transfer) in reservoir rocks [1].

After 1970, thermal conductivity was also used as a parameter in the development of hydraulic simulation models, due to the increased cost of discovery and preparation for extraction of oil and associated gas from new hydrocarbon reservoirs [2].

Models for calculating and estimating thermal conductivity were developed when tertiary oil recovery was discussed, using thermal techniques (injection of steam into the reservoir, underground combustion, flushing the collecting rocks with hot water, injection of CO2 and flue gas, etc.) [3].

All these models developed had the ultimate goal of increasing the recovery factor of crude oil at the lowest possible price [4].

Any systematic geothermal research requires knowledge of how to transfer heat in the research environment [5, 6].

Heat transfer in oil and gas fields takes place through three main processes, namely: conduction, convection, and radiation.

Heat transfer by conduction occurs only in solid media by molecular interaction [7].

It is the main mechanism of heat transfer in the Earth's crust and the most important in geothermal probe research.

Convective heat transfer is associated with the free movement of fluids between two environments at different temperatures.

It is becoming important in geothermal areas, in particular in areas with volcanic activity and in areas with active groundwater circulation [8].

The mechanism of heat transfer by convection must be taken into account in geothermal research conducted in boreholes, because it plays a significant role in changing the natural thermal regime of the geological formations crossed.

Radiative heat transfer occurs only on the Earth's surface due to the exchange of heat between the Earth and the Sun, the rocks affected by this transfer being those from the surface or the first layers in depth (maximum 10 m).

For temperatures encountered at usual probe depths, including deep probes, the radiative transfer is negligible.

The ability of deposits of useful mineral substances to transmit and absorb thermal energy depends on the thermal conductivity of the constituent rocks.

The experimental law of thermal conduction in rocks and civil structures or Fourier's law very well defines the transfer of heat through conduction and is represented by the relation:

$$Q = -\lambda \bullet A \bullet \text{grad } T \tag{1}$$

But the nature of the body through which the heat transfer takes place is characterized by a parameter *λ*, defined in the literature as the coefficient of thermal conductivity (the amount of heat required to increase by 1 K the temperature of a surface equal to a unit of measurement, in a time unit), *A* is the heat transfer area (surface area), and *T* is the temperature difference between the heat transfer zone at the inlet and outlet:

$$\lambda = \frac{Q}{A\left|-\frac{\partial T}{\partial n}\right|}\tag{2}$$

Thermal conductivity defines the ability to accumulate and transfer a quantity of heat by the collecting rocks and the constituent fluids of the deposits of useful mineral substances.

The thermal processes that develop within the oil and gas deposits, following the application of a heat treatment or the extraction process, can be due to:


*Estimation of Equivalent Thermal Conductivity Value Using Correlation Relationships… DOI: http://dx.doi.org/10.5772/intechopen.106453*

In non-ionized gases, gases at *t* ≤ 1800°C, the conductive transport of heat takes place mainly under the effect of molecular oscillations (photonic gas), which have a small amplitude, and as a result they are bodies that are poorly conductive heat.

In the case of Newtonian liquids and non-metallic solids, heat transfer through conductivity takes place both through the oscillations of molecules, because the distance between them is relatively small, and through radiation [9].

The coefficient of thermal conductivity varies with the nature of the body, with its state of aggregation, with temperature and pressure, with body moisture, with porosity, with the nature and concentration of impurities contained in the body, etc. (**Table 1**).

In the case of solutions (emulsions), the thermal conductivity is equal to the values:



#### **Table 1.**

*Properties of porous media saturated with various fluids, at 32.2°C (90°F) [10].*

The coefficient of thermal conductivity can be written as a scalar value in the case of isotropic media.

In the case of anisotropic media (inhomogeneous crystals or stratified rocks), the coefficient of thermal conductivity will be defined vectorially (in the directions of orientation):

$$
\lambda\_{jk} = \begin{vmatrix}
\lambda\_{11} & \lambda\_{12} & \lambda\_{13} \\
\lambda\_{21} & \lambda\_{22} & \lambda\_{23} \\
\vdots & \lambda\_{32} & \lambda\_{33} \\
\end{vmatrix} \tag{3}
$$

Onsanger's postulate shows that the thermal conductivity matrix is symmetrical and therefore [11–13]:

Since the experiments did not confirm the existence of the rotary conduction *λjk* ¼ 0, for *j* 6¼ *k*), the matrix (3) is reduced to the equation:

$$
\lambda\_{jk} = \lambda\_{kj}, j \neq k \tag{4}
$$

$$Q = -\lambda \mathbf{\hat{A}} \cdot \mathbf{\hat{g}} \text{rad } T \tag{5}$$
