## 2 Materials and Methods  
### Theoretical Laws Versus Empirical Laws  
Scientific laws can be described as reasonings that determine a univocal relationship between different parameters or properties of an analysed medium or process, and they can generally be represented by a mathematical expression. Theoretical laws are generally considered to be those that enunciate a certain principle that relates to these properties or are based on other general laws and accepted principles. Conversely, empirical laws are based on empirical data, and the criterion for generating the function that relates the analysed variables simply involves data fitting to a certain function. Nevertheless, an empirical law can facilitate the subsequent development of a theoretical law. The qualification of \"laws\" given to these relationships applies to phenomena that involve a great generality, e.g., [PERSON]'s second law, and those whose impact is limited to a specific field, e.g., [PERSON]'s law [8] for water flow in semi-permeable porous media and [PERSON]'s first law [9] in petrophysics. A conventional way for accordingly differentiating laws is to qualify the former as universal laws. The labelling of laws is generally reserved for equations in which an analysed relationship between different parameters is established for the first time. Although once established, these relationships typically undergo improvements of their applied coefficients; they must not be considered as new laws. In other cases, certain definitions may change the final expression of an established law; for example, [PERSON]'s law [10] was determined before the definition of viscosity. Interestingly, relationships of great interest are not always formalised as laws. As an example, starting from empirical values, [PERSON] [11] established that the ratio between the resistivities of a solid porous medium \(\rho_{0}\) and fluid that fills its pores \(\rho_{\rm W}\) presents a constant value, which was initially called the resistivity factor and later the formation factor \(F\). [PERSON] [9] later empirically determined that \(F=1/\mathcal{O}^{m}\), where \(\mathcal{O}\) is the porosity of the analysed medium and \(m\) is its characteristic parameter, which would eventually be referred to as the cementation exponent. Apart from the confusion involved in the naming of this exponent, because it does not solely depend on the presence of cement in the analysed medium, this relationship is known in petrophysics as [PERSON]'s first law. However, the establishment of the formation factor was not attributed to the character of a law, even though this factor is an intrinsic parameter of geological media and provides considerably greater characterisation. The application range of a given relationship must also be considered to qualify an obtained law. Although the qualification as a law for empirical laws is relative--and somewhat pretentious--compared with universal laws, it can be said that a relationship is considered a law when it is applicable to a large number of cases in a given field. For example, although water is considered a reference fluid and NaCl is a characteristic ionic bonding compound, the relationship between conductivity (\(\sigma\)) in \(\mu\)S/cm and concentration (\(\rm C_{C}\)) in g/cm\({}^{3}\) of a NaCl solution in water, given by \(\rm C_{C}(NaCl)=\sigma^{2}/[1500\cdot(\sigma+500)]\)[12] should not be considered an empirical law because this relationship does not hold for other salts. An objection that is often posed to new empirical laws is their lack of theoretical basis, even though some empirical laws have achieved recognition similar to that of theoretical laws. The most recognised example is the law of universal gravitation. However, a fact that offsets the importance of empirical laws is that some of the most recognised theoretical equations have arisen from one or more empirical laws, as in the case of [PERSON]'s equations for electromagnetic fields, which combines the previous laws of [PERSON], Gauss, and Faraday.