The saturation in water or hydrocarbon is an important petrophysical parameter used for the evaluation of oil and gas reservoirs. It represents the amount of hydrocarbons in a reservoir. There are many relations to determine the water saturation from well logs by using the physical properties of rocks. The accurate determination of the hydrocarbon formation or the water saturation is given by the accuracy of the parameters used for calculating and by the relations used. This paper makes an analysis of the relations for water saturation calculation using the Walter H. Fertl classification. The four types of relations were modified using the MacLaurin series of the exponential function. It also analyses the cases when the water saturation is not to be found in the variation range [0,1]. The new relations giver values that are always greater than 0 and we have established the conditions for the water saturation to be less than 1. In the final part of the paper we make an application which confirms the theoretical aspects presented in the first part of the paper.
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