Energy Storage Systems (ESSs) potentially enhance the flexibility of power grids, and their operators can benefit from various streams of revenues to recover the investment. This study targets the estimation of revenues expected from the provision of Frequency Containment Reserve (FCR), or primary reserve, in the European market. A reference model is introduced, where the FCR activation is decided based on the actual frequency measurements (Model 1). As those measurements may not be systematically available, this paper proposes two additional models in the form of offline approaches that enable the ESS operator to determine the economic viability of targeting the FCR market without the need for actual frequency data. Model 2 is an improved version of a conventional formulation based on a constant coefficient of activated energy concerning the battery-rated power (i.e. reserved capacity). Model 3 is a novel simplified model based on a variable activation coefficient that depends on the total activated reserve by the system operator. The validity of the proposed models is assessed compared to the exact formulation over six months considering the French market in 2021. Results show that adopting Model 2 s is preferable in the cases where the quantity of activated energy is high (high-frequency gain), resulting in a 3 % error compared to Model 1. However, in the opposite case (low-frequency gain), Model 3 is favorable to use, with an error of 2 %.