Since more than a decade, wireless sensor networks is a very attractive field in computer science and networking. Battery management is a crucial issue in the area of wireless sensor networks. The communication between a source node and a destination one may fail if both nodes are located inside a deep shadow-fading zone. Relay-selection strategy has been used in order to extend amplify-and-forward (AF) cooperative networks lifetime. The communication could not be achieved if the signal-to-noise ratio (SNR) at the destination could not reach a reasonable threshold. In the literature, various relay selection schemes have been used under the assumption that batteries are linear, but their effectiveness is not guaranteed when realistic nonlinear battery models are considered. In this paper, we review some relay selection schemes with linear battery mode that were proposed to extend network lifetime. Then, a realistic nonlinear battery model is applied with these schemes. Through numerical studies, we give a performances comparison between these techniques. The results show that the maximum energy-efficiency index MEI and the minimum outage probability MOP schemes give the best network lifetime extension.