Searchable encryption (SE) supports privacy-preserving searches over encrypted data. Recent studies on SE have focused on improving efficiency of the schemes. However, it was shown that most of the previous SE schemes could reveal the client's queries even if they are encrypted, thereby leading to privacy violation. In order to solve the problem, several forward private SE schemes have been proposed in a single client environment. However, the previous forward private SE schemes have never been analyzed in multi-client settings. In this paper, we briefly review the previous forward private SE schemes. Then, we conduct a comparative analysis of them in terms of performance and forward privacy. Our analysis demonstrates the previous forward secure SE schemes highly depend on the file-counter. Lastly, we show that they are not scalable in multi-client settings due to the performance and security issue from the file-counter.