Apple Watch 1st generation

For the series 1 Apple increased the warranty to 3 years for a swollen battery. If your series 1 is older than 3 years then your only option would be to pay for a repair but you can often find series 3 Apple Watches for around the same price as a repair would be for the series 1. Here is an article about the extended warranty for swollen batteries.

https://9to5mac.com/2017/04/28/apple-watch-expanded-swollen-battery-repair-coverage-warranty/

if you can scrape it up, series 6 is much nicer with 32gb of storage to handle updates and the health capabilities are excellent