A boiler system having a series of boilers. Each boiler includes a shell having an upstream end, a downstream end, and a hollow interior. The boilers also have an oxidizer inlet entering the hollow interior adjacent the upstream end of the shell and a fuel nozzle positioned adjacent the upstream end of the shell for introducing fuel into the hollow interior of the shell. Each boiler includes a flue duct connected to the shell adjacent the downstream end for transporting flue gas from the hollow interior. Oxygen is delivered to the oxidizer inlet of the first boiler in the series. Flue gas from the immediately preceding boiler in the series is delivered through the oxidizer inlet of each boiler subsequent to the first boiler in the series.