A combustion system, comprising: an oxidant preheater fluidly connected to a primary oxidant source and to a secondary oxidant source and operable to provide a preheated primary oxidant stream and a preheated secondary oxidant stream; a fuel source; a combustor, fluidly connected to recover at least one of said preheated primary oxidant stream and said preheated secondary oxidant stream from said oxidant preheater, and a fuel stream from said fuel source for combustion, to produce a combustion gas stream, and fluidly connected to admit said combustion gas stream into said oxidant preheater; a feedwater source; an integrated heat exchanger having a hot side fluidly connected to said combustor and a cold side fluidly connected to recover at least one of a water and/or condensate stream from said feedwater source, to produce a high pressure steam stream from said cold side; a particulate collector fluidly connected to recover said combustion gas stream (35, 36) from said oxidant preheater, for forming a first treated combustion gas stream (38, 40); a direct contact cooler fluidly connected to recover a first portion of said first treated combustion gas stream (103, 111) from said particulate collector; and a temperature swing adsorptive gas separator; fluidly connected to recover said first portion of said treated combustion gas stream (103, 111) from said direct contact cooler as a feed stream comprising at least a first component; fluidly connected to recover a second portion of said first treated combustion gas stream from said particulate collector as a regeneration stream; fluidly connected to release a first product stream into an ambient environment, wherein said temperature swing adsorptive gas separator is operable to separate at least a portion of said first component from said feed stream to produce a second product stream. an oxidant preheater fluidly connected to a primary oxidant source and to a secondary oxidant source and operable to provide a preheated primary oxidant stream and a preheated secondary oxidant stream; a fuel source; a combustor, fluidly connected to recover at least one of said preheated primary oxidant stream and said preheated secondary oxidant stream from said oxidant preheater, and a fuel stream from said fuel source for combustion, to produce a combustion gas stream, and fluidly connected to admit said combustion gas stream into said oxidant preheater; a feedwater source; an integrated heat exchanger having a hot side fluidly connected to said combustor and a cold side fluidly connected to recover at least one of a water and/or condensate stream from said feedwater source, to produce a high pressure steam stream from said cold side; a particulate collector fluidly connected to recover said combustion gas stream (35, 36) from said oxidant preheater, for forming a first treated combustion gas stream (38, 40); a direct contact cooler fluidly connected to recover a first portion of said first treated combustion gas stream (103, 111) from said particulate collector; and a temperature swing adsorptive gas separator; fluidly connected to recover said first portion of said treated combustion gas stream (103, 111) from said direct contact cooler as a feed stream comprising at least a first component; fluidly connected to recover a second portion of said first treated combustion gas stream from said particulate collector as a regeneration stream; fluidly connected to release a first product stream into an ambient environment, wherein said temperature swing adsorptive gas separator is operable to separate at least a portion of said first component from said feed stream to produce a second product stream.