An oxy-combustor is provided which comprises a combustion vessel including at least one solid fuel slurry inlet port, at least one oxygen inlet port and at least one supercritical fluid inlet port, wherein the combustion vessel is operable at an operating pressure of at least 1,100 psi; an interior of the combustion vessel comprises a combustion chamber and a supercritical fluid infusion chamber surrounding at least a part of the combustion chamber, the supercritical fluid infusion chamber and the combustion chamber are separated by a porous liner surrounding the combustion chamber, and the supercritical infusion chamber is located between the porous liner and an outer casing of the combustion vessel.