A process for upgrading a petroleum-based composition comprising: combining a supercritical water stream with a pressurized, heated petroleum-based composition in a mixing device to create a combined feed stream, introducing the combined feed stream into an upgrading reactor system comprising at least one supercritical upgrading reactor operating at a temperature greater than a critical temperature of water and a pressure greater than a critical pressure of water, where the supercritical upgrading reactor comprises a first catalyst layer and a second catalyst layer, the second catalyst layer disposed vertically below the first catalyst layer in the supercritical upgrading reactor where the first catalyst layer is a heterogeneous porous metal containing catalyst having a first void volume ratio and the second catalyst layer is a heterogeneous porous metal containing catalyst having a second void volume ratio, and where the second void volume ratio is lesser than the first void volume ratio, passing the combined feed stream through the first catalyst layer and the second catalyst layer, where light hydrocarbons in the combined feed stream at least partially flow through the first catalyst layer and the second catalyst layer while heavy hydrocarbons in the combined feed stream are at least partially sifted in voids of the first catalyst layer, voids of the second catalyst layer, or both; at least partially converting the sifted heavy hydrocarbons to light hydrocarbons in the first catalyst layer or the second catalyst layer in the presence of the supercritical water; and passing upgraded product comprising light hydrocarbons and the converted light hydrocarbons out of the supercritical upgrading reactor. combining a supercritical water stream with a pressurized, heated petroleum-based composition in a mixing device to create a combined feed stream, introducing the combined feed stream into an upgrading reactor system comprising at least one supercritical upgrading reactor operating at a temperature greater than a critical temperature of water and a pressure greater than a critical pressure of water, where the supercritical upgrading reactor comprises a first catalyst layer and a second catalyst layer, the second catalyst layer disposed vertically below the first catalyst layer in the supercritical upgrading reactor where the first catalyst layer is a heterogeneous porous metal containing catalyst having a first void volume ratio and the second catalyst layer is a heterogeneous porous metal containing catalyst having a second void volume ratio, and where the second void volume ratio is lesser than the first void volume ratio, where the supercritical upgrading reactor comprises a first catalyst layer and a second catalyst layer, the second catalyst layer disposed vertically below the first catalyst layer in the supercritical upgrading reactor where the first catalyst layer is a heterogeneous porous metal containing catalyst having a first void volume ratio and the second catalyst layer is a heterogeneous porous metal containing catalyst having a second void volume ratio, and where the second void volume ratio is lesser than the first void volume ratio, passing the combined feed stream through the first catalyst layer and the second catalyst layer, where light hydrocarbons in the combined feed stream at least partially flow through the first catalyst layer and the second catalyst layer while heavy hydrocarbons in the combined feed stream are at least partially sifted in voids of the first catalyst layer, voids of the second catalyst layer, or both; at least partially converting the sifted heavy hydrocarbons to light hydrocarbons in the first catalyst layer or the second catalyst layer in the presence of the supercritical water; and passing upgraded product comprising light hydrocarbons and the converted light hydrocarbons out of the supercritical upgrading reactor.