In one aspect, the inventive process comprises a process for pyrolyzing a hydrocarbon feedstock containing nonvolatiles in a regenerative pyrolysis reactor system. The process comprises: (a) heating the nonvolatile-containing hydrocarbon feedstock upstream of a regenerative pyrolysis reactor system to a temperature sufficient to form a vapor phase that is essentially free of nonvolatiles and a liquid phase containing the nonvolatiles; (b) separating said vapor phase from said liquid phase; (c) feeding the separated vapor phase and methane to the pyrolysis reactor system; and (d) converting the methane and separated vapor phase in said pyrolysis reactor system to form a pyrolysis product. In another aspect, the invention includes a separation process that feeds multiple pyrolysis reactors.