Embodiments of the invention include apparatus and systems for hydrocarbon synthesis and methods regarding the same. In an embodiment, the invention includes a method for creating a hydrocarbon product stream comprising reacting a reaction mixture in the presence of a catalyst inside of a reaction vessel to form a product mixture, the reaction mixture comprising a carbon source and water. The temperature inside the reaction vessel can be between 450 degrees Celsius and 600 degrees Celsius and the pressure inside the reaction vessel can be above supercritical pressure for water. In an embodiment, the invention includes an extrusion reactor system for creating a hydrocarbon product stream. The temperature inside the extrusion reactor housing between 450 degrees Celsius and 600 degrees Celsius. Pressure inside the reaction vessel can be above supercritical pressure for water. Other embodiments are also included herein.