Duckweed biomass is gasified in a thermochemical-based superstructure to produce gasoline, diesel, and kerosene using a synthesis gas intermediate. The superstructure includes multiple pathways for conversion of the synthesis gas to liquid hydrocarbons via Fischer-Tropsch synthesis or intermediate methanol synthesis. Low-temperature and high-temperature Fischer-Tropsch processes are examined using both iron and cobalt based catalysts. Methanol may be converted to hydrocarbons via the methanol-to-gasoline or methanol-to-olefins processes. The hydrocarbons will be refined into the final liquid products using ZSM-5 catalytic conversion, oligomerization, alkylation, isomerization, hydrotreating, reforming, and hydrocracking. A process synthesis framework is outlined to select the refining pathway that will produce the liquid fuels as the lowest possible cost. A rigorous deterministic branch-and-bound global optimization strategy will be incorporated to theoretically guarantee that the overall cost of the solution chosen by the synthesis framework is within a small fraction of the best possible value. A heat, power, and water integration is incorporated within the process synthesis framework to ensure that the cost of utility production and wastewater treatment are simultaneously included with the synthesis of the core refining processes. The proposed process synthesis framework is demonstrated using four case studies which determine the effect of refinery capacity and liquid fuel composition on the overall system cost, the refinery topological design, the process material/energy balances, and the life cycle greenhouse gas emissions.