Global optimization of a MINLP process synthesis model for thermochemical based conversion of hybrid coal, biomass, and natural gas to liquid fuels

A global optimization framework is proposed for a thermochemical based process superstructure to produce a novel hybrid energy refinery which will convert carbon-based feedstocks (i.e., coal, biomass, and natural gas) to liquid transportation fuels. The mathematical model for process synthesis includes simultaneous heat, power, and water integration and is formulated as a mixed-integer nonlinear optimization (MINLP) problem with nonconvex functions. The MINLP model is large-scale and includes 15,439 continuous variables, 30 binary variables, 15,406 equality constraints, 230 inequality constraints, and 335 nonconvex terms. The nonconvex terms arise from 274 bilinear terms, 1 quadrilinear term, and 60 concave cost functions. The proposed framework utilizes piecewise linear underestimators for the nonconvex terms to provide tight relaxations when calculating the lower bound. The bilinear terms are relaxed using a partitioning scheme that depends logarithmically on the number of binary variables, while the concave functions are relaxed using a linear partitioning scheme. The framework was tested on twelve case studies featuring three different plant capacities and four different feedstock-carbon conversion percentages and is able to solve each study to within a 3.22-8.56% optimality gap after 100 CPU hours. For 50% feedstock carbon conversion, the proposed global optimization framework shows that the break-even oil prices for liquid fuels production are $61.36/bbl for the small case study, $60.45/bbl for the medium case study, and $55.43/bbl for the large case study, while the corresponding efficiencies are 73.9%, 70.5%, and 70.1%, respectively.