Superstructure Optimization with Embedded Neural Networks for Sustainable Aviation Fuel Production

Technical Summary: Superstructure Optimization with Embedded Neural Networks for Sustainable Aviation Fuel Production

Problem Statement
The defossilization of aviation requires the large-scale production of Sustainable Aviation Fuels (SAFs), specifically kerosene-range hydrocarbons (C8–C16). Designing economically and environmentally optimal SAF production pathways is a complex multi-dimensional optimization problem. It involves a vast array of raw materials (biomass, captured CO2, renewable H2), intermediate chemistries, and conversion technologies. Conventional superstructure optimization approaches often rely on oversimplified assumptions, such as linear process models, fixed operating conditions, and lumped component representations. These simplifications fail to capture the nonlinear thermodynamic relationships and composition-dependent behaviors critical to SAF synthesis, particularly in processes like Fischer-Tropsch (FT) conversion where product selectivity is highly sensitive to operating parameters. Furthermore, existing methods often lack the flexibility to simultaneously optimize discrete process choices and continuous operating variables (e.g., temperature, pressure, feed composition) while accounting for detailed mixture compositions and carbon management strategies.

Methodology
The authors propose an advanced multi-objective optimization framework that integrates Artificial Neural Networks (ANNs) as data-driven surrogate models within a Mixed-Integer Quadratically Constrained Programming (MIQCP) formulation.

• Superstructure Formulation: The framework models the production network as a generalized graph with explicit inlet and outlet ports for processes. Unlike traditional approaches, streams are represented as mixtures where mass fractions are decision variables. This allows for the simultaneous optimization of process topology and stream compositions.
• Embedding ANNs: To address the nonlinearity of key subprocesses without rendering the optimization intractable, three critical processes—biomass gasification, Reverse Water-Gas Shift (RWGS), and FT synthesis—are modeled using ANNs trained on rigorous Aspen Plus® simulation data. These ANNs capture the nonlinear dependence of output compositions, selectivity, and energy demands on operating conditions (e.g., reactor temperature, pressure, inlet ratios).
• Mathematical Integration: The trained ReLU-activated ANNs are embedded into the MIQCP problem using Mixed-Integer Linear Programming (MILP) reformulations (via the Optimization & Machine Learning Toolkit, OMLT). This approach preserves the computational tractability of the global optimization while accurately representing complex nonlinear behaviors.
• Optimization Objectives: The framework solves a multi-objective problem minimizing total annualized costs (CAPEX and OPEX) while systematically constraining total CO2 emissions (including production and combustion). The $\epsilon$-constraint method is used to generate Pareto-optimal frontiers.
• System Boundaries: The study considers a comprehensive superstructure including biomass gasification (miscanthus, wheat straw, pine chips), autothermal reforming (ATR) of natural gas, direct air capture (DAC), water electrolysis, and carbon sequestration (CS).

Key Contributions

1. Advanced MIQCP Formulation: Development of a superstructure formulation that explicitly incorporates stream compositions as decision variables, enabling the optimization of mass fractions across the network.
2. Embedded Surrogate Modeling: Successful integration of ANNs into a global optimization framework to model nonlinear process behaviors, allowing operating conditions (temperature, pressure, feed composition) to be treated as decision variables rather than fixed parameters.
3. Application to FT-Based SAF: Application of this framework to the synthesis of kerosene via FT, demonstrating the capability to handle complex mixture constraints and carbon management.
4. Demonstration of Flexibility: Proof that allowing greater degrees of freedom at the unit operation level, enabled by neural network surrogates, leads to superior system performance in terms of cost and CO2 intensity compared to fixed-parameter designs.

Results

• Cost vs. Emissions Trade-off: Under unconstrained CO2 emissions, the least-cost configuration relies exclusively on the fossil-based ATR route ($0.79/kg kerosene) with high emissions (4.47 kg CO2/kg). Imposing carbon constraints necessitates the integration of biomass gasification and DAC-CS.
• Optimal Pathways: At the zero-emission limit, hybrid configurations combining ATR and biomass gasification achieve the lowest costs ($2.38/kg), followed closely by biomass-only gasification ($2.43/kg). Both outperform the ATR-only pathway with DAC-CS (~$2.65/kg).
• DAC-Only Limitations: Pathways relying exclusively on atmospheric CO2 (DAC) and water electrolysis are found to be prohibitively expensive (~$10.8/kg), highlighting the thermodynamic and economic penalties of using fully oxidized carbon sources.
• Carbon Abatement: The CO2 abatement cost for biomass-based SAF is estimated at approximately $390/tCO2. Achieving net-zero or negative emissions requires carbon sequestration; biomass alone is insufficient due to supply chain emissions.
• Adaptability vs. Fixed Design: A sensitivity analysis comparing "adaptable" (optimized operating conditions) vs. "fixed" (predetermined conditions) designs reveals that adaptability yields up to 20% cost savings. Optimal operating parameters (e.g., FT reactor pressure, gasification temperature) shift significantly in response to external factors like electricity prices.
• Heat Integration: The economic benefit of heat integration is found to be design-dependent. It offers marginal savings (7%) in biomass-based systems but becomes critical (14% savings) in systems relying on DAC due to the high thermal demand of CO2 desorption.

Significance and Claims
The paper claims that the proposed methodology overcomes the inherent limitations of conventional superstructure-based approaches by enabling the joint optimization of discrete system decisions and continuous operating parameters within a rigorous mathematical framework. By embedding data-driven surrogate models, the study demonstrates that accounting for variable stream compositions and nonlinear process behaviors is essential for identifying truly optimal SAF production routes. The results underscore that cost-effective, climate-aligned SAF production depends on introducing carbon in thermodynamically favorable forms (biomass or methane) rather than as fully oxidized CO2. Furthermore, the study highlights that the flexibility to adapt process operating conditions to changing techno-economic environments is a critical, often overlooked, driver of economic performance, offering significant cost reductions over static design approaches. The authors note that while the framework is robust, its accuracy is contingent on the fidelity of the underlying process simulations used to train the ANNs, and future work could expand the scope to include more subprocesses and downstream upgrading technologies.