This document contains digital supplementary material for the article “An Extended Superstructure Formulation for Non-Isobaric Flowsheet Synthesis”, submitted to the peer-reviewed proceedings of the 36th European Symposium on Computer-Aided Process Engineering (ESCAPE 2026).

Supplementary material for "Techno-Economic Assessment of Decarbonization Pathways for Methanol and Formaldehyde Production: A Superstructure Optimization Approach" (ESCAPE36, Sheffield, June 2026)

This study presents a mixed-integer bilinear optimization model for the cost-optimal design of a Northern European hydrogen supply chain with integrated CCS, focusing on exports from Norway to Germany and CO2 sequestration in Norway. The model is formulated as a superstructure problem and implemented in Pyomo, considering multiple locations for infrastructure nodes and transport options for hydrogen, wood chips, and CO2.

This study presents a mixed-integer bilinear optimization model for the cost-optimal design of a Northern European hydrogen supply chain with integrated CCS, focusing on exports from Norway to Germany and CO2 sequestration in Norway. The model is formulated as a superstructure problem and implemented in Pyomo, considering multiple locations for infrastructure nodes and transport options for hydrogen, wood chips, and CO2.

Supply chain superstructure optimization model for export of either wood chips or compressed hydrogen from Norway to Germany

CCS is a well investigated and fairly promising technology for reducing the emission of carbon dioxide (CO2) to the atmosphere. However, it is rarely implemented in the industry due to its high cost. Therefore, this work proposes a cost optimized CCS chain which can be operated flexibly and safely. For the capture process a post combustion chemical absorption technology is chosen due to its retrofitting possibility to already existing power plants and its low capture cost. In order to find a cost efficient absorption process for different scenarios, the five most promising process configurations from previous work are combined into a superstructure in a rigorous rate based reactive Aspen Plus model. This in turn is optimized by a two-stage stochastic programming approach in Matlab. The optimal supply chain network is identified by a tailor made transshipment model implemented in GAMS, which accounts for the most promising transportation units, storage sites as well as direct utilizatio... [more]

Algal biomass production, mineralization, and chemical conversion as promising carbon dioxide utilization processes are compared with regard to economic as well as environmental factors. The production of the chemicals methanol, dimethyl ether, and dimethyl carbonate is selected as the most viable alternative among all options. The integrated production of the proposed chemicals is evaluated for a wide range of trade-offs between economic potential and environmental impact by applying multi-objective superstructure optimization. The results indicate that direct hydrogenation of CO2 to methanol with subsequent dehydration to dimethyl ether is on the verge of profitability (including capture cost) while achieving a positive net CO2 consumption of ca. 68% of supplied CO2 when direct and indirect emissions are accounted for; and 85% when only direct emissions are considered.

Climate change, primarily caused by the excessive emission of greenhouse gases, particularly carbon dioxide (CO2), has intensified global efforts toward achieving carbon neutrality. In this context, renewable energy and CO2 utilization technologies have emerged as key strategies for reducing reliance on fossil fuels and mitigating environmental impacts. In this work, a superstructure model is developed to integrate renewable energy network and chemical production processes. The energy network integrates wind, solar, and biomass energy, complemented by storage systems to enhance reliability and reduce reliance on external power sources. The reaction network features various pathways that utilize CO2 as a raw material to produce high value-added chemicals such as polyglycolic acid (PGA), ethylene-vinyl acetate (EVA), and dimethyl carbonate (DMC), allowing for efficient conversion and resource utilization. A mixed-integer linear programming (MILP) model is formulated to minimize productio... [more]

Liquid-liquid extraction (LLX) is an essential technique for separating heat-sensitive, highly diluted, or azeotropic mixtures. However, the design and optimization of LLX processes can be challenging due to mass transfer limitations and complex fluid dynamics. While distillation can often be modeled using equilibrium-based (EQ-based) approaches with (constant) height equivalent to theoretical stage (HETS) values, these kinetic effects can limit the applicability of EQ-based LLX models for conceptual design. Non-equilibrium (NEQ) or rate-based modeling can account for detailed mass transfer and fluid dynamics but further increases the nonlinearity and complexity of the respective optimization problems, which should account for closed-loop solvent recovery. To successfully address these complexities, we propose an integrated methodology combining NEQ-based simulation with EQ-based superstructure optimization to design a hybrid extraction-distillation process. An NEQ model is first used... [more]

Critical minerals and rare earth elements play an important role in our climate change initiatives, particularly in applications related with energy storage. Here, we use discrete optimization approaches to design a process for the recovery of Lithium and Cobalt from battery recycling, through membrane separation. Our contribution involves proposing a Generalized Disjunctive Programming (GDP) model for the optimal design of a multistage diafiltration cascade for Li-Co separation. By solving the resulting nonconvex mixed-integer nonlinear program model to global optimality, we investigated scalability and solution quality variations with changes in the number of stages and elements per stage. Results demonstrate the computational tractability of the nonlinear GDP formulation for design of membrane separation processes while opening the door for decomposition strategies for multicomponent separation cascades. Future work aims to extend the GDP formulation to account for stage installatio... [more]

This work presents the synthesis of heat-integrated water networks (HIWNs) by using mathematical programming. A new superstructure is synthesised by combining a water network and a modified heat exchanger network. Based on the proposed superstructure, a mixed-integer nonlinear programming (MINLP) model is developed. The model is solved by using a one-step solution strategy enabling different initialisations and the generation of multiple solutions, from which the best one is chosen. The results show that the proposed model can be effectively used for solving HIWN problems of different complexities, including large-scale problems.

Microalgae have attracted great research interest as a feedstock for producing a wide range of end-products. However, recent studies show that the tight processing integration technology for microalgae-based biorefinery makes production less economical and even has a negative impact on sustainability. In this study, a new two-tier superstructure optimization design methodology is proposed to locate the optimal processing pathway. This model is developed based on the decomposition strategy and the relationship-based investigation, coupling an outer-tier structure with an inner-tier structure, wherein the outlet flows of the middle stages is relaxed and then an appropriate level of redundancy for designing the processing is provided. Two scenarios are developed to compare the most promising biorefinery configurations under two different design option favors. By solving the mixed integer nonlinear programming model with the objective functions of maximizing the yield of the desired produc... [more]

This work presents a superstructure optimization study for the production of renewable fuels with a focus on jet fuel. Power-to-X via the methanol (MTJ) and Fischer−Tropsch (FT) route is combined with Biomass-to-X (BtX) via an algae-based biorefinery to an integrated Power- and Biomass-to-X (PBtX) process. Possible integration by algae remnant utilization for H2/CO2 production, wastewater recycling and heat integration is included. Modeling is performed using the novel Open sUperstrucTure moDeling and OptimizatiOn fRamework (OUTDOOR). Novel methods to account for advanced mass balances and uncertain input data are included. Economic optimization proposes a PBtX process. This process combines algae processing with MTJ and depicts a highly mass- and energy integrated plant. It produces fuels at 211 EUR/MWhLHV (ca. 2530 EUR/t), a cost reduction of 21% to 11.5% compared to stand-alone electricity- or bio-based production at algae costs of 25 EUR/tAlgae-sludge and electricity costs of 72 EU... [more]

Genome-scale models have become indispensable tools for the study of cellular growth. These models have been progressively improving over the past two decades, enabling accurate predictions of metabolic fluxes and key phenotypes under a variety of growth conditions. In this work, an efficient computational method is proposed to incorporate genome-scale models into superstructure optimization settings, introducing them as viable growth models to simulate the cultivation section of biorefinaries. We perform techno-economic and life-cycle analyses of an algal biorefinery with five processing sections to determine optimal processing pathways and technologies. Formulation of this problem results in a mixed-integer nonlinear program, in which the net present value is maximized with respect to mass flowrates and design parameters. We use a genome-scale metabolic model of Chlamydomonas reinhardtii to predict growth rates in the cultivation section. We study algae cultivation in open ponds, in... [more]

Growing social and economic pressures demand technological innovations that enable the widespread usage of unconventional sources of water. These challenges motivate the emerging fit-for-purpose paradigm, wherein water is provided at the precise quality level of the intended application. Unfortunately, to date, fundamental advances in materials and nanotechnology have been slow to advance this paradigm. Using examples from membrane science and engineering, we highlight the critical need to bridge research at the molecular and nano-scales with development at the device and systems-scales to fully realize sustainable fit-for-purpose water technology. Specifically, we present four opportunities for computing and data science to accelerate convergence of sustainable water research: materials informatics and inverse design, model-based design of experiments, superstructure optimization, and uncertainty quantification. As such, we highlight opportunities to collaboratively revolutionize mole... [more]