- The paper introduces a novel graph-based optimisation framework using hypergraphs to model integrated supply chains with renewable variability and technology inflexibility.
- The paper shows that combining hybrid solar and wind resources with flexible operations can lower synthetic methane costs by up to 10% compared to inflexible systems.
- The paper finds that financing conditions and technology costs, such as a 0% WACC yielding ~40% cost reduction, critically influence overall production economics.
This paper investigates the economic feasibility of producing carbon-neutral synthetic fuels in remote areas with abundant, high-quality renewable resources and exporting them to demand centers. The core challenge addressed is the integrated planning and optimization of complex energy supply chains involving multiple technologies and geographical locations, considering the inherent variability of renewable energy sources.
The authors propose a graph-based optimisation modelling framework tailored for strategic planning of such supply chains. In this framework, the planning problem is abstracted as a hypergraph (N,E), where nodes n∈N represent subsystems like technologies, plants, or processes, each with its own parameters, variables (internal Xn and coupling Zn), constraints, and local objective function Fn. Hyperedges e∈E connect sets of nodes and define constraints (equality He(Ze)=0 or inequality Ge(Ze)≤0) that couple the coupling variables of the incident nodes n∈e. The overall problem is formulated as a linear program (or mixed-integer linear program if discrete variables are introduced, though this paper focuses on LP) minimizing the sum of local objectives subject to all node and hyperedge constraints.
This framework is applied to model a synthetic methane supply chain using a static investment model where investment decisions are made at the start of a multi-year horizon, and operational decisions are made hourly. Two generic node types are introduced:
- Conversion nodes: Model technologies that transform commodities (e.g., electrolysis, methanation). They include parameters for conversion factors (ϕin), time lags (τin), availability (πtn), minimum operating level (μn), ramping constraints (Δi,+n,Δi,−n), and economic parameters for CAPEX (ζn), FOM (θfn), and VOM (θt,vn). Capacity is an internal variable (Kn), and commodity flows are external variables (qitn).
- Storage nodes: Model technologies that store a single commodity (e.g., batteries, hydrogen tanks). They include parameters for self-discharge (ηSn), charge/discharge efficiency (η+n,η−n), minimum inventory level (σn), and flow asymmetry (ρn). They have internal variables for inventory level (etn), stock capacity (En), and flow capacity (Kn), and external variables for in/outflows (qitn,qjtn). Their objective function includes stock and flow components for CAPEX (ςn,ζn), FOM (ϑfn,θfn), and VOM (ϑt,vn,θt,vn).
A generic Conservation hyperedge is used to enforce flow conservation of a specific commodity across the nodes it connects, potentially with exogenous injections/withdrawals (λte).
The framework is implemented using the open-source graph-based optimisation modelling language (GBOML) and compiler, which interfaces with standard LP/MILP solvers like Gurobi. The authors emphasize that the code and data for their case paper are publicly available for transparency and reproducibility.
The case paper analyzes the economics of producing carbon-neutral synthetic methane in a remote inland cluster in North Africa (Algeria), transporting power to a coastal hub for synthesis and liquefaction, and shipping it to a Northwestern European destination (Figure 2 in the paper). The supply chain includes:
- Inland Cluster: Solar PV and Wind power generation (based on 5 years of hourly ERA5 weather data), Battery storage, HVDC interconnection sending power to the coast.
- Coastal Hub: HVDC reception, Electrolysis (PEM), Methanation (Sabatier, cooled fixed-bed), Direct Air Capture (DAC, based on Keith et al. [2018]), Water Desalination (Reverse Osmosis), Compressed H₂ storage, Liquefied CO₂ storage, Methane Liquefaction, Liquefied CH₄ storage, Liquefied CH₄ carriers (stylized model of shipping).
- Destination: Liquefied CH₄ storage, Methane Regasification, Demand node (10 TWh/yr HHV, assumed flat profile).
The model runs over a 5-year horizon (2015-2019) with hourly resolution (T=43824). Investment costs are annualised using a Weighted Average Cost of Capital (WACC). The reference scenario assumes a uniform WACC of 7% across all technologies.
Results:
In the reference scenario (Solar+Wind, 7% WACC), the synthetic methane cost at destination is 149.7 €/MWh (HHV). The cost breakdown shows that electricity generation, transport, and storage (56.6%) account for the largest share, followed by hydrogen production/storage (25%). Methanation (7.7%), DAC (7.9%), and the full methane chain (liquefaction, storage, transport, regasification, 12.5%) have smaller shares. A high curtailment rate (5.26 TWh, ~25% of useful production) is observed, attributed to the difficulty in absorbing highly variable renewable output with inflexible downstream processes (methanation, DAC, desalination) without uneconomical storage scales. Plants upstream of inflexible ones, especially solar PV, are oversized to smooth flows.
A sensitivity analysis explores the impact of key factors:
- Solar PV only: Excluding wind increases the cost to ~202 €/MWh (~35% higher). This is due to lower solar capacity factors, higher variability, and the need for significantly larger (and less utilized) upstream capacity (solar PV, electrolysis, storage) to feed inflexible plants.
- System Flexibility: Relaxing operational constraints for methanation, DAC, and desalination plants leads to ~6% cost savings (down to ~140 €/MWh). This allows for smaller battery and hydrogen storage capacity but requires slightly larger methanation and DAC capacity and significantly larger liquefied methane storage to buffer discontinuous transport.
- Investment Costs:
- Increasing Electrolysis and DAC CAPEX/FOM by 50% increases cost to ~168.1 €/MWh (~12% higher).
- Decreasing Electrolysis, DAC, or Methanation CAPEX/FOM individually by 50% results in smaller cost reductions (<= 10% for electrolysis, <= 5% for DAC/methanation).
- Decreasing all three costs by 50% gives cost savings of ~16% (125.1 €/MWh), indicating that overall investment costs are not the most sensitive parameter compared to resource profiles and flexibility.
- DAC Energy Consumption: Replacing hydrogen consumption for high-temperature heat in DAC with electricity (consuming 5x more electricity per ton CO₂, but no hydrogen) decreases cost by ~10% (to ~135 €/MWh). This is because hydrogen production is a major cost driver.
- Financing Costs: Setting WACC to 0% (annualised CAPEX as CAPEX/Lifetime) yields the lowest cost of 88.3 €/MWh, a ~40% reduction from the reference scenario, highlighting the significant impact of financing assumptions.
The authors compare their results to previous studies (e.g., Zeman [2008], Fasihi [2015, 2017], SolarPVCosts [arXiv ID not provided in paper but referenced]) and find their cost estimates are significantly higher (150-200 €/MWh vs. 65-150 €/MWh). They attribute this discrepancy to the low temporal resolution and low technical detail of models used in previous work, which fail to capture the system-wide effects of renewable variability and technological inflexibility, leading to underestimation of required storage and oversizing costs. Their hourly resolution, integrated supply chain model, and representation of operational constraints provide a more accurate assessment.
Practical Implications:
The paper suggests that producing carbon-neutral synthetic methane in remote North African locations and exporting it to Europe could be economically viable by 2030, though potentially more expensive than some earlier estimates. The cost is highly sensitive to the combination of renewable resources (hybrid solar+wind is crucial), financing costs, and the operational flexibility of conversion technologies like methanation and direct air capture. Implementing this pathway requires substantial investments in renewable energy capacity, power transmission (HVDC), and Power-to-Gas infrastructure. Hydrogen and buffer storage systems are critical for managing renewable variability but add significant cost. Future research should focus on cost reductions for technologies like electrolysis, DAC, and methanation, exploring alternative DAC processes, and potentially improving the flexibility of these processes. Analyzing other regions and energy carriers (e.g., hydrogen, ammonia, methanol) is also needed to understand the full range of sustainable energy options. The graph-based modelling framework provides a flexible tool for performing such integrated system analyses.