1. Introduction
Due to the urgent threat of climate change induced by anthropogenic greenhouse gas (GHG) emissions, various countries have set out targets for an extensive reduction in CO2 and other GHG. In some sectors such as electricity generation, the defossilization is progressing fast in countries such as Germany, achieving shares of renewable energy production of about 50% in 2020. However, other sectors such as the (petro)chemical industry as well as the mobility sector are much harder to defossilize.
There are already a plethora of different renewable processes to produce petroleum and petrochemical products such as jet fuel as diesel but also platform chemicals, such as light olefins, aromatics or methanol. Bio-based processes (Biomass-to-X = BtX) such as biorefineries utilize energy crops but also waste streams, lignocellulose materials and even micro- and macro algae to produce fuels and biochemicals [
1,
2]. Electricity-based processes, so-called Power-to-X (PtX) processes, apply water electrolysis in combination with carbon capture to produce mixtures of hydrogen (H
2) and carbon dioxide (CO
2), that serve as reacting agent in methanol or Fischer–Tropsch synthesis to produce hydrocarbons [
3]. However, each process alternative has its own characteristics in terms of cost, utility demands, efficiency or consumption of raw materials such as fresh water.
In order to find an optimal (sustainable) process design, the different concepts have to be compared to each other under specific boundary conditions. What is more, not only should stand-alone processes be reviewed, but also partly or totally integrated Power- and Biomass-to-X processes (PBtX) have to be considered, leading to a vast number of potential process designs.
One way to investigate optimal process designs where many different process layouts are available is the application of superstructure optimization. Superstructure optimization is a methodology for process synthesis which utilizes mathematical models and optimization algorithms to identify optimal process flowsheets for given objective functions [
4]. A superstructure represents a large number of possible flowsheets, where unit-operations are described as generic blocks by mass, energy and cost balances [
4,
5]. Using mathematical modeling, the unit-operations and possible flowsheets are translated into a mathematical program which can be solved using state-of-the art optimization solvers [
1,
6].
Relevant work regarding superstructure optimization in the area of biorefinery process design was carried out by Gong and You, Bertran et al., Galanopoulos et al., Niziolek et al. and Onel et al. Gong et al. utilized superstructure optimization to identify cost- and emission optimal algae biorefineries producing biodiesel, green diesel and other value-added products [
7]. They concluded that manufacturing algal bioproducts reduces GHG by 63% compared to the petrochemical counterparts. Combining biodiesel production with value-added products also reduces the costs of the biodiesel to the level of cost-competitiveness to other biodiesel products. Galanopoulos et al. combined a biorefinery based on wheat-straw for the production of bioethanol and levulinic acid with an algae-based biorefinery for biodiesel and glycerol production. The integration of wastewater and CO
2 from wheat-straw refinery as a raw material in algae cultivation and the recycling of algae remnant as a raw material for bioethanol production results in a cost reduction of about 40% for open pond cultivation [
8]. Niziolek et al. investigated the bio-based production of aromatics via methanol amongst others. Their superstructure includes biomass gasification, methanol synthesis, methanol-to-aromatics and several recycling schemes for light gases such as combustion for energy production or conversion in autothermal reforming. Different biomass feedstocks are studied, namely corn stover, switchgrass and hardwood. They calculate payback times of roughly 9 years for the most profitable process configuration. Onel et al. set up a superstructure using forest residues and natural gas to produce liquid transportation fuels and olefins by utilizing the Fischer–Tropsch route [
9]. They also incorporated heat, power and water integration in their model. They concluded that the optimal process configuration depends on the desired fuels and olefins and that such a combined production could lead to economic viability [
9].
In the field of PtX superstructure optimization work has been performed by Sanchez et al., Uebbing et al. and Kenkel et al. [
10,
11,
12]. Sánchez et al. investigated a superstructure of ammonia-based electricity production. In their problem, decisions on gas clean-up after electricity production in a combined gas and steam turbine as well as final N
2/Air separation are made. The MINLP uses detailed sub-models for, e.g., ammonia decomposition and aims to minimize operation costs of power production. Results show that power production costs can vary between 0.05 and 0.81 EUR/kWh depending on plant capacity and ammonia price [
10]. Uebbing et al. investigated a CO
2 methanation superstructure combining biogas processing and water electrolysis to provide synthetic natural gas for the gas grid. They combine detailed unit models with indirect heat integration and optimized for maximal exergetic efficiency and minimal capital costs. Results show that using solid oxide electrolysis for H
2 supply has a higher exergetic efficiency than using alkaline electrolysis [
11]. However, this comes at the price of substantial higher capital costs. Kenkel et al. investigated bi-criteria power-to-methanol process designs with different CO
2 sources and different electrolyzer types in combination with direct hydrogenation of CO
2 to methanol [
12]. In their work, green methanol is produced cost-optimally by a combination of low-pressure alkaline electrolysis, CO
2 from flue gases captured by amine scrubbing and utilization of purge gases for steam production. Using this process layout methanol is produced at ca. 900 EUR/t, with H
2 supply contributing over 70% of the total costs [
12].
In addition to superstructure-based studies, several conventional techno-economic studies on the production of liquid fuels have been performed by Schemme et al., Liebner et al., Albrecht et al. and König et al. among others [
3,
13,
14,
15]. Schemme et al. investigated costs of several H
2 process routes for fuels such as gasoline, diesel and DME. They conclude that DME is the cheapest option with ca. 1.85 EUR/l
Diesel equivalent [
14]. Liebner et al. compare their MtSynFuels process with the Fischer–Tropsch route for the production of fuels and calculate production of roughly 180
$/t using natural gas as raw material [
14]. Albrecht et al. propose a standardized method for techno-economic evaluation of alternative fuels and demonstrate it on a combined Power-and Biomass-to-X process using the Fischer–Tropsch route including PEM electrolysis and biomass pyrolysis among other technology steps. They estimate fuel production costs in the range of 1.2–2.8 EUR/l [
3]. König modeled a Fischer–Tropsch process for the production of jet fuel and calculated costs at 3.38 EUR/kg [
15].
While PtX as well as BtX and even PBtX processes a have been investigated, no superstructure optimization has been performed to find optimal integrated PBtX process designs for the production of jet fuel as one major mid- to long term required liquid fuel in the transport sector. To close this knowledge gap, we present a superstructure optimization study, which aims to find cost optimal process designs from an integrated PBtX jet fuel refinery. This renewable refinery combines HEFA (hydroprocessed esters and fatty acids) production from microalgae as well as remnant biogas processing together with water electrolysis, carbon capture and thermochemical conversion of H2/CO2 to jet fuel via the methanol (methanol-to-jet = MTJ) or Fischer–Tropsch (FT) route. Such a comprehensive superstructure has not been investigated in literature yet, and the deep integration of PtX and BtX processes, including novel technologies with uncertain data requires an advanced modeling approach as well as methodologies to handle the emerging uncertainties. In the course of this study, the Open sUperstrucTure moDeling and OptimizatiOn fRamework (OUTDOOR), a python-based superstructure modeling and optimization tool is enhanced to facilitate such complex investigations.
This paper is structured as follows: First, the superstructure of the integrated refinery is described in detail (
Section 2), then the problem statement and solution approach are given (
Section 3).
Section 4 presents the results of the process synthesis and gives a discussion on the cost efficiency of novel processes as well as integrated concepts. Finally, a conclusion is presented and further investigation is proposed.
4. Results and Discussion
4.1. Model Characteristics and Computational Performance
The superstructure model consists of 685,497 constraints and 24,4823 variables, of which 1600 are binary. The base case optimization was performed on a server using four 2.2 GHz cores with a total RAM of 300 GB available. Utilizing Gurobi 9.1.2 as an optimization solver, the base case takes a total 2033 s resulting in an optimal solution with a 0.01% remaining optimality gap, which is Gurobi’s default threshold. Of those 2033 s, 11% are required by OUTDOOR’s automated superstructure construction and model building, 35% are invested in transferring the python model to the Gurobi solver and 53% are actually required by the solver. It is notable that roughly 16% of the solver time is required in order to reduce the optimality gap from 1% to 0.01%.
The screening algorithm requires numerous sequential optimizations. Therefore, the different scenarios were calculated in parallel on an external server, where each scenario was assigned a maximum number of four 2.2 GHz cores, with a total RAM of 300 GB. During the screening, the single-run solver times vary, depending on the parameter set, and can consume considerably more time (up to >19,000 s) than the base case optimization. In order to reduce calculation time, a remaining optimality gap of 0.1% was allowed for the screening algorithm, leading to total computing times of 42,044 to 87,514 s, depending on the scenario.
4.2. Base Case Results
For the given base case: Electricity costs of 72 EUR/MWh, algae lipid content of 25 wt.-%, algae-sludge costs of 25 EUR/t and MTJ costs of 1500 EUR/t
Jet are required for an optimal process design that depicts a highly integrated BtX and PtX process. The detailed flowsheet is depicted in
Figure 13. In total 240,000 MWh/a (approximately 20 kt fuels/a) are produced at net production costs of 253 EUR/MWh
LHV (approximately 2993 EUR/t
Fuels). The fuels shares are 47% jet fuel, 23% diesel, 18% gasoline and 12% LPG. Fuels are produced to 52% based on MTJ using algae residue and additional biogas and 48% using hydrotreating of algae bio-oil. Additional CO
2 is not used and H
2 from electrolysis is only used in hydrotreating and not as main feed. Algae-sludge is used as raw material and pretreated by sonication. Subsequent lipid extraction is designed as supercritical CO
2 extraction. Lipids are afterwards refined to HEFA using hydrodeoxygenation. Algae residue is converted to biogas by anaerobic digestion. Liquid remnants is treated by centrifugation which separates solid fertilizer as a by-product and remaining water for usage in the co-located algae farm. The remaining biogas is mixed with additionally bought biogas from a biogas plant and converted to raw SynFeed by TRIR. Part of the raw SynFeed is upgraded with selexol-based CO
2 capture. The captured CO
2 is not required anymore and vented. The low-detail model of algae cultivation does not include the acquisition of CO
2. However, in the proposed flowsheet, vented CO
2 from the TRIR-SEL, BIO-U and HEAT GEN process could provide approximately 30% of the cultivation CO
2 demand. The purified SynFeed is mixed with the remaining SynFeed to meet the specification of methanol synthesis. The produced SynFeed is compressed to 70 bar and converted to methanol, and methanol is upgraded to fuels by MTJ. A high-pressure alkaline electrolysis unit produces small amounts of H
2 which are utilized in hydrodesoxygenation of bio-oil (BIO-U) and hydrotreating in MTJ. The O
2 by-product of the HP-AEL is used in TRIR to produce the required heat via partial oxidation. Purge gas from the methanol synthesis is combusted to produce superheated steam, which is used to decrease the external steam demand. Wastewater from methanol distillation, MTJ and BIO-U is treated in WWT first, and afterwards used as a raw material in TRIR and HP-AEL.
Heat integration reduces the external heat demand from ca. 6.49 MW to 0.02 MW. Ca 18% of the recovered heat is produced in purge gas treatment and the remaining 82% is gained from waste heat of methanol synthesis and flash as well as hydrodeoxygenation of bio-oils and intercooling of the TRIR process. The model does not include detailed HEX-matching. However, based on the given temperature levels, a first indication of matches can be provided. In such a matching, high-temperature heat from HEAT GEN, MeOH SYN, TRIR and BIO-U would be used for medium temperature demand in BIO-U. Heat from cooling in MeOH FLASH and TRIR would be coupled with the distillation column of the SUP-CO2-EXT. Finally, waste heat from BIO-U or TRIR would be used in the AAD. Additionally, 18.11 MW of cooling utility are required. The total electricity demand is ca. 30 MW, of which 20 MW are required by the HP-AEL.
Table 9 presents the cost breakdown of the NPC. It can be seen that the major cost drivers are capital costs with 43.3% and raw materials with 27.5%; the third and fourth largest share are electricity costs (17%), and operating and maintenance (16.6%).
Figure 14 shows the breakdown of capital costs (left) and electricity demand (right). Largest capital cost shares are generated by MTJ (24.3%), TRIR (15.6%), anaerobic digestion (16.6%) and BIO-U (17.8%).
Electricity is mainly consumed by the high-pressure alkaline electrolysis and the H2 compressor (66.8%) as well as the supercritical CO2 extraction (16.3%). Raw material costs mainly originate from raw algae-sludge purchase (64.7%) and raw biogas (35%).
When comparing the combined PBtX refinery with a purely electricity-based MTJ or FT refinery, a cost reduction ca. 21% and 28% can be achieved, respectively. If compared to a stand-alone biorefinery, where algae residue is converted to a liquid bio-methane by-product, a cost reduction of 11.5% is achieved. A comparison to the literature is not as simple due to the numerous assumptions. Wassermann et al. reported lower MTJ-based jet fuel costs of ca. 2225 EUR/t
Jet [
47]. However, they also used reduced electricity costs of 50 EUR/MWh and lower MTJ process costs of about 400 EUR/t
Jet based on large scale applications [
47]. If both factors are included in the comparison, the total costs of fuel are again in the same range. König calculated FT-based jet fuel prices of 3380 EUR/t
Fuel [
15]. However, he had increased electricity costs of 104 EUR/MWh, but a substantially larger plant with 526 kt
Jet/a output and high full load hours of 8760 h/a, leading to reduced capital cost shares [
15]. In general, all of the results are in the same region depending on the chosen assumptions.
In terms of environmental impacts, the optimal base case comes with negative greenhouse gas emissions of –3.7
, while requiring 960
of water. When compared to the stand-alone options, greenhouse gas emissions are in the same region for all options. Water demand, on the other hand, is another matter. Algae cultivation requires substantially more water than water electrolysis and carbon capture. Due to avoided burdens for by-products, electricity-based processes even generate negative water demands of ca. –7.5
.
Table 10 presents costs and GHG emissions of conventional production of the given yearly product loads considering the actual product distribution and reference GHG emissions and costs from
Table 7. Based on these values and the calculated costs and emissions of the renewable refinery, CO
2 abatement costs of ca. 561
arise (see
Table 11).
4.3. Optimal Design Screening Algorithm Results
Figure 15 and
Figure 16 present the results of the optimal design screening algorithm for the electricity price of 72 EUR/MWh.
Figure 15 depicts an algae lipid content of 25 wt.-% and
Figure 16 depicts a lipid content of 50 wt.-%.
It can be seen that, for 72 EUR/MWhel and 25% lipids, fuel costs vary between ca. 177 and 331 EUR/MWhLHV (2092–3912 EUR/t) for algae costs between 5 and 105 EUR/tAlgae-sludge and MTJ costs between 680 and 2800 EUR/tJet. Four distinct operating windows appear for different algae costs and total MTJ processing costs. For low algae and MTJ costs, a combination such as presented in the base case is most profitable. For MTJ costs higher then 1500 EUR/tJet, this step is replaced by Fischer–Tropsch synthesis. If algae costs exceed approximately 40 EUR/tAlgae-sludge, a purely electricity-based production is chosen based on methanol synthesis for MTJ costs up to ca. 2400 EUR/tJet. For even higher costs, an FT-based production is most economic.
If the lipid content in the raw algae is elevated (
Figure 16), the total fuel costs range changes to 2150–3912 EUR/t. The maximum cost value is still associated with a purely electricity-based production; hence it is independent from the lipid content. The minimal price is slightly elevated compared to a lower lipid content. Nonetheless, the costs for combined process concepts are on average about 10% cheaper compared to the case with 25% lipids. This can be explained by the bio-based nature of the combined process: While alkaline electrolysis plays a role in the overall process scheme, the main feedstock for the products is based on algae. If the content of lipids which can be converted directly to fuels rises, this leads to smaller capacities in anaerobic digestion, biogas reforming and MTJ. These processes are the most expensive ones in the total process design, which makes capacity reduction a good cost saver.
Additionally, to the four operating windows recorded previously, now a purely bio-based production is most economic for low algae costs of up to 35 EUR/tAlgae-sludge and MTJ costs higher than 1000–1250 EUR/tJet. Furthermore, the operating window for an integrated design is increased for higher algae costs up to 70–95 EUR/tAlgae-sludge depending on the MTJ costs.
Figure 17 and
Figure 18 display the screening results for an electricity price of 36 EUR/MWh.
Figure 17 again depicts an algae lipid content of 25%, while
Figure 18 depicts a lipid content of 50%. It is evident from
Figure 17 the total costs range for decreased electricity price also decreases to ca. 165–263 EUR/MWh (1950–3109 EUR/t
Fuel). This is equivalent to a 10% to 20% cost reduction compared to the higher electricity price. Especially for purely electricity-based production, the share of electricity costs is high, explaining the increased cost reduction at the high-end of the price range. In general, it can be seen that the operating windows for stand-alone MTJ and FT production processes are increased compared to the cases with higher electricity price. Nonetheless, for low algae costs up to 30–40 EUR/t
Algae-sludge a combination with methanol or Fischer–Tropsch synthesis is still beneficial. As shown in
Figure 17, an operating window for a stand-alone biorefinery also emerges for very low algae costs of 5 EUR/t
Algae-sludge and MTJ costs above 1000 EUR/t
Jet.
Figure 18 shows the results for a lipid content of 50% for a decreased electricity price. It follows the logic of the other graphs. Both stand-alone electricity-based and bio-based production operating windows are increased. For low algae costs, pure algae-based production is most economic. Due to high lipid content, this is the case for algae costs up to 40 EUR/t. The optimal region for integrated process design is very small. Due to the low electricity price, stand-alone MTJ or FT is quickly more economic than a combined process. The total cost range is between 156 and 262 EUR/MWh (1844–3109 EUR/t). The maximum cost value is again similar to scenario 3, due to the independency of the FT process from the algae lipid content. The minimum value is slightly lower, due to more economic usage of algae-oil and lower CAPEX for algae residue treatment, similar to scenario 1 and 2.
All four figures indicate that for stand-alone PtX processes MTJ is more economic up to MTJ costs of 2000–2300 EUR/t
Jet. Although the Fischer–Tropsch synthesis produces fuels at 1160 EUR/t
Jet at this capacity, it is less efficient. The reduced efficiency originates from the large usage of internally produced fuel gas for the reverse water-gas-shift reactor. Hence, only 22% of the FT inlet is converted into usable fuels compared to ca. 28% in MTJ. Due to this efficiency disadvantage and an increased H
2 demand for synthesis and upgrading compared to MTJ, the electrolyzer capacity is about 16% higher for FT. This difference can explain the allowed increased costs of MTJ. A reversed effect that strengthens this hypothesis can be observed
Figure 15 if is compared to
Figure 17. With reduced electricity costs, its general share of the total costs is decreasing. This effect leads to a smaller allowed operating window of MTJ compared to FT.
5. Conclusions
This work presented a superstructure optimization study of an integrated biorefinery and Power-to-X process to produce liquid fuels, with a focus on jet fuel. Unlike other superstructure optimization studies, it includes a wide range of electricity- and biomass-based processes and allows a deep integration to benefit from synergy effects.
The Open sUperstrucTure moDeling and OptimizatiOn fRamework (OUTDOOR) was utilized for modeling and optimization. It was improved for novel functionalities such as advanced mass balances, which allow flexible mass integration between PtX and BtX concepts. Furthermore, a screening algorithm to handle uncertain input data—as they often emerge with novel processes—is incorporated. The results indicate that a coupled algae biorefinery and methanol-to-jet based production of jet fuel is economic superior to stand-alone BtX or PtX processes for a wide range of algae production costs and MTJ processing costs. While this work presented a coupling of BtX to the methanol route as superior to the Fischer–Tropsch route for a wide range of MTJ processing costs, it is important to notice that MTJ as well as FT processes can be designed in various ways, utilizing differing process selection, reaction conditions or catalysts. This variety also leads to diverse performances in terms of efficiencies and costs. Therefore, the study at hand should not be seen as a general ranking. Furthermore, the detailed design and engineering of such plants is always highly dependent on the boundary conditions. The increased freshwater demand of the cost-optimal PBtX plant, on the other hand, may be unproblematic for regions with water abundancy; this would be different for water-scarce countries, e.g., Spain, which in turn may have higher solar radiation and thus increased algae growth rates. Moreover, electricity prices as well as used algae strains (saline vs. fresh water) influence the decision on the technology choice. In the end, the complexity of integrated PBtX plant has to be considered. Nonetheless, to meet the decided targets on greenhouse gas reductions, different alternatives for renewable refineries have to be explored, and integrated concepts should not be discarded directly due to potential economic and environmental benefits. In the end, renewable processes have to be designed which meet the different criteria of sustainability while still being flexible enough to react on changing feedstock availability and product demand. Here, the presented framework, methodology and case study provide a promising first start.