Exploitation of the far-offshore wind energy resource by fleets of energy ships - Part 2: Updated ship design and cost of energy estimate

. This paper deals with a new concept for the conversion of far-offshore wind energy into sustainable fuel. It relies on autonomous sailing energy ships and manned support tankers. Energy ships are wind-propelled ships that generate electricity using water turbines attached underneath their hull. Since energy ships are not grid-connected, they include onboard power-to-X plants for storage of the produced energy. In the present work, the energy vector X is methanol. 15 In the first part of this study (Babarit et al., 2020), an energy ship design has been proposed and its energy performance has been assessed. In this second part, the aim is to estimate the energy and economic performance of such system. In collaboration with ocean engineering, marine renewable energy and wind-assisted propulsion’s experts, the energy ship design of the first part has been revised and updated. Based on this new design, a complete FARWIND energy system is proposed, and its costs (CAPEX and OPEX) are estimated. Results of the models show (i) that this FARWIND system could 20 produce approximately 70,000 tonnes of methanol per annum (approximately 400 GWh per annum of chemical energy) at a cost in the range 1.2 to 3.6 €/kg, (ii) that this cost may be comparable to that of methanol produced by offshore wind farms in the long term, and (iii) that FARWIND-produced methanol (and offshore wind farms-produced methanol) could compete with gasoline on the EU transportation fuel market in the long term. stack replacement. Indeed, PEM electrolyzers’ stack lifetime is in the order of 50,000 hours.


Introduction 25
To date, fuels such as oil, natural gas and coal account for approximately 80% of primary energy consumption globally (BP, 2018). Although this share is expected to decrease with the development of renewable power generation and the electrification of the global economy, some sectors may be difficult to electrify (e.g., aviation, freight). Therefore, if a global temperature change of less than 2°C-as set out in the Paris agreement-is to be achieved, there is a critical need to develop low-carbon alternatives to fossil fuels. 30 https://doi.org/10.5194/wes-2021-39 Preprint. Discussion started: 7 June 2021 c Author(s) 2021. CC BY 4.0 License. discussed in section 4. Using those estimates and the estimates of annual methanol production, the cost of energy is estimated in section 5 and market perspectives are discussed. Conclusions are presented in Section 6. The energy ship design considered in this study is a revision of that presented in (Babarit et al., 2020), see Fig. 3. It is still an 80 m long catamaran with four 5 m diameter Flettner rotors and two water turbines. The hull shape is the same.
However, the height of the Flettner rotors is increased from 30 m to 35 m, and the rated power of each water turbine is 60 reduced from 900 kW to 800 kW. The complete characteristics of the ship are summarized in Tab

Rotors
The rotors technical specifications (dimensions, mass, maximum rotor drive power) used in this study are based on 65 that of the largest currently available Flettner rotor (Norsepower, 2021).
The propulsive force of a Flettner rotor depends on the lift coefficient CL and the drag coefficient CD (Equation 2 in (Babarit et al., 2020), which depend themselves on the ratio of the rotational velocity of the rotor to the apparent wind speed (spin ratio SR). In (Babarit et al., 2020), we used the experimental data of (Charrier, 1979) for the aerodynamic coefficients of a Flettner's rotor as function of the rotor's spin ratio SR. However, these experiments were carried out at low Reynolds 70 numbers (~10,000). Recently, formula based on full scale data (Reynolds number over 10 6 ) have been published (Tillig & Ringsberg, 2020). That data has been used in the present study ( Fig. Figure 3) as it corresponds better to real conditions. Moreover, rotors must be powered for them to spin. In (Babarit et al., 2020), we assumed that the rotors power consumption is constant (four times 40 kW), whereas in practice it depends on the wind loading. In their work, (Tillig & https://doi.org/10.5194/wes-2021-39 Preprint. Discussion started: 7 June 2021 c Author(s) 2021. CC BY 4.0 License.
Ringsberg, 2020) have developed a formula to estimate a rotor's power consumption as function of the spin ratio. We used 75 that formula in the present study.  Figure 3 Comparison of aerodynamic coefficients of Flettner rotors according to (Charrier, 1979) and (Tillig & Ringsberg, 2020) In (Babarit et al., 2020), the effect of aerodynamic interactions between rotors was neglected. In the present study, it has been estimated using the approach proposed by (Roncin & Kobus, 2004) in which each rotor is modelled by a horseshoe 80 vortex. The implementation follows that of (Bordogna, 2020).

Figure 4 Effect of aerodynamic interactions on the propulsive force
The total propulsive force (with and without aerodynamic interactions) and the propulsive force from each rotor are shown in Figure 4 for rated conditions (10 m/s true wind speed, 90° true wind direction, SR = 3, 10 m/s ship velocity). They 85 show that the interaction effect cannot be neglected as the total propulsive force is 69% of that without interactions. A similar interaction effect has been found for other wind speeds (not reported here). Consequently, the model has been updated. The total propulsive force (Eq. 2 in (Babarit et al., 2020.) has been reduced by a constant factor of 30% for all wind conditions. https://doi.org/10.5194/wes-2021-39 Preprint. Discussion started: 7 June 2021 c Author(s) 2021. CC BY 4.0 License.
The Earth atmospheric boundary layer was also not considered in the energy performance estimate in (Babarit et al., 90 2020). In the present study, a power law has been assumed with an exponent of 0.14. Thus, in the updated model, the wind speed W in Eq. 3 of (Babarit et al., 2020) is given by: Where Z is 22.5 m (half the height of the rotor + 5 m). 95

Hull
The hull shape is the same as for the preliminary design. However, the hull mass estimate has been refined. The revised mass estimate is based on a preliminary scantling of the hull structure which has been developed using rule NR600 of Bureau Veritas (EMEC, 2020). The corresponding hull weight estimate is 560 t, which is more than twice the estimate of the preliminary design. Moreover, the updated design assumes taller rotors (35 m), which are 20 tons heavier than the 30 m 100 rotors of the preliminary design. Consequently, the total displacement of the updated design is 1,035 tons (660 tons for the preliminary design).
Due to the increased displacement, the wetted surface increases to 1,064m². The wave resistance coefficient has also been updated (see Figure 5). As for the preliminary design, it was calculated using the software REVA (Delhommeau and Maisonneuve, 1987). One can see that the residuary resistance coefficient (wave making) is greater for the updated 105 design than for the initial design, which is due to the increased displacement.

Water turbine 110
The water turbines' dimensions are the same as for the initial design (4 m diameter rotor). However, their mass is increased to 15 tons each (7.4 tons each for the initial design). Based on expert's advice, the water turbine's energy efficiency has been reduced to 75% (80% for the initial design). The rated power is decreased to 800 kW (900 kW for the initial design).

Power-to-methanol plant 115
For rated wind conditions (10 m/s true wind speed, 90° true wind angle), the ship velocity is almost 10 m/s (see section 2.7). The water turbines' power production is 1,600 kW. The Flettner rotors' power consumption is approximately 420 kW. Assuming a further 50 kW power consumption for the auxiliary subsystems, the net power production available to the electrolyzer of the power-to-methanol plant is 1,130 kW (1,420 kW for the initial design). The weight estimate of an electrolyzer of such rated power is 28 t (35 t for the initial design). 120 Assuming the same 60% efficiency for the electrolyzer as for the initial design, the rated power of the H2-tomethanol plant is 680 kW (850 kW for the initial design). Its weight estimate is 17 t (24 t for the initial design).

Storage tanks
The capacities of the storage tanks (CO2 and methanol) are set such as they can accommodate 7 days of production at rated power (approx. 17 t of methanol). Thus, the CO2 tank weight is 15 t and that of the methanol tank is 4 t. 125

Auxiliary equipment
As for the initial design, the weight of the auxiliary subsystems is taken equal to 10% of the total mass budget excluding the hull weight (41 t).
https://doi.org/10.5194/wes-2021-39 Preprint. Discussion started: 7 June 2021 c Author(s) 2021. CC BY 4.0 License. The velocity and power performance of the updated design has been calculated using the model presented in (Babarit et al., 2020). The results are shown in Figure 6 as function of the wind conditions (true wind speed and true wind angle). 135 Overall, the velocity and power performance of the updated design resemble that of the initial design (albeit 10 to 20% smaller). As for the initial design, rated power (1,600 kW) is achieved from a true wind speed of 10 m/s and a true wind angle of 90°. However, a major difference is that the rotors power consumption depends on the spin ratio in the updated design velocity and power performance prediction model, whereas it was fixed in (Babarit et al., 2020). Therefore, the net power keeps increasing with increasing wind speed (see panel (d)) despite the generated power has reached rated power 140 (1,600 kW).
As for the initial design, the water turbine's induction factor and the rotors' spin ratio were optimized to maximize power production for each data point while satisfying constraints (maximum rotation velocity and thrust force for the rotors, maximum power generation for the water turbine). Due to those constraints, there can be several settings (induction factor, spin ratio) for the same power generation, which explain the noisy behavior for the ship velocity in panel (a). 145

Specifications of the proposed FARWIND energy system
In the FARWIND energy system concept, the energy ships are deployed in fleets and are supported by tankers which collect the produced methanol and transport it to a shore-based terminal, see Figure 1. The tankers also provide the energy ships with CO2. In this section, we estimate the characteristics and number of the tankers, and the number of energy ships in a FARWIND system. 150

Tanker design
In the considered energy ship design, the methanol storage tank capacity allows storage of one week of methanol production at full capacity. Therefore, each energy ship of the fleet must meet a tanker for methanol collection and CO2 refill at least once a week (to avoid stops in the production process because the methanol tank is full or because the CO2 tank is empty). 155 Thus, let us estimate the number of energy ships that can be served by one tanker. This depends on the duration of the CO2-loading and methanol-unloading operations. We assume that these operations take six hours on average, and that they are carried out continuously (including at night). Therefore, one tanker can service 28 energy ships per week (7 days/week x 24 hours/day / 6 hours/operation). As the capacity of an energy ship's methanol tank is 17 tonnes (23 tonnes for the CO2 tank), the tanker may collect up to 473 t of methanol and supply 650 t of CO2 every week. 160 It is assumed that the tankers are operated by a crew, and that the duration of their mission is four weeks. At the end of each four-weeks mission, the tanker returns to a shore-based terminal to change crew, unload the methanol, and load CO2. Therefore, their total methanol capacity must be 1,891 t (4 weeks x 473 t/week) and their total CO2 capacity must be 2,601 t (4 w x 650 t/w). Assuming the CO2 will be stored as liquid in a cryogenic storage tank, and extrapolating from (Chart, 2019), the empty weight of a 2,600 t capacity CO2 storage vessel is estimated to be 1,700 t. For methanol, the mass of the required 165 tank is estimated to be 410 t. The tanker will be carrying maximum cargo weight (4,720 t) when it leaves the terminal (full CO2 tank and empty methanol tank). This cargo weight is relatively similar to the average vessel size of small crude oil (3,600 deadweight (dwt)), chemical (4,900 dwt) and LPG vessels (3,500 dwt) (Lindstad et al., 2012). According to (MAN Energy Solutions, 2019), the propulsion power of a 5,000 t deadweight bulk carrier is 1,410 kW for a service speed of 12 knots. These are the values which we used for the service speed and propulsion power of the tanker. 170

FARWIND system design
Following , it is assumed that the fleet of energy ships is deployed at a distance of 1,000 km from the terminal. Therefore, the tankers must travel 1,000 km to meet the energy ships, and a further 1,000 km when returning to the terminal. At a service speed of 12 knots, the tanker's round-trip will take 90 hours. Considering the duration of unloading/loading operations and other maintenance operations, we estimate that the tanker will be away from the fleet of 175 energy ships for a duration of one week.
To ensure continuous operation of the energy ships, the tanker must be replaced immediately when it leaves the production zone. Therefore, each group of 28 energy ships must be supported by more than one tanker. It can be shown that the minimum number of tankers per fleet must be at least 1.25, meaning that the optimal FARWIND system comprises a fleet of 112 energy ships supported by five tankers. Over a year, the number of roundtrips between the terminal and the production 180 zone is 10.4 for each tanker. The maximum methanol production of that system (assuming 100% capacity factor for the energy ships) is approximately 100,000 t per annum.

Annual methanol production of the proposed FARWIND system design
Since energy ships are mobile, their route schedules can be dynamically optimized based on weather forecasts in order to maximize energy production. This was performed using a modified version of the weather-routing software QTVLM (Abd-185 Jamil et al., 2019). The coordinates of the starting and arrival point are: N 50.5; W 18.9 (approximately 1,000 km from the port of Brest, France). Over the three years 2015, 2016 and 2017, it was found that an average capacity factor of over 75% can be achieved.
That estimate does not consider downtime due to maintenance (availability). According to (Sheng, 2013) and (Pfaffel, 2017), the failure rate of wind turbines is in the order of one failure per annum. Given the greater complexity of the energy ship 190 system (additional energy conversion subsystems in comparison to a wind turbine e.g. power-to-methanol plant), it is assumed that the average failure rate of energy ships is two failures per annum. The corresponding downtime is driven by accessibility and repair time. As accessibility at sea can be challenging and as energy ships are mobile, it is assumed that https://doi.org/10.5194/wes-2021-39 Preprint. Discussion started: 7 June 2021 c Author(s) 2021. CC BY 4.0 License. most of the repairs are performed at a port. Moreover, it is assumed that despite the failure, the energy ship is able to sail to that port at an average velocity of 10 knots (corresponding to half the rated velocity) without assistance (e.g. tug boat). 195 Assuming that the distance between the production area and a port (with a dedicated shipyard) is 1,000 kms, it would take approximately two days for that energy ship to go to the port. Assuming a further 3 days for the repair and 2 days for the energy ship to go back to the production area, the downtime per failure is 7 days. Thus, for a failure rate of two failures per annum, the total downtime per annum is two weeks corresponding to a 96% availability.
Taking into account that availability estimate, it appears that a capacity factor of 72% can be achieved. The corresponding 200 annual methanol production would be 70,600 t per annum. Note that it would require the supply of 97,400 t of CO2, as the production of 1 kg of methanol requires 1.38 kg of CO2.  According to (Kuuskoski, 2019), the cost of four 30 m Flettner rotors is in the range 3,000 to 3,500 k€. For four 45 m tall Flettner rotors, we assumed that the cost is approximately proportional to the rotor mass excluding foundation. That mass being 42 tonnes for a 30 m tall rotor and 59 tonnes for a 35 m tall rotor (Norsepower, 2021), we retain a Flettner rotors' cost in the range 4,200 to 4,900 k€.
The water turbine cost estimate assumes that it is proportional to its rated power. We assume that the price is in the range 215 800 to 1,700 €/kW, which yields a water turbine cost in the range 1,280 to 1,720 k€.
Ship common systems, ship assembly and systems integration typically represent 20% of the total cost of a ship according to (Shetelig, 2013). We applied this ratio to the sum of the hull cost, Flettner rotor cost and water turbines cost. The other equipments were not taken into account because their installation factor is taken into account separately.
Holl et al. (Holl et al., 2016) has developed scaling laws for the cost of the electrolyzer and the freshwater production unit 220 based on market surveys. They depend on the nominal power of the equipment. Applying the electrolyzer scaling law to the 1,130 kW capacity electrolyzer of the energy ship results in an estimated cost of 1,400 k€, equivalent to 1,250 €/kW. This is in agreement with the range 1,000 to 1,950 €/kW reported in (Schmidt et al., 2017) for PEM electrolyzers (which we used in this study). As for the freshwater production, the application of the scaling law of Holl et al. yielded a cost estimate of 9 k€, which is very small in comparison to the other costs. 225 According to (Brynolf et al., 2018), the cost of a hydrogen-to-methanol plant is in the range 600 -1,200 €/kW of methanol.
As the estimated efficiency of the power-to-methanol conversion process is 49% (Babarit et al., 2020), it corresponds to 300 to 600 €/kW of electrolyzer input power. Thus, we retain 400 -700 k€ for the hydrogen-to-methanol plant capital cost.
For the liquid CO2 and methanol storage tanks, suppliers and prices can be found on the internet (e.g. https://www.gitank.com/methanol-storage-tanks, (Chart, 2019)); typical costs are 300 €/ton of capacity for methanol and 230 1,000 €/ton of capacity for liquid CO2. Overall, their costs are negligible in comparison to other costs.
The electrolyzer and hydrogen-to-methanol costs do not include installation and assembly, transportation, building, etc.
Those costs are usually taken into account using an installation factor. According to (NREL, 2014), the lower end of the installation factor is 1.2 and up to 2 for the higher end. This leads to a cost of 300 -2,900 k€.

Capital cost of a first of a kind FARWIND energy system 235
According to the discussion in section 3.2, a FARWIND energy system should include a fleet of 112 energy ships and 5 tankers. One can expect the unit cost for a fleet of 112 energy ships to be significantly smaller than the cost of an energy ship prototype. To take this into account, a learning rate of 10% was assumed on the unit cost of the energy ship as function of the built capacity, see Tab. 2. It can be noted that such learning rate corresponds to what was observed for wind turbines (Lindman and Soderholm, 2012). It leads to a range of capital cost of 620 to 1,110 M€ for the first fleet of energy ships. It 240 corresponds to an average unit cost of 5,500 to 9,900 k€ per energy ship.
For the tanker, according to (Lindstad et al., 2012), the price of commercial ships is in the range 500 € to 4,750 € per ton of dwt, depending on the type of ships and size. The lower price is for crude oil tankers greater than 140,000 dwt, while the https://doi.org/10.5194/wes-2021-39 Preprint. Discussion started: 7 June 2021 c Author(s) 2021. CC BY 4.0 License.
higher price is for roll-in/roll-off (ro-ro) ships of 7,000 dwt. In the present study, we retain a cost range of 2,500 to 4,000 €/ton of deadweight, leading to a tanker cost in the range 12,500 to 20,000 k€. 245 Thus, overall, the total capital cost of a FARWIND system comprised of 112 energy ships and 5 tankers is expected to be in the range of 680 to 1,210 M€ (3,700 to 6,700 k€ per megawatt of installed capacity).

Operational expenditures
Expected operation and maintenance (O&M) costs, including the cost of CO2 supply, are summarized in Tab Table 3 Estimates of the operation and maintenance of a first-of-a-kind FARWIND energy system

Energy ships and tankers operation and maintenance cost
According to (Holl et al., 2016), the maintenance cost of the water turbine is in the range 4 to 13% of the capital cost, and that of the freshwater production unit is between 10 and 20%. According to (Chardonnet et al., 2017), the maintenance cost for the electrolyzer is in the order of 4% of capital cost. It is 2 -5% according to (Brynolf et al., 2018). It is unclear whether 255 those maintenance takes into stack replacement. Indeed, PEM electrolyzers' stack lifetime is in the order of 50,000 hours. Thus, assuming a capacity factor of 72%, they would have to be replaced every 8 years. According to (Brynholf et al., 2018), stack replacement cost is 60% of the electrolyzer cost. It leads to an additional 7.5% maintenance cost for the electrolyzer.
Thus, we retain 7.5 -11.5% for the maintenance cost of the electrolyzer. The same range is assumed for the hydrogen to methanol plant. 260 For the Flettner rotors, the maintenance cost is expected to be in the order of 3.5% of the rotors' capital cost (Kuuskoksi, 2020). For the other subsystems (hull, auxiliaries, storage tanks), it is expected that the maintenance costs would be small; a 2% maintenance cost was arbitrarily selected. Overall maintenance costs for the energy ship are thus in the order of 3.7 to 5.3%.
For the tanker, following (Holl et al., 2016), we estimate operation and maintenance costs to be 4 to 10%. 265

CO2 supply cost
The ambition of the FARWIND energy system is to provide a sustainable alternative to the use of liquid fossil fuels (e.g. oil). Therefore, as mentioned in the introduction, the CO2 must be captured directly or indirectly from the atmosphere.
According to (Keith et al., 2018), the cost for direct air capture (DAC) using large-scale wet absorption DAC technology is in the range 80 to 204 €/ton of CO2. The cost of CO2 capture from biogas upgrading is in the order of 15 to 100 €/ton of CO2 270 (Li et al., 2017). In the case of CO2 capture from flue gases from combustion of biomass or FARWIND-produced methanol, the cost of carbon capture is in the order of 35 to 50 €/ton (assuming that it would be similar to that for capture of CO2 from power production processes involving coal or natural gas (Irlam, 2017)). Note that for both biogas upgrading and biomass or methanol combustion, the CO2 concentration in the source is much greater than in ambient air, which results in a more effective capture than with DAC. 275 Carbon dioxide may also be extracted from seawater (Willauer et al., 2012). Indeed, some of the CO2 present in the atmosphere dissolves in the ocean. However, this new technology is in its early stages of development (Willauer et al., 2017).
In any case, the captured CO2 must be liquefied for efficient transportation. The energy requirement for CO2 liquefaction is in the order of 0.1 kWh/kgCO2 according to (Oi et al., 2016), which is low; hence its associated cost is expected to be 280 negligible.
Therefore, we estimate the cost of CO2 production to be in the range 20 to 200 €/ton. As 97,400 t of CO2 are required to produce 70,600 t of methanol, the CO2 supply cost is estimated to be in the range 2-20 M€ per annum.

Insurance cost
Insurance cost is generally taken as 0.6% of CAPEX per year for vessels at the concept stage. However, for a new 285 technology, this percentage of CAPEX may be higher, potentially as high as 1 -2%. In this study, we have retained 0.6 -1.2%.

Short-term cost
The levelized cost of methanol LCOM can be calculated as (Holl et al., 2016): 290 where I is the total capital cost, is the total O&M rate, is the annual methanol production, and = (1+ ) is the capital recovery factor, in which i is the weighted average cost of capital (WACC) and n is the lifetime in years. Assuming a WACC in the range 6-10% and a lifetime of 20 -25 years, the capital recovery factor is in the range 7.8-11.7%. The 295 methanol cost is thus in the range 1.2-3.6 €/kg (225 to 660 €/MWhth).
This cost is three to nine times greater than current market price for methanol (0.4 €/kg ≈ 72 €/MWh in the first quarter of 2021). However, it does not consider a price on GHG emissions. At least 0.675 kg of CO2 is produced per kg of methanol produced using conventional processes (which are based on coal or natural gas) (Martin and Grossmann, 2017). In 2018, the carbon tax was 44.6 €/ton in France and 110 €/ton in Sweden; if CO2 emissions were taken into account, the methanol price 300 would increase by 6 €/MWhth and 13 €/MWhth respectively. Thus, unfortunately, even with a rather significant carbon tax, the cost of methanol produced with a first-of-a-kind FARWIND system would not be competitive.  Figure 7 shows the cost breakdown for an average cost scenario. One can see that the main cost sources are the financing cost (33% of total methanol cost), the energy ship's capital cost (hull + Flettner rotors + water turbines + auxiliaries and integration, 17% of total methanol cost), and operation and maintenance cost of the FARWINDERs (16%).
The total cost of energy storage -including the power-to-methanol plants capital cost and maintenance cost, CO2 supply, and tankers capital cost and operation and maintenance cost -accounts for 25% of total cost. However, as for the energy ships, one can expect that the cost of FARWIND systems will decrease with increasing 315 installed capacity. Fig. 8 shows the expected cost reduction for the methanol cost as function of the installed capacity. A learning rate of 10% was assumed (as for the energy ships, see section 4.2). One can see that it would take thousands of GW of installed capacity to achieve competitiveness with methanol produced from fossil fuels.
Let us now consider the perspective of FARWIND-produced fuel for the transportation fuel market. Indeed, methanol can be blended with gasoline in low quantities for use in existing road vehicles. According to (Methanol Institute, 2014), the 320 blend can include up to 15% methanol by volume (M15 fuel). Moreover, flexible fuel vehicles which can run on an 85%-15% methanol-gasoline mix (M85 fuel) have been developed and commercialized (e.g. the 1996 Ford Taurus); and M100 https://doi.org/10.5194/wes-2021-39 Preprint. Discussion started: 7 June 2021 c Author(s) 2021. CC BY 4.0 License.
(100% methanol) vehicles are in development (Olah et al., 2018). Thus, FARWIND-produced methanol could be used as a low-carbon substitute to oil on the transportation fuel market. Let us compare the cost of FARWIND-produced methanol to the gasoline price in the EU. Gasoline price ranges from 1.1 €/L (Bulgaria) to 1.7 €/L (Netherlands), the price differences arising from different policies on fuel taxes in different countries (European Commission, 2019). This price range is equivalent to 112 to 173 €/MWhth, since the standard density of 330 gasoline traded in the EU is 0.755 kg/L and its energy content is approximately 13 kWhth/kg. Thus, as can be seen in Figure   9 and provided that taxes policies are favourable to FARWIND-produced methanol, it may take "only" a few tens of GW of installed capacity to be competitive with gasoline on the EU transportation fuel market.

Comparison with methanol production by offshore wind turbines
Finally, let us compare the cost of methanol production by FARWIND systems and offshore wind turbines. In this 335 respect, we assume that the first-of-a-kind FARWIND system is deployed by 2030. At that time, according to (IRENA, 2019), the global offshore wind energy capacity will have reached 230 GW.
The key economic drivers in power-to-gas or power-to-liquid processes are the cost of input electricity to the power-to-gas/liquid plant and the power-to-gas/liquid plant capacity factor (Fasihi et al., 2016;Ioannou and Brennan, 2019).
Based on that data, one can calculate the methanol production cost using: 340 where I' is the capital cost of the power-to-methanol plant, ′ is the O&M rate of the power-to-methanol plant plus the insurance rate, is the plant capacity factor, is the rated power of the plant, is the plant efficiency (49%, see (Babarit et al., 2020)), is cost of input electricity to the power-to-methanol plant, 2 is the CO2 cost per unit 345 mass and is the lower-heating-value of methanol per unit mass (the factor 1.38 corresponds to the fact that it takes 1.38 kg of CO2 to produce 1 kg of methanol).   Table 4 shows the cost assumption for the power-to-methanol plant of the offshore wind farm. The capital cost is assumed to be a third of that of the first-of-a-kind FARWIND system as the power-to-methanol plant would be much larger 350 (Brynolf et al. 2018) and as it may be shore-based. According to (IRENA, 2019), the cost of electricity from offshore wind farms will be in the range 40 to 80 €/MWh by 2030 with capacity factors in the range 36 to 58%. Therefore, using Eq. 2, we find that the methanol production cost by offshore wind farms would be in the range 110 to 375 €/MWhth (0.6 to 2.1 €/kg) by 2030. Thus, by 2030, the cost of methanol produced by a FARWIND energy system (1.3 to 2.1 €/kg) would not be competitive with that produced by a shore-based power-to-methanol plant powered by a large offshore wind farm. 355 However, that would be the case for a first of a kind for FARWIND, whereas it would be for an expected global capacity of 230 GW for offshore wind turbines. Therefore, provided that sufficient FARWIND capacity is installed, FARWIND-produced methanol may become comparable to that of offshore wind farms-produced methanol. This is shown in Figure 10 which shows a comparison of the long-term methanol cost produced by FARWIND systems and by offshore wind farms. A learning rate of 10% was assumed both for the FARWIND systems and for the methanol-producing offshore 360 wind farms. However, for the offshore wind farm, it has been taken into account that the cost of input electricity assumes an installed 230 GW global offshore wind capacity. Therefore, it can be expected that it would take a further 230 GW to achieve a cost reduction of 10% of that part of the methanol cost (second term in Eq. 2.). Thus, the methanol production cost of offshore wind farms as function of the installed capacity (in GW) can be written: ( ) = ( ( + ′) ′ 8760 × × × + 1.38 × 2 ) × 0.9 log 2 0.2 + × 0.9 log 2 230+ 230

Figure 10
Comparison of long term methanol cost produced by FARWIND systems and offshore wind farms as function of the installed capacity

Conclusions
In this paper, we proposed an energy system for sustainable methanol production from the far-offshore wind energy resource. It is based on an autonomous fleet of 112 energy ships and 5 manned tankers for the collection and transport of the 375 produced methanol, as well as the supply of CO2 to the energy ships. Its methanol production is expected to be in the order of 70,600 t per annum (approximately 390 GWh per annum of chemical energy). The cost of this methanol is expected to be in the range 1.2-3.6 €/kg for the first-of-a-kind FARWIND system, which is significantly greater than the current market price for fossil fuel-derived methanol (0.4 €/kg). However, methanol can be used as a substitute to fossil fuels on the fuel transportation market: since the price of transportation fuel is high in most European countries, and assuming that a cost 380 reduction similar to that observed for land-based wind energy can be achieved, the cost of FARWIND-produced methanol could compete with gasoline in the EU.
The cost of methanol produced by a first-of-a-kind FARWIND system is unlikely to be competitive with that produced by a large shore-based power-to-methanol plant powered by an offshore wind farm. However, provided that https://doi.org/10.5194/wes-2021-39 Preprint. Discussion started: 7 June 2021 c Author(s) 2021. CC BY 4.0 License. sufficient FARWIND capacity is installed, FARWIND-produced methanol may become comparable to that of offshore wind 385 farms-produced methanol. Moreover, one should note that the cost of FARWIND-produced methanol is based on a particular energy ship design, which might be optimized to reduce costs.