**1. Introduction**

In order to mitigate anthropogenic climate change, a considerable reduction in the emission of climate-damaging emissions is necessary. For this purpose, it is essential to either electrify sectors or convert them to the use of alternative fuels in order to minimize dependence on fossil fuels. As a result of the introduction of various sustainable technologies, the energy and household sectors, for example, have seen the first reductions in greenhouse gas emissions [1]. The reduction of emissions in the transport sector, however, presents a bigger challenge. Heavy haulage, ship, and air traffic, in particular, can only be converted to electrified drivetrains to a limited extent. As a result, it can be expected that the demand for liquid fuels with high energy densities will remain high in the future [2]. One way of achieving CO2-neutrality for the transport sector involves the power-to-liquid concept. 'Power-to-liquid' is a collective term for various technologies employed in the production of liquid energy carriers through the use of renewable electrical energy with the addition of carbon dioxide (CO2) [3]. The energy carriers produced in this way can be

**Citation:** Peters, R.; Wegener, N.; Samsun, R.C.; Schorn, F.; Riese, J.; Grünewald, M.; Stolten, D. A Techno-Economic Assessment of Fischer–Tropsch Fuels Based on Syngas from Co-Electrolysis. *Processes* **2022**, *10*, 699. https:// doi.org/10.3390/pr10040699

Academic Editors: Alon Kuperman and Alessandro Lampasi

Received: 23 February 2022 Accepted: 30 March 2022 Published: 4 April 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

converted back into electricity and thus function as electricity storage systems that can be used for other applications. In the event that the energy sources are used as fuels in the transport sector, this is referred to as 'power-to-fuel'. If both the required electrical energy and CO2 are obtained from renewable sources, fuels can be produced in a CO2-neutral manner using power-to-fuel processes. Thus, these represent a possibility for effectively defossilizing the transport sector [4]. Various power-to-fuel concepts already exist. On one hand, the production of alternative fuels such as methanol or dimethyl ether (DME) is a focus of research [5]. However, on the other hand, researchers are also exploring the synthesis of traditional fuels such as gasoline, kerosene, and diesel, as the existing infrastructure and greater applicability of these represent an advantage over alternatives [6]. For the structured processing of these tasks, this paper was divided into the following sections:


#### **2. Background**

In 2012, the German transport sector consumed 2772 PJ (≈770 TWh) of energy. Around 26.9% of this energy requirement was accounted for by gasoline, 51% by diesel, and 15.7% by aviation fuels [7].

On one hand, as vehicles with alternative drivetrains such as battery- or fuel cell-based ones are increasingly being used, it is expected that gasoline will lose its importance in the long term. On the other hand, due to the lack of alternatives in freight and air traffic, it can be assumed that the fuels diesel and kerosene will also be of great importance over the longer term [2].

Accordingly, the production of renewable diesel and kerosene is of both academic and industrial interest. A major advantage of synthetically-produced diesel and kerosene is that they are compatible with existing infrastructures and can be used in current vehicles [4]. The prerequisite for use is the fulfillment of the fuel specifications, which are set out in the relevant standards. Synthetically-produced diesel must comply with EN 15940 in Europe. ASTM 7566 applies to Jet A-1 kerosene used in civil aviation. This allows conventionallyproduced Jet A-1 to be mixed with up to 50% synthetically-produced kerosene, depending on the synthesis route [8]. This synthetic kerosene is called synthesized paraffinic kerosene (SPK). An extract of the most important parameters for diesel (class A) according to EN 15940 and for SPK produced via a Fischer–Tropsch synthesis according to ASTM 7566 is discussed in more detail in Section 5.1. Class A describes diesel with an increased cetane

number, which is a characteristic value of the ignitability of diesel fuels. The higher the cetane number, the more readily ignitable the diesel fuel [9].

One possibility of producing renewable, synthetic fuels is via the power-to-fuel concept. Schemme et al. [10] discussed the power-to-fuel concept as a solution to the present challenges of the transport sector in terms of the energy transition by coupling the energy and transport sectors. According to this concept, renewable electricity is used to produce hydrogen via water electrolysis, offering a storage possibility for volatile renewable energy sources. In the following synthesis step, renewable fuels are synthesized in a reaction or a series of reactions and further treatment steps combining the produced hydrogen with carbon dioxide from various possible sources. Different electrolysis technologies can be utilized for the generation of hydrogen.

In 2014, Sunfire GmbH commissioned the "Fuel 1" demonstration plant in Dresden, Germany. At this facility, high-temperature water electrolysis (SOEC) is used to provide hydrogen. The hydrogen is then mixed with carbon monoxide, which is generated in a reverse water–gas shift reactor and converted into so-called blue crude by means of Fischer– Tropsch synthesis. Blue crude is a renewable crude oil that can be further processed in a conventional refinery into synthetic gasoline, kerosene, or diesel, for example [11]. The plant was run for 1500 h [12] and produced one barrel (159 L) of blue crude per day [13].

In 2017, the VTT Technical Research Center of Finland and the Lappeenranta University of Technology operated a demonstration plant in Lappeenranta (Finland) for around 300 operating hours as part of the "SOLETAIR" project [14]. Fischer–Tropsch synthesis was also used in this system. CO2 was obtained through direct air capture and converted into carbon monoxide in a reverse water–gas shift reactor. The hydrogen was provided via PEM electrolysis [15].

As part of the Kopernikus project "Power-to-X", funded by the Federal Ministry of Education and Research, the so-called SUNFIRE-SYNLINK was put into operation in Karlsruhe (Germany) in 2019 [16]. A co-electrolysis system from Sunfire GmbH was used to produce synthesis gas. This was combined with a Fischer–Tropsch reactor from INERATEC and a hydrocracker unit from the Karlsruhe Institute of Technology to produce synthetic fuels. The CO2 required was obtained using Climeworks' direct air capture (DAC) technology. The co-electrolysis currently in use has an output of 10 kW, but Sunfire plans to upscale the process to an industrial scale [17].

An industrial-scale plant is being planned by the Norwegian company, Nordic Electrofuel (formerly Nordic Blue Crude). The plant is to be built and commissioned in Herøya Industripark (Norway) by 2022. The use of high-pressure alkaline electrolysis is planned and the plant is set to achieve an initial production capacity of 10 million liters per year. The required CO2 is to be supplied from both industrial sources and via DAC technology. Originally, the use of a co-electrolysis unit from Sunfire GmbH was planned for the plant planned by Nordic Electrofuel [17]. However, the business partners separated in 2020 and Sunfire GmbH founded the industrial consortium, Norsk e-Fuel [18,19], together with Climeworks, Paul Wurth (SMS Group), and Valinor. Norsk e-Fuel also plans to build a plant capable of producing 10 million liters of synthetic kerosene per year at Herøya Industrial Park (Norway). This facility is scheduled to be commissioned in 2023 and expanded to a production capacity of 100 million liters of renewable fuels by 2026 [20]. Amongst other things, the co-electrolysis technology from Sunfire GmbH and the DAC technology from Climeworks are to be used in it [18,20].

In Rotterdam, the Hague Airport announced a study in 2019 in which, in collaboration with several European partners, a demonstration plant for the production of aviation fuel was to be developed. The plant is expected to produce around 1000 L of renewable fuel, but there has not yet been a specific date for its commissioning [21]. Based on this study, the two startups Synkero and Zenid were presented on 8 February 2021 [22,23]. Both of these plan to build a plant for the production of synthetic kerosene, but each is pursuing different concepts for providing the required CO2. Although Zenid's goal is a plant that obtains the CO2 exclusively by means of DAC technology [24], Synkero also considers other CO2 sources such as industrial exhaust gases or biogenic sources [25].

Figure 1 illustrates a special power-to-fuel concept for the production of synthetic fuels, which is to be examined in more detail within the scope of this work. Initially, synthesis gas consisting of hydrogen (H2) and carbon monoxide (CO) is produced from water and CO2 using renewable electrical energy. The resulting synthesis gas is then converted into liquid fuels.

**Figure 1.** Schematic of a power-to-fuel process with co-electrolysis.

What is special about the power-to-fuel concept shown in Figure 1 is that the synthesis feed gas is produced using what is known as co-electrolysis. This allows for the production of synthesis gas in a single step, and so there is no need to produce hydrogen and carbon monoxide separately. In addition, co-electrolysis offers some energetic advantages over other synthesis gas production routes. For example, it is possible to substitute some of the electrical energy required for electrolysis with excess thermal energy from fuel synthesis. Therefore, the combination of co-electrolysis with Fischer–Tropsch synthesis represents an interesting basis for power-to-fuel processes. In this route, synthesis gas is converted into hydrocarbons by means of strongly exothermic reactions, which are then processed into fuels such as gasoline, diesel, or kerosene. The heat of reactions that occur during Fischer– Tropsch synthesis can be used to operate co-electrolysis, which opens up the possibility of improving the overall efficiency of power-to-fuel processes.

The aim of this work was to develop a power-to-fuel process based on co-electrolysis, in combination with a Fischer–Tropsch synthesis, and to model and simulate the process in the Aspen Plus program. The entire process chain, starting with CO2 and water through to fuel, should be considered. Then, the developed power-to-fuel process should be technoeconomically analyzed and compared to alternative power-to-fuel processes.

#### **3. Basic Process Units of PtF System Design**

The following section presents the technical basics of the most important components of the modeled power-to-fuel process. The power-to-fuel system developed within the scope of this work consists of a water electrolysis, co-electrolysis, Fischer–Tropsch synthesis, hydrocracker, reformer, and carrier steam distillation. This section deals with the basics of these system components.

#### *3.1. Electrolysis and Co-Electrolysis*

Depending on the electrolyte or ionic charge carrier used, a distinction is made between three different electrolysis methods. Alkaline electrolysis and PEM electrolysis are already available on the megawatt scale, and hydrogen thus produced can achieve high purities of over 99% [6,26]. In addition, alkaline and PEM electrolysis can be operated under pressures of 60 to 80 bar, thus reducing the need for compressor power for downstream processes [6].

In contrast, the solid oxide electrolyzer cell (SOEC) is not yet commercially available in the megawatt range. Operation under pressure is also still in the development phase. However, due to their high operating temperature, SOECs offer thermodynamic advantages over other electrolysis types. Therefore, it is theoretically possible to achieve electrical efficiencies of over 100% based on the calorific value of the products [6]. Typical operating temperatures of a SOEC are 800–1000 ◦C [27] or 700–1000 ◦C [28], depending on the literature source. In addition, due to its high operating temperature, it has improved kinetics [29] and can be operated as a so-called co-electrolysis unit [30]. In co-electrolysis, not only water, but also CO2 is broken down. This electrolysis process is especially interesting for power-to-liquid (PtL) and power-to-fuel (PtF) processes as it makes it possible to produce synthesis gas consisting of hydrogen and carbon monoxide in a single process step [6,30].

The electrochemical reactions that take place at the cathode and anode are as follows. Cathode:

$$\text{H}\_2\text{O} + 2\text{e}^- \rightarrow \text{H}\_2 + \text{O}^{2-} \tag{1}$$

$$\text{CO}\_2 + 2\text{e}^- \rightarrow \text{CO} + \text{O}^{2-} \tag{2}$$

Anode:

$$2\text{O}^{2-} \rightarrow \text{O}\_2 + 4\text{e}^- \tag{3}$$

The minimum energy expenditure for the decomposition of water or CO2 corresponds to the enthalpy of reaction Δ*HR*, which in the case of the usual operating conditions of coelectrolysis (860 ◦C, 1 bar) is 249 kJ/mol for water and 283 kJ/mol for CO2 [30]. According to the second law of thermodynamics, the reaction enthalpy is composed of the free Gibbs energy Δ*GR* and the reaction entropy Δ*SR*, multiplied by the temperature *T* as follows [31]:

$$
\Delta H\_R = \Delta G\_R + T \cdot \Delta S\_R \tag{4}
$$

Here, Δ*GR* is the part of the reaction enthalpy that must be provided in the form of electricity during electrolysis, whereas *T*·Δ*SR* can be supplied to the reaction in the form of heat [32]. An advantage of high-temperature electrolysis compared to other electrolysis types is that if the water evaporates outside the electrolysis cell, this energy must no longer be introduced into the cell in the form of electricity [29]. After evaporation with increasing temperature, the total energy requirement of the reaction remains almost constant, but the amount of electrical energy that is absolutely necessary significantly decreases. On the basis of these two facts, valuable electrical energy can be saved with high-temperature electrolysis in comparison to, for example, PEM electrolysis. Considering the thermal energy that is exchanged, the internal thermal losses are of particular importance in electrolysis, as they can be used to provide the heat of the reaction. The case in which the thermal losses correspond precisely to the heat of the reaction is referred to as the thermoneutral operating point, and the electrical voltage applied to the SOEC at this operating point is correspondingly referred to as the thermoneutral voltage [3]. At the thermoneutral operating point, the entire electrical energy *Eel* supplied to the electrolysis cell is converted into chemical potential energy and the following applies to cell efficiency at thermoneutral point *ηcell*,*TN* [31]:

$$
\eta\_{\rm cell,TN} = \frac{\Delta H\_R}{E\_{\rm cI}} = 1\tag{5}
$$

Due to the simultaneous presence of H2O, CO2, H2, and CO at the cathode of the SOEC and the high operating temperatures, in addition to the reactions listed in Equations (1)–(3), the so-called water–gas shift reaction (WGS) or reverse water–gas shift reaction (RWGS) must also be considered in the co-electrolysis [33]. The reverse water–gas shift reaction is favored at the high operating temperatures of a SOEC [34].

$$\text{CO} + \text{H}\_2\text{O} \leftrightarrow \text{CO}\_2 + \text{H}\_2\tag{6}$$

In addition, methanation reactions (Equations (7) and (8)) can occur at the cathode of a SOEC [33]:

$$\text{CH} + \text{3H}\_2 \leftrightarrow \text{CH}\_4 + \text{H}\_2\text{O} \tag{7}$$

$$\rm{CO\_2 + 4H\_2 \leftrightarrow CH\_4 + 2H\_2O} \tag{8}$$

Finally, the Boudouard reaction (Equation (9)) must be taken into account, and can lead to the precipitation of solid carbon under certain operating conditions of a SOEC [33]:

$$\text{2CO} \leftrightarrow \text{CO}\_2 + \text{C}\_{(s)}\tag{9}$$

According to Equation (5) the efficiency of co-electrolysis at the thermo-neutral operating point corresponds to 100%. According to Peters et al. [22], however, SOECs are not usually operated with an exactly thermoneutral voltage, so the heat must be either added or removed. In addition, the efficiency of the entire system is influenced by other factors such as the power required for the compression and storage of the products or the losses of the voltage converter to rectify the alternating current. Therefore, in order to assess the efficiency of the overall system (*ηSOEC*), the degree of efficiency is usually defined through the calorific value of the product (*Mass flow rate of product mproduct multiplied by its lower heating value H*<sup>0</sup> *<sup>u</sup>*) in relation to the electrical (*Eel*,total) and thermal energy (*Eth*,total) used [22]:

$$\eta\_{SOEC} = \frac{m\_{product} \cdot H\_u^0}{E\_{el, \text{total}} + E\_{th, \text{total}}} \tag{10}$$

#### *3.2. Fischer–Tropsch Synthesis*

Fischer–Tropsch synthesis is a process in which a synthesis gas consisting of hydrogen and carbon monoxide is converted into liquid hydrocarbons [9]. This results in a wide range of hydrocarbon chains of different lengths with chain length n, according to the following equation [33]:

$$(2n+1)\cdot\text{H}\_2 + n\cdot\text{CO} \to \text{C}\_n\text{H}\_{2n+2} + n\cdot\text{H}\_2\text{O}\tag{11}$$

Another reaction that occurs in the Fischer–Tropsch synthesis process is the water–gas shift reaction already described in Equation (6). The methanation reactions (Equations (7) and (8)) and the Boudouard reaction described in Equation (9) can also occur [35]. Which reactions take place to which extent during the Fischer–Tropsch synthesis and also the product distribution of it are determined by the process parameters [35].

A distinction is made between high-temperature Fischer–Tropsch synthesis (HTFT) and low-temperature Fischer–Tropsch synthesis (LTFT) [36]. High temperatures (300–350 ◦C), with iron as a catalyst, favor short chain lengths and therefore shift the product distribution in the direction of (liquid) gases (*n* = 1–4) and synthetic gasoline (*n* = 5–12) [6,35]. Lower temperatures (200–240 ◦C) in combination with iron or cobalt catalysts, in contrast, favor the formation of longer hydrocarbon chains (i.e., middle distillates such as kerosene (*n* = 8–16) [37] and diesel (*n* = 10–23) as well as long-chain ones (*n* > 22)) [6,35]. In addition, cobalt catalysts suppress the water–gas shift reaction, and low temperatures reduce the formation of methane and solid carbon. The operating pressure also has a direct influence on the product distribution [35]. Typical operating pressures in Fischer–Tropsch synthesis are between 1 and 40 bar, with higher pressures resulting in longer average hydrocarbon chain lengths [35]. Another influencing factor on Fischer–Tropsch synthesis is the ratio of H2 to CO. Typically, H2/CO ratios of around two are used, with the average chain length of the product decreasing with higher ratios and increasing with lower ones [33].

The product distribution can be approximately determined using the Anderson– Schulz–Flory distribution [36]. With this, both the mass fractions *wn* (Equation (12)) and molar fractions *xn* (Equation (13)) of the respective hydrocarbon chains with chain length n can be determined [35]:

$$w\_n = \mathfrak{a}^{n-1} \cdot (1-\mathfrak{a})^2 \cdot n \tag{12}$$

$$
\pi\_n = \pi^{n-1} \cdot (1-\alpha) \tag{13}
$$

Here, α stands for the chain growth probability, which is determined by reactor design and operating conditions. The chain growth probability can be either determined empirically or taken from the literature. The influence of chain growth probability on the product distribution is discussed further in Appendix A. In Vervloet et al. [38], the approach in Equation (14) was given for α for the low-temperature Fischer–Tropsch synthesis assumed in this work and the use of a cobalt catalyst. In this model, the chain growth probability is determined through the ratio between the chain growth rate and chain growth termination rate:

$$\alpha = \frac{1}{1 + k\_{\text{\tiny\text{\tiny {}^{\text{CH}\_{2}}}}} \frac{1}{\exp\left(\frac{\Delta E\_{\text{R}}}{R} \left(\frac{1}{493.15} - \frac{1}{T}\right)\right)}}\tag{14}$$

where

*kα* is the ratio of the speeds of the chain growth rate and chain growth termination rate (*k<sup>α</sup>* = 0.0567);

*cH*<sup>2</sup> is the hydrogen concentration in mol/m3;

*cCO* is the carbon monoxide concentration in mol/m3;

*β* is the exponential parameter for selectivity (*β* = 1.76);

Δ*E<sup>α</sup>* is the difference of activation energies for chain growth and chain growth termination (Δ*E<sup>α</sup>* = 120.4 kJ mol);

*R* is the ideal gas constant (*R* = 8.314 <sup>J</sup> mol); and

*T* is the reactor temperature in K.

The influence of the chain growth probability on the product distribution is illustrated in (Figure A1 in Appendix A, which shows the product distribution of a Fischer–Tropsch synthesis for α = 0.88 and α = 0.92 for C1 to C60.

#### *3.3. Hydrocrackers*

Hydrocracking refers to a chemical process in which long-chain, higher-molecular hydrocarbon chains are split into shorter ones through the addition of hydrogen. The distribution of the chain lengths of the products is strongly influenced by the catalyst used and the selected process conditions. Therefore, these must always be adapted to the respective application [39,40]. For power-to-fuel processes, chain lengths in the range from *n* = 5 to *n* = 20 are of great importance, as these hydrocarbon chains are required for the production of synthetic gasoline, kerosene, and diesel [36]. One possibility for maximizing these fractions in the product of the hydrocracker is the use of so-called "ideal hydrocracking" [41,42]. As a power-to-fuel process is to be modeled and simulated within the scope of this work, the focus in the following was on ideal hydrocracking.

The most important properties of ideal hydrocracking are defined as follows, drawing on Bouchy et al. [41]. If *Cn*-molecules are cracked, the selectivity to all *C*4- to *Cn*−<sup>4</sup> hydrocarbons is identical, the selectivity to *C*<sup>3</sup> and *Cn*−<sup>3</sup> is half of that, and *C*1, *C*2, *Cn*−<sup>1</sup>

and *Cn*−<sup>2</sup> cannot be formed. Furthermore, only primary cracking occurs. Exclusively primary hydrocracking means that the shorter hydrocarbons that are created after a longer hydrocarbon chain has been cracked cannot be cracked any further [39]. In the case of non-ideal hydrocracking, the proportion of middle distillates is significantly lower than in ideal hydrocracking. In addition, a large peak of the *C*<sup>3</sup> to *C*<sup>5</sup> hydrocarbons was identified by Wegener [43]. This course is due to the occurrence of secondary cracking, which cracks the middle distillates, with the proportion of short-chain hydrocarbons increasing.

According to Bouchy et al., ideal bifunctional catalysts with a hydrogenation/dehydrogenation function and an acid function can be used, whereby it must be ensured that the reaction taking place at the acid function is the limiting one [41]. In addition, it is important to ensure that the pore structure of the catalyst is correct, so that no undesired increased cracking occurs at the ends of the hydrocarbon chains, which can lead to the stronger formation of short-chain gases [41,44].

As already described, the operating conditions also have a major influence on the product distribution of a hydrocracker. Conventional hydrocracking, depending on the literature source, is carried out at temperatures ranging from 350–430 ◦C and pressures of 100–200 bar [41], or in the upper range of 290–445 ◦C and 10–200 bar [40]. Ideal hydrocracking takes place under significantly milder process conditions, with temperatures in the range of 324–372 ◦C and pressures of 35–70 bar [41].

In addition, in order to suppress soot formation and catalyst deactivation, it must be ensured that the proportion of H2 in the feed stream is high enough [39]. In the literature, values of 6–15% by weight are recommended [45]. With hydrocracking, conversions of up to 99% can be theoretically achieved [39]. However, according to Bouchy et al. [41], conversions that are too high for ideal hydrocracking become problematic, as secondary cracking inevitably occurs, even with ideal hydrocracking at very high conversions.

#### *3.4. Reformers–Steam Reforming and Partial Oxidation*

Reformers make it possible to convert hydrocarbons into synthesis gas. Various reactions and side reactions take place simultaneously in a reformer, with steam reforming and partial oxidation playing the greatest role [4].

In steam reforming, hydrocarbons are converted into carbon monoxide and hydrogen with the addition of steam. The general reaction equation for steam reforming is as follows:

$$\rm C\_nH\_{2n+2} + n \cdot H\_2O \to n \cdot CO + (2n+1) \cdot H\_2 \tag{15}$$

This is a strongly endothermic reaction which, with the exception of methane (*n* = 1), can be regarded as irreversible at the normal operating temperatures of over 500 ◦C for reformers [46]. The partial oxidation of hydrocarbons is an exothermic reaction with the general reaction equation:

$$\rm{^1C\_nH\_{2n+2}} + \frac{n}{2} \cdot \rm{^0C\_2} \rightarrow n \cdot \rm{CO} + (n+1) \cdot \rm{H\_2} \tag{16}$$

If the supply of oxygen is regulated, the degree of reaction of the partial oxidation can also be adjusted. Accordingly, if both reactions are carried out at the same time, the required heat of reaction for the steam reforming can be provided via partial oxidation. A reformer can be operated endothermically, exothermically, or autothermically through the oxygen supply in the overall balance [46]. As already noted, numerous side reactions occur in a reformer. Due to the high operating temperatures and the simultaneous presence of water, hydrogen, carbon monoxide, and CO2, the water–gas shift reaction (Equation (6)) takes place [46]. In addition, soot can form due to various reaction mechanisms. These reactions are, in particular, the Boudouard reaction (Equation (9)), methane splitting (Equation (17)), and CO or CO2 hydrogenation (Equations (18) and (19)) [46]. These soot formation reactions are undesirable during operation of the reformer, and can be suppressed by means of a

suitable starting material composition. According to Rostrup-Nielsen [47], H2O/C rates of 0.6 are suitable for this:

$$\text{CH}\_4 \leftrightarrow \text{H}\_2 + \text{C}\_{(s)}\tag{17}$$

$$\text{ClO} + \text{H}\_2 \leftrightarrow \text{H}\_2\text{O} + \text{C}\_{(s)}\tag{18}$$

$$\text{CO}\_2 + 2\text{H}\_2 \leftrightarrow 2\text{H}\_2\text{O} + \text{C}\_{(s)}\tag{19}$$

#### *3.5. Carrier Steam Distillation*

In the petrochemical industry, what is known as carrier steam distillation is usually used to separate hydrocarbon mixtures. Carrier steam distillation constitutes a special case of distillation that enables mixtures to be gently separated. It uses the addition of the vapor pressures of immiscible liquids. The mixture to be separated is evaporated with a low-boiling entrainer (often water) so that the boiling temperature is reduced. The desired fractions can then be drawn off from the carrier steam distillation column via side draws, and the entrainer can then be separated off again [48].

At this point, it should be noted that the petrochemical products are rarely specific chemicals, but are usually mixtures of different components with different properties. To characterize these mixtures and design separation processes, therefore, boiling point ranges or specific temperatures along these boiling curves are generally used. The temperature at which the mixture begins to evaporate is referred to as the initial boiling point (IBP), and the temperature at which the mixture has completely evaporated is called the final boiling point (FBP). The temperature at which a certain volume, for example, 10% of the liquid has evaporated is called the 10% point or T10. More information on the characteristic points is presented by Wegener [43] concerning the boiling curve of jet A-1 aircraft fuel [48].

#### *3.6. Technology Readiness Level*

In this section, the well-known technology readiness level (TRL) method is used to evaluate the power-to-fuel process developed in this paper. The TRL method indicates the maturity of a technology on a scale from 1 to 9. The method was originally developed by NASA [49] and is now used with adapted definitions in various areas [50]. In this work, the definitions established by the European Commission for the renewable energy sector are employed [51].

The TRLs of CO2 capture technologies range from medium to very high. According to Schmidt et al. [8], for example, CO2 separation from industrial waste gases by means of amine scrubbing (MEA) is already in use and has a TRL of 9. The separation of CO2 from the air, however, is still at an earlier stage of development and assigned a TRL of 6 [8]. As described in Section 3.1, high-temperature electrolysis was used as part of "Fuel 1" by Sunfire GmbH in a larger demonstration plant and therefore assigned a TRL of 5 [13]. High-temperature co-electrolysis has only just started its test phase using the SUNFIRE-SYNLINK technology in 2019, and accordingly has not yet reached the same level of maturity as high-temperature water electrolysis. The remaining technologies used as part of the developed power-to-fuel process are highly developed technologies that are already in use on an industrial scale. The TRLs of these are correspondingly high. There are no specific statements regarding the values for the TRL of carrier steam distillations and reformers, but Luyben [48] describes the industrial use of carrier steam distillations and, it is well known that reformers are used in large-scale processes.

The TRLs of the individual components of the power-to-fuel process considered in this work are, with the exception of high-temperature electrolysis and CO2 separation from the ambient air, very high. However, according to Schmidt et al. [8] and Marchese et al. [33], the TRL of a power-to-fuel process automatically falls to the lowest TRL in the process chain. According to this, the TRL of the developed power-to-fuel process in this work was assessed as 3 due to the low TRL level of the co-electrolysis step.

#### **4. Modeling and Simulation in ASPEN PLUS**

This section is dedicated to the modeling of the power-to-fuel process in Aspen Plus. For this purpose, the material data and property data models used are first presented. Then, the procedural design of the individual process components as well as the respective selected operating conditions are explained in more detail. For the sake of clarity, the relevant sections of the process flow diagram created in Aspen Plus are shown in Sections 4.2–4.6. When modeling the process, care is taken to ensure that the simulation is suitable for any mass flows.

#### *4.1. Material Property Data and Material Property Data Models*

As part of the power-to-fuel process developed, a low-temperature Fischer–Tropsch synthesis was used. Hence, with respect to de Klerk [36,52] and Dry [53], only straightchain, unbranched alkanes with the empirical formula *CnH*2*n*+<sup>2</sup> were considered. The material data of the hydrocarbons *C*<sup>1</sup> to *C*<sup>29</sup> were obtained from the database integrated in Aspen Plus. Based on Schemme [54], the *C*30+-hydrocarbons were viewed as three groups of pseudo-components, with the *C*30−35-, the *C*36−47-, and *C*48+-hydrocarbons grouped together. A representative molecular structure was selected for each of the three pseudo-components. The American Petroleum Institute (API) method, with the data given in Table 1, was used to calculate the thermodynamic properties of the pseudocomponents. The Aspen Plus database was used for the material data of components H2, H2O, CO, and CO2. The material data models used were selected on the basis of the general recommendations of Carlson [55] and other application-specific literature. A total of four different material data models were used to simulate the process.

**Table 1.** Properties of the pseudo-components [56].


The equation of state of Soave–Redlich–Kwong is widely used in the field of gas processing. In the context of this work, the equation of state with reference to Marchese et al. [33] was used as a material data model for the modeled electrolysis types. In order to be able to more precisely calculate the phase equilibrium between gas and liquid in the presence of hydrocarbons and light gases such as CO2 and H2 in the supercritical range, the Soave–Redlich–Kwong equation of state can be extended to the RKS–BM material data model with the Boston–Mathias alpha function. Drawing on Schemme [54], this model was used to calculate the reformer and the parts of the product separation with very low proportions of pseudo-components. The material model Braun K-10 was used to calculate the material flows with higher proportions of pseudo-components. This material data model was especially developed for calculating hydrocarbon mixtures with both real and pseudo-components, and was used in simulations for the Fischer–Tropsch reactor and hydrocracker. The NRTL model enables the description of gas–liquid equilibria as well as liquid–liquid equilibria of strongly non-ideal mixtures. The activity coefficients of the liquid phases are calculated on the basis of experimentally-determined binary interaction parameters. The calculation of CO, CO2, and H2 also takes Henry's law into account. In the simulation, the NRTL–RK material data model was used to calculate the carrier steam distillation. In general, the calculation of the gas phase is by default carried out using ideal gas law. In this work, the Redlich–Kwong equation of state was used instead to describe the gas phase. The NRTL–RK material data model was also used for heat exchangers in which a large proportion of water is in liquid form.

#### *4.2. Co-Electrolysis and Water Electrolysis*

As Aspen Plus does not have a stored model for the simulation of high-temperature electrolysis, a combination of different Aspen Plus blocks, also known as "Unit Operations", must be used to calculate co- and water electrolysis. In addition, so-called design specs are employed to establish the required process conditions. Similar configurations for simulating high-temperature electrolysis have already been used by Cinti et al. and Marchese et al. [31,33]. The simulation flow diagram for co-electrolysis is shown in Figure 2. It should be noted that not all heat flows of the process can be seen directly in the flow diagram. Various operating resources were used in the simulation to provide the required heating or cooling capacity. For instance, W-5 is an air cooler and W-6 a water cooler, each of which uses the corresponding operating media "air" and "cooling water". The balancing of the resources used was carried out through the "utilities" function integrated in Aspen Plus and is discussed in greater detail in Section 5 The same applies to all of the following flow diagrams.

**Figure 2.** Excerpt from the process flow diagram: co-electrolysis.

First, the mixture of CO2 and water, which is present at 1 bar, is warmed up over several stages in a heat exchanger and the water is evaporated. For this purpose, both the waste heat from co-electrolysis and the product flow of the Fischer–Tropsch synthesis as well as part of the waste heat from the Fischer–Tropsch reactor itself, was used. In addition, an electric heater was used with W-2, which ensured that the feed stream reached the electrolysis inlet temperature of 780 ◦C. The hot gas stream consisting of water vapor and CO2 then enters the electrolysis cell. As already described, the electrolysis cell consisted of several unit operations with which the cathode (RG-1, RS-1, RG-2), the electrolyte (S-1), and anode (GW-1, W-3) were modeled. The feed stream was combined with a recycling stream and passed into a first equilibrium reactor (RG-1). Taking into account the equilibrium reactions that occur (WGS or RWGS: Equation (6), methanation: Equations (8) and (9)), this determines the composition of the gas flow by minimizing the Gibbs energy. Due to the high temperatures, it was assumed that the reaction equilibrium would be reached quickly (see Sun, et al. [57]). The Boudouard reaction (Equation (9)) was not taken into account in the simulation because, according to Sun, Chen, Jensen, Ebbesen, Graves and Mogensen [57], there is no deposition of solid carbon under the selected operating conditions of 800 ◦C and 1 bar. In the next step, the gas flow passes into the stoichiometric reactor RS-1, in which the electrolysis reactions (Equations (1)–(3)) take place. The conversion of RS-1 was automatically set with a design spec so that the total conversion of the electrolysis cell reactant utilization (RU) corresponded to the specified RU (see Equation (20) [33]). The

total turnover was set at 70% with reference to Sun, Chen, Jensen, Ebbesen, Graves and Mogensen [57] and Marchese, Giglio, Santarelli and Lanzini [33]:

$$RLI = \frac{\dot{n}\_{\text{react, in}} - \dot{n}\_{\text{react, out}}}{\dot{n}\_{\text{react, in}}} \tag{20}$$

The electrolyte was modeled as a simple separator block (S-1), which separates the oxygen produced by the electrolysis reactions. The composition of the synthesis gas was then adjusted in parallel to RG-1 in a further equilibrium reactor (RG-2). While most of the synthesis gas then leaves the electrolysis segment, a portion of the stream is fed back. The size of the returned portion was set using a design spec so that the H2 concentration in the feed of the electrolysis was at least 10 mol% in order to avoid oxidation of the nickel-based cathode [27,58]. Synthesis gas leaving the electrolysis cell is gradually cooled down for improved energetic utilization, and the unconverted water is condensed out. The synthesis gas is then compressed to 30 bar by a multi-stage compressor and merged with the reformed synthesis gas (see Section 4.6). Thereby, the H2/CO ratio required for the Fischer–Tropsch synthesis was available after mixing of the synthesis gas streams and a further design spec was used that adjusts the ratio of water to CO2 in the feed stream of the co-electrolysis system accordingly.

MW-1 and MW-2 represent multi-component counter-flow heat exchangers, which were used to recover the process heat for educt conditioning. W-1 is a heater used for further educt conditioning. V-1 represents a compressor. The separator block B-1 is used to separate the vapor phase and the liquid phase at equilibrium.

The oxygen stream separated by the separator block functioning as an electrolyte was mixed with an air stream on the anode side of the electrolytic cell. According to Cinti et al. [31], it is common practice to carry the oxygen through a stream of air in order to prevent the cell performance from being negatively influenced by a high concentration of the oxygen. The amount of air flow was set by a design spec so that the partial pressure of the oxygen after mixing with the air was 0.5 bar [31]. The air flow was warmed up as much as possible using a counter flow heat exchanger (GW-1) before it entered the electrolysis cell. As the cell temperature of 800 ◦C was not reached as a result, a heat exchanger block (W-3) was used to take into account the additional heating output that must be provided by the electrolysis cell. The air flow was then cooled in two steps and left the system air-enriched with oxygen.

A simplified flow chart of the water electrolysis for hydrogen provision for the hydrocracker is displayed in Figure 3. Its structure corresponded to that of co-electrolysis, but with the simplification that no equilibrium reactors were used. These were not required, as there was no CO2 or CO present in the water electrolysis segment. Another difference is that the hydrogen was compressed to the operating pressure of the hydrocracker of 50 bar. Using the same logic as in the previous figure, W-7 and W-8 were heaters for steam generation, assisting the multi-component counter-flow heat exchanger MW-3. RS-3 was the stoichiometric reactor representing the water electrolysis. The separator block S-2 divided the products to anode and cathode sections. W-9 and W-10 were used to cool the product mixtures of the water electrolysis, GW-2 was a counter-flow heat exchanger used for pre-heating air feed, and V-2 was used to compress the produced hydrogen.

For the techno-economic analysis of the power-to-fuel process, it is necessary to determine the performance of the co- and water-electrolysis processes. For this purpose, the calorific value of the product flows could be output via Aspen Plus and the electrolysis output could then be calculated using a specified efficiency (see Equation (10)).

**Figure 3.** Excerpt from the process flow diagram: water electrolysis.

#### *4.3. Fischer–Tropsch Synthesis and Product Separation*

The flow chart of the Fischer–Tropsch synthesis and the subsequent product separation is shown in Figure 4. The synthesis gas from the co-electrolysis was mixed with the synthesis gas from the reformer and fed into the Fischer–Tropsch reactor (RS-2). This was modeled as an isothermal bubble column reactor with a pressure of 30 bar and a temperature of 210 ◦C. A stoichiometric reactor was used for modeling, in which the reaction equations for 32 parallel reactions according to Equation (11) were stored (for *n* = 1 to *n* = 29 and the pseudo components corresponded to *n* = 32, *n* = 41 and *n* = 61). The conversions of the various reactions were determined using a calculator block with an integrated Excel file, based on the ASF distribution (Equation (12)), with the chain growth probability α calculated using Equation (14). The modeling was therefore suitable for calculations with variable H2/CO ratios; however, a ratio of 1.8 was chosen in the context of this work in order to maximize the proportion of middle distillates in the product of the Fischer–Tropsch synthesis. Under the selected operating conditions and the set H2/CO ratio, there was a chain growth probability of approximately 0.92. According to de Klerk [36], this value is in the range of typical industrial low-temperature Fischer–Tropsch syntheses. The total conversion of carbon monoxide was set at 80%, reflecting the work of Becker, et al. [59], Trippe [35], and Schemme [54].

As the stoichiometric reactor used only had one product stream, in a first step (B-2) the product from the Fischer–Tropsch reactor was divided isothermally and isobarically into gas and liquid phases. The liquid phase, which consisted mainly of *C*20+-hydrocarbons, was fed to the hydrocracker, while the gas phase was cooled isobarically in several steps to 40 ◦C, with part of the waste heat being used in the co-electrolysis process. After cooling, the light gases were separated from the middle distillates in the next container (B-3). Almost all of the *C*8+ hydrocarbons that could be used for kerosene and diesel were sent to the carrier steam distillation, and the short-chain hydrocarbons were sent to the reformer. In addition, the differences in density and polarity of the water and hydrocarbons in both tanks were used to separate the water produced by the Fischer–Tropsch synthesis. In order to avoid soot formation in the reformer, some of the separated water was fed into the reformer. The proportion fed into the reformer was determined with a design spec corresponding to the selected H2O/C ratio (see Section 4.6).

**Figure 4.** Excerpt from the process flow diagram: Fischer–Tropsch synthesis and product separation.
