*5.1. Fuel Property Analysis*

The mass fractions of the various carbon chains in the kerosene and diesel produced as well as the mass-related average molecules of the respective fuels are shown in Figure 8. The kerosene withdrawn from the carrier steam distillation column contained almost no *C*1- to *C*7-hydrocarbons and approximately 8.3% by weight of *C*8-hydrocarbons. The mass fraction of *C*<sup>9</sup> to *C*<sup>11</sup> is between 18 and 19% by weight and the fraction of *C*<sup>12</sup> is around 16.5% by weight. The proportion of longer hydrocarbons steadily decreased, with *C*<sup>13</sup> being contained in kerosene at approximately 11.6% by weight, *C*<sup>14</sup> at approximately 5.4% by weight, and *C*<sup>15</sup> at approximately 1.8% by weight. Carbons with a chain length of 16 and longer are only contained in kerosene to a very small extent, with a total of around 0.7% by weight. The mass average chain length of the hydrocarbons in kerosene is 10.9. The diesel fuel produced consisted of approximately 0.7% by weight of carbons with a chain length of eleven or less. The mass fraction of longer hydrocarbon chains increased steadily from *C*<sup>12</sup> at about 2% by weight, to *C*<sup>15</sup> at 11.5% by weight. The curve of the mass fractions then flattened out and the *C*16- to *C*20-hydrocarbons were each contained in the diesel fuel at approximately 12.2% by weight. The mass fraction of longer hydrocarbons initially dropped sharply at 2.1% by weight for *C*21, and then dropped uniformly with increasing chain lengths to approximately 0.3% by weight of *C*<sup>28</sup> hydrocarbons. The proportion of *C*29-hydrocarbons was around 1.2% by weight. The mass-related average chain length of diesel fuel was 17.5.

**Figure 8.** Product distribution of the produced kerosene and diesel fraction.

In the literature, chain lengths of between 8 and 16 carbon atoms were assigned to the kerosene fraction [37]. Carbons with these chain lengths made up more than 99.5% by weight of the kerosene produced in the simulation. The product distribution of synthetic kerosene was therefore in the range of typical aircraft fuels. The sharp drop in the mass fractions from *C*<sup>20</sup> to *C*<sup>21</sup> in the diesel produced can be explained by the fact that the proportion of *C*21+-hydrocarbons in the feed of the distillation column was also low. This was, in turn, due to the majority of the *C*21+ hydrocarbons produced in the Fischer–Tropsch reactor being fed directly to the hydrocracker and cracked there. The comparatively high proportion of *C*<sup>29</sup> can be attributed to the fact that, as described in Section 4.4, the pseudocomponents were combined with the *C*<sup>29</sup> hydrocarbons. Therefore, the 1.2 wt.% not only consisted of *C*<sup>29</sup> hydrocarbons, but also contained all of the hydrocarbons with a chain length of 30 or more. Which hydrocarbon chains are assigned to diesel varies with the literature source. For example, Trippe [35] only counted the *C*<sup>13</sup> to *C*<sup>20</sup> hydrocarbons in the diesel fraction, whereas Bacha, et al. [60] and Dieterich et al. [6] assigned hydrocarbons with chain lengths of 10 to 22 or 23 to the diesel fraction. The synthetic diesel fuel produced in the simulated power-to-fuel process consisted of approximately 86.8% by weight of *C*<sup>13</sup> to *C*<sup>20</sup> and approximately 95% by weight of *C*<sup>13</sup> to *C*23. Accordingly, the product composition of the diesel produced fell within the range of typical diesel fuels. Both the product composition of the synthetic kerosene and that of the synthetic diesel were therefore within the acceptable range.

In the next step, the boiling curves of the fuels produced in the simulation were calculated and compared with the real boiling curves of kerosene Jet A-1 and diesel (see Figures 9 and 10). The boiling curves were calculated using the D86CRV method integrated in Aspen Plus, which calculates the boiling curve of a mixture of substances at atmospheric pressure.

**Figure 9.** Boiling curves of jet fuel in comparison to Jet A-1 (boiling curve according to Edwards [61]).

**Figure 10.** Boiling curves of diesel in comparison (boiling curve of "typical diesel fuel" according to Bacha et al. [4]).

The calculated boiling curve of synthetic kerosene and that of Jet A-1, according to Edwards [61], are shown in Figure 9. Both curves were almost identical, with the most noticeable difference being that the IBP of the synthetic kerosene of the simulation (137 ◦C) was below that of the reference kerosene of type Jet A-1 of approximately 150 ◦C. The T5 points of the boiling curves deviated by approximately 7 K at 155 ◦C for the calculated value and approximately 162 ◦C for the reference. With the exception of the T90 point, the boiling curves deviated from each other by less than 3 K in the area from T10 to the FBP, the deviation at the T90 point being approximately 5 K. Overall, it can be concluded that the boiling behavior of the kerosene produced in the simulated power-to-fuel process corresponded well to that of jet A-1 kerosene.

Figure 10 shows the calculated boiling curve of the synthetic diesel fuel produced and the boiling curve of a "typical" diesel fuel according to Bacha et al. [60]. A comparatively large difference could be seen between the IBP of the two boiling curves. The IBP of the reference diesel was around 140 ◦C, whereas that of the diesel fuel produced was around 228 ◦C; about 88 K higher. The boiling curves converged as the proportion of evaporated volume increased. The T10 points were about 55 K apart at about 210 ◦C for the reference diesel and 265 ◦C for the calculated boiling curve, whereas the T50 points differed by about 16 K at approximately 283 ◦C and 299 ◦C.

As the proportion of evaporated fuel increased, the boiling curves further converged. The FBP of the reference diesel was around 390 ◦C and that of the calculated boiling curve was around 400 ◦C. Overall, the deviations between the boiling curves of the reference and synthetic diesels were greater than those between the boiling curves of kerosene. Larger deviations could be found, especially in the area spanning the IBP to the T50 point. When comparing the compositions of the two diesel fuels, however, it was noticeable that the reference diesel according to Bacha et al. [60] had a comparatively higher proportion of short-chain light hydrocarbons. The average chain length of the hydrocarbons of the reference diesel was approximately 16, and accordingly, below the average chain length of the diesel fuel produced of 17.9. The deviations in the boiling curve can be explained by the correspondingly different compositions of diesel fuels. In order to determine whether the kerosene and diesel fraction produced is suitable for use as fuels, the requirements of the respective standards were checked in the next step. Table 2 compares the requirements of the standards and corresponding characteristic values of the fuels calculated in the simulation. In addition, the calorific values of synthetic kerosene and diesel are given, which were calculated using the Aspen Plus component properties (property sets) QVALNET.

The T10, T95, and T90 temperatures as well as the FBP of the synthetic kerosene were read from the boiling curves and were in the required range for both the synthetic kerosene and synthetic diesel. The densities of the two fuels were determined by the Aspen Plus component property RHOLSTD. The density of the FT SPK (738 kg/m3) was at the lower end of the permitted range, but still met the requirements of ASTM 7566. The density of the synthetic diesel was also within the required range at 779 kg/m3. The Aspen Plus component property CETANENO was used to determine the cetane number of synthetic diesel. This yielded a cetane number of 109.2 for pure n-hexadecane (C16H34). According to Dry [53], however, the actual cetane number of n-hexadecane is 100. Accordingly, it can be assumed that the actual cetane number of synthetic diesel is below the calculated value of 120. The freezing point of kerosene cannot be calculated using Aspen Plus. Due to the very high proportion of n-alkanes in the product of the Fischer– Tropsch synthesis [9], and therefore a very high proportion of n-alkanes in kerosene, there is the possibility that an after-treatment of the kerosene is necessary in order to improve the low-temperature properties. One possibility would be isomerization, as isoalkanes have a significantly lower freezing point [62]. On the basis of this sub-section, it should be noted that both of the synthetic fuels produced, namely kerosene and diesel, met the requirements of the respective standards. However, if the synthetic kerosene is to be used as a mixture component for Jet A-1, an after-treatment may be necessary to improve the low-temperature properties.

The following section deals with the balance of the process and presents the amount of energy and material required to produce the synthetic fuels.

#### *5.2. Balancing the Power-to-Fuel Process*

The simulation of the PtF process created in Aspen Plus is essentially suitable for calculating any mass flows. The process balance based on the production output is discussed in the following section. For this purpose, the unit liter diesel equivalent lDE was defined as 35.9 MJ. First, the materials required for the production of synthetic fuels are discussed. Then, the process balance is considered from an energetic point of view, whereby the balance of the equipment used is also presented. The material balance is shown in Figure 11

as an overview. It should be noted that not all process-internal heat flows are shown in the figure. The heat flows shown in Figure 11 are those that have a major influence on the overall process, and are discussed in more detail below. If 1 lDE is produced in the simulation, this liter consists of 38.9% synthetic kerosene and 61.1% synthetic diesel. A total of 3.99 kg of water per liter of diesel equivalent produced is required as a feed for the water and co-electrolysis as a material for the production of the fuels, of which approximately 0.18 kg of water is used for pure water electrolysis. In addition, CO2 is required for the co-electrolysis process. The required amount is approximately 2.54 kg CO2/lDE. In addition to water and CO2, the power-to-fuel process requires oxygen to operate the reformer. For each liter of diesel equivalent produced, around 0.34 kg of oxygen is required. Due to internal returns and recycling streams in the process, the only waste streams that arise are oxygen-enriched air streams from electrolysis and separated water. An overview of the material balance of the process is presented in Table A1 (Appendix B). In the developed power-to-fuel process, there are various heat sinks and heat sources. In order to minimize the energy requirement, an energy integration was carried out. Heat sinks and sources were partially coupled to each other via direct heat exchange between material flows, and the required heating or cooling capacity was partially provided by operating equipment.

**Figure 11.** Energy-specific material balance of the developed fuel synthesis.

The low- and medium-pressure saturated steam were used as both a heating medium and coolant by generating the corresponding steam. For example, the Fischer–Tropsch reactor was cooled by generating medium-pressure saturated steam with the waste heat from the reaction. In addition, it was assumed that low-pressure saturated steam was used as an entrainer for the operation of the carrier steam distillation column, and this consumption was correspondingly taken into account in the balance. Electricity is required to operate the compressors and pumps as well as the two electrical heaters W-2 (see Figure 2) and W-8 (see Figure 3). An isentropic efficiency of 76% was assumed for the compressors and of 60% for the pumps. The electricity demand for water and co-electrolysis was considered separately.

Table A3 in Appendix B shows that the demand for both low-pressure and mediumpressure steam can not only be covered within the process, but there is even usable thermal energy left over. As displayed in Figure 11, this thermal energy can be discharged from the process and used, for instance, for carbon capture. This heat coupling is examined in greater detail in Section 6.3. The table does not include the heating power required to operate the carrier steam distillation column and the hydrocracker of 0.39 MJ/IDE and 0.41 MJ/IDE, respectively. As both the distillation column and hydrocracker are operated at over 300 ◦C, it is not possible to provide this heat demand using low- or medium-pressure steam. In order that no valuable electrical energy must be used to provide heating power, the reformer was operated exothermically instead of autothermically, as is common in many industrial applications [46]. The heat made available in this way can, as Figure 11 indicates, be used to operate the hydrocracker and distillation column. Thermal oils can be used for heat transfer as they enable heat transfer at temperatures of up to 400 ◦C [63]. As a result, with the exception of the high-temperature heat required to operate the water and co-electrolysis, all of the required process heat can be provided via internal heat integration. As described in Section 3.1, the electrical power required for the electrolysis can be calculated using the calorific value of the electrolysis products and determining the efficiency. The calorific value and output of the products can, in parallel to the calorific value of synthetic fuels, be determined using the Aspen Plus component property, QVALNET. For the electrical efficiency of high-temperature electrolysis, values from 60% to over 100% can be found in the literature, depending on the mode of operation of the SOEC and how the balance space of the electrolysis system is selected [64]. If, for example, the required heat is not included in the calculation, if this is potentially available free of charge as waste heat from another process, the efficiency of the electrolysis system improves accordingly. In the developed power-to-fuel process, the low-temperature heat for the evaporation of the water is provided through heat integration and therefore does not need to be taken into account when determining the electrolysis efficiency. However, the required hightemperature heat cannot be provided through heat integration but must be supplied to the system in the form of electrical energy. Therefore, it must be taken into account in the efficiency calculation. In this case, Peters et al. [64] specified an electrolysis efficiency *ηSOEC* of approximately 80% for approximately thermo-neutral operation. At this degree of efficiency, however, compression work for storing the electrolysis products is also included. Although this type of compression was not carried out in the developed power-to-fuel process, an electrolysis efficiency of 80% was selected to be on the safe side, in order not to underestimate the required electrical power of the electrolyzers. The amount of synthesis gas or hydrogen calculated in Aspen Plus and the specified efficiency result in the electrical energy required to operate the electrolyzers of approximately 3.09 MJ/lDE for water electrolysis and 58.78 MJ/lDE for co-electrolysis. One of the greatest advantages of energy integration, which is made possible by a combination of high-temperature electrolysis and Fischer–Tropsch synthesis, can also be made clear on the basis of these values. As shown in simplified form in Figure 12, the feed stream of the co-electrolysis is evaporated and preheated in a heat exchanger section (see Figure 2). About 16.4 MJ/lDE of thermal energy was added to the feed stream. For this purpose, the waste heat from the Fischer–Tropsch synthesis was used, amongst other things, via the energy integration. Without energy integration, this amount of energy would need to be added to the high-temperature electrolysis. Conversely, this means that the energy requirement for co-electrolysis is reduced by more than 20% through the energy integration, and that excess thermal energy is also available and can be used for CO2 separation (see Section 5.3).

**Figure 12.** Simplified balance for co-electrolysis.

Once the power-to-fuel process has been fully balanced, the overall efficiency of the process, referred to as the PtF or PtL efficiency, can be determined. As the fuel synthesis does not need to be supplied with external thermal energy, the efficiency is calculated on the basis of the production output and electrical energy requirement. The electrical energy requirement was made up of the energy requirement of 58.78 MJ/lDE for co-electrolysis, the energy requirement of 3.09 MJ/lDE for water electrolysis, and the energy requirement for operating all other system components of 6.89 MJ/lDE (see Table A3). It should be noted that CO2 separation is not yet taken into account at this point. The following section deals with the influence of CO2 separation on the PtL efficiency. This results in a power-to-fuel efficiency for fuel synthesis of:

$$\eta\_{PTL} = \frac{35.9 \frac{Mf}{l\_{DE}}}{6.89 \frac{Mf}{l\_{DE}} + 3.09 \frac{Mf}{l\_{DE}} + 58.78 \frac{Mf}{l\_{DE}}} = 52.21\% \tag{21}$$

It becomes clear that the electrical power required for high-temperature electrolysis and so the electrolysis efficiency exerts the greatest influence on the power-to-fuel efficiency. To take a closer look at this effect, Figure 13 displays the overall efficiency of the process versus that of high-temperature electrolysis. The overall efficiency of the process is linearly dependent on the electrolysis efficiency. For an *ηSOEC* of 60%, the *ηPTL* drops to 40%. However, according to Peters et al. [64], electrolysis efficiencies of less than 70% only occur when the low-temperature heat for evaporation of the water must be provided by electrical energy. As this heat is available in the developed power-to-fuel process via the energy integration, an electrolysis efficiency of 70% was assumed for the worst case. Accordingly, the lowest possible power-to-fuel efficiency was around 46.26%. In the event that high-temperature heat is available and correspondingly does not need to be provided by electrical energy, electrolysis efficiencies of 100% and higher are possible. If the developed power-to-fuel process is to be built, for instance, in a network location where such high-temperature heat is available, a power-to-fuel efficiency of 63.67% is theoretically possible with an electrolysis efficiency of 100%. At this point, it should be noted that the assumed lower limit of the efficiency of 70% and also the 80% chosen for the base case represent conservative assumptions. Due to the energy integration carried out and the fact that in the developed fuel synthesis no compression of the electrolysis products for storage was carried out, the electrolysis efficiency tended to be in the range above 80%, rather than in that from 70% to 80% [64].

**Figure 13.** Power-to-fuel efficiency as a function of electrolysis efficiency.
