*5.3. Heat Recuperation and CO2 Separation*

The possibility of energy integration is often mentioned in the literature as a great advantage of PtL processes based on Fischer–Tropsch synthesis. Energy integration has already been carried out for the developed process in order to provide the required process heat. However, the values listed in Table A3 in Appendix B demonstrate that there are still large amounts of excess heat available that can be removed from the process in the form of low- and medium-pressure steam. In the following, it should be determined whether this heat can be used for CO2 separation in order to provide the CO2 required for co-electrolysis. In addition, the influence of such a process coupling on the efficiency of the entire process chain from CO2 separation to synthetic fuel was examined. For the separation of CO2 from biogases and from industrial exhaust gases, heat is required at a temperature level [65,66] that exceeds that of the excess low-pressure steam. Therefore, only the excess mediumpressure steam is considered in the following. For every liter of diesel-equivalent produced, the power-to-fuel process produces 9.191 MJ of medium-pressure steam. This energy can then be converted into the amount of energy released per unit of CO2 consumed.

$$\frac{9.191 \frac{Ml}{l\_{DE}}}{2.54 \frac{kg\_{CO2}}{l\_{DE}}} = 3.619 \frac{Ml}{kg\_{CO2}} = 1.005 \frac{MWh}{t\_{CO2}} \tag{22}$$

Accordingly, in the developed power-to-fuel process, 1.005 MWh of thermal energy was generated per ton of CO2 consumed, which can in turn be used for CO2 separation. The resulting thermal coverage for the separation of CO2 from the CO2 sources of biogas, industrial waste gas (cement works), and ambient air are given in Table 3. For the sake of completeness, the thermal and electrical energy requirements are also listed.

**Table 3.** Thermal coverage for CO2 separation from various CO2 sources.


The heat required to separate a ton of CO2 from biogases is comparatively low, at 0.631 MWh, and so the entire thermal energy requirement can be covered by the excess medium-pressure steam and even remaining, unused medium-pressure steam. The separation of CO2 from the ambient air requires the largest amount of thermal energy with 1.5 MWh per ton of CO2. About 67% of this can be provided through the excess mediumpressure steam. As an example of the separation of CO2 from industrial waste gases, separation from the waste gases of a cement plant by means of amine scrubbing was selected at this point. This technology requires 1.03 MWh of thermal energy to separate one ton of CO2. Accordingly, 97.6% of this thermal energy can be provided through waste heat from the developed power-to-fuel process. The degrees of coverage listed in Table 3 make it clear that the developed PtF process can be coupled with CO2 separation in order to provide the thermal energy required for CO2 separation. In order to examine the influence of such a coupling in greater detail, Figure 14 shows the efficiencies of the entire process chain for the case of the coupling of CO2 capture and the PtF process, and for the case that both processes are operated separately.

**Figure 14.** Coupling of the modeled synthesis with CO2 capture technologies.

If the separation of CO2 from biogas is conducted independently of the modeled PtF process, the efficiency of the process chain is approximately 48.1%. If both technologies are coupled, the entire thermal energy requirement can be provided by the fuel synthesis, so that the overall efficiency is 52.1% (i.e., almost the efficiency of the PtF process without taking CO2 separation into account). The remaining difference in results from the electrical energy requirement for CO2 separation are listed in Table 3. The efficiency of the entire process chain with CO2 separation from ambient air was lower due to the high thermal and electrical expenditure of the technology (see Figure 14).

Nevertheless, by coupling the technologies, the efficiency can be increased from 41.3% to 46.1% (i.e., 4.8 percentage points). The greatest increase in efficiency can be seen in the coupling of the developed fuel synthesis with CO2 separation from the exhaust gases of a cement works. By coupling the technologies, the efficiency can be increased by 5.8 percentage points, from 44.9% to 50.7%. Overall, it can be said that a coupling of the developed fuel synthesis with CO2 separation technologies is both possible and advantageous. The excess heat incurred by the Fischer–Tropsch synthesis can be discharged from the process in the form of medium-pressure steam and used to operate various CO2 separation technologies. This makes it possible to increase the efficiency of the entire process chain, from CO2 to synthetic fuel, by up to around 4.87 percentage points, depending on the CO2 source used.

#### *5.4. Comparison to a Related Analysis for E-Fuels Based on Low-Temperature Electrolysis*

In order to be able to better assess the calculated power-to-fuel efficiency of the developed fuel synthesis, it was compared with the efficiencies of alternative PtF or PtL processes. Three PtL processes developed and examined by Schemme [54] were considered. The comparison is possible, as Schemme [54] assumed the same boundary conditions and efficiencies for ancillary units as in this work. In two of the processes considered, alternative fuels were the target product, with methanol being produced in the first process and dimethyl ether (DME) in the second. In the third process considered, synthetic kerosene

and synthetic diesel were also produced through a Fischer–Tropsch synthesis, with the synthesis gas for the Fischer–Tropsch reaction being generated via a reverse water–gas shift reactor. The hydrogen supply for all three processes was provided through PEM electrolysis, for which an electrolysis efficiency of 70% was assumed. The PtL efficiencies of the three processes are compared in Figure 15 with the PtL efficiencies of the fuel synthesis developed herein for different electrolysis efficiencies. It should be noted that efficiencies are only really comparable if all of the reference points for determining them are known [67].

**Figure 15.** Comparison of the PtL efficiency of the developed fuel synthesis with those of alternative PtL processes (ηPTl of methanol, DME, and FT with the RWGS process according to Schemme [54]).

Therefore, the following comparison should not serve as a precise quantitative assessment of the processes, but represents a qualitative classification of the developed fuel synthesis. The efficiencies shown in Figure 15 are the PtL efficiencies for the case that the processes are coupled with CO2 separation from industrial exhaust gases. With the three efficiencies according to Schemme [54], CO2 separation from industrial exhaust gases was also assumed, but with the difference that only an electrical energy requirement of 0.333 MWh per ton of CO2 was taken into account, and the thermal energy requirement was not. Accordingly, it can be assumed that the actual PtL efficiencies of the processes from Schemme [54], taking into account the thermal energy requirement, are below the specified values. The efficiencies of the methanol and DME processes in particular were probably overestimated, as significantly less excess heat is produced in these processes than in those that employ a Fischer–Tropsch synthesis (see Schemme [54]). The PtF efficiency of the developed fuel synthesis is shown in Figure 15 for two different cases. For the standard configuration shown in blue, the PtL efficiency of around 45% for an *ηSOEC* of 70% was below the efficiencies of all reference processes. With an electrolysis efficiency of 80%, the PtL efficiency of the developed fuel synthesis corresponded to that of the Fischer–Tropsch process with a RWGS reactor at around 51.1%. With increasing electrolysis efficiency, the PtL efficiency also further increased. With an *ηSOEC* of 100%, the PtL efficiency of the developed fuel synthesis was approximately 61.4% and above the power-to-liquid efficiencies of the methanol and DME syntheses of 57.6% and 60%, respectively. The conclusion for this is that co-electrolysis only achieves the same PtL efficiency with a 10 percentage point higher efficiency than the process configuration of PEM electrolysis, RWGS reactor, and Fischer–Tropsch synthesis, as assumed by Schemme [54]. However, the specified efficiencies for high-temperature electrolysis described by Peters et al. [64] partially take into account a compression of the electrolysis products to 70 bar for storage, which was not carried out in the developed fuel synthesis. Accordingly, it can be assumed that the required electrolysis power was overestimated and therefore the PtF efficiency was underestimated. To compensate for this effect, the PtF efficiency was recalculated, neglecting the compression of the synthesis gas to 30 bar by V-1 (cf. Figure 2). The resulting PtF efficiencies are highlighted in green in Figure 15. With an efficiency of the high-temperature electrolysis of 70%, the ηPTL was around 48.2% at a similar level to the Fischer–Tropsch process investigated by Schemme [54], with a PEM electrolysis efficiency of 70%. The PtF efficiency of the fuel synthesis developed in this work, neglecting V-1, further increased with *ηSOEC*, with a PtF efficiency of approximately 67.4% being calculated for an *ηSOEC* of 100%. Figure 15 thus shows the great potential of PtF processes based on co-electrolysis, and thus also the potential of the developed fuel synthesis. With an electrolysis efficiency of 70%, the high-temperature electrolysis-based process achieved similar efficiencies as the PEM electrolysis-based process. However, with high-temperature electrolysis, there is the possibility of substituting electrical energy with thermal energy and thus achieving very high electrolysis efficiencies and therefore also very high PtF efficiencies.

#### **6. Techno-Economic Analysis**

This section is dedicated to the analysis of the economic aspects of the developed PtF process. As the developed model is suitable for calculation with any feed stream, it is necessary to determine an order of magnitude for the process for investigation. According to a report by the Intergovernmental Panel on Climate Change [68], the cement industry emits around 932 megatons of CO2 annually. For the number of cement works of 1175 given in the same source, assuming 8000 annual operating hours, this approximately corresponds to an average CO2 production of 99.15 tons per hour and plant. Based on this value, a CO2 feed stream of 100 tons per hour are defined for the techno-economic analysis in this work. This corresponds to a total production capacity of around 39,400 lDE per hour of synthetic kerosene and diesel, with a total energy consumption of around 750 MW. In the following, the methodology described by Schemme et al. and Peters et al. [69,70] was used to calculate the costs of manufacturing, whereby the investment costs for the system as well as the material and personnel costs for operating it, were first determined. The cost of the product was then determined on the basis of the specific costs. A sensitivity analysis was carried out in order to examine the influence of various cost factors on the production costs in greater detail. Finally, the calculated production costs of the developed fuel synthesis were compared with alternative PtF or PtL processes. The cost of product to be expected for the reference year 2030 was also calculated as part of the economic analysis, with all costs being converted to 2019 equivalents. Accordingly, all cost information below relates to the year 2019, unless stated otherwise.

#### *6.1. Investment Cost*

The first step in calculating the cost of the product was to determine the system's investment costs. The calculation of the component costs, with the exception of the reactors and electrolysis, was conducted with the Turton method using the CAPCOST Excel tool; the methodology is explained in Schemme [54]. The investment costs for the reactors and electrolysis are calculated separately. Due to the large number of components required, the investment costs for each of the system components are not discussed individually below. A detailed breakdown of the investment costs is presented in Table 4. To calculate the component costs using the Excel tool CAPCOST, the material, operating pressure, and component-specific size parameters Z must be specified. In the cost accounting, it was assumed that all system components were made of stainless steel. The operating pressures were taken from the Aspen Plus simulation, whereby an additional safety factor of 1.5 was taken into account for all pressures. The size parameters Z were determined depending on

the component group. For the pumps, compressors, and drives, the respective nominal capacities are required as size parameters for CAPCOST. These can be taken directly from Aspen Plus, taking the efficiency into account. For the cost calculation of the distillation column and the two strippers, the diameters and heights of the respective apparatuses are required. The Aspen Plus Tray sizing function was used to determine the diameter, assuming sieve trays with a distance of approximately 0.6 m (2 feet) from one another. The heights of the columns and strippers were calculated using the number of trays and the distance between them. An additional distance between the top floor and head or the lowest floor and the sump of 1.5 m was taken into account—a so-called disengagement space. The size parameter for calculating the heat exchanger corresponded to the heat transfer area of the respective heat exchanger.


**Table 4.** Investment costs for the modeled power-to-fuel process.

In the next step, the investment costs for the three reactors were determined using the corresponding equations published Baliban et al. [71]. The calculation method presented here requires the capacities of the Fischer–Tropsch reactor, the hydrocracker, and the reformer. These can be read from the Aspen Plus simulation and are listed in Table A4 in Appendix B. It should be noted that the capacity of the Fischer–Tropsch reactor was above the permitted smax value and that two Fischer-Tropsch reactors were therefore operated in parallel. The determined investment costs for the reactors are shown in Table 4.

To calculate the investment costs for high-temperature electrolysis, the electrical performance of the water and co-electrolysis processes must be determined. For this purpose, as in Section 5.2, an electrolysis efficiency was calculated and the required electrolysis output determined through the calorific value of the electrolysis products. An electrolysis efficiency of 80% was assumed for the "base case." This resulted in an output of approximately 643.4 MW for the co-electrolysis and of about 33.8 MW for the water electrolysis. Table 4 gives the forecasts for the investment costs for high-temperature electrolysis for the year 2030. As part of this cost calculation, the data from Brynolf, et al. [72] was employed, as these also expressly apply to SOECs in co-electrolysis operation. The reference case was based on Brynolf et al. [72], given a mean value of €764 (=ˆ 700 € 2015) per kilowatt assumed for the investment costs for high-temperature electrolysis. The sum of the investment costs for the system components resulted in investment costs of around €949.9 mil. for the entire system. It can clearly be seen that the investment costs for the high-temperature electrolysis, totaling around €517 million and thus with a share of over 50%, made up by far the largest share of the total investment costs. Next up were the investment costs for the heat exchangers and compressors at around 14% and 13%, respectively. Costs for the Fischer–Tropsch reactor and hydrocracker made up a considerable part of the total investment costs at around 9% and 7%, respectively, whereas the costs for the remaining system components only played a subordinate role, at less than 2%. Due to the high share of investment costs for high-temperature electrolysis, the influence of the electrolysis efficiency and investment

costs for the electrolysis against the cost of the product is discussed in greater depth in Section 6.4.3.

#### *6.2. Material and Personnel Costs*

The material costs were derived from the costs of the raw materials required for production and those for the required resources. The amounts of the respective materials can either be taken directly from the Aspen simulation or determined using the data shown in Figure 11. If the required quantities for raw materials and operating resources are known, the annual material costs are determined using a specific price for the respective material. An annual operating time of 8000 h was assumed for calculation of the costs. The calculated material costs for the raw materials are presented in Table 5. For the CO2 price, the base case was assumed to be €70 per ton. This is the lowest price that can be expected in the short- to medium-term for CO2 that is separated from the exhaust gases of a cement plant (see Schemme [54]). Overall, it can be seen that the costs for CO2 make up the largest part of the raw material costs, at €56 million out of a total of around €64 million. The influence of the costs of CO2 on the production costs was considered in the sensitivity analysis.

**Table 5.** Raw material costs for the PtF process.


<sup>1</sup> Brynolf et al. [72]. <sup>2</sup> Cheaper also in the literature: Fraunhofer-Institut [73]. 70 €/t was chosen to not underestimate the costs. <sup>3</sup> Cheaper also in the literature: INTRATEC [74]. 0.1 €/t was chosen to not underestimate the costs.

The annual material costs for the required equipment are presented in Table 6. For the base case of the cost calculation, an electricity price of €40 per MWh was assumed, which was the approximate average electricity exchange price in Germany for 2019 according to the 'energy charts' provided by the Fraunhofer Institute [75]. Table 6 shows that electricity costs made up the majority of operating costs. Therefore, Section 6.4.1 examines in greater detail how the price of electricity influences the cost of the product.

**Table 6.** Operating costs for the power-to-fuel process.


<sup>1</sup> Cheaper also in the literature: INTRATEC [74]. 0.1 €/t was chosen not to underestimate costs. <sup>2</sup> 'Energy charts' [75].

To calculate the annual personnel costs Cp using Equation (23), the number of work steps with particulate solids P and the number of system components to be monitored or controlled NNP must be determined. In the developed power-to-fuel process, no work steps were carried out with particulate solids, and P was accordingly zero. The number of system components to be monitored and the total NNP were as follows: 65 compressors, one column, 181 heat exchangers, three reactors, and 14 electrolyzers.

The high number of compressors and heat exchangers compared to the modeling resulted from the fact that in the Excel tool CAPCOST, the highest possible compressor output of a single compressor was limited to 3000 kW, and the largest possible heat exchanger surface of a single heat exchanger to 1000 m2. The required electrolysis power for the base case was determined to be approximately 643.4 MW for the co-electrolysis and 33.8 MW for the water electrolysis processes. According to Brynolf et al. [59], the maximum output by an SOEC to be expected by 2030 is 50 MW. Accordingly, a total of 14 SOEC units are required for the power-to-fuel process. This results in a value of 264 for NNP. The average annual gross salary of a full-time employee in the chemical industry in Germany in 2019 was €58,896; see [76]. Taking into account the non-wage labor costs of approximately 23% (see [77]), the annual personnel costs can be calculated using Equation (23), whereby PAYROLL is determined as €76,488 according to [76,77].

$$\begin{array}{ll} \mathbf{C}\_P &= 5.38 \cdot \sqrt{6.29 + 31.7 \cdot \mathbf{P}^2 + 0.23 \cdot N\_{NP}} \cdot \text{PAYROLL} \\ &= 5.38 \cdot \sqrt{6.29 + 31.7 \cdot 0^2 + 0.23 \cdot 264} \cdot \text{76,488\%} \\ &\approx 3,365,561\% \end{array} \tag{23}$$

#### *6.3. Product Cost*

Using Equation (24), annual production costs were calculated. However, a depreciation period t and an interest rate i must first be specified in order to determine the annuity. According to Brynolf et al. [59], lifetimes of between 10 and 20 years are to be expected for SOEC systems and maximum lifetimes of less than 90,000 operating hours for SOEC stacks. According to Schmidt et al. [78], for SOEC stacks, maximum operating times of over 100,000 h or, according to one of the experts questioned, of just 30,000 h, can be expected. A depreciation period of 12 years was assumed for the base case of the cost calculation, which corresponded to a total of approximately 96,000 operating hours with an annual operating time of 8000 h. Different values can be found for the interest rate in the literature for power-to-fuel processes such as an interest rate of 4% in Schmidt, et al. [79] and 8% in Buddenberg et al. [80]. An interest rate of 5% was selected for the base case of cost accounting. The influence of the selected depreciation period and selected interest rate was examined as part of the sensitivity analysis. If the depreciation period and interest rate are selected, the annual production costs can be calculated according to Equation (24):

$$\begin{aligned} COM &= 0.151 \cdot FCI + 2.284 \cdot \mathcal{C}\_P + 1.031 \cdot (\mathcal{C}\_R + \mathcal{C}\_B) \\ &+ FCI \cdot \left(\frac{i \cdot (1 + i)^t}{(1 + i)^t - 1} + i \cdot 0.15\right) \\ &= 582.1 \text{ } MI. \euro \end{aligned} \tag{24}$$

With:

Investment costs *FCI* = €949.9 million, see Table 4; Personnel costs *Cp* = €3.37 million, see Equation (23); Raw material costs *CR* = €63.6 million, see Table 6; Operating costs *CB* = €243.5 million, see Table 6; Depreciation period *t* = 12; Interest rate *i* = 0.05.

For the specified feed stream of 100 tons of CO2 per hour, the production output of the power-to-fuel process totaled around 39,400 L of diesel equivalent per hour. The specific production costs result from Equation (25):

$$
\omega com = \frac{582.1 \cdot 10^6 \frac{\text{g}}{\text{a}}}{39400 \frac{l\_{DE}}{\text{h}} \cdot 8000 \frac{\text{h}}{\text{a}}} \approx 1.85 \frac{\text{e}}{l\_{DE}} \tag{25}
$$

Table 7 shows the cost allocation based on Otto [81]. As a result, the base case under consideration resulted in fuel production costs of around €1.85 per liter of diesel equivalent. Several important influencing factors on the cost of product could also be identified. At almost 42%, the operating resources made up the largest share of fuel production costs. It can be seen in Table 6 that the majority of operating costs were caused by electricity costs, and therefore the electricity price exerts a strong influence on the cost of the product.


**Table 7.** Distribution of the fuel production costs according to Otto [81].

The annuity accounted for the second largest share of fuel production costs, the amount of which depends on the selected interest rate and the selected depreciation period as well as on the investment costs FCI. In addition, the FCI have, according to the cost allocation by Otto [81], a direct impact on several other cost components such as maintenance and repair work. Over 50% of the total investment costs are made up by those for high-temperature electrolysis. Accordingly, it can be assumed that the investment costs for the electrolysis have a major influence on fuel production costs. The investment costs for high-temperature electrolysis depend, on one hand, on the specific investment costs per kilowatt of power and, on the other, on the efficiency of the high-temperature electrolysis. The last important cost factor can be identified as the CO2 costs, as these account for almost 90% of the raw material costs (see Table 2) and so almost 10% of the total cost of the product. Overall, the electricity price, efficiency of high-temperature electrolysis, specific investment costs for high-temperature electrolysis, depreciation period, and interest rate as well as the price of CO2 are identified as important cost items. The influence of these factors is examined in more detail in the following section.

#### *6.4. Sensitivity Analysis*

A sensitivity analysis is presented in this section to examine the influence of the cost factors identified in Sections 6.1–6.3. For this purpose, the assumptions for the electricity price, electrolysis efficiency, specific investment costs for the electrolysis, depreciation period, and interest rate as well as the CO2 costs were varied and the fuel production costs calculated. The other cost factors were left at the values assumed for the base case (see Table 8). Finally, the influences of the respective cost factors were compared in the form of a so-called tornado diagram.

**Table 8.** Assumptions for the base case.


6.4.1. Influence of the Electricity Price

Figure 16 displays the production costs in relation to the assumed electricity price. For the sake of clarity, the cost components "production staff", "monitoring and office staff",

"auxiliary materials", "laboratory costs", and "patent and license fees" were combined into "other production costs" in this and the following figures.

**Figure 16.** Production costs depending on the electricity price.

The electricity price was varied based on the €40 per megawatt hour assumed for the base case plus or minus 50%. For €20 per megawatt hour, the cost of the product was approximately €1.5/lDE, and for €60 per megawatt hour, it was around €2.2/lDE. The operating costs, which mainly consisted of electricity, made up around 25% at €20/MWh and over 50% of the cost of the product at €60/MWh. The share of electricity costs in the production costs and, accordingly, their influence on the production costs, was very high. Thus, the local electricity price should be considered as an important criterion when choosing locations.

#### 6.4.2. Influence of Electrolysis Efficiency

Figure 17shows the fuel production costs as a function of the electrolysis efficiency. In Section 6.2, it was noted that electrolysis efficiencies of less than 70% are not to be expected for the developed fuel synthesis. Therefore, the efficiency of high-temperature electrolysis was varied from 70% to 100% for the sensitivity analysis. For an efficiency *ηSOEC* of 70%, the cost of product was around €2.0/lDE. The levelized costs of the product decreased with increasing electrolysis efficiency, and for an efficiency *ηSOEC* of 100%, the levelized costs of the product were around €1.6/lDE. It can be seen in Figure 17 that with increasing electrolysis efficiency, both the operating material costs and cost items that are dependent on the investment costs for the system fell. This was due to the fact that the required electrolysis power decreased with increasing electrolysis efficiency, which in turn reduced the investment costs required for the electrolysis and its power consumption. As stated above, the electrolysis efficiency is strongly influenced by the extent to which hightemperature heat is available for the operation of the water and co-electrolysis. Accordingly, when choosing a location for fuel synthesis, it should be determined whether such hightemperature heat is generated in an existing system, and if heat coupling is possible.

**Figure 17.** Product production costs depending on the electrolysis efficiency *ηSOEC*.

6.4.3. Influence of the Specific Investment Costs for Electrolysis

Figure 18 shows the cost of the product as a function of the specific investment costs for water and co-electrolysis. Brynolf et al. [72] provide a value of €436/kW (=ˆ 400 €/kW @ 2015) as the lower limit and a value of €1091/kW (=ˆ 1000 €/kW @ 2015) as the upper limit for the specific investment costs for high-temperature electrolysis expected by 2030 (see Table 4). For the sensitivity analysis, the specific investment costs were varied accordingly. The cost of product for €436/kW was around €1.7/lDE, and for €1091/kW, there was a product cost of around €2.0/lDE. This corresponded to a deviation from the fuel production costs for the base case of €764/kW of around ±10%. The influence of the specific investment costs was, accordingly, significantly less than that of the electricity price, for instance. However, it must be noted that the projection of Brynolf et al. [72] only applies in the event that major technical advances are made by 2030 and are therefore to be considered target values. It is important to invest in research and development so that the developed fuel synthesis or other power-to-fuel processes based on SOEC technology can be implemented in the future.

**Figure 18.** Product production costs as a function of electrolyzer investment costs.

#### 6.4.4. Influence of the Depreciation Period and Interest Rate

The cost of product as a function of the selected depreciation period and selected interest rate are shown in Figure 19. The cost of product for a short depreciation period of nine years with a high interest rate of 7% and a long depreciation period of 15 years with a low interest rate of 3% were compared with the base case of 12 years and 5%, respectively. In the worst case, with a short depreciation period and high interest rate, the cost of product was €2.0/lDE, and in the favorable case with a long depreciation period and low interest rate, the cost of product was €1.7/lDE. This deviation from the base case resulted from the annuity, which was reduced by almost 45% from the unfavorable case to the favorable one. Accordingly, the location-dependent investment conditions should also be taken into account when choosing a location.
