Methods and Tools: Explain the methodologies and tools used in the studies outlined in the paper.'' 3.6 Challenges for Successful Implementation of Power-to-X Technologies Power-to-X technologies face a number of challenges for successful implementation, some of which differ from those of classical process systems. Here, technical challenges are discussed and political boundary conditions, e.g., carbon tax or climate targets [49], social acceptance, e.g., preferences for potential Power-to-X products [50], and similar issues are excluded. 3.6.1 Process: Efficient Flexible Operation Power-to-X processes are energy-intensive by definition, and therefore, energy efficiency is of prime importance both for economic and environmental reasons [6, 48, 51]. Beyond high efficiency at a single design point, Power-to-X processes aiming at DSM or electricity storage need to retain high efficiency over a wide range of operating conditions to be able to operate according to electricity price or some other signal for availability of electricity [33] instead of operating at steady-state like today’s process systems. Such changes in operating conditions also need to occur sufficiently fast to follow the changes in electricity supply in the desired time scale. Processes with inherently fast dynamic response can thus easily be used for DSM by appropriate scheduling, e.g., seawater reverse osmosis [41]. Other processes exhibiting slower dynamic response, such as ASU [36], demand advanced control strategies to enable flexible operation for DSM. Additional challenges are associated with the implications of flexible operation on the performance and lifetime of plant equipment and, in particular, catalysts that are not fully understood yet [52].''

Methods and Tools: Explain the methodologies and tools used in the studies outlined in the paper.''3 Beneficial Utilization of Electricity by Power-to-X Here, Power-to-X processes are defined as processes with the goal to exploit the environmental and economic potential of renewable electricity. This comprises the production of gases and liquids from renewable electricity as well as the provision of heat with the intention to replace fossil-based products, which is called e-Production. Additionally, this definition encompasses the older fields of electricity storage and DSM. With this definition, Power-to-X is not restricted to technologies for the conversion of predominantly electric power into products that are currently based on fossil sources. With DSM, it also incorporates approaches that enable the utilization of renewable electricity for industrial processes that have not been able to utilize such in an effective way until now. We believe that such a broad definition is useful to highlight the relationship and overlap of these fields that become particularly apparent in many Power-to-X technologies falling into more than one of these three categories (gray areas in Fig. 3). We explicitly confine our definition to processes that aim at utilizing renewable electricity and exclude, e.g., general energy management technologies from our definition of Power-to-X. However, contrary to their intended purpose, associated technologies could in principle also utilize other types of energy sources, e.g., for producing synthetic fuels from nuclear power in one country and transport it to another one. In the following, these three main approaches for a beneficial utilization of renewable electricity are briefly introduced, their relations are identified, and their opportunities and common challenges are stated''

Methods and Tools: Explain the methodologies and tools used in the studies outlined in the paper:''Powerto-heat [28], and Power-to-chemicals [7] individually, some of them also collectively [6, 29]. The publications typically consider different performance indicators, i.e., economics, sustainability, efficiency, infrastructure, technology readiness level, etc., as well as a variety of boundary conditions to provide a holistic assessment of the technology. The diversity in boundary conditions and assumptions makes the comparison between the publications difficult. Going through the broad range of different literature on Power-to-X technologies, it is noticeable that their applications in most cases aim at the conversion of predominantly electric power into products that are currently based on fossil energy sources. Therein, the scientific community distinguishes between the product’s state, i.e., Power-to-gas or Power-toliquid, and the product’s intended purpose, i.e., Power-tofuel or Power-to-heat. This product-oriented classification has two shortcomings. First, the notations are ambiguous. Either of the terms Power-to-liquid and Power-to-fuel are used for the same notion. Additionally, ‘‘liquid’’ may refer to fuels, a chemical feedstock, or both, and ‘‘fuel’’ may refer to a liquid, a gas, or both. However, the intended purpose of the product or – even more precisely – of the Power-to-X application is very important for its environmental assessment [6, 29]. Second, the broad usage of the terminology Power-to-[K] and the missing definition lead to the question which technologies to include and which not. For instance, there are DSM endeavors in which some electricity-intensive industrial processes are explicitly operated flexibly to make them utilize renewable electricity effectively (cf. Sect. 3.1). Such approaches are commonly not considered Power-to-X technologies, although flexible operation is a key aspect in many Power-to-[K] processes, and they pursue the same goal of improving the utilization of renewable electricity. This indicates a connection to more established process concepts that were excluded in the keyword search illustrated in Fig. 1. To indicate the increasing interest also in those, Fig. 2 exemplarily shows the number of publications related to some of them using a selection of keywords. In addition to the increasing general interest in these established technologies, the high amount of literature on demand side management with regard to renewable electricity utilization highlights its relevance for Power-to-X processes. Therefore, a broader definition of Power-to-X and a classification based on the way Power-to-X pursues the common goal of a beneficial utilization of renewable electricity are proposed. 3 Beneficial Utilization of Electricity by Power-to-X Here, Power-to-X processes are defined as processes with the goal to exploit the environmental and economic potential of renewable electricity''

Methods and Tools: Explain the methodologies and tools used in the studies outlined in the paper. ''The common understanding of Power-to-X is exclusively the use of renewable electricity to manufacture products currently based on fossil sources. In this paper, it is argued that beyond such e-Production many of these technologies also include aspects related to demand side management and temporal storage of electricity. Therefore, a definition of Powerto-X is suggested that encompasses all three aspects. It is discussed, which of these are relevant under which conditions and illustrative examples are highlighted, which show how process systems engineering can help address common challenges for Power-to-X technologies.''

Methods and Tools: Explain the methodologies and tools used in the studies outlined in the paper'' 3.5 When is Their Application Beneficial? Given that Power-to-X technologies aim at achieving economic and/or environmental benefits by utilizing renewable electricity, the question arises which approach is favorable under which conditions. In Fig. 4, general trends are given where the decisive factors that affect the economic viability are twofold: the average electricity price and its fluctuations.Herein, the fluctuations indicate the absolute changes in price with time. From the environmental point of view, particularly for mitigating greenhouse gas (GHG) emissions, the Power-to-X applications are evaluated according to the average electricity carbon footprint and its absolute fluctuations over time. E-production in steady-state operation becomes more viable with decreasing average electricity price as this is its major operating cost factor. This way, e-products can become cost-competitive with fossil-based products only if the average electricity price is low. Similarly, e-Production must consume electricity with a low carbon footprint to result in low GHG emissions. By utilizing electricity with a high carbon footprint, GHG emissions might even exceed those of fossil-based products [48]. For steady-state operation, the fluctuations in both factors have no influence on process economics and environmental impact, because the plant does not adapt to those fluctuations. Power-to-X applications for DSM and electricity storage are economically beneficial if the fluctuations in electricity prices are high. In such a case, the capacity of processes operated under DSM and processes for electricity storage can be increased when electricity is available at low costs and the load can be reduced or the energy can be reconverted at high electricity prices, respectively. The benefit needs to recoup the capital investment for gaining operational flexibility. The achievable cost savings do not depend on the average price, because the (absolute) revenue of both buying and reselling electricity and of shifting periods of electricity consumption only depends on the magnitude of fluctuation. Electricity storage facilities and DSM favor a high fluctuation in carbon footprint of the electricity mix in order to exploit the environmental potential. Electricity is used/ stored when the share of RES in the electricity grid is high and reconverted when the share is low [35]. As already stated in Sect. 3.4, combinations of these applications can outperform individual applications. One combination could be DSM for e-Production with an increased production rate when electricity prices are low. Then, equipment oversizing that enables flexible operation should be addressed in process design. The considered fluctuations occur on very different time scales: hourly, daily, or even seasonal.''

Methods and Tools: Explain the methodologies and tools used in the studies outlined in the paper:''2 Increasing Awareness of Power-to-X With the project ‘‘Strategieplattform Power-to-Gas’’ [8], which was initiated in 2011 with the objective to improve and promote Power-to-gas technologies, the terminology Power-to-[K] has been used increasingly in the scientific community during the last years (Fig. 1). The extensive presence of this terminology indicates an increasing interest in related technologies, such that the terminology was also included in the German energy strategy [9], which high- lights its relevance. The more general term Power-to-X was introduced later on to combine all related Power-to-[K] technologies under one common terminology. This termi- nology is often used in the context of sector coupling, where Power-to-X technologies are considered a key element. Interestingly, there is a correlation between the number of publications on Power-to-[...] technologies and the amount of compensation payments for curtailed energy in Germany, which have both increased seemingly exponen- tially in the last decade (Fig. 1). Taking the number of publi- cations as an indicator for public investments into R&D, the correlation may indicate the high effort in avoiding elec- tricity curtailments by investing in Power-to-X technolo- gies. This gets even more plausible by interpreting the much steeper increase of compensation payments for curtailed electricity compared to the linear increase in share of RES in total electricity produced: the potentially usable energy from RES seems to be higher than what the current (grid) technology can handle without curtailment. To identify the key interests in Power-to-X technologies, recent studies are categorized into their main object of investigation and examples for each field are given in the following. Many early publications on Power-to-X evaluate to which extent the integration of a distinct technology into the ener- gy system [13–15] and process industry [1, 16, 17] is benefi- cial, and how they influence one another. Typically, future energy scenarios are developed, and the technology is as- sessed based on performance, economic, and environmental indicators. Independent of the sector the technology is applied in, the authors highlight the need for a consistent and predictable energy policy for a successful integration. Coupled with technological progress, such technologies may even become economically attractive. Concerning the environmental impacts of Power-to-X technologies, Koj et al. [18] give a review of life-cycle assessment (LCA) studies based on their understanding of Power-to-X.The question about the integration of Power-to-X into an existing energy system or industry intrinsically includes the question which Powerto-X technology is suited best for which energy scenario. Most publications consider Power-to-gas [19–23], Power-to-liquid, often also referred to as Power-to-fuel [24–27],''