**Author details**

*Bioethics in Medicine and Society*

**5. Conclusion**

Clinical Research. According to the current legislation in Turkey, ethics committee members are required to receive basic training on good clinical practices and clinical research before starting to work in these boards. If possible, an equal gender

Development of good empirical practices have been guiding ethical discussions and specifying a normative approach and framework for human research at the same time. CAM field necessitates evidence-based results on clinical research. Due to their approaches of preventing illnesses and providing treatment that have been preferred by many individuals, TM and CAM practices and research are expected to progress. Clinical research is essential in ensuring medical advances, and it establishes the bond between theory and practice in the field of medicine. In addition to determining effectiveness of a treatment, strength of the evidences on the medical application should be evaluated. The right path with CAM and TM clinical research and practices would include not to disacknowledge them, but to pave the way for the scientific research on the ones that have the potential to be beneficial and to bring the proven benefits to modern medicine. One challenge with these practices would be the fact that a considerable amount of CAM and TM data are not systematic and standardized, which have made them difficult to scientifically accept. In order to assist the international acceptance of CAM and TM data to pave the way for CAM and TM databases, meta-analyses and so on, good clinical practice guides being made specific to these areas is essential. For all human research, informed consent must be obtained from the voluntary participants. Throughout this process, it is imperative to show respect to participants' dignity, to omit forcing potential voluntary participants in any pecuniary and nonpecuniary way, to care on their confidentiality, and to pay utmost attention on privacy of their data. New treatment procedures and medications as results of clinical research are for public welfare, but

distribution among members should be provided in ethics committees.

the benefit of the voluntary participant must be prioritized.

framework of the countries that the ethical committees belong to.

The author declares that there is no conflict of interest.

When it comes to CAM and TM clinical research, a framework to their ethical evaluation is suggested herein. For clinical research on CAM and TM, legal arrangements are necessary regardless of geographical region, belief and cultural differences. Ethical committees for clinical practices and researches should be established specifically for CAM and TM research. In these committees, physicians from different fields of specialization who participated in clinical research conducted according to good clinical practices, physicians having expertise on CAM and TM, legal experts with specialization on medical law and patients' rights, pharmacology and pharmacognosy specialists, along with medical ethics and public health experts. Instructions should be prepared to cover how these committees to work and make decisions; number of members and their employment periods, duties and authorities in these committees; how the applications to these committees are to be done, and how the decisions are to be delivered to the researcher(s); within the legal

**88**

**Conflict of interest**

Omur Sayligil Eskisehir Osmangazi University, Faculty of Medicine, Department of History of Medicine and Ethics, Eskisehir, Turkey

\*Address all correspondence to<EMAIL_ADDRESS>
© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


6. Conductor self-damping and dampers

The influence of external and internal damping mechanisms was considered in the conductor vibration model. The factors considered included the following [1, 32]:

The high voltage transmission line damped model is expressed in Eq. (48) as:

$$EI\frac{\partial^4 y(\mathbf{x},t)}{\partial \mathbf{x}^4} - S\frac{\partial^2 y(\mathbf{x},t)}{\partial \mathbf{x}^2} + \beta I \frac{\partial^5 y(\mathbf{x},t)}{\partial \mathbf{x}^4 \partial t} + \mathbb{C} \frac{\partial y(\mathbf{x},t)}{\partial t} + \rho A \frac{\partial^2 y(\mathbf{x},t)}{\partial t^2} = f(\mathbf{x},t) \tag{48}$$

Where C and β represent damping constants. In the presence of axial load, viscous air damping, strain rate damping or Kelvin-Voigt damping, high voltage transmission line integrity can be managed.

There are various types of dampers that can be used to reduce vibration. The dampers are excited by the vibration of the power conductor and the vibration of their masses connected by the massager cable help to damp out energy. Stockbridge dampers are commonly installed on high voltage transmission lines to reduce aeolian vibrations. Stockbridge dampers can be symmetrical or asymmetrical in their design. An example of dampers installed on high voltage transmission lines is shown in Figure 1. The design of Stockbridge dampers follows the principle of cantilever beams with mass at the free ends. The contribution of dampers to power conductor vibration mitigation is to lower the severity of the vibration to a level that might prevent failure to the line.

Figure 1. Asymmetrical damper.


**2. Migration challenge**

Soft power is important not only because of its influence on a sociocultural space but also because of increase in anthropogenic mobiles (moving people), which today are considered a tool of geopolitics.

We also consider migration challenge and associated use of soft power tools that cause disturbances in social ecology.

In 2017, the number of migrants reached 258 million people. Over the past 17 years, the total number of migrants has increased from 173 million by 49% according to the International Migration Report [6]. The growth of migrants' mobility and the impact of migration flows on almost all countries' development include the international migration issue.

Migration processes are dependent on a structure of social relations and cannot be studied in isolation from various social, economic and political phenomena in which they occur (according to a modern theory of migration considered from a geographical point of view [7]).

Migrants' studies (including surveys) are highly important in terms of migration policy analysis in the European countries. They are performing migrants' surveys regularly for accessing migrants' living conditions, political preferences, etc. The best foreign practice has shown that migrants' studies are highly important in terms of society's structural changes projection.

Migrants not only affect population dynamics, changing its structure, but also to some extent influence local community life: the larger the proportion of migrants, the greater their impact on the local community.

In order to obtain up-to-date information on both state and sociocultural perspectives, a competent migration policy development is highly necessary taking into account different aspects of globalization phenomenon.

Therefore, it is necessary to research migrants' inclusion mechanisms in local cultural and political environment as a condition for sociocultural sustainability as well as public diplomacy as the most important "soft power" tool where migrants' role is rather high.

Europe remains migrants' most attractive region. Largest migrant groups consist mostly of people coming from the Middle East and Africa. At the same time, migration is being characterized with irregularity: migrants' distribution across Europe can be characterized with both low and high concentrations. Rather different situation is being witnessed in Northern Europe.

Increase in both migrants' flows and a concentration reduces naturally the share of a recipient community: there is a significant increase of Arab origin population in France, of Turkish-Arab origin in Germany and of Indopakistan and Arab origin in the UK.

Hereby, we apply the Pareto rule in order both to analyze and evaluate influencing factor effectiveness. Migrants' excess of over 20% is known as a threshold

**313**

**Figure 4.**

*Public Diplomacy in Cross-Border Cooperation DOI: http://dx.doi.org/10.5772/intechopen.92663*

*Foreign migrants as a percentage of total population of Europe.*

*Foreign migrants as a percentage of total population of Northern Europe.*

*Foreign migrants as a percentage of total population of Eastern Europe.*

*Foreign migrants as a percentage of total population of Southern Europe.*

environment.

**Figure 1.**

**Figure 2.**

**Figure 3.**

after which sociocultural relation structure changes significantly. The interval amounting to "10–20%" is a transition zone. It shows migrants' increasing influence till a critical value. This is not an exact criterion, but rather a mnemonic rule that identifies an important meaning, namely a serious shift in a social

**Figures 1**–**5** provide data for various European countries and regions [6].

#### *Public Diplomacy in Cross-Border Cooperation DOI: http://dx.doi.org/10.5772/intechopen.92663*

after which sociocultural relation structure changes significantly. The interval amounting to "10–20%" is a transition zone. It shows migrants' increasing influence till a critical value. This is not an exact criterion, but rather a mnemonic rule that identifies an important meaning, namely a serious shift in a social environment.

**Figure 1.**

*Heritage*

Soft power tools are also witnessed in Russian communications. It has become an integral component of modern international politics in Russia as a comprehensive toolkit for solving foreign policy issues based on civil society demands, information and communication, humanitarian and other alternative classical diplomacy methods and technologies [4]. Moreover, Russia has enormous potential for public diplomacy development. It's most important pillar is presented with a so-called Russian world when millions of people abroad feel a strong need to keep in touch

Soft power is important not only because of its influence on a sociocultural space

We also consider migration challenge and associated use of soft power tools that

Migration processes are dependent on a structure of social relations and cannot be studied in isolation from various social, economic and political phenomena in which they occur (according to a modern theory of migration considered from a

Migrants' studies (including surveys) are highly important in terms of migration policy analysis in the European countries. They are performing migrants' surveys regularly for accessing migrants' living conditions, political preferences, etc. The best foreign practice has shown that migrants' studies are highly important in terms

Migrants not only affect population dynamics, changing its structure, but also to some extent influence local community life: the larger the proportion of migrants,

In order to obtain up-to-date information on both state and sociocultural perspectives, a competent migration policy development is highly necessary taking

Therefore, it is necessary to research migrants' inclusion mechanisms in local cultural and political environment as a condition for sociocultural sustainability as well as public diplomacy as the most important "soft power" tool where migrants'

Europe remains migrants' most attractive region. Largest migrant groups consist mostly of people coming from the Middle East and Africa. At the same time, migration is being characterized with irregularity: migrants' distribution across Europe can be characterized with both low and high concentrations. Rather different

Increase in both migrants' flows and a concentration reduces naturally the share of a recipient community: there is a significant increase of Arab origin population in France, of Turkish-Arab origin in Germany and of Indopakistan and Arab origin

Hereby, we apply the Pareto rule in order both to analyze and evaluate influencing factor effectiveness. Migrants' excess of over 20% is known as a threshold

but also because of increase in anthropogenic mobiles (moving people), which

In 2017, the number of migrants reached 258 million people. Over the past 17 years, the total number of migrants has increased from 173 million by 49% according to the International Migration Report [6]. The growth of migrants' mobility and the impact of migration flows on almost all countries' development

with Russia, Russian language and its culture [5].

today are considered a tool of geopolitics.

include the international migration issue.

of society's structural changes projection.

the greater their impact on the local community.

situation is being witnessed in Northern Europe.

into account different aspects of globalization phenomenon.

geographical point of view [7]).

role is rather high.

cause disturbances in social ecology.

**2. Migration challenge**

**312**

in the UK.

*Foreign migrants as a percentage of total population of Europe.*

**Figure 2.**

*Foreign migrants as a percentage of total population of Northern Europe.*

**Figure 3.**

*Foreign migrants as a percentage of total population of Eastern Europe.*

**Figure 4.**

*Foreign migrants as a percentage of total population of Southern Europe.*

**Figure 5.**

*Foreign migrants as a percentage of total population of Western Europe.*

There are three groups of countries to be shaped based upon **Figures 1**–**5** mentioned above. The first group of countries is without any significant migration challenges (migrants make up less than 10% of the recipient community in Finland and Central Eastern Europe), the second group, where migration challenges are pretty visible (migrants make up 10–15% in Croatia, Spain, Slovenia, Iceland and Denmark) and a third group, where migration challenges are highly critical (more than 15% of migrants in Germany, Sweden, Ireland, Austria and Norway).

The figures show that serious difficulties in trend preserving are being witnessed in Western and Northern Europe (in accordance with Pareto rule), while Northern Europe alongside with Southern Europe is showing much higher migrants' growth rates.

These circumstances shall be taken into account, since soft power becomes an instrument not only for migrants' integration but also for mutual influence on representatives' identity coming from different cultures.

Finland stands out quite separately out of a number of some other Northern Europe countries, which is undoubtedly an interest for research. Finland borders with Russia possessing a large diaspora of the Russian-speaking population (29,000 people), which turns out to be a serious public diplomacy resource in promoting "Russian world" abroad. Migration policy in Finland is considered to be highly adaptive and balanced, primarily preserving national interests and human capital. While analyzing reasons for Finland's success, we are highlighting the main aspects: high human capital quality of foreign migrants coming to Finland, successful information dissemination for migrants coming to Finland and successful migrants' integration in a Finnish labor market.

#### **3. Regional dimension: Karelia and Finland**

Public diplomacy has a regional dimension as well. It also acquires special significance in terms of border areas, where it is necessary to maintain a climate of trust and stable international relations and use neighborhood for a balanced sociocultural development of its territories. Cross-border mobility and active communication practices are transforming sociocultural space of border areas [8, 9]. It transforms in terms of an increase in a number of border crossings, contacts between people and joint actions; its structure becomes diverse, open to interaction and adoption of social innovations.

The European vector of public diplomacy is represented with a large number of NGOs and a wide range of opportunities coming from the European Union (educational programs, Northern Dimension partnerships, cross-border cooperation programs, etc.) [10]. Public organizations represent different sectors of population interests in a social and cultural space in order to achieve social, charitable, cultural, educational, political, scientific and managerial goals.

**315**

and social sphere.

community.

interactions of sociocultural practices.

*Public Diplomacy in Cross-Border Cooperation DOI: http://dx.doi.org/10.5772/intechopen.92663*

set out in the European Neighborhood Policy [10].

Since 1996, Russia and Finland have been participating in regional cross-border

In a survey by the Organization for Economic Co-operation and Development (OECD), four factors that are critical for the development of cross-border cooperation were identified [11]. Given the current challenges, we reformulate them as follows: the transformation of global geospace; institutional order; institutional and

At the same time, cross-border cooperation is considered as a form of population socialization in neighboring regions in a context of cultural diversity, a multiethnic community formation within transboundary spaces. Border zones are characterized with a specific cultural phenomena, readiness for its cultural interaction and a

In this regard, it is necessary to apply soft power tools effectively. The latter is important not only because of sociocultural space sustainable development but also due to the increase in anthropogenic mobiles (moving people), which today are increasingly showing the property of a geopolitical tool and, in this regard, are becoming an important factor in relation to border territories affecting economy

Geopolitical challenges affect reality perception by residents of border regions and pose a choice of the cultural world to which they want to belong to. Modern globalization processes are associated not only with economic and political processes but also with cultural self-identification and social relations stability structure. Migration flows exacerbate and actualize the issues of sociocultural characteristics of communities introducing a different cultural and spiritual-value component that could change the existing social, cultural and psychological settings of the host

Border regions interaction leads to "the interpenetration of cultures, their mutual enrichment, contributing to a new sociocultural cross-border space." Transboundary sociocultural space is also considered as a variety of intercultural

At the Republic of Karelia, there are lots of attributes produced in Finnish language-a sociopolitical magazine "Carelia" and a monthly children's magazine "Kipinä" ("Sparkle"). A number of Russian-language media are also active in Finland, of which the largest local Russian-language newspaper is "Spektr." Finnish

social roots and an appropriate culture of cooperation; and identity.

certain commonality of the world population outlook [12].

cooperation programs actively. In 2000, the Karelia Euroregion was founded combining the Republic of Karelia of the Russian Federation and the Finnish border provinces of Kainuu, North Karelia and Northern Ostrobothnia. The Republic of Karelia has adopted a regional cross-border cooperation program-a response to cross-border initiatives of the European Union, in particular, the Interreg IIIB and Interreg IIIA programs (including the Interreg IIIA-Karelia subprogram). The role of an effective platform for discussing initiatives and coordinating plans for crossborder cooperation programs is presented by the Karelia Euroregion. Cross-border and multilateral cooperation programs are unique tools for developing local and regional territorial initiatives. For over 5 years of the program's implementation, 66 projects were implemented amounting to 42 million euros, 30% of which were used to finance infrastructure projects including modernization of the Mäpp Värtsilä-Niirala [10]. Such cooperation practices as a cross-border shopping tourism, joint projects implementation and public diplomacy are widespread here. The Karelia Cross-Border Cooperation Program 2014–2020 (Karelia/CBC) is ongoing currently. It is called upon to strengthen Russian-Finnish inter-regional cross-border cooperation with the support of the Russian Federation, Finland and the European Union. The program is cross-border in nature and contributes to the implementation of strategic and thematic tasks of cross-border cooperation at the European level, as

#### *Public Diplomacy in Cross-Border Cooperation DOI: http://dx.doi.org/10.5772/intechopen.92663*

*Heritage*

**Figure 5.**

migrants' growth rates.

integration in a Finnish labor market.

**3. Regional dimension: Karelia and Finland**

educational, political, scientific and managerial goals.

There are three groups of countries to be shaped based upon **Figures 1**–**5** mentioned above. The first group of countries is without any significant migration challenges (migrants make up less than 10% of the recipient community in Finland and Central Eastern Europe), the second group, where migration challenges are pretty visible (migrants make up 10–15% in Croatia, Spain, Slovenia, Iceland and Denmark) and a third group, where migration challenges are highly critical (more

than 15% of migrants in Germany, Sweden, Ireland, Austria and Norway). The figures show that serious difficulties in trend preserving are being witnessed in Western and Northern Europe (in accordance with Pareto rule), while Northern Europe alongside with Southern Europe is showing much higher

representatives' identity coming from different cultures.

*Foreign migrants as a percentage of total population of Western Europe.*

These circumstances shall be taken into account, since soft power becomes an instrument not only for migrants' integration but also for mutual influence on

Finland stands out quite separately out of a number of some other Northern Europe countries, which is undoubtedly an interest for research. Finland borders with Russia possessing a large diaspora of the Russian-speaking population (29,000 people), which turns out to be a serious public diplomacy resource in promoting "Russian world" abroad. Migration policy in Finland is considered to be highly adaptive and balanced, primarily preserving national interests and human capital. While analyzing reasons for Finland's success, we are highlighting the main aspects: high human capital quality of foreign migrants coming to Finland, successful information dissemination for migrants coming to Finland and successful migrants'

Public diplomacy has a regional dimension as well. It also acquires special significance in terms of border areas, where it is necessary to maintain a climate of trust and stable international relations and use neighborhood for a balanced sociocultural development of its territories. Cross-border mobility and active communication practices are transforming sociocultural space of border areas [8, 9]. It transforms in terms of an increase in a number of border crossings, contacts between people and joint actions; its structure becomes diverse, open to interaction and adoption of social innovations. The European vector of public diplomacy is represented with a large number of NGOs and a wide range of opportunities coming from the European Union (educational programs, Northern Dimension partnerships, cross-border cooperation programs, etc.) [10]. Public organizations represent different sectors of population interests in a social and cultural space in order to achieve social, charitable, cultural,

**314**

Since 1996, Russia and Finland have been participating in regional cross-border cooperation programs actively. In 2000, the Karelia Euroregion was founded combining the Republic of Karelia of the Russian Federation and the Finnish border provinces of Kainuu, North Karelia and Northern Ostrobothnia. The Republic of Karelia has adopted a regional cross-border cooperation program-a response to cross-border initiatives of the European Union, in particular, the Interreg IIIB and Interreg IIIA programs (including the Interreg IIIA-Karelia subprogram). The role of an effective platform for discussing initiatives and coordinating plans for crossborder cooperation programs is presented by the Karelia Euroregion. Cross-border and multilateral cooperation programs are unique tools for developing local and regional territorial initiatives. For over 5 years of the program's implementation, 66 projects were implemented amounting to 42 million euros, 30% of which were used to finance infrastructure projects including modernization of the Mäpp Värtsilä-Niirala [10]. Such cooperation practices as a cross-border shopping tourism, joint projects implementation and public diplomacy are widespread here. The Karelia Cross-Border Cooperation Program 2014–2020 (Karelia/CBC) is ongoing currently. It is called upon to strengthen Russian-Finnish inter-regional cross-border cooperation with the support of the Russian Federation, Finland and the European Union. The program is cross-border in nature and contributes to the implementation of strategic and thematic tasks of cross-border cooperation at the European level, as set out in the European Neighborhood Policy [10].

In a survey by the Organization for Economic Co-operation and Development (OECD), four factors that are critical for the development of cross-border cooperation were identified [11]. Given the current challenges, we reformulate them as follows: the transformation of global geospace; institutional order; institutional and social roots and an appropriate culture of cooperation; and identity.

At the same time, cross-border cooperation is considered as a form of population socialization in neighboring regions in a context of cultural diversity, a multiethnic community formation within transboundary spaces. Border zones are characterized with a specific cultural phenomena, readiness for its cultural interaction and a certain commonality of the world population outlook [12].

In this regard, it is necessary to apply soft power tools effectively. The latter is important not only because of sociocultural space sustainable development but also due to the increase in anthropogenic mobiles (moving people), which today are increasingly showing the property of a geopolitical tool and, in this regard, are becoming an important factor in relation to border territories affecting economy and social sphere.

Geopolitical challenges affect reality perception by residents of border regions and pose a choice of the cultural world to which they want to belong to. Modern globalization processes are associated not only with economic and political processes but also with cultural self-identification and social relations stability structure. Migration flows exacerbate and actualize the issues of sociocultural characteristics of communities introducing a different cultural and spiritual-value component that could change the existing social, cultural and psychological settings of the host community.

Border regions interaction leads to "the interpenetration of cultures, their mutual enrichment, contributing to a new sociocultural cross-border space." Transboundary sociocultural space is also considered as a variety of intercultural interactions of sociocultural practices.

 A number of Russian-language media are also active in Finland, of which the largest local Russian-language newspaper is "Spektr." Finnish language training is carried out by the Department of Baltic-Finnish Philology at Petrozavodsk State University, at secondary schools and preschools, as well as in a number of commercial centers for foreign language study. There has been a tendency toward an increase in the number of children learning national languages. In preschool educational institutions in the academic year 2017–2018, Karelian, Veps and Finnish languages were studied by 1166 pupils, and at schools by 6820 pupils [8].

In North Karelia (Finland), Russian language is taught both at schools and higher educational institutions. In 2017, there were about 3881 foreign citizens from 106 countries in North Karelia, of which the largest were Russians (43.2%), the next largest were Estonians (5.2%) and Somalis and Thais (a total of 3.8%) [13]. About 2344 foreign citizens lived in Joensuu, of which 955 were from Russia with a total population of 76,067 people [14].

In the framework of cooperation with Finnish partners, permanent organizers of the events are the friendship societies Karelia-Finland and Finland-Russia, literature and concert programs and exhibitions, a week of Finnish cinema, and touring activities of creative groups. The National Theater of the Republic of Karelia is the only theater outside Finland where performances are staged in Finnish, Karelian and Russian languages.

The greatest manifestation of cross-border sociocultural specificity is observed in the following areas: culture and art, project activities, education, tourism and information space [8].

The border position of the Republic of Karelia (Russia) and North Karelia (Finland) contributes to everyday neighborhood practices development, new forms of interaction emergence based on past experience. Cross-border interaction has a positive effect on the development of good neighborly relations and activates local communities not only to create networks of cooperation and establish direct ties, but also to develop initiatives of local communities, increase mutual understanding, trust and awareness.

The increasing role of border and cross-border territories in terms of sociocultural space transformation causes a significant research interest.


**1. Introduction**

Large scale energy storage systems are required to facilitate the penetration of variable renewable energies in the electricity grids [1–4]. Underground space from abandoned mines can be used as underground reservoirs for underground pumped storage hydropower (UPSH) and compressed air energy storage (CAES) systems [5–11]. Pumped storage hydropower (PSH) is the most mature large-scale energy storage technology, and the round trip efficiency is typically in the range of 70–80% [12,13]. Diabatic CAES (D-CAES) is an alternative to PSH that requires lower capital costs and the round trip energy efficiency is around 40–50% [14]. D-CAES systems use natural gas to heat the compressed air in the decompression period. However, Adiabatic CAES (A-CAES) allows the storage of the thermal energy during the air compression period, avoiding the consumption of natural gas, therefore increasing the round trip energy efficiency up to 70–75% [15–17].

**Citation:** Prado, L.Á.d.; Menéndez, J.; Bernardo-Sánchez, A.; Galdo, M.; Loredo, J.; Fernández-Oro, J.M. Thermodynamic Analysis of Compressed Air Energy Storage (CAES) Reservoirs in Abandoned Mines Using Different Sealing Layers. *Appl. Sci.* **2021**, *11*, 2573. https://doi.org/10.3390/app11062573

Academic Editor: Luisa F. Cabeza

Received: 16 February 2021 Accepted: 11 March 2021 Published: 13 March 2021

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

**Copyright:** © 2021 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/).

During the operation of A-CAES plants, the air is stored in the underground reservoir at high pressures during the charge period. Then, in the discharge period, the pressurized air is released, heated (stored heat), and expanded to generate electricity as the pressure within the reservoir is reduced. During the storage period, between charging and discharging, the air pressure and temperature vary depending on the storage time. The amount of stored energy depends on the reservoir volume and the thermodynamic conditions. The air temperature variations depend on the thermal conductivity of the sealing layer, concrete lining and rock mass. Therefore, the air temperature and pressure fluctuations are essential to design the reservoir volume, to select the appropriate compressor and turbines and to ensure safe operating conditions. Kushnir et al. [18] developed a study to determine the temperature and pressure variations within compressed air energy storage caverns and showed that the heat transfer reduces the temperature and pressure variations during the compression and decompression periods, leading to a higher storage capacity. Thermodynamic models were performed to determine temperature and pressure variations within adiabatic caverns of compressed air energy storage plants [19]. The results showed that the storage volume is highly dependent on the air maximum to minimum pressure ratio. Safaei and Aziz [20] carried out a thermodynamic analysis of three compressed air energy storage systems. They concluded that A-CAES with physical heat storage is the most efficient option with an exergy efficiency of 69.5%.

A pilot-scale demonstration of A-CAES was built in Switzerland [21,22]. The cavern was 120 m long and 4.9 m in diameter with a usable volume of 1942 m3 . A packed-bed of rocks for thermal energy storage was located inside the cavern. Charging temperatures of 550 ◦C and air pressures between 0 and 0.7 MPa were employed in the test and constant heat transfer coefficients of 5 and 10 W m−2 K −1 were considered in the simulations. The estimated round trip efficiency of the pilot plant reached 63–74%. Schmidt et al. [23] analyzed the effect of the cyclic loading on the geomechanical performance of CAES systems for lined and unlined tunnels in closed mines. The cycling loading operation was simulated for 10,000 cycles considering an operating pressure within the reservoir from 4.5 to 7.5 MPa. They observed moderate deformations and small thickness of plastic zones, while an increase of the initial volume of less than 0.5% was reached.

Jiang et al. [24] carried out experimental and numerical investigations of a lined rock cavern to analyze the thermodynamic process within the underground cavern. The volume of the cavern was 28.8 m3 with 5 m length and 2.9 m in diameter. A 2 cm thick RFP was employed as sealing layer around the compressed air. The air pressure reached 6 MPa at constant mass flow rate (0.12 kg s−1 ). Zhou et al. [25] developed a numerical simulation for the coupled thermo-mechanical performance of a lined rock cavern for CAES systems. An air pressure range from 4.5 to 6.9 MPa was considered for 100 cycles with a thickness of concrete lining of 0 and 0.1 m. They concluded that significant air temperature fluctuation was observed in sealing layer and concrete lining and no fluctuation occurred in the rock mass. An analytical study was proposed to estimate the geomechanical performance caused by air temperature and pressure variations in CAES systems [26]. Khaledy et al. [27] studied the thermo-mechanical responses of CAES systems in rock salt caverns. They concluded that the stability of the salt cavern is affected by the internal operating conditions with the air temperature increasing the volume convergence. Li et al. [28] carried out a failure study for gas storage by thermo-mechanical modelling in salt caverns. The results showed an affected area by the air and temperature operating conditions up to 10 m in the rock mass from the cavern walls. Round trip efficiencies between 70.5 and 75.1% were estimated by Barbour et al. [29] in A-CAES systems for continuous operation with packed bed thermal energy storage. The thermodynamic and geomechanical performance was studied by Rutqvist et al. [30] in lined rock caverns. They found that 97% of the thermal energy injected in the charge period could be recovered in the discharge period. Deng et al. [31] designed a new CAES systems with constant gas pressure and temperature in closed coal mines. A power output of 18 MW and a generating time of 1.76 h were obtained for a mine tunnel with 10,000 m3 of volume at 500 m depth. The ADELE project was studied

in Germany to install an A-CAES plant with a storage capacity of 360 MWh and output power of 90 MW [2]. was studied in Germany to install an A-CAES plant with a storage capacity of 360 MWh and output power of 90 MW [2]. In this paper, abandoned mines are proposed as underground reservoirs for large

closed coal mines. A power output of 18 MW and a generating time of 1.76 h were obtained for a mine tunnel with 10,000 m3 of volume at 500 m depth. The ADELE project

*Appl. Sci.* **2021**, *11*, x FOR PEER REVIEW 3 of 19

In this paper, abandoned mines are proposed as underground reservoirs for large scale energy storage systems. A 200 m3 tunnel in an abandoned coal mine was investigated as compressed air reservoir for A-CAES plants, where the ambient air is stored at high pressure.  One-dimensional analytical and threedimensional CFD numerical models were conducted considering fiber-reinforced plastic (FRP) and steel as sealing layers and a typical operational pressure from 5 to 8 MPa. In the analytical model, air mass flow rates of 0.22 and −0.45 kg s−1 have been considered for 30 cycles of compression and decompression, respectively. To reduce the computational time, the numerical simulation has been conducted for five cycles with air mass flow rates of 50 and −75 kg s−1 . The air temperature and pressure fluctuations were estimated in the simulations. The temperature and the heat flux were also analyzed on the contact surfaces of the solids considering both FRP and steel sealing layers and the heat convection from the air to the sealing layers was calculated. Finally, the energy balance through the sealing layer was obtained during air charging and discharging. scale energy storage systems. A 200 m3 tunnel in an abandoned coal mine was investigated as compressed air reservoir for A-CAES plants, where the ambient air is stored at high pressure.  One-dimensional analytical and three-dimensional CFD numerical models were conducted considering fiber-reinforced plastic (FRP) and steel as sealing layers and a typical operational pressure from 5 to 8 MPa. In the analytical model, air mass flow rates of 0.22 and −0.45 kg s−1 have been considered for 30 cycles of compression and decompression, respectively. To reduce the computational time, the numerical simulation has been conducted for five cycles with air mass flow rates of 50 and −75 kg s−1. The air temperature and pressure fluctuations were estimated in the simulations. The temperature and the heat flux were also analyzed on the contact surfaces of the solids considering both FRP and steel sealing layers and the heat convection from the air to the sealing layers was calculated. Finally, the energy balance through the sealing layer was obtained during air charging and discharging.

### **2. Materials and Methods 2. Materials and Methods**

### *2.1. Problem Statement 2.1. Problem Statement*

Underground space in abandoned mines may be used as compressed air storage systems for CAES plants. The simplified schematic diagram of the CAES system is shown in Figure 1. The compressor and turbine facilities are installed above the ground, while the compressed air reservoir is underground. The ambient air is compressed during off-peak periods and stored at high pressure in the underground reservoir (charge period). Then, when the electricity is required, the compressed air is released, heated, and expanded during peak hours in conventional gas turbines, driving a generator for power production (discharge period). The charge and discharge processes are carried out with a typical operating pressure range from 5 to 8 MPa. To reduce air leakage, two different sealing layers, FRP, and steel, have been employed in the present study. The air temperature and pressure fluctuations are estimated for both FRP and steel sealing layers. Underground space in abandoned mines may be used as compressed air storage systems for CAES plants. The simplified schematic diagram of the CAES system is shown in Figure 1. The compressor and turbine facilities are installed above the ground, while the compressed air reservoir is underground. The ambient air is compressed during off-peak periods and stored at high pressure in the underground reservoir (charge period). Then, when the electricity is required, the compressed air is released, heated, and expanded during peak hours in conventional gas turbines, driving a generator for power production (discharge period). The charge and discharge processes are carried out with a typical operating pressure range from 5 to 8 MPa. To reduce air leakage, two different sealing layers, FRP, and steel, have been employed in the present study. The air temperature and pressure fluctuations are estimated for both FRP and steel sealing layers.

**Figure 1.** Schematic diagram of compressed air energy storage (CAES) system in abandoned underground mines. Compressor and turbine facilities installed on the surface and underground compressed air reservoir with an operating pressure range from 5 to 8 MPa. **Figure 1.** Schematic diagram of compressed air energy storage (CAES) system in abandoned underground mines. Compressor and turbine facilities installed on the surface and underground compressed air reservoir with an operating pressure range from 5 to 8 MPa.

### *2.2. Analytical Model 2.2. Analytical Model*

A one-dimensional analytical model has been developed in MATLAB to study the thermodynamic performance during the operation time of the CAES system in a closed mine. Figure 2 shows the scheme of the 50 m long model. A lined tunnel with a usable volume of 200 m3 and a cross section of 8 m2 has been considered.  The evolution of the temperature (*Ta*), density (*ρa*) and air pressure (*Pa*) over time has been analyzed considering different air mass flow rates (*m˙* ). The heat flux through the contact surfaces, i.e., air-sealing layer ( . *Q*1 ), sealing layer-concrete ( . *Q*2 ), and concrete-sandstone ( . *Q*3 ), has been estimated. Finally, the temperature on the sealing layer wall (*T*1), concrete wall (*T*2), and sandstone wall (*T*3) have also been estimated during the operation time considering an external temperature (*T*4) of 300 K. A one-dimensional analytical model has been developed in MATLAB to study the thermodynamic performance during the operation time of the CAES system in a closed mine. Figure 2 shows the scheme of the 50 m long model. A lined tunnel with a usable volume of 200 m3 and a cross section of 8 m2 has been considered.  The evolution of the temperature (*Ta*), density (*ρa*) and air pressure (*Pa*) over time has been analyzed considering different air mass flow rates (*ṁ*). The heat flux through the contact surfaces, i.e., air-sealing layer (ܳሶ ଵ), sealing layer-concrete (ܳሶ ଶ), and concrete-sandstone (ܳሶ ଷ), has been estimated. Finally, the temperature on the sealing layer wall (*T*1), concrete wall (*T*2), and sandstone wall (*T*3) have also been estimated during the operation time considering an external temperature (*T*4) of 300 K.

**Figure 2.** Scheme of the deep tunnel with a sealing layer, concrete lining and sandstone rock mass. (**a**) 3D model (not to scale); (**b**) Cross section. **Figure 2.** Scheme of the deep tunnel with a sealing layer, concrete lining and sandstone rock mass. (**a**) 3D model (not to scale); (**b**) Cross section.

The energy equation has been applied following Equation (1), where ܳሶ is the net heat transfer, ܹ ሶ is the net work done, *e* is the specific energy, *ρ* is the density in kg m−3, *V* is the reservoir volume, *v* is the air velocity and *S* is the cross section of the tunnel. In the air domain, the first term of Equation (2) represents the heat convection from the air to the sealing layer, which depends on the film coefficient of heat transfer (*h*), in Wm−2 K−1, the sealing layer surface in contact with the fluid (*A*1) and the temperature difference between the air and the concrete wall (*Ta-T*1). The second term of Equation (2) corresponds to the energy variation within the reservoir where the air pressure increases, which depends on the air mass inside the reservoir (*m*), the specific heat at constant volume (*Cv*) and the air temperature (*Ta*). Finally, the third term represents the input and output of energy in the control volume due to the energy provided by the air jet in the form of heat (*T*0) and kinetic energy. The air mass inside the reservoir at an instant of time, *t*, depends on the initial air mass (*m*0) and the air mass flow rate (*ṁ*), and is obtained by applying Equation (3). The energy equation has been applied following Equation (1), where *Q* is the net heat transfer, . *W* is the net work done, *e* is the specific energy, *ρ* is the density in kg m−3 , *V* is the reservoir volume, *v* is the air velocity and *S* is the cross section of the tunnel. In the air domain, the first term of Equation (2) represents the heat convection from the air to the sealing layer, which depends on the film coefficient of heat transfer (*h*), in Wm−2 K−1 , the sealing layer surface in contact with the fluid (*A*1) and the temperature difference between the air and the concrete wall (*Ta-T*1). The second term of Equation (2) corresponds to the energy variation within the reservoir where the air pressure increases, which depends on the air mass inside the reservoir (*m*), the specific heat at constant volume (*Cv*) and the air temperature (*Ta*). Finally, the third term represents the input and output of energy in the control volume due to the energy provided by the air jet in the form of heat (*T*0) and kinetic energy. The air mass inside the reservoir at an instant of time, *t*, depends on the initial air mass (*m*0) and the air mass flow rate (*m˙* ), and is obtained by applying Equation (3).

$$
\dot{Q} - \dot{W} = \frac{\partial}{\partial t} \int \rho e \, dV + \oint \rho \mathcal{E} \, (\mathfrak{d}dS) \tag{1}
$$

.

$$-hA\_1(T\_a - T\_1) = \frac{d}{dt}(m\mathbb{C}\_{\mathbb{P}}T\_a) - \dot{m}\left(\mathbb{C}\_{\mathbb{P}}T\_0 + RT\_0 + \frac{v^2}{2}\right) \tag{2}$$

*m* = *m*0 + . *m t* (3)

After some algebra, the air temperature (*Ta*) is calculated by applying Equation (4). The air temperature and density increase as the air pressure increases in the reservoir, and therefore the wall temperature increases by heat convection.

$$\frac{dT\_a}{dt} = \frac{\dot{m}}{m} \left[ \frac{\mathbb{C}\_p}{\mathbb{C}\_v} T\_0 + \frac{1}{2\mathbb{C}\_v} \left( \frac{\dot{m}}{m} L \right)^2 - T\_a \right] - \frac{h2\pi r\_1 L}{\mathbb{C}\_v m} (T\_a - T\_1) \tag{4}$$

The temperatures on the sealing layer wall (*T*1), the concrete wall (*T*2) and sandstone wall (*T*3) are obtained applying the equations of non-stationary heat transfer in sealing layer, concrete and sandstone domains (solid regions) considering an external temperature (*T*4) of 300 K and a temperature of the air mass flow inlet (*T*0) of 310 K. The heat flux reaches the sealing layer by convection. A part of this heat is transmitted to the concrete by conduction while another part increases the temperature of the sealing layer. A similar mechanism takes place for the concrete lining. Equations (5)–(7) represent the heat transmission on the sealing layer, concrete and sandstone formation, respectively.

$$\frac{dT\_1}{dt} = \frac{2\mathcal{U}\_\text{lt}}{m\_\text{s}\mathcal{C}\_{ps}}(T\_a - T\_1) - \frac{2\mathcal{U}\_\text{s}}{m\_\text{s}\mathcal{C}\_{ps}}(T\_1 - T\_2) - \frac{dT\_2}{dt} \tag{5}$$

$$\frac{dT\_2}{dt} = \frac{2\mathcal{U}\_\mathrm{s}}{m\_\mathrm{c}\mathcal{C}\_{pc}}(T\_1 - T\_2) - \frac{2\mathcal{U}\_\mathrm{c}}{m\_\mathrm{c}\mathcal{C}\_{pc}}(T\_2 - T\_3) \tag{6}$$

$$\frac{dT\_3}{dt} = \frac{2U\_\text{c}}{m\_\text{ss}\mathcal{C}\_{\text{pss}}}(T\_2 - T\_3) - \frac{2U\_\text{ss}}{m\_\text{ss}\mathcal{C}\_{\text{pss}}}(T\_3 - T\_4) \tag{7}$$

where *Uh* , *Us*, *Uc*, and *Uss* are the convection transmittance, sealing layer transmittance, concrete transmittance, and sandstone transmittance, respectively. These thermal coefficients are evaluated according to

$$\mathbf{U}\_h = h 2 \pi r\_1 \mathbf{L} \tag{8}$$

$$\mathcal{U}\_s = \frac{2\pi \mathcal{K}\_s L}{Ln\left(\frac{r\_2}{r\_1}\right)}\tag{9}$$

$$\mathcal{U}\_{\mathbb{C}} = \frac{2\pi K\_{\mathbb{C}}L}{Ln\left(\frac{r\_2}{r\_2}\right)}\tag{10}$$

$$\mathcal{U}\_{\rm ss} = \frac{2\pi K\_{\rm ss} L}{L n\left(\frac{r\_4}{r\_3}\right)}\tag{11}$$

In these expressions, *h* is the film coefficient of heat transfer, in Wm−2 K −1 ; *L* is the tunnel length, in m; *Ks , Kc* and *Kss* are the thermal conductivity of sealing layer, concrete and sandstone, in Wm−1 K −1 ; *Cps , Cpc*, and *Cpss* are the specific heat at constant pressure for the sealing layer, reinforced concrete and sandstone, in J kg−1 K −1 ; and *r*1*, r*2*, r*3, and *r*4 are the (equivalent) radius of sealing layer, concrete, sandstone and external walls, in m (Figure 2b). Note that due to the geometrical characteristics of the tunnel, the heat transfer formulation in cylindrical coordinates has been used for Equations (8)–(11).

For the evaluation of the convection film coefficient, the correlation proposed by Woodfield et al. [32] and Heath et al. [33] for the measurement of heat transfer coefficients in high-pressure vessels during gas charging was considered. In particular, a mixed (natural and forced) convection is modelled as a combination of both unsteady Reynolds and Rayleigh numbers. For the present investigation, a slight correction has been introduced for the exponent of the Rayleigh number, resulting the Nusselt number in the following expression:

$$Nu = 0.56 \, Re^{0.67} + 0.104 \, Ra^{0.34} \tag{12}$$

where *Re* is defined as the Reynolds number of the incoming mass flow rate (*Re* = 4 . *m*/2*µπr*1) and *Ra* is computed from the instantaneous thermal properties of the air (*Ra* = *gβ*(*Ta* − *T*1)*Cpρ* 2*L* 3/(*µK*)), being *g* the gravity acceleration, *β* is the volumetric thermal expansion coefficient, *Cp* the specific heat coefficient at constant pressure, *ρ* the density, *L* the tunnel length, *µ* the dynamic viscosity and *K* the thermal conductivity. The film coefficient is thus computed as

$$h = Nu \frac{K}{L} \tag{13}$$

Finally, a backward Euler explicit discretization has been employed over Equations (3)–(7) to resolve the coupled system of equations. A typical time-step of 0.01 s was applied to provide an accurate temporal description of the different temperatures. The model was resolved iteratively until a maximum prescribe pressure was reached inside the reservoir.

In addition, according to Kushnir et al. [18] and Zhou et al. [25], the air has been considered as a real gas through a compressibility factor (Z) that it is computed using the Berthelot gas state equation. Finally, considering a density value uniformly distributed in the volume, the pressure value of the CAES may be obtained at any instant by applying Equations (14) and (15).

$$P\_a = \left(\frac{R}{V}\right) Z m T\_a \tag{14}$$

$$Z = 1 - \frac{9}{128} \left(\frac{P\_a}{P\_c}\right) \left(\frac{T\_c}{T}\right) \left(\frac{6T\_c^2}{T^2} - 1\right) \tag{15}$$

where *Tc* and *Pc* the air temperature and the air pressure at critical conditions, assumed to be 132.65 K and 3.76 MPa. The contact surfaces between air-sealing layer (*A*1 = 2*πr*1*L*), sealing layer-concrete (*A*2~2*πr*2*L*), concrete-sandstone (*A*3~2*πr*3*L*), and sandstone-exterior (*A*4~2*πr*4*L*), are 359, 365, 545, and 1610 m2 , respectively. Note that, in order to model a complete cycle of compression (storing energy) and expansion (releasing energy) of the CAES system, the energy balance for the air domain—Equation (4)—needs to be rewritten as a function of the discharge mass flow rate (*m˙ out < 0*) and the air temperature within the reservoir, according to Equation (16):

$$\frac{dT\_a}{dt} = \frac{\dot{m}\_{out}}{m} \left[ \left( \frac{\mathbb{C}\_p}{\mathbb{C}\_v} - 1 \right) T\_a + \frac{1}{2\mathbb{C}\_v} \left( \frac{\dot{m}\_{out}}{m} L \right)^2 \right] - \frac{h2\pi r\_1 L}{\mathbb{C}\_v m} (T\_a - T\_1) \tag{16}$$

Air mass flow rates of 0.22 kg s−1 and −0.45 kg s−1 have been considered in the charge and discharge periods, respectively, for both RFP and steel sealing layers. The thermal properties and the volume of air, reinforced concrete, sandstone rock mass and sealing layers considered in the model are shown in Table 1 [24,25]. Note significant differences between the thermal conductivity of FRP and steel.

**Table 1.** Thermal properties and volume of air, concrete, sealing layers and sandstone rock mass.

### *2.3. CFD Numerical Model 2.3. CFD Numerical Model*

### 2.3.1. Model Geometry, Mesh and Boundary Conditions 2.3.1. Model Geometry, Mesh and Boundary Conditions

*Appl. Sci.* **2021**, *11*, x FOR PEER REVIEW 7 of 19

A 3D numerical model of a horseshoe-shaped tunnel located inside a closed mine was conducted to simulate the compression and decompression processes (air charging and discharging) that occur in the tunnel during the operation of the CAES plant. The computational domain is a tunnel with 8 m2 of cross section and 50 m in length and includes both the fluid area and the solid areas around the fluid. The configuration of the simulated tunnel is illustrated in Figure 3. To improve the geomechanical performance, a 4 m2 circular cross-section has been designed for the compressed air (blue area in Figure 3). The tunnel is reinforced with a 35 cm thick concrete lining and is finished with a dead-end. To avoid thermal leakage, a 20 mm thick sealing layer is considered between the air and concrete lining. Two types of sealing materials are considered: FRP and steel. The external part of the model corresponds to the 2.5 m thick sandstone rock mass existing in the mine. The total cross section of the model is 57.13 m2 (8 × 8 m) and the model volume is 2587 m3 . In addition, the useful volume of air reaches 200.53 m3 . The entire geometry is meshed with 2,690,038 hexahedral and tetrahedral cells. Finer mesh was defined in the sealing layer, concrete and air zones, with higher grid density in those regions where the gradients of the flow characteristics are extremely important. A 3D numerical model of a horseshoe-shaped tunnel located inside a closed mine was conducted to simulate the compression and decompression processes (air charging and discharging) that occur in the tunnel during the operation of the CAES plant. The computational domain is a tunnel with 8 m2 of cross section and 50 m in length and includes both the fluid area and the solid areas around the fluid. The configuration of the simulated tunnel is illustrated in Figure 3. To improve the geomechanical performance, a 4 m2 circular cross-section has been designed for the compressed air (blue area in Figure 3). The tunnel is reinforced with a 35 cm thick concrete lining and is finished with a deadend. To avoid thermal leakage, a 20 mm thick sealing layer is considered between the air and concrete lining. Two types of sealing materials are considered: FRP and steel. The external part of the model corresponds to the 2.5 m thick sandstone rock mass existing in the mine. The total cross section of the model is 57.13 m2 (8 × 8 m) and the model volume is 2587 m3. In addition, the useful volume of air reaches 200.53 m3. The entire geometry is meshed with 2,690,038 hexahedral and tetrahedral cells. Finer mesh was defined in the sealing layer, concrete and air zones, with higher grid density in those regions where the gradients of the flow characteristics are extremely important.

Sealing layer (Steel) 500 45 7.24 76.5

**Figure 3.** Computational domain. Mesh and boundary conditions used in CFD simulations. **Figure 3.** Computational domain. Mesh and boundary conditions used in CFD simulations.

Four different type of materials (air, sealing layer, concrete, and sandstone) are used to simulate the heat transfer process between the air inside the mine and the surrounding media. In addition, as in the analytical model, FRP and steel are considered as sealing layers. The air is defined as real-gas to allow the simulation of the compression process. To reproduce the concrete layer existing between the sealing layer and the sandstone, a solid material zone is defined. The sandstone and sealing layer zones are also defined as Four different type of materials (air, sealing layer, concrete, and sandstone) are used to simulate the heat transfer process between the air inside the mine and the surrounding media. In addition, as in the analytical model, FRP and steel are considered as sealing layers. The air is defined as real-gas to allow the simulation of the compression process. To reproduce the concrete layer existing between the sealing layer and the sandstone, a solid material zone is defined. The sandstone and sealing layer zones are also defined as solid materials. In addition, a series of thermal properties are imposed on the sandstone, concrete and sealing zones to simulate the conduction heat transfer.

The numerical simulation of the compression/expansion process was carried out with the commercial software ANSYS Fluent® 16.2. This code was used to solve the full 3-D Unsteady Reynolds-Averaged Navier–Stokes (URANS) equations for compressible flow. The coupling between velocity and pressure was resolved by the SIMPLE algorithm. The spatial and temporal derivatives of the governing equations for the fluid flow were calculated by means of a second-order discretization, and the pressure interpolation PREssure STaggering Option (PRESTO) scheme has been used. Turbulent closure was established by the RNG k–ε model together with standard wall functions. In addition, the resolution of the energy equation for both fluid and solid volumes was activated. A constant mass flow rate was imposed as an inlet boundary condition for each model and an interface condition was established for solid/solid and solid/fluid surfaces. To reduce the computational time, air mass flow rates of 50 kg s−1 and −75 kg s−1 were considered in the numerical simulations. In Section 3.3, these mass flow rates are also employed in the analytical model to carry out the comparative analysis. In addition, a constant temperature of 300 K was considered in the sandstone surface. Moreover, a no-slip shear condition was imposed on the walls. The material properties used in the numerical model have been indicated in Table 1. A fixed time step of 5 × 10−2 s was selected for the simulations to ensure their stable convergence. The convergence criteria is based on the residual values of the solution solved in the numerical domain. A typical threshold of 10−5 was set for continuity, momentum and energy equations.


**3. Stratified Institutions**

*Models with states* appear in myriad forms in computing science and logic. Classes of examples include at least

The institution theory answer to this is given by the theory of *stratified institutions* introduced in [51,60] and further developed or invoked in works such as [52,53,56–58], etc. Informally, the main idea behind the concept of stratified institution as introduced in [51,60] is to enhance the concept of institution with 'states' for the models. Thus, each model *M* comes equipped with a *set* [[*M*]] that has to satisfy some structural axioms. The following definition has been given in [52] and represents an important upgrade of the original definition from [51], the main reason being to make the definition of stratified institutions really usable for conducting in-depth model theory. A slightly different upgrade has been proposed in [53], which is however strongly convergent to the upgrade proposed in [52].

A *stratified institution* S is a tuple (*Sign*S, *Sen*S, *Mod*S, [[\_]]S, |=S ) consisting of:

Until this point, this definition is identical to that of an ordinary institution. However, now comes the additional structure that provides explicitly the states of the models.

$$\text{Mod}^{\mathcal{S}}(\varphi)M'\ (\vdash^{\mathcal{S}})\mathop{\mathbb{L}}^{[M']\_{\varphi}w}\_{\mathcal{P}}\ \text{of}\ \text{and}\ \text{only}\ \text{if}\ \ M'\ (\vdash^{\mathcal{S}})^w\_{\varphi\Box}\ \text{Sen}^{\mathcal{S}}(\varphi)\rho\tag{2}$$

holds for any signature morphism *ϕ*, *M* ∈ |*Mod*S (*ϕ*✷)|, *w* ∈ [[*M* ]]S *ϕ*✷, *ρ* ∈ *Sen*S (✷*ϕ*). As for ordinary institutions, when appropriate, we shall also use simplified notations without superscripts or subscripts that are clear from the context.

The lax natural transformation property of [[\_]] is depicted in the diagram below

with the following compositionality property for each Σ -model *M* :

$$\left[\left[M^{\prime\prime}\right]\_{\left(q\circ q^{\prime}\right)} = \left[M^{\prime\prime}\right]\_{q^{\prime}\prime} \left[\left[M\text{od}\left(q^{\prime}\right)M^{\prime\prime}\right]\right]\_{q^{\prime}}.\tag{3}$$

Moreover, the natural transformation property of each [[\_]]*ϕ* is given by the commutativity of the following diagram:

$$\begin{array}{c} \begin{array}{c} \left[M'\right] \left[\Sigma'\right] \xrightarrow{\left[M'\right]\_{\mathcal{F}}} \left[\operatorname{Mod}(\boldsymbol{\varrho})M'\right] \Sigma\\ \left[h'\right] \end{array} \end{array} \qquad \begin{array}{c} \left[M'\right] \left[\Sigma'\right] \xrightarrow{\left[M'\right]\_{\mathcal{F}}} \left[\operatorname{Mod}(\boldsymbol{\varrho})M'\right] \Sigma\\ \left[h'\right] \end{array} \qquad\qquad \begin{array}{c} \left[\left[\operatorname{Mod}(\boldsymbol{\varrho})h'\right]\Sigma\\ \left[\left[N'\right]\right]\_{\Sigma'} \xrightarrow{\left[N'\right]\_{\mathcal{F}}} \left[\operatorname{Mod}(\boldsymbol{\varrho})N'\right] \Sigma \end{array} \end{array} \tag{4}$$

The satisfaction relation can be presented as a natural transformation

$$\left| = : \operatorname{Sen} \Rightarrow \left[ \left[ \operatorname{Mod}(\\_) \to \mathbf{Set} \right] \right] \right| $$

where the functor [[*Mod*(\_) → **Set**]] : *Sign* → **Set** is defined by

$$\mathbb{E}[\operatorname{Mod}(\varrho) \to \mathbf{Set}](f)(\mathcal{M}') = [\![\mathcal{M}']\!]\_{\varrho}^{-1}(f(\operatorname{Mod}(\varrho)\mathcal{M}')).$$

A straightforward check reveals that the Satisfaction Condition (2) appears exactly as the naturality property of |=:

$$\begin{array}{l} \tiny\begin{array}{l} \Sigma\\ \Leftrightarrow\\ \Sigma'\\ \end{array} \end{array} \begin{array}{l} \scriptstyle \mathit{Sen}(\Sigma) \xrightarrow{\left\| \begin{array}{l} \vdash \Sigma\\ \Longrightarrow\\ \end{array} \right\|} \begin{array}{l} \llbracket \mathit{Mod}(\Sigma) \rightarrow \mathit{Set} \end{array} \end{array} \begin{array}{l} \scriptstyle \mathit{[Mod}(\Sigma) \rightarrow \mathit{Set} \end{array} \end{array} \begin{array}{l} \scriptstyle \mathit{[Mod}(\Sigma) \rightarrow \mathit{Set} \end{array} \begin{array}{l} \scriptstyle \mathit{Set} \end{array} \end{array}$$

Ordinary institutions are the stratified institutions for which [[*M*]]Σ is always a singleton set. In the upgraded definition, the surjectivity condition on [[*M* ]]*ϕ* from [51] has been removed, as it can be made explicit when necessary. This is motivated by the fact that most of the results developed do not depend upon this condition which, however, holds in all examples known by us. On the one hand, in many important concrete situations (Kripke semantics, automata, etc.), [[*M* ]]*ϕ* are even identities, which makes [[\_]] a strict rather than a lax natural transformation. However, on the other hand, there are interesting examples when the stratification is properly lax, such as in the OFOL example below or the representation of 3/2 institutions as stratified institutions developed in [58].

The literature on stratified institutions shows many model theories that are captured as stratified institutions. Here, we recall some of them in a very succint form; for a more detailed form, one may find them in [52,57,58].

That was the brief presentation of the concept of stratified institution together with a list of relevant concrete examples. In the remaining part of this section, we will present some of the most important model theoretic developments with stratified institutions as follows:

## *3.1. Flattening Stratified Institutions to Ordinary Institutions*

Given any stratified institution S = (*Sign*, *Sen*, *Mod*, [[\_]], |=), in [52], we have built an ordinary institution S = (*Sign*, *Sen*, *Mod* , |= ) as follows:

$$(\mathcal{M}od^\sharp(\mathcal{q})(\mathcal{M}', w') = (\mathcal{M}od(\mathcal{q})\mathcal{M}', [\![\mathcal{M}']\!]\_{\mathcal{q}}w'); \mathcal{q}$$

– For each Σ-model *M*, each *w* ∈ [[*M*]]Σ, and each *ρ* ∈ *Sen*(Σ)

$$((M, w) \mathop{\mid\=}^{\sharp}\_{\Sigma} \rho) = (M \mathop{\mid\=}^{w}\_{\Sigma} \rho). \tag{5}$$

In [57], the construction of S is explained as a categorical universal construction. That explanation involves the concept of *morphism of stratified institutions* which is an extension of the notorious concept of *morphism of institutions* (cf. [18,44,46], etc.). Both concepts represent mappings that preserve the mathematical structure of stratified institutions and of ordinary institutions, respectively, in the same way group homomorphisms preserve the group structure, or the continuous functions preserve the structure of topological spaces. Thus, (\_) arises as a left-adjoint functor from the category **SINS** of strict stratified institutions to the category **INS** of ordinary institutions. One way to present this is that for each institution B, there exists a stratified institution B and an institution morphism *ε*B : B → B such that for each morphism of institutions(Φ, *α*, *β*) : S → B, there exists a unique strict stratified institution morphism (Φ, *α*, *β* ) : S → B such that the following diagram commutes:

The construction S , called the *flattening of* S, on the one hand reduces stratified institutions to ordinary institutions without any loss of information. It is helpful for transferring concepts and results from the simpler world of ordinary institution theory to that of stratified institutions. One important example of that is given by the model amalgamation property, which is one of the most fundamental properties of institutions with vast consequences both in computing science and in institutional model theory (cf. [25,44,65], etc.). Model amalgamation in S defines the so-called *stratified model amalgamation* in S [57], which is more refined than plain model amalgamation in S and is a characteristic only to stratified institutions. On the other hand, it is important to avoid the trap of believing that in this way, the theory of stratified institutions can be dealt with entirely within the

ordinary institution theoretic framework. The reason for this cannot be the case that the institutions S are not any institutions, as they have a very specific structure given by the stratified structure of S.

Another way to reduce a stratified institution to an ordinary institution is to flatten only the satisfaction relation, i.e.,

$$\text{If } M \vdash^\* \rho \text{ if and only if } \ M \vdash^w \rho \text{ for each } w \in \lbrack M \rbrack.$$

This yields an institution when the stratification is surjective (i.e., for each signature morphism *ϕ* and each *ϕ*✷-model *M* , [[*M* ]]*ϕ* is surjective). However, in this institution, denoted S∗, the locality aspect of S—which is very important—is lost. In the literature, S∗ and S are known as the *global* and the *local*, respectively, institutions associated to S. They can be regarded as high abstractions of the global and of the local satisfaction in modal logic.


**Abstract**

This chapter describes the pectin production process from citrus residues. It discusses the importance of essential oils removal before processing through steam distillation, hydrodistillation, or solvent extraction. Also, it presents different extraction methods (acid hydrolysis, microwave-assisted acid hydrolysis, and hydrodistillation) that have been employed and different solvents that can be used for its purification. Since all these processing parameters can affect the final pectin yield and quality, a discussion is made on which processing options and conditions could be used based on recently reported data. The best operational conditions based on the percentages of pectin recovery and their relationship with quality parameters, such as the galacturonic acid content and degree of esterification are presented. Finally, a discussion is made regarding the opportunities for its integration under the biorefinery concept that could help to enhance several economic and environmental aspects of the process.

**Keywords:** pectin, citrus residues, bioactive compounds, biorefinery, sustainability


*4.3. Smart City 3.0*

Smart city 3.0 is the third phase of smart city development, which is characterized by a focus on innovation, resilience, and adaptability in the face of emerging challenges and opportunities. During Smart City 3.0, cities are leveraging emerging technologies, such as blockchain, the IoT, and autonomous systems, to create more resilient and adaptive urban environments [200]. This includes the use of smart infrastructure systems, such as selfhealing power grids and automated water management systems, to enhance the reliability and resilience of critical urban services. Another key feature of Smart City 3.0 is the use of innovation ecosystems and digital innovation hubs to foster innovation and entrepreneurship in urban areas. This includes the establishment of co-working spaces, incubators, and accelerators to support startups and small businesses, as well as the integration of universities and research institutions into the urban innovation ecosystem [201].

#### *4.4. Smart City 4.0*

Smart city 4.0 is a theoretical concept that refers to the next phase of smart city development beyond smart city 3.0. While Smart City 4.0 is not yet fully defined, it is expected to build on the foundations of previous phases and further integrate emerging technologies, such as artificial intelligence, 5G networks, and edge computing, to create even more intelligent, responsive, and interconnected urban environments [202]. It is likely to focus on creating highly personalized and immersive experiences for citizens and visitors, through the use of virtual reality (VR) and augmented reality (AR) technologies, and the development of smart spaces that adapt to individual needs and preferences. It is also expected to involve greater collaboration between cities and private sector partners, as well as more decentralized and distributed models of governance [203].

#### *4.5. Global Smart Cities*

#### 4.5.1. Singapore

Singapore is known for its advanced transportation system, which includes an extensive network of public buses, trains, and taxis. The city also uses smart sensors and data analytics to manage traffic flow and reduce congestion. Additionally, Singapore has implemented a number of smart solutions to improve energy efficiency and reduce its carbon footprint [204,205]. The following are the features of the smart city of Singapore:

energy consumption. This data is then analyzed to identify patterns and trends, which helps authorities to make informed decisions [179,204].


*3.1. Description of the Company Studied*

The subject of the research is a company manufacturing plastic garbage bags. It is a three shift serial production, with 8-h shifts. The roller welding machines, which weld and perforate finished rolls of polyethylene film, constitute a critical element of the whole process. Among all the machines in the production line, the efficiency of the roller welding machines is the lowest, they have the highest failure rate and their downtimes lead to substantial increase in costs, making them a bottleneck in the process. This is why they became the subject of the study. The analysis was carried out on the example of a selected model, marked with the H2 symbol.

The analysis of the activities carried out when operating the roller welding machines allowed to distinguish the states of the machine. They are presented in the Table 1.

Among the selected states, those directly related to the production process should be distinguished: S1—manufacturing process, S4—necessary maintenance activities to keep the machine in good working order and to prepare it for the manufacturing process. Planned employee breaks, resulting from the Labor Code (S5), also constitute a necessary element of the manufacturing process. Other states should be identified as undesirable. These include the stoppage in the manufacturing process, due to lack of orders, S3, and lack of raw materials, S6.

The relationships between the individual states are shown in Figure 1.

**Figure 1.** Diagram of the inter-state transitions of the process studied.

#### *3.2. Studying Markov's Property*

In the first stage, the lack of memory characteristic of the process was assessed. The goodness of fit test χ2 was used for the study, defining at the level of significance α = 0.05 the zero hypothesis assuming that the chain studied meets the Markov property, and the alternative hypothesis that the Markov property is not met [11]. The test statistic χ2 = 228.7, while related to it *p*-value = 0.264, which means that there are no grounds to reject the zero hypothesis on the chain meeting the Markov property.