Challenges in Assessing Useful Exergy and Its Significance for Economic Development Studies: An Examination of Mozambique’s Economics Sectors, 1971–2014

Abstract

This chapter presents and analyses the outcomes derived from estimating useful exergy data associated with the final electricity usage in Mozambique’s productive sectors—encompassing industry, commerce, and services—covering Mozambique, from 1971 to 2014. At the time of carrying out the research, the availability of International Energy Agency (IEA) data relating to Mozambique was only from 1971 to 2014. The societal exergy analysis methodology used to estimate useful exergy involved first converting the final electricity use into its exergetic equivalent. Then, this exergy was categorized according to its specific end uses. Finally, the useful exergy was calculated by applying the appropriate efficiency rates for each usage category. The electricity consumption data, measured in GWh, was sourced from the IEA database. The findings indicate a significant increase in final electricity consumption starting in 2000. While there was a noticeable rise in useful exergy in the trade and services sector, the industry sector’s contribution remained dominant. The most significant contributions to total useful exergy were mechanical work in the industry sector, followed by high-temperature heat production. As useful exergy represents the effective portion of exergy reflecting energy usage outcomes, it emerges as a crucial concept for analyzing the link between energy consumption and economic growth.

1. Introduction

While mainstream economics traditionally emphasizes capital and labor as the primary factors of production, this chapter contends that energy and exergy are equally vital for the production process and economic growth analyses. This perspective aligns with the first two laws of thermodynamics asserting that in all real processes, energy is conserved (first Law) but degraded (second Law). The degradation of energy can be measured as a loss of its ability to perform mechanical work, commonly referred to as exergy [1].

Considerable evidence supports the contention that energy is crucial for economic growth, and in the production process, there is no substitute for energy. Although different energy sources can be substituted, energy as a whole cannot. Hence, energy is as integral to the production process as capital and labor. Without energy, generating a product is impossible, making energy more than a mere component of production costs; it is an intrinsic part of the production process. Analyzing the relationship between energy consumption and economic dynamics is more effective when using useful exergy, that is. the exergy of the heat produced by the electric radiator or mechanical work produced by the electric motor, compared to final electricity consumption (FEC) [2, 3].

Despite the significance of energy, there is a notable absence of exergy studies, particularly in African countries. No useful exergy research related to Mozambique has been found [2, 3]. Concerning Africa, the research conducted by Ref. [4] focused on determining the exergetic efficiencies of electricity and fuel consumption in South Africa, examining various sectors and overall usage. Their study estimated that the exergetic efficiency of the mining industry, the most dominant sector in South Africa, is approximately 83%. Ultimately, the researchers argue that the performance of exergy utilization in the South African industry can be enhanced by adopting different forms of conservation. Turning to Ref. [5], their analysis encompasses Ghana and the United Kingdom. They examine the relationship between the imperative to reduce energy consumption and Gross Domestic Product (GDP) growth (absolute decoupling), considering climate change objectives by 2030. The researchers conclude that achieving “absolute decoupling” between primary energy consumption and economic activity will be very challenging for both Ghana, as a growing economy requiring more energy to sustain its growth, and the United Kingdom, where energy consumption is expected to remain constant in the future to ensure GDP growth. Additionally, they assert that energy efficiencies alone are not effective in reducing primary energy consumption or carbon dioxide (CO2) emissions.

Regarding global studies on exergy, Ref. [6] analyses the exergetic efficiencies inherent to the different forms of exergy use while [7] reconstructs the different forms of electricity use in the United States of America (USA) economy, from 1900 to 1998, using different data sources. The electricity uses were classified into: lighting, heating (high and low temperatures), mechanical work, electrolysis, and electronic devices. Results showed that the USA largest consumption was for mechanical work and that the final to useful aggregated exergy efficiency of electricity remained unchanged during the twentieth century. This is consistent with results obtained by Ref. [8] that show that despite technological evolution, the World final-to-useful end-use efficiency was surprisingly constant (∼48%), due to “efficiency dilution,” wherein individual end-use efficiency gains are offset by increasing uptake of less efficient end uses.

The study [9] discusses the usefulness of the concept of exergy for all systems subject to mass and energy flows and argues that economic and ecological systems are highly coupled, given the possibility of irreversible depletion of the available planetary stocks of exergy.

This chapter aims to present and analyses the results and constraints of constructing useful exergy data associated with the FEC of Mozambique’s economic productive sector, encompassing industry, commerce, and services from 1971 to 2014. This period is imposed by the availability of IEA data relating to Mozambique, which at the time of carrying out the research, were only from 1971 to 2014.

These data hold significance for studying the role of useful exergy in Mozambique’s economic growth, thereby contributing to the ongoing debate on this subject.

Economic growth, quantified by the evolution of GDP, is not solely dependent on input availability but also on effective work derived from FEC. Consequently, from an engineering standpoint, production—whether industrial or otherwise—requires energy-driven work [1].

In the production process, useful exergy is essential because work transforms inputs into final products. Useful exergy finds applications in various sectors, such as industry, where it powers machines through mechanical drive, involving the conversion of electricity into mechanical energy [10]. Additionally, it plays a crucial role in heating processes, such as those employed in smelting or firing processes within heater systems.

Addressing the relevance of energy in Mozambique’s economy, the Industrial Policy and Strategy for 2016–2025 (IPS) identifies poor electricity access in many regions, particularly outside urban areas, and high electricity costs as key structural constraints for industrial development in the country.

Following this introduction, the second section delves into the concept of useful exergy, the third section presents data and methods, the fourth section outlines the results, and the final section encompasses the discussion and conclusions.

2. From exergy to useful exergy

Exergy is the useful part of the energy of a system in a specific environment, that is. the maximum amount of work, whether mechanical, heat generation, lighting, or other, that a system can perform until achieving equilibrium with its environment [10].

For a closed system in steady state, the exergy balance corresponds to the Eq. (1) [4]:

$$\sum _r{E}^{Q^r}-E^w-I=0$$E1

Where:

$E^{Q^r}$ and $E^w$ indicate the values of exergy associated with heat transfer $(Q^r)$ and the performance of the work (W) provided by the system.

Also, according to Ref. [4], when the heat transfer $(Q^r)$ occurs in a space with uniform temperature, $T_r$, and $T_o$, and the environment temperature¹, then the associated thermal exergy is given by:

$$E^{Q^r}=\left(1-\frac{T_0}{T_r}\right).Q^r$$E2

On the other hand, the exergy of mechanical work is expressed as being [4]:

$$E^w=W$$E3

The exergy flows, $E^{Q^r}$ and $E^w$, measure the quality of the energy flow in its state of use, akin to an energy service, resulting in what is commonly referred to as “useful work” [1].

I denotes the exergy consumed or lost due to irreversibility, conferred by the second law of thermodynamics.

In a real process, the exergy destruction is the quality of energy that is destroyed, which is proportional to the entropy production [12]. Therefore, the consumption of exergy is greater than zero for any irreversible process and equal to zero for reversible processes.

The idea of exergy as the maximum amount of work that can be produced from a given energy flow is conceptually shared among exergy authors [3, 13], and so it will be understood in this chapter, as the part of the energy used to generate work during production processes, while the useful exergy is obtained as a result of applying the conversion efficiencies related to each end use.

3. Data and methods

The methodology applied for the construction of useful exergy series is the societal exergy analysis [14]. The FEC data are in GWh. The data are from IEA database, covering the period of 1971 to 2014, by sectors of activity, excluding, in this chapter, the residential sector. There is no data related to the Mozambican agricultural sector.

The total FEC trend, in Figure 1, indicates that there are two distinct periods: first, from 1971 to 1999 and, second, from 2000 to 2014. The second period is strongly influenced by the beginning of MOZAL’s activities in Mozambique, an industry of aluminum smelter with final electricity consumption corresponding to 45% of the country’s consumption.

Figure 1.

Exergy by end uses: Industrial sector.

The methods followed three steps: (1) the conversion of FEC into exergy, (2) the allocation of final exergy consumption, per sector, to the different end uses, and (3) the application of the final exergy efficiencies, according to end uses, to obtain the useful exergy data per sectors for Mozambique. The total useful exergy data was obtained by summing the disaggregated results.

Exergy conversion factors were applied to obtain exergy data. In the case of electricity, the conversion factor to exergy is equal to one.

The end uses for industrial, commercial and services sectors followed the end uses obtained from the literature [7, 15, 16], which indicate types of end uses, such as mechanical drive, heat, lighting, cooling, and other uses.

In the case of industry, five end uses have been identified: the use of electricity for mechanical work, heat production, lighting, cooling, and electrolysis processes. For the commerce and services sector, four use-ends were found for lighting, cooling, heat, and electronics uses.

Useful work, which is useful exergy, is calculated as [12]:

$$U_{tjk}={\epsilon }_{tk}\varphi E_{tjk}$$E4

Where:

1. j—represents economic sectors,

2. k—indicates the category of usage types,

3. t—is the time,

4. ${\epsilon }_{tk}$ —are the exergy efficiencies by usage types;

5. $\varphi$ —denotes the exergetic factor for each type of energy source (the exergetic factor is equal to 1 for electricity), and.

6. $E_{tjk}$ —is the exergy obtained by type of use for each production sector.

Considering the specified end uses for each sector, it is essential to apply the corresponding exergy efficiencies to derive the useful exergy for each sector. Examining mechanical drive, historical data indicates that in 1970, industrial engines demonstrated an average efficiency of approximately 70%. Subsequent advancements led to an increased average efficiency, reaching around 85% in 1980 and further climbing to 90% in the 2000s [7].

A comprehensive investigation into lighting within the US industrial sector in 1946 disclosed that lighting efficiencies accounted for about 7.7% of industrial electricity consumption at that time [7]. The efficiency of lighting is contingent upon the type of lamp used. In 1970, the efficiency for incandescent lamps was 5%, while that for fluorescent lamps was 20% [7]. Determining the applicable efficiency should consider the predominant lamp type in use within production units. However, in many instances, data related to the predominant lamp types in different economic sectors is not available. Over time, lighting efficiencies exhibited notable improvements from 7% in 1940 to 8.5% in 1960, 11% in 1980, and further advancing to 13% in 2000 [7].

In the context of cooling associated with air conditioning, the efficiency is estimated to be around 0.3 [8]. Refrigeration, on the other hand, experienced a notable efficiency increase from 75% in 1960 to 85% in 2000, attributed to advancements in equipment enhancing overall efficiency [7]. The efficiency of heat at high temperatures also underwent changes over time, progressing from 87% in the 60s and 70s to 89% in 1980, culminating in 90% by 2000 [7].

Heat exergy efficiencies are calculated using Carnot efficiency. The exergetic efficiency of heat production depends on the environment and the system temperature [15]. For heat production, three subcategories were established giving the system temperature: High-temperature heat (HTH), for temperatures above 500°C (industrial uses); medium temperature heat (MTH), for temperatures between 500°C and 120°C; and Low-temperature heat (LTH), for uses below 120°C [15]. LTH uses can be further disaggregated into three other sub-subcategories: LTH 1, for uses between 120°C and 90°C; LTH2, for uses between 90°C and 50°C; and LTH3, for uses below 50°C. In this study, LTH2 was assumed for commerce and service sectors [15]. For LTH, electric heat has an exergetic efficiency of around 10% [10].

In this study, the efficiencies adopted were adapted from Ref. [15] for mechanical work, heat production, lighting, cooling, and others, as discussed in point 4 of this paper. The efficiencies applied are part of Appendices A and B.

4. Results

4.1 Exergy allocations by end uses

Results of exergy by end uses are shown in Figures 1 and 2.

Figure 2.

Exergy by end uses: Commercial and service sector.

Figure 1 shows the exergy allocated by end uses in the production processes of industrial sector, including mechanical drive, applied for running machines, cooling, lightning, heat and electrolysis processes applied, especially in aluminum industries..

Up until 1999, the predominant utilization of exergy in the industrial sector was in mechanical drive. However, starting from 2000 onwards, the most significant application shifted to electrolysis, corresponding to the introduction of the aluminum industry, particularly with the establishment of MOZAL. In contrast, for the commerce and service sector, among the end uses found in this sector, the primary use throughout the entire period remained cooling, as depicted in Figure 2.

Figures 1 and 2 illustrate the exergy uses in both sectors, giving the pattern of uses according to the energy needs of each sector.

The next stage was to obtain the useful exergy data by applying exergy efficiencies related to each type of end uses. Details about the efficiencies applied are in Appendices A and B at the final of the chapter..

4.2 Useful exergy data

Figure 3 shows the useful exergy data obtained for industrial and for commercial and services, including the total useful exergy of both sectors.

Figure 3.

Useful exergy by sector and total.

The findings indicate that the total useful exergy is primarily influenced by the useful exergy generated within the industrial sector.

4.2.1 Total useful exergy

Figure 4 illustrates the total useful exergy, revealing a dynamic pattern akin to that of FEC. This resemblance can be attributed to the diminished impact of heat end uses in Mozambique. As previously highlighted, the conversion of electricity to exergy follows a nearly one-to-one ratio for various end uses, with the exception of processes involving heat.

Figure 4.

Total useful exergy.

From 2000 onwards, the energy needs of the industrial sector arose steadily as a result of the sector recovery and the effectiveness of direct international investment, like that of the implementation of MOZAL, accrued after the cease-fire in 1992, and after the implementations of the first democratic government.

Figure 5 provides a detailed depiction of the useful exergy within the commercial and service sector. The findings reveal a seasonal dynamic in this sector from 1971 to 1991, followed by a steady growth trend from 1992 until 2011. This upward trajectory corresponds to the postwar period, specifically after the conclusion of the conflict in 1992. Conversely, the decline in 2000 is associated with the occurrence of a significant flood that affected the economy.

Figure 5.

Useful exergy of commercial and services sector.

4.2.2 Efficiency of useful exergy

Figure 6 illustrates the overall efficiency of useful exergy. The efficiency of useful exergy represents the ratio of useful exergy to FEC (both total and by sectors). This ratio serves as an indicator of the efficient utilization of the FEC.

Figure 6.

Total efficiency of useful exergy.

The results indicate that from 2000 onwards, despite the increase in total useful exergy, the overall efficiency of useful exergy was lower than in the previous period. This is attributed to the substantial contribution of electrolytic uses during this period, which exhibit lower efficiencies compared to mechanical drive, the dominant factor in the preceding period. Below are the total efficiencies of useful exergy categorized by sectors: Industrial, commercial, and services sectors ²:

Figure 7, depicting the total efficiency of useful exergy by sectors, reveals a notably high efficiency for the industrial sector. This is attributed to the substantial utilization of both FEC and useful exergy within that sector, as compared to the commercial and service sector. The disparities in energy demand between the two sectors also contribute to this variation.

Figure 7.

Total efficiency of useful exergy by sectors.

5. Conclusions

The total amount of useful exergy remained nearly constant from 1971 until 1990, experiencing moderate growth between 1991 and 1999. Subsequently, an explosive growth phase occurred between 2000 and 2004, maintaining an upward trajectory until 2013. A brief stagnation in 2001 and 2002 is attributed to the 2000 floods, impacting the productive sector and the economy at large.

The total useful exergy is strongly influenced by the industrial sector. Although the useful exergy of the commerce and services sector has shown modest growth, the total useful exergy had a significant growth induced by the growth of the useful exergy of the industrial sector.

However, a closer examination of the commerce and services sector reveals a change in dynamic trends over time. From 1971 to 1978, there was an increasing trend, followed by a decline from 1979 to 1985, coinciding with a period of economic crisis and the introduction of the Economic Structural Adjustment Plan in 1987. From 1986 to 1999, the useful exergy of the commerce and services sector grew rapidly. Despite a notable drop in 2000 due to severe floods, there was a recovery in 2001. However, a substantial decline occurred between 2012 and 2013.

Regarding end uses, the industry sector’s mechanical work made the greatest contribution to total useful exergy. Post-2000, the total efficiency of useful exergy was lower than in the preceding period.

Several limitations affect this analysis, including a lack of detailed data on various economic sectors, especially the absence of data on FEC uses and the agriculture sector for Mozambique. Additionally, detailed efficiencies associated with different end uses suitable for the technological stage of underdeveloped countries are unavailable. Despite these constraints, this study serves as a foundational point for future research, incorporating diverse energy sources for determining the country’s total useful exergy.

In conclusion, useful exergy, as an indicator of the outcome of energy use, holds significance for analyzing the nexus between energy consumption and economic growth. Policymakers must prioritize providing records of energy end uses and exergy efficiencies sensitive to the technological stage of underdeveloped countries, such as Mozambique. This is crucial for conducting more precise and accurate analyses of the dynamic relationship between energy and economic factors.

Acknowledgments

The authors wish to thank Tiago Domingos, from IST - Lisbon University, for his invaluable suggestions.

This work was supported by the FCT (Fundação para a Ciência e a Tecnologia) [grant number UIDB/05069/2020].

Conflict of interest

The authors declare no conflict of interest.

Appendix A

See Table A1.

Year	Electrolysis (%)	Mechanical drive (%)	Cooling (%)	Light (%)	Heat (%)	HTH (aluminum) (%)
1970	32.41	83.45	11.31	0.90	32.37	62.51
1971	32.66	83.67	11.29	1.14	32.67	62.58
1972	32.91	83.88	11.28	2.74	32.96	62.64
1973	33.16	84.10	11.26	2.74	33.08	62.52
1974	33.41	84.28	11.28	2.75	33.31	62.54
1975	33.66	84.46	11.30	2.73	33.52	62.54
1976	33.91	84.65	11.33	2.72	33.71	62.52
1977	34.17	84.83	11.35	2.71	33.90	62.52
1978	34.42	85.01	11.37	2.71	34.05	62.48
1979	34.67	85.19	11.39	2.70	34.27	62.52
1980	34.92	85.38	11.42	2.69	34.40	62.48
1981	35.17	85.56	11.44	2.68	34.49	62.41
1982	35.42	85.74	11.46	2.68	34.71	62.47
1983	35.68	85.92	11.48	2.67	34.87	62.47
1984	35.93	86.11	11.51	2.66	35.05	62.51
1985	36.18	86.29	11.53	2.66	35.14	62.46
1986	36.43	86.47	11.55	2.65	35.30	62.48
1987	36.70	86.72	11.58	2.69	35.34	62.39
1988	36.96	86.97	11.61	2.72	35.54	62.47
1989	37.23	87.23	11.64	2.76	35.55	62.37
1990	37.50	87.48	11.67	2.80	35.70	62.4
1991	37.77	87.73	11.70	2.83	35.86	62.46
1992	38.03	87.98	11.74	2.87	35.98	62.47
1993	38.30	88.24	11.77	2.91	36.15	62.55
1994	38.57	88.49	11.80	2.95	36.14	62.45
1995	38.83	88.74	11.83	2.98	36.09	62.30
1996	39.10	88.99	11.86	3.02	36.31	62.43
1997	39.37	89.25	11.89	3.06	36.27	62.32
1998	39.64	89.50	11.92	3.10	36.44	62.41
1999	39.90	89.75	11.95	3.13	36.55	62.45
2000	40.17	90.00	11.98	3.17	36.58	62.41
2001	40.44	90.25	12.01	3.21	36.62	62.45
2002	40.70	90.51	12.04	3.24	36.60	62.42
2003	40.97	90.76	12.07	3.28	36.56	62.38
2004	41.24	91.01	12.10	3.32	36.58	62.41
2005	41.51	91.26	12.13	3.36	36.58	62.41
2006	41.74	91.52	12.14	3.41	36.52	62.34
2007	41.98	91.77	12.16	3.47	36.61	62.43
2008	42.22	92.02	12.17	3.52	36.61	62.43
2009	42.46	92.28	12.18	3.58	36.50	62.33
2010	42.69	92.53	12.19	3.63	36.56	62.38
2011	42.93	92.79	12.20	3.69	36.49	62.32
2012	43.17	93.04	12.21	3.75	36.58	62.41
2013	43.41	93.29	12.22	3.80	36.61	62.43
2014	43.64	93.55	12.23	3.86	36.57	62.39

Table A1.

Industry exergy efficiencies by type of uses.

Source: Felício et al. [15].

Appendix B

See Table A2.

Year	LTH2 (%)	Light (%)	Mechanical drive (%)	Cooling (refrig) (%)	Cooling (AC) (%)	Electronics (%)
1970	20.18	0.90	76.33	14.70	4.17	0.04
1971	20.32	1.14	76.41	14.68	4.17	0.04
1972	20.46	2.74	76.50	14.66	4.17	0.04
1973	20.21	2.74	76.59	14.64	4.17	0.04
1974	20.24	2.75	76.72	14.67	4.17	0.05
1975	20.24	2.73	76.84	14.69	4.17	0.06
1976	20.21	2.72	76.97	14.72	4.17	0.08
1977	20.21	2.71	77.09	14.75	4.17	0.09
1978	20.13	2.71	77.22	14.77	4.17	0.10
1979	20.21	2.70	77.34	14.80	4.17	0.11
1980	20.13	2.69	77.47	14.82	4.17	0.13
1981	19.9	2.68	77.59	14.85	4.17	0.14
1982	20.1	2.68	77.72	14.88	4.17	0.15
1983	20.10	2.67	77.84	14.90	4.17	0.16
1984	20.18	2.66	77.97	14.93	4.17	0.18
1985	20.07	2.66	78.09	14.96	4.17	0.19
1986	20.13	2.65	78.22	14.98	4.17	0.20
1987	19.94	2.69	78.31	15.02	4.24	0.27
1988	20.10	2.72	78.40	15.06	4.31	0.34
1989	19.88	2.76	78.49	15.09	4.38	0.41
1990	19.96	2.80	78.59	15.13	4.45	0.49
1991	20.07	2.83	78.68	15.16	4.52	0.56
1992	20.10	2.87	78.77	15.20	4.59	0.63
1993	20.27	2.91	78.87	15.24	4.66	0.70
1994	20.05	2.95	78.96	15.27	4.73	0.77
1995	19.74	2.98	79.05	15.31	4.80	0.84
1996	20.02	3.02	79.14	15.34	4.87	0.92
1997	19.77	3.06	79.24	15.38	4.94	0.99
1998	19.96	3.10	79.33	15.42	5.01	1.06
1999	20.05	3.13	79.42	15.45	5.08	1.13
2000	19.96	3.17	79.52	15.49	5.15	1.20
2001	20.05	3.21	79.61	15.53	5.22	1.27
2002	19.99	3.24	79.70	15.56	5.29	1.34
2003	19.91	3.28	79.80	15.60	5.36	1.42
2004	19.96	3.32	79.89	15.63	5.43	1.49
2005	19.96	3.36	79.98	15.67	5.50	1.56
2006	19.83	3.41	80.09	15.68	5.16	1.60
2007	20.02	3.47	80.21	15.70	4.83	1.64
2008	20.02	3.52	80.32	15.71	4.50	1.69
2009	19.80	3.58	80.43	15.72	4.16	1.73
2010	19.91	3.63	80.54	15.73	3.83	1.77
2011	19.77	3.69	80.66	15.75	3.49	1.81
2012	19.96	3.75	80.77	15.76	3.16	1.86
2013	20.02	3.80	80.88	15.77	2.82	1.90
2014	19.94	3.86	80.99	15.78	2.49	1.94

Table A2.

Commerce and services exergy efficiencies by type of uses.

Source: Felício et al. [15].

Acronyms

FEC	Final electricity consumption
GDP	Gross domestic product
CO2	Carbon dioxide
IEA	International energy agency
ISP	Industrial policy and strategy
HTH	High-temperature heat
LTH	Low-temperature heat
USA	United States of America