Using Exergy-Based Metrics in Assessing Sustainability of Fossil-Fueled Thermal Energy Systems

Abstract

This chapter examines the importance of exergy-based parameters like exergy efficiency, environmental compatibility, sustainability index, depletion number, and improvement potential of hydrocarbon fuel utilization. The main import of system exergy efficiency is relatively well-known. A hydrocarbon fuel environmental compatibility (ζ) evaluates the fuel exergy performance when its combustion gases emission abatement exergy is factored in. A fuel with low emission abatement exergy has a high environmental compatibility and, thus, high sustainability. Another metric is the depletion number, Dp. This measures the rate of fuel exergy destruction with respect to the fuel input exergy. Since fuel exergy flow is directly related to its material flow, its exergy destruction is similarly directly related to its material depletion. Hence, fuel utilization sustainability necessitates a low Dp. Dp indicates the fraction of input energy resources degraded through entropy creation, turning them into thermodynamic states of no useful energy values. The sustainability index is the reciprocal of Dp. The Improvement Potential (IP) is, mathematically, the product of the square of Dp and the fuel input exergy. When IP is high, it means the exergy losses are too high and there is a big room for exergy efficiency improvement.

1. Introduction

Every activity in the cosmos, anywhere, anytime, involves energy utilzsation through its transformation. This transformation process is guided and dictated by relevant natural laws. The most important and relevant natural laws in energy transformation are the first and second laws of thermodynamics. While the first law stipulates energy quantity conservation, the second law draws attention to the fact that energy types are in different quality grades and that, aside from photosynthesis, energy transformation processes lead to energy quality degradation. Exergy is a concept that facilitates the ranking of energy types based on their quality grades, as a consequence of the second law of thermodynamics.

The inevitability of energy utilization with the inescapability of the dictates of the second law of thermodynamics throws up the challenge of not only energy utilization efficiency but also the sustainability of energy resource utilization. According to the famed Brundtland report, sustainable development is to “ensure that humanity meets the needs of the present without compromising the ability of future generations to meet their own needs” [1]. With the first industrial revolution in Europe (1800), coal became a major energy resource joined about a century later by petroleum. To maintain a good standard of living, modern society depends on many types of services, which conventionally, are rendered through combustion of fossil fuels. Therefore, although there are increasing drives toward alternative energy sources, there are also genuine needs to utilize the fossilized hydrocarbon fuels in as sustainable a manner as possible.

This chapter’s contribution is thus about the metrics that can be used to assess the degree of sustainability of combustion of fossil carbon-based fuels. Exergy-based metrics are suitable for sustainability assessment of energy utilization due to the fact that, by definition, exergy combines both system and environmental properties. One definition of exergy is the maximum extractable work from a given system at a specified state till it attains thermodynamic equilibrium with the environment [2]. Thermodynamic equilibrium entails all manners of equilibria: mechanical, thermal, chemical, and so on, between the system and the environment. This is when all types of gradients: pressure gradient, temperature gradient, mass concentration gradient, and so on, cease between the system and the environment.

Conversely, for environmental harmony and ecological balance, a system should only release substances to the atmosphere in the ‘dead state’, when they are supposed to have zero exergy and zero disturbance in the environment. This is why exergy efficiency and its functions become very important in assessing energy and the environmental sustainability of energy utilization. This is because the more exergy efficient a process or system is, the less its exergy destruction level and the more its degree of sustainability [3].

Exergy reflects the quality of a resource, giving insight into which material or energy streams are worth recovering: streams with high exergy content have more potential for value extraction. Its foundation on the second law of thermodynamics provides an engineering understanding of the irreversibilities generated during production. One significant aspect of exergy efficiency is that it covers both energy and materials as a single indicator [4]. All other metrics considered in this chapter are functions of exergy efficiency, directly or indirectly.

Indeed, not only energy is degraded through entropy creation, but material resources are degraded as well [5, 6]. Besides, exergy destruction is synonymous with energy resource depletion. The easiest to understand is thermal energy emanating from combustion of hydrocarbon fuel. Some quantity of the fuel would be responsible for the degraded part of the energy or the destroyed exergy. The metric that directly takes care of material resource degradation is called depletion number.

Another metric, closely-related to depletion number, is the sustainability index. It is the reciprocal of depletion number and, therefore, a measure of resource conservation [7, 8]. The fourth metric in this chapter is exergetic improvement potential. When used in a system or process detailed analysis, it suggests feasible improvements in the system through the reduction of irreversibilities. The analysis starts with identification of areas of exergy destruction and possible technical ameliorations in the system within the limitations of the second law of thermodynamics [9].

Central to sustainable development is environmental protection. That is why there is a clamor for eco-friendly energy utilization. Hence, the fifth and last metric in the chapter is environmental compatibility. It measures the degree of eco-friendliness of a fuel. The major independent variable in the metric is the emission abatement exergy. Essentially, it compares the fuel’s ordinary chemical exergy with its overall chemical exergy when the emission abatement exergy (as a result of its combustion) is factored in [10, 11].

2. Methodology

2.1 Exergy efficiency, ψ

This is defined by several authors [12, 13], as the ratio between the exergy delivered to the user, B_out, and the exergy input, B_in:

$$\psi =\frac{B_{\mathit{\text{out}}}}{B_{\mathit{\text{in}}}}\dots \left(0\le \mathrm{\psi }<1\right)$$E1

Its lowest value is zero when the entire input exergy is destroyed. The highest value of unity is practically unattainable, due to the constraints imposed by the natural, second law of thermodynamics. Exergy efficiency is a dimensionless metric, sometimes expressed as a percentage.

For the cases considered in this chapter, the input exergy is always the fuel chemical exergy. The fuel chemical exergies have been found to be related to their heating values through an exergy factor [14]: φ_f. The fuel heating value, HV, its chemical exergy, ε_f, and the exergy factor are related as follows:

$${\mathrm{\epsilon }}_{\mathrm{f}}={\mathrm{\phi }}_{\mathrm{f}}\mathrm{HV}$$E2

The fuel heating value can either be the higher heating value, HHV, or the lower heating value, LHV. When the system is multi-component, like in fuel-mix analyses, the overall system efficiency is given by:

$${\psi }_{\mathit{\text{overall}}}=\frac{{\sum }_{i=1}^n{\psi }_i{B}_{\mathit{\text{in}},i}}{{\sum }_{i=1}^n{B}_{\mathit{\text{in}},i}}$$E3

$$={\sum }_{i=1}^n{\psi }_{i}B{\prime }_{\mathit{\text{in}},i}$$E4

In Eqs. (3) and (4), the “i” subscript refers to the i-th component. Eq. (4) is in terms of fractional exergy, B′ [15].

2.2 Depletion number, D_p

Depletion number is the ratio of the magnitude of exergy destruction within a system or process, B_d, to the magnitude of the exergy input [5]:

$$D_p=\frac{B_d}{B_{\mathit{\text{in}}}}$$E5

$$\mathrm{But},{\mathrm{B}}_{\mathrm{d}}={\mathrm{B}}_{\text{in}}–{\mathrm{B}}_{\text{out}}$$E6

Hence, the depletion number is related to the system or process exergy efficiency thus:

$${\mathrm{D}}_{\mathrm{p}}=1–\mathrm{\psi }$$E7

It is also a dimensionless metric, expressible as a percentage as well. As a metric, it is complementary to exergy efficiency.

Also, in a multi-component system,

$${\mathrm{D}}_{\mathrm{p},\text{overall}}=1–{\mathrm{\psi }}_{\text{overall}}=\frac{{\sum }_{i=1}^n{D}_{p,i}{B}_{\mathit{\text{in}},i}}{{\sum }_{i=1}^n{B}_{\mathit{\text{in}},i}}=\sum _{i=1}^n{D}_{p,i}\underset{\mathit{\text{in}},i}{\overset{\prime }{B}}$$E8

The lower the exergy efficiency, or higher the depletion number, the farther away from thermodynamic equilibrium the effluents from such a system or process and the more unsustainable it is.

2.3 Sustainability index, SI

SI is the reciprocal or multiplicative inverse of Depletion Number [16]. Hence,

$$\mathrm{SI}=1/{\mathrm{D}}_{\mathrm{p}}=\frac{1}{1-\psi }$$E9

The minimum value of SI is unity, when ψ is zero. It has no maximum value or upper bound. It is also a dimensionless metric. Since it is the reciprocal of depletion number, the practical indication of SI is clear: resource conservation. Hence, higher values (>1) indicate resource conservation and sustainability.

2.4 Improvement potential, IP

IP is an exergy-based sustainability metric [[17] in [13]] defined as:

$$\mathrm{IP}=\left(1–\mathrm{\psi }\right)\left({\mathrm{B}}_{\text{in}}–{\mathrm{B}}_{\text{out}}\right)={\left(1–\mathrm{\psi }\right)}^2{\mathrm{B}}_{\text{in}}$$E10

In practice, IP is a function of two variables, namely, ψ and B_in (= mφ_fHV). It is a quadratic function of ψ (with a repeated solution of unity) and an increasing linear function of B_in, or fuel supply mass, m, since φ_fHV is constant for any particular fuel.

It is non-dimensionless. Its unit is that of exergy. When ψ is zero, exergy is fully destroyed and IP is maximum at the value of the input exergy. The improvement challenge is then at its peak. It is instructive to note that system or process improvement through ψ increment is tantamount to reducing B_in (the fuel supply mass rate) at the same B_out level, thus conserving fuel material resources.

The importance of this metric is in the fact that it indicates the available opportunity to improve the system performance. This opportunity cannot be higher than the fuel chemical exergy at 100% exergy efficiency. Hence, the fuel high chemical exergy is an opportunity that can be harnessed with high system or process exergy efficiency.

2.5 Environmental compatibility, ξ

Environmental compatibility of energy utilization is a measure of energy resource sustainability, defined [10, 11] as the ratio of the net input fuel exergy to its gross exergy when combustion emission abatement exergy is added. When the emission abatement exergy is independently supplied (from a non-Carbon-based fuel source), the environmental compatibility is:

$$\xi =\frac{B_{\mathit{\text{in}}}}{B_{\mathit{\text{in}}}+B_{\mathit{EA}}}=\frac{1}{1+\frac{B_{\mathit{EA}}}{B_{\mathit{\text{in}}}}}={\left(1+\frac{B_{\mathit{EA}}}{B_{\mathit{\text{in}}}}\right)}^{-1}$$E11

B_EA is the emission abatement exergy.

If the abatement exergy is low, then ξ is high. The abatement exergy is to offset the ecological imbalance produced as a result of exergy destruction, manifesting as emissions. Mathematically, the value of ξ depends on the ratio of B_EA value to that of B_in. It is also dimensionless.

In the alternative case, when emission abatement exergy is obtained from the supplied fuel exergy, the following expression is used for environmental compatibility, ξ [18]:

$$\xi =\frac{B_{\mathit{\text{in}}}-B_{\mathit{EA}}}{B_{\mathit{\text{in}}}}=1-\frac{B_{\mathit{EA}}}{B_{\mathit{\text{in}}}}$$E12

Both equations produce the same maximum value of unity (100%), when the abatement exergy is nil. Besides, a binomial expansion of Eq. (11) converges to Eq. (12) for small values of the ratio B_EA/B_in (x):

$$\xi ={\left(1+\frac{B_{\mathit{EA}}}{B_{\mathit{\text{in}}}}\right)}^{-1}=1–\mathrm{x}+{\mathrm{x}}^2–{\mathrm{x}}^3+{\mathrm{x}}^4–{\mathrm{x}}^5+\dots +{\left(–\mathrm{x}\right)}^{\mathrm{n}}$$E13

|x| ≤ 1; x = B_EA/B_in.

Dewulf et al. [19] quoted Dewulf et al. [10] that the abatement exergy of CO₂ is 5.86 MJ/kg. Cornelissen [9], as quoted by Dewulf et al. [19], obtained abatement exergy values for SO_x, NO_x and phosphate as 57, 16 and 18 MJ/kg, respectively. Also, in Tang et al. [18], the abatement exergy values for CO₂, SO₂ and NO_x were found to be 5.9, 57.0 and 16.0 MJ/kg, respectively. Hendriks [20], referenced by De Swaan Arons [21], reported that 5.862 MJ abatement exergy would be required per kg CO₂ produced from non-renewable energy sources as well.

For instance, to obtain CO₂ abatement exergy of a fuel (MJ/kg of fuel), we multiply chemical exergy value of the fuel consumed (MJ/kg of fuel) by the effective CO₂ emission factor (kg of CO₂/MJ of fuel, in Table 1) to obtain the mass of CO₂ produced (kg per kg of fuel), and then multiply by 5.862 MJ per kg of CO₂. This procedure was followed to obtain the data in Table 2 from the ones in Table 1 and Garg et al. [22]. Data in Table 2 formed the basis for Figure 1.

Fuel	LHV (MJ/kg)	Exergy factor
LPG	47.3	1.056
Kerosene	43.8	1.07
Diesel Fuel	43.0	1.07
Gasoline	44.3	1.07
Natural Gas	48.0	1.04
Residual Fuel Oil	40.4	1.07
Blast Furnace Gas	2.7	1.06

Table 1.

Selected fuel data [22, 23].

Fuel	Chemical exergy, εf (Bin) (MJ/kg)	Default carbon content, A (kg/MJ of fuel)	Effective CO2 emission factor, A × 44/12	CO2 mass per mass of fuel (kg/kg)	BEA (MJ/kg of fuel)	BEA/Bin
LPG	49.9488	0.0172	0.0631	3.1518	18.4757	0.3699
Kerosene	46.866	0.0196	0.0719	3.3697	19.7530	0.4215
Diesel Fuel	46.01	0.0202	0.0741	3.4093	19.9856	0.4344
Gasoline	47.401	0.0189	0.0693	3.2849	19.2560	0.4062
Natural Gas	49.92	0.0153	0.0561	2.8005	16.4166	0.3289
Residual Fuel Oil	43.228	0.0211	0.0774	3.3458	19.6134	0.4537
Blast Furnace Gas	2.808	0.0708	0.2596	0.7290	4.2731	1.5218

Table 2.

Chemical exergy and CO₂ data on selected fuels [22, this work].

Figure 1.

The two environmental compatibility functions of B_EA/B_in for CO₂ emission for selected fuels in practice.

In Table 2, effective CO₂ emission factor, (A × 44/12), is mass of CO₂ produced per MJ of fuel used.

The emission factor value for blast furnace gas includes carbon dioxide originally contained in this gas as well as that formed due to combustion of this gas. Blast furnace gas produces the highest quantity of CO₂ per unit of fuel exergy utilized [22].

3. Results and discussion

3.1 Exergy efficiency

Lowest value of exergy efficiency is zero, as total exergy destruction is possible. However, a maximum value of 100% for exergy is unattainable, due to the constraints imposed by the second law of thermodynamics. These two facts affect the extreme values of other metrics which are direct functions of system or process exergy efficiency. Apart from environmental compatibility, exergy efficiency is an independent variable of other metrics considered in this chapter. Indeed, it is the sole independent variable of depletion number and sustainability index and one of the two independent variables of improvement potential.

3.2 Depletion number

D_p ranges from unity, when ψ is zero, to close zero when ψ is very high. Hence, its maximum value is unity. However, it can never be zero, since ψ can never be unity. It is a decreasing, linear function of ψ, approaching zero as ψ approaches unity, as shown Figure 2. The smaller its value is, the better. For an efficiency of 40%, for instance, the depletion number is 0.60.

Figure 2.

Depletion number as a function of exergy efficiency.

3.3 Sustainability index

It is an increasing function of ψ, with no defined upper bound, as shown in Figure 3. It can also be seen in Figure 3 that SI seems to increase astronomically beyond an exergy efficiency value of 0.9. This observation is brought out more vividly in Figure 4.

Figure 3.

Sustainability index as a function of exergy efficiency.

Figure 4.

Sustainability index increment rate.

Indeed, a binomial expansion of Eq. (9) gives SI as a monotonously increasing power function of exergy efficiency, sum of a geometric progression with common ratio of ψ:

$$\mathrm{SI}=1+\mathrm{\psi }+{\mathrm{\psi }}^2+{\mathrm{\psi }}^3+\dots +{\mathrm{\psi }}^{\mathrm{n}-1}\left(0\le \mathrm{\psi }<1\right)$$E14

The way SI increases in Figures 3 and 4 is not surprising, considering Eq. (14). Figure 4 is a plot of the first derivative of Figure 3, and (considering Eq. (14)), is still a plot of a power function of ψ. However, as the power of ψ comes down, the value goes up, since ψ < 1. This is why the scale on the vertical axis of Figure 4 is higher than that of Figure 3. When exergy is fully destroyed and ψ is zero, SI attains its minimum value of unity. At any other attainable value of ψ, it (SI) keeps on increasing, being a power function of ψ. Hence, any favorable value of SI must be very high. For instance, for an efficiency of 40%, SI is 1.67; whereas if the efficiency is doubled (80%), SI becomes 5.0.

3.4 Improvement potential

Improvement Potential is a function of two variables: exergy efficiency and input exergy. However, for a particular fuel (fixed chemical exergy per unit mass), IP has only ψ as a variable, as shown Figure 5. It is also shown in Figure 5 that the potential decreases as the efficiency is improved. This is expected to be done through process or system performance improvement. Since the potential is exhausted at the highest attainable exergy efficiency, a further opportunity is only possible at a higher value of chemical exergy. Noting that chemical exergy is a fuel property, the practical implication of this further potential enhancement is fuel substitution. Figure 6 explains this fact further graphically by comparing different fuels based on their chemical exergies.

Figure 5.

Specific improvement potential as a function of exergy efficiency.

Figure 6.

Improvement potentials of fuels as functions of exergy efficiency.

There, it is seen that, at a particular value of system or process efficiency, the residual fuel oil has a lower improvement potential than natural gas. In other words, for the same quantity of fuel consumption, a higher efficiency can be attained with improved process or system technology with natural gas, than with residual fuel oil. It is well known that gas fuel utilization is, in general, more sustainable that liquid fuel utilization. An exception to this is a fuel like the Blast Furnace gas, which has a very low chemical exergy.

3.5 Environmental compatibility

Like the previously mentioned metrics, environmental compatibility is a function of a ratio of two exergies. But unlike them, it is not a function of exergy efficiency. Rather, it is a function of the ratio of abatement exergy to the input exergy, as can be seen in Figure 7 for CO₂ emission. High carbon fuels have high abatement exergies and low environmental compatibilities. It is easily understood that if other emissions like SO₂ and NO_x are considered, fuels with high abatement exergies like high sulfur fuels would have low environmental compatibilities. The fact that the independent variable on the abscissa of Figure 7 is invariably a property of a fuel suggests that fuel substitution is a strong factor to be considered in improving environmental compatibility of a process or system. However, it is also noteworthy that system engineering maintenance is a factor too. A properly and promptly maintained system will definitely be more environmentally compliant, even with same fuel type.

Figure 7.

The two general environmental compatibility functions of B_EA/B_in for CO₂ emission in principle.

The fact that Eqs. (11) and (12) are about two different approaches to measure the parameter is responsible for the different values obtained, especially at higher exergy ratios (Figures 1 and 7). Besides, the fact that environmental compatibility values obtained through Eq. (11) are higher than those obtained through Eq. (12) is also logical. The emission abatement exergy in Eq. (11) is obtained through non-carbon-based sources, while the one in Eq. (12) is obtained through the same carbon-based sources. It is also expected that Eq. (12) would yield a negative value for environmental compatibility for a fuel like blast furnace gas with B_EA more than B_in (Figure 1).

It is indeed outrageous and unsustainable for B_EA to be close to, equal to, or more than B_in. This is because the practical implication is that the entire input fuel chemical exergy is used to abate its combustion emissions. In this case, there will no net gain from the fuel combustion process. Hence, both equations are equivalent and applicable under practical, sustainable situations. Under this situation, the minimum value of environmental compatibility is zero, using Eq. (11) or Eq. (13).

4. Conclusion

Five exergy-based metrics of sustainable energy utilization have been considered in this chapter. They are exergy efficiency, depletion number, sustainability index, improvement potential and environmental compatibility. The first three metrics are functions of exergy efficiency. They can always be influenced for improvement through ingenuous process path or system technology design. The fourth one is a function of both exergy efficiency and input exergy. Being a function of both exergy input and efficiency, its improvement can be effected through fuel substitution as well as process path and system technology design. The fifth metric is a function of the ratio of emission abatement exergy to the input exergy. Since the emission abatement exergy is a strong function of the fuel, its improvement is mainly dependent on fuel substitution. However, all of them are separate functions of system condition, and may therefore be improved through prompt and adequate system maintenance. They all underscore the importance of exergy in sustainability analyses and eco-friendliness of energy utilization.