Cooling systems are required in some types of power plants as the excess heat can severely damage the equipment involved in the transformation process, or it may reduce the efficiency of the power plant [25]. Three types of cooling systems can be used in thermal power plants [11]: once-through systems (open-loop), wet-tower systems (closed-loop), and dry cooling systems (refrigerant-radiator systems).

Ecuador is a South American country located in the equatorial line. Most Ecuadorian electricity in the country's mix is produced by hydropower and thermal power plants. In 2020, hydropower produced 77.9% of the country's electricity, while thermal power plants produced 20.3% [27]. Only a small fraction of its electricity is produced by other renewables such as solar, wind and biomass [27].

Thermal power plants in the country mainly use oil derivatives as their fuels as the country does not have large coal or natural gas reserves, but it has a large and well-matured oil industry [23]. The preferred fuel for large thermal power plants in the country is fuel oil #4 and #6 [27]. This study focuses on Ecuadorian oil derivatives-fired thermal power plants that run under the Rankine thermodynamic cycle. Biomass-fired power plants may have significant grey WF as the working principle of both types is similar [25]. Nonetheless, considering that Ecuadorian biomass power plants are a by-product of sugarcane production [23], there are uncertainties because the discharged heat from the electricity generation system is used in sugar or molasses production.

Moreover, this study assesses grey WFs of thermal power plants but considers only thermal pollution as the primary pollutant. Other pollutants such as nitrogen, hydrocarbons, and other pollutants may affect the grey WF [4]. However, these are not considered in the WF accounting.

Finally, as discussed previously, the grey WF of thermal power plants is only significant for once-through systems. Thus, this study focused only on thermal power plants using once-through cooling systems.

According to the annual report of the Agency of Regulation and Control of Energy and Non-renewable Resources (ARCERNNR) [27], Ecuador had 185 active thermal power plants in 2020, including plants whose primary movers are gas turbines, steam turbines and internal combustion engines. However, not everyone may produce a significant grey WF because they have different cooling systems. Most Ecuadorian thermal power plants are Internal Combustion Engines (in number, not production), which use dry cooling systems in principle. Thus, it is necessary to inventory the current Ecuadorian electricity mix to find the cooling technology used in each thermal power plant and then define which one may produce a significant grey WF.

For this, the technology and infrastructure of each active thermal power plant in the mix were evaluated. The starting point is the work by Vaca-Jiménez et al. [23] that serves as the base of the power plants database. Nonetheless, that paper considers only the active power plants until 2018 and must be updated. For that, the updated data from the System of Data of Electricity Generation (SISDAT) database [27] were downloaded and compared with the list provided by Vaca-Jiménez et al. [23]. The result is a list of existing thermal power plants.

Then, each thermal power plant was sorted according to its technology and cooling systems. First, the power plants were classified by the turbine technology (primary mover), which shows the thermodynamic cycle they use. Thus, it provides information regarding water uses, as described in Vaca-Jiménez et al. [23]. A thermal power plant may have different turbine technologies under the same roof to diversify fuels and resources or improve efficiency. So, the power plants were sorted into similar technologies using the SISDAT database's metadata. As described previously, active cooling systems are required for power plants working with steam turbines (Rankine Cycle). However, there may be cases in which other thermal power plants also use active cooling. Satellite imaging from Google Earth® was used to identify the cooling system infrastructure to avoid missing them in the assessment. The cooling system infrastructure is identified following the guidelines described by Diehl et al. [28].

Finally, with the detailed list of thermal power plants, potential ones that may produce significant grey WF were identified. Those power plants were used as case studies to calculate the grey WF.

In principle, the calculation of the grey WF requires historical data on the inlets and outlets of the power plant's cooling system. The problem with this is that thermal power plants in Ecuador are not required to log these temperatures, so they do not have a historical record. However, thermal power plants in the country must report electricity output and fuel consumption. These data are fully available to access in the SISDAT database [29]. Thus, any assessment of the water discharged by the cooling systems must be based on these two variables.

The operation of a thermal power plant and its cooling system can be modelled based on the theoretical energy balances and heat transfer equations of the elements of the power plant. There is a need to estimate the temperature of the discharge water of the cooling system of the power plants, T_dis. For that, the study started by modelling the energy balance on the entire plant, considering it a black box. Figure 1 shows the scheme of the energy balance.

Figure 1.

Energy balance (inlets and outlets) considered in the model of the thermal power plants

As observed in Figure 1, the power plant has only one energy input: fuel combustion. Conversely, it has three energy outputs: i) the energy in the turbine that generates the rotation of the turbine shaft, E_t; ii) the heat that is discharged to the atmosphere by the flue gases that were not taking advantage in the boiler, E_gas; and iii) the heat that is discharged by the cooling water, E_cooling. The equation of the energy balance is:

$E_{in}=E_{gas}+E_t+E_{cooling}$ (1)

The difference between E_in and E_gas is the fuel energy the water uses to achieve its phase change and superheating in the boiler. This useful energy can be defined in terms of the efficiency of the boiler as described in Tanuma [30]:

$E_{in}-E_{gas}=E_b={\eta }_b\times {\displaystyle \sum _{i=1}^n{\left(H\times B\right)}_i}$ (2)

where: η_b is the efficiency of the boiler, H is the heating value of the fuel in J/m³ of fuel, and B is the volume of fuel consumed in a defined period in m³. There is a sum from i = 1 to n in eq. (2) because many thermal power plants in the country use more than one type of fuel [23]. The heating value used for the model was obtained from [23], and the η_b ranges from [30]. Finally, the volume of fuel consumed was obtained from the power plant as they reported it in the SISDAT [29].

In terms of the E_t, the energy from the steam is transformed into kinetic energy on the turbine shaft, which is connected to the electricity generator. This steam-shaft-generator conversion of energy has two efficiencies. In the first case, there is the thermal-to-kinetic efficiency, η_t, due to the losses involved in transforming the turbine blades’ movement to the shaft, i.e., friction on the bearings. In the second case, there is a kinetic-to-electricity efficiency, η_g, due to the transformation of energy in the electricity generator. Based on energy balances, the efficiencies involved are as follows:

${\eta }_t=\frac{E_{shaft}}{E_t}$ (3)

${\eta }_g=\frac{E_g}{E_{shaft}}$ (4)

Using eqs. (3) and (4) and solving them for the E_t, eq. (5) was obtained, which relates this energy output with electricity generation as follows:

$E_t=\frac{E_g}{{\eta }_t\times {\eta }_g}$ (5)

The value of E_g is reported by each power plant and obtained from SISDAT [29]. The values of η_t and η_g range from 0.37 to 0.47, and 0.98 to 0.99, respectively [30]. The exact values per power plant were obtained from [31].

Then, the E_cooling is calculated based on the sensitive heat gained from the cooling water in the condenser using the following equation:

$E_{cooling}=\rho \times Q\times C{p}_w\times \left(T_{dis}-T_{act}\right)$ (6)

where: ρ is the density of the cooling water in kg/m³, Q is the volume of water discharged by the cooling system in m³ (or the integration of the volumetric flow over a certain period), Cp_w is the specific heat of the water at the range of temperature of the discharged water, and finally T_act is the temperature of the inlet of the cooling water, which is the same as the body of water receiving the discharge. Values of ρ and Cp_w were derived from Graham et al. [32].

Then, eqs. (2), (5) and (6) were inserted into eq. (1) and the difference in temperature between T_dis and T_act, times Q was solved, as shown in the following equation:

$$\left(T_{dis}-T_{act}\right)\times Q=\frac{{\eta }_b\times {\displaystyle {\sum }_{i=1}^n{\left(H\times B\right)}_i-\left(\frac{E_g}{{\eta }_t\times {\eta }_g}\right)}}{\rho \times C{p}_W}$$ (7)

The product $$\left(T_{dis}-T_{act}\right)\times Q$$ is obtained from eq. (7) using the multiannual monthly average of B and E_g. Both, from the period between 2000 to 2020.

According to the WF manual [4], the grey WF is calculated based on the volume of pollutants discharged into the water. It describes the hypothetical volume of water that needs to be included alongside the pollutant to dilute it until its concentration is within the established limits. The limits depend on regional guidelines and regulations that norm water discharge. The equation for the grey WF in m³, considering the thermal pollution alone, is as follows:

$$W{F}_{grey}\left[x,t\right]=\frac{\left(T_{dis}-T_{act}\right)\left[x,t\right]}{\left(T_{\mathit{max}}-T_{nat}\right)\left[x,t\right]}\times Q$$ (8)

where: x denotes the place where the power plant is located (basin), t is the temporal characteristics of the grey WF due to the spatial and temporal limitations of the WF. T_max is the maximum permissible temperature of the discharged water and T_nat is the natural temperature of the body of water receiving the discharge. The product (T_dis − T_act) × Q is obtained from eq. (7).

Sometimes it is impossible to define the natural temperature of a body of water because the estimations of the indicators, like the grey WF, are done after the discharge (ex-post). Furthermore, there are no historical records of the temperature of water bodies in the country until very recently, so any attempt to estimate this value would be based on best guesses. That is why there is the possibility of using the difference between (T_max − T_nat) as a range of permissible temperature change in the body of water, ΔT_adm, instead of individual values. Thus, the equation used for the grey WF for this approach changes as follows:

$$W{F}_{grey}\left[x,t\right]=\frac{\left(T_{dis}-T_{act}\right)\left[x,t\right]}{\Delta T_{adm}\left[x,t\right]}\times Q$$ (9)

The ΔT_adm is defined based on regional regulations. In Ecuador, the regulations establish 5 °C maximum permissible temperature increase to preserve the ecosystem of both fresh and saline water [33].

Once the grey WF was estimated for each studied thermal power plant, the values obtained in the previous sections were contextualised to shed light on the possible environmental impact.

First, the possible impact on the body of water regarding the volumetric capacity of the water available to dissipate the pollutant (defined as Water Pollution Level, WPL) was assessed.

$$WPL\left[x,t\right]=\frac{W{F}_{grey}\left[x,t\right]}{R_{ava}\left[x,t\right]}\times 100\%$$ (10)

where: R_ava is the volume of water available in the water body in m³, and the sum of grey WF is defined as there may be cases where more than one thermal power plant is in the same basin. The volume of water available was obtained from the nearest hydrological probe using data from the Ecuadorian Meteorological and Hydrological Office (INAMHI) [34], or in the case of the tidal estimations, the Oceanographic Institute of the Ecuadorian Navy (INOCAR) [35].

Second, the calculated grey WF was compared to existing and validated water use indicators. In this case, the comparison was made with similar studies and previous estimations of the blue and green WFs of the same studied power plants. The values for comparison between similar studies were derived from Chini et al. [36] and for the other components of the WF of Ecuadorian power plants from Vaca-Jiménez et al. [23].

The model used to estimate the grey WF is based on the available data of the power plants, namely, electricity generation and fuel consumption. Energy balances were used to relate those data to the temperature of the water discharged by the cooling system. Thus, the boiler, turbine, and generator efficiencies were used.

The major source of uncertainty in this model comes from these efficiencies, as the η_b, η_t, and η_g have ranges that depend on many variables beyond this analysis's scope. Data of η_t, and per power plant studied were obtained from CELEC EP – Electroguayas [31].

The calculation of the uncertainty of the grey WF is then defined by the η_b. Tanuma [30] specifies that this efficiency ranges from 0.86 to 0.93. The theoretical, maximum, and minimum values of the product (T_dis − T_act) × Q per month were calculated using this range in equation (9).

Five of the 185 thermal power plants operated in Ecuador in 2020 had two types of primary movers (e.g., gas and steam turbines), totalling 190 generation groups in the country. Of those, 170 were Internal Combustion Engines (Diesel engines and Otto engines), 14 were Brayton power plants (gas turbines as the prime mover), and 6 were Rankine power plants (steam turbines as the prime mover). As described previously, the Brayton power plants do not require cooling systems and were not assessed further.

After the cooling system infrastructure assessment using satellite data, there was found that, on the one hand, 169 of the Internal Combustion Engines that were operational during 2020 used dry cooling systems, with refrigerant and radiators, to dissipate the heat from the engines. These power plants do not produce a grey WF regarding water pollution. One power plant, Guangopolo 1, is the only Internal Combustion Engine plant that uses active cooling for its engines. It takes its water from the nearby Guangopolo reservoir (that serves the Guangopolo hydropower plant) and uses it in a wet tower cooling system. As described previously, the wet tower cooling system does not produce a significant grey WF regarding thermal water pollution. Thus, this power plant was not further studied.

On the other hand, three of the six Rankine power plants operational in 2020 use wet-tower cooling systems. These power plants do not produce grey WF of thermal pollution. The other three power plants use once-through cooling systems, so they were selected for further study. Table 1 shows the list and the characteristics of the three studied power plants.

The grey WF related to the thermal pollution of the electricity generation is presented per power plant.

Gonzalo Zevallos

Figure 2 shows the multiannual monthly average of the volumetric grey WF against the multiannual monthly average of fuel consumption.

Figure 2.

Gonzalo Zevallos power plant − multiannual monthly average of the grey WF and fuel consumption

Figure 2 indicates a large grey WF that varies significantly through the year. The largest uncertainty of the volumetric grey WF, displayed in the figure as error bars, is observed from October to March, corresponding to the months when the fuel consumption is high. Moreover, the grey WF variation trend does not directly relate to fuel consumption. The variable part of the equation used to calculate the grey WF is defined by eq. (7), which relates fuel consumption with electricity generation. Thus, the monthly variation trend is determined by the relation between electricity generation, fuel consumption, and boiler, turbine and generator efficiencies.

Figure 3 shows the multiannual monthly average of the grey WF per unit of electricity generated.

Figure 3.

Gonzalo Zevallos power plant − multiannual monthly average of the grey WF per unit of electricity generated and the electricity generated

Figure 3 also shows a large monthly variability. The trend follows an inverse relation with the electricity the power plant generates. Thus, a large grey WF is observed in the middle of the year, corresponding to the lowest electricity production. This inverse relationship is due to the combination of Ecuadorian regulations regarding the permissible temperature in the water bodies and the amount of electricity generated per fuel consumed. The power plants never achieve the maximum temperature permissible for the discharge water, so the maximum temperature difference defines the permissible temperature. This maximum temperature difference remains the same throughout the year. The most influential factor in calculating the grey WF is the relation between the electricity generated against the amount of fuel consumed. In the case of Gonzalo Zevallos, during the middle of the year, the power plant is working very inefficiently compared to the other months of the year, so the amount of electricity produced per unit of fuel consumed is the lowest.

Moreover, the reason behind the temporal variability of the electricity generation and the fuel consumption of Gonzalo Zevallos throughout the year is the decrease in electricity demand. During those months, Ecuadorian hydropower plants provide more electricity to the grid displacing the thermal power plants [37].

Trinitaria

Figure 4 shows the multiannual monthly average of the volumetric grey WF against the multiannual monthly average of fuel consumption. Figure 5 shows the multiannual monthly average of the grey WF per unit of electricity generated for the Trinitaria power plant.

Figure 4.

Trinitaria power plant − multiannual monthly average of the grey WF and the fuel consumption

Figure 5.

Trinitaria power plant − multiannual monthly average of the grey WF per unit of electricity generated and the electricity generated

Figures 4 and 5 show similar trends to those observed in Figures 2 and 3. Nonetheless, besides the magnitude of the fuel consumption and electricity generation, the main difference between these two sets of results is that the electricity production and fuel consumption from Trinitaria have less variation throughout the year than in the case of Gonzalo Zevallos.

Despite being similar to the other two power plants, Trinitaria produces more electricity than Gonzalo Zevallos during the months with larger hydropower production in the grid because Gonzalo Zevallos has two generation units while Trinitaria only has one. Therefore, it is easier for Gonzalo Zevallos to reduce its production significantly without turning off the whole power plant by shutting down one of the generation units.

Moreover, it is also the case that during the middle of the year, Trinitaria is working under a lower ratio between electricity generated and fuel consumed, so the grey WF is larger than the rest of the year.

Aníbal Santos

Figure 6 shows the multiannual monthly average of the volumetric grey WF against the multiannual monthly average of fuel consumption. Figure 7 shows the multiannual monthly average of the grey WF per unit of electricity generated for the Anibal Santos power plant.

Figure 6.

Aníbal Santos power plant − multiannual monthly average of the grey WF and the fuel consumption

Figure 7.

Aníbal Santos power plant − multiannual monthly average of the grey WF per unit of electricity generated and the electricity generated

There is a stark difference between Figures 6 and 7 compared to Gonzalo Zevallos and Trinitaria. First, the uncertainty is much less in this power plant than in the other two. For Gonzalo Zevallos and Trinitaria, the difference between the uncertainty calculation's lower and upper end can be threefold or sixfold, respectively. However, for Aníbal Santos, this difference is only about 25%.

Furthermore, Aníbal Santos has a smaller grey WF than its counterparts during June and July. This is because there is practically no generation from the power plant during those months due to the seasonality of the electricity generation in the Ecuadorian mix [23], and the little generation they produce is ensured to be produced with a higher ratio of electricity generated against fuel consumed than its counterparts.

Two estimations define the possible impact of the grey WF in the water bodies: WPL and the comparison between WF colours. For the WPL, the grey WF of the power plants needs to be summed up if more than one discharges its water into the same basin. In our case study, two power plants, Gonzalo Zevallos and Aníbal Santos, discharge into the same water body. Figure 8 shows the WPL of Gonzalo Zevallos and Aníbal Santos against the monthly variation of water availability in the Tres Bocas Estuary.

Figure 8.

Thermal Water Pollution Level of Gonzalo Zevallos and Aníbal Santos into the Tres Bocas Estuary

Figure 8 shows that the Tres Bocas Estuary is thermally polluted. Seven months of the year, the estuary has a WPL above 100%, meaning that the available water, in the closeness of the discharge of Aníbal Santos and Gonzalo Zevallos, is not enough to dilute the warm water from these power plants.

Figure 9 shows the WPL of Trinitaria against the monthly variation of water availability in the El Muerto Estuary. Contrary to what was observed in Figure 8 for the Tres Bocas Estuary, El Muerto Estuary has enough water, in the closeness of Trinitaria, to dilute the warm water discharged by this power plant.

Figure 9.

Thermal Water Pollution Level of Trinitaria on El Muerto Estuary

Regarding the comparison to other WF colours, Figure 10 shows the difference in the order of magnitude of the annual blue and grey WFs of the thermal power plants assessed. It shows that the grey WF of these three power plants can be up to three orders of magnitude larger than the blue WF. It also shows that the three power plants have similar blue and grey WFs.

Figure 10.

Comparison between grey and blue WF of the three power plants; the blue WF was derived from Vaca-Jiménez et al. [23]

The WF concept was conceived as an environmental impact indicator of anthropogenic activities described as the actual volumetric requirement of freshwater [4]. According to that definition, any use of saline water should be considered with a value of zero. The reasoning behind the discrimination of types of water considers that freshwater availability is limited, freshwater bodies have limited volumes compared to saline water bodies, and freshwater is used for other anthropogenic purposes [38].

Despite this, the description and calculation of the grey WF of the Ecuadorian power plants are relevant because the saline water used by these power plants is not seawater but the water of estuaries. As freshwater, estuaries have limited water availability volumes [8]. They do not have the practical infinite water availability of oceans to dissolve any pollutant. Moreover, estuaries’ ecosystem has a delicate balance, as they have shallower water than seawater [7]. The impact of thermal pollution can be larger than in seawater [39]. Therefore, the impact of the large grey WF on these water bodies is, arguably, as significant as those of freshwater bodies. Considering that once-through cooling systems using saline water in thermal power plants are common [40], the discussion of the thermal water pollution due to electricity generation by these power plants must include those using estuaries as their source of cooling water.

Nonetheless, this indicates that the comparison of the grey WF with other colours of the WF is only representative of volume and should not be considered a valid comparable indicator of environmental impact between components of the total WF.

There is a significant lack of precise data to calculate the grey WF. This situation increases the uncertainty of the calculations and, therefore, the possible conclusions that can be drawn from the results.

To reduce the uncertainties, the results were presented within a range considering the differences in the efficiencies of the boiler, turbine, and electric generator. Similar approaches have been used in previous studies. The difference between the range of uncertainty presented in the results depends on the combination of these efficiencies. Based on what was reported by CELEC-EP Electroguayas [31], Gonzalo Zevallos has a combined turbine and generator efficiency of 0.3871, while Trinitaria of 0.4594 and Aníbal Santos of 0.4165. That is why Gonzalo Zevallos has a larger range of uncertainty than the other two power plants.

Furthermore, the order of magnitude of our grey WF is around the same as those reported in the literature, i.e., Chini et al. [36], so the uncertainty is acceptable. Unfortunately, due to the novelty of this study, in which the grey WF of a saline water body is assessed; the method used to calculate this grey WF; and the different characteristics of the power plants studied in this paper (type of fuel and climate), further comparisons with other results obtained in the literature is not possible, i.e., against the work made by Chai et al. [12].

Moreover, due to a lack of available data regarding the natural discharge of the water bodies where the thermally polluted water was discharged, the assessment was made using the available data from the nearest hydrological probe. Such a major assumption introduces considerable uncertainty to the results.

All in all, the grey WF calculated for Ecuadorian thermal power plants only represents the possible impact of thermal pollution and must be used as such. More detailed work needs to be done to estimate a more precise grey WF of these power plants and the possible environmental impact on the bodies of water.