Exergy-Based Sustainability Assessment of Gold Mining in Colombia: A Comparative Analysis of Open-Pit and Alluvial Mining

Highlights

• Exergy analysis quantifies the sustainability of a process based on the environmental burden generated by using energy resources.
• Open-pit mining relies on fossil fuels (53%), while alluvial mining is mostly water-dependent (94%)
• Strategies include improving efficiency, minimizing exergy losses, using renewables, and adopting circular economy principles.
• Exergy efficiency is improved by reduction in exergy inputs and exergy emissions/waste, i.e., reduction in the loss of useful energy.
• Findings highlight inefficiencies, guiding resource optimization, and reduced environmental impact.

Abstract

Thermodynamic methods such as exergy analysis enable the evaluation of environmental load (environmental impacts) by quantifying entropy generation and exergy destruction associated with using renewable and non-renewable resources throughout a production system. Based on the principle that environmental impacts occur when exergy is dissipated into the environment, this study applies exergy analysis as a tool for assessing the sustainability of gold mining in Colombia. Two extraction technologies—open-pit and alluvial mining—are evaluated by calculating exergy efficiencies, cumulative exergy demand (CExD), and associated environmental impacts. The results reveal significant differences between the two methods: open-pit mining is heavily dependent on fossil fuels (53% of input exergy), with 99.62% of total exergy destroyed, resulting in an exergy efficiency of just 0.37% and a sustainability index (SI) of 1.00. In contrast, alluvial mining relies predominantly on water (94%), with 69% of input exergy destroyed, an exergy efficiency of 31%, and an SI of 1.46. Four strategies are proposed to reduce environmental burdens: improving efficiency, minimizing exergy losses, integrating renewable energy, and adopting circular economy principles. This study presents the first application of exergy analysis to comprehensively assess the exergy cost of gold production, from extraction through refining, casting, and molding, highlighting critical exergy hotspots and offering a thermodynamic foundation for optimizing resource use in mineral processing.

1. Introduction

Mineral reserves are finite, yet mineral demand tends to increase, specifically those essential for the Fourth Industrial Revolution and energy transition [1]. In this context, mining companies face increasing social pressure to demonstrate long-term environmental and social responsibility [2]. Sustainability has become a central concept in discussions about the future of human society and the economy.

However, there is a widespread perception that mining cannot be a sustainable activity. This view stems from the fact that mining operations are inherently temporary and rely on non-renewable resources, which will eventually be depleted [3,4,5]. In addition, non-renewable resources that will be scarce one day are now being extracted, and future generations will not be able to use them [6,7].

As a result, sustainability in the mining industry has become a key global concern. The sector is increasingly expected to align with the United Nations Sustainable Development [8]. The mining sector is challenged to implement sustainable mining industrial practices [9]. While many non-governmental organizations (NGOs) argue that mining is fundamentally unsustainable and that a sustainable society should reduce mineral extraction over time [10], the International Council on Mining and Metals (ICMM) maintains that mining is essential for development, though its impact should be minimized [11].

To cope with these challenges, thermodynamic methods, particularly exergy analysis, have been implemented to assess environmental load and improve process efficiency. Exergy analysis calculates the exergy destroyed by a process and improves the efficiency of the energy system as a way to reduce its environmental impact [12,13]. The goal is to minimize exergy degradation, thereby reducing environmental damage. Waste streams containing residual exergy also contribute to environmental harm, as they release unused energy that remains out of equilibrium with the environment [14,15].

Exergy analysis provides a holistic and comprehensive assessment of mineral extraction’s economic and environmental costs. It accounts for the natural and human capital consumed throughout the life cycle, from the cradle to the grave. Furthermore, it enables the estimation of exergy replacement costs, that is, the resources and energy needed to return extracted minerals to their original state [16,17,18].

In this research, exergy analysis will be used as an indicator of the energy quality of resources to assess the sustainability of two gold mining systems in Colombia: open pit and alluvial mining. The assessment spans the full production chain, from extraction to casting and molding. It includes quantifying the cumulative energy/exergy demand, input/output exergy, destroyed exergy, relative irreversibility, product exergy efficiency, exergy efficiency, and sustainable index (SI).

To date, no study has applied exergy analysis to quantify the exergy cost of gold production or any other mineral across all stages from extraction through refining, casting, and molding. This research fills that gap by identifying critical exergy losses and offering a thermodynamic perspective for optimizing resource use in mining.

Exergy Analysis in the Mining Sector

To speak of sustainability in extracting non-renewable resources, the use rates of these non-renewable resources must not exceed the rates at which renewable substitutes are developed. Likewise, polluting emission rates should not exceed the corresponding assimilation capacity of the environment (planetary boundaries) [19,20]. It should be noted that exergy analysis is a way to evaluate mineral resources strategically, but it is not the only methodological tool available to do so [7]. However, several studies have used exergy analysis and thermoeconomic tools to assess the problem of depletion of non-renewable resources and the degree of scarcity. In this context, exergy replacement cost represents humankind’s effort to return minerals to their original conditions from a “commercially dead state” [21,22]. This “commercially dead state” refers to a hypothetical depleted planet called Thanatia, where all minerals have been depleted and dispersed, and all fossil fuels have been burned. To make these minerals useful, they would need to be returned to the conditions of composition and concentration in which they were originally found, using the best technologies available [23,24].

Exergy analysis has been implemented to evaluate the most sustainable hydrogen routes (blue, green, and brown) by the exergy-destroyed indicator [25]. In 2023, Cano-Londoño et al. (2023) integrated exergy analysis into Life Cycle Assessment (ExLCA) to evaluate the sustainability of open-pit and alluvial gold mining in Colombia with a life cycle assessment approach [3]. Results were used to propose mitigation strategies for environmental impact. In 2022, Seabra and Caldeira-Pires used the embodied exergy as a sustainability indicator to corroborate that this indicator increase is proportional to the decrease in the ore grades [1]. In 2018, a methodology to determine the loss of mineral wealth based on the exergy replacement cost was carried out in twenty Latin American countries, taking 2013 as the base year. In 2017, Whiting et al. evaluated the sustainability of fossil fuels and non-fuel mineral depletion by a Life Cycle Exergy Assessment (LCEA) that goes from the cradle to the grave and by exergy replacement cost that goes from the grave to the cradle [7]. Dominguez et al. state that mines with more concentrated ore do not require large energy consumption in their extraction process and benefit from their concentration. However, their replacement cost will be high because minerals with high exergy content are exhausted. This is in contrast to mines with low-grade ore, such as gold, which require large amounts of energy in their extraction process (high extraction exergy cost), and their benefit and replacement costs are low [26]. Carmona and collaborators (2015) concluded that the market price of minerals should reflect the physical value assigned by nature to produce a mineral in a given deposit and that Colombia is losing its mineral wealth through exports sold to the world market [22]. Valero et al. (2014) proposed a framework for accounting for mineral depletion by exergy and economic mineral balance of Spain as a case study [7,16]. Likewise, in 2010, Valero and Valero estimated, from geological data when the peak production of 51 minerals could be achieved, the amount of exergy resources available on the planet and the possible exhaustion behavior [7] by using the combined methodology of the Hubbert Peak Model and the exergy approach, which was also used for the case of lithium [23].

Other works carried out using exergy analysis in the mining sector include the recycling of ferrous waste, the production and use of a laptop [27], nickel production [27], and factors that affect energy and exergy demand of mine water management options [28]. It is noteworthy that the objective of this research is not to evaluate exergy replacement costs; it is to assess the sustainability of two gold mining processes by the exergy indicators derived from the exergy of the gold production or the exergy cost of the extractive process from the cradle to the gate; the former assesses the resource from an entropic planet to mine, and the latter assesses the resource from mine to market.

2. Case Study: Open-Pit and Alluvial Mining Technologies in Colombia

The exploitation of gold in Colombia is based on two types of deposits, based on geological formation conditions. Primary deposits are characterized by underground exploitation (mineral deposits in situ where initial exploitation occurs in surface areas and then in depth) [29]. Secondary or alluvial deposits involve open-pit exploitation. After the weathering processes of a primary reservoir, these have a natural mechanical disintegration, and gold particles are transported at certain distances by the action of water. The particles concentrate in water channels, giving rise to the known “gold placer” [30,31]. The extraction of gold by hydrometallurgical methods, as well as the beneficiation of gold ore using the techniques of centrifugal concentration, gravity, and flotation, is well described in the literature [31]. About 18% of gold production in Colombia comes from reef farms, and 82% comes from alluvial operations [17,32].

This research addresses two types of extractive technologies as a case study: open-pit and alluvial mining technology for exploiting primary and secondary deposits, respectively.

Table 1. Input/output descriptions in open-pit and alluvial mining technology.

	Open-Pit Mining Technology	Alluvial (or Placer) Mining Technology	Unit
Input
Water	l 5.70 × 107	a 9.79 × 107	ton/year
Energy (electrical)	m 2.03 × 1012	b 2.53 × 1011	kJ/year
Energy (gas)	n 1.68 × 1010	c 1.60 × 107	kJ/year
Energy (diesel)	o 1.15 × 1012	d 1.12 × 109	kJ/year
Oxygen (air)	p 3.75 × 105	e 40	ton/year
Others	** 1.01 × 106	* 318.8	ton/year
Output
Inert material removed (sterile mineral)	q 6.94 × 107	f 1.06 × 108	ton/year
Vegetation cover harbors (clearing and stripping)	r 1.33 × 103	g 60	ton/year
Sludge tails (wet weight)	s 2.42 × 107	h 4.52 × 103	ton/year
Energy losses	t 1.24 × 1012	i 4.74 × 1010	kJ/year
Emissions of substances to air, water, and soil by combustion, detonation, trituration, leakage, etc.	u 2.22 × 103	---	ton/year
Stored material containing minerals of interest	v 3.98 × 107	---	ton/year
Ferrous metal co-product (dry weight, 55% iron)	---	1.55	ton/year
Silver co-product (dry weight)	w 21.55	---	ton/year
Gold (dry weight)	x 19.05	j 3.10	ton/year
Recycling
Water	y 4.79 × 107	k 4.42 × 105	ton/year

^a Water in alluvial mining technology (ton/year): Exploration (1.25E+02), clearing and stripping (1.15E+06), float up of suction dredger (1.00E+07), mechanical screening (7.46E+07), hydraulic jigs (1.12E+07), sluice boxes (4.84E+05), Physical separation (4.46E+05), Waste Tailings Treatment Plant (3.80E-01), Services (9.38E+03 water for domestic use, not used into operational process). ^b Electrical energy in alluvial mining technology (kJ/year): clearing and stripping (9.98E+10), dipper dredger (6.86E+10), mechanical screening (4.47E+10), hydraulic jigs (2.33E+10), sluice boxes (2.76E+09), physical separation (1.92E+08), filtration-separation (7.67E+07), chemical separation (1.15E+08), WTTP (4.77E+07), tailings pond (6.95E+07), services (1.35E+10 to support suction dredger, dipper dredger and administrative offices). Hydropower run-of-river electricity production supplies 100% of the energy demand from alluvial mining. ^c Gas energy (propane) in alluvial mining technology (kJ/year): drying and separation of ferrous minerals (1.60E+07). ^d Diesel fuel (derived from petroleum) in alluvial mining technology (kJ/year): Exploration (2.86E+08), Casting and molding (4.33E+06), Services (8.34E+08 to support suction dredger, dipper dredger). ^e Oxygen (air) in alluvial mining technology (ton/year): drying and separation (20), tailings pond (20). ^f Inert material removed (sterile mineral in dry weight) in alluvial mining technology (ton/year): reserves evaluation, exploration (5.61E+02); reserves evaluation, clearing and stripping (3.65E+07); mineral extraction, dipper dredger (6.95E+07). ^g Vegetation covered harbors in alluvial mining technology (ton/year): clearing and stripping (60 corresponding to 140 hectares). ^h Sludge tails (wet weight) in alluvial mining technology 4.52E+03 with 98.7% humidity. ⁱ Energy losses in alluvial mining technology (KJ/year): clearing and stripping (9.98E+09), dipper dredger (6.86E+09), mechanical screening (2.41E+10), hydraulic jigs (2.33E+09), sluice boxes (7.73E+08), physical separation (1.92E+07), filtration-separation (2.15E+07), chemical separation (3.22E+07), WTTP (1.34E+07), tailing pond (1.94E+07), services (3.10E+09 to support suction dredger, dipper dredger and administrative offices), drying and separation of ferrous minerals (1.60E+06), Exploration (1.80E+08), Casting and molding (1.99E+03). Note: energy losses are calculated on equipment efficiency. ^j Gold (dry weight) in alluvial mining technology (ingot/year): 155 each 20kg. ^k Recycling in alluvial mining technology, water treated from WTTP to physical separation. ^l Water in open-pit Mining Technology (ton/year): clearing and stripping (5.65E+06 water for irrigation to minimize PST in the air), mineral excavation (5.08E+06 06 spray irrigation systems to minimize PST in the air), secondary milling (3.59E+07), gravimetric separation (8.32E+06), floatation (2.08E+06), elution (6.96E+05). The primary crushing step is not significant in spray irrigation systems, which is not quantified in the process. * Others in alluvial mining technology (ton/year): 1. Services (7.3 organic material in domestic wastewater). 2. Chemicals: chemical separation (emulsifying agent 0.1; foaming agent 0.23; flotation agent 0.48), WTTP (coagulating agent 0.45), Casting and molding (Sodium borate 232.68 as a fluxing agent; calcium carbonate 77.56). ^m Electrical energy in open-pit mining technology (kJ/year): mineral excavation (8.08E+10), primary crushing (7.82E+10), secondary milling (1.36E+12), gravimetric separation (2.15E+09), floatation (1.97E+11), leaching (4.45E+10), carbon adsorption (8.05E+09), detoxification (2.02E+08), tailings pond (5.34E+10), elution and carbon regeneration (3.90E+10), casting and electro-winning (7.99E+09), other services (1.55E+11 administrative offices, public services). ⁿ Gas energy (liquefied petroleum gas) in open-pit mining technology (kJ/year): other services (1.68E+10). ^o Diesel fuel (derived from petroleum) in open-pit mining technology (kJ/year): mineral excavation (1.14E+12), casting and electro-winning (1.35E+09), other services (5.35E+09 lightweight vehicles). ^p Oxygen (air) in open-pit mining technology (ton/year): flotation (2.27E+04), leaching (3.75E+05). ^q Inert material removed (sterile mineral in dry weight) in open-pit mining technology (ton/year): reserves evaluation, clearing and stripping (1.09E+03); mineral excavation (6.93E+07). ^r Vegetation covered harbors in open-pit mining technology (ton/year): clearing and stripping (1.33E+03 vegetation covered harbors). ^s Sludge tails (wet weight) in open-pit mining technology (ton/year): 2.42E+07 with 2.36E-04% humidity. ^t Energy losses open-pit mining technology (KJ/year): mineral excavation (7.48E+11), primary crushing (1.49E+10), secondary milling (2.59E+11), gravimetric separation (2.15E+08), floatation (5.50E+10), leaching (4.45E+09), carbon adsorption (3.62E+09), detoxification (5.64E+07), tailings pond (5.34E+09), elution and carbon regeneration (1.09E+10), casting and electro-winning (1.65E+09), other services (1.39E+11 administrative offices, public services). Note: energy losses are calculated on equipment efficiency. ^u Emissions, Total Suspended Particles (TSP) in open-pit mining technology (ton/year): mineral excavation (1.75E+03), primary crushing (2.41E+01), secondary milling (7.09E01), tailings pond (3.75E+02). ^v Stored material with mineral of interest (ton/year): 55% of the extracted material (3.98E+07) with a significant gold concentration is stored (3.98E+07) for beneficiation in the future when the mine is reaching its lifespan. ^w Silver (dry weight) in open-pit mining technology (ingot/year): Average 1078 each 20kg. ^x Gold (dry weight) in open-pit mining technology (ingot/year): Average 952 each 20kg. ^y Recycling in open-pit mining technology, water treated from WTTP to all the process. ** Others in open-pit mining technology (ton/year): 1. Chemicals: mineral excavation (1.41E+04 Ammonium Nitrate—Fuel Oil ANFO, 95% ammonium nitrate and 5% kerosene), chemical separation (1.08E+01 NaOH; 8.99E+01 NaCN), floatation (Potassium Ammonium Xanthate 5.29E+02; 4.37E+02 flotation agent), leaching (1.87E+03 NaCN, 2.19E+03 CaO), carbon adsorption (2.67E+03 activated carbon), detoxification (1.5E+02 CaO; 1.10E+00 H₂O₂; 1.27E+02 Na₂S₂O₅), tailings pond (flocculating agent 3.11E+02), elution and carbon regeneration (9.91E+05 inorganic chemicals). Note 1: --- data not considered in this study. Note 2: A key contribution of this study is the detailed inventory of material and energy flows for two gold mining technologies based on primary data obtained directly from mining companies. The open-pit mining data correspond to projected operations over 11 years (2014–2025), while the alluvial mining data reflect actual operational records from a 6-year period (2012–2018). Despite variations in extraction methods, the selected sites represent medium-scale mining practices in Colombia. Assuming no losses during casting and molding, the open-pit mine yields approximately 19 tonnes of gold and 21 tonnes of silver annually, equivalent to about 952 gold and 1077 silver ingots. In comparison, the alluvial mine produces around 3 tonnes of gold annually (≈155 ingots). Detailed inventory data are available in [33].

describes the input and output flows of the two studied systems, as shown in Figure 1 and Figure 2.

2.1. Open-Pit Mining Technology

Figure 1 details the extractive process by open-pit mining technology [14]. Land preparation involves clearing and stripping vegetation cover and organic soil; residual biomass is stored for restoration in subsequent years. Mineral excavation is performed by conventional extraction methods: drilling, blasting, loading, and hauling.

Ore beneficiation is carried out through physical−chemical processes. It starts with the size reduction of the excavated mineral using primary crushing and primary and secondary milling. Irrigation water is used in this step to minimize the impacts of total particulate matter (TSP) emitted. From the last stage, two process lines are obtained; the first flow goes to a flotation process to concentrate sulfide minerals containing gold (96.3% and 79.5% of gold and silver are recovered in this stage, respectively) [3]. The mineral coming from flotation that cannot be easily treated by conventional physical-chemical processes, such as crushing, milling, and flotation, goes through an intensive leaching process (34.7% and 10% of gold and silver are recovered in this process), and tailings are stored in a tailing pond. Gold recoverable by gravity (GRG) from the milling process and the thickest fraction of flotation concentrate are fed to the gravimetric concentration circuit [3].

Gold and other metals extracted from the leaching process (cyanidation) and gravimetric separation are adsorbed on activated carbon in a carbon-in-pulp circuit (CIP). These are then released into the elution column under certain pressure and temperature conditions. This gold-rich solution proceeds to the electrowinning process (elution), where selective precipitation is made by electrolysis. Once the electrowinning of gold and silver is obtained, it is sent to the casting furnace. Assuming no losses in the smelting and casting process, 19.04 tons of gold per year and 21.55 tons of silver per year are estimated, which are approximately 952 and 1077 gold and silver ingots, respectively, with a 900 millesimal fineness.

Tailings comprise flotation tails, with 96.5% of the total industrial wastewater generated in the beneficiation process, and leaching and carbon adsorption tails corresponding to the remaining 3.5%. The last two are treated by a detoxification system, where the solution of the circuit is oxidized by applying hydrogen peroxide (H₂O₂) before being stored in the tailings pool, where a dewatering process takes place, and recirculation is carried out; 98% of the water of the whole extraction and benefits process is recirculated.

Sterile carbon from the elution process (gold-uncharged carbon) is sent to a carbon-reversing furnace for reactivation and reuse in the CIP process. About 83.98% of the water in the entire process is recirculated. Notably, services used for this process are not considered an operational system (administrative offices, public services, lightweight vehicles, and emergency support plant).

2.2. Alluvial Mining Technology

The alluvial mining process is described in detail in [3] and Figure 2. First, sediment deposits conducive to exploiting alluvial gold (exploration stage) are selected. Then, preparation and access to the exploitation zone continue with clearing and stripping by suction dredgers, where vegetation cover is changed to bare soil by cutting and removing the superficial horizons of the soil [30].

The operation and beneficiation activities of the mineral occur simultaneously at the exploitation site. Mineral excavation consists of sand, gravel, clay, and minerals of interest, carried out by a Dipper dredger, which pulls the ore up from the riverbed. The physical beneficiation of the gold follows this through size classification (mechanical screening) and gravimetric concentration by hydraulic jigs and sluice boxes. As a result of these initial stages, two process flows are produced: The first waste line is composed of sterile material such as gravel, sands, clays, and silts, which returns to the river, and a second process flow (wet), rich in gold mixed with sands, ferrous metals, and other impurities, continues in the process line to increase the concentration and purification of gold (floatation stage) [33].

Approximately 11% of ore (dry basis) enters the continuous flotation stage in the beneficiation line to the filtration and separation stage, where 99% of the process stream moisture is chemically removed for further concentration. The objective is to recover 4% of the gold not obtained during the flotation stage. These gold-rich flows (wet basis) from the flotation and chemical separation process continue in the drying line, where the water is removed. The separation of gold from ferrous minerals corresponds to 3% of the gold-rich flow line [14,17].

The gold obtained from concentrates is melted. On average, the casting process is performed for 40 min with 20 kg of gold, using suitable flux loads. With a crank and gear, the tilting furnace facilitates emptying casting steel or ingot molds. Diesel fuel is injected with pressurized air for more efficient combustion, consuming 5 gal/h and 680 fuel m³/h of air. Assuming no losses in the smelting and casting process, 3103 tons/year are melted, approximately 155 ingots with a 900 millesimal fineness [3].

Tailings generated in the filtration−separation and chemical separation stages are sent to the Waste Tailings Treatment Plant (WTTP), where 99% of the water used in the beneficiation process is recovered and reused, along with the water obtained from the dewatering tailings pond. Ferrous metal is stored for future economic uses as a co-product of the process.

It is noteworthy that services used in the process, not in an operational system, such as administrative offices, public services, lightweight vehicles, emergency support plant, domestic wastewater treatment, and fuel by helicopter, are considered and accounted for.

3. Methodology

Given the finite availability of natural resources and the high global demand for energy, it is increasingly critical to understand how energy and resources are degraded. This understanding enables the development of systematic approaches to improving process performance and minimizing environmental impacts [6,15,34]. Traditional energy balance analyses are insufficient in this regard, as they do not account for the degradation or quality of energy and materials throughout a process, including inputs, products, and waste streams [35].

Exergy analysis provides a more comprehensive framework by quantifying the quality and usefulness of energy flows. This thermodynamic approach, which integrates the First and Second Laws of Thermodynamics, enables evaluation of how efficiently a process converts available energy into useful work. A higher exergy efficiency indicates a process that operates closer to its thermodynamic ideal, thereby supporting more sustainable operations.

As mentioned above, this research aims to assess and compare Colombia’s sustainability of the open-pit and alluvial mining technologies through exergy indicators. Exergy analysis is employed to evaluate the capacity of each process stream to perform work, recognizing that this capacity diminishes due to exergy destruction. The defined environmental reference conditions influence the extent of this destruction [36,37]. This study proceeds with the following three steps:

(1) The stages of each mining process were identified, and the stages where the greatest exergy losses, i.e., destroyed exergy, were determined. Likewise, other exergy indicators were calculated, such as cumulative energy/exergy demand (the sum of the total primary energy and the sum of the exergy of all resources required to provide a process or product separately), input/output exergy, relative irreversibility, exergy efficiency, exergy efficiency of the product (for valorization of those residues with usable energy content), and sustainable index for all the stages of both mining processes.

(2) Sensitivity analysis was carried out to evaluate the effect of a decrease in the work invested in the process (up to 40%) on the exergy efficiency and sustainable index (SI).

In this study, the chemical exergy of each stream was calculated assuming an ideal mixture. This assumption is justified based on the very low concentrations of gold and trace metals (typically <1 ppm in Colombian deposits), which result in dilute systems where interactions between components are minimal. Under these conditions, activity coefficients approach unity, making the ideal behavior a reasonable approximation [38].

This modeling approach is also consistent with prior exergy studies in mineral systems with similar dilution levels (e.g., [38,39]). While non-ideal interactions could be relevant in systems with higher concentrations, the influence on the overall exergy balance is negligible in this case, especially given the dominance of gangue minerals in mass and energy terms. An estimated deviation below 5% was considered acceptable for the objectives of this system-level sustainability assessment.

3.1. Identification of Exergy Loss Stages

Unlike the First Law of Thermodynamics, the Second Law shows that each process generates entropy. This indicates that the loss of energy quality plays an important role in calculating energy efficiency [40]. As already mentioned, exergy analysis is a technique based on a linear combination of the First and Second Laws of Thermodynamics. It provides an alternative process comparison, allowing us to identify how close the process is to ideality and the causes and locations of energy losses and environmental impacts [25]. A direct way to emit less waste to the environment is to have more efficient processes and use fewer resources. Thus, this analysis allows us to improve and optimize the design of the evaluated process.

The exergy of a resource counts the minimum work necessary to form it from its constituent elements found in the reference environment [36,39] or the maximum amount of work that can be obtained by carrying the components of the resource to its most common state in the natural environment, depending on the reference [38,40]. A concentrated mineral deposit “contrasts” with the reference environment, and it has exergy, which increases with the mineral concentration [39]. The Reference Environment (RE) can be assumed to be a thermodynamically dead planet, i.e., a hypothetical and homogeneous Earth [39]. All substances have been reacted and mixed without kinetic or potential energy at ambient pressure and temperature [21]. However, in this work, thermodynamic data and reference states were taken from Szargut et al. (1988) [36].

In the gold extraction process using open-pit mining and alluvial mining, analysis stages were described by Cano-Londoño et al. (2023) [3]. Here, it is necessary to establish flows of matter and energy at each stage and the composition of each stream involved in performing an exergy analysis. It is also essential to know the standard chemical exergy of each component. For the case of minerals, standard chemical exergy values are used as reported by [41]. The most representative compounds modeled engraving, sands, and clays (for both systems—open-pit and alluvial mining technology, the composition of the mineral excavated was taken as the composition of the main element of the continental crust reported in “the composition of the continental crust”. In the case of engraving, sands, and clays in alluvial mining technology, the composition is the same.) [42]. We gave a value of chemical exergy (Table S1-1, Supplementary S1). The assumption led to an error of less than 5% concerning composition. Table S1-2 (Supplementary S1) also presents the chemical properties of pure compounds in both mining systems.

The exergy of each stream was calculated from the mass fraction and the standard energy of each compound, and the exergy of the mixture according to Equation (1). In the case of this balance, it was assumed that the mixture is ideal. This is valid because the gold composition in the mineral mixture is very diluted, so it can be said that the activity coefficients are ideal due to the chemical activity between the components being negligible [36].

Since all streams that come out of the process dissipate their energy into the environment and are not used to generate useful work, the term of physical excerption was neglected in calculating each stream-specific exergy.

$${ϵ}_{chem}=\sum _{i=1}^n{x}_i{ϵ}_{chem,0}+RT\sum _{i=1}^n{x}_i\mathrm{l}\mathrm{n}\left(x_i\right)$$

(1)

The chemical exergy was calculated for the case of chemical substances that participate in the process but are not tabulated in references, like flocculation and flotation agents, foamers, and other substances used in gold extraction. We used the Gibbs-free energy and the Joback method of contribution of atomic groups to estimate their thermodynamic properties [43,44] using Equation (2) (Supplementary S2):

$$\begin{array}{c}{C}_x{H}_y{O}_z{N}_a{S}_b+\left(x+{\displaystyle \frac{y}{4}}+{\displaystyle \frac{z}{2}}+b\right)O_{2\left(g\right)}\to xC{O}_2+{\displaystyle \frac{y}{2}}{H}_2{O}_{\left(l\right)}+{\displaystyle \frac{a}{2}}{N}_{2\left(g\right)}+bS{O}_{2\left(g\right)}\\ e=x{e}_{C{O}_2}+{\displaystyle \frac{y}{2}}{e}_{H_2{O}_{\left(l\right)}}+{\displaystyle \frac{a}{2}}{e}_{N_{2\left(g\right)}}+b{e}_{S{O}_{2\left(g\right)}}-\Delta G_{f,298}\\ \Delta G_{f,298}=53.88+\sum N{D}_{G_i}\end{array}$$

(2)

In Equation (2), N is the number of the atomic group (i.e., ${CH}_2,{CH}_3$, and phenyl radical), and $D_{G_i}$ is the contribution of this group to Gibbs formation energy. This is tabulated in [34]. The average errors reported with this method are of the order of 8 to 9 kJ/mol.

For the case of vegetation cover, its chemical exergy was calculated using the method developed by Qian et al. [45], where $\Delta rs°$ is the standard specific entropy change of the combustion reaction in kJ kg⁻¹ K⁻¹ using Equation (3). The standard specific entropy was calculated by the correlation proposed by Song et al. using Equations (4) and (5) [34]:

$$\Delta rs°=xS°{CO}_2+{\displaystyle \frac{y}{2}}S°H_{2}O+{\displaystyle \frac{a}{2}}S°N_2+bS°S{O}_2-\left(x+{\displaystyle \frac{y}{4}}-{\displaystyle \frac{z}{2}}+b\right)S°O_2-s°biomass$$

(3)

$$s°biomass=0.0055C+0.0954H+0.0096O+0.0098N+0.0138S, \mathrm{k}\mathrm{J}·{\mathrm{k}\mathrm{g}}^{-1}·{\mathrm{K}}^{-1}$$

(4)

$$e=x{e}_{C{O}_2}+{\displaystyle \frac{y}{2}}{e}_{H_2{O}_{\left(l\right)}}+{\displaystyle \frac{a}{2}}{e}_{N_{2\left(g\right)}}+b{e}_{S{O}_{2\left(g\right)}}+HHV+T_o{\Delta }_{r}s°$$

(5)

where ${S°CO}_2$, ${S°H}_{2}O$, ${S°N}_2$, ${S°SO}_2$, and ${S°O}_2$ are standard entropies of carbon dioxide, water (liquid phase), nitrogen, sulfur dioxide, and oxygen, respectively, in kJ mol⁻¹ K⁻¹ [45]. Supplementary S3 and ref. [45] explains this topic in more detail.

Finally, the exergy balance in each stage of the process was developed considering the work performed and all the inputs and outputs to find exergy destroyed (E) by stage Equation (6) [45]:

$$E={\dot{m_{in}}ϵ}_{chem,in}-{\dot{m_{out}}ϵ}_{chem,out}+W_{in}-W_{out}$$

(6)

$$E=-\dot{m_{in}}\left(h_{in}-h_{out}\right)+\dot{m_{out}}\left(S_{in}-S_{out}\right)T+\dot{m_{in}}{ϵ}_{chem,in}-{\dot{m_{out}}ϵ}_{chem,out}+W_{in}-W_{out}$$

• Efficiency of the First Law

Energy efficiency (η) is defined as the ratio of the total energy for useful products or activities and the total energy input [37,46]. It evaluates how the energy content of inputs or raw materials, whether renewable or non-renewable, is exploited using First Law balances (Equation (7)). The ratio of the energy produced ($E_{prod})$and total input energy ($E_{in})$ [36] gives the efficiency as shown in Equation (7):

$$\eta ={\displaystyle \frac{E_{prod}}{E_{in}}}$$

(7)

• Efficiency of the Second Law (exergy efficiency)

The exergy efficiency $\tau$ is used to measure the degree of use of a resource [36]. It provides a tool to identify the waste and energy losses of the process by detecting areas that require technological improvements [47]. In this way, the performance of the system was evaluated to convert exergy input into exergy associated with products (it was expressed in Equation (8) as the relationship between produced exergy ($E_{prod})$ usable by the system and total input exergy ($E_{in})$ [36]:

$$\tau ={\displaystyle \frac{E_{prod}}{E_{in}}}$$

(8)

3.2. Exergy Sustainability Assessment

Analyzing the energy consumption and transformation within these systems is crucial in evaluating the sustainability and efficiency of mineral exploitation. Energy and exergy analysis comprehensively explains how useful energy is utilized, conserved and lost throughout the process. By examining indicators such as energy balance, cumulative energy demand (CEnD), and energy efficiency, we can identify opportunities for improvement and develop strategies to minimize environmental impacts. The following sections detail the methodologies and equations used to perform a thorough energy analysis, emphasizing the importance of quantifying the total energy demand and the quality of energy transformations in the system.

• Cumulative energy demand $\left(CEnD\right)$

Cumulative energy demand ($CEnD$) is used to assess the energy demand of primary energy sources throughout the production chain. Nevertheless, the quality of energy is not taken into account. It is an indicator of environmental impacts regarding system energy consumption. Equation (9) is the sum of the energy demand ${CEnD}_i$ for each i-process energy demand:

$$CEnD\sum _i={CEnD}_i$$

(9)

• Cumulative exergy demand ($CExD$)

The cumulative exergy demand ($CExD$) indicator is introduced to depict total exergy removal from nature to provide a given good or service, summing up the exergy ${CExD}_i$ of all required resources [36]:

$$CExD\sum _i={CExD}_i$$

(10)

$CExD$ assesses the quality of energy demand and includes exergy of energy carriers and non-energetic materials. CExD is equivalent to the cumulative exergy definition of Szargut, 2005, and it is expressed by the sum of the exergy demand of each process as shown in Equation (10) [37].

• Exergy efficiency of the product

Exergy efficiency of the product ${\beta }_i$ is defined as the amount of exergy that the product i ($E_{prod-i})$ contains divided by the amount of total exergy that enters the process ${(E}_{in}),$ as shown in Equation (11). This relationship between the analyzed product’s exergy and total input exergy indicates the fraction of available exergy used by the stream of interest [37]:

$${\beta }_i={\displaystyle \frac{E_{prod-i}}{E_{in}}}$$

(11)

• Ecological efficiency

Ecological efficiency is the difference between the renewable exergy resources ${\beta }_{n-r}$ and non-renewable exergy ${\beta }_r$. This indicator considers the environmental impact associated with using renewable resources compared to non-renewable resources:

$${\beta }_{ecol}={\displaystyle \frac{{\beta }_i({\beta }_{n-r}+{\beta }_r)}{{\beta }_{n-r}+{\beta }_i{\beta }_r}}$$

(12)

When renewable resources are used, the indicator acquires a value of 1, and when only non-renewable resources are used, the indicator is equal to the exergy efficiency ${\beta }_i$, as shown in Equation (12) [47].

• Exergy sustainability index

The relationship between exergy and the environment provides information of the environmental impacts of implementing a process. When the usable exergy of a system approaches 100%, environmental impacts approach zero. In 2005, Szargut defined the exergy sustainability index (concerning exergy efficiency) as the inverse of the depletion number (Equation (13)) [37,48]:

$$SI={\displaystyle \frac{1}{D_p}}$$

(13)

$$D_p={\displaystyle \frac{E_D}{E_{in}}}$$

(14)

where $SI$ is the sustainability index, $D_p$ is the depletion number, $E_D$ is the exergy destroyed in the system (irreversibilities), and $E_{in}$is the exergy input of the system.

• Relative irreversibility

Relative irreversibility allows us to visualize the contribution to the exergy destroyed by each process within the system. It is defined as exergy destroyed in i subprocess over total exergy destroyed (Equation (15)) [33]:

$$I_i={\displaystyle \frac{{Ex}_{destroyedi}}{{Ex}_{destroyed}}}$$

(15)

• Environmental exergy indicator

Finally, the environmental exergy indicator addresses the sustainability index [3], also called the environmental exergy indicator. It relates to the exergy of the products $E_{prod}$ and the exergy of the renewable resources ${\beta }_r$, non-renewable ${\beta }_{n-r}$, destroyed exergy ${Ex}_{destroyed}$, and exergy of deactivation${\beta }_{DE}$ defined as the exergy necessary to treat the waste generated in the process [49]:

$$\gamma ={\displaystyle \frac{\sum E_{prod}}{\sum {\beta }_{n-r}+\sum {\beta }_r+\sum {\beta }_{DE}+{Ex}_{destroyed}}}$$

(16)

• Environmentally unfavorable when $0<\gamma <1$;
• Internally and externally reversible process, with the exclusive use of renewable resources when $\gamma =1$;
• Environmentally favorable when $\gamma >1$;
• Internally and externally reversible process, with the exclusive use of renewable resources when $\gamma \to \infty$.

4. Results and Discussion

4.1. Energy/Exergy Indicators

Table 2. Energy and exergy indicators (thermodynamic approach) for open-pit mining technology.

Process	Energy Consumption [kW]	Input Exergy [kW]	Output Exergy [kW]	Destroyed Exergy [kW]	Exergy Efficiency [%]	Depletion Number (Dp)	Sustainable Index (SI)	Exergy Renewable Resource [GW]	Exergy Non-Renewable Resource [GW]	Ecology Efficiency [GW]	Exergy Environmental Indicator $\left(\mathit{\gamma }\right)$
Stripping	2.39 × 107	2.40 × 107	1.73 × 105	2.38 × 107	0.72	0.993	1.01	9.61 × 103	2.39 × 107	0.721
Extraction	1.36 × 108	1.38 × 108	2.21 × 106	1.36 × 108	1.60	0.984	1.02	8.65 × 103	1.38 × 108	1.604
Crushing	3.29 × 100	1.03 × 106	1.01 × 106	2.12 × 104	97.95	0.021	48.72	0.00 × 100	1.57 × 106	97.14
Milling	4.79 × 101	1.63 × 106	1.58 × 106	4.85 × 104	97.03	0.030	33.68	6.32 × 104	1.03 × 106	97.95
Gravimetric separation	7.56 × 10−2	7.98 × 105	7.76 × 105	2.26 × 104	97.16	0.028	35.26	1.47 × 104	7.84 × 105	97.21
Floatation	6.92 × 100	8.06 × 105	8.05 × 105	3.59 × 102	99.96	0.000	2245.13	3.67 × 103	8.02 × 105	99.96
Leaching	1.57 × 100	3.58 × 104	3.37 × 104	2.14 × 103	94.04	0.060	16.77	0.00 × 100	3.58 × 104	94.04
Adsorption	2.83 × 10−1	2.97 × 104	2.97 × 104	1.95 × 10−1	100.00	0.000	152,383.17	0.00 × 100	2.97 × 104	100.0
Adsorption R.	0.00 × 100	4.29 × 101	4.29 × 101	0.00 × 100	100.00	0.000	0.00	0.00 × 100	4.29 × 101	100.0
Detoxification	710 × 10−3	3.67 × 104	3.58 × 104	9.29 × 102	97.47	0.025	39.49	0.00 × 100	3.67 × 104	97.47
Tails	1.88 × 100	1.87 × 109	8.95 × 105	1.87 × 109	0.05	1.000	1.00	0.00 × 100	1.87 × 109	0.048
Elution	1.37 × 100	1.49 × 104	1.44 × 104	4.73 × 102	96.82	0.032	31.46	1.21 × 103	1.37 × 104	97.07
Regeneration	1.17 × 101	5.11 × 104	5.11 × 104	1.58 × 100	100.00	0.000	32,309.98	0.00 × 100	5.11 × 104	100.00
Casting	1.67 × 101	1.86 × 101	1.93 × 100	1.67 × 101	10.35	0.897	1.12	0.00 × 100	1.87 × 100	10.35
Global	1.60 × 108 *	1.62 × 108 **	2.54 × 106	1.59 × 108	1.57	0.98	1.02	1.01 × 105	1.62 × 108	1.58	5.95 × 10−9

* Cumulative energy demand; ** cumulative exergy demand.

and

Table 3. Exergy indicators (thermodynamic performance metrics) for each stage of the alluvial gold mining process.

Process	Cumulative Energy Demand [kW]	Input Exergy [kW]	Output Exergy [kW]	Destroyed Exergy [kW]	Exergy Efficiency [%]	Depletion Number (Dp)	Sustainable Index (SI)	Exergy Renewable Resource [GW]	Exergy Non-Renewable Resource [GW]	Ecology Efficiency [GW]	Exergy Environmental Indicator $\left(\mathit{\gamma }\right)$
Exploration	3.27 × 104	3.27 × 104	3.00 × 101	3.27 × 104	0.09	0.999	1.00	1.55 × 101	3.27 × 104	0.09
Stripping	1.14 × 107	1.28 × 107	1.33 × 106	1.14 × 107	10.46	0.895	1.12	1.43 × 105	1.26 × 107	10.61
Bucket-line	1.01 × 107	1.25 × 107	2.37 × 106	1.01 × 107	19.01	0.810	1.23	0.00 × 100	1.25 × 107	19.05
Screening	1.02 × 107	2.17 × 107	1.14 × 107	1.02 × 107	52.72	0.473	2.11	9.25 × 106	1.24 × 107	66.12
Jig	2.66 × 106	1.72 × 107	1.45 × 107	2.66 × 106	84.50	0.155	6.45	1.39 × 106	1.58 × 107	85.60
Sluice boxes	9.00 × 104	3.18 × 105	2.28 × 105	9.01 × 104	71.70	0.283	3.53	6.00 × 104	2.59 × 105	75.80
Services	1.65 × 106	1.65 × 106	1.17 × 103	1.65 × 106	0.07	0.999	1.00	1.16 × 103	1.65 × 106	0.07
Floatation	5.16 × 105	1.81 × 106	1.30 × 106	5.16 × 105	71.57	0.284	3.52	1.30 × 106	5.16 × 105	89.86
Filtration−separation	2.06 × 105	1.50 × 106	1.30 × 106	2.06 × 105	86.29	0.137	7.30	0.00 × 100	1.50 × 106	100.00
Chemical separation	3.09 × 105	3.09 × 105	1.43 × 101	3.09 × 105	0.00	1.000	1.00	0.00 × 100	3.09 × 105	0.01
Drying and separation	4.30 × 104	4.31 × 104	1.37 × 102	4.30 × 104	0.32	0.997	1.00	0.00 × 100	4.31 × 104	0.32
WTTP	1.28 × 105	1.43 × 106	1.30 × 106	1.28 × 105	91.03	0.090	11.15	1.30 × 106	1.28 × 105	99.12
Tailing pond	1.87 × 105	2.00 × 105	1.30 × 104	1.87 × 105	6.52	0.935	1.07	0.00 × 100	2.00 × 105	6.53
Casting and Molding	6.99 × 102	4.36 × 107	1.95 × 100	4.36 × 107	0.00	1.000	1.00	0.00 × 100	7.01 × 102	0.00
Global	3.76 × 107 *	5.20 × 107 **	1.44 × 107	3.76 × 107	27.75	0.723	1.38	1.22 × 107	4.12 × 107	34.56	1.14 × 10−10

* Cumulative energy demand; ** cumulative exergy demand.

present energy and exergy indicators for open-pit and alluvial mining. Open-pit mining requires a greater energy demand (1.60 × 10⁸ kW) and accumulated exergy (1.62 × 10⁸ kW) compared to the alluvial mining process (3.76 × 10⁷ kW and 5.20 × 10⁷ kW, respectively). Supplementary S4 and Supplementary S5 describe both processes, including mass, energy, and exergy balances.

It is important to note that this accumulative exergy demand includes deactivation exergy, defined as the actual decontamination cost [37]. For open-pit mining, this cost refers to the exergy invested in the tails, detoxification, and regeneration stages, with a value equal to 1.87 × 10⁹ kW. In alluvial mining, it refers to the waste tails treatment plant stage, with a value equal to 1.43 × 10⁶ kW.

Regarding exergy, the alluvial process presents a higher sustainability index (SI) with a value equal to 1.38 compared to the open-pit process with an SI equal to 1.02. This difference is reflected in the generation of entropy or destroyed exergy. This is due to the system’s fourfold higher thermodynamic irreversibilities in an open-pit process (1.59 × 10⁸ kW) versus an alluvial process (3.76 × 10⁷ kW).

For open-pit mining, 98.64% (1.57 × 10⁸ kW) of destroyed exergy is allocated to gold production, and 1.36% (2.17 × 10⁶ kW) is allocated to silver production, based on the economic allocation method and the average Colombian gold and silver market prices in 2019 at €36.21 and €0.50 per gram [3], respectively. In contrast, for alluvial mining, the allocation for gold and ferrous minerals produced was not considered because the price of ferrous ore in the Colombian market is equal to €3.00 × 10⁻⁵ per gram, which means that 99.99% of the exergy is allocated to gold production.

Exergy efficiency is directly related to the sustainability index. When the exergy efficiency of a process is low, sustainability is also low because input resources are not fully exploited. This results in waste products with a high energy content and causes environmental impacts (environmental load). Exergy efficiency for open-pit mining is 1.57%, and that is 27.75% for alluvial mining.

In open-pit mining, the stages that contribute the most to exergy destruction are tails and extraction, which are the most unsustainable. This is unlike alluvial mining, where the contribution to the overall process of exergy destruction is more distributed between stages, with casting and molding being the most influential stages, followed by stripping. This implies that the alluvial mining process is more sustainable in exergy terms compared to the open-pit mining process. This gap is primarily due to process-specific thermodynamic irreversibilities inherent to each mining method. This significant gap is rooted in process-specific thermodynamic irreversibilities. In open-pit mining, the most substantial exergy destruction originates from combustion engines used in excavation and haulage equipment, where only a fraction of the chemical exergy of diesel is converted into mechanical work; most of it is lost as heat and friction. Crushing and grinding units further contribute to irreversible losses through mechanical dissipation. Additionally, the leaching and detoxification stages involve chemical reactions with high entropy generation and exergy loss due to low reaction efficiencies and dilution of target elements. Finally, tailings management represents another major source of irreversibility due to the release of high-entropy effluents.

In contrast, alluvial mining relies primarily on gravitational and hydraulic separation. These operations involve lower energy inputs and fewer chemical transformations, resulting in less entropy generation and lower exergy destruction. Moreover, the absence of high-temperature or pressure-dependent steps further reduces the thermodynamic irreversibilities in the alluvial process chain.

These differences explain the orders-of-magnitude disparity in exergy efficiency between the two mining technologies. By linking each stage of the process to its dominant irreversibility mechanism, the exergy analysis provides a powerful diagnostic tool for identifying and prioritizing opportunities for improvement.

Table 2 shows the most common ore beneficiation phases (milling, gravimetric separation, and flotation). Refining (leaching, carbon adsorption, elution, and regeneration) and foundering show good use of the exergy resource in the open-pit mining process. Carbon adsorption and regeneration are the most sustainable phases, while mine operation (stripping), mining (mineral excavation), and waste treatment (detoxification and tailing pond) are the less sustainable steps.

Figure 3 shows the fraction of energy available in the output stream of each process (stream of interest and waste) concerning the input exergy. Only in the crushing, milling, leaching, and foundry stages does the stream of interest (gold stream) have the largest fraction of usable energy. In contrast, in the remaining stages, the exergy entering the process is transformed into waste, not products. Since stripping, adsorption, detoxification, tails, and regeneration are waste-generating processes, they have no associated stream of interest. However, in the tail stage, the water stream (A7) is recirculated within the process. Table 3 shows the exergy indicators (thermodynamic approach) for alluvial mining technology, which will be discussed later.

Unlike the casting stage, gold and silver streams have a similar available energy fraction, with the gold stream exhibiting a higher value (0.01 and 0.093 for gold and silver, respectively). Streams with potential use are sterile materials with low gold content generated during extraction and stored for future use to extend the mine’s lifespan (S1). The residual stream of the gravimetric separation process is recirculated to the grinding process to be used, and the residual stream of the floatation process (S7)—mostly water (0.65)—carries a high energy content that is used in the tailings process for dehydration of mining sludge for water recirculation. Most waste streams can be used in mining, although improving process technology in the stripping stage is necessary.

In the alluvial mining process, the greatest exergy use is in the refining (floatation, filtration−separation, chemical separation, drying, and separation) and waste treatment phases. The Waste Tails Treatment Plant (WTTP) and filtration−separation stages present the best exergy sustainability index. Unlike the mine operation (exploration and stripping), mining (dredging), ore beneficiation (screening, sluice boxes), and casting and molding stages, which have lower exergy efficiency. However, this phase’s gravimetric concentration by hydraulic jigs has a high SI of 6.45, indicating the potential for efficient resource use and valorization of residual streams with usable exergy content (Figure 4).

Figure 4 indicates the fraction of available exergy in the stream of interest (gold) used in each stage of the alluvial mining process. In the bucket line, screening, and floatation stages, the stream of interest carries the largest fraction of available energy. This is because the flow of residual streams in the first two processes is not as big as the one of interest. In the last stage, it can be said that the two output streams (S23 and S19) are used within the process.

In the other stages of the process, such as hydraulic jigs and sluice boxes, the residual streams are mainly made up of large quantities of water and sand (S17 and S17a are returned to the water source where the extractive process takes place) and a small flow that continues in the process line.

Finally, in the circuit of physical−chemical beneficiation in the flotation stage, where the greatest gold recovery occurs (S23), the processes that follow it do not have such a significant recovery, and the residual streams contain the most exergy. Notably, in the Waste Tails Treatment Plant (WTTP) and the tailing pond stage, the residual water from both processes is recovered and recirculated, allowing a significant exergy use of these waste streams (A15 and A13). Lastly, it is necessary to recover the energy contained in exhaust gases of the casting and molding stage.

The ecological efficiency and environmental exergy indicators were evaluated in both mining processes. In open-pit mining, the stages that present greater ecological efficiency are gravimetric separation, regeneration, floatation, crushing, milling, adsorption, and elution. The last process is where resources are better used. Alluvial mining processes are the filtration−separation, floatation, and WTTP, with the flotation process being the most efficient use of renewable resources.

The two processes are environmentally unfavorable concerning the environmental exergy indicator. However, alluvial mining is less unfavorable, with an indicator value equal to 1.14 × 10⁻¹⁰. This indicator is consistent with the SI calculated by Szagut [37].

Figure 5 and Figure 6 show the Grassmann exergy diagram for each stage of the open-pit and alluvial mining process in percentages and the global process by streams [GW], respectively.

Figure 5 presents the global exergy distribution for open-pit gold mining using a Grassmann diagram [24]. The figure visualizes how exergy flows are introduced, transformed and destroyed across the various stages of the process chain.

The diagram reveals that extraction and tailing management stages dominate the overall exergy destruction. In particular, the extraction step, which involves drilling, blasting, and material hauling, is a major contributor due to the intensive use of diesel and the associated combustion irreversibilities. Likewise, the tailings stage stands out as the single largest source of exergy destruction, primarily because of the detoxification and handling of massive amounts of waste with low exergy density.

Notably, while small in total exergy input, the casting stage presents considerable thermodynamic losses due to combustion for melting metals, indicating a potential hotspot for optimization—e.g., by integrating waste heat recovery or using more efficient furnaces.

Figure 6 presents the global exergy distribution for the alluvial gold mining process using a Grassmann diagram.

Compared to open-pit mining, the alluvial process shows a more balanced distribution of exergy destruction across stages, with no single step dominating the losses. However, significant exergy destruction occurs in the hydraulic jigs, bucket-line dredging, and mechanical screening, primarily due to the handling of large volumes of water and sediments with relatively low gold content. These operations involve mechanical work and generate substantial frictional and hydraulic losses.

In contrast, the flotation and filtration−separation stages demonstrate relatively better exergy performance. These stages involve more precise separation techniques and show higher-fraction usable exergy in the product stream, as reflected by the narrower loss arrows and thicker output flows in the diagram. This aligns with the numerical indicators highlighting flotation and the WTTP (Waste Tailing Treatment Plant) as the most efficient stages.

Notably, the casting and separation stage exhibits a very high level of exergy destruction relative to its product output, with a large portion of the exergy input being dissipated as waste heat and exhaust gases. This thermodynamic hotspot could be a prime target for optimization via waste heat recovery or improvements in furnace efficiency.

Overall, the Grassmann diagram reinforces the conclusion that, while alluvial mining is more sustainable in exergy terms than open-pit mining, there are still opportunities for improvement. Optimization should focus on stages with high mechanical losses and thermal inefficiencies, particularly dredging, casting, and screening.

4.2. Sensitivity Analysis

The sensitivity analysis evaluated the difference in exergy efficiency and sustainability index of each stage of the process with respect to the baseline (process without change). We assumed a decrease in work (W in kW) of up to 40% at each stage of the process (Figure 7 and Figure 8).

For the alluvial mining process, the implemented work reduction does not present any variation in exergy efficiency (concerning the baseline) of the exploration, services, chemical separation, and drying and separation stages. The most significant change is presented in screening, bucket-line, sluice boxes, and flotation, with an improvement in exergy efficiency of 12% for the first stage and 9% for the others (Figure 7a). It is important to highlight how the smelting process is not sensitive to change, knowing that it is the stage that contributes the most to global destined exergy. On the other hand, the improvement in the response variable does not have a linear behavior with work variation at each stage.

Concerning the sustainability index, there are no variations (concerning the baseline) in those stages that are not sensitive to the change in exergy efficiency. Although the biggest changes are presented in the WTTP, filtration−separation, and Jig, with an improvement of 38% (6.77), 37% (4.19), and 36% (3.63), note that these stages present greater SIs in the baseline case (Figure 7b).

For the open-pit mining process, it can be said generally that there is no significant effect on exergy efficiency and SI (concerning baseline) when work consumed in each stage of the process is reduced by up to 40%. Concerning exergy efficiency, the casting stage presents an improvement of 5.82%, followed by extraction (1.04%) and the stripping stage (0.48%) (Figure 8a).

Regarding the SI, there is a significant effect in the regeneration and adsorption stages (Figure 8b), with 74% and 58% improvements, respectively. These stages present the best sustainability index in the baseline scenario. Note that the regeneration stage reaches its highest SI when work consumed is reduced by 20%, achieving the highest exergy efficiency in this stage.

Finally, in global terms, both processes improve the overall exergy efficiency by 0.1% for open-pit mining and 5% for alluvial mining. For the global sustainability index, open-pit mining did not affect the decrease in work consumed in the process, unlike the alluvial mining process, which obtained an improvement of 7% in this index.

5. Discussion and Conclusions

Exergy analysis enables the quantification of sustainability by measuring the environmental burden associated with the use of renewable and non-renewable resources. In exergy terms, a more sustainable or efficient process makes better use of the available energy. The exergy contained in these resources is a measure of potential use, and inefficient use generates waste streams whose exergy content can be a measure of the potential to cause environmental damage. Additionally, it allows the estimation of the exergy cost of decontaminating those wastes, which is referred to as “deactivation exergy”.

In open-pit mining, several waste streams such as S1, S6, and S7 carry a high exergy content that is partially recovered or reused within the process (e.g., in extraction and flotation). The same case is presented in alluvial mining, where wastewater streams A13 and A15 from the tailing pond and WTTP are successfully recirculated, and residual gases from the casting process can potentially be recovered. However, it is noteworthy that each stage is interdependent with the others. An improvement in one of these stages can modify the exergy losses in the others, sometimes even increasing the overall destruction if not holistically optimized.

Although the alluvial mining process generates a lower environmental load (compared to open-pit mining), it is more subject to improvements in its exergy indicators (exergy efficiency and sustainable index) when mechanical work input is reduced by 40% and alluvial minimal achieves a 5% increase of exergy efficiency and a global improvement of 7% in the sustainability index (SI), compared to negligible gains in open-pit mining. This is because of the relatively small share of mechanical work (7% of the total exergy input) in open-pit operations.

Both mining processes (especially the open-pit mining technology), seen from a thermodynamic point of view, are considered anti-exergy since there is a decrease in exergy between the initial state of the input and the end of the output. This gives rise to waste with a high exergy content, and improvements can only be achieved by changing the technology for a much more efficient one and by changing the process configuration. Hence, there is a need to use methodologies complementary to exergy analysis, such as thermoeconomic analysis, which allows for justifying exergy and economic costs through the market price of gold. That is, the market price of gold internalizes the externalities generated in the process. This market price bears the exergy losses of the process and, in turn, allows for the recovery of the natural and human capital invested in the process from the cradle to the gate.

To reduce the environmental impact associated with the gold production life cycle from the cradle to the gate for the two extractive systems described in this study, four strategies should be implemented:

• Improving efficiency by reducing the exergy required in tail stages and extraction (in the open-pit mining process, casting and molding, and screening), where large exergy supplies are required.
• Increasing efficiency by reducing exergy emissions and residues in the casting and molding stage in alluvial mining and the stripping stage in open-pit mining, or by adding value to those exergetically exploitable streams. For example, S1 and S7 are used in extraction and flotation processes in open-pit mining, and S6 is used in the stripping process in alluvial mining. When released into the environment, these cause environmental degradation due to reactions that occur while achieving a balance or equilibrium with the environment.
• Using external exergy resources, such as renewable resources from nature (solar, wind, and hydraulic), as proposed by the exergy analysis method from a life-cycle perspective, where all direct and indirect resources used for the elaboration can be deemed sustainable. Open-pit mining relies on fossil fuels for approximately 53% of its exergy input, primarily through diesel combustion in excavation and transport. Replacing these inputs with renewable sources such as solar or hydropower, particularly for electricity-driven equipment, can significantly reduce exergy destruction associated with internal combustion processes. However, this strategy must consider Colombia’s contextual barriers, including limited electricity grid coverage in remote mining regions, high capital investment costs, and the prevalence of informal operations. Future work should explore scenario-based modeling to quantify the effect of progressive electrification on exergy efficiency and the sustainability index (SI). A complete techno-economic and logistical assessment is needed to define the actual feasibility of this transition in medium-scale mining operations.
• Applying the concept of circular economy and the nexus with the exergy [50] would imply a reduction in the consumption of resources in two ways:

  4.1.

  By implementing circular economy principles with thermodynamic considerations, Circular economy strategies aim to valorize residual streams (e.g., tailings, process water, and waste heat) by reintegrating them into the process or recovering their remaining exergy. In theory, this reduces both the consumption of virgin resources and the environmental burden from waste.

  4.2.

  By reducing the use of virgin resources within the process by reusing resources, since the rate of use of non-renewable resources must not exceed the rates at which renewable substitutes are developed. Nonetheless, not all residual streams are thermodynamically viable for recovery. For example, stream S7, which is composed of 65% water, has low exergy density and high entropy. According to the Second Law of Thermodynamics, recovering useful exergy from such dilute, high-entropy streams would require substantial energy input and is likely infeasible from both thermodynamic and economic perspectives [50,51].

Therefore, this strategy should focus on high-potential residuals, such as waste heat from the casting and molding stage or water recovery systems that already demonstrate high exergy retention (e.g., in the WTTP). Implementing circular economy approaches in mining contexts also requires considering regulatory, infrastructural, and organizational challenges in Colombia, such as the limited enforcement of environmental policies and the high rate of informal mining operations.

This study applied exergy analysis to evaluate and compare the sustainability of Colombia’s open-pit and alluvial gold mining. The results demonstrate a clear disparity in thermodynamic performance, with open-pit mining showing significantly higher exergy destruction and lower overall efficiency.

The exergy analysis identified critical hotspots (such as extraction, tailings management, and casting) representing key opportunities for reducing environmental impacts. In contrast, alluvial mining showed better exergy utilization in beneficiation and water recovery stages and higher sensitivity to improvements in energy use.

By quantifying irreversibilities across the process chain, this work highlights the potential of exergy analysis as a diagnostic tool for identifying sustainability gaps and guiding interventions. While strategies such as renewable integration and circular economy implementation show promise, their real-world application in Colombia requires further techno-economic assessment and context-specific planning.

Ultimately, this research contributes to a growing field that leverages thermodynamic principles for sustainability assessment and offers a replicable framework for evaluating resource-intensive industries beyond conventional energy or emissions metrics.