Exergy Assessment and Exergetic Resilience of the Large-Scale Gas Oil Hydrocracking Process

Abstract

Fossil fuels remain essential to the world’s energy supply, but the decline in the quality of the oil extracted has increased the relevance of processes such as hydrocracking. Despite its potential, this process involves high energy consumption. In order to assess its efficiency, an exergy analysis of a conventional hydrocracking unit was carried out using Computer Aided Process Engineering (CAPE) tools. After simulations, the physical and chemical exergies of the input and output streams were calculated, which showed a remarkable energy efficiency of 98.76%, attributable to the high exergy content of the products obtained (171,243,917.70 MJ/h) compared to the residues generated (1,065,290.8 MJ/h). The most significant irreversibilities were found in the Recycle Gas Sweetening stage, while the lowest exergy efficiency, 87.16%, was observed in the Residual Gas Sweetening phase. By valorizing the waste, the overall efficiency of the process increased to 99.26%, which allowed for a 40% reduction in the total irreversibilities. Optimization of the stages with the highest unavoidable losses and better energy integration of the process are suggested to maximize its performance.

1. Introduction

Crude oil remains a significant source of energy worldwide [1], particularly in Latin America and the Caribbean, where it constituted approximately two-thirds of the region’s energy matrix in 2022 [2]. While the transition to non-conventional renewable energy resources is essential for mitigating climate change, the current energy landscape necessitates a balanced approach. The continued, albeit diminishing, role of oil and gas is acknowledged, especially considering the existing infrastructure and the need for reliable energy access during the transition [3,4]. This is not a competition between fossil fuels and renewables but rather a strategic integration where fossil fuels provide essential support while renewable energy technologies mature and scale up.

The oil and gas industry will continue to play a role in the coming decades, even in scenarios aiming for substantial progress toward net-zero [5,6]. While a reduction in demand for fossil fuels is anticipated, they will be needed to bridge the gap and ensure energy security during the transition. Reports, such as McKinsey’s Global Energy Outlook, project continued energy demand growth, highlighting the challenge of meeting this demand while simultaneously shifting to cleaner energy sources [7]. Currently, a significant portion of global primary energy demand is still met by fossil fuels [8], underscoring the urgency of improving the sustainability of their extraction and processing [9]. This includes not only enhancing energy efficiency in existing operations but also actively pursuing strategies to minimize the environmental impact of fossil fuel use. Crucially, this means implementing cleaner technologies like carbon capture, utilization, and storage (CCUS), exploring the use of lower-carbon fuels, and minimizing fugitive emissions. The focus must be on transitioning toward cleaner and more responsible utilization of fossil fuels as a necessary step toward a future powered primarily by renewable energy.

Refining involves the transformation of crude oil into a range of valuable hydrocarbon products. This series of processes employs chemicals, catalysts, heat, and pressure to separate and recombine the fundamental hydrocarbon molecules naturally found in crude oil into groups of similar compounds. The petroleum refining sector has consistently evolved to address the shifting demands for more diverse and higher-quality products. This ongoing evolution has progressively enhanced product attributes, including the octane rating of gasoline and the cetane rating of diesel. Initially, the refining process was limited to the straightforward distillation of crude oil. In the 1920s, advancements led to the development of thermal cracking techniques such as visbreaking and coking. By the 1960s, processes, including catalytic cracking, alkylation, isomerization, hydrocracking, and reforming, were introduced to boost gasoline yields and enhance anti-knock properties. In the 21st century, refineries utilize both catalytic and non-catalytic methods to comply with updated product specifications and to convert fewer desirable fractions into more valuable liquid fuels, petrochemical feedstocks, and electricity [10].

Globally sourced crude oil is increasingly heavier and contains a higher concentration of heteroatoms, such as sulfur, which negatively impacts its overall quality. Concurrently, fuel demand continues to rise due to population growth, and quality standards for petroleum products are becoming increasingly stringent. This escalating global requirement has driven the adoption of unconventional heavy oil feedstocks, including heavy oils, natural bitumen, heavy residual fractions (such as vacuum residues and fuel oil), and oil sands in the refining process. As a result, there is an urgent need to enhance existing technologies for processing these heavy oils and residues alongside the development of new technologies in modern oil refining [11].

Also, the high demand for fossil fuels has raised environmental concerns and led to the implementation of new regulations in Europe and the United States that require less polluting fuels by reducing SOx and NOx [11]. This challenge of reducing the pressure of petroleum products on the natural ecosystem [12], mainly associated with the emission of these greenhouse gases, has become a crucial environmental objective since this environmental impact limits the economic growth and social development of countries [1,4]. Faced with this situation, the oil industry is forced to optimize its efficiency and accelerate the transformation of its processes to actively contribute to the transition toward cleaner energy sources [13,14] in a context where the price of crude oil and renewable energy reserves play a crucial role [4]. Improving the energy efficiency of existing industrial processes can be key to accelerating the reduction in emissions. However, it is also essential to consider economic indicators since the chemical and petrochemical sector represents approximately 28% of global industrial energy consumption, according to the International Energy Agency (IEA) [15].

International Maritime Organization (IMO) regulations on SOx and NOx emissions will have a considerable impact on the industry, with projected additional global costs for the petrochemical sector of between USD 7–9 billion annually by 2030 and USD 13–14 billion annually by 2050, in USD 2000 terms [16]. Furthermore, refineries remain major emitters of environmental pollutants. Deep oil processing units consume more energy than crude distillation due to the endothermic nature of the hydrocracking reactions involved and the separation of products and by-products. Nevertheless, these secondary processes are crucial to improving plant profitability and increasing the conversion of residues into higher-value products. Hydrocracking is one of the most widespread secondary refinery processes, but research on the energy efficiency of this unit, particularly with respect to the utilization of waste streams from the process and the optimization of equipment operating conditions to minimize the exergy destroyed, is limited in the literature, especially in industrial plants operating at large scale [17].

Hydrocracking is a versatile process that has the ability to treat a wide range of feedstocks with different characteristics to generate various products. Unlike conventional thermal cracking, fluidized catalytic cracking (FCC), and delayed coking, hydrocracking stands out for its efficiency in converting gas oils into lighter products, providing middle distillates such as jet fuels and high-quality gas oils. Regarding feedstocks, this process is especially useful for those that are difficult to process by catalytic cracking or reforming due to their high content of polycyclic aromatics and/or high concentrations of sulfur and nitrogen compounds, which are the main catalyst poisons. These feedstocks include heavy gas oils, FCC cycle oils, deasphalted oil, and coke or visbreaking gas oil [10].

The hydrocracking process is one of the main sources for the production of low-sulfur diesel and aromatic compounds, as well as high-smoke-point jet fuel. The products generated, having a higher hydrogen content, offer better combustion properties, which comply with new fuel quality regulations [18]. However, its widespread implementation faces significant obstacles, such as the high capital and energy investment required, as well as its high operating costs. For example, catalytic hydrocracking technology applied to vacuum gas oil processing requires highly sophisticated equipment and operation under extremely high hydrogen pressures, which can reach up to 200 atmospheres [19,20]. The total cost to build a hydrocracking plant has been estimated to exceed USD 1 billion [21]. Therefore, improving the efficiency of the hydrocracking process is a vital issue.

To optimize reactor performance and maximize production, it is essential that the industrial process operates under optimal conditions. Hydrocracking is a process that requires a significant amount of energy since it is carried out under high temperature and pressure conditions. However, operating costs can be significantly reduced through process optimization. In addition, raw material costs represent an important factor in the total cost of production, which can be minimized through greater efficiency in the use of resources and energy [22]. The energy quality of the fuels generated through the hydrocracking process, that is, their ability to produce energy with high efficiency, can be evaluated through exergy analysis. This analysis measures the processes in terms of the amount and quality of the energy flows involved [23,24,25]. Exergy is a thermodynamic property that allows for the quantification and comparison of the energy quality of different systems [26,27].

Exergy analysis has established itself as a useful tool for the analysis and optimization of chemical processes [28]. This method is based on the principles of mass conservation, energy conversion, and the second law of thermodynamics and is used to evaluate, design, and improve the use of energy in different systems. By performing an exergy balance on a process or an entire plant, it is possible to determine how much of the usable work potential has been consumed (or irreversibly lost) during the process, which allows for the identification of sources of inefficiency [29]. Furthermore, when combined with Computer-Aided Process Engineering (CAPE), exergy analysis facilitates the identification of improvement opportunities in terms of energy efficiency and sustainability [30]. CAPE allows us to manage multiple variables and complex systems that characterize industrial processes [31].

Currently, it is common to find research on energy conversion systems that apply the concept of exergy. Examples of this are exergy analysis applied to ethylene production [32], amine treatment units [33], olefin plants [34], hydrogen production units [35], vaccine production plants [36], and microalgae oil extraction [37], among others. However, there is a significant gap in the application of exergy analysis specifically to industrial gas oil hydrocracking process, especially when combined with exergy resilience analysis. While exergy analysis has been applied to several refining processes, the unique challenges and high energy demands of hydrocracking, coupled with the increasing importance of process resilience to fluctuations in operating conditions and waste stream management, call for more focused research. For this reason, in this work, an exergy analysis of an industrial gas oil hydrocracking plant was carried out, calculating the overall exergy efficiency, as well as the residues exergy, the destroyed exergy, the industrial services exergy, and the exergy efficiency of each stage of the process. Since hydrocracking consumes a large amount of energy, which implies high operating costs and potential pollution, its exergy analysis allows for identifying opportunities for improvement. These improvement points were determined through exergy resilience, which revealed the most inefficient stages (with low exergy efficiency) and evaluated how the overall exergy efficiency of the process improved by reducing avoidable losses related to process residues.

2. Materials and Methods

The methodology implemented for the exergy analysis of the gas oil hydrocracking process was structured in several key stages. Initially, the material and energy balance of the process was performed, establishing the operating conditions of the equipment and the process parameters (mass flows, temperature, and pressure) based on data obtained from the literature and reports from operating refineries. The process was simulated using Aspen Hysys^®, a software specialized in simulating crude oil refining processes, obtaining extended material and energy balances. From these results, the state of each pure substance and mixture was determined, helping to calculate the corresponding thermodynamic properties.

The exergy analysis was carried out in a dual manner, with a global and a local evaluation. The global analysis consisted of calculating the exergy of the incoming and outgoing streams of the process. On the other hand, the local analysis evaluated the exergies associated with the industrial services (work and heat) entering at each stage, thus determining the local exergy inputs and outputs. The output streams, which were mostly intermediate process streams, were classified into products and residues, and the corresponding exergies were quantified at each stage according to their characterization.

This information allowed for the identification of the stages with the greatest irreversibilities or exergy destruction caused by avoidable or unavoidable losses, a critical aspect of improving both the energy efficiency and the environmental performance of the process. Finally, an exergy resilience analysis was performed to identify opportunities for improvement and their impact on the overall exergy efficiency of the system. Figure 1 presents a schematic diagram illustrating the methodology used for the exergy evaluation and the exergy resilience of the gas oil hydrocracking process on an industrial scale.

2.1. Process Description

The hydrocracking process involves the catalytic cracking of heavy petroleum fractions—Medium Vacuum Gas Oil (MVGO), Heavy Gas Oil (HKGO), and Light Cycle Gas Oil (LCGO)— in the presence of hydrogen under high pressure and temperature conditions in order to produce high-quality fuels such as diesel, gasoline, kerosene, and light gas oils. This procedure is carried out over several technical phases carefully designed to maximize efficiency and comply with environmental regulations [10].

The first section of the process, referred to as the Reaction Section, includes three stages: the Reaction Stage I, the Reaction Stage II, and Mixing I. In the first reaction stage, the raw materials (stream 1) are circulated through a series of heat exchangers to increase the temperature of the feedstock before entering the heater. This initial arrangement optimizes energy use by reducing the consumption of natural gas, which is used to condition the feed stream to the first hydrocracking reactor. In addition, the exchangers play a crucial role in mitigating CO₂ and CO emissions, which is in line with environmental regulations. Once the cracking and hydrogenation reactions are completed in the reactor, assisted by quench hydrogen streams (stream 3 and stream 13), the resulting hydrocarbons (stream 14) are cooled by passing through a series of heat exchangers again. In the Reaction Stage II, unconverted oil (stream 18), a by-product of hydrocracking, is processed and serves as raw material for fuel production. This oil is heated in a heater to temperatures between 540 and 610 K. Unlike the first phase, this stage does not have a preheating train, although the operating conditions at which the unconverted oil reaches a desired temperature are close to the requirements for entering the second hydrocracking reactor, which optimizes fuel consumption and reduces emissions. Figure 2 presents the flow diagram of the reaction section of the hydrocracking process, including the stages of reaction I and II and mixing I.

The hydrocracked hydrocarbon streams from both reaction stages (stream 17 and stream 23) are mixed in a third stage referred to as Mixing I, and then, stream 24 enters the section known as Separation of Hydrogen Streams and Purification of Recycled Hydrogen, which is presented in Figure 3. The first phase of this section is Recycle Gas Sweetening. In this stage, the hydrocarbon mixture (stream 24) undergoes a hot flash separator, where a sudden pressure drop separates the hydrogen-rich gas (stream 25), which exits from the top of the liquid (stream 55) and moves downward. The top gas is cooled through heat exchangers, mixed with fresh water (stream 30), and further cooled with an air cooler. This gas (stream 32) contains impurities that need to be removed, so it passes through a three-phase separator or tricanter, where it separates into two liquid phases: a hydrocarbon stream (stream 35) and a sour water stream (stream 34), and a hydrogen-rich gas phase (stream 33). The gas stream is cooled again and sent to another flash separator, producing a recycled gas with higher hydrogen purity (stream 37C). Finally, this gas is treated in an absorption or washing tower, where contaminants such as H₂S are removed using an amine process (stream 39). The fifth stage corresponds to a Hot Flash Separation of the bottom stream from the hot separator. In this stage, the stream (stream 56) is separated into two phases: a gas phase (stream 57), which is combined with washing water (stream 58), and a liquid phase (stream 77), which is sent to the stripping section.

The following stages correspond to Mixing III, where stream 35, coming from the Recycle Gas Sweetening stage and composed of hydrocarbons, is combined with stream 60, a hydrogen-rich gas generated in the Hot Flash Separation stage. Likewise, in the Mixing IV stage, stream 34, corresponding to the sour water from the Recycle Gas Sweetening stage, and stream 38, composed of hydrocarbons from the flash separator of the same stage, are mixed.

After these last two stages, the streams resulting from the mixture (stream 61 and stream 62) enter the Decantation stage, where the residual gas obtained (stream 64) contains impurities that must be eliminated. For this purpose, this gas is subjected to a separation process called Residual Gas Separation, which uses a flash evaporator. On the other hand, the hydrocarbon stream generated in the Decantation stage (stream 72) is combined with the bottom stream of the flash evaporator of the Residual Gas Separation, heated, and directed to the Stripping stage.

The following stages, presented in Figure 4, are focused on the conditioning of make-up hydrogen and the purification of residual gas of the hydrocracking unit. The Compression stage involves the compression of the recycle gas (stream 41C). The Separation I stage is responsible for the separation of the flows corresponding to the cooling and recycling hydrogen streams that are introduced in the reaction stages (stream 13 and stream 20). The Conditioning stage involves the treatment of the make-up hydrogen (stream 45), a fresh hydrogen that enters the process and is subjected to cooling and compression. Subsequently, the process continues with the Mixing II and Separation II stages, where various process streams are combined or separated for their subsequent entry into previous or subsequent stages.

On the other hand, the residual gas (stream 68C) is subjected to an amine scrubbing process (Residual Gas Sweetening), similar to that previously used with the recycle gas. The gas (stream 71C) then passes to the Adsorption Purification Section, which comprises the Pressure Swing Adsorption (PSA) stage, in which a pure hydrogen stream is separated from other components present in the residual gas (PSA residues stream). This process is based on the affinity of the different gases toward a porous adsorbent material, allowing for the production of high-purity hydrogen.

The next section, detailed in Figure 5, is the Stripping Section, where liquid streams from the hot and cold flash separators, as well as the residual gas separator drum, are introduced into a stripper (stream 75 and stream 77), which operates similarly to a distillation tower. At this stage, medium-pressure steam (stream 78) is introduced, which ascends through the tower, stripping the liquid stream of unwanted compounds such as ammonia and hydrogen sulfide. These compounds are expelled as sour water (stream 79) and sour gases (stream 80), while light fractions, such as naphtha and liquefied petroleum gas (LPG), are removed at the top of the tower (stream 81).

Heavy hydrocarbons exiting the bottom of the stripper (stream 88) are sent to a Fractionation stage (Figure 6), where they are separated into different components according to their boiling point using low-pressure steam (stream 93). During this stage, the stream entering the distillation tower is separated into different products, such as ultra-low sulfur diesel (stream 104), kerosene (stream 109), UCO, and, to a lesser extent, naphtha (stream 114). This unconverted oil is divided into two streams: one is recycled to the second reaction stage (stream 18), while the other is sent to the Fluid Catalytic Cracking (FCC) unit (stream 97).

The last two sections of this process include two smaller distillation towers. The first of these corresponds to the Debutanization Stage (Figure 7), where butane (stream 87), the main component of Liquefied Petroleum Gas, is separated from the naphtha (stream 115), which exits through the bottom of the tower. This naphtha stream is mixed with the stream coming from the top of the fractionator (stream 114), giving rise to Mixing V, which is part of the Naphtha Separation Section (Figure 8). The resulting stream (stream 117) is directed to the final stage of this process. At this stage, the stream is separated into light naphtha (stream 121), which exits through the top, and heavy naphtha (stream 125), which is extracted through the bottom. Both products are sent to the Raw Materials and Products unit.

Figure 2, Figure 3, Figure 4, Figure 5, Figure 6, Figure 7 and Figure 8 provide a detailed representation of the large-scale hydrocracking process, where all unit operations are accurately illustrated, including the stages considered in the exergy evaluation. These process flow diagrams facilitate the visualization of the interactions between units and mass flows within the system, allowing for a more complete analysis of the process behavior at the operational level.

2.2. Exergy Analysis Using Computer-Aided Process Engineering (CAPE)

Thermodynamics is used to describe the behavior, performance, and efficiency of energy conversion systems. Conventional thermodynamic analysis is primarily based on the first law of thermodynamics, which states the conservation of energy [38]. Specifically, energy analysis of a system compares the incoming and outgoing energy, where the output energy flow can be broken down into products and residues. Efficiency is calculated as the ratio of energy quantities and is used to evaluate different systems. However, this analysis does not always accurately identify thermodynamic losses, as the first law does not account for potential work lost in energy conversion processes [39,40,41].

Exergy analysis, based on the second law of thermodynamics, considers process irreversibilities, providing a more detailed trace of energy and chemical use [9]. Exergy is defined as the maximum amount of work that a stream or system can produce when in equilibrium with a reference environment and measures the quality or utility of energy [39,40,41,42]. Unlike energy, which is conserved in any process, exergy can be destroyed due to irreversibilities, which increases the generation of entropy. This entropy generation is due to phenomena such as friction, finite gradient heat transfer, non-ideal chemical reactions, and mixing of substances. As a result, exergy degrades and decreases its ability to be converted into useful work, which limits the efficiency of energy systems [43]. The term exergy was proposed by the Slovenian Rant in 1953 [44] to describe the “technical capacity for work”, although Gibbs and Maxwell had already treated it under the concept of “available energy”, which expresses the capacity of a system to produce useful work when it proceeds from an arbitrary initial state to its stable equilibrium state through a series of reversible processes [45,46]. In the following decades, exergy analysis was developed in-depth thanks to various works by Gaggioli, Moran, Fratzscher, Beyer, Szargut, Brodyanski, and many others in the United States and Europe, consolidating its use for the evaluation of energetic and chemical processes [47].

Exergy analysis unifies the concepts of energy efficiency and energy quality. While energy efficiency measures the amount of energy converted, exergy efficiency considers the quality of that energy [39,40,41,42]. This analysis is more accurate in identifying energy losses, which, in turn, clearly determine the locations, causes, and sources of deviations from ideality in a system and in optimizing both economic performance and environmental impact, providing a complete understanding of energy conversion systems [48]. In applying exergy analysis to different processes and cycles, a fundamental aspect is to calculate the exergy value of the process streams. This value depends on the reference state selected for the components of the material system since different choices lead to different results in the exergy analysis. For the methodology applied in the exergy analysis of the large-scale hydrocracking process, the reference state is set to $T_0$ = 298.15 and $P_0$ = 1 atm, following the approach proposed in the seminal work of Szargut et al. (1998), where the average composition of the Earth’s atmosphere, seawater, and the Earth’s crust is used as the basis for chemical equilibrium [49].

As mentioned above, performing the exergy analysis involves applying both the first and second laws of thermodynamics, following a series of Equations (1)–(16) [50]. The exergy balance presented in Equation (1) states that the exergy losses are the difference between the total exergy input and the total exergy output, and such losses are unavoidable due to the second law of thermodynamics [51]. In a chemical process, there are three types of streams: material streams, power streams, and heat streams. The exergy of a material stream is calculated by summing the chemical exergy, physical exergy, and mixture exergy.

The total exergy inputs to a system are related to the mass flows entering the system (process streams) and to the required utilities (mechanical work, cooling, heating, etc.) [51], as illustrated in Equation (2). The output exergy, which corresponds to the product and residue streams exiting the system, is expressed in Equation (3). Furthermore, the exergy related to mass flow, excluding electrical, magnetic, nuclear, and surface tension effects, is calculated using Equation (4). In most processes, the contributions from kinetic exergy $\left({\dot{E}x}_{kinetic}\right)$ and potential exergy $\left({\dot{E}x}_{potential}\right)$ are negligible when compared to the chemical and physical exergy. The chemical exergy $\left({\dot{E}x}_{chem}\right)$ is determined through Equation (5), where $\left({{\dot{E}x}^0}_{chem,i}\right)$ represents the standard chemical exergy of component i in the mixture, $y_i$ is the molar or mass fraction of component i, and R is the universal gas constant.

The calculation of standard chemical exergy involves a two-step process. The initial step focuses on determining the standard chemical exergy values for the pure components of the reference environment (${{\dot{E}x}^0}_{chem,REF-i}$). This is accomplished using Equation (6), where $P_{REF-i}$ represents the partial pressure of the component, evaluated at a mean atmospheric pressure of 0.98 atm as described by Szargut et al. (1988). $P_0$ denotes the standard reference overall pressure, typically 1 atm [52]. The established literature sources provide tabulated chemical exergy values for the constituent elements of the reference environment [31,50].

For components not present in the reference environment, standard chemical exergy values $\left({{\dot{E}x}^0}_{chem,i}\right)$ are determined using Equation (7). In this equation, $v_j$ represents the number of atoms of element j in component i; $\left({\dot{E}x}_{chem-j}^0\right)$ is the standard chemical exergy of element j at a reference temperature $T_0$ and pressure $P_0$. The values of ${\dot{E}x}_{chem-j}^0$ are derived from a consistent set of reference environment species. $\Delta {G^0}_{f,i}$, represents the standard Gibbs free energy of formation for component i [52].

The physical exergy $\left({\dot{E}x}_{phy}\right)$ is calculated using Equation (8), which relates the reference ambient temperature $\left(T_o\right)$, the enthalpy of the mixture $\left(\dot{H}\right)$, and the entropy of the mixture $\left(\dot{S}\right)$ at the actual process conditions to the enthalpy $\left({\dot{H}}_0\right)$ and entropy $\left({\dot{S}}_0\right)$ of the mixture under reference ambient conditions. When the process stream behaves as an ideal gas with a constant heat capacity $\left(C_p\right)$, the physical exergy of the mixture is calculated using Equation (9); for solids and liquids with constant heat capacity $\left(C_p\right)$, a similar approach is applied to utilize Equation (10).

To calculate the physical exergy of the process streams, the Aspen Hysys^® simulator was utilized to determine the exergies associated with each flow. Since exergy is defined as the maximum potential work available, work interaction, from an energy perspective, is equivalent to exergy [53]. Therefore, the exergy present in a workflow indicates the amount of work related to it, assuming that the volume of the system streams remains constant [54].

The exergy of utilities is calculated using Equation (11), which accounts for the sum of the exergy for work $\left({\dot{E}x}_{work}\right)$ and the exergy for heat $\left({\dot{E}x}_{heat}\right)$.

The formulas for calculating both forms of exergy are presented in Equations (12) and (13). The exergy of an electric power stream is straightforward, as 1 MJ/h of electricity corresponds directly to 1 MJ/h of exergy. The work that enters the system is always considered positive. Work that comes out of a system and is not used is considered irreversibility. Conversely, the exergy of a heat stream at constant temperature and reference pressure is derived using the concept of Carnot efficiency using $T_0$ = 298.15 K as the temperature of the boundaries in the heat exergy [49].

Ultimately, the total exergy destroyed includes both unavoidable losses, associated with the irreversibilities inherent to the process derived from energy conversion, such as heat dissipation in irreversible processes or the restrictions imposed by the second law of thermodynamics; and avoidable losses, which correspond to the fraction of exergy susceptible to reduction through improvements in design, operation, system integration or current handling [55]. The latter represents the potential for exergy recovery if the residues were to be transformed into valuable products or by-products. The unavoidable losses are calculated by subtracting the exergy of the products from the total exergy inputs, as indicated in Equation (14). The exergy efficiency of a process is defined by Equation (15), which considers the total exergy destruction in relation to the total exergy inputs, while the percentage of exergy destroyed at a specific stage i of the process can be determined as shown in Equation (16).

All the equations needed to calculate the exergy, including those related to the material, heat, power streams, and the exergy losses, are presented in

Table 1. Equations applied in the exergy assessment of the gas oil hydrocracking process.

Name	Symbol	Equation	No.
Exergy losses (MJ/h)	${\dot{E}x}_{loss}$	${\dot{E}x}_{loss}={\dot{E}x}_{total-in}-{\dot{E}x}_{total-out}$	(1)
Total input exergy (MJ/h)	${\dot{E}x}_{total-in}$	${\dot{E}x}_{total-in}=\sum {\dot{E}x}_{mass}+\sum {\dot{E}x}_{utilities}$	(2)
Total output exergy (MJ/h)	${\dot{E}x}_{total-out}$	${\dot{E}x}_{total-out}=\sum {\dot{E}x}_{product}+\sum {\dot{E}x}_{residues}$	(3)
Total exergy of a substance (MJ/h)	${\dot{E}x}_{mass}$	${\dot{E}x}_{mass}={\dot{E}x}_{phy}+{\dot{E}x}_{chem}+{\dot{E}x}_{potential}+{\dot{E}x}_{kinetic}$	(4)
Chemical exergy of a mixture (MJ/h)	${\dot{E}x}_{chem-mix}$	${\dot{E}x}_{chem-mix}={\displaystyle \sum _i}{y}_i·{Ex}_{chem-j}^0+R{T}_0{\displaystyle \sum _i}{y}_i·ln(y_i)$	(5)
Standard chemical exergy for component i not present in the reference environment (MJ/h)	${{\dot{E}x}^0}_{chem,REF-i}$	${{\dot{E}x}^0}_{chem,REF-i}=R{T}_{0}ln\left[{\displaystyle \frac{P_0}{P_{REF-i}}}\right]$	(6)
Standard chemical exergy of component i of the reference environment (MJ/h)	${{\dot{E}x}^0}_{chem,i}$	${{\dot{E}x}^0}_{chem,i}={∆G}_f^0-{\displaystyle \sum _j}{v}_j{\dot{E}x}_{chem-j}^0$	(7)
Physical exergy (MJ/h)	${\dot{E}x}_{phy}$	${\dot{E}x}_{phy}=\left(\dot{H}-{\dot{H}}_0\right)-T_0(\dot{S}-{\dot{S}}_0)$	(8)
Physical exergy of an ideal gas (MJ/h)	${\dot{E}x}_{phy}$	${\dot{E}x}_{phy}=C_p\left(T-T_0\right)-T_0\left(C_{p}ln{\displaystyle \frac{T}{T_0}}-Rln{\displaystyle \frac{P}{P_0}}\right)$	(9)
Physical exergy of a substance in solid or liquid state (MJ/h)	${\dot{E}x}_{phy}$	${\dot{E}x}_{phy}=C_p\left[\left(T-T_0\right)-T_{0}ln{\displaystyle \frac{T}{T_0}}\right]-v_m(P-P_0)$	(10)
Utilities exergy (MJ/h)	${\dot{E}x}_{utilities}$	${\dot{E}x}_{utilities}={\dot{E}x}_{work}+{\dot{E}x}_{heat}$	(11)
Exergy per work (MJ/h)	${\dot{E}x}_{work}$	${\dot{E}x}_{work}=\dot{W}$	(12)
Exergy per heat (MJ/h)	${\dot{E}x}_{heat}$	${\dot{E}x}_{heat}=\sum \left(1-{\displaystyle \frac{T_0}{T}}\right){\dot{Q}}_i$	(13)
Total destroyed exergy (MJ/h)	${\dot{E}x}_{destroyed}$	${\dot{E}x}_{destroyed}=\sum {\dot{E}x}_{in}-\sum {\dot{E}x}_{products}$	(14)
Exergetic efficiency (%)	${\eta }_{Exergy}$	${\eta }_{Exergy}=1-\left({\displaystyle \frac{{\dot{E}x}_{destroyed}}{{\dot{E}x}_{in}}}\right)·100\mathrm{\%}$	(15)
Destroyed exergy (%)	${\mathrm{\%}Ex}_{destroyed,i}$	${\mathrm{\%}Ex}_{destroyed,i}=\left({\displaystyle \frac{{\dot{E}x}_{destroyed,i}}{{\dot{E}x}_{total-destroyed}}}\right)·100\mathrm{\%}$	(16)

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2.3. Exergetic Resilience Analysis

The concept of “exergy resilience” is introduced for the first time in this work, referring to a comprehensive analysis of a system or process in order to optimize its exergy performance. This assessment focuses on identifying key stages within the process and their ability to adapt to variations in their exergy environment. In other words, the impacts of various variables on the overall exergy efficiency of the process are investigated, based on the methodology proposed by González-Delgado et al. [54], where in each scenario, one variable is modified while the others are kept constant. The selection of these variables is based on the findings of the global exergy analysis, prioritizing those stages with low efficiency or with significant losses, both avoidable and unavoidable. This study focuses on describing how waste reuse increases efficiency, how local exergy efficiency influences global efficiency, and how reducing unavoidable losses can improve overall performance. For specific stages that present low efficiency, a selection is made to evaluate the impact of improving local efficiency on the overall efficiency of the process. For stages that generate significant avoidable losses, we examine how efficiency could be improved if these residues were treated as a “product”, which also helps to assess their possible integration into the system. Finally, we analyze the unavoidable losses of the process in relation to energy production, allowing us to identify the areas where losses are most critical and which should be prioritized in future research, such as energy integration.

On the other hand, exergy resilience, in the context of this study, is defined as the assessment of the ability of the gas oil hydrocracking process to maintain its exergy efficiency in the face of variations in operating and energy conditions. Unlike a sensitivity analysis, which examines the impact of individual changes in specific parameters, exergy resilience analyzes the integrated behavior of the system in the face of perturbations from multiple factors. This approach allows for identifying critical points and proposing optimization strategies that consider the interaction between various process variables. In this study, exergy resilience is evaluated through cumulative impact analysis, where it was determined how the sequential elimination of irreversibilities at each stage of the process affects the overall exergy efficiency; stream integration evaluation, where it was examined how variations in input variables influence the overall process performance, considering the interdependence between process streams, and optimization of interdependent variables, where the effect of simultaneous changes in multiple operating parameters (temperature, pressure, etc.) on exergy efficiency was evaluated. Exergy resilience provides a holistic view of process behavior in the face of complex changes, allowing for the identification of strategies to improve its robustness and energy efficiency.

Exergetic resilience allows us to evaluate the capacity of the gas oil hydrocracking process to maintain its exergetic efficiency in the face of operational and energy variations. Unlike conventional exergetic analysis, which offers a static view, exergetic resilience analyzes the integrated behavior of the system in the face of multiple disturbances. This provides a more complete understanding of the process, identifying critical points and opportunities for optimization to improve its robustness and energy efficiency.

3. Results and Discussion

In order to perform an accurate exergy analysis, it is essential to have detailed information on the operating conditions of the process, as well as the associated material and energy flows. In this regard,

Table 2. Operational conditions of the process main streams.

Stream Number	1	3	13	18	20	21
Stream	Charge	Recycle Hydrogen	Quench Hydrogen to Reaction Stage I	UCO	Quench Hydrogen to Reaction Stage II	Recycle Hydrogen to Reaction Stage II
Temperature (K)	385.37	391.48	338.71	610.93	338.71	391.48
Pressure (atm)	4.40	165.60	165.60	153.70	165.60	165.60
Mass flow (kg/h)	221,147	22,515	34,398	185,381	8574	22,645
Mass composition
Liquid water	0.000	0.000	0.000	0.000	0.000	0.000
Water steam	0.000	0.002	0.004	0.000	0.004	0.002
Ammonia (Vapor phase)	0.000	0.000	0.000	0.000	0.000	0.000
Hydrogen sulfide (Vapor phase)	0.000	0.000	0.000	0.000	0.000	0.000
Hydrogen (Vapor phase)	0.000	0.584	0.522	0.000	0.522	0.584
Methane (Vapor phase)	0.000	0.203	0.233	0.000	0.233	0.203
LPG (Liquid phase)	0.000	0.000	0.000	0.000	0.000	0.000
LPG (Vapor phase)	0.000	0.154	0.161	0.000	0.161	0.154
Light Naphta (Liquid phase)	0.000	0.000	0.000	0.000	0.000	0.000
Light Naphta (Vapor phase)	0.000	0.040	0.070	0.000	0.070	0.040
Charge (Liquid phase)	1.000	0.000	0.000	0.000	0.000	0.000
Charge (Vapor phase)	0.000	0.000	0.000	0.000	0.000	0.000
Heavy Naphta (Liquid Phase)	0.000	0.000	0.000	0.000	0.000	0.000
Heavy Naphta (Vapor Phase)	0.000	0.015	0.011	0.000	0.011	0.015
Kerosene (Liquid phase)	0.000	0.000	0.000	0.000	0.000	0.000
Kerosene (Vapor phase)	0.000	0.001	0.000	0.000	0.000	0.001
Diesel (Liquid phase)	0.000	0.000	0.000	0.000	0.000	0.000
Diesel (Vapor phase)	0.000	0.000	0.000	0.000	0.000	0.000
UCO (Liquid phase)	0.000	0.000	0.000	1.000	0.000	0.000
UCO (Vapor phase)	0.000	0.000	0.000	0.000	0.000	0.000
Nitrogen (Vapor phase)	0.000	0.000	0.000	0.000	0.000	0.000
Oxygen (Vapor phase)	0.000	0.000	0.000	0.000	0.000	0.000
Carbon Dioxide (Vapor phase)	0.000	0.000	0.000	0.000	0.000	0.000
Carbon Monoxide (Vapor phase)	0.000	0.000	0.000	0.000	0.000	0.000
Methyldiethanolamine (Liquid phase)	0.000	0.000	0.000	0.000	0.000	0.000
	1.000	1.000	1.000	1.000	1.000	1.000

and

Table 3. Operational conditions of the process main streams (continuation).

Stream Number	24	45	Hydrogen (Final Product)	87	97	104	109	121	125
Stream	Effluent of Reactors	Make-Up hydrogen		LPG	UCO to FCC	Diesel	Kerosene	Light Naphta	Heavy Naphta
Temperature (K)	565.86	298.15	337.44	316.72	610.93	316.48	316.48	311.34	316.48
Pressure (atm)	145.67	21.28	24.82	11.21	153.70	2.00	2.00	10.87	10.39
Mass flow (kg/h)	495,135	32,628	25,513	3774	9114	106,595	60,537	9801	31,093
Mass composition
Liquid water	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
Water steam	0.000	0.001	0.004	0.000	0.000	0.000	0.000	0.000	0.000
Ammonia (Vapor phase)	0.002	0.000	0.000	0.001	0.000	0.000	0.000	0.000	0.000
Hydrogen sulfide (Vapor phase)	0.005	0.000	0.000	0.015	0.000	0.000	0.000	0.000	0.000
Hydrogen (Vapor phase)	0.087	0.608	0.540	0.000	0.000	0.000	0.000	0.000	0.000
Methane (Vapor phase)	0.040	0.192	0.224	0.002	0.000	0.000	0.000	0.000	0.000
LPG (Liquid phase)	0.003	0.000	0.000	0.968	0.000	0.000	0.000	0.255	0.000
LPG (Vapor phase)	0.040	0.152	0.155	0.000	0.000	0.000	0.000	0.000	0.000
Light Naphta (Liquid phase)	0.003	0.000	0.000	0.013	0.000	0.000	0.000	0.703	0.000
Light Naphta (Vapor phase)	0.025	0.029	0.067	0.000	0.000	0.000	0.000	0.000	0.000
Charge (Liquid phase)	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
Charge (Vapor phase)	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
Heavy Naphta (Liquid Phase)	0.016	0.000	0.000	0.000	0.000	0.000	0.007	0.042	0.982
Heavy Naphta (Vapor Phase)	0.050	0.016	0.010	0.000	0.000	0.000	0.000	0.000	0.000
Kerosene (Liquid phase)	0.055	0.000	0.000	0.000	0.000	0.015	0.993	0.000	0.018
Kerosene (Vapor phase)	0.071	0.001	0.000	0.000	0.000	0.000	0.000	0.000	0.000
Diesel (Liquid phase)	0.167	0.000	0.000	0.000	0.000	0.959	0.000	0.000	0.000
Diesel (Vapor phase)	0.039	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
UCO (Liquid phase)	0.392	0.000	0.000	0.000	1.000	0.025	0.000	0.000	0.000
UCO (Vapor phase)	0.006	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
Nitrogen (Vapor phase)	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
Oxygen (Vapor phase)	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
Carbon Dioxide (Vapor phase)	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
Carbon Monoxide (Vapor phase)	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
Methyldiethanolamine (Liquid phase)	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000

present the data of the key process streams, which include product fractions of interest and intermediate streams with a high exergy content. The operating parameters recorded include temperature, pressure, and composition of the streams. This information forms the basis for applying the exergy equations, allowing for the identification of the critical stages of the process, as described in the methodology.

The hydrocracking process of gas oils operates under extreme conditions, reaching temperatures of up to 741 K and pressures of approximately 166 atmospheres. The Fractionation and Reaction Stages exhibit the highest temperatures and pressures of the process, as evidenced by streams 18 and 97, which correspond to the unconverted oil exiting from the bottom of the fractionator, along with streams 14 and 22, representing the hydrocracked hydrocarbons from reactors I and II, respectively. These extreme conditions result from the conditioning of replacement and recycling hydrogen, as well as the highly exothermic hydrotreating reactions occurring in the reactors.

In general terms, the operational parameters of the process display very high temperature and pressure values, except for the streams containing final products or intermediate distillates (naphtha, LPG, Kerosene/Jet Fuel, and Diesel), such as streams 86, 104, 109, 120, and 123, which predominantly originate from the upper part of the separation towers or in the cooling systems with heat exchangers.

Subsequently,

Table 4. Physical exergy and chemical exergy of all streams in the exergy analysis of the gas oil hydrocracking process.

Stream	Physical Exergy (MJ/h)	Chemical Exergy (MJ/h)
1—Charge	5879.95	10,386,290.72
3—Recycle Hydrogen	90,823.93	1,996,917.04
Air—1	10,340.72	245.50
Fuel gas—1	57,371.85	3663.51
13—Quench hydrogen to Reaction Stage I	123,030.01	2,903,214.98
17—Hydrocracked Hydrocarbons from Reaction Stage I	280,533.41	14,867,259.35
18—UCO	59,159.07	8,526,068.65
Air—2	2542.79	60.37
Fuel gas—2	4972.03	900.86
20—Quench hydrogen to Reaction Stage II	30,666.59	723,658.44
21—Recycle hydrogen to Reaction Stage II	91,346.71	2,008,377.59
23—Hydrocracked Hydrocarbons from Reaction Stage II	168,973.98	11,171,370.30
24—Effluent of reactors	448,804.63	26,037,710.54
30—Wash water	495.78	1089.02
34—Sour water	590.79	9907.72
35—Hydrocarbons from Recycle Gas Sweetening	3691.87	4,497,309.68
38—Hydrocarbons from Recycle Gas Sweetening	26.51	22,684.92
39—Poor Amine	1027.09	669,458.17
40—Rich Amine	870.34	724,018.20
41C—Recycle gas Cutter	278,039.12	6,796,742.54
43—Recycle gas	155,393.08	3,666,870.24
Hydrogen to PSA Stage	87,815.13	2,072,207.37
44—Recycle gas to Mixing II	44,821.28	1,057,664.94
45—Make-up hydrogen	78,531.54	2,947,722.12
52—Compressed Hydrogen	136,160.01	2,947,730.08
54—Hydrogen to Separation II	182,170.10	4,005,318.74
56—Hot flash gas from Recycle Gas Sweetening	77,141.91	14,742,538.66
58—Wash water	54.53	119.79
60—Cooled gas	3009.96	455,829.67
62—Hydrocarbons with sour water	4996.09	4,950,770.45
63—Sour water	615.52	32,496.32
64—Overhead gas from Decantation	282.38	10,116.98
68C—Gas Cutter	3777.30	206,076.79
69—Poor Amine	4413.24	228,925.93
70—Rich Amine	15.31	29,990.44
71C—Residual gas Cutter	10.03	3858.31
Residues from PSA	4372.02	225,166.73
Hydrogen (Final Product)	477.40	114,158.67
73—Hydrocarbons from Residual Gas Separation	58,708.02	2,204,443.10
75—Hydrocarbons mix to Stripping Stage	0.32	1011.99
77—Hot flash liquid	15,800.66	4,773,518.44
78—Medium steam	70,552.96	14,288,392.29
79—Sour water	3451.94	2111.17
80—Sour gas	6.26	1023.24
81—Naphta	604.70	115,014.58
84—Sour water	153.67	799,115.05
85—Sour gas	0.00	0.55
87—Liquefied Petroleum Gas	23.12	7605.37
88—Hydrocarbons from the Stripping Stage	141,889.20	18,148,257.77
Air—3	4126.08	97.96
Fuel gas—3	8026.05	1461.79
93—Low steam	2854.43	2018.86
97—UCO to FCC	2908.38	419,160.27
104—Diesel	138.24	5,015,731.21
109—Kerosene	78.83	2,857,000.32
111—Recycling water	127.58	164.51
112—Fuel gas	0.16	32.42
114—Naphta to Naphta Separator	5441.81	1,335,600.40
115—Light/Heavy Naphta	500.97	610,235.07
117—Mixture to Naphta Separator	957.41	1,945,255.25
119—Recycling water	0.07	1.35
121—Light Naphta	67.53	472,412.19
125—Heavy Naphta	80.26	1,473,608.08

presents the key streams necessary to carry out an accurate exergy balance in a staged process. The chemical exergies of the process streams are determined using the chemical exergies of the individual components under standard pressure and temperature conditions, as referenced in the specialized literature. If the chemical exergy is unavailable, it is calculated from the standard exergies of the atoms that compose the corresponding molecules.

Alternatively, the physical exergies of the streams involved in the gasoil hydrocracking process were calculated based on the simulation performed with Aspen Hysys^®. Additionally, it is observed that the operating parameters of the hydrocracking process significantly influenced the exergy value of the streams, with a notable contribution from physical exergy, reaching up to 448,804.63 MJ/h. This high value is directly related to the large mass flows of the processed streams.

As for chemical exergy, the streams show substantial values, reaching up to 26,037,711 MJ/h. The chemical composition of these streams is the predominant factor behind these exergy values, especially due to the presence of substances such as hydrogen, fuels (liquefied petroleum gas, light and heavy naphtha, kerosene, diesel), and other derived products like unconverted oil (UCO).

3.1. Exergy Analysis of the Gasoil Hydrocracking Process

In

Table 5. Results of the exergetic assessment of the gas oil hydrocracking process by stages.

Stage	${\dot{\mathit{E}}\mathit{x}}_{\mathit{w}\mathit{o}\mathit{r}\mathit{k}}$ (MJ/h)	${\dot{\mathit{E}}\mathit{x}}_{\mathit{h}\mathit{e}\mathit{a}\mathit{t}}$ (MJ/h)	Residues Exergy –Out (MJ/h)	Total Irreversibilities (MJ/h)	Destroyed Exergy (%)	Exergetic Efficiency (%)
Reaction Stage I	6641.02	109,019.55	61,035.37	484,610.65	22.53%	96.90%
Reaction Stage II	0.00	196.14	5872.89	101,732.07	4.73%	99.11%
Mixing I	0.00	0.00	0,00	1621.87	0.08%	99.99%
Recycle Gas Sweetening	72.00	14,734.91	735,387.05	755,216.93	35.10%	97.22%
Hot Flash Separation	1.73	0.00	0.00	2071.74	0.10%	99.99%
Compression	15,195.91	0.00	0.00	5205.54	0.24%	99.93%
Separation I	0.00	0.00	0.00	41,693.29	1.94%	98.91%
Conditioning	80,613.13	0.00	0.00	22,976.70	1.07%	99.26%
Mixing II	0.00	0.00	0.00	306.90	0.01%	99.99%
Separation II	0.00	0.00	0.00	23.58	0.00%	100.00%
Mixing III	0.00	0.00	0.00	98.10	0.00%	99.70%
Mixing IV	0.00	0.00	0.00	4074.64	0.19%	99.92%
Decantation	0.00	27,701.84	10,399.36	18,419.34	0.86%	99.63%
Residual Gas Separation	0.00	0.00	0.00	121.31	0.01%	99.95%
Residual Gas Sweetening	0.00	0.00	3868.34	33,806.16	1.57%	87.16%
Pressure Swing Adsorption	0.00	214.61	114,636.07	126,624.74	5.89%	94.70%
Stripping	0.00	90,239.58	116,648.78	154,651.34	7.19%	99.20%
Fractionation	8951.68	284,788.73	9812.51	371,697.53	17.28%	98.00%
Debutanization	18.18	3147.94	7629.04	10,072.81	0.47%	98.74%
Mixing V	0.00	0.00	0.00	5565.60	0.26%	99.71%
Naphtha Separation	89.07	10,693.41	1.42	10,827.07	0.50%	99.45%
Total	111,582.72	540,736.7	1,065,290.83	2,151,417.91	100.00%

and Figure 9, the exergetic performance of the different stages of the industrial gas oil hydrocracking process is presented, along with their contribution to key exergetic parameters, such as irreversibilities, exergy losses, utility exergy, and residues exergy. When analyzing local efficiency, the stage with the lowest value corresponds to the Residual Gas Sweetening stage, with 87.16%, followed by the Pressure Swing Adsorption (PSA) stage (94.70%), the Reaction Stage I (96.90%), and the Recycle Gas Sweetening stage (97.22%). These values suggest favorable exergetic performance, as most of the employed exergy is transferred to the product streams with minimal waste or by-product generation. However, the Recycle Gas Sweetening stage exhibited the highest irreversibilities, with 755,216.93 MJ/h, which are related to avoidable losses or residues with an exergy content of 735,387.05 MJ/h. These losses are associated with streams with high exergy values, such as the rich amine exiting the absorber tower and the sour waters leaving the three-phase separator. Nevertheless, both streams contain no significant fractions of products of interest, indicating that the separation processes in this unit operate with high efficiency.

As for the stages responsible for the production of LPG, naphtha, kerosene/jet fuel, and diesel—such as Stripping, Fractionation, Debutanization, and Naphtha Separation, as well as Decantation—the analysis shows the following: the Stripping, Debutanization, and Decantation stages are associated with avoidable losses related to residues (116,648.78 MJ/h, 7629.04 MJ/h, and 10,399.36 MJ/h, respectively). In these stages, energy use is mainly linked to heat, as utility exergy does not represent a significant value due to the limited use of mechanical equipment, except for a pump in the Debutanization stage. Process efficiency is also favored by the fact that the separation towers are small (with fewer than 15 trays), allowing for a controlled temperature profile, while in Decantation, a three-phase separator with minimal energy consumption is used. Exergy losses in these stages are primarily associated with the high exergy content of hydrogen sulfide and ammonia in the residual sour water and gas streams.

With respect to the Reaction Stage I, it registered the highest exergy losses of the process (423,575.28 MJ/h), with the exothermic nature of the hydrotreating reactions being the dominant factor in exergy destruction. In contrast, the second reaction stage showed losses of only 95,859.18 MJ/h. This difference is due to the feed conditions in the hydrocracker I, which contains a mixture of alkanes, naphthenes, olefins, and aromatics. During hydrocracking and hydrotreating reactions, the conversion of these substances into middle distillates releases a large amount of heat, hindering reactor efficiency. Moreover, the hydrocracker I feed stream requires significant energy conditioning through pumps, heat exchangers, and furnaces to reach operational conditions. In contrast, the unconverted oil entering hydrocracker II already approaches the necessary conditions, reducing energy consumption. This is reflected in the utility exergy of the Reaction Stage II (196.14 MJ/h) compared to that of the Reaction Stage I (115,660.57 MJ/h), suggesting the need for a more detailed analysis of energy flows to identify the exact sources of the losses.

As for the peculiar stages of Mixing I–V, Hot Flash Separation, Compression, Separation II, and Residual Gas Separation, they do not generate waste streams. This means that the irreversibilities observed in these stages correspond solely to exergy losses due to entropy generation in the system. In these stages, exergy losses were minimal (1621.87 MJ/h, 306.90 MJ/h, 98.10 MJ/h, 4074.64 MJ/h, 5565.60 MJ/h, 2071.74 MJ/h, 5205.54 MJ/h, 23.58 MJ/h, and 121.3 MJ/h, respectively) compared to other parts of the process. These low losses can be attributed to minimal entropy variation, likely because there were no drastic changes in the temperature and pressure parameters of the outlet streams relative to the initial conditions. Additionally, energy dissipation was probably low, either due to the absence of significant friction with pipe walls or minimal turbulence, suggesting efficient energy management in these stages. Regarding the compression process, the compressors were simulated in Aspen Hysys^® with an isentropic efficiency of 85%, based on values reported by Dincer and Rosen [56]. These compression-related exergy losses, also known as mechanical–electrical losses, arise from imperfections in electrical, mechanical, and isentropic efficiencies. This highlights the importance of carefully selecting compression equipment, as poorly performing components can significantly decrease overall system efficiency.

Finally, concerning the Fractionation stage, it presented the highest utility exergy (293,740.42 MJ/h) and the second-highest exergy losses (361,885.01 MJ/h), surpassed only by the Reaction Stage I. These losses are due to thermal and mechanical inefficiencies related to the large number of heat exchangers and air coolers required to maintain the products in proper conditions for delivery to the Raw Materials and Products Unit. In Naphtha Separation, exergy losses were mostly unavoidable (10,825.65 MJ/h), mainly related to system conditions and equipment operation.

Figure 10 illustrates the overall process performance, highlighting an exergy efficiency of 98.76%, indicating outstanding energy management in the production of high-value-added fuels. This efficiency compares favorably with other processes in the petrochemical sector, as shown in

Table 6. Comparison of global exergetic efficiency between several petrochemical processes.

Process	Global Exergetic Efficiency	Reference
Ethylene production	80.90%	[32]
Amine treatment unit	83.81%	[33]
Hydrogen production unit	66.60%	[35]
Large-scale gas oil hydrocracking process	98.76%	This study

. This high performance is due to a significant proportion of the input exergy being preserved in the output streams, most of which are products. Hydrocracking is a highly efficient process in which a portion of the feedstock, such as unconverted oil (UCO), is recovered within the same cycle and recirculated to maximize the production of middle distillates. Furthermore, the cooling hydrogen streams entering the process are mostly recovered in the Residual Gas Production, Separation, and Recycle Hydrogen Conditioning Section, significantly reducing the need for fresh hydrogen addition (make-up hydrogen). This not only optimizes hydrogen usage but also favors the production of final products with high exergy content compared to the low amount of residues generated in the process. This level of efficiency was expected, as hydrocracking is a mature technology that has been well-established for decades in the petrochemical industry with a proven operational track record.

Regarding waste, the total exergy associated with it reached 1,065,290.83 MJ/h, indicating a notable potential for reuse, as the waste streams have high physical and chemical exergy content. On the other hand, unavoidable exergy losses accounted for 51% of the total irreversibilities in the process (2,151,417.91 MJ/h), amounting to 1,086,127.08 MJ/h. In terms of utilities, a total of 652,319.43 MJ/h was recorded, with heat being the primary energy source for the process, contributing a total exergy of 540,736.71 MJ/h, compared to a lower exergy associated with mechanical work (111,582.72 MJ/h). It is worth noting that the exergy associated with utilities was lower than that of unavoidable losses, highlighting that the greatest exergy losses are related to changes in the exergy content of the streams throughout the process rather than inefficiencies linked to heat or power flows. This suggests that a significant amount of exergy present in the process streams is not effectively utilized and, therefore, wasted.

Although the gas oil hydrocracking process exhibits considerably high overall exergy efficiency, this analysis is based on specific operating conditions, including a constant feed flow and fixed operating parameters (temperature, pressure, and inlet stream composition). Consequently, a parametric sensitivity analysis was performed to evaluate the impact of variations in pressure, temperature, and stream composition on the key variables of the exergy analysis: overall efficiency, total irreversibilities, exergy losses, waste exergy, industrial products, and services.

Variations in the temperature of the process streams, particularly in the feed stream (a mixture of heavy gas oils not processed in previous units, such as Fluidized Catalytic Cracking, Vacuum Distillation, and Delayed Coking), can significantly affect the performance of the hydrocracker unit. Fluctuations in the inlet temperature may require higher fuel consumption in the reaction stage I furnace to reach optimal reaction conditions in the hydrocrackers, which implies an increase in pollutant gas emissions (in case of incomplete combustion). Typical hydrogen consumption in hydrocracking (including pretreatment) ranges from 200–420 Nm³/m³/wt% conversion, with a heat release of 2.1–4.2 kcal/m³ H₂, resulting in an approximate temperature rise of 0.006 °C/Nm³/m³ of H₂ consumed. The optimum reaction temperature for efficient conversion is between 630 and 660 °K. Lower temperatures can inhibit hydrotreating and hydrocracking reactions, favoring the production of heavy fractions (unconverted oil) instead of light fuels (naphtha and LPG), which alters the chemical exergy of the products. In addition, fluctuations in the temperature differential of the heat exchangers can generate irreversibilities, increasing the physical exergy of the streams and modifying the exergy value of the heat entering the process. However, the equipment configuration of the hydrocracking process is designed to mitigate the impact of these fluctuations and ensure optimal reaction, separation, and purification conditions. The physical exergy of the streams does not represent a substantial proportion of the total exergy, so significant temperature changes are required to affect the overall efficiency. It is crucial to note that temperature influences avoidable process losses associated with the exergy lost in residual streams. In this analysis, avoidable losses were identified in high-exergy waste streams from high-temperature and high-pressure processes. Reducing the temperature of these streams could reduce losses and improve overall efficiency.

Similarly, abrupt pressure variations can increase irreversibilities in compression or pumping processes, increasing the work energy entering the system. If equipment is not designed to withstand these fluctuations, it can compromise hydrocracking and hydrotreating reactions, as well as separation processes in flash drums and absorption towers. In addition, pressure can affect the temperature profile in distillation towers, altering the separation of valuable products.

The hydrocracking process operates with heavy oil fractions, specifically a mixture of light, medium, and heavy gas oils, whose composition depends on the performance of previous processing units. While the proportion of these components tends to be relatively stable (14–15% LCGO, 22–32% HKGO, and 52–53% MVGO) under normal operating conditions, significant variations can affect reactor processing. An increase in the heavy hydrocarbon fraction not only modifies the chemical exergy of the streams but also alters the operating conditions and product distribution, favoring the production of less valuable fractions and complex compounds with heteroatoms (sulfur, nitrogen, and oxygen). This can increase hydrogen consumption in hydrotreatment, heat release, and energy demand in contaminant removal, affecting overall efficiency.

Consequently, if equipment is not adapted to handle variations in feedstock composition, more energy will be required to achieve the desired production of light fuels, which can result in increased exergy destruction and decreased overall efficiency.

Figure 11 illustrates the contribution of the various stages to the total irreversibilities of the process. The Recycle Gas Sweetening stage contributes the most, accounting for 35.10% of the total. This high contribution is due to the waste streams with elevated exergy content, such as the sour water from the three-phase separator and the rich amine exiting the absorber tower. These streams contain components with high-standard chemical exergy, such as hydrogen sulfide (H₂S), ammonia (NH₃), and methyldiethanolamine (MDEA) in the amine stream. The rest of the stages show substantially lower contributions, with Reaction Stage I reaching 23% and the Fractionation Stage 17%. This indicates that although waste is also generated in these phases, the exergy losses are not as significant, primarily relating to exergy degradation due to entropic effects, such as thermal dissipation and temperature conditions of the streams.

However, it is feasible to recover waste from the stages with the greatest impact on irreversibilities, such as Stripping (7.19%), Pressure Swing Adsorption (5.89%), and Reaction Stage II (4.73%). On the other hand, other stages require a detailed technical analysis to modify their operating conditions, as they virtually do not generate residues with significant exergy content. Additionally, out of the 21 process stages, 11 do not generate residues, explaining why their contribution to the system’s total irreversibilities is less than 2%.

3.2. Exergetic Resilience Analysis of the Gasoil Hydrocracking Process

To evaluate the exergy resilience of the process, different scenarios are proposed to analyze the impact of operating variables on overall exergy efficiency. Figure 12 illustrates the effect of waste valorization in the industrial-scale hydrocracking process of gas oils, considering three scenarios: a baseline case without valorization (Scenario 1) and two cases where waste streams are treated as products. In Scenario 2, sour water and recycled water streams from the Recycle Gas Sweetening, Decantation, Stripping, Fractionation, Debutanization, and Naphtha Separation stages are included. In Scenario 3, in addition to the sour water streams from the previous scenario, rich amines from the Recycle Gas Sweetening and Residual Gas Sweetening stages, along with the residues generated in the PSA, are also incorporated. Although the improvement in overall efficiency between Scenario 1 and Scenario 2 may seem marginal, with an increase from 98.76% to 98.77%, the absolute reduction is considerable, achieving a decrease of 22,221.43 MJ/h in total irreversibilities. However, when analyzing Scenario 3, a significant 40% reduction is observed compared to Scenario 1, with irreversibilities decreasing by 865,614.38 MJ/h.

The main difference between Scenarios 2 and 3 lies in the presence of streams with high exergy content, particularly in the gas sweetening and PSA stages. Specifically, the rich amine streams from the Recycle Gas Sweetening and Residual Gas Sweetening stages exhibit mass flows of 60,600.60 kg/h and 2757.38 kg/h, respectively, while the PSA waste stream reaches a flow of 2.388,84 kg/h, all at an approximate temperature of 315 K. This contrasts with the sour water and recycle water streams, whose flow rates range between 32 kg/h and 4200 kg/h, with the exception of a sour water stream of 25,390.57 kg/h from the Recycle Gas Sweetening stage and another of 28,528.14 kg/h from the Decantation stage, with temperatures ranging between 310 K and 370 K.

It is important to note that water, both in its liquid and gaseous phases, is one of the components with the lowest chemical exergy, contributing to the relatively low exergy value of these waste streams compared to other streams. Nevertheless, the exergy associated with the waste suggests that stream reuse is a viable approach that can significantly improve process efficiency.

Figure 13 illustrates how the overall efficiency of the process is affected when exergy losses in the most critical stage are minimized. Based on the results shown in Figure 4, a significant opportunity to improve the process efficiency is identified through the optimization of its stages. The system’s overall exergy efficiency increases to 98.78% when irreversibilities in the evaluated stage are reduced to 100%. Specifically, the Residual Gas Sweetening stage does not require external utilities, implying that there is no exergy input related to utilities. Additionally, this stage generates a minimal amount of waste, such that the avoidable exergy losses from said waste represent only 11% of the total irreversibilities in the stage. This suggests that most exergy losses are unavoidable, resulting from the increase in entropy in the system, as established by the second law of thermodynamics.

Therefore, reducing irreversibilities in this stage will not only be achieved through the valorization of high-exergy-content waste streams, such as rich amine, but also by optimizing the design and operation of key equipment, such as the absorber tower, and improving energy efficiency in the heat exchanger. However, if total elimination of irreversibilities (100%) is not feasible, a 60% reduction could enable the process to reach an efficiency of at least 98.77%, similar to that obtained when all sour and recycled water streams in the process are considered “products.” It should be noted that although the percentage increase in overall efficiency may seem small, in terms of MJ/h, it represents a significant reduction in total irreversibilities. Thus, it is essential to evaluate which measures are most suitable and feasible for the process and to what extent thermodynamics allows for efficiency optimization, whether through energy/mass integration or equipment optimization.

Figure 14 illustrates the cumulative effect of the exergy associated with both products and waste on the overall efficiency of the process. In this process, these losses are attributed to two main factors: the significant use of energy in the form of heat within the utilities and the reduction in the exergy content of the process streams, linked to the exergy associated with the mass of these streams.

Figure 14 shows the resilience of the gas oil hydrocracking process when the unavoidable losses at each stage tend to disappear. In other words, it is observed how the overall exergy efficiency of the process is affected as the exergy is destroyed, originating from the operation of the equipment, and the operating conditions of the process streams at each stage are reduced to zero. The numbers indicated in the figure correspond to the various stages of this process. For example, the value at point 2 reflects the total accumulated exergy, which includes both products and waste, corresponding to Reaction Stage I and Reaction Stage II. As we move toward point 21, the accumulated value includes the total output exergy of the previous stages, adding those of Stage 20 and Stage 21. In this sense, the graph illustrates that when the unavoidable losses of a stage tend to be zero, the total output exergy, which includes products and waste, approaches the exergy value of the input streams (exergy by mass and by utilities).

At point 2, the overall exergy efficiency is shown when the unavoidable losses of Reaction Stage I are zero, which causes a decrease in the total overall exergy losses of the process. Although, at this point, the losses due to increased entropy are not present, the avoidable exergy losses related to waste still exist. Therefore, this point reflects the total accumulated exergy since it groups the output exergy of stages 1 and 2. The graph adopts a step-like behavior as the unavoidable losses are eliminated at the different stages, which increases the total accumulated output exergy. At the last point, the scenario is reached where the unavoidable losses are zero throughout the process, and the overall exergy efficiency is maximum (99.99%). Here, the total accumulated exergy corresponds to the sum of all the output exergies of the previous stages. In the base case, the overall exergy efficiency of the process is 98.76%, as shown in Figure 5. However, by eliminating the unavoidable losses of Reaction Stage I, the efficiency rises to approximately 99.62%. Furthermore, there are regions in the graph where the overall exergy efficiency remains virtually unchanged, as occurs in points 9 to 15, corresponding to the stages of Mixing II, Separation II, Mixing III, Mixing IV, Decantation, Residual Gas Separation, and Residual Gas Sweetening. These stages are characterized by minimal unavoidable losses, and local exergy losses are dominated by those associated with the waste. A similar behavior is observed in points 19 to 21, which correspond to the stages of Debutanization, Mixing V, and Naphta Separation. This suggests that in these stages, there is an adequate use of energy, the equipment works correctly, and there are no significant increases in the entropy of the system.

The distance between the points of the graph on the ordinate axis allows us to identify which stages of the process present higher unavoidable losses compared to others, indicating the potential for process optimization by identifying the less efficient stages. This behavior highlights the considerable potential for improving the overall efficiency of the process by reducing unavoidable losses. Although eliminating them completely can be complex, significant reductions could be obtained through improvements in the process units, process integration, and a more detailed analysis of the phenomena at each stage. In addition, a thorough study of industrial services is required to optimize operating conditions, especially in units with higher inefficiencies. Therefore, it is recommended to complement this exergy analysis with a detailed study of mass and energy integration, which will allow for precise identification of exergy irreversibilities and propose measures to improve energy use, optimizing the mapping of the streams involved in the process and thus maximizing overall efficiency.

4. Conclusions

The exergy analysis conducted in this work on the industrial-scale gas oil hydrocracking process, using Computer-Aided Process Engineering (CAPE), revealed a remarkable energy efficiency of 98.76%. This figure breaks down into 51% of unavoidable exergy losses and 49% of avoidable losses. The substantial production of middle distillates and high-value chemicals is key to this efficiency, as their exergy content (171,243,917.70 MJ/h) significantly surpasses that of the generated residues (1,065,290.83 MJ/h), which includes sour water and sour gases. The contribution of each unit operation was evaluated, identifying the Residual Gas Sweetening and Pressure Swing Adsorption (PSA) stages as the least efficient parts of the process, with exergy efficiencies of 87.16% and 94.70%, respectively. Notably, the Recycle Gas Sweetening stage presents the highest irreversibilities (755,216.93 MJ/h), attributed to avoidable losses.

Through an exergy resilience analysis, it was demonstrated that valorizing the residual streams increased the overall efficiency to 99.26% and reduced irreversibilities by 40%. This analysis not only quantified the potential efficiency gains but also highlighted the specific contributions of each stage to the overall performance. For instance, improvements in the Residual Gas Sweetening stage alone could raise the efficiency to 98.78%. Additionally, the resilience analysis emphasized the significance of targeting avoidable losses, where eliminating them from the initial process stages increased the efficiency to 99.62%.

The relationship between unavoidable losses and overall exergy efficiency becomes crucial, as reducing these losses in critical stages, such as Residual Gas Sweetening, directly enhances process performance. While the current efficiency is notably high, a focused effort on minimizing unavoidable losses remains essential. Implementing improvements in equipment performance, optimizing operating conditions, and enhancing energy and mass integration can significantly reduce irreversibilities, contributing to a more sustainable process. Exergy resilience analysis provided a more comprehensive understanding of the system’s behavior beyond conventional exergy analysis. It served as a tool to identify areas with the highest improvement potential and assess the resilience of the process under different scenarios.

Although this integrated approach offers valuable insights for guiding future optimization efforts in the hydrocracking industry, this exergetic resilience study presented considered an ideal scenario to show the maximum potential for improvement. However, actual plant conditions introduce factors that reduce the energy efficiency of hydrocracking. These include catalyst deactivation by coke, equipment wear, plant shutdowns, and separator separation efficiency, where recycled streams may have lower purity and chemical exergy. In addition, variations in operating conditions (temperature, pressure, feed flow) affect separation efficiency and product production. The composition of the feed influences hydrogen consumption, the production of light compounds, and heat transfer efficiency. Due to these considerations, it is expected that the exergetic efficiency in real conditions will decrease, estimating a range between 85% and 90%. These factors should be considered in future studies to obtain a more accurate assessment of process performance under real operating conditions.