Technical–Economic Assessment and FP²O Technical–Economic Resilience Analysis of the Gas Oil Hydrocracking Process at Large Scale

Abstract

The increasing requirement for distillates, accompanied by higher quantities of heavy crude oil in world production, has positioned gas oil hydrocracking as one of the most significant processes in refineries. In the petrochemical industry, hydrocracking is an essential process that converts heavy hydrocarbons into lighter and more valuable products such as LPG (liquefied petroleum gas), diesel, kerosene, light naphtha, and heavy naphtha. This method uses hydrogen and a catalyst to break down the gas oil feedstock through hydrogenation and hydrocracking reactions. However, the gas oil hydrocracking process faces significant technical, economic, and financial obstacles that must be overcome to reveal its full potential. In this study, a computer-assisted technical–economic evaluation and an evaluation of the technical–economic resilience of the gas oil hydrocracking process at an industrial scale was carried out. Twelve technical–economic and three financial indicators were evaluated to identify this type of process’s current commercial status and to analyze possible economic performance parameter optimizations. The economic indicators listed include gross profit (GP), profitability after taxes (PAT), economic potential (EP), cumulative cash flow (CCF), payback period (PBP), depreciable payback period (DPBP), return on investment (ROI), internal rate of return (IRR), net present value (NPV), annual cost/revenues (ACR), break-even point (BEP), and on-stream efficiency at the BEP. On the other hand, the financial indicators proposed by the methodology are earnings before taxes (EBT), earnings before interest and taxes (EBIT), and earnings before interest, taxes, depreciation, and amortization (EBITDA). The technical–economic resilience of the process was also evaluated, considering the costs of raw materials, the market prices of the products, and processing capacity. The gas oil hydrocracking plant described, with a useful life of 20 years and a processing capacity of 1,937,247.91 tonnes per year, achieved a gross profit (GP) of USD 58.97 million and a return after tax (PAT) of USD 39.77 million for the first year, operating at maximum capacity. The results indicated that the process is attractive under a commercial approach, presenting a net present value (NPV) of USD 68.87 million at the end of the last year of operation and a cumulative cash flow (CCF) of less than one year⁻¹ (0.34 years⁻¹) for the first year at full processing capacity, which shows that in this process, variable costs have more weight on the economic indicators than fixed costs.

1. Introduction

Oil is by far the most traded commodity globally. Although its price declined during the latter part of the 2010s, crude oil still represented a substantial portion of international trade, and its share has grown even further with the increase in prices since 2021. The price of crude oil is commonly used as an indicator to evaluate global economic conditions. However, the structure of the global oil market is quite unique, as variations in quality significantly impact the prices of different crude oils, and transactions are based on a limited set of physical benchmarks, whose availability and quality also change over time [1]. In this context, oil refineries must process large quantities of heavy crude oil containing high levels of impurities, such as heteroatoms and complex mixtures of aromatic compounds with a broad range of molecular sizes and chemical structures [2]. Enhancing the properties of these feedstocks through processes like catalytic hydrocracking and hydrotreating is crucial for producing valuable light products, where the adaptability of the feedstock and its characteristics significantly influence product selectivity and operational conditions [3]. Furthermore, changes in feedstock quality impact the functioning of industrial units, directly affecting both the performance and the economics of the process [4]. Therefore, it is essential to quantify these effects beforehand in order to predict variations in product selectivity and quality, as well as to adjust operating conditions accordingly [5].

In this order of ideas, hydrocracking is considered the most adaptable process in contemporary petroleum refining, offering operational flexibility in terms of both feedstock and products. This flexibility allows refineries to achieve the most cost-effective balance between supply and demand [6]. This process is commonly used in modern refineries to transform heavier hydrocarbons into more valuable products like gasoline, diesel, and jet fuel [7]. Hydrocracking is typically performed in the industry using two fixed-bed reactors: one for hydrotreating and the other for hydrocracking [8]. This process employs hydrogen and a catalyst to break down large hydrocarbon molecules into smaller ones [9], and it operates at high hydrogen partial pressures with catalysts that have lower performance and conversion efficiency [10]. In this sense, due to the rising global demand for high-quality middle distillates, while the demand for residues and fuel oil is declining, hydrocracking has become the primary conversion process that helps achieve the dual goals of producing greater quantities of high-quality middle distillates. Given that hydrocracking requires significant capital investment, many refiners are exploring the option of converting their existing vacuum gas oil hydrotreating units into mild hydrocracking units [11]. In this sense, hydrocracking is less prevalent than hydrotreating; however, the number of “mild” hydrocrackers with partial conversion is growing as refiners invest in new units to comply with clean fuel regulations [12].

According to the above, the increase in demand for intermediate distillates has favored the application of hydrocracking, however, to achieve high conversions from heavy vacuum gas oils, high pressures are required, which leads to very high investment costs and hydrogen consumption. For this reason, special emphasis has been placed on operation at moderate pressures, already commercially available, which represent interesting economic incentives [13]. In this sense, the economic aspect is an essential component when designing a new process or reconditioning an existing one, because many of the technical, environmental, energy, and safety decisions are strongly impacted by economic factors. To carry out this study, the technical–economic evaluation and the technical–economic resilience analysis with FP²O (Feedstock–Product–Process–Operating) methodology, developed by Herrera-Rodríguez and colleagues (2024) when implementing it in a PVC production process, were implemented, with an extension for a multi-product process [14].

In this work, the technical–economic evaluation and the FP²O technical–economic resilience analysis of a gas oil hydrocracking process on an industrial scale were carried out. In this study, 12 technical–economic indicators and 3 financial indicators were evaluated to identify the current commercial status of this type of process and analyze possible improvements in the economic performance parameters. The economic indicators listed include gross profit (GP), because it allows determining economic income without or with the inclusion of depreciation (DGP). Profitability after tax (PAT), since it is a more realistic measure of the net profit of the process. Economic potential (EP), because it shows the operational utility of the process. Cumulative cash flow (CCF), since it relates the profits of the process and the capital investment to determine if a process is attractive or not. Pay-back period (PBP), because it measures how quickly the direct fixed capital investment (DFCI) can be recovered. Depreciable payback period (DPBP), since it measures the period that it takes a company to recover the cost of an investment considering depreciation de-ductions. Return on investment (ROI), because it determines the profits or benefits that are obtained after making an investment. The internal rate of return (IRR), since it represents the rate at which the net present value (NPV) of the investment is zero. Net present value (NPV), because it represents the sum of all the profits accumulated in the periods of operation of the plant brought to the present value. Annual cost/revenue (ACR), since it is a uniform annual value that distributes the NPV over a period of time. And the break-even point and efficiency at the BEP (Break-Even Point), because they allow the evaluation of the minimum capacity at which the gas oil hydrocracking process can operate without incur-ring losses.

On the other hand, the financial indicators proposed by the methodology are earnings before taxes (EBT), since they are a measure of a process’s pre-tax profits. Earnings before interest and taxes (EBIT), because they are a measure of a company’s operating profits. And earnings before interest, taxes, depreciation, and amortization (EBITDA), since they are a measure of a company’s operating cash flow to compare the profitability of companies with different levels of debt or tax obligations. Some of these technical–economic and financial indicators were used by Tesfaye and colleagues (2021) on the extraction of starch from waste avocado seeds [15].

Additionally, a technical–economic resilience analysis was established using the FP²O methodology, in which comparative graphs will be made of some technical–economic and financial indicators with process variables, such as processing capacity, production capacity, cost of products and cost of raw materials; as developed in the work carried out by Herrera-Rodríguez and colleagues (2024) on the economic resilience of the PVC suspension production process [14]. This methodology has also been implemented in other processes such as hydrogen production through indirect gasification [16]. Highlighting that the FP²O methodology allows diagnosing the process considering technical indicators such as processing capacity and economic indicators such as annual profits and annual operating costs, allowing the process to be analyzed globally from a technical–economic point of view, to identify opportunities for improvement.

The purpose of this work is to perform a thorough technical–economic assessment of the gas oil hydrocracking process at an industrial scale. This evaluation applies a comprehensive set of 12 technical–economic and 3 financial indicators to assess the process’s commercial viability and identify areas for economic optimization. Additionally, the FP²O methodology is used for the first time in a multi-product process, being an extension of the methodology previously developed by the authors. This method examines the process’s technical–economic resilience by analyzing sensitivities to variations in raw material costs, product market prices, processing capacities, and operating costs. This localized analysis provides unique insights specific to the region, contributing valuable data to the global literature on hydrocracking processes and offering implications for markets with similar operational environments.

2. Materials and Methods

2.1. Process Description

Figure 1 illustrates the reaction stage of the gas oil hydrocracking process. The gas oil hydrocracking process starts with preheating and heating the gas oil feed, which includes Medium Vacuum Gas Oil (MVGO), Heavy Gas Oil (HKGO), and Light Cycle Oil (LCO). This feed (stream 1), amounting to 1,937,247.91 t/year at 112 °C and 0.34 MPa, is first pumped (P-100), mixed (MIX-100) with hydrogen (stream 3), and passed through a series of heat exchangers (E-100, E-101 and E-102) in the preheating system before entering a first heater (FH-100). It then flows (stream 12) into the first hydrocracker (HCR-100) at 379 °C and 16.40 MPa, where it reacts with recycled hydrogen (stream 13) introduced at 65 °C and 16.68 MPa. Simultaneously, the unconverted oil (UCO), a by-product of the process, is removed from the bottom of the fractionator. A portion of this UCO is sent to the FCC unit, while the rest is recirculated within the system (stream 18). After reheating in a second heater (FH-101), it enters (stream 19) the second hydrocracker (HCR-101) at 382 °C and 15.47 MPa, where it reacts with two streams of recycled hydrogen (streams 20 and 21) at 16.68 MPa, one at 65 °C and the other at 118 °C. Finally, the output streams (streams 14 and 22) from both reactors pass through a cooling system through heat exchangers (E-103, E-104, E-105, and E-106) and combine (MIX-102), forming a mixture (stream 24) at 293 °C and 14.66 MPa, which then enters the hot separator (V-100) (see Figure 1 and Figure 2) [17].

A hydrocracking unit encompasses two main types of reactions: hydrotreating and hydrocracking, these reactions are influenced by increasing temperatures within the reactor beds. In this context, hydrotreatment reactions are among the first to occur within hydrocrackers and typically occur more rapidly than hydrocracking reactions. Key hydrotreating processes include the removal of sulfur (Equations (1) [18] and (2) [17]), nitrogen (Equations (3) [18] and (4) [17]), and the saturation of olefins (Equations (5) [12] and (6) [17]). Secondary hydrotreating reactions involve removing oxygen (Equations (7) and (8)) [19], metals, halides like chlorine and bromine, and other non-metals, and aromatic saturation (Equations (9) [18] and (10) [12]). In contrast, hydrocracking reactions primarily involve breaking large molecules, akin to the cracking reactions in Fluidized Catalytic Cracking (FCC), combined with hydrogenation. Major hydrocracking reactions include the breakdown of aromatics (Equations (11) and (12)) [12], naphthenes (Equations (13) [12] and (14) [17]), and paraffins (Equations (15) and (16)) [12].

$${C_{12}H}_{8}S+{2H}_2\overrightarrow{metal}{C_{12}H}_{10}+H_{2}S$$

(1)

$${C_{5}H}_{12}S+H_2\overrightarrow{metal}{C_{5}H}_{12}+H_{2}S$$

(2)

$${C_{5}H}_{5}N+{5H}_2\overrightarrow{metal}{C_{5}H}_{12}+{NH}_3$$

(3)

$${C_{9}H}_{7}N+{5H}_2\overrightarrow{metal}{{C_{6}H}_6+C_{3}H}_8+{NH}_3$$

(4)

$${C_{10}H}_{12}+H_2\overrightarrow{metal}{C_{10}H}_{14}$$

(5)

$${R-CH=CH}_2+H_2\overrightarrow{metal}{RC{H}_{2}CH}_3$$

(6)

$${C_{6}H}_{5}OH+H_2\overrightarrow{metal}{C_{6}H}_6+H_{2}O$$

(7)

$${C_{7}H}_{13}OOH+{3H}_2\overrightarrow{metal}{C_{7}H}_{16}+{2H}_{2}O$$

(8)

$${C_{7}H}_8+{3H}_2\overrightarrow{metal}{C_{7}H}_{14}$$

(9)

$${C_{10}H}_8+{2H}_2\stackrel{⃡}{metal}{C_{10}H}_{12}$$

(10)

$${C_{10}H}_{14}+H_2\overrightarrow{metal}{C_{7}H}_8+{C_{3}H}_8$$

(11)

$${C_{11}H}_{16}+H_2\overrightarrow{metal}{C_{7}H}_8+{C_{4}H}_{10}$$

(12)

$${C_{15}H}_{28}+{2H}_2\overrightarrow{metal}{C_{15}H}_{32}$$

(13)

$${C_{10}H}_{20}+{4H}_2\overrightarrow{metal}{C_{6}H}_{12}+{4CH}_4$$

(14)

$${C_{6}H}_{14}\stackrel{⃡}{metal}{C_{6}H}_{12}+H_2$$

(15)

$${C_{4}H}_{10}\stackrel{⃡}{metal}{C_{4}H}_8+H_2$$

(16)

Figure 2 and Figure 3 illustrate the preliminary separation stage, and the make-up and recycling gas, absorption towers, and PSA stages of the gas oil hydrocracking process, respectively. In this sense, the gas oil hydrocracking process involves several separation stages. Initially, stream 24 is divided into high-pressure (top-stream 25) and low-pressure (bottom-stream 55) sections in a hot separator (V-100). Stream 25 is cooled through a series of heat exchangers (E-107, E-108, E-109, and E-110), washed (MIX-103) with fresh water (stream 30) at 43 °C and 14.55 MPa, and passed through an air cooler (AC-100), and then enters (stream 32) into a cold separator (V-101). In the cold separator (V-101), stream 32 separates into a gas phase (stream 33) and two liquid phases—light (stream 35) and heavy (stream 34). Stream 33 is further cooled in a heat exchanger (E-111) before entering a recycle gas separator drum (V-102), where stream 36 splits into top (stream 37) and bottom (stream 38) streams (see Figure 2). Stream 37, hydrogen-rich, is scrubbed in a tower (T-100) using poor amine (stream 39) at 49 °C and 14.48 MPa to remove contaminants like hydrogen sulfide and ammonia, generating a rich amine (stream 40) sent to the amine regeneration unit. The scrubbed hydrogen (stream 41) passes through a compressor (K-100), then a separator (TEE-101), which sends some (stream Hydrogen-TEE-101) of the scrubbed hydrogen to the PSA unit; some (stream 43) to a second separator (TEE-102), where recycled hydrogen streams 13 and 20 from the reaction stage are produced; and some (stream 44) to a mixer (MIX-107), where the scrubbed hydrogen (stream 44) is mixed with make-up hydrogen (stream 45) processed by compressors (K-101, K102, and K-103), air coolers (AC-102 and AC-103), and heat exchangers (E-112 and E-113) at 25 °C and 2.05 MPa before being separated (TEE-103) into streams 3 and 21 and returned to the reaction stage (see Figure 1 and Figure 3).

Meanwhile, stream 38 combines (MIX-106) with stream 34 and moves (stream 62) to a cold flash drum (V-104) for further separation. Concurrently, stream 55 passes through a valve (VLV-101) and flows into a hot flash drum (V-103), separating into the top (stream 57) and bottom (stream 76) streams. Stream 57 undergoes washing (MIX-104) with fresh water (58) and cooling (AC-101), and mixes (MIX-105) with stream 35 before entering (stream 61) into the cold flash drum (V-104), where it separates into a gas phase (stream 64) and two liquid phases—light (stream 72) and heavy (stream 63) (see Figure 2). Figure 4 illustrates the stripping and debutanization stages of the gas oil hydrocracking process. Stream 76 is directed through a valve (VLV-102) to the stripping tower (T-102) for further treatment (see Figure 4). Stream 64 is mixed (MIX-108) with a hydrogen-rich stream (stream 65), cooled in a heat exchanger (E-115), and directed to a residual gas separator drum (V-105), where it splits into two streams (see Figure 2). The top stream (stream 68), high in hydrogen content, is sent to a residual gas scrubbing tower (T-101) for the removal of contaminants like hydrogen sulfide and ammonia using poor amine (stream 69) at 49 °C and 2.48 MPa, with the resulting rich amine (stream 70) processed in the amine regeneration unit. The purified hydrogen stream (stream 71) then moves to the PSA (Pressure Swing Adsorption) unit, where impurities are removed (stream Residues-PSA), and purified hydrogen (stream Hydrogen-PSA) is mixed (MIX-110) with stream Hydrogen-TEE-101 from the make-up and recycling gas sections, yielding a hydrogen by-product at 64 °C and 2.41 MPa (see Figure 3). Concurrently, the bottom stream from the residual gas separator (stream 73) merges (MIX-109) with stream 72, is heated in a heat exchanger (E-116), and flows into the stripping tower (T-102) (see Figure 2 and Figure 4) [17].

Next, in the stripping stage, two streams—one at 241 °C and 2.41 MPa (stream 75), and another at 297 °C and 0.94 MPa (stream 77)—along with medium-pressure steam (stream 78) at 184 °C and 0.96 MPa, are introduced into the column (T-102). Here, lighter components like LPG, light naphtha, and part of the heavy naphtha are separated at the top (stream 81), while heavier fractions such as the remainder of the heavy naphtha, kerosene, diesel, and UCO exit at the bottom (stream 88). Figure 5 illustrates the fractionation stage of the gas oil hydrocracking process. Stream 81 is pumped (P-101), heated in a heat exchanger (E-117), and sent to the debutanizer (T-103), while stream 88 is pumped (P-103), preheated (E-119), heated (FH-102), and transferred to the fractionation tower (T-104) (see Figure 5). Waste emissions, including sour water (stream 79) and sour gases (stream 80), are generated at the stripper’s top drum. In the debutanization stage, the stream from the stripper top (stream 83) enters at 134 °C and 1.12 MPa to the debutanizer (T-103), separating LPG at the top (stream 86) from light naphtha and part of the heavy naphtha at the bottom (stream 115). This results in an LPG product stream (stream 87) of 33,056.32 t/year at 43 °C and 1.03 MPa, with additional sour water (stream 84) and sour gases (stream 85) emitted from the top drum [17].

Now, the fractionation stage comprises three distillation columns in series. The process begins with an inlet stream (stream 92) at 379 °C and 0.14 MPa entering the first column (T-104), along with a low-pressure steam (stream 93) at 167 °C and 0.37 MPa. Here, diesel, kerosene, and a portion of heavy naphtha are separated at the top (stream 98), while UCO exits through the bottom (stream 94). After pumping (P-104) and cooling (E-120), 4.7% of the UCO is sent to the FCC (stream 97) at 338 °C and 15.47 MPa, while the rest (stream 18) is reheated (FH-101) and recirculated to the reaction stage (see Figure 1 and Figure 5). In the second column (T-105), an inlet stream (stream 98) at 282 °C and 0.03 MPa separates kerosene and part of the heavy naphtha at the top (stream 105), with diesel exiting through the bottom (stream 99). This diesel stream is pumped (P-105), cooled, and processed through heat exchangers (E-121, E-122, and E-123) and an air cooler (AC-105), yielding a product (stream 104) of 933,777.85 t/year at 43 °C and 0.10 MPa. The third column (T-106) processes an inlet stream (stream 105) at 190 °C and 0.07 MPa, separating heavy naphtha at the top (stream 113) and kerosene at the bottom (stream 106). This kerosene stream is pumped (P-106), cooled, and processed through an air cooler (AC-106) and a heat exchanger (E-124), yielding a product (stream 109) of 530,300.87 t/year of kerosene at 43 °C and 0.10 MPa. Waste emissions are released from the fractionator’s top drum, including sour water (stream 111), and small amounts of fuel gas (stream 112). Heavy naphtha from the top drum (stream 113) is pumped (P-108) and combined (MIX-111) with the debutanizer’s bottom stream (stream 115), rich in light and heavy naphtha, before entering the naphtha separator tower (T-107) (see Figure 5 and Figure 6) [17]. Figure 6 illustrates the naphtha separation stage of the gas oil hydrocracking process.

Finally, the process proceeds to the naphtha separation stage, where the incoming stream (stream 117) enters at 98 °C and 0.15 MPa. In this stage, light naphtha is separated from heavy naphtha, with light naphtha found at the top (stream 120) and heavy naphtha at the bottom (stream 122). Waste emissions, such as sour water (stream 119), are produced in the top drum of the naphtha separator (T-107). The light naphtha-rich stream (stream 120) is pumped (P-110), yielding a product stream (stream 121) of 85,857.88 t/year at 38 °C and 1.00 MPa. Meanwhile, the heavy naphtha-rich stream (stream 122) is pumped (P-111) and cooled using an air cooler (AC-107) and heat exchanger (E-125), yielding a product stream (stream 125) of 272,373.56 t/year at 43 °C and 0.95 MPa [17].

2.2. Technical–Economic Evaluation

A technical–economic evaluation was conducted to identify the key variables in the industrial-scale hydrocracking of gas oils. For the first time, the methodology is being extended to a multi-product process. The operating conditions, including pressure, temperature, and the mass composition of the process streams, were defined, and the required equipment was determined to model the process using Aspen HYSYS^® simulation. To establish a gas oil hydrocracking plant, it was necessary to gather information on equipment prices, process profits, labor, taxes, and land costs, as well as to apply equations (17–40) that allow for evaluating the process’s performance from an economic perspective. The total capital investment (TCI) is calculated using Equation (17), where FCI (fixed capital investment) represents the funds required for equipment, civil structures, land preparation, control systems, and facilities, among other things. WCI refers to the working capital investment, and SUC stands for start-up costs, which include legal fees, advertising, and employee training, estimated at 10% of FCI [20].

Now, costs directly related to processing capacity, such as buildings, piping, and purchased equipment (FOB, Free on Board), are calculated using Equation (18). In some cases, the cost of a piece of equipment is available from a previous study; in this situation, it is necessary to correlate the cost of the equipment as a function of time due to inflation and other economic factors. For this, cost indexes were used, which are indicators of how the cost of the equipment varies over time. The Marshall and Swift (M&S) Equipment Cost Index (ECI) is commonly used; the calculation is done with Equation (19). Additionally, the costs associated with plant operation are divided into direct production costs (DPCs), fixed charges (FCHs), plant overhead (POH), and general expenses (GEs), according to Equation (20). Annualized fixed costs (AFCs) are determined using Equation (21). Operating costs (OCs) are calculated per unit of product. The total operating costs for one year of operation or total annualized costs (TACs) are expressed in Equation (22), which is derived from the annualized fixed costs (AFCs) and the annualized operating costs (AOCs). To provide a more comparative view, annualized operating costs per unit of raw material (NAOCs) are given by Equation (23) [21].

$$TCI=FCI+WCI+SUC$$

(17)

$$FO{B}_B=FO{B}_A{\left({\displaystyle \frac{{Capacity}_B}{{Capacity}_A}}\right)}^{0.6}$$

(18)

$$FO{B}_{t2}=FO{B}_{t1}\left({\displaystyle \frac{EC{I}_{t2}}{EC{I}_{t1}}}\right)$$

(19)

$$OC=DPC+FCH+POH+GE$$

(20)

$$AFC={\displaystyle \frac{FC{I}_0-FC{I}_s}{N}}$$

(21)

$$TAC=AFC+AOC$$

(22)

$$NAOC={\displaystyle \frac{AOC}{m_{RM}}}$$

(23)

where $FO{B}_B$ and $FO{B}_A$ are the FOB price for B capacity and the FOB price for A capacity, respectively. $FO{B}_{t2}$ and $FO{B}_{t1}$ are the FOB price at time 2 and the FOB price at time 1, respectively.$EC{I}_{t2}$ and $EC{I}_{t1}$ are the Equipment Cost Index at time 2 and the Equipment Cost Index at time 1, respectively. $FC{I}_0$, $FC{I}_s$, and $N$ are the initial value of the FCI, the salvage value of the FCI, and the recovery period (years), respectively. $m_{RM}$ is the mass flow of the raw material (t/year).

2.3. Technical–Economic Resilience Analysis via FP²O Methodology

A technical–economic resilience analysis was proposed and implemented using the FP²O (Feedstock–Product–Process–Operating) methodology to analyze the impact of specific factors that provide insight into the behavior of the gas oil hydrocracking process on an industrial scale. It is worth mentioning that this methodology was previously implemented for a PVC suspension production process, and it is expected to use the approach used in it to diagnose the gas oil hydrocracking process [14]. These factors include product sales prices, processing capacity, raw material costs, and normalized variable operating costs (NVOCs). NVOCs are defined as the operating costs per unit of raw material and is calculated by considering the AOCs, FCHs, and raw material flow, using Equation (24) [22].

$$NVOC={\displaystyle \frac{VOC}{m_{RM}}}={\displaystyle \frac{AOC-FCH}{m_{RM}}}$$

(24)

where $VOC$ is the variable operating costs.

For the first time, the methodology is being extended to a multi-product process. Fourteen graphs were developed to identify the level of resilience and sensitivity of a gas oil hydrocracking plant, operating with a useful life of 20 years, to variations in the sales prices of the five main products of the process, raw material costs, processing capacity, and NVOCs, as well as the location of the BEP (Break-Even Point) and NPV (Net Present Value). In this sense, to analyze the resilience of the process with the sales prices of the products, four graphs were made comparing this parameter with the on-stream efficiency at the BEP and different technical–economic indicators such as PAT (Profitability After Taxes) and DGP (Gross Depreciable Profit), and financial indicators such as EBITDA (Earnings Before Interest, Taxes, Depreciation, and Amortization). Subsequently, to analyze the resilience of the process concerning raw material costs, four graphs were made comparing this parameter with the on-stream efficiency at the BEP and different technical–economic indicators such as the PAT, DGP, IRR (Internal Rate of Return) and NVOCs, and financial indicators such as EBITDA. Then, to analyze the resilience of the process concerning processing capacity, two graphs were made comparing this parameter with annual sales, AOCs (Annualized Operating Costs), and normalized FCI (Fixed Capital Investment). Then, to analyze the resilience of the process concerning NVOCs, two graphs were made comparing this parameter with ROI (Return on Investment) and PBP (Payback Period). Additionally, two graphs were created to describe the location of the BEP and NPV [14].

Additionally, the operating break-even point (BEP) was determined using Equation (25), which considers the gas oil processing capacity and the fluctuations in gas oil prices and raw material costs when production is below the plant’s maximum capacity over time. These parameters were calculated using Equations (26) and (27). Key economic indicators, such as gross profit including depreciation (DGP), were calculated using Equation (28), and the plant’s profit after tax (PAT), interest, and loans were derived from Equation (29). The relationship between process benefits and capital investment (CCF, cumulative cash flow) was also evaluated using Equation (30), where a process is considered attractive if this ratio is less than 1 [22].

$$BEP=m_i{C}_i^v-TAC=0$$

(25)

$$m_{BEP}={\displaystyle \frac{AFC+FCH}{\left(\sum _i\frac{C_i^v}{{\theta }_i}\right)-NVOC}}\mathrm{with}{\theta }_i={\displaystyle \frac{m_{RM}}{m_i}}$$

(26)

$${\eta }_{On-stream}^{BEP}={\displaystyle \frac{m_{BEP}}{m_{max}}}$$

(27)

$$DGP={\sum }_i{m}_i{C}_i^v-TAC$$

(28)

$$PAT=DGP\left(1-itr\right)$$

(29)

$$CCF={\displaystyle \frac{\sum _i{m}_i{C}_i^v-AOC}{TCI}}$$

(30)

where $C_i^v$ and $m_i$ are the selling price of the product (USD/year) and the mass flow of the product (t/year), respectively. ${\eta }_{On-stream}^{BEP}$ is the on-stream efficiency at the BEP. $m_{BEP}$ and $m_{max}$ are the mass flow of the raw material at the BEP and the maximum mass flow of the raw material, respectively. $itr$ is the tax rate.

This analysis also incorporates other key economic indicators. The payback period (PBP), which accounts for the time value of money, is calculated using Equation (31). However, if the effect of money’s changing value over time is to be included, the depreciable payback period (DPBP) must be computed using a cumulative function between two periods, as shown in Equation (32). The project’s profitability (ROI, return on investment) is assessed using Equation (33), while the cumulative sum of all profits during the plant’s operational period is calculated through the net present value (NPV) in Equation (34). Additionally, the economic potentials are derived using Equations (35)–(37). The first potential represents the profit from subtracting raw material purchase expenses from sales revenue. The second potential is obtained by subtracting the costs of industrial process utilities (U) from the first potential. The third potential is calculated by subtracting annualized operating costs from sales revenue. Finally, financial indicators are used to assess the operating performance of the process, particularly in terms of profitability before taxes, interest, or depreciation. Earnings Before Interest and Taxes (EBIT) measures the operating profit of a chemical process and is calculated using Equation (38). Earnings Before Taxes (EBT) indicates the profit before tax deductions, calculated using Equation (39). Earnings Before Interest, Taxes, Depreciation, and Amortization (EBITDA) is a measure of the company’s operating cash flow, calculated using Equation (40) [23].

$$PBP={\displaystyle \frac{FCI}{PAT}}$$

(31)

$$\begin{array}{c}DPBP=ybeforePBPoccurs+\\ [nonFCIexpenses-\left({\displaystyle \frac{CumulativeNPVybeforerecovery}{CumulativeNPVyafterrecovery-CumulativeNPVybeforerecovery}}\right)]\end{array}$$

(32)

$$\%ROI={\displaystyle \frac{PAT}{TCI}}\times 100\%$$

(33)

$$NPV={\sum }_{n}AC{F}_n{\left(1+i\right)}^{-n}$$

(34)

$$E{P}_1={\sum }_i{m}_i{C}_i^v-{\sum }_j{m}_j{C}_j^{RM}$$

(35)

$$E{P}_2={\sum }_i{m}_i{C}_i^v-{\sum }_j{m}_j{C}_j^{RM}-U$$

(36)

$$E{P}_3={\sum }_i{m}_i{C}_i^v-AOC$$

(37)

$$EBIT=Revenue-AOC+FCH-insurance$$

(38)

$$EBT=EBIT-interest/rent$$

(39)

$$EBITDA=EBIT+depreciation+amortization$$

(40)

where $y$ is years. $AC{F}_n$, $i$ and $n$ are the net profit for year n, the inflation rate, and time in years, respectively. $C_j^{RM}$ and $m_j$ are the cost of the raw material (USD/year) and the mass flow of the raw material (t/year), respectively.

Table 1. Considerations for technical–economic resilience analysis of the gas oil hydrocracking process.

Item	Value
Processing capacity (t/year)	1,937,247.91
Main product flow (t/year)	933,777.85
Raw material cost (USD/t)	350.00
Main product cost (USD/kg)	1282.50
Plant life (years)	20
Salvage value	10% of depreciable FCI
Construction time	3 years
Location	Latin America
Tax rate	35%
Discount rate	12.75%
Capacity operated	50% the first year, 70% the second year, 100% from the third year onwards
Subsidies (USD/year)	0
Process type	Proven process
Process control	Digital
Type of project	Plant on unconstructed land
Type of soil	Soft clay
Contingency percentage (%)	60
Tank design code	ASME
Vessel diameter specification	Internal diameter
Operator hour cost (USD/h)	30
Supervisor hourly cost (USD/h)	35
Salaries per year	13
Utilities	Gas, water, steam, electricity
Process fluids	Liquid–gas
Depreciation method	Linear

outlines the techno-economic factors taken into account in the analysis. The total capital investment (TCI) was determined by factoring in the costs of equipment and installation, land acquisition and improvements, electrical systems, instrumentation, buildings, service facilities, engineering and supervision, construction, legal fees, contractor charges, contingencies, working capital investment, and start-up costs. These calculations were carried out following the approach outlined by El-Halwagi (2017) [23] and applying the methodology proposed by Peters and Timmerhaus (2003) [20].

3. Results and Discussion

The indicators for the technical–economic assessment, including land costs, yard improvements, pipelines, electrical expenses, contractor fees, construction costs, legal expenses, the sale price of a gas oil hydrocracking unit, and the assembly of the plant, facilitated the generation of results for technical–economic resilience.

3.1. Technical–Economic Evaluation Analysis

To determine the cost of a gas oil hydrocracking unit, and from there establish the technical, economic, and financial parameters and indicators of the process, an exhaustive review of the literature regarding different hydrocracking plants was carried out, particularly highlighting the research developed by Arrieta Chacón in 2006, which establishes that the total capital investment (TCI) for a gas oil hydrocracking process that operates with a capacity of 40,000 barrels per day is at least 116 million dollars [24]. Then, the sixteenth rule was applied with Equation (18) to estimate the TCI of a gas oil hydrocracking unit that operates with a processing capacity of 1,937,247.91 t/year [21]. Additionally, the Marshall and Swift indices of 2006 and 2022 were used to approximate the economic data to the present [25]; the calculation was made with Equation (19). In this way, it was possible to obtain, from the TCI, that the estimated cost of a gas oil hydrocracking unit for the year 2022 that operates with a processing capacity of 1,937,247.91 t/year is USD 15,218,349.15. Now,

Table 2. Total product cost for the gas oil hydrocracking plant.

Total Product Cost (TPC)	Total (USD/Year)
Raw materials	821,863,576.21
Utilities (U)	971,422,578.00
Maintenance and repairs (MR)	4,580,753.53
Operating supplies	687,113.03
Operating labor (OL)	2,041,200.00
Direct supervision and clerical labor	306,180.00
Laboratory charges	204,120.00
Patents and royalties	916,150.71
Direct production costs (DPCs)	1,802,021,671.48
Depreciation and amortization (DA)	4,126,330.58
Local taxes	2,748,452.12
Insurance	916,150.71
Interest/rent	1,740,686.34
Fixed charges (FCHs)	9,531,619.75
Plant overhead (POH)	1,224,720.00
Total manufacturing cost (TMC)	1,812,778,011.23
General expenses (GEs)	453,194,502.81
Total product cost (TPC)	2,265,972,514.03

shows the contribution of each parameter to the total product cost (TPC) in the gas oil hydrocracking process.

Table 3. Capital costs for the gas oil hydrocracking plant.

Capital Costs	Total
Cost of equipment (USD)	15,218,349.15
Delivered purchased equipment cost (USD)	18,262,018.98
Purchased equipment (installed; USD)	5,478,605.69
Instrumentation (installed; USD)	2,191,442.28
Piping (installed; USD)	5,478,605.69
Electrical network (installed; USD)	3,469,783.61
Buildings (including services; USD)	9,131,009.49
Services facilities (installed; USD)	7,304,807.59
Total DFCI (USD)	51,316,273.33
Land (USD)	730,480.76
Land improvements (USD)	7,304,807.59
Engineering and supervision (USD)	9,496,249.87
Equipment (R+D; USD)	1,826,201.90
Construction costs (USD)	6,209,086.45
Legal expenses (USD)	182,620.19
Contractors’ fees (USD)	3,592,139.13
Contingency (USD)	10,957,211.39
Total IFCI (USD)	40,298,797.28
Fixed capital investment (FCI; USD)	91,615,070.61
Working capital (WCI; USD)	73,292,056.49
Start-up (SUC; USD)	9,161,507.06
Total capital investment (TCI; USD)	174,068,634.17
Salvage value FCI (USD)	9,088,458.99
Annualized fixed costs (AFCs; USD/year)	4,126,330.58

presents the results of the technical–economic evaluation, including the direct fixed capital investment (DFCI) with the initial investment required, the costs related to the installation of equipment, instrumentation, pipes, electrical network and services, and the indirect fixed capital investment with the costs related to the development of the land and the required civil works (including engineering and supervision, like the costs of design and engineering of the construction, equipment such as research and development equipment, and construction costs, considering construction and temporary operation, purchase, and rental of construction machinery, office staff located at the construction site, construction payroll, and other general construction expenses), and the legal expenses, contractor fees, and contingency. Additionally, Table 3 shows fixed capital investment (FCI), working capital (WCI), start-up (SUC), total capital investment (TCI), salvage value FCI, and annualized fixed costs (AFCs).

Based on the results presented in Table 3, it is evident that the gas oil hydrocracking process demands a more considerable TCI (USD 174.07 MM) compared to processes in the chemical industry that use biomass as raw material, such as the hydrogen production process from empty fruit bunches of African palms (EFB) through indirect gasification, with a TCI of USD 99.01 MM for route 1 (Pressure Swing Adsorption) and a TCI of USD 80.81 MM for route 2 (Selexol-Based Adsorption) [16]. On the other hand, the TCI of the gas oil hydrocracking process was also compared with other units in the refineries, such as the fluidized catalytic cracking (FCC) unit, where a higher TCI (USD 291.44 MM-USD 387.71 MM) was obtained than that of the process studied [26]. In addition, it was compared with the fuel oil hydrotreatment unit, where a lower TCI (USD 87.14 MM) was obtained than that of the gas oil hydrocracking process [27]. Similarly, the TCI value obtained for the gas oil hydrocracking process in Table 3 is considered lower compared to those of other processes in the petrochemical industry, with raw materials derived from petroleum, such as the production of PVC by suspension from vinyl chloride monomer (VCM) and ethylene with a TCI of USD 609.88 MM [14]. However, if a large-scale production process of C9 aromatic hydrocarbon resin derived from cracked petroleum is considered, the TCI of this unit (USD 5.8 MM-USD 6.2 MM) is lower than that of the process studied [28]. All of the above indicates that the results for TCI in the gas oil hydrocracking process are attractive compared to rigorous processes such as PVC production in the petrochemical field and FCC in the oil and gas sector. This may be due to the types of technologies implemented in each of the processes mentioned.

Finally,

Table 4. Technical–economic indicators for the gas oil hydrocracking plant.

Indicator	Total
Gross profit (depreciation not included) (GP; USD)	58,966,096.31
Gross profit (depreciation included) (DGP; USD)	54,839,765.73
Profitability after tax (PAT; USD)	39,772,178.30
Economic potentials 1 (EP1; USD/year)	1,503,075,034.13
Economic potentials 2 (EP2; USD/year)	531,652,456.13
Economic potentials 3 (EP3; USD/year)	58,966,096.31
Cumulative cash flow (CCF; 1/year)	0.34
Payback period (PBP; years)	2.29
Depreciable payback period (DPBP; years)	4.14
Return on investment (% ROI)	22.85
Net present value (NPV; MMUSD)	68.87
Annual cost/revenue (ACR)	9.66
Internal rate of return (% IRR)	29.34
Normalized variable operating costs (NVOCs; USD/t-rm)	1164.77
Annualized total operating costs (AOCs; USD/year)	2,265,972,514.03

and

Table 5. Financial indicators for the gas oil hydrocracking plant.

Indicator	Total
Earnings before taxes (EBT; USD)	53,099,079.39
Earnings before interest and taxes (EBIT; USD)	54,839,765.73
Earnings before interest, taxes, depreciation, and amortization (EBITDA; USD)	67,581,565.35

present the results of the technical–economic and financial indicators calculated for the gas oil hydrocracking process under specific assumptions in order to assess the viability of this unit. The payback period (PBP) in the present study was 2.29 years (less than 3 years), supporting an increase in the NVOCs, while the payback period considering depreciation (DPBP) is 4.14 years (less than 5 years). These data are considered positive compared to other processes in the industry. For processes involving hydrocracking units, such as biorefineries comprising hydrotreating, hydrocracking, and steam reforming sections, to generate biofuel by fast pyrolysis and gasification, payback periods of 3.5 years have been reported [29], and for hydrocracking-like processes, such as a catalytic distillation process for alkylation desulfurization of fluid catalytic cracking gasoline, payback periods of 3 years have been reported [30].

Regarding the technical–economic indicators, a GP and a DGP higher than 50 MMUSD were obtained, which is positive, as they are considerably high values. On the other hand, the economic potentials 1 (EP₁), 2 (EP₂), and 3 (EP₃) are also significantly high, being higher than 1500 MMUSD, 500 MMUSD, and 50 MMUSD, respectively. Now, given that the cash flow (CCF) is 0.34 years⁻¹, that is, less than 1 year⁻¹, it can be considered that the gas oil hydrocracking process is an economically attractive project, although it presents a not-very-high rate of return, an IRR of 29.34%. On the other hand, it can be observed that the rate of return on investment (ROI) is 22.85% and the annual cost revenue (ACR) is 9.66, which is lower than expected. Additionally, it is reflected that the gas oil hydrocracking plant generates an income (NPV) of 68.87 MMUSD with low annual benefits, which indicates that this process has the opportunity for economic improvement. Finally, regarding the financial indicators, an EBT, EBIT, and EBITDA of over 50 MMUSD were obtained, which is positive, as they are relatively high values.

3.2. FP²O Technical–Economic Resilience Analysis

Figure 7, Figure 8, Figure 9 and Figure 10 represent the technical–economic resilience of the gas oil hydrocracking process in relation to the sales price of the five main products (diesel, kerosene, LPG, light naphtha, and heavy naphtha). Figure 7 establishes a relationship between the sum of the sales price of the five products, the EBITDA and the PAT. Figure 8 compares the sum of the sales price of the five products, the DGP and the PAT. Figure 9 relates the sum of the sales price of the five products with the on-stream efficiency at the BEP. Figure 10 establishes a comparison between the sales price of the five products separately with the on-stream efficiency at the BEP.

Figure 7 shows that the Earnings Before Interest, Taxes, Depreciation, and Amortization (EBITDA) of the gas oil hydrocracking process are more resilient to changes in the sum of the prices of the products compared to the Profitability After Taxes (PAT), because the slope of the former is steeper than that of the latter. The intersection of both lines indicates a critical point in terms of the sales price of the products and the annual income; losses are generated below approximately 5.62 USD/kg. This indicates that the process is in a favorable zone, because for a joint sales price of 5.84 USD/kg, positive values are obtained for the EBITDA (67.58 MMUSD/y) and the PAT (39.77 MMUSD/y). Additionally, by comparing the sales price at the critical point with the sales price of the process, the sensitivity of the process to a decrease in the sales price of the products as a whole can be identified. The further the current state of the process is from the intersection, the more resilient the process is. In this case, the two values are relatively close, so the process is highly sensitive to a decrease in the sum of the sales prices of the products.

Figure 8 shows that the Depreciable Gross Profit (DGP) of the gas oil hydrocracking process is more resilient to changes in the sum of product prices compared to the Profitability After Taxes (PAT), because the slope of the former is steeper than that of the latter. The intersection of both lines indicates a critical point in terms of the sales price of the products and the annual income; losses are generated below approximately 5.72 USD/kg. This indicates that the process is in a favorable zone, because for a joint sales price of 5.84 USD/kg, positive values are obtained for the DGP (54.84 MMUSD/y) and the PAT (39.77 MMUSD/y). Additionally, by comparing the sales price at the critical point with the sales price of the process, the sensitivity of the process to a decrease in the sales price of the products as a whole can be identified. The further the current state of the process is from the intersection, the more resilient the process is. In this case, the two values are relatively close, so the process is highly sensitive to a decrease in the sum of the sales prices of the products.

Figure 9 shows three regions. The first region, between USD 5.68/kg and USD 5.76/kg, indicates that in this section, the on-stream efficiency at the BEP of the process is sensitive to small changes in the joint sales price of the products; therefore, the process is not resilient in this section, that is, a small decrease in the sales price of the products generates a considerable increase in the on-stream efficiency at the BEP; this is shown in the graph by having an asymptotic behavior with the y-axis. The second region, between USD 5.76/kg and USD 5.92/kg, is a transition region and is the section where the gas oil hydrocracking process is currently located, with an on-stream efficiency at the BEP of 13.92% at a joint sales price of USD 5.84/kg. An acceptable level of profitability can be obtained here because, as it is not a very sensitive area like the first one, greater operability is allowed in the face of changes in the sales price. Finally, in the third region, for joint sales prices above 5.92 USD/kg, sharp increases in the sales price of the products do not have a significant effect on the on-stream efficiency at the break-even point, and it ceases to be a dependent variable of this criterion, so, in the face of large increases or decreases in the sales price of the products within this range, the repercussions on the on-stream efficiency at the BEP will not be visible.

Figure 10 shows five curves related to the five main products of the gas oil hydrocracking process. Each of these curves presents the same three regions described in Figure 9; the only difference is that in Figure 10, the prices of the products are taken separately, but not the sum of them, as was considered in Figure 9. According to the graph, it is established that the most sensitive products in terms of on-stream efficiency at the BEP to changes in the sales price are, in descending order of sensitivity, diesel (1.28 USD/kg), kerosene (1.33 USD/kg), and heavy naphtha (1.05 USD/kg), because in these three curves with asymptotic behavior with the y-axis, the process is located in the first region, which affects the profitability of the process and indicates a lower operability in the face of changes in the sales price of these three products. On the other hand, the most resilient products are, in descending order of resilience, LPG (0.95 USD/kg) and light gasoline (1.24 USD/kg), because in these two curves with less-pronounced asymptotic behavior with the y-axis, the process is located in the second region, where an acceptable level of profitability can be obtained because, the second region not being an area with much sensitivity like the first, greater operability is allowed in the face of changes in the sales price of these two products.

Figure 11, Figure 12, Figure 13 and Figure 14 represent the technical–economic resilience of the gas oil hydrocracking process in relation to the cost of the raw materials (gas oils, hydrogen, demineralized water and MDEA). Figure 11 establishes a relationship between the cost of the feedstock, EBITDA, and PAT. Figure 12 compares the cost of the feedstock, DGP, and PAT. Figure 13 relates the cost of the feedstock with the on-stream efficiency at the BEP. Figure 14 establishes a comparison between the cost of the feedstock, IRR, and NVOCs.

Figure 11 shows that the Earnings Before Interest, Taxes, Depreciation, and Amortization (EBITDA) of the gas oil hydrocracking process are more resilient to changes in the cost of raw materials compared to the Profitability After Taxes (PAT), because the slope of the former is steeper than that of the latter. The intersection of both lines indicates a critical point in terms of the cost of raw materials and annual income; losses are generated below approximately 455 USD/t. This indicates that the process is in a favorable zone, because for a raw material cost of 424.24 USD/kg, positive values are obtained for the EBITDA (67.58 MMUSD/y) and the PAT (39.77 MMUSD/y). Additionally, by comparing the cost of raw materials at the critical point with the cost of raw materials in the process, the sensitivity of the process to an increase in the cost of raw materials can be identified. The further the current state of the process is from the intersection, the more resilient the process is. In this case, the two values are relatively close, so the process is highly sensitive to an increase in the cost of raw materials.

Figure 12 shows that the Depreciable Gross Profit (DGP) of the gas oil hydrocracking process is more resilient to changes in raw material costs compared to the Profitability After Taxes (PAT), because the slope of the former is steeper than that of the latter. The intersection of both lines indicates a critical point in terms of raw material cost and annual income; below approximately 455 USD/t, losses are generated. This indicates that the process is in a favorable zone, because for a raw material cost of 424.24 USD/kg, positive values are obtained for the DGP (54.84 MMUSD/y) and the PAT (39.77 MMUSD/y). Additionally, by comparing the cost of raw materials at the critical point with the cost of raw materials in the process, the sensitivity of the process to an increase in the cost of raw materials can be identified. The further the current state of the process is from the intersection, the more resilient the process is. In this case, the two values are relatively close, so the process is highly sensitive to an increase in the cost of raw materials.

In Figure 13, three regions can be observed. In the first region, between 0 USD/t and 300 USD/t, pronounced decreases in the cost of raw materials do not have a significant effect on the on-stream efficiency at the break-even point, and it is no longer a dependent variable of this criterion; therefore, in the event of large increases or decreases in the cost of raw materials within this interval, the repercussions on the on-stream efficiency at the BEP will not be visible. The second region, between 300 USD/t and 430 USD/t, is a transition region and is the section where the process is currently located, with an on-stream efficiency at a BEP of 13.92% at a raw material cost of 424.24 USD/t. An acceptable level of profitability can be obtained here because, as it is not a very sensitive area like the first, greater operability is allowed in the face of changes in the cost of raw materials. Finally, the third region, for raw material costs higher than 430 USD/t, indicates that in this section, the on-stream efficiency at the BEP of the process is sensitive to small changes in the cost of the raw material; therefore, the process is not resilient in this section, that is, a small increase in the cost of the raw material generates a considerable increase in the on-stream efficiency at the BEP; this is manifested in the graph by having an asymptotic behavior with the y axis.

Figure 14 illustrates the relationship between the Internal Rate of Return (IRR), Normalized Variable Operating Costs (NVOCs), and feedstock costs. The gas oil hydrocracking process shows an IRR of 29.34%, an NVOC of 1164.77 USD/t, and a feedstock cost of 424.24 USD/t. Economic resilience analysis reveals that the IRR is inversely related to feedstock costs, while NVOCs are directly related to these costs; thus, NVOCs and the IRR are inversely related. In other words, if NVOCs are high relative to the cash flows generated, the IRR could be negatively impacted because higher operating costs would reduce net revenues, thereby lowering the project’s profitability. On the other hand, if NVOCs are low in comparison to cash flows, the IRR may increase as net income rises.

Figure 15 and Figure 16 represent the technical–economic resilience of the gas oil hydrocracking process in relation to the processing capacity of the plant. Figure 15 establishes a relationship between the process processing capacity, the annual sales, and the AOCs. Figure 16 establishes a comparison between the process processing capacity and the normalized FCIs.

Figure 15 shows that the Annualized Operating Costs (AOCs) of the gas oil hydrocracking process are more resilient to changes in the plant’s processing capacity compared to the annual sales, because the slope of the former is steeper than that of the latter. The intersection of both lines indicates the equilibrium processing capacity in terms of the AOCs and the annual sales, which for this process is approximately 2.15 Mt/y; therefore, below this processing capacity, the annual sales exceed the AOCs, which is positive, unlike what happens when the equilibrium processing capacity is exceeded, where the AOCs exceed the annual sales. This indicates that the process is in a favorable zone, because for a processing capacity of 1.94 Mt/y, annual sales (2324.94 MMUSD/y) are obtained that are higher than the AOCs (2265.97 MMUSD/y). Additionally, by comparing the processing capacity at equilibrium with the processing capacity of the process, the sensitivity of the process to an increase in its processing capacity can be identified. The further the processing capacity of the process is from the intersection, the more resilient the process is. In this case, the two values are relatively close, so the process is highly sensitive to an increase in processing capacity.

Figure 16 shows an inverse relationship between normalized fixed costs and processing capacity in a gas oil hydrocracking plant. The process was assumed to have an installed capacity of 1.94 megatons per year, with a normalized Fixed Capital Investment (FCI) of $2.98 per megaton. Fixed costs stay the same regardless of the volume of products produced. This means that as production capacity increases, the fixed costs are spread across a larger number of units, resulting in a lower fixed cost per unit as production rises, which can lead to a reduction in unit costs.

Figure 17 and Figure 18 represent the technical–economic resilience of the gas oil hydrocracking process in relation to NVOCs. Figure 17 establishes a relationship between the NVOCs of the process and the ROIs. Figure 18 establishes a comparison between the NVOCs of the process and the PBPs.

Figure 17 shows the influence that Normalized Variable Operating Costs (NVOCs), such as industrial services, maintenance and repair, labor, and supervision, among others, have on the Return on Investment (ROI) percentage of the process. The graph shows a strong linear dependence of the return on investment with respect to variable costs, which have a critical value of around 1196 dollars per ton, from which the return on investment becomes null; for the gas oil hydrocracking process studied, this value is slightly far from the current NVOCs (1164.77 dollars per ton), which provides a small elongation of this indicator, making the process little resilient to changes in variable costs. At the local level, in Latin America, there are some social problems, such as the supply of electricity service [31], high labor costs, and employee strikes [32], that can strongly impact this indicator. On the other hand, when analyzing the other vertex of the triangle, the maximum return on investment value that this process can provide is 100% in a hypothetical scenario where variable costs tend to zero. The ROI value obtained in the gas oil hydrocracking plant (22.85%) is higher than that of other hydrocracking processes, where values between 12.19 and 16.36% are obtained [33], which reinforces the high economic potential of this process.

Figure 18 shows the sensitivity and resilience analysis of the Payback Period (PBP); an important observation to make is the high sensitivity of this plant to changes in the Normalized Variable Operating Costs (NVOCs). Due to this strong impact, modest changes in operating costs can make the difference between making the project attractive and going bankrupt; this high sensitivity is detrimental to the process, but inevitable when working with raw materials with volatile prices such as gas oils. In this sense, when operating costs are equal to the sales price of the products, the gross profit before taxes becomes zero and the FCI is not recovered; this has the effect of making the PBP tend to infinity. In the gas oil hydrocracking plant analyzed, this happens when operating costs approach 1200 dollars per ton; in this area, identified as the out-of-control region, the differences are not marked in years, but in decades, for a small variation in operating costs. Additionally, it is possible to detect a region of relative stability for NVOC values up to approximately 1000 dollars per ton, and, from there, a transition region until a loss of control occurs in the economics of the process, detecting a critical point at approximately 1180 dollars per ton of gas oils. The process studied is below this critical point, reaching a PBP of 2.57 years with NVOCs of 1164.77 USD/t, which is positive because it does not take many years to recover the investment, but, being so close to the value of the critical point, makes the process less resilient to slight changes in the NVOCs.

Figure 19 represents the technical–economic resilience of the gas oil hydrocracking process in relation to the plant processing capacity, annual fixed charges, annual sales, AOCs, and annual variable charges. Break-even analysis aims to identify the conditions where total production costs match the process revenues. Figure 19 presents a graphical depiction of the expenses and revenues of the gas oil hydrocracking process in relation to the processing flow rate.

In Figure 19, annual fixed charges are shown as a horizontal line since they are essentially unaffected by the processing level. For the hydrocracking process analyzed, these charges total 24,364.82 MUSD/year. In contrast, the variable charges, amounting to 2,241,607.69 MUSD/year for this process, are plotted over the processing range. Often, variable charges are directly proportional to the processing level, starting at zero when no processing occurs and increasing to their maximum value as the processing rate reaches its peak. The fixed and variable charges are combined by superimposing the variable charges, starting from the value of the fixed charges. This results in the line representing the annualized total operating costs (AOCs), which, in this case, is 2,265,972.51 MUSD/year. On the other hand, the annual sales, which amount to 2,324,938.61 MUSD/year for this process, are represented by a line that begins at the origin and increases to the maximum revenue as the processing rate reaches its highest level. The point where the AOC line intersects with the annual sales line is known as the break-even point (BEP). Below the BEP, AOCs exceed annual sales, indicating that the process is operating at a loss. Above the BEP, the process generates profits, which is reflected in the current state of the gas oil hydrocracking plant being studied, as it operates well above the BEP [21].

Figure 20 represents the technical–economic resilience of the gas oil hydrocracking process in relation to the net present value and the useful life of the plant.

Figure 20 shows that the useful life of the gas oil hydrocracking process is 20 years, as specified in Table 1, reaching 68.87 MMUSD/y of Net Present Value (NPV); this means that after paying all the expenses of the process, the project income will give a net value of $68.87 million in present dollars. It is worth noting that the process begins to have a positive net present value shortly after 9 years, which is beneficial because it reduces the chances that a suspension of the project at some point in its useful life prevents the recovery of the investment in the plant.

4. Conclusions

This study presents a comprehensive technical–economic assessment and a resilience analysis of a hydrocracking plant designed to process gas oil into various products, including diesel, kerosene, LPG, light naphtha, and heavy naphtha. The evaluation was conducted for an annual gas oil load of 1,937,247.91 tons, and the findings indicate that the plant can operate at full capacity while maintaining favorable technical, economic, and financial performance indicators. Specifically, the plant achieves a net present value (NPV) of USD 68.87 million and an internal rate of return (IRR) of 29.34%. A key observation from the study was that the cost of raw material procurement represents the most significant factor influencing the plant’s technical–economic resilience. This cost, alongside the pricing of the final products, plays a crucial role in determining the overall economic viability of the operation. The plant’s total capital investment (TCI) is estimated at USD 174.07 million, while the annualized total operating costs (AOCs) are projected at USD 2.27 billion. The payback period (PBP) for the investment is 2.29 years, and when accounting for depreciation, the payback period (DPBP) extends to 4.14 years. Additionally, the analysis identified the break-even production capacity at 269,572.64 tons per year, which corresponds to an on-stream efficiency at the BEP of 13.92%. Based on these findings, the study recommends focusing on strategies to either reduce production costs or increase the selling prices of the five products, although the latter is inherently dependent on market conditions and fluctuations. Finally, while the project demonstrates strong financial viability under current conditions, ongoing efforts to optimize operational costs or improve market pricing will be essential to enhance the long-term sustainability and resilience of the plant.